BUSINESS
FINANCE
12e
PEIRSO N
BROW N
EASTON
HOW ARD
PINDER
BUSINESS
FINANCE
Monash University
L
University of Melbourne
University of Newcastle
Monash University
—
Graw
Hill
Education
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National Library o f Australia Cataloguing-in-Publication Data
Author:
Peirson, Graham, author.
Title:
Business finance / Graham Peirson, Rob Brown, Steve Easton,
Sean Pinder, Peter Howard.
Edition:
12th edition
ISBN:
9781743078976 (paperback)
Notes:
Includes index.
Subjects:
Business enterprises-Finance.
Cash management.
Corporations-Finance.
Other Authors/Contributors:
Brown, Rob, author.
Easton, Stephen Andrew, author.
Pinder, Sean, author.
Howard, Peter, author.
Dewey Number:
658.15
Published in Australia by
McGraw-Hill Education (Australia) Pty Ltd
Level 2, 82 Waterloo Road, North Ryde NSW 2113
Publisher: Jillian Gibbs
Senior product developer: Jane Roy
Production editor: Tami Rex
Permissions editor: Haidi Bernhardt
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Internal design: David Rosemeyer
Typeset in Chapparal Pro 10/12 pt by diacriTech, India
Printed in China on 70gsm matt art by China Translation and Printing Services Ltd
PUBLISHER'S FOREW ORD
When this endeavour began 44 years ago, few could have foreseen the success of this publication, and few
could have imagined how proud we would be to have published a resource that has guided well over 2 0 0 0 0 0
undergraduate students through their introduction to business finance. This title has become one of McGraw-Hill
Education Australia's longest-standing and most successful textbooks. It is with the greatest pleasure that McGrawHill Australia now presents the twelfth edition of Business Finance by Graham Peirson, Rob Brown, Steve Easton,
Peter Howard and Sean Pinder.
This text is an original work—not an adaptation of US material. The founding authors, Graham Peirson and Ron
Bird, embarked on an ambitious undertaking: to write a meaningful introduction to the fascinating field of business
finance, specifically for students in Australia and New Zealand. They succeeded, and the first edition was published
in 1972. As a testament to the consistent value of the work and its ongoing relevance for generations of students and
instructors, Business Finance continues to sell thousands of copies each year. In a market increasingly crowded with
competitive texts, it is a credit to our author team that Business Finance continues as the market leader in its field.
To our authors and the academic community who have so staunchly supported this publication we say thank you.
Quality content is clearly the key. The twelfth edition author team has worked hard, in consultation with instructors
across Australia and New Zealand, to ensure that the text and its digital resource package provide recent data and
up-to-date thinking in an accessible format that will engage students and instructors alike. This twelfth edition has
done just that, demonstrating the authors, commitment to refining their text and ensuring that Business Finance not
only retains a reputation for currency, but emerges once again as the standard setter.
Our focus at McGraw-Hill is wholly on providing superior content. W ith Business Finance twelfth edition we are
confident we offer you the best there is.
M c G ra w -H ill Education A u stra lia , 2 0 1 4
v
^1
■
BRIEF C O N TEN TS
CHAPTER 1
Introduction
CHAPTER 2
Consumption, investment and the capital market
10
CHAPTER 3
The time value o f money: on introduction to financial mathematics
28
CHAPTER 4
A pplying the time value o f money to security valuation
74
CHAPTER 5
Project evaluation: principles and methods
103
CHAPTER 6
The application o f project evaluation methods
129
CHAPTER 7
Risk and return
772
CHAPTER 8
The capital market
210
CHAPTER 9
Sources o f finance: equity
232
CHAPTER 10
Sources o f finance: debt
275
CHAPTER 11
Payout policy
315
CHAPTER 12
Principles o f capital structure
3 56
CHAPTER 13
C apital structure decisions
3 93
CHAPTER 14
The cost o f capital
417
CHAPTER 15
Leasing and other equipment finance
450
CHAPTER 16
C apital market efficiency
477
CHAPTER 17
Futures contracts and swops
507
CHAPTER 18
Options and contingent claims
5 63
CHAPTER 19
Analysis o f takeovers
605
CHAPTER 2 0
Managem ent o f short-term assets: inventory
646
CHAPTER 21
Managem ent o f short-term assets: liqu id assets and accounts receivable
666
1
C O N TEN TS
Publisher's foreword
V
Preface
X X V //
About the authors
x x v iii
Acknowledgments
Chapter 1
Digital resources
xxx i
Highlights o f this edition
xxx ii
How to use this book
xxxiv
XXX
Introduction
Learning objectives
ID
FINANCE AS AN AREA OF STUDY
2
IB
FINANCIAL DECISIONS
2
IB
BUSINESS STRUCTURES
3
1.3.1 Sole proprietorship
3
1.3.2 Partnership
3
1.3.3 Company
4
IQ
THE COMPANY'S FINANCIAL OBJECTIVE
5
IB
FUNDAMENTAL CONCEPTS IN FINANCE
5
ID
1.5.1 Value
5
1.5.2 The time value of money
5
1.5.3 Risk aversion
6
1.5.4 Nominal and real amounts
6
1.5.5 Market e仟iciency and asset pricing
6
1.5.6 Derivative securities
7
1.5.7 Arbitrage
7
1.5.8 Agency relationships
7
OUTLINE OF THE BOOK
Summary
8
8
Key terms
8
Questions
9
Chapter 2
Consumption, investment and the capital market
10
Learning objectives
JO
m
INTRODUCTION
11
^
FISHERY SEPARATION THEOREM: A SIMPLIFIED EXAMPLE
11
2.2.1
11
Introduction to the example
2.2.2 Assumptions
11
2.2.3 The shareholders7 consumption opportunities and preferences
12
2.2.4 Solution: introduce a capital market
12
2.2.5 An analysis using rates of return
13
2.2.6 A solution requiring borrowing
13
C ontents
Q |
B |
2.2.7 Fisher's Separation Theorem and net present value
13
2.2.8 Fisher’s Separation Theorem: summary
14
FISHERS SEPARATION THEOREM: A FORMAL APPROACH
14
2.3.1
14
Assumptions
2.3.2 The company
15
2.3.3 The shareholders
15
2.3.4 The company’s decision
16
2.3.5 Solution: introduce a capital market
16
2.3.6 Proving there is an optimal policy
19
2.3.7 Identifying the optimal policy
21
2.3.8 Implications for financial decision making
22
INVESTORS'REACTIONS TO MANAGERS'
2.4.1
DECISIONS
Certainty
24
25
2.4.2 The introduction of uncertainty
25
Summary
26
Key terms
26
Questions
26
Problems
26
References
27
The time value of money: an introduction to
financial mathematics
28
Learning objectives
28
m
INTRODUCTION
29
|B
FUNDAMENTAL CONCEPTS OF FINANCIAL MATHEMATICS
29
3.2.1 Cashflows
29
3.2.2 Rate of return
29
3.2.3 Interest rate
30
3.2.4 Time value of money
30
SIMPLE INTEREST
31
3.3.1 The basic idea of simple interest
31
3.3.2 Formula development: future sum
31
3.3.3 Formula development: present value
32
3.3.4 Applications of simple interest
32
COMPOUND INTEREST
33
3.4.1 The basic idea of compound interest
33
3.4.2 Formula development: future sum and present value
34
3.4.3 Nominal and effective interest rates
37
3.4.4 Compound interest: two special cases and a generalisation
40
VALUATION OF CONTRACTS WITH MULTIPLE CASH FLOWS
46
3.5.1
46
IQ
IB
Introduction
3.5.2 Value additivity
46
ix
C ontents
|Q
IB
|Q
3.5.3 Formula development: valuation as at any date
48
3.5.4 Measuring the rate of return
49
ANNUITIES
50
3.6.1
50
Definition and types of annuity
3.6.2 Formula development: present value of an ordinary annuity
51
3.6.3 Formula development: present values of annuities-due, deferred annuities and
ordinary perpetuities
52
3.6.4 Future value of annuities
56
PRINCIPAL-AND-INTEREST LOAN CONTRACTS
58
3.7.1
58
Basic features of the contract
3.7.2 Principal and interest components
59
3.7.3 Balance owing at any given date
60
3.7.4 Loan term required
61
3.7.5 Changing the interest rate
62
GENERAL ANNUITIES
63
Summary
66
Key terms
66
Self-test problems
66
Questions
67
Problems
67
References
73
Applying the time value of money to security valuation 74
Learning objectives
74
ED
INTRODUCTION
75
IQ
FINANCIAL ASSET VALUATION UNDER CERTAINTY
75
m
VALUATION OF SHARES
76
4.3.1
Valuation of shares assuming certainly
76
4.3.2 Valuation of shares under uncertainty
77
4.3.3 Share valuation and the price-earnings ratio
79
|Q
VALUATION OF DEBT SECURITIES
80
EB
INTEREST RATE RISK
81
ED
THE TERM STRUCTURE OF INTEREST RATES
4.6.1
EB
W hat is the term structure?
82
82
4.6.2 Using the term structure to price a bond
83
4.6.3 Term structure theories: expectations and liquidity (risk) premium
85
4.6.4 Empirical evidence
88
4.6.5 Inflation and the term structure
89
THE DEFAULT-RISK STRUCTURE OF INTEREST RATES
89
C ontents
W
ED
OTHER FACTORS AFFECTING INTEREST RATE STRUCTURES
91
Summary
92
Key terms
92
Self-test problems
92
Questions
93
Problems
93
References
96
APPENDIX 4.1 DURATION AND IMMUNISATION
97
Introduction
97
Bond duration
97
Duration and interest elasticity
99
Duration and bond price changes
100
Duration and immunisation
100
I Project evaluation: principles and methods
103
Learning objectives
103
m
INTRODUCTION
104
Q
THE CAPITAL-EXPENDITURE PROCESS
104
E 9
METHODS OF PROJECT EVALUATION
104
5.3.1
107
0 3
Q
Q
Discounted cash flow methods
THE DISCOUNTED CASH FLOW METHODS COMPARED
108
5.4.1
108
Net present value
5.4.2 Internal rate of return
109
5.4.3 Choosing between the discounted cash flow methods
112
5.4.4 Benefit-cost ratio (profitability index)
1 17
OTHER METHODS OF PROJECT EVALUATION
118
5.5.1
1 18
Accounting rate of return
5.5.2 Payback period
120
5.5.3 Economic value added (EVA)
121
PROJECT EVALUATION AND REAL OPTIONS ANALYSIS
123
5.6.1
123
Real options analysis
5.6.2 W ho uses real options analysis?
124
Summary
125
Key terms
125
Self-test problems
125
Questions
125
Problems
126
References
128
xi
C ontents
Chapter 6
The application of project evaluation methods
129
Learning objectives
129
INTRODUCTION
130
APPLICATION 〇 F THE NET PRESENT VAUJE METHOD
130
6.2.1
130
Estimation of cash flows in projectevaluation
6.2.2 Illustration of cash-flow information in project evaluation
133
TAX ISSUES IN PROJECT EVALUATION
134
6.3.1
134
Effect of taxes on net cash flows
6.3.2 Illustration of cash-flow information inproject evaluation with taxes
137
COMPARING MUTUALLY EXCLUSIVE PROJECTS THAT HAVE DIFFERENT LIVES
139
DECIDING WHEN TO RETIRE (ABANDON) OR REPLACE A PROJECT
146
6.5.1
146
Retirement decisions
6.5.2 Replacement decisions
147
ANALYSING PROJECT RISK
149
6.6.1
149
Sensitivity analysis
6.6.2 Break-even analysis
151
6.6.3 Simulation
152
DECISION-TREE ANALYSIS
153
QUALITATIVE FACTORS AND THE SELECTION OF PROJECTS
156
PROJECT SELECTION WITH RESOURCE CONSTRAINTS
157
Summary
159
Key terms
159
Self-test problems
159
Questions
160
Problems
161
References
171
Chapter 7
Risk and return
172
Learning objectives
172
INTRODUCTION
173
RETURN AND RISK
173
THE INVESTORS UTILITY FUNCTION
176
THE RISK OF ASSETS
179
PORTFOLIO THEORY AND DIVERSIFICATION
179
7.5.1
180
Gains from diversification
7.5.2 Diversification with multiple assets
184
7.5.3 Systematic and unsystematic risk
186
7.5.4 The risk of an individual asset
187
7.5.5 The efficient frontier
189
C ontents
m
THE PRICING OF RISKY ASSETS
190
7.6.1
191
The capital market line
7.6.2 The Capital Asset Pricing Model (CAPM) and the security market line
192
7.6.3 Implementation of the CAPM
195
7.6.4 Risk, return and the CAPM
197
■
ADDITIONAL FACTORS THAT EXPLAIN RETURNS
197
Q
PORTFOLIO PERFORMANCE APPRAISAL
198
7.8.1
Alternative measures of portfolio performance
203
Key terms
204
Self-test problems
204
Questions
204
Problems
205
References
208
The capital market
Learning objectives
211
21 1
8.1.2
The capital market
211
8.1.3
Types of financial market
212
8.1.4
Developments in Australia's financial markets
212
FINANCIAL AGENCY INSTITUTIONS
8.2.1
Brokers and the stock exchange
FINANCIAL INTERMEDIARIES
8.3.1
IQ
210
8.1.1 The flow of funds
8.2.2 Investment banks
HI
210
INTRODUCTION
8.1.5 Business funding
■
199
Summary
Banks
214
215
216
217
220
220
8.3.2 Money market corporations
223
8.3.3 Finance companies
223
8.3.4 Securitisation
223
INVESTING INSTITUTIONS
8.4.1
Insurance companies and superannuation funds
224
225
8.4.2 Unit trusts and investment companies
228
8.4.3 Overseas sources and markets
229
Summary
230
Key terms
230
Questions
230
References
231
C ontents
I Sources of finance: equity
Learning objectives
BD
INTRODUCTION
Q
THE CHARACTERISTICS OF ORDINARY SHARES
9.2.1
Fully paid and partly paid shares
9.2.2 Limited liability
d
233
234
234
234
234
9.2.4 The rights of shareholders
235
9.2.5 Advantages and disadvantages of equity as a source of finance
235
PRIVATE EQUITY
236
9.3.1
236
W hat is private equity?
9.3.2 Information problems and new ventures
237
9.3.3 Sources of finance for new ventures
237
9.3.4 Finance from business angels
238
9.3.5 Finance from private equity funds
238
INFORMATION DISCLOSURE
Offers of unlisted securities
240
240
9.4.2 Offers of listed securities
241
9.4.3 Offers that do not need disclosure
241
FLOATING A PUBLIC COMPANY
9.5.1
242
Public versus private ownership
242
9.5.2 Initial public offering of ordinary shares
243
9.5.3 Pricing a new issue
243
9.5.4 Underwriting and managing a newissue
244
9.5.5 Selling a new issue
246
9.5.6 The costs of floating a company
246
9.5.7 Long-term performance of IPOs
250
SUBSEQUENT ISSUES OF ORDINARY SHARES
252
9.6.1
253
Rights issues
9.6.2 Placements (private issues)
260
9.6.3 Contributing shares and instalment receipts
262
9.6.4 Share purchase plans
262
9.6.5 Company-issued share options
262
9.6.6 Choosing between equity-raising methods
263
m
EMPLOYEE SHARE PLANS
B 3
INTERNAL FUNDS
9.8.1
®
232
9.2.3 No liability companies
9.4.1
Q
232
Dividend reinvestment plans
MANAGING A COMPANY'S EQUITY STRUCTURE
9.9.1
Bonus issues and share splits
9.9.2 Share consolidations
265
266
267
268
268
269
C ontents
Summary
270
Key terms
270
Questions
271
Problems
272
References
273
Chapter 10
Sources of finance: debt
Learning objectives
275
275
BT8B1 INTRODUCTION
276
1BH
GENERAL CHARACTERISTICS OF DEBT
277
10.2.1
The interest cost of debt
278
10.2.2
Effect of debt on risk
279
10.2.3
Effect of debt on control
279
10.2.4
Security for debt
280
10 3 ■ SHORT-TERM BORROWING FROM BANKS AND OTHER FINANCIAL INSTITUTIONS
282
10.3.1
Bank overdraft
282
10.3.2
Debtor finance
283
10.3.3
Inventory loans
284
10.3.4
Bridging finance
284
10 4 ■ LONG-TERM BORROWING FROM BANKS AND OTHER FINANCIAL INSTITUTIONS
285
10.4.1
Long-term loan choices available to borrowers
285
10.4.2
Variable-rate term loans
286
10.4.3
Fixed-rate term loans
287
10.4.4 Other features of term loans
287
10.4.5
288
W hy do borrowers use term loans instead of security issues?
10 5 ■ DEBT SECURITIES
289
10.5.1
Debt securities: the general principles
289
10.5.2
Commercial paper
290
10.5.3
Bills of exchange
292
10.5.4
Debentures
295
10.5.5
Unsecured notes
297
10.5.6 Corporate bonds
297
10 6 ■ PROJECT FINANCE
301
10.6.1
The main features of project finance
301
10.6.2
When is project finance attractive?
302
10 7 ■ HYBRIDS OF DEBT AND EQUITY
302
10.7.1
Convertible notes and convertible bonds
303
10.7.2
Preference shares
305
Summary
309
Key terms
309
C ontents
Self-test problems
310
Questions
310
Problems
311
References
313
Chapter 1 1
Payout policy
Learning objectives
3 75
INTRODUCTION
316
11.1.1
Dividend declaration procedures
317
11.1.3
317
IS
Legal and tax considerations
PAYOUT POLICY IMPORTANT TO SHAREHOLDERS?
11.2.1
Alternative payout policies
318
319
319
1 1.2.2 Managers and payout decisions
320
11.2.3
321
The irrelevance of payout policy
1 1.2.4 The importance of full payout
323
11.2.5
324
Payout policy in practice
TRANSACTION COSTS AND FLOTATION COSTS
324
|
1 1.3.1 Transaction costs
324
1 1.3.2 Flotation costs
325
DIVIDENDS AND TAXES
325
1 1.4.1 Dividends and the imputation tax system
325
1 1.4.2 Imputation and capital gains tax
327
1 1.4.3 Dividend policy with imputation and capital gains tax
328
gl
1 1.4.4 The market value of franking credits
329
INFORMATION EFFECTS AND SIGNA山 NG TO INVESTORS
332
AGENCY COSTS AND CORPORATE GOVERNANCE
335
BEHAVIOURAL FACTORS AND CATERING THEORY
339
SHARE BUYBACKS
339
11.8.1
340
W hy do companies repurchase shares?
1 1.8.2 Share repurchases in Australia
343
DIVIDEND REINVESTMENT PLANS AND DIVIDEND ELECTION SCHEMES
346
PAYOUT POLICY AND COMPANY LIFE CYCLE
347
I
DD
DD
316
11.1.2 Types of dividend
11.1.4 Repurchasing shares
DD
315
Summary
349
Key terms
349
Questions
350
Problems
351
References
353
C ontents
Chapter 12
Principles of capital structure
356
Learning objectives
356
INTRODUCTION
357
12.2
THE EFFECTS OF FINANCIAL LEVERAGE
357
12.3
THE MODIGLIANI AND MILLER ANALYSIS (NO TAX CASE)
361
12.3.1
|B |
12.4
12.5
12.6
12.7
Modigliani and Miller's Proposition 1
361
12.3.2 Modigliani and Miller's Proposition 2
365
12.3.3
368
Modigliani and Miller's Proposition 3
12.3.4 W hy is the M M analysis important?
369
THE EFFECTS OF TAXES ON CAPITAL STRUCTURE UNDER A CLASSICAL TAX SYSTEM
369
12.4.1
Company income tax
369
12.4.2 Company tax and personal tax
371
12.4.3
373
Miller's analysis
12.4.4 The scope of Miller's analysis
374
THE EFFECTS OF TAXES ON CAPITAL STRUCTURE UNDER AN IMPUTATION TAX SYSTEM
374
12.5.1
374
W hat is an imputation tax system?
12.5.2 The effects of tax on capital structure decisions under an imputation tax system
376
THE COSTS OF FINANCIAL DISTRESS
377
12.6.1
Bankruptcy costs
377
12.6.2
Indirect costs of financial distress
378
AGENCY COSTS
379
12.7.1
Conflicts of interest between lenders and shareholders
379
12.7.2
Conflicts of interest between shareholders and company managers
380
12.8
OPTIAAAL CAPITAL STRUCTURE: THE STATIC TRADE-OFF THEORY
381
12.9
CAPITAL STRUCTURE WITH INFORMATION ASYMMETRY
382
12.9.1
Pecking order theory
382
12.9.2
Information asymmetry and the undervaluation of a company's assets
383
12.9.3
Information asymmetry and the overvaluation of a company's assets
385
12.9.4 Implications of information asymmetry for financing policy
386
Summary
387
Key terms
387
Self-test problems
387
Questions
388
Problems
389
References
392
Capital structure decisions
13.1
393
Learning objectives
393
INTRODUCTION
394
13.1.1
394
Company financing: some initial facts
XVII
C ontents
13.2
13.3
EVIDENCE ON CAPITAL STRUCTURE
395
13.2.1
Evidence on taxes
395
13.2.2
Evidence on the costs of financial distress
397
13.2.3
Evidence on agency costs
399
13.2.4
Evidence on information costs and the pecking order theory
401
13.2.5
Evidence from dual issues and spin-offs
403
13.2.6
Evidence on the choice of maturity and priority of debt
404
13.2.7 Evidence from surveys
405
ASSESSING THE THEORIES OF CAPITAL STRUCTURE
406
13.3.1
How useful is the static trade-off theory?
406
13.3.2
How useful is the pecking order theory?
407
13.4
FINANCING AS A MARKETING PROBLEM
408
13.5
DETERMINING A FINANCING STRATEGY
409
13.5.1
Business risk
409
13.5.2 Asset characteristics
410
13.5.3 Tax position
410
13.5.4 Maintaining reserve borrowing capacity ('financial slack')
411
13.5.5
411
Other factors
Summary
412
Key terms
412
Questions
413
References
414
The cost of ca pital
Learning objectives
417
|Q |
INTRODUCTION
418
B 〇
RISK, RETURN AND THE COST OF CAPITAL
418
14.2.1
Risk independence
419
14.3
TAXES AND THE COST OF CAPITAL
419
14.4
ALTERNATIVE APPROACHES TO ESTIMATION OF THE COST OF CAPITAL
421
14.4.1
421
14.5
14.6
Direct use of the CAPM
14.4.2 The weighted average cost of capital (WACC)
422
ESTIMATION OF THE COST OF CAPITAL: AN EXTENDED EXAMPLE
423
14.5.1
424
The cost of debt
14.5.2 The cost of preference shares
427
14.5.3 The cost of ordinary shares
427
14.5.4 The company's cost of capital
429
14.5.5
430
Issue costs and the cost of capital
PROJECT AND COMPANY COST OF CAPITAL
431
14.6.1
432
Calculating the cost of capital for divisions using the 'pure play7 approach
14.6.2 Calculating the cost of capital for divisions using the direct estimation approach
x v iii
417
434
[ED
EVALUATION TECHNIQUES
436
USING CERTAINTY EQUIVALENTS TO ALLOW FOR RISK
437
Summary
440
Key terms
440
Self-test problems
441
Questions
441
Problems
442
References
446
APPENDIX 14.1 THE COST OF CAPITAL UNDER ALTERNATIVE TAX SYSTEMS
Introduction
447
Deriving cost of capital formulae
447
Summary
449
Chapter 15
[Q l
447
Leasing and other equipment finance
450
Learning objectives
450
INTRODUCTION
451
451
15.2.1
Finance leases
15.2.2 Operating leases
452
453
15.2.3
Sale and lease-back agreements
453
15.2.4
Leveraged leasing
454
15.2.5
Cross-border leasing
455
[ Q | ACCOUNTING AND TAXATION TREATMENT OF LEASES
15.3.1
Accounting for leases
455
455
15.3.2 Taxation treatment of leases
456
15.4
SETTING LEASE RENTALS
456
15.5
EVALUATION OF FINANCE LEASES
458
15.5.1
Leasing decisions and investment decisions
460
15.5.2 The value of leasing in competitive capital markets
461
15.5.3
462
Establishing an advantage for leasing
15.5.4 Taxes and the size of leasing gains
463
15.5.5
464
Leasing and the imputation tax system
15.6
EVALUATION OF OPERATING LEASES
465
15.7
ADVANTAGES AND DISADVANTAGES OF LEASING
466
15.7.1
Possible advantages of leasing
466
15.7.2
Leasing policy
469
15.8
CHATTEL MORTGAGES AND HIRE-PURCHASE
471
15.8.1
471
Equipment finance and the goods and services tax
C ontents
Summary
472
Key terms
472
Self-test problems
472
Questions
473
Problems
474
References
475
Chapter 16
Capital market efficiency
477
Learning objectives
4 77
16.1
INTRODUCTION
478
16.2
THE EFFICIENT AAARKET HYPOTHESIS
478
16.2.1
479
16.3
16.4
A non-instantaneous price reaction
16.2.2 A biased price reaction
479
16.2.3
480
Categories of capital market efficiency
16.2.4 Market efficiency and the joint test problem
480
TESTS 〇 F RETURN PREDICTABILITY
481
16.3.1
481
The relationship between past and future returns
16.3.2 The presence of seasonal effects in returns
482
16.3.3
483
Predicting future returns on the basis of other forecast variables
EVENT STUDIES
487
16.4.1
487
The methodology of event studies
16.4.2
Evidence: profit and dividend announcements in Australia
491
16.4.3
Other events
493
TESTS FOR PRIVATE INFORMATION
493
16.6
MARKET EFFICIENCY AT THE MACRO LEVEL
495
16.7
BEHAVIOURAL FINANCE AND MARKET EFFICIENCY
495
16.8
IMPLICATIONS OF THE EVIDENCE WITH RESPECT TO MARKET EFFICIENCY
497
16.8.1
Implications for investors in securities
497
16.8.2
Implications for financial managers
499
Summary
501
Key terms
501
Questions
501
References
503
Chapter 17
Futures contracts and swaps
507
Learning objectives
5 07
17.1
INTRODUCTION
508
17.2
WHAT IS A FUTURES CONTRACT?
509
17.2.1
Forward contracts and futures contracts
509
17.2.2
How a futures market is organised
509
C ontents
17.2.3
Deposits, margins and the mark-to-market rule
51 1
17.2.4 The present value of a futures contract
512
17.3
THE AUSTRALIAN SECURITIES EXCHANGE
512
17.4
DETERMINANTS OF FUTURES PRICES
513
17.5
FUTURES MARKET STRATEGIES: SPECULATING AND HEDGING
515
17.5.1
Introduction
515
17.5.2
Speculating
516
17.5.3
Hedging
517
17.6
17.5.4 Some reasons why hedging with futures is imperfect
518
17.5.5
521
17.5.6 Selecting the number of futures contracts
522
FINANCIAL FUTURES ON THE AUSTRALIAN SECURITIES EXCHANGE: THE 90-DAY
BANK-ACCEPTED BILL FUTURES CONTRACT
525
17.6.1
A brief review of bank bills
525
17.6.1
Specification of the bank-accepted bill futures contract
526
Uses of the bank bill futures contract
527
17.6.2
17.7
Hedging and regretting
FINANCIAL FUTURES ON THE AUSTRALIAN SECURITIES EXCHANGE: THE 10-YEAR
TREASURY BOND FUTURES CONTRACT
532
17.7.1
A brief review of bond pricing
532
17.7.2
Specification of the 10-year bond futures contract
533
17.7.3
Uses of the 10-year bond futures contract
533
FINANCIAL FUTURES ON THE AUSTRALIAN SECURITIES EXCHANGE: THE 30-DAY
INTERBANK CASH RATE FUTURES CONTRACT
535
FINANCIAL FUTURES ON THE AUSTRALIAN SECURITIES EXCHANGE: THE SHARE
PRICE INDEX S&P/ASX 200 (SPI 200) FUTURES CONTRACT
536
17.9.1
A brief review of Australian Securities Exchange indices
536
17.9.2
Specification of the S&P/ASX 200 futures contract
537
17.9.3
Uses of the S&P/ASX 200 futures contract
537
17.10 VALUATION OF FINANCIAL FUTURES CONTRACTS
540
17.8
17.9
Valuation of bank bill futures contracts
540
17.10.2 Valuation of share price index futures contracts
541
FORWARD-RATE AGREEMENTS
542
SWAPS
544
17.10.1
17.12.1
17.1
W hat is a swap?
2.2 Interest rate swaps
544
544
CURRENCY SWAPS
551
Summary
556
Key terms
557
Self-test problems
557
Questions
557
Problems
558
References
562
C ontents
Chapter 18
(E D
Options and contingent claims
563
Learning objectives
563
INTRODUCTION
564
564
18.2.1
W hat is an option?
1 8.2.2 How options are created and traded
565
1 8.2.3 Option contracts and futures contracts
566
1 8.2.4 Payoff structures for calls and puts
566
1 8.2.5 Factors affecting call option prices
567
1 8.2.6 Some basic features of put option pricing
571
18.2.7
573
Put-call parity
1 8.2.8 The minimum value of calls and puts
B H
^ 1
564
576
BINOMIAL OPTION PRICING
577
1 8.3.1 The basic idea: pricing a single-period calloption using the binomial approach
577
1 8.3.2 Risk neutrality as a solution method
579
1 8.3.3 Binomial option pricing with many time periods
579
1 8.3.4 Applying the binomial approach to other option problems
582
THE BLACK-SCHOLES MODEL OF CALL OPTION PRICING
582
18.4.1
Assumptions
1 8.4.2 The Black-Scholes equation
1 8.4.3
A brief assessment of the Black-Scholes model
582
583
587
OPTIONS ON FOREIGN CURRENCY
588
18.5.1
589
W hat is an option on foreign currency?
1 8.5.2 Combinations of options on foreign currency
590
18.6
OPTIONS, FORWARDS AND FUTURES
591
18.7
OPTIONS ON FUTURES
593
1 8.7.1
W hat is an option on a futures contract?
593
Uses of options on futures
593
1 8.7.2
18.8
18.7.3
Pricing options on futures
594
18.7.4
Specification of the SPI 200 futures options contract
594
CONTINGENT CLAIMS
595
18.8.1
W hat is a contingent claim?
595
18.8.2
Rights issues
595
18.8.3 Convertible bonds
596
1 8.8.4 Valuation of levered shares and risky zero-coupon debt
596
1 8.8.5 Valuation of levered shares and risky coupon-paying debt
596
1 8.8.6
597
Project evaluation and Veal’ options
Summary
599
Key terms
599
Self-test problems
599
C ontents
Questions
600
Problems
601
References
604
.；
,
19.2
19 3
19 4
19 5
1 Analysis of takeovers
I
Learning objectives
605
INTRODUCTION
606
19.1.1
606
Fluctuations in takeover activity
19.1.2 Types of takeover
607
REASONS FOR TAKEOVERS
608
19.2.1
Evaluation of the reasons for takeovers
609
19.2.2
Survey evidence of the motives for takeovers
613
19.2.3
The roles of takeovers
613
■ECONOMIC EVALUATION OF TAKEOVERS
Comments on estimation of takeover gains
615
19.3.2
Comparing gains and costs
616
19.3.3
Estimating cost for a share-exchange takeover
617
■ALTERNATIVE VALUATION APPROACHES
618
19.4.1
Valuation based on earnings
618
19.4.2
Valuation based on assets
619
■REGULATION AND TAX EFFECTS OF TAKEOVERS
7 |
614
19.3.1
619
19.5.1
Off-market bids
620
19.5.2
Market bids
621
19.5.3
Disclosure requirements
621
19.5.4
Creeping takeover
622
19.5.5
Partial takeovers
622
19.5.6
Schemes of arrangement
622
19.5.7 Other controls on takeovers
623
19.5.8 Tax effects of takeovers
623
19.5.9
624
Break fees, takeovers and corporate governance
1 1 9 . 6 1 TAKEOVER DEFENCES
W
605
625
19.6.1
Poison pills
625
19.6.2
Acquisition by friendly parties
625
19.6.3
Disclosure of favourable information
625
19.6.4 Claims and appeals
626
19.6.5 The effects of takeover defences
626
CORPORATE RESTRUCTURING
627
19.7.1
Divestitures
627
19.7.2
Spin-offs
627
19.7.3
Buyouts
628
XXIII
C ontents
EMPIRICAL EVIDENCE ON TAKEOVERS
630
19.8.1
631
The target company
19.8.2 The acquiring company
631
19.8.3
Are takeovers poor investments?
633
19.8.4
Distinguishing between good and bad takeovers
636
19.8.5 The net effects of takeovers
636
19.8.6 The sources of gains from takeovers
637
Summary
639
Key terms
639
Self-test problems
640
Questions
640
Problems
642
References
643
Chapter 20
B Q
Management of short-term assets: inventory
646
Learning objectives
646
INTRODUCTION
647
THE IMPORTANCE OF SHORT-TERM FINANCIAL DECISIONS
647
TYPES OF SHORT-TERM ASSET
648
20.3.1
Inventory
648
20.3.2
Liquid assets (cash and short-term investments)
648
20.3.3
Accounts receivable (debtors)
648
B Q
THE NEED FOR SHORT-TERM ASSET MANAGEMENT
648
Q fl
SHORT-TERM ASSETS AND SHORT-TERM LIABILITIES
649
E H
OVERVIEW OF INVENTORY MANAGEMENT
650
B Q
E 0
INVENTORY COSTS: RETAILING AND WHOLESALING
650
20.7.1
Acquisition costs
650
20.7.2
Carrying costs
651
20.7.3
Stockout costs
651
INVENTORY COSTS: MANUFACTURING
651
20.8.1
Inventories of raw materials
651
20.8.2
Inventories of finished goods
652
in v e n t o r y
MANAGEMENT UNDER CERTAINTY
652
20.9.1
The economic order quantity (EOQ) model
652
20.9.2
Cost estimation
655
20.9.3
The EOQ model with positive lead time
656
20.9.4 The EOQ model with quantity discounts
657
E S S INVENTORY MANAGEMENT UNDER UNCERTAINTY
20.10.1
658
Specifying an acceptable probability of stockout
660
20.10.2 Specifying an acceptable expected customer service level
660
20.11 INVENTORY MANAGEMENT AND THE 'JUST-IN-TIME' SYSTEM
661
Summary
662
Key terms
663
Self-test problems
663
Questions
663
Problems
664
References
665
Chapter 21
Management of short-term assets:丨
iquid assets and
accounts receivable
666
Learning objectives
666
O H
INTRODUCTION
667
w xn
OVERVIEW OF LIQUIDITY MANAGEMENT
667
21.2.1
W hat are liq u id ' assets?
667
21.2.2
Liquidity management and treasury management
667
21.2.3
Centralisation of liquidity management
668
Q Q
Q Q
21.2.4 Motives for holding liquid assets
669
21.2.5
669
Major issues in liquidity management
CASH BUDGETING
670
21.3.1
Forecasting cash receipts
670
21.3.2
Forecasting cash payments
671
THE CHOICE OF SHORT-TERM SECURITIES
673
TYPES OF SHORT-TERM INVESTMENT
674
21.5.1
Deposits of funds with financial institutions
674
21.5.2
Discounting of commercial bills
674
21 6 | THE CORPORATE TREASURER AND LIQUIDITY MANAGEMENT
Q Q
Q Q
675
OVERVIEW OF ACCOUNTS RECEIVABLE MANAGEMENT
675
21.7.1
675
What are accounts receivable?
CREDIT POLICY
677
21.8.1
The decision to offer credit
677
21.8.2
Selection of credit-worthy customers
677
21.8.3
Limit of credit extended
680
21.8.4 Credit terms
680
COLLECTION POLICY
681
EVALUATION OF ALTERNATIVE CREDIT AND COLLECTION POLICIES
682
Summary
686
Key terms
687
Self-test problems
687
Questions
687
C ontents
Problems
688
References
689
APPENDIX 21.1 FINANCIAL STATEMENT ANALYSIS
xxvi
690
Introduction
690
Measurement and interpretation of several financial ratios
690
Usefulness of financial ratio analysis
695
Financial ratios and short-term asset management
696
Appendix A Numerical tables
698
Appendix B Solutions to self-test problems
709
Glossary
725
Index
736
PREFACE
W
This book is designed primarily for use in a first subject in the principles and practice of finance. Our main objectives
are to introduce readers to finance theory and to the tools of financial decision making in the context of the
Australian institutional environment. Nevertheless, it is also suitable for students who have completed an introductory
subject on capital markets and financial institutions. It also contains sufficient material for two subjects in finance.
Readers who are familiar with previous editions of the book will notice changes that go well beyond the updating
that might be expected from a new edition. New finance theories and new empirical evidence are presented with
each edition. For example, in this edition both new theoretical material and related empirical evidence have been
incorporated on the determinants of payout policy (Chapter 1 1), the capital structure decision (Chapter 13) and the
analysis of takeovers (Chapter 19). Some of this new material provides more detailed coverage, compared with
previous editions, of the expanding area of behavioural finance—an area where investor psychology is incorporated
into research design. Theories and evidence with respect to market efficiency (Chapter 16) are also updated.
Since the eleventh edition, Eugene Fama and Robert Shiller have each been awarded the Nobel Memorial Prize in
Economic Sciences for their work examining market efficiency. Both have made a fundamental contribution to our
understanding of market efficiency yet they have different views as to the extent that markets are efficient. Like the
Nobel Prize Committee, the approach we take is to highlight the range of evidence in this area.
Practice in finance also necessitates updates. For example, since the last edition there have been on-going
developments in financial markets, including in Australia, and changes in the functions of banks. M any of these
developments result from the Global Financial Crisis and are incorporated in Chapter 8.
Rather than distort the coherent flow of the book by altering its structure to reflect these changes in principles and
practice, new material is embedded into the existing structure. Indeed, the major structural change in this edition is
the omission of international finance as a separate chapter and instead embedding material where appropriate into
relevant chapters; in particular into Chapter 17, which now incorporates a detailed discussion of swaps.
Finally, we wish to express our special thanks to Graham Peirson and Peter Howard who have both retired
from active authorship but have made a substantial contribution to the foundations of the book. Graham deserves
particular mention. Having been central to the book from the first edition, he continues to make a great contribution
to each new edition by providing valuable comments on the draft of each chapter. Graham brings not only a deep
knowledge but also an uncanny ability to detect flaws in logic and in writing style. His thoroughness has again
prevented many such flaws from appearing in print.
ROB BROWN
♦
STEVE EASTON
♦
SEAN PINDER
August 2014
x x v ii
ABO U T THE AUTHORS
G rah am Peirson
Graham Peirson is Emeritus Professor of Accounting and Finance at Monash
University. He has published widely in academic and professional journals and
is also coauthor of Issues in Financial Accounting; Accounting: An Introduction;
Financial Accounting: An Introduction; and Financial Accounting Theory.
Graham is a graduate of Adelaide University, and has taught at Adelaide
University, the University of California (Berkeley), the University of Illinois, the
University of Florida and the University of Washington. He has also taught short
courses for a range of clients, including the Australian Competition and
Consumer Commission and the National Australia Bank.
Rob Brown
Rob Brown is Emeritus Professor of Finance at the University of Melbourne. He
has published many research papers in international journals, including
Economica, the Journal o f Banking and Finance, the Journal o f Multinational
Financial Monogementand \he Journal o f Fixed Income. He is a former associate
editor (finance) of Accounting and Finance, the research journal of the
Accounting and Finance Association of Australia and New Zealand. Rob has
taught at the University of Sydney, Lancaster University and Monash University,
and been a visiting scholar at the University of British Columbia (Canada) and
the University of Manchester (UK). His current research interests are analysts'
investment recommendations.
Steve Easton
Steve Easton is Professor of Finance at the University of Newcastle, where he
previously served as Head of the Department of Accounting and Finance and
Dean of the Faculty of Economics and Commerce. His research work has been
accepted for publication in a wide range of journals, including the Journal o f
Futures Markets, Economico and the Journal o f Banking and Finance. Steve has
taught at Adelaide University, Lancaster University and Monash University. He
has also provided short courses for a range of private and public sector
organisations, including Australia Post, Macquarie Generation, State Forests of
New South Wales and the Tasmanian Chamber of Commerce and Industry. His
current research interests are in asset pricing, portfolio management and
corporate governance.
XXVIII
Peter H o w a rd
Peter Howard taught finance at Monash University for more than 25 years.
Before this he worked for eight years as an engineer in the petrochemical and
mining industries. He has extensive experience in project evaluation and has
taught on short courses for a range of clients, including BHP Billiton and the
National Australia Bank. Peter has published in academic and professional
journals on lease evaluation and the effects of imputation on payout and
financing decisions. He has extensive teaching experience at both postgraduate
and undergraduate levels. Since retiring from Monash University he has
maintained a strong interest in the finance literature and the operation of
Australian financial markets.
Sean Pinder
Sean Pinder is an Associate Professor in the Department of Finance at the
University of Melbourne. Prior to this he held positions at Monash University and
the University of Newcastle and taught at the postgraduate level at Lancaster
University in England and the Melbourne Business School. He has undertaken a
range of consulting activities for international firms and has developed and
delivered professional short courses on treasury risk management, derivatives
and capital budgeting issues for major Australian and international companies.
Sean has an extensive research profile, with his work appearing in leading
Australian and international journals. He has received a number of prizes for
his research and teaching.
A C K N O W LE D G M E N T S
We have received valuable assistance from a number of people, including Philip G. Brown, Chris Deeley, Paul
Docherty, Stefan Petry and Michael Seamer.
We would like to join McGraw-Hill in thanking academic colleagues who provided their valuable time and
expertise in aligning the learning resources with this edition of our book. They include:
♦ Mariya Yesseleva-Pionka, Monash University
♦
Neil Hartnett, University of Newcastle
♦ Damian Bridge, Macquarie University
♦ Md Akhtaruzzaman, University of Newcastle
We also owe a debt of thanks to the following reviewers of earlier editions who have helped us shape the text
you hold today: John Ablett (University of Western Sydney), David Allen (Edith Cowan University), Vicki Baard
(Macquarie University), Robert Bianchi (Griffith University), Barry Burgan (University of Adelaide), Nicholas Carline
(Lancaster University, UK), Meena Chavan (Macquarie University), Andrew Child (Monash University), Scott Dobbs
(University of Wollongong), Samson Ekanayake (Deakin University), Don Geyer (Charles Sturt University), Abeyratna
Gunasekarage (Monash University), Neil Hartnett (University of Newcastle), Darren Henry (La Trobe University),
Ben Jacobsen (James Cook University), Sian Owen (University of New South Wales), Judy Paterson (University of
Canberra), Alex Proimos (Macquarie University), Boyd Scheuber (University of Southern Queensland), Chander
Shekhar (University of Melbourne), Jing Shi (Australian National University), Yew Lee Tan (Victoria University),
Madhu Veeraraghavan (Monash University) and David W oodliff (University of Western Australia).
In addition, we thank publisher Jillian Gibbs and senior product developer Jane Roy.
Thanks also to Kate Easton for her suggestions for the cover design of this book.
Finally, and most importantly, we thank our wives—Chris, Rayna, Diane, Dawn and Debra—for their support
during this project.
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HIGHLIGHTS OF THIS EDITION
CHAPTER 1
CHAPTER 8
►
►
Delivers a simple, concise overview of the essential
Update on developments in Australian financial
markets.
concepts of corporate finance.
►
Expanded discussion of the functions of banks.
CHAPTER 2
►
Provides detailed coverage of Fisher’s Separation
Theorem and the company’s objective to maximise
CHAPTER 9
►
Provides greater detail on the various accelerated
rights issue structures that have developed in the
current value.
Australian market and recent evidence on the
CHAPTER 3
popularity of, and costs associated with, the main
►
methods of raising equity capital.
Introduces simple interest, compound interest and
the time value of money in one logically structured
chapter.
CHAPTER 10
►
►
Greater emphasis on zero-coupon rates and the
zero-rate curve.
►
►
New section on pricing off the zero curve.
Features a new Finance in action piece on the
failure of the Banksia Financial Group.
CHAPTER 4
►
►
Updating of discussion of debtor finance.
Expanded overview of the growth of the debenture
and corporate debt markets in Australia.
Includes estimates of the Australian
zero-rate curve.
►
Updates Australian corporate and government
►
ratings.
Expanded explanation of liquidity (risk) premium
approach to the term structure.
BRIEF CONTENTS
CHAPTER 1
CHAPTER 2
CHAPTER 3
CHAPTER 5
►
Provides international survey evidence of capital
CHAPTER 4
budgeting practices.
►
Features an in-depth discussion of the application
CHAPTER 5
of real options analysis as well as evidence of the
extent of usage of the technique.
CHAPTER 6
►
Is dedicated specifically to applying methods of
project evaluation.
►
Includes a new section dealing specifically with
how taxes should be incorporated into project
evaluation techniques.
CHAPTER 7
►
Updates empirical evidence concerning the market
risk premium in an international and domestic
context.
►
Includes a detailed discussion of models that
incorporate factors other than systematic risk in
explaining expected returns.
►
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER
7
8
9
10
11
12
13
14
15
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER
16
17
18
19
20
Updates estimates of the systematic risk of
Australian firms.
►
CHAPTER 6
Addresses alternative methods of appraising the
performance of an investment portfolio.
CHAPTER 21
Introduction ...................................... 1
Consumption, investment and the
capital market ................................ 10
The time value of money: an
introduction to financial
mathematics....................................28
Applying the time value of money
to security valuation ...................... 74
Project evaluation: principles and
methods ......................................103
The application of project
evaluation methods.................... 129
Risk and return ........................... 172
The capital market .......................210
Sources of finance: e q u ity ...........232
Sources of finance: debt ............. 275
Payout policy ...............................315
Principles of capital structure ...... 356
Capital structure decisions ..........393
The cost of capital ...................... 417
Leasing and other equipment
finance ..........................................450
Capital market efficiency ............477
Futures contracts and swaps........ 507
Options and contingent claims ..563
Analysis of takeovers ..................605
Management of short-term assets:
inventory .....................................646
Management of short-term assets:
liquid assets and accounts
receivable..................................... 666
H ighlights
^
►
Expanded discussion of convertible securities and
►
of this edition
Features a new Finance in action piece illustrating
why they are issued.
the impact of expectations in share market reaction
Restructure of the discussion of preference shares.
to announcements.
CHAPTER 1 1
CHAPTER 17
►
Includes changes in the legal requirements for
payment of dividends.
►
Includes updated exchange contracts values and
►
Emphasises the importance of a 'full payout' policy
►
exchange indices throughout.
The chapter now includes a detailed discussion
►
►
and de-emphasises the dividend irrelevance theorem.
of swaps, including a comprehensively revised
Highlights recent evidence on the market value of
discussion of interest rate swaps which emphasises
franking credits.
the different uses of swaps.
Discusses recent research on the growing
importance of share buybacks and the substitution
of buybacks for dividends.
於
CHAPTER 1 8
►
relationship between an option's market price
Includes an explanation of behavioural factors that
and characteristics such as its term-to-expiry and
may affect payout policy.
►
exercise price.
Features a new Finance in action piece on ANZ
Bank’s dividend announcement.
Includes updated examples illustrating the
►
Features a Finance in action piece describing how
CHAPTER 12
options written on a share price index are used to
create a Volatility Index (VIX), which then provides
►
useful information to investors about the level of
Updates of examples.
uncertainty in the market.
CHAPTER 13
►
Features a new Finance in action piece on the
benefits of the no-debt decision of a company that
CHAPTER 19
►
►
Includes recent Australian evidence on surveys of
►
activity.
Includes recent empirical evidence on the costs of
►
►
financial distress.
Includes recent empirical evidence with respect to
agency costs.
►
Updates the discussion of the regulation of takeover
activity.
Extensively updates the empirical evidence
presented on the wealth effects of alternative forms
CHAPTER 14
►
Includes a new section providing survey evidence
of the motives of acquiring managers for takeover
chief financial officers.
►
►
Updates empirical evidence on the fluctuations in
takeover activity over time.
had previously experienced a financial collapse.
of takeovers and corporate restructuring including
Updates empirical evidence on the value of
the role of investor psychology in determining what
imputation tax credits in Australia.
an appropriate bid price may need to be in order
A streamlined discussion of the impact of taxes on
to ensure success of a bid.
the process of project evaluation.
►
Features a new Finance in action piece dealing with
CHAPTER 2 0
the new approach taken by the Australian Energy
►
CHAPTER 15
►
►
or advanced student.
►
A new Finance in action piece on inventory
management problems at Treasury W ine Estates.
Updated evidence on the use of lease finance by
Australian companies.
CHAPTER 21
Includes a discussion of the proposed changes to the
►
by the International Accounting Standards Board
CHAPTER 16
Provides concise but thorough coverage of short­
term assets, focusing on liquid assets and accounts
receivable, for the curious or advanced student.
accounting standards relating to leases as put forward
►
Provides concise but thorough coverage of short­
term assets, focusing on inventory, for the curious
Regulator to estimate an appropriate weighted
average cost of capital for energy distributors.
►
Provides, in the appendix, a completely updated
Incorporates a range of new evidence with respect
comprehensive example demonstrating the
application of financial statement analysis
to the extent to which markets are efficient.
techniques in practice.
XXXIII
H O W TO USE THIS B O O K
L e arn in g objectives list the information you will learn by studying the chapter. They are restated in the margins
in appropriate locations and so become useful revision tools.
LEARNING OBJECTIVES
After studying this chapter you should be able to:
1
understand how assets are valued under conditions of certainty
m
2
use the tools of financial mathematics to value equity securities
3
explain the main differences between the valuation of ordinary shares based on dividends and on
earnings
4
use the tools of financial mathematics to value debt securities
5
explain the nature of interest rate risk
6
understand the theories that are used to explain the term structure of interest rates
7
understand the effect of default risk on interest rates
8
apply the concept of duration to immunise a bond investment.
LEARNING
OBJECTIVE 1
Understand how
assets are valued
under conditions of
certainty
C h ap fe r introductions give you an overview of the chapter's most important points and contextualise the topics
to the wide area of business finance.
Introduction
I n C h a p t e r 1 w e d is c u s s e d b r ie f ly t h e im p o r t a n t c o n c e p t o f t h e t im e v a lu e o f m o n e y . I n C h a p te r 3 w e
p r e s e n te d s o m e m a t h e m a t ic a l to o ls u s e f u l i n a n a ly s in g p ro b le m s in v o lv in g t h e t im e v a lu e o f m o n e y .
I n p a r t i c u la r , w e s h o w e d h o w p ro m is e d s tre a m s o f f u t u r e ca sh flo w s c a n b e v a lu e d , p r o v id e d t h a t th e
r e q u ir e d r a te o f r e t u r n is k n o w n .
I n t h i s c h a p te r w e a p p ly th e s e to o ls t o t h e v a lu a t io n o f d e b t a n d e q u it y s e c u r itie s . I n i t i a l l y w e
a s s u m e t h a t t h e s e c u r it y s f u t u r e c a s h flo w s a re k n o w n w i t h c e r ta in ty . L a t e r in t h e c h a p te r w e in tr o d u c e
u n c e r t a in t y , b u t o n ly i n a lim it e d w a y . A m o re f o r m a l a n d d e ta ile d t r e a t m e n t o f u n c e r t a in t y is g iv e n in
C h a p te r 6 .
K e y term s are defined in the margins beside the term's first appearance in the text. These terms are then listed in
the glossary at the end of the book.
T h e le a s t c o m p lic a te d m e a s u re o f t h e t e r m
s tr u c tu r e o f in t e r e s t ra te s is t h e m a r k e t y ie ld o n a
g o v e r n m e n t b o n d t h a t p a y s n o in t e r e s t d u r in g it s lif e , b u t p a y s a fix e d s u m a t m a t u r it y . S u c h a b o n d is
ZERO-COUPON BONDS
(ze r o s )
bonds that pay only
one cash flow, the
payment at maturity
k n o w n as a z e r o - c o u p o n b o n d ( o f te n a b b r e v ia te d ju s t t o a z e r o ) .
T h e p ric e o f a z e ro w i t h a fa c e v a lu e o f F d o lla r s a n d a t e r m o f n y e a rs is s im p ly :
P〇 = (l+z„)n
Example 4.
Rankine Ltd is currently paying a dividend of 90 cents per share. If investors expect this dividend
to be maintained and require a rate of return of 15 per cent on the investment, what is the value of
Rankine’s shares?
SOLUTION
The value of Rankine's shares is calculated as follows:
0
歷0 .1 5
= $ 6.00
xxxiv
E x a m p le s are provided
throughout the text to illustrate
the practical application of
the theory and working
providing guidance for
students.
How
TO USE THIS BOOK
Finance in action
F,NANCE
ON GUARD AGAINST A BOND FALL
IN ACTION
----------------------------- ------------ ------- ---- ----------------- ---------------------- ------------------- -----------In an artide published in 2013, financial journalist Christopher Joye reminds readers of interest
rate risk, which flows from the connection between interest rates and bond prices.
Bond traders have been making out like bandits since the global financial crisis. A portfolio of
Australian government bonds with maturities longer than 10 years has delivered annual total
returns of over 12 per cent since December 2007.
Yet the preconditions for the mother-of-all bond market reckonings are sliding into place.
This contingency, which AM P^ Shane O liver believes is a 'significant risk', could result in
wiping more than $60 billion off Aussie bond values, with steep capital losses.
To properly understand these risks, one needs to appreciate how extraordinary current
circumstances are. W hen doing so, it helps to keep in mind a key principle: bonds that pay
fixed, a$ opposed to variable, rates hove prices that are inversely related to external interest
rates.
If you invested in a bond paying an annual fixed coupon of, say, 3 per cent, and market
interest rates surge to 5 per cent, that bond would be worth substantially less than when you
bought it. The converse is also true: if market rates decline ... it would be worth more.
This is why Australian government bond prices have soared since 2007: market yields
have fallen sharply as global central banks have floored policy rates close to zero and printed
unprecedented amounts of money to fund public and private debt.
is a feature containing
interesting items from the
business media that relate
the theory to real-world
practice.
Source: 'O n guard against a bond fall', Christopher Joye, Australian Financial Review, 5 January 2013, p. 39.
S u m m a rie s give students
a checklist of the topics
covered in the chapter and
SUMMARY
•
Financial assets such as bonds and shares can be
valued by discounting their future cash flows to
present values and summing these present values.
The discount rate used is the required rate of return
or opportunity cost of capital.
• If the future cash flows from an asset are certain,
the required rate of return will reflect only the
effect of time on the value of money.
• If the future cash flows are uncertain, investors
will also require compensation for risk and the
rate will be increased by the inclusion o f a risk
premium.
serve as a useful revision
tool when preparing for
exams.
•
•
and a price-earnings ratio. The value of this ratio
depends mainly on risk and expected growth in
earnings.
Debt securities (bonds) are priced by discounting
their future coupon interest payments and face
value. For any company, the interest rate required by
lenders will be less than the required rate of return
on the company's ordinary shares. The price of a
debf security is inversely related to the interest rate
required by investors.
Interest rates at any given time will usually be different
for different terms to maturity. This pattern is known
Self-test p ro b le m s
f jt
at the end of selected
SELF-TEST PROBLEMS
1 Richards Ltd pays annual dividends on its ordinary shares. The latest dividend was 75 cents per share
and was paid yesterday. Dividends are expected to grow at 8 per cent per annum for the next 2 years,
after which a growth rate of 4 per cent per annum will be maintained indefinitely. Estimate the value of
one share if the required rate of return is 14 per cent per annum.
2 A government bond with a face value of $100 and a coupon interest rate of 11 per cent per annum
matures in 3 years, time. Inferest payments occur twice each year and a payment has just been made.
If the current market yield on the bond is 13 per cent per annum, what is the current price of the bond?
3 The current interest rates (yields) on zero-coupon government bxinds are as follows:
1
13.90
2
11.70
3
10.50
chapters cover all the
topics within the chapter
for thorough exam
preparation.
Assume that the term structure can be explained purely by expectations of future interest rates, and
therefore there is no liquidity (or risk) premium. Calculate the expected 1-year rates for the next 2 years.
Solutions to self-test p r o b lem s a r e a v a ila b le in A p p e n d ix B.
Additional e n d -of-ch ap te r
q u e stio n s a n d p ro b le m s
provide further practice and
cA
Valuation under certainly [LO 1]
A promise to pay $10000 in 4 years, time is certain to be kept. If the risk-free rate for a 4-year term is 5.5 per
cent per annum, what is the value of this promise today? Do we know what the value will be in a year's time?
Why or why not?
2
Valuation of shares [LO 2]
Assume that today is the last day of 2014. Rednip Ltd is expected to pay annual dividends of 64 cents in
2015 (Year 1). Assume that this dividend is expected to grow at an annual rate of 10 per cent and investors
require a rate of return of 20 per cent per annum,
develop deeper understanding
of the topics covered. They
are linked back to the learning
objectives for each chapter.
PROBLEMS
1
a) Estimate Rednip Ltd's share price today.
XXXV
CHAPTER CONTENTS
m
Finance as an area of study
2
m
The company's financial objective
m
Financial decisions
2
KB
Fundamental concepts in finance
KQ
Busi门
ess structures
3
IB
Outline of the book
LEARNING OBJECTIVES
After studying this chapter you should be able to:
1
describe the structure of finance as an area of study
2
identify the major decisions made by financial managers and investors
3 identify the major types of business entities
4 specify the objective of the company
5 identify and explain the fundamental concepts in finance.
B usiness finance
Finance as an area of study
LEARNING
OBJECTIVE 1
Describe the structure
of finance as an area
of study
This book introduces the reader to the area o f study know n as finance. Although financial issues have
been studied fo r centuries, i t is only relatively recently— in the last 50 years or so— th a t finance has
emerged as an area o f study in its own rig ht, w ith a well-established body o f theory and evidence. In the
chapters th a t follow, we w ill introduce you to the m ajor issues in finance.
Finance can be described as having tw o m ain components, which are:1
•
•
corporate finance
investments.
Corporate finance takes the view point o f the company. The m ain issues involved are the choice o f
assets, the financing decision and the dividend decision. Imagine th a t a group o f investors has set up a
new company. The investors are the shareholders (that is, the owners) o f the company. The company must
decide2 w hat assets i t w ill buy and how i t w ill fund the purchase o f these assets. The company may use its
own m oney— th a t is, the money contributed by the shareholders— to fund the purchase, or i t may borrow
the money. O r it may use b oth shareholders* funds and borrowed funds. When the company has been
operating fo r a tim e, it may have made a p ro fit. I f so, it may decide to d istribute some or all o f the p ro fit to
the shareholders. Such a d istrib u tio n is called a dividend. I f the dividend paid is less than the p ro fit, then
some o f the p ro fit is retained w ith in the company, and w ill be used to fu nd asset acquisitions and/or debt
repayment. Corporate finance is also concerned w ith corporate governance issues. For example, should
the Board o f Directors include some outsiders*? Should senior managers be granted shares to encourage
them to make decisions th a t are in the best interests o f the shareholders?
Investments takes the view point o f the investor rather than the company. Investors are concerned
about the re tu rn they w ill earn on an investm ent — the more the better. But unless investors are w illin g
to take a risk, they cannot expect to earn a high return. A ll investors dream o f fin d in g an investm ent
th a t produces high returns at low risk— b u t m ost w ill never fin d one. So, investors m ust make a trade­
o ff between retu rn and risk. In investm ents, this balancing o f risk and re tu rn is a m ajor issue. A large
p art o f the solution is fo r investors to choose a diversified set o f assets in w hich to invest. Investments
is also about the pricing o f securities such as shares and bonds. These securities are traded in financial
markets, many o f which are very active, w ith transactions ru n n in g in to the m illions o f dollars every day.
How does the risk o f a security affect the price at which i t w ill trade in these financial markets? W hat
factors, other than risk, m ig ht also be im portant? And how m ig h t the price be expected to change in
the future?
Financial decisions
LEARNING
OBJECTIVE 2
In this book we focus on financial decisions made by companies and investors. Some o f these decisions are:
Corporate (or company) decisions:
Identify fhe major
decisions made by
financial managers
and investors
Asset management: W hat new assets should the company acquire? How much should i t pay fo r
these assets?
W orking capital management: How much cash should the company hold? How much inventory?
Capital structure: How much should the company borrow?
Payout policy: How much should the company pay out to its shareholders?
Mergers and acquisitions: Should the company take over another company?
1
2
A third component, financial markets and institutions, overlaps to some extent with corporate finance and investments. The
focus o f this component is on the markets for various securities and the design of financial instruments. It also considers the
financial issues faced by banks and other financial institutions.
Strictly speaking, a company is just a legal structure, and hence cannot have any personal qualities, such as the ability to make
decisions. Company decisions are in fact made by people such as the company s directors. However, for ease of exposition, we
attribute personal qualities to companies.
C hapter o ne Introduction
Investor decisions:
•
•
Portfolio theory: How can an investor achieve a better trade-off between risk and return?
Asset pricing: How much is a particular security w orth? W hat is the relationship between long-term
interest rates and short-term interest rates?
Busi门ess structures
When a business is being established, one o f the firs t decisions th a t has to be made concerns the type o f
business structure th a t is to be used. In Australia, although many small businesses are sole proprietorships
or partnerships, nearly all large businesses, and many thousands o f small businesses, are companies.
Hence, in this book, our focus is on companies. But to place the corporate (company) form in context, we
firs t discuss the advantages and disadvantages o f sole proprietorships and partnerships.
LEARNING
OBJECTIVE 3
Identify the major
types of business
entities
1.3.1 I Sole proprietorship
A sole proprietorship is a business owned by one person. M any small service businesses, retail stores
and professional practices are operated as sole proprietorships.
SOLE PROPRIETORSHIP
business owned by
one person
Advantages
The advantages o f a sole proprietorship structure include:
•
•
•
Control o f the business rests w ith the owner, so it is relatively easy to make decisions and there is no
scope fo r disagreements between owners.
I t is easy and inexpensive to form , and to dissolve.
It is n o t treated as a separate e n tity fo r tax purposes. Therefore, any business p rofits belong to the
owner and are taxed only once as p art o f the owner s assessable income.
Disadvantages
The disadvantages o f a sole proprietorship structure include:
•
•
•
It is n o t a separate legal e n tity and therefore the owner has unlim ite d lia b ility fo r debts incurred by
the business. In other words, all obligations o f the business are personal obligations o f the owner.
The size o f the business is lim ite d by the wealth o f the owner and by the am ount th a t can be
borrowed. I t can be d ifficu lt to raise funds fo r expansion because lenders are usually reluctant to
lend large amounts to individuals.
Ownership o f a sole proprietorship can be transferred only by selling the business to a new owner. I f
a sole proprietorship is n o t sold, then i t w ill cease to exist when the owner retires or dies.
1 .3.2! Partnership
A partn ersh ip is a business owned by tw o or more people acting as partners. M any small service
PARTNERSHIP
businesses, retail stores and professional practices are operated as partnerships.
business owned by
two or more people
acting as partners
Advantages
The advantages o f a partnership structure include:
•
•
I t is easy and inexpensive to fo rm because there are no legal requirements th a t need to be met. A ll
th a t is necessary is an agreement, preferably in w ritin g to avoid future disagreements, by those
form ing the partnership.
A partnership can combine the wealth and talents o f several individuals, and employees can be
offered the prospect o f becoming partners (owners) in the future.
B usiness finance
Disadvantages
There are also im p o rta n t disadvantages o f a partnership structure, including:
•
•
•
Partnerships are n o t separate legal entities and the partners are therefore personally liable for
obligations (including debts) entered in to by the partnership.
It can be d ifficu lt fo r partners to w ithdraw th e ir investm ent because the partnership w ill term inate
i f a p artne rs interest in the partnership is sold or a partner dies. In either case, a new partnership
w ill have to be formed.
Disputes between partners or form er partners can be very damaging.
.3 .3 1Company
COMPANY
separate legal entity
formed under the
Corporations Act
2001; shareholders
are the owners of a
company
A com pany is a separate legal e n tity form ed under the Corporations A ct 2001. The owners o f a company
are called shareholders because th e ir ownership interests are represented by shares in the company s
capital. Companies vary greatly in size. They range from large companies listed on a stock exchange w ith
many thousands o f shareholders to small fam ily companies carrying on a relatively small-scale business.
In a large company, the shareholders and the managers are usually separate groups. The shareholders
elect the Board o f Directors, which appoints managers to run the company on behalf o f the shareholders.
Advantages
Companies have several advantages, including:
•
LIMITED LIABILITY
legal concept that
protects shareholders
whose liability to meet
a company’s debts is
limited to any amount
unpaid on the shares
they hold
•
•
A company is a legal e n tity d istin ct from the owners, which enables it to conduct its operations in
its own name. A company can buy, own and sell property; it can sue or be sued in its own name; and
i t can enter into contracts w ith other entities. The shareholders o f m ost companies have lim ited
liability. This means th a t i f the company fails and i t is unable to pay its debts, the owners o f fu lly
paid shares are n o t obliged to contribute fu rth e r funds to meet the company s debts. However, if
shares are p a rtly paid, then shareholders can be obliged to contribute any unpaid amount.
A company has an indefinite life, which means that, unlike a sole proprietorship or partnership, its
existence and operations are unaffected by the death or retirem ent o f its owners.
The Corporations Act 2001 distinguishes between public companies, which may in vite members
o f the public to invest in them, and proprietary companies, which have no such power. Public
companies may be listed on a stock exchange, which facilitates trading in the company s shares.
Ownership o f shares in a listed public company can be transferred very easily w ith o u t any effect on
the company s operations, which are conducted by employees. Stock exchange lis tin g also makes
it relatively easy fo r public companies to raise capital by issuing additional shares th a t are sold to
existing shareholders or to new investors.
Disadvantages
The corporate form o f ownership also has some disadvantages, which include:
•
•
•
•
•
A company is more expensive to establish than a sole proprietorship or a partnership.
A company is subject to more onerous regulation. For example, there are extensive reporting
requirements, p articularly fo r listed public companies. Capital raising by companies is also highly
regulated. For example, shares and other securities can be issued only i f investors are provided w ith
info rm a tio n to make inform ed decisions about whether to invest in those securities.
It can be d ifficu lt to m otivate managers and staff who are employees o f a company. In comparison,
sole proprietorships and partnerships are managed by people who are also owners o f the business
and who w ill see a direct lin k between th e ir efforts and the rewards they receive.
Because a company is owned by one group (the shareholders) b ut may be run by a d ifferent group
(the managers), there can be conflicts o f interest between those who own the company and those
who make decisions on th e ir behalf. These conflicts result in agency costs1which are discussed
fu rth e r in Section 1.5.8.
The taxation treatm ent o f companies can be a disadvantage. Company profits are subject to
income tax and shareholders may also be taxed when they receive dividends paid o ut o f the profits.
C hapter o ne Introduction
Therefore, the use o f a company structure can involve double taxation. However, the extent o f this
problem depends on the type o f taxation system imposed by the government. Under Australian tax
law, many shareholders are n ot subject to double taxation.
Much o f this book concerns listed public companies. However, m ost o f the concepts in this book
are also relevant to other form s o f business entity. There w ill, o f course, be differences in the details,
depending on the e n tity s size and the nature o f its business. In addition, many o f the ideas considered in
this book can be applied to n o t-fo r-p ro fit entities, including public sector entities.
Rational solutions to investm ent and financing problems can only be achieved i f the company s objective
is clearly specified. The objective assumed in m ost o f this book is th a t management seeks to maximise
the m arket value o f the company s ordinary shares. Because an alternative term fo r shares is equityt this
objective is often expressed as the m axim isation o f the m arket value o f shareholdersJequity. I t is consistent
w ith the economists assumption th a t companies seek to maximise economic p ro fit. I f the m arket value
o f a company s ordinary shares is maximised, then the opportunities open to the shareholders are also
maximised— greater wealth implies more choices. For example, i f a shareholder wishes to sell his or her
shares in order to finance greater consumption, the higher the share price, the greater are his or her
consumption opportunities.
In Section 1.4 we stated th a t we assume th a t management seeks to maximise the m arket value o f
shareholders’ equity. To achieve this objective, the financial manager m ust understand how financial
markets work. To finance a company s investments, securities, such as shares and debt securities, w ill
need to be issued— th a t is, these securities w ill need to be sold to investors. Subsequently, investors may
choose to sell th e ir securities to other investors in financial markets. The actions o f buyers and sellers
in financial markets w ill determ ine the prices o f the securities and therefore the m arket value o f the
company. The m arket value, V, o f a company may be expressed as:
LEARNING
OBJECTIVE 4
Specify the objective
of the company
LEARNING
OBJECTIVE 5
Identify and explain
the fundamental
concepts in finance
V= D+ E
where
D = the m arket value o f the company s debt
E = the m arket value o f the company s equity (shares)
The value th a t the financial markets place on a company s debt and equity securities w ill depend on the
risk and expected return on investments in those securities. In tu rn , the risk and retu rn o f the securities
w ill depend on the risk and return th a t the company achieves on the investments it makes in its assets. In
finance, the success o f an investm ent is judged by its a b ility to generate more cash than originally outlaid
on the investment. This w ill enable the company to make interest payments to lenders and repay the
amount borrowed, and to make payouts, such as dividends, to shareholders.
The tim e value o f money principle is based on the proposition th a t an individual w ill always prefer to
receive a dollar today rather than receive a dollar at any later date. Even i f the individual does n ot want
to spend the dollar today, he or she would rather receive the dollar today and then invest it, rather than
receive the dollar at a later date. Therefore, a dollar is w o rth more Qess), the sooner (later) i t is to be
received, all other things being equal.This principle is discussed and applied in Chapter 3. Some fu rth e r
applications are considered in Chapter 4.
TIME VALUE OF M ONEY
principle that a dollar
is worth more (less),
the sooner (later) it
is to be received, all
other things being
equal
B usiness finance
1 .5 .3 1 Risk aversion
RISK-AVERSE INVESTOR
an investor who
dislikes risk and who
will only choose a
risky investment if the
expected return is high
enough to compensate
for bearing the risk
In finance, i t is usually assumed th a t investors display risk aversion, which means th a t they do not like
risk. Given a choice between tw o investments th a t have the same expected return, b u t one has lower risk,
a risk-averse investor w ill choose the one w ith the lower risk. Risk aversion does n o t im ply that an
investor w ill reject all risky investments. Rather, it implies th a t an investor w ill choose a risky investment
only i f the expected retu rn on the investm ent is high enough to compensate the investor fo r bearing the
risk. Because investors are risk averse, we expect th a t in the long term , the average re tu rn on high-risk
investments w ill exceed the average retu rn on low -risk investm ents— i f this were n o t so, no-one would
invest in the high-risk investments. For example, in the long term , shares produce higher returns than
bank deposits because shares are riskier than bank deposits. The relationship between ris k and expected
return is discussed in Chapter 7.
The purchasing power o f money changes as a result o f price increases (inflation) and price decreases
(deflation). D uring a period o f in fla tio n there is an increase in the general level o f prices, w ith a consequent
decrease in the purchasing power o f money. In contrast, during a period o f deflation there is a decrease in
the general level o f prices, w ith a consequent increase in the purchasing power o f money. I t is necessary,
therefore, to distinguish between the nominal or face value o f money and the real or inflation-adjusted
value o f money. For example, i f the annual rate o f in fla tio n is 3 per cent, the real value o f a dollar is
decreasing annually by 3 per cent— th a t is, relative to the purchasing power o f a dollar today, a dollar next
year w ill be w orth only 97 cents in real term s.3
Returns on investments may be measured in either nom inal or real terms. In m ost financial markets,
trading is conducted in nom inal terms. Similarly, m ost financial contracts are w ritte n in nom inal terms.
For example, the interest rate agreed to in a loan m ust be paid whatever the future in fla tio n rate turns out
to be. Such an interest rate is called a nominal interest rate. An interest rate may also be expressed in real
terms, w hich is equal to the nom inal interest rate after taking out the effect o f infla tion . I f the nom inal
rate o f retu rn on an investm ent exceeds the in fla tio n rate, then the real rate o f return is positive— th a t is,
the investm ent w ill increase the investors purchasing power.
An efficient financial market is one composed o f numerous w ell-inform ed individuals whose trading
activities cause prices to adjust instantaneously and w ith o u t bias in response to new inform ation. Price
changes are therefore caused by new inform a tion becoming available. The concept o f m arket efficiency
means th a t we should expect securities and other assets to be fa irly priced, given th e ir risk and expected
return.
In Section 1.5.3 we explained that, because investors are risk averse, higher-risk investments w ill
need to offer investors higher expected returns— th a t is, in the long term , risk and expected return w ill
be positively related. But w hat are the details o f this relationship? The capital asset pricing model (CAPM)
provides one answer to this question. According to the CAPM, risk can be a ttributed to tw o sources:
a
b
market-wide factors, such as changes in interest rates and foreign exchange rates— this is called
systematic risk (also referred to as non-diversiftable or market risk)
factors th a t are specific to a p articular company, such as the possible discovery o f a new m ineral
deposit by a m ining company— this is called unsystematic risk (also referred to as diversifiable or
unique risk).
W hile unsystematic risk can be largely elim inated by the investor holding a well-diversified portfolio,
systematic risk cannot be eliminated.
A nother model th a t has been developed to measure the riskiness o f an investm ent and to establish
the trade-off between risk and expected retu rn is the Fama-French model. According to the CAPM and
3
This result is an approximation. With a rate of inflation of 3 per cent per annum, $1 today is equivalent to $1.03 next year and
it follows that a dollar next year is worth $1/1.03 = $0.970874 today. This issue is discussed further in Chapter 3.
C hapter one Introduction
the Fama-French model, risk-averse investors can diversify th e ir investments to elim inate unsystematic
risk. Consequently, the m arket w ill only reward investors by offering a higher expected retu rn fo r bearing
systematic or m arket risk. Both models are discussed in Chapter 7. M arket efficiency is considered in
detail in Chapter 16.
Derivative securities include forward contracts, futures contracts, options and swaps. In each case, the
value o f the derivative security depends on the value o f some underlying security. For example, the value
o f an option to buy a share in Wesfarmers Ltd depends heavily on the m arket value o f a Wesfarmers
share. In this case, the option is the derivative, while the Wesfarmers share is the prim ary security, or
underlying asset. Real assets, like a coal m ine or an idea fo r a new product, may also have features that
resemble derivatives. For example, the owner o f a coal m ine has the option to close the m ine and reopen
it later. Derivative securities are considered in Chapters 17 and 18.
Arbitrage plays a central role in finance. I f two identical assets were to trade in the same market at different
ARBITRAGE
prices, and i f there were no transaction costs, then an arbitrage opp ortu nity would exist. A risk-free p ro fit
could be made by traders simultaneously purchasing at the lower price and selling at the higher price.
This situation could n ot persist because competition among traders would force up the price o f the lowerpriced asset and/or force down the price o f the higher-priced asset u n til the prices o f the two assets were
the same. Arbitrage therefore precludes perfect substitutes from selling at different prices in the same
market. I t follows th a t the financial prices we observe m ust be set by the financial markets in such a way
th a t arbitrage is n ot possible. This idea is simple yet remarkably powerful. It has applications throughout
finance in such diverse areas as the capital structure decision (how much should a company borrow?),
payout policy, interna tion al finance, option pricing and the term structure o f interest rates.
simultaneous
transactions in
different markets that
result in an immediate
risk-free profit
In Section 1.3.3 we m entioned th a t one o f the disadvantages o f the corporate structure is the p ossibility
th a t managers may pursue th e ir own objectives rather than the interests o f the shareholders. For example,
a company th a t operates in a mature ind ustry where there are few grow th opportunities may have surplus
cash th a t cannot be invested p rofitably in its usual fields o f operation. The company s shareholders would
benefit i f the surplus were paid to them as a dividend or used to buy back shares. But the managers may
decide instead to use the cash to acquire another company th a t operates in a different industry. This
investm ent may benefit managers by giving them greater opportunities fo r prom otion and higher pay
justified by the increase in company size. However, the acquisition may n o t increase shareholders* wealth.
There can therefore be a conflict o f interest between shareholders and managers.
M aking an unprofitable takeover is only one way in which managers may pursue th e ir own interests at
the expense o f the shareholders. O ther examples include managers w orking less energetically than they
could and managers directly diverting the company s resources to th e ir own benefit, such as by acquiring
expensive company cars, taking unnecessary business trips to exotic locations, and so on.
The relationship between shareholders and managers is an example o f an agency relationship. In an
agency relationship, one party, the principal, delegates decision-making a u th o rity to another party, the
agent. In a company run by managers, the managers are the agents and the shareholders are the principals.
Shareholders are aware o f the possibility th a t managers may pursue th e ir own objectives and w ill try
to lim it this behaviour by monitoring the behaviour o f managers and by in s titu tin g contracts designed
to align the interests o f managers and shareholders. For example, a Board o f Directors th a t includes
a significant number o f non-executive directors can be effective in m on itoring managers on behalf o f
shareholders. In addition, many companies employ management remuneration schemes designed to give
managers an incentive to maximise shareholders* wealth. For example, these schemes often provide
senior executives, particularly the chief executive, w ith options to purchase shares in the company at
an attractive price. Finally, i f agency costs are high, the company w ill probably be poorly run and, in
B usiness finance
consequence, its share price w ill be low and it may become a target fo r takeover. Existing managers
generally fare badly when such a change o f control occurs, so the desire to avoid being taken over can also
lim it the self-interested behaviour o f managers.
Agency theory has been used to examine various corporate financial decisions including capital
structure, dividend and share repurchase decisions, and leasing decisions. The application o f agency
theory to these decisions is discussed in Chapters 1 1 ,1 2 ,1 3 and 15.
O utline of the book
The ideas introduced in this chapter are developed in the remainder o f the book.
•
•
•
•
•
•
•
In Chapters 2 to 7, fundam ental concepts underlying finance theory are developed.
Chapters 8, 9 and 10 consider sources o f finance fo r companies, and the in s titu tio n a l framework in
which financing decisions are made.
In Chapters 1 1,12 and 13, payout decisions and financing decisions are discussed.
Chapter 14 then considers the measurement o f the cost o f capital to be used in project evaluation,
while Chapter 15 provides an analysis o f leases.
Chapter 16 reviews the literature on m arket efficiency, while Chapters 17 and 18 consider futures
contracts and options respectively.
Chapter 19 reviews the theory and evidence on takeovers.
In Chapters 20 and 21 the principles outlined earlier in the book are applied to short-term asset
management, including inventory, cash and accounts receivable.
awldvHu
M3IA3W 3M〇
SUMMARY
In this chapter, we have introduced the key themes to
be addressed in the book.
• The two main components of finance are corporate
finance and investments. This book focuses on
financial decisions made by companies (corporate
decisions), w hich include asset and w orking
capital management decisions, capital structure
and borrow ing decisions, payout policy and
merger and acquisition decisions; and financial
decisions made by investors (investor decisions),
including portfolio and risk decisions and asset
pricing decisions.
KEY TERMS
arbitrage 7
company 4
limited liability 4
partnership 3
8
The objective assumed in most of this book is that
management seeks to maximise the market value
of the company's ordinary shares (shareholders'
equity). To do this, the financial manager must
understand how financial markets work. The
fundamental concepts in finance include value, the
time value of money, risk aversion, nominal versus real
values, market efficiency and asset pricing, derivative
securities, arbitrage and agency relationships. The
market value (V) of a company can be expressed as
the market value of the company's debt (D) plus the
market value of the company's equity (£).
risk-averse investor 6
sole proprietorship 3
time value of money 5
C hapter o ne Introduction
QUESTIONS
1
[LO 2】Distinguish between investment decisions and financing decisions.
2
[LO 3] Explain the following:
a) a sole proprietorship
b) a partnership
c) a company.
3
[LO 3] Outline the advantages and disadvantages of a sole proprietorship.
4
[LO 3] Outline the advantages and disadvantages of a partnership.
5
[LO 3] W hat advantages does a company have over a sole proprietorship and a partnership?
6
[LO 3] W hich types o f investors have limited liability? Explain your answer.
7
[LO 5] W h y do people usually prefer to receive $1 today instead of in a year's time?
8
[LO 5 】 Comment on this statement: A company should borrow during times o f high inflation because it con
repay the loan in cheaper dollars.
9
[LO 5] W h a t is the relationship between diversifiable and non-diversifiable risk? How does this distinction
affect the reward that investors receive for bearing risk?
CHAPTER O N E REVIEW
itu
10 [L0 5]
W h a t is meant by the term 'efficient market'? How does competition between traders promote
efficiency?
11
[LO 5] W h a t is meant by the term 'arbitrage7?
12
[L0 5] W h a t is meant by the term 'agency relationships'?
9
CHAPTER TWO
Consumption,
investment and the
capital market
CHAPTER CONTENTS
HI
Introduction
Fisher’s Separation Theorem: a sim plified
exam ple
11
ii
BS
m
Fisher's Separation Theorem: a form al
a pproach
14
Investors' reactions to m anagers' decisions
24
LEARNING OBJECTIVES
After studying this chapter you should be able to:
1
explain how a com pany's m anagers can, in principle, make financial decisions that w ill be
supported by all shareholders
2
explain how the existence o f a capital m arket makes it possible for the com pany to make
decisions acceptable to all shareholders
3
命
identify a com pany's optim al investm ent/dividend p olicy under conditions o f certainty.
C hapter t w o C o n s u m p t io n ,
investment a n d the capital market
^ ^ J ~ ln t r o d u c t io n
In this chapter we present a theoretical fram ework, know n as ‘Fisher’s Separation Theorem’，th a t shows
im p orta nt relationships between companies, th e ir shareholders and the capital m arket. We use this
fram ework to make some observations on investm ent decisions, financing decisions and dividend policy.
Although the fram ework we present is simple and rather abstract, it provides im p o rta n t insights into
some fundam ental issues in finance. To introduce the framework, we present in Section 2.2 a sim plified
numerical example th a t captures many o f the m ain lessons o f the theorem. Readers who do n o t wish to
develop a detailed technical understanding o f the theorem may wish to read only Section 2.2.
Fishers Separation Theorem can be traced to the w ork o f Irv in g Fisher1
2 and is widely regarded as laying a
foundation fo r many fundam ental results o f finance theory. The theorem considers the follow ing situation.
Suppose th a t a company has to decide how much it should pay to its shareholders in dividends and how
much it should retain fo r investm ent in the company. The more the company pays out in dividends, the
less there is available fo r investm ent; the more the company invests, the less there is available to pay
out as dividends. M ig h t some shareholders want high dividends (and therefore low investment), while
other shareholders w ant ju s t the opposite? I f so, w ill the company be forced to make a decision that w ill
disappoint some o f its shareholders? Fishers answers are, yes, there may be this type o f disagreement
among the shareholders b ut, no, i f there is a capital m arket then there is a way to please all shareholders.
In this section, we outline a sim plified example o f Fishers Separation Theorem th a t preserves much o f its
flavour b u t is based on in tu itio n rather than a rigorous, technical approach.
Assume th a t a company is operating under conditions o f certainty, th a t there are tw o tim e dates (‘now,
and ‘later’）and th a t there are tw o equal shareholders (‘A ’ and ‘B’). The company m ust decide3 how
much o f its current resources i t should invest and how much it should pay out as a current dividend.
An investm ent now generates a retu rn later, and the company then pays out all its resources as a final
dividend. Shareholders can use th e ir dividends to finance consumption. In itially, there is no capital
m arket b ut at a later stage in the analysis i t is assumed th a t transactions in a capital m arket are possible.
The existence o f the capital m arket enables individuals (including the shareholders A and B) to borrow
and lend fo r one period at a fixed interest rate.
It is fu rth e r assumed th a t the company has $8000 in resources and has identified tw o possible
investm ent projects called ‘Project Small’ and ‘Project Upgrade’.
•
•
Project Small requires an in itia l outlay o f $5000 now and w ill produce a cash inflow o f $5700 later.
Project Upgrade requires a further outlay o f $2000 now and w ill produce a further cash inflo w o f
$2200 later.
I t is also assumed th a t it is impossible to invest only in Project Upgrade. Together, projects Small and
Upgrade constitute P roject Large*. Clearly, Project Large requires an outlay o f $5000 + $2000 = $7000
now and w ill produce a cash inflo w o f $5700 + $2200 = $7900 later. I f the company invests only in Project
1
2
3
This section is drawn from Brown (1996).
Fisher (1930). See also Hirshleifer (1970).
In fact, decisions are made by managers rather than by an inanimate company* but for ease of expression we frequently refer
to a company making a decision. We have assumed that managers will seek to maximise the interests of the shareholders.
LEARNING
OBJECTIVE 1
Explain how a
company's managers
can, in principle,
make financial
decisions that will
be supported by all
shareholders
B usiness finance
Small, it can pay a dividend o f $8000 - $5000 = $3000 now b u t i f it invests in Project Large, i t can pay a
dividend o f only $8000 - $7000 = $1000 now.
This situation is summarised in Table 2.1.
TABLE 2.1 Investment/dividend opportunities facing the company
Project
Investment outlay
now ($)
Dividend now (equals
$8000 minus outlay) ($)
Dividend later ($)
Small
5000
3000
5700
Upgrade
2000
n.a.(a)
2200
Large
7000
1000
7900
Not applicable because Project Upgrade is not a stand-alone project.
2 .2 .3 1 The shareholders' consumption opportunities and
preferences
Recalling th a t Shareholders A and B hold equal shares, the consumption opportunities each faces are equal
to h a lf the to ta l dividends paid by the company as shown in Table 2.1. For sim plicity, i t is also assumed
th a t a dividend paid now cannot be stored in order to finance consumption later.4 The consumption
o pportunities facing each shareholder are shown in Table 2.2.
TABLE 2.2 Consumption opportunities facing each shareholder
Project selected by the company
Consumption per shareholder
now ($)
Consumption per shareholder
later ($)
Small
1500
2850
Large
500
3950
Suppose th a t Shareholder A wishes to consume $1500 now, w hile Shareholder B wishes to consume
only $500 now. Thus, Shareholder A wants a relatively high dividend now and therefore wants the
company to invest in Project Small. Shareholder B, o f course, is in the opposite position. Desiring only
a low level o f consumption now, Shareholder B wants the company to adopt a high level o f investm ent
and thus wants the company to invest in Project Large. Clearly, the company cannot make a decision that
w ill satisfy b oth shareholders simultaneously and therefore i t is n o t possible to say which investm ent is
optim al. The company w ill be forced to make a decision th a t w ill be opposed by one o f its tw o shareholders.
2 .2 .4 1 Solution: introduce a capital market
LEARNING
OBJECTIVE 2
Explain how the
existence of a capital
market makes it
possible for the
company to make
decisions acceptable
to all shareholders
命
A solution can be found i f there is a capital m arket in which the shareholders can borrow and lend on
th e ir personal accounts. In this example, it is assumed th a t the interest rate in the capital m arket is
12 per cent per period. I t is now possible to state th a t there is an optim al decision th a t w ill be supported
by b oth shareholders. This decision is th a t the company should invest in Project Small and should reject
the o pp o rtu n ity to invest in the upgrade th a t w ill convert Project Small to Project Large. In other words,
allowing Shareholder B access to the capital m arket has caused B to change his or her support from
w anting the company to invest in Project Large to w anting the company to invest in Project Small.
4
This assumption simplifies the analysis but is not necessary. It is a simple matter to permit resources to be carried from one
period to the next. In the absence of a capital market, resources can be carried forward in time at an interest rate of zero.
However, any consumption opportunities opened up by allowing resources to be carried forward at an interest rate of zero
will be more restricted than the opportunities that become available when a capital market is introduced and interest rates
are positive.
C hapter t w o C o n s u m p t io n ,
investment a n d the capital market
How do we know Shareholder B w ill react in this way? The answer is th a t the capital m arket allows
Shareholder B to make financial arrangements that, from Bs view point, provide an even better outcome
than is possible i f the company invests in Project Large. This result can be proved as follows. When the
company invests in Project Small, Shareholder B w ill receive a current dividend o f $1500. This w ill finance
Bs desired current consum ption o f $500, w ith $1000 le ft over. This sum o f $1000 can be le n t in the
capital m arket fo r one period at an interest rate o f 12 per cent, thus producing a later cash in flo w to B o f
$1000 x 1.12 = $1120. This sum can then be added to the future dividend o f $2850. Therefore, on the later
date, Shareholder B can consume resources to the value o f $1120 + $2850 = $3970. If, instead, Project
Large were undertaken, Shareholder B could consume only $3950 on the later date (see Table 2.2).
Therefore, provided there is a capital market, the shareholders w ill be unanimous and the company can
make investm ent and dividend decisions confident th a t these decisions are optim al from the view point
o f all shareholders.
2 .2 .5 1 An analysis using rates of return
The analysis can be recast in terms o f rates o f return. The rates o f retu rn on the projects are:
Project Small:
$5700-5000
Project Upgrade:
$5000
$2 2 0 0 -2 0 0 0
$2000
14%
= 10%
Comparing these rates o f retu rn w ith the interest rate o f 12 per cent, the optim al decision is to accept
Project Small (because 14 per cent exceeds 12 per cent) and to reject Project Upgrade (because 10 per cent
is less than 12 per cent). In effect, the cost o f investing is the o pp o rtu n ity cost o f forgoing the capital
m arket return o f 12 per cent. For Project Small, the benefit (14 per cent) exceeds the o pp o rtu n ity cost
(12 per cent), while fo r Project Upgrade the benefit (10 per cent) is lower than the o pp o rtu n ity cost
(12 per cent).
Note also th a t while the apparent rate o f retu rn on Project Large is ($7900 - $7000)/$7000 = 12.86
per cent, this rate o f retu rn is in fact a weighted average o f the rates o f retu rn on the component projects
Small and Upgrade. I t is not valid to suggest th a t the company should invest in Project Large merely
because 12.86 per cent exceeds 12 per cent.
2.2.61 A solution requiring borrowing
In Section 2.2.4, the interest rate (12 per cent) fell between the rates o f retu rn on Project Small (14 per
cent) and Project Upgrade (10 per cent). Therefore, Project Small was accepted and, in tu rn , this decision
required Shareholder B to lend in the capital m arket. I f the interest rate had been lower than the rate o f
return on both projects— say i t had been 9 per cent— then the optim al decision would have been to invest
in both projects. In other words, Project Large would have been accepted. Therefore, the current dividend
would have been only $500 per shareholder. W hile this decision would clearly have won the support o f
Shareholder B, who wishes to consume only $500 now, a current dividend o f $500 per shareholder w ill be
insufficient fo r Shareholder A to finance his or her desired current consumption o f $1500.
In this case, Shareholder A m ust borrow $1000 from the capital m arket. A t an interest rate o f 9 per
cent per period, the required repayment later is $1000 x 1.09 = $1090. This am ount is paid out o f the later
dividend o f $3950, thus leaving Shareholder A w ith $3950 - $1090 = $2860 to finance later consumption.
This level exceeds the $2850 o f later consum ption th a t would have been available to Shareholder A i f the
company had invested in only Project Small. Therefore, Shareholder A w ill also support the decision to
invest in Project Large and there is again a unanimous decision.
2 .2 .7 1 Fisher's Separation Theorem and net present value
The problem facing the company s manager can also be solved by calculating a measure know n as a
projects *net present value* (NPV). This measure is extremely im p o rta n t and is referred to in a num ber o f
later chapters. It is discussed in detail in Chapter 5. A t this p o in t we provide only a very b rie f introduction.
LEARNING
OBJECTIVE 3
Identify a company's
optimal investment/
dividend policy under
conditions of certainty
B usiness finance
To calculate a projects net present value, we firs t use the projects required rate o f retu rn to convert
future cash flows to th e ir equivalent values today. We then subtract the in itia l outlay required. I f the result
is a positive number, then the project is an acceptable investm ent; i f the result is a negative number, then
the project is n o t acceptable. In the in itia l example o f Project Small and Project Upgrade presented in
Section 2.2.4, the interest rate in the capital m arket is 12 per cent. In this example, it is also the required
rate o f retu rn on the project. The net present value calculations are:
iV W o f Project Small = ---------- $5000 = $89.29 > 0
1.12
N P V o f Project Upgrade =
1.12
- $2000 = -$35.71 < 0
Project Small is an acceptable investm ent because its NPV is positive, while Project Upgrade is not
an acceptable investm ent because its NPV is negative. Thus, use o f the NPV rule has led to the same
investm ent decision as we discussed earlier in Section 2.2.4. N ot only does an optim al decision exist, it
can also be found by applying the NPV rule.
2 .2 .8 | Fisher’s Separation Theorem: summary
LEARNING
OBJECTIVE 1
Explain how a
company’s managers
can, in principle,
make financial
decisions that will
be supported by all
shareholders
In the absence o f a capital market, the shareholders disagreed on what decisions the company should
make on th e ir behalf. This problem could be solved* only by imposing a solution to the detrim ent o f
one o f the shareholders. But i f there is a capital m arket, the shareholders are sure to reach a unanimous
decision. Thus, there is an optim al investm ent/dividend decision.
This resolution is possible because the existence o f the capital m arket enables one o f the shareholders
to achieve a result th a t fo r h im or her was indisputably b etter than the result th a t the company alone
could provide, given the investm ent o pportunities available. An o ptim al decision exists, and can be
identified by the company s managers i f they use the net present value (NPV) rule to analyse investm ent
proposals.
2.3
Fisher’s Separation Theorem:
a formal approach
The conclusions th a t we reached largely by in tu itio n in Section 2.2 are reached in a more rigorous fashion
in this section.
2.3.1 | Assumptions
The assumed objective o f a company is to maximise the m arket value o f its ordinary shares. A company s
managers, therefore, have to make investment, financing and dividend decisions consistent w ith that
objective. The managers* job would be easier i f there were a consistent set o f decision rules th a t could be
employed in m aking investm ent, financing and dividend decisions. The w ork o f Irv in g Fisher provides
a fram ework in which such rules can be developed. In itia lly these decision rules are developed in a very
sim plified setting. However, the decision rules are applicable even when more realistic assumptions are
made.
The assumptions in Fishers analysis are:
a
b
C
d
e
命
There are only two points in tim e: the present (Time 1) and a later tim e (Time 2).
There is no uncertainty, and hence the outcome o f all decisions is know n now to everybody.
There are no imperfections in the capital market,
A ll decision makers are rational.
The company s managers wish to use the company s resources according to the wishes o f the
shareholders.
C hapter t w o C o n s u m p t io n ,
investment a n d the capital market
2 .3 .2 |T h e company
The company is endowed w ith a fixed am ount o f resources at Time 1 and the managers have to decide how
much o f these resources should be invested and how much should be paid out as dividends. Any resources
not paid out at Time 1 are invested, and the level o f this investm ent determines the resources available
to pay dividends at Time 2.
The opportunities available to the company are summarised in a production p o ssib ilities curve
(PPC) as illustrated in Figure 2.1.
Figure 2.1 Production possibilities curve
PRODUCTION
POSSIBILITIES CURVE
curve that displays
the investment
opportunities and
outcomes available
to the company;
its shape therefore
determines the
combinations of
current dividends,
investments and future
dividends that a
company can achieve
l^l
s8Jno
0s
EJ
9J
(N
l—
The horizontal axis measures resources available to the company at Time 1. Assume th a t the company
has 200 units o f resources available to it. It could pay this am ount as a dividend at Time 1. In this case,
investm ent would be zero and dividends at Time 2 w ould also be zero. The p oint (200, 0) represents this
extreme decision. A t the other extreme, the company could pay no dividend at Time 1 and invest the
whole o f the company s resources. This decision would result in 250 units being available fo r d is trib u tio n
as a dividend at Time 2 and is represented by the p o in t (0, 250). Point Q is an interm ediate case in which a
dividend o f 150 units is paid at Time 1, leaving 50 units to be invested. The PPC shows th a t an investm ent
o f 50 units at Time 1 can be transform ed in to 160 units o f resources at Time 2. Therefore the dividend at
Time 2 is 160 units.
INDIFFERENCE CURVE
2 .3 .3 |T h e shareholders
Shareholders forgo current consumption by investing in the company at Time 1 in order to receive a retu rn
th a t then increases th e ir consum ption o pportunities at Time 2. A persons preference fo r consumption at
Time 1 (Cj) or at Time 2 (C2) is represented by indifference curves as depicted in Figure 2.2. The term
indifference indicates th a t the person derives equal u tility from the bundles o f C and C2 represented
curve showing a set
of combinations such
that an individual
derives equal utility
from (and thus is
indifferent between)
any combinations in
the set
A
B usiness finance
by all points on a single curve; fo r example, equal u tility is derived from points X and Y in Figure 2.2.
However, any p o in t on a higher indifference curve is preferred to all points on lower curves; fo r example,
Z is preferred to X and Y.
The slope o f an indifference curve at any p o in t shows the consumer s willingness to trade o ff Cx fo r C2.
I t can be seen from Figure 2.2 th a t the indifference curves are convex; they approach the horizontal
as the level o f C1 increases and approach the vertical as the level o f C2 increases. The im plication is th a t a
consumers desire to increase consumption fu rth e r at a given tim e decreases as the level o f consumption
at th a t tim e increases.
:igure 2.2 Indifference curves of a representative shareholder
2 .3 .4 1 The company’s decision
We now b ring together the company and the shareholders in an attem pt to id e n tify the decision the
company should make. We assume th a t there are two shareholders,
and (B\
In Figure 2.3, indifference curves fo r Shareholder A are labelled A v A 2 and A 3 and indifference
curves fo r Shareholder B are labelled Bv B2 and B3. I f the company chooses p o in t A — th a t is, a current
dividend o f 90 and investm ent o f 110, yielding a dividend o f 228 at Time 2— then shareholder As u tility
is maximised. However, Shareholder Bs u tility is n o t maximised at this point; i t is maximised only i f
the company chooses p o in t B. This requires a current dividend o f 160 and investm ent o f 40, yielding a
dividend o f 144 at Time 2.
In short, the company is unable to reach a decision th a t w ill lead simultaneously to m axim um u tility
fo r both shareholders. This situation poses a severe dilemma fo r the company because i t means th a t the
company m ust consider the preferences o f each o f its shareholders when m aking investm ent decisions.
In other words, there is no simple decision rule th a t w ill satisfy all shareholders. Such a rule does exist,
however, i f there is a capital market.
LEARNING
OBJECTIVE 2
Explain how the
existence of a capital
market makes it
possible for the
company to make
decisions acceptable
to all shareholders
命
2.3^5| Soluti on: introduce a capital market
In this simple model, the capital m arket can be thought o f as a place where current resources may be
transform ed into future resources and vice versa. The rate at which these transform ations may be made
is in effect an interest rate. We assume th a t the capital m arket is frictionless, and therefore the interest
rate fo r borrowers is equal to the interest rate fo r lenders. For example, i f the interest rate is 10 per cent
C hapter t w o C o n s u m p t io n ,
90
160
investment a n d the capital market
200*2
0
5
Time 1 resources ( q i
per period, and 100 u nits o f current resources are placed w ith the capital m arket fo r one period, then
100 x 1.1 = 110 units o f resources become available at Time 2. In effect, this is lending to the capital
market. Similarly, i f a person has a claim to receive 110 units o f resources at Time 2, the capital m arket
may be used to transform this claim in to 110/1.1 = 100 units o f resources at Time 1. This transaction
corresponds to a person borrow ing 100 units at Time 1 and repaying the loan w ith a payment o f
110 u nits at Time 2.
Suppose th a t a person has claims on resources in both periods. For example, a person may have an
income o f 100 units at Time 1 and an income o f 165 units at Time 2. W hat consumption opportunities
are available i f the interest rate is 10 per cent per period? A t one extreme, the person may choose to
consume only at Time 2. In this case, consumption at Time 1 is zero and consumption at Time 2 is
165 + 100 x 1.1 = 275 units. A t the other extreme, the person may choose to consume only at Time 1.
In this case, consum ption at Time 2 is zero and consum ption at Time 1 is (165/1.1) + 100 = 250 units.
Therefore, this persons claim on current resources is 250 units. In short, this persons wealth at Time 1 is
250 units. Figure 2.4 illustrates this case.
The line join in g these tw o extreme positions is shown in Figure 2.4 and may be called a m arket
opportunity line as i t defines all combinations o f consumption possibilities at the tw o Times, consistent
w ith an in itia l wealth level o f 250 units. I f a person can reach any one p o in t on this line, then by borrow ing
or lending, all other points on the line are also available to the person. For example, i f a person can reach
point A (100 units at Time 1 and 165 units at Time 2), then the person can also reach p o in t
(140 units
at Time 1 and 121 units at Time 2), by borrow ing 40 units today and repaying 44 units at Time 2.
The equation o f a m arket o pp o rtu n ity line can be derived as follows. I f a persons income at Time 1 is
Cx and at Time 2 is C2, and the interest rate is i per period, then the persons wealth W1 at Time 1 is:
…
^
C2
MARKET
OPPORTUNITY LINE
line that shows the
combinations of
current and future
consumption that an
individual can achieve
from a given wealth
level, using capital
market transactions
B usiness finance
Figure 2.4 Market opportunity line
Equivalently, this equation can be w ritte n as:
W \(l + /) = C“ 1 + /) + C2
or
C2 = - ( l + i)C 1 + Wl ( l + i)
This is a linear equation w ith slope -(1 + 〇 and intercept ^ ( 1 + i). W ith a current wealth level o f 250
and an interest rate o f 10 per cent per period the equation is:
C2 = - ( 1 + 0.1)C1 + 250(1.1)
and therefore
C2 = - l . l C 1 + 275
To illustrate fu rth e r the interpretatio n o f m arket o pp o rtu n ity lines, suppose th a t the person is offered
a choice o f two income streams, A or B. Stream A consists o f 100 units at Time 1 and 165 units at Time 2,
w hile Stream B consists o f 120 units at Time 1 and 55 units at Time 2. I t has already been shown that
i f the interest rate is 10 per cent, Stream A corresponds to a wealth level o f 250 units at Time 1 and the
equation o f the m arket o pp o rtu n ity line is C2 = -1.1C 1 + 275. The wealth level corresponding to Stream
B is 120 + 55/1.1 = 170 units. The equation o f the m arket o pp o rtu n ity line fo r Stream B is C2 = -1.1C1 +
187. These lines, together w ith the persons indifference curves, are shown in Figure 2.5.
Figure 2.5 shows th a t this person w ill maximise u tility by accepting income Stream A and then use
a capital m arket transaction to convert Stream A to Stream A \ As we have seen, Stream A provides an
income o f 100 units at Time 1 and 165 units at Time 2, and a wealth level o f 250 units. The person then
enters the capital m arket and borrows 40 units at Time 1, achieving a consumption level o f 140 units
at Time 1. In return, the persons claim on Time 2 resources is reduced by 44 units (fro m 165 units to
121 units). The loan repayment required at Time 2 is, o f course, 44 units (since 40 x 1.1 = 44).
命
C hapter t w o C o n s u m p tio n ,
investment a n d the capital market
Figure 2.5 Consumption opportunities offered by two wealth levels
Had Stream B been accepted, the optim al p o in t would have been B \ which could have been achieved by
lending 120 - 80 = 40 units at Time 1 and consuming 55 + (40)(1.1) = 99 units at Time 2. However, p o in t
is on a lower indifference curve than p o in t A / and therefore yields lower u tility . To summarise: Stream
A should be chosen because i t corresponds to a higher wealth level, which, in tu rn , ensures th a t higher
u tility can be achieved, given access to a capital market.
2 .3 .6 1 Proving there is an optimal policy
Fishers Separation Theorem provides the optim al solution and involves all three elements: the company,
the shareholders and the capital market.
Suppose th a t the company has E units o f resources and is considering three investm ent/dividend
policies, shown in Figure 2.6 as points Pv P2 and P.
A m arket o pp ortu nity line w ith slope -(1 + z) has been drawn through each o f the three points. The line
through P1 shows th a t i f policy P1 were adopted, the shareholders* wealth would increase from E to Wv
Similarly, i f policy P2 were adopted, the shareholders* wealth would increase to W2i and i f policy P were
adopted, the shareholders’ wealth would be PV. Because the u tility o f shareholders depends directly on
th eir wealth, they w ill unanim ously prefer policy P because the resulting wealth level W is the maximum
achievable. Relative to policy P, i t is clear th a t
represents too little investm ent by the company, whereas
P2 represents too much investm ent by the company. Policy P, which occurs at the p o in t o f tangency
between the PPC and the m arket o p p o rtu n ity line, is the optim al policy fo r the company and w ill receive
the support o f all shareholders. This result may be shown more form ally by superimposing representative
indifference curves fo r shareholders A and B on Figure 2.6. This is shown in Figure 2.7.
The company chooses policy P; th a t is, i t invests (E - C p and pays dividends o f C* at Time 1 and C*2
at Time 2. Shareholder A enters the capital m arket and lends resources so th a t this shareholders personal
optim al p oint PA is reached. Shareholder B borrows from the capital m arket in order to reach PB, which
B usiness finance
Figure 2.6 Effect of company policy on shareholder wealth
Figure 2.7 Fisher’s Separation Theorem: two shareholders with access to a
capital market
is Bs personal optim al p oint. A ny policy other than P w ill result in lower u tility fo r both shareholders. For
example, i f the company were to choose policy Pv then Shareholder As m axim um u tility would occur at
p o in t P^, which is on a lower indifference curve than p o in t PA, w hile Shareholder Bs m axim um u tility
would occur at p o in t P^, which is on a lower indifference curve than p o in t PB. The same conclusion holds
i f the company were to choose policy P2.
There is, therefore, just one policy P th a t w ill maximise the u tility o f all shareholders simultaneously.
Regardless o f differences in th e ir u tility functions (preferences), all shareholders w ill support the
company s decision to choose policy P. In this sense, the company and its shareholders are separate. The
company does not need to consult each shareholder before it makes its decision because it knows in
C hapter t w o C o n s u m p tio n ,
investment
advance th a t all shareholders, regardless o f differences in th e ir personal preferences, w ill support the
choice o f policy P. Since policy P does n o t require knowledge o f any shareholders u tility function, it
follows th a t P m ig ht be identifiable using data directly available to the company. That this is in fact the
case is proved in the follow ing section.
2 .3 .7 | Identifying the optimal policy
Suppose th a t a company is endowed w ith E units o f current resources and is considering a num ber o f
small investm ent projects, each requiring an outlay o f A units o f resources. I t has compiled a lis t o f these
projects, ranked from the highest rate o f return to the lowest. The project w ith the highest rate o f retu rn
w ill return C2 units at Tim e 2. The company proposes the follow ing decision rule: accept the project i f and
only if:
R e tu m a tT im e 2 _ A > 〇
This is illustrated in Figure 2.8.
Figure 2.8
I t is clear from Figure 2.8 th a t C; > △ (1 + f) and therefore:
Under the proposed rule, the project is accepted. Fishers Separation Theorem also recommends
acceptance since policy P has n ot yet been achieved. Now consider the second project, w hich also requires
an outlay o f A and which returns Cf，
2 at Time 2. Reading from Figure 2.8, it is found that:
C2 + C2 〉 C*2 + △(!■ + /)
and therefore
Both Fishers Separation Theorem and the decision rule recommend acceptance o f this second project.
Projects w ill continue to be accepted u n til policy P is reached. Beyond th a t point, both the theorem and
the rule recommend rejection o f all fu rth e r projects on the list. This is shown in Figure 2.9.
B usiness finance
Reading from Figure 2.9 it is found that:
C2 " + A(1 + i) > C2 " + C2 "
and therefore
-△ < 0
Therefore, both the proposed rule and the theorem recommend rejection o f this project.
The proposed rule and the theorem are completely consistent. A ll projects th a t are acceptable according
to the theorem are also acceptable according to the rule. A ll projects rejected by the theorem are also
rejected by the rule. Therefore, a company th a t always applies this rule to its investm ent decisions w ill be
able to locate the optim al investm ent/dividend policy and w ill maximise the wealth o f its shareholders.
In tu rn , the shareholders can use the capital m arket to achieve th e ir preferred consum ption patterns and
thereby maximise u tility.
The name given to this rule is the net present value rule. The retu rn next period is divided by the
factor (1 + z) to convert the future retu rn in to a present value. The investm ent outlay is then subtracted
from the present value to give the net present value (iVPV). I f the iVPVis positive, the project w ill increase
the wealth o f the shareholders and should therefore be accepted. I f the NPV is negative, the project w ill
decrease the wealth o f the shareholders and should therefore be rejected. The NPV rule is frequently used
in practice and is considered fu rth e r in Chapter 5.
2 .3 .8 1 Implications for financial decision making
A num ber o f im plications fo r investm ent, financing and dividend decisions can be drawn from Fishers
analysis. These im plications w ill hold where there are perfect markets fo r both capital and inform ation.
However, Fishers analysis is unaffected by the intro du ction o f uncertainty, provided it is assumed that
all participants have the same expectations.5 Further, although the presentation o f Fishers analysis has
5
Fama and Miller (1972, pp. 301-4).
C hapter t w o C o n s u m p t io n ,
investment a n d the capital market
been confined to a case involving only tw o periods, its im plications are unaffected by extension to the
m ultiperiod case.6
The investment decision
Fishers Separation Theorem means th a t a company can make investm ent decisions in the interests o f
every shareholder，regardless o f differences between shareholders’ preferences— th a t is, a company can
make an investm ent decision w ith which every shareholder w ill agree. Moreover, there is a rule th a t
w ill ide ntify th a t decision: a company should invest up to the p o in t where the net present value o f the
marginal u n it o f investm ent is zero. In this simple model, an equivalent rule is to invest up to the p o in t
where the rate o f retu rn on the m arginal u n it o f investm ent equals the m arket interest rate. These tw o
rules and other commonly implem ented investm ent evaluation techniques are considered in Chapter 5 in
the context o f certainty. This discussion is extended in Chapter 6 to investm ent evaluation where there
is uncertainty.
The financing decision
In Fishers analysis there is a single m arket interest rate. In effect, there is no d istinction between debt and
equity securities, and the cost to the company o f acquiring funds is independent o f the type o f security
issued. I t follows th a t the value o f the company and the wealth o f its shareholders are independent o f
the company’s capital structure. As a result, the financing decision can be described as ‘irrelevant’. When
the financing decision is discussed in Chapter 12 this result is confirm ed in a less restrictive framework.
The dividend decision
In Fishers analysis, all resources n ot invested at Time 1 are distributed to shareholders as dividends,
and all returns at Time 2 are also distributed as dividends_ th a t is, it is assumed th a t the company does
not borrow or lend in the capital market, although its shareholders may do so. Suppose, however, that
the company is perm itted to borrow o r lend in the capital market. In th a t case, the company has greater
choice in its dividend policy, while m aintaining the same level o f investm ent. For example, the company
could pay a higher dividend at Time 1 and borrow the resources needed to m aintain investm ent at the
optim al level given by the p o in t o f tangency between the PPC and the m arket o p p o rtu n ity line. This is
illustrated in Figure 2.10.
ure 2.10
6
ibid” pp. 64-7.
B usiness finance
Compared w ith the basic Fisher analysis (Fig. 2.7), the company in Figure 2.10 pays a larger dividend
at Time 1 (C**> C^) and a smaller dividend at Time 2 (C^* < C*2). To m aintain the company s investment
level at E - C*, the company borrows C** - C\ from the capital m arket. A t Time 2 the company s gross
retu rn is
b u t the loan repayment reduces the net retu rn at Time 2 to C^. In short, the company、
investm ent decision is unchanged b ut its dividend decision is different. The im p o rta n t p o in t to note
is th a t the new policy Pr lies on the same m arket o pp o rtu n ity line as the original *Fisher policy* P and
therefore the wealth o f shareholders is unchanged. The ability o f shareholders to maximise th e ir u tility is
also unchanged. As explained previously, i f any one p o in t on a m arket o p p o rtu n ity line is attainable, then,
by borrow ing or lending, all other points on the line are also attainable. From the shareholders’ p o in t o f
view, therefore, p o in t Pr is no b etter or worse than p o in t P.
In summary, provided th a t the company does n o t alter its investm ent decision, the dividend decision
does n o t affect shareholders* wealth. In this sense dividend policy is irrelevant. This proposition is
discussed fu rth e r in Chapter 11.
2.4
Investors' reactions to managers/
decisions
The lin k between decisions made by a company s managers and the resultant actions by investors is
illustrated in Figure 2.11.
Figure 2.11
supplies funds to
transact in
A company s managers may, on behalf o f the company, make an investm ent decision, a financing
decision o r a dividend decision. In fo rm atio n about this decision is transm itted to investors. On the basis
o f this inform ation, investors may adjust th e ir expectations o f future returns from an investm ent in the
company, and revise th e ir valuation o f the company s shares. Investors w ill then compare the current
m arket price o f the company s shares w ith th e ir revised valuation and either buy or sell shares in the
company. Investors* actions in the share m arket w ill determ ine the new m arket price o f the company s
shares.
令
C hapter t w o C o n s u m p t io n ,
investment a n d the capital market
Pursuing a goal o f m axim ising the m arket value o f a company s shares is easy when there are no m arket
imperfections and no uncertainty. Managers know w ith certainty an investm ents cash flows and its net
present value. Therefore, they w ill know whether acceptance o f the investm ent w ill increase the m arket
value o f the company s shares. As all investors also know the investm ents net present value, there w ill
be an immediate increase in the price o f the company s shares to reflect the resulting increase in the
wealth o f the company. Further, managers and investors know th a t financing and dividend decisions are
irrelevant and therefore these decisions w ill have no effect on the m arket value o f the comp any s shares.
In practice there is uncertainty. W hat effect w ill the acceptance o f an investm ent proposal have on the
m arket value o f a company s shares? As is illustrated in Figure 2.11, any change in the company s share
price w ill depend on the reaction o f investors to the decisions made by the managers. Obviously there can
be no reaction unless investors obtain inform a tion about th a t decision. When there is uncertainty, the
effect on the share price o f decisions made by managers is no longer perfectly predictable. A sim plification
is to assume that everyone agrees about the probability d istrib u tio n o f the outcomes o f all decisions. This
means th a t although there is uncertainty, the exact nature o f th a t uncertainty is agreed on by all. In this
case, when investors obtain inform ation, the share price w ill adjust im m ediately to reflect the new best
estimate o f the ‘tru e ’ value o f the company.
Sufficient conditions fo r this to arise are: *... a m arket in which (i) there are no transaction costs in
trading securities, (ii) all available inform a tion is costlessly available to all m arket participants and (iii) all
agree on the im plications o f current inform a tion fo r the current price and d istrib u tio n o f future prices
o f each security’.7
As these conditions are n o t satisfied in existing capital markets, it is fortunate th a t they are sufficient
b ut not necessary conditions.8 For example, managers* decisions may s till have an impact on share prices
even though there are transaction costs and/or there are only a lim ite d number o f investors who have
access to inform a tion about these decisions.
I t is true th a t departures from the sufficient conditions give rise to the problem th a t managers are
unable to predict w ith certainty the impact th a t a particular decision w ill have on a company s share price.
Fortunately there is a great deal o f empirical evidence on the reaction o f share prices to the release o f
inform ation. This evidence is reviewed in Chapter 16. A t this p o in t we sim ply note th a t there is evidence
in well-developed capital markets (such as the Australian capital market) th a t there are investors who
react quickly to the receipt o f new inform ation, w ith the result th a t this in fo rm a tio n w ill be reflected
in security prices. In general, therefore, managers should n o t depart from a course th a t they expect w ill
increase the value o f the company’s shares.
7
8
Fama (1970, p. 387).
ibid” pp. 387-8.
B usiness finance
SUMMARY
•
•
•
A company's shareholders are likely to be a diverse
group, with different preferences regarding current
and future consumption. Therefore, it might be
thought that when making decisions on investments
and dividends, a company’s managers would find
it impossible to meet the wishes of all shareholders.
Fisher showed that, provided there is a capital
market through which shareholders can borrow and
lend, a company can make decisions that w ill be
supported by all shareholders.
The company should invest up to the point where
the return on the marginal investment equals the
•
interest rate in the capital market. Therefore, the
optimal decisions can be identified using net present
value (NPV) analysis. These decisions will maximise
the wealth of the shareholders. In this sense, the
company and its shareholders are 'separate7; the
company's managers can make optimal decisions
without having to discover the preferences of
individual shareholders.
Although the w orld of business is considerably more
complicated than Fisher's simple model, the central
messages of his theorem remain a useful guide for
company managers.
KEY TERMS
indifference curve 15
market opportunity line
tu
production possibilities curve
15
17
QUESTIONS
1
[LO 2] Outline the roles played by companies, shareholders and the capital market in Fisher's analysis.
2
[LO 3] Fisher's Separation Theorem ties together many o f the basic notions that underlie much o f modern
finance theory: wealth maximisation, utility maximisation and net present value. Discuss.
3
[LO 3] W h a t is Fisher's Separation Theorem? W h a t are its major implications for financial decision making?
4
[LO 3] Financial decision making is a trivial task in a w orld o f certainty. Discuss.
5
[LO 3 】W hat are the implications for financial decision making when the interest rate on borrowing is
greater than the interest rate on lending?
PROBLEMS
1
Calculating consumption possibilities with and without a capital market [LO 2]
Assume a three-date model in which a rational person has an endowment of $ 2 0 0 0 now, $ 1 0 0 0 in Year 1
and $50 0 in Year 2. If the person wishes to consume $40 0 now and $ 12 00 in Year 2, what could she
consume in Year 1 if:
a) there is no capital market
b) there is a capital market in which the interest rate is 5 per cent per year?
2
Investment decisions: applying Fisher's Separation Theorem [LO 3]
A company faces a similar situation to the one described in Section 2.2. It has two equal shareholders
(A and B)x is operating under conditions of certainty in a two-period framework ('now7 and later') and is
considering an investment in Project Small, which can be upgraded to Project Large. Project Small requires
an outlay of $1 1 0 0 0 0 today and will return $121 0 0 0 later. Project Upgrade requires an outlay of $ 6 0 0 0 0
today and will return $ 6 5 0 0 0 later. The company has $ 2 0 0 0 0 0 in resources. There is a capital market in
which the interest rate for both borrowing and lending is 5 per cent per period.
a)
26
Using the net present value rule, show that the company should invest in Project Large (that is, it should
invest in both Project Small and Project Upgrade).
C hapter t w o C o n s u m p t io n ,
investment a n d the capital market
c) Suppose that Shareholder A wishes to consume $ 4 0 0 0 0 today. What does she do? How much will she be
able to consume later? Show that this outcome is better for Shareholder A than if the company had invested
only in Project Small.
d) Suppose instead that Shareholder A wishes to consume equal amounts now and later, and the company
invests in Project Large. What does she do? Show that this action will deliver the desired outcome for
Shareholder A.
Investment decisions: applying FisheKs Separation Theorem [LO 3]
Consider exactly the same situation as in Problem 2, except that the interest rate is 9 per cent per period.
a) Using the net present value rule, show that the company should invest only in Project Small.
b) How much will the company pay each shareholder in dividends today, and how much will it pay each
shareholder in dividends later?
c) Suppose that Shareholder A wishes to consume $ 4 0 0 0 0 today. What does she do? How much will she be
able to consume later?
d) Compare Shareholder A's consumption in Problem 2(c) with her consumption in Problem 3(c).
Investment planning [LO 3]
CHAPTER T w o REVIEW
b) How much will the company pay each shareholder in dividends today, and how much will it pay each
shareholder in dividends later?
Consider the following situation:
• A company starts with $12 million in cash.
• The interest rate is 15 per cent.
• The optimal policy for the company is to invest $6 million in assets.
• The net present value of this investment is $2 million.
Answer the following questions:
a) In 1 year’s time, how much will the company receive from the investment?
b) Draw, to scale, the Fisher diagram that represents this case.
c) What are the marginal and average rates of return on the investment?
d) What is the total wealth of the company's shareholders immediately after the investment plan is announced?
Effect of an interest rate decrease [LO 3]
Redraw your diagram for Problem 4 to show the effect of an interest rate decrease on the company's
investment plan. Show the net present value of the revised investment plan. Would all investors be made better
off by the decrease in interest rates and the consequential revision in the investment plan? Give reasons for
youranswer.
Effect of higher investment [LO 3]
Return to the diagram you have drawn for Problem 4. Suppose that the company decides to invest
$7.5 million— that is, $1.5 million more than before. Redraw the market opportunity line consistent with
this new level of investment. What effect has the increased level of investment had on the company's
shareholders?
REFERENCES
Brown, R.L., 'Fisher’s Separation Theorem: an alternative
approach^ Accounting Research Journal, 1996, vol. 9,
no. 1, pp. 7 8 -8 1 .
Fama, E., 'Efficient capital markets: a review o f theory and
empirical w ork', Journal of Finance, M a y 1970,
pp. 3 8 3 -4 1 7 .
Fama, E. & Miller, M .; The Theory of Finance, Holt, Rinehart &
Winston, N ew York, 1972.
Fisher, I., The Theory of Interest, M acm illan Company,
N e w York, 1930.
Hirshleifer, J.; Investment, Interest a n d Capital, Prentice-Hall,
Englewood Cliffs, N e w Jersey, 1970.
27
CHAPTER CONTENTS
ED
HH
Introduction
29
H3
Valuation of contracts with multiple
cash flows
46
Annuities
50
Fundamental concepts of financial
mathematics
29
HH
Simple interest
31
田
Principal-and-interest loan contracts
58
m
Compound interest
33
BH
General annuities
63
LEARNING OBJECTIVES
Z
After studying this chapter you should be able to:
1
understand and solve problems involving simple interest and compound interest, including accumulating,
discounting and making comparisons using the effective interest rate
2
value, as at any date, contracts involving multiple cash flows
3
distinguish between different types of annuity and calculate their present value and future value
4 apply your knowledge of annuities to solve a range of problems, including problems involving
principal-and-interest loan contracts
5
distinguish between simple and general annuities and make basic calculations involving general annuities.
C hapter THREE T he TIME VALUE 〇F MONEY: AN INTRODUCTION TO FINANCIAL /sAATHEMATICS
Financial mathematics provides the finance specialist w ith some extremely useful tools w ith which to
solve financial problems. In this chapter, we present the m ajor tools o f financial mathematics and indicate
some o f th e ir im p o rta n t applications. You w ill fin d th a t a thorough understanding o f these tools, and
how they may be used, w ill be very valuable when you study later chapters. Although you w ill fin d a
large number o f formulae in this chapter, you w ill n ot master financial mathematics i f you sim ply try
to memorise the formulae. I f you fu lly understand the approach and the logic th a t are embodied in the
formulae, you w ill n o t need to memorise them.
3.2
Fundamental concepts of financial
mathematics
In this section, we explain four fundam ental concepts used in financial mathematics: cash flows, rate o f
return, interest rate and tim e value o f money.
3 .2 .1 1 Cash flows
Financial mathematics concerns the analysis o f cash flows between parties to a financial con tract.1
For example, when money is borrowed there is an in itia l flow o f cash from the lender to the borrower,
and subsequently one (or more) cash (re)payment(s) from the borrower to the lender. In financial
mathematics, as in finance generally, we are concerned w ith the cash flow consequences o f a decision or
a contract. How much cash w ill flow between the parties? When w ill these cash flows occur? These are
the basic questions th a t m ust firs t be answered when analysing a financial contract using the tools o f
financial mathematics. We are n o t concerned w ith the possible non-cash consequences o f a contract, such
as effects on reported p ro fit; nor are we concerned w ith effects on parties outside the contract.
CASH FLOW
payment (cash
outflow) or receipt
(cash inflow) of money
FINAN C IAL CONTRACT
arrangement,
agreement or
investment that
produces cash flows
3 .2 .2 ! Rate of return
Financial decision makers usually fin d it convenient to relate the cash inflows th a t result from a contract
to the cash outflows th a t the contract requires. Typically, this inform a tion is presented as a rate of
return. Where there are only tw o cash flows in a financial contract— one at the sta rt o f the contract and
another at the end— the rate o f retu rn is usually measured by:2
Ci - C
〇
C〇
where C1 = cash in flo w at Time 1
C〇= cash outflow at Time 0
r = rate o f retu rn per period
The value o f C1 - C〇measures the dollar return to the investor. D ividing the dollar return by C〇
, which
is the investm ent outlay, measures the rate o f return. Example 3.1 illustrates the calculation o f a rate o f
return.
Note th a t a rate o f retu rn is always measured over a tim e period. In Example 3.1 the tim e period is
1 year. It is meaningless to state th a t an investm ent has returned, say, 20 per cent w ith o u t also specifying
the tim e period involved.
1
2
We use the term contract* broadly. For example, we include depositing money in a bank as an act carried out as part of the
contract between the depositor and the bank.
There are other measures. For example, under some circumstances it is convenient to measure the rate of return by EnCCj/Cg)
[natural logarithm]. This measure is discussed further in Section 3.4.4.
RATE OF RETURN
calculation that
expresses the ratio
of net cash inflows to
cash outflows
B usiness finance
Example 3.1
bB
On 1 January 2014, Paul buys an antique clock for $ 2 00 00. On 1 January 2015, the clock is sold
for $2 4 0 0 0 . What rate of return has been achieved?
SOLUTION
Using Equation 3.1, the rate of return is:
r= Ci ~ C 〇
C〇
_ $24 0 0 0 -$ 2 0 0 0 0
$20000
$4000
_ $20000
4
= 20% per annum
3 2 3 | Interest rate
INTEREST RATE
rate of return on debt
DEBT
financial contract in
which the receiver of
the initial cash (the
borrower) promises a
particular cash flow,
usually calculated
using an interest rate,
to the provider of
funds (the lender)
TIME VALUE OF MONEY
principle that a dollar
is worth more (less),
the sooner (later) it
is to be received, all
other things being
equal
The term in te r e st ra te 1 is an im p o rta n t special case o f the more general term 4rate o f return* and is
used when the financial contract is in the fo rm o f debt. A lthough a precise defin itio n o f debt is difficult,
the general principle involved is th a t one party (the borrower) provides a specific promise regarding the
future cash flow(s) payable to the other party (the lender). Debt may be contrasted w ith agreements
where no particular promise is made regarding the future cash flows. For example, when Paul purchased
the antique clock in Example 3.1 he was n ot promised any particular future cash inflow. Similarly, where
an investm ent is made in ordinary shares, the shareholder is n o t promised any p articular cash inflow(s)
from the investment.
3 .2 .4 |T im e value of money
One o f the m ost im p o rta n t principles o f finance is th a t money has a tim e value. This principle means
th a t a given sum o f money (say, a cash flow o f $100) should be valued differently, depending on when the
cash flow is to occur.
Suppose you have the choice o f receiving $100 either today or in 1 years tim e. As a rational person you
w ill choose to take the money today. Even i f you do n ot plan to spend the money u n til 1 year later, you w ill
s till choose to take the money today rather than in 1 years tim e because you w ill be able to earn interest
on the money during the coming year. Because o f the interest you w ill earn, you w ill have more than $100
in 1 year’s tim e. Obviously, from your p o in t o f view this is better than receiving only $100 in 1 year’s time.
By choosing to take the $100 today, rather than $100 in 1 years tim e, you are in effect saying th a t $100
received today is more valuable to you than the promise o f $100 to be received in 1 years tim e. To p ut this
another way, you have im plied th a t $100 to be received in 1 years tim e is w o rth less than $100 today. You
have recognised th a t money has a tim e value.3
An im p o rta n t consequence o f the fact th a t money has a tim e value is th a t we cannot validly add cash
flows th a t w ill occur on different dates. Suppose you are offered $100 today and a fu rth e r $100 in 1 years
time. How much is this offer w o rth to you? A t this stage we cannot answer this question, except to say
th a t the value today is less than $200. The value today o f the cash flow o f $100 in 1 years tim e is less than
3
Other reasons for taking the money today, rather than later, are risk (you are not certain that the future cash flow will be paid)
and e x p ected in flation (you fear that in a years time the purchasing power of $100 will be lower than it is today). While these
reasons are valid, note that money has a time value, even in the absence of these reasons—that is, even if the risk is zero
(you are certain that the future cash flow will be paid) and you expect that the inflation rate next year will be zero or negative
(purchasing power either will not change or will increase), you will s till take the $100 today, in preference to $100 later,
simply because interest rates are positive.
C hapter three T he
time value of m o n e y : a n introduction t o financial mathematics
$100, so the to ta l value today o f the tw o cash flows m ust be less than $200. In financial mathematics it is
extremely im p o rta n t never to attem pt to add cash flows th a t w ill occur on different dates.
3.3
Simple interest
3.3.1 | The basic idea of simple interest
Many financial contracts specify the interest rate to be paid, rather than specifying explicitly the cash
payment(s) required. Suppose, fo r example, th a t you borrow $1000, and agree to repay the loan by making
a lum p sum payment in 1 years tim e at an interest rate o f 12 per cent per annum. Then:
Interest owed = 0.12 x $1000 = $120
Lump sum payment = $1000 + $120 = $1120
This example is, o f course, very straightforw ard. O nly one tim e period is involved— in this case it
happens to be 1 year— and the interest rate is quoted on a m atching (annual) basis. There is little scope
fo r confusion in this case. But suppose the contract had specified a lum p sum repayment after 2 years, but
the interest rate was quoted as 12 per cent per annum. How do we apply an annual rate to a period that is
n ot equal to 1 year?
To answer this question we need a rule or convention to enable us to apply an annual interest rate to
a period o f 2 years. There are several ways in which this can be done, one o f which is sim ple in terest.
A distinguishing feature o f simple interest is that, during the entire term o f the loan, interest is computed
on the original sum borrowed. For example, suppose th a t a loan o f $100 m ust be repaid in a lum p sum
after 2 years. Simple interest is to be charged at the rate o f 12 per cent per annum. Because simple interest
is being used, interest in both years is charged on the sum o f $100. The interest in each year is thus $12, so
the lum p sum repayment is $124. Therefore, the interest rate payable at the m a tu rity (term ination) o f the
loan w ill in fact be 2 x 12 per cent = 24 per cent. Similarly, i f payment was instead due after h a lf a year, a
simple interest rate o f 12 per cent per annum means that, in fact, interest w ill be paid at the rate o f V2 x
12 per cent = 6 per cent per half-year. Example 3.2 illustrates simple interest.
LEARNING
OBJECTIVE 1
Understand and solve
problems involving
simple interest
and compound
interest, including
accumulating,
discounting and
making comparisons
using the effective
interest rate
SIMPLE INTEREST
method of calculating
interest in which,
during the entire term
of the loan, interest
is computed on the
original sum borrowed
Example 3.2
Molly's Bakeries Ltd borrows $ 1 0 0 0 0 and agrees to repay the loan by a lump sum payment in
6 months7 time. The interest rate is 8 per cent per annum (simple). Calculate the lump sum payment.
6
SOLUTION
Interest rate per half-year = - x 8%
2
=4%
Interest payable = $10000 x 0.04
=$400
Lump sum payable = $ 1 0 0 0 0 + $400
= $10400
3 .3 .2 | Formula development: future sum
Suppose an am ount P— also know n as the principal — is borrowed and w ill be repaid in a lum p sum. The
interest rate is r per period (for example, per annum) and repayment is required after t periods. Using
simple interest, the interest payable is based on the original principal, so the interest owing after one
PRINCIPAL
amount borrowed at
the outset of a loan
B usiness finance
FUTURE SUM
amount to which a
present sum, such as
a principal, will grow
(accumulate) at a
future date, through
the operation of
interest
period is P x r. A fte r t periods the interest payable is sim ply P x r x t. Therefore, the required future sum
5, th a t w ill repay the am ount borrowed, is given by:
S = principal and interest
= P + P rt
S = P (l + rt)
I
3.2
Example 3.3 illustrates the use o f Equation 3.2 to calculate a future sum using simple interest.
Example 3.3
a) Use Equation 3.2 to calculate Molly’s repayment of a loan of $ 1 0 0 0 0 after 6 months if simple
interest is used and the interest rate is 8 per cent per annum.
b) W hat would be the repayment if the lump sum repayment were instead required after 15 months?
SOLUTION
a) S = P(1 + rt)
=
$10000
$10000
1+0.08
X
6
、
,T2,
1.04
$10400
b) S = P(1 + rt)
=$10000
=
$10000 1+0.08
$ 10000x
'1 5 、
.T2,
1.10
$11000
3 .3 .3 1 Formula development: present value
PRESENT VALUE
amount that
corresponds to today's
value of a promised
future sum
In many practical cases, we know the future repayment S, the interest rate r and the tim e period t, and
our problem is to fin d the principal P (or presen t value) th a t is implied. In this case we simply rearrange
Equation 3.2 to find:
1 + rr
3.3
The present value P is the sum o f money th a t corresponds to today s value o f the future sum promised.
The fact th a t P is n ot equal to S follows from the fact th a t money has a tim e value. Im portantly, P in
Equation 3.3 can also be thought o f as a price. I f a prospective borrower promises to pay a sum S in t years*
time, then given the interest rate r, we can calculate the price (value) o f the borrowers promised future
payment o f S. In other words, i f we view the loan from the lenders perspective, the principal represents
the price (or present value) paid by the lender, to secure from the borrower, the promise to pay the future
cash flow required by the contract. Looked at from the borrow ers view point, the promised future cash
flow has been sold by the borrower to the lender fo r its present value, which is the loan principal.
3.3.4 | Applications of simple interest
There are many commercial applications o f simple interest. For example, simple interest is used for
Treasury notes, bills o f exchange and many bank deposits. Because large sums o f money are often
C hapter three T he
time value of m o n e y : a n introduction t o financial mathematics
involved, there m ust be clear rules or conventions used in applying simple interest. These conventions
can differ between countries. Using bills o f exchange as an example, the Australian conventions are:
a
b
C
d
Interest rates are quoted on an annual basis.
The tim e period t is calculated as the exact num ber o f days divided by 365.
In a leap year, 29 February is included in the num ber o f days, b ut the year is s till assumed to consist
o f 365 days.
Calculations are made to the nearest cent.
Bills o f exchange are discussed in detail in Section 10.5.3. The conventions used in Australia are
illustrated in Examples 3.4 and 3.5.
Example 3.4
Stars Ltd borrows $ 1 0 0 0 0 0 on 20 January 201 2, to be repaid in a lump sum on 2 March 2012. The
interest rate is 8.75 per cent per annum. Calculate the lump sum repayment.
SOLUTION
The time period involved is 42 days, consisting of 1 1 days in January, 29 days in February and 2 days
in March; note that we do not count both 20 January and 2 March but we d o count 29 February
because 2012 is a leap year.
Using Equation 3.2 and the conventions explained in this section the lump sum repayment is:
S = P(1 +rf)
=$10 00 0 0 1 + (0 .0 8 7 5 )( 盖
)
=$10 00 0 0 x 1.010068493
$101 006.85
Example 3.5
Moon Ltd promises to pay $ 5 0 0 0 0 0 in 6 0 days’ time. For a company with M oon’s credit standing the
market interest rate for a loan period of 6 0 days is 14.4 per cent per annum. How much can Moon
borrow?
SOLUTION
Using Equation 3.3 and the conventions explained in this section, Moon can borrow the sum of:
P=丄
1 + rt
$500000
= 1 + ( 0 .144)(盛
）
$500000
_ 1.023 671 232
=$488 438.07
3.4
Com pound interest
COM PO U N D INTEREST
3 .4 .1 1 The basic idea of compound interest
When interest is received by a lender, the interest can then be le n t to another borrower and, in due
course, w ill earn fu rth e r interest. The basic idea o f com p ou n d in te r e st is th a t interest is periodically
interest calculated
each period on the
principal amount and
on any interest earned
on the investment up
to that point
B usiness finance
added to the principal. Thus interest generates fu rth e r interest, which then generates s till more interest,
and so on. This process is illustrated in Example 3.6.
Example 3.6
i s
On 31 December 2013, Kee Saw deposited $ 1 0 0 0 0 0 in a bank account that paid interest at the rate
of 5 per cent per annum. How much was in the account after 4 years?
SOLUTION
The history of Kee Saw ’s account is as follows:
Balance
31 December 2013
Account opened
$100000.00
31 December 2014
Interest
0.05 x $100000.00 = $5000.00
$105000.00
Interest
0.05 x $105000.00 = $5250.00
$110250.00
Interest
0.05 x $110250.00 = $5512.50
$115762.50
Interest
0.05 x $115762.50 = $5788.13
$121550.63
31 December 2015
31 December 2016
31 December 2017
As the growth in Kee Saw 's account balance makes clear, with compound interest, the
amount of interest each year increases. For example, in the first year the interest received was
$ 5 0 0 0 .0 0 but in the fourth year the interest received was $5788.13. After 4 years, Kee Saw ’s
account balance is $ 1 2 1 5 5 0 .6 3 but had the account been paid interest at the fixed amount
of $ 5 0 0 0 per annum — that is, if Kee Saw had not been able to reinvest interest to earn further
interest— the balance would have been only $ 1 2 0 0 0 0 . Therefore, in 4 years, Kee Saw earned
$1 55 0 .6 3 of 'interest on interest'.
3 .4 .2 1 Formula development: future sum and present value
ACCUMULATION
process by which,
through the operation
of interest, a present
sum becomes a
greater sum in
the future
Assume th a t a principal o f P dollars is deposited— th a t is, lent to a bank o r o ther financial in s titu tio n —
fo r a term o f n periods, w ith interest paid at the rate i per period at the end o f each period. O ur task is to
develop a form ula fo r the future sum 5 th a t w ill be accum ulated after m periods, allowing fo r compound
interest.
A fte r one period the interest earned is iP, so the account balance at the end o f the firs t period is
P + iP = P(1 + 〇. In fact the balance (or accumulated sum) at the end o f any given period is simply the
balance a t the sta rt o f th a t period m ultiplie d by (1 + 〇. D uring the second period interest w ill be earned
on the am ount P(1 + 〇.
So:
Balance at end o f Period 2 =
=
=
=
命
(balance at start o f Period 2) x (1 + /)
(balance at end o f Period 1) x (1 + /)
P(1 4- i) x (1 + i)
P(1 + 〇2
CHAPTER THREE T he TIME VALUE 〇F MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
Similarly:
Balance at end o f Period 3 = (balance at start o f Period 3) x (1 -h /)
= (balance at end o f Period 2) x (1 + /)
= P(1 + i)2 x (1 + i)
= P(1 + 〇3
Generalising from this discussion, the sum accumulated after n periods is given by P(1 + i)nf so the
form ula fo r the future sum S is:
3.4
S = P ( l + i) n
The corresponding form ula to find the present value P o f a future sum S is:
^
S
3.5
where
5 = future sum a fter n periods
P = principal (or price or present value)
i = interest rate per period
n = num ber o f periods
To illustrate Equation 3.4 we use the inform a tion in Example 3.6. The value o f Kee Saws deposit after
selected terms is shown in Table 3.1.
TABLE 3.1 Accumulated value (future sum) of $100000 at 5 per cent per annum
Date
Number of years completed
31 December 2014
1
$100000 (1.05)
105000.00
31 December 2015
2
$100000(1.05)2
110250.00
31 December 2016
3
$100000 (1.05)3
115 762.50
31 December 2017
4
$100000(1.05)4
121550.63
31 December 2018
5
$100000 (1.05)5
127628.16
31 December 2023
10
$100000 (1.05)10
162889.46
31 December 2033
20
$100000 (1.05)20
265 329.77
31 December 2063
50
$100000 (1.05)50
1146739.98
Calculation
Accumulated value ($)
The effect o f compound interest becomes more pronounced as the number o f periods becomes large.
For example, after 50 years, the value o f Kee Saws account is nearly $1.15 m illion, or more than 10 times
the amount w ith which he opened the account.
£ 6000 DEBT GREW TO £116 000_____________________________
If you don't repay a loan, and a lot of time passes, the debt can grow to unmanageable
proportions, as happened to an unfortunate borrower in Manchester in the United Kingdom.
A grandmother has been forced to put her house up for sale after she ended up owing a
massive £1 16 0 0 0 — on a £ 6 0 0 0 loan. Esther 〇sei, 57, borrowed the money in 1 9 8 8 to pay
for her father's funeral and to buy a new cooker for her Clayton home.
continued
Finance
in ACTION
B usiness finance
continued
But she could not meet the cost of the loan and 1 8 years later, the amount she owed had
grown to £1 16 0 0 0 . .. Esther said: 1 borrowed the money when I was grieving for my father.
I just signed the papers/
W h en the lender applied to take possession of her home, Esther sought help by going
to the North Manchester Law Centre. Lawyers negotiated a deal at Manchester County
Court . . . A law centre spokesperson said Esther should never have entered into the loan
agreement. 'It was a very high rate of interest/
/ 5 、 l/n
Autnors7 note: Equation 3.4 can be rearranged to: /= f - J
- 1. Substituting S = £1 16 000,
P = £ 6 0 0 0 and n = 1 8 years into this equation, gives / = 17.89 per cent per annum.
However, this may not have been the contract interest rate because the final debt may
have included unpaid fees.
Source: '£ 6 0 0 0 debt grew to £116 0 0 0 7, Jo Rostron, Manchester M etro News, 21 July 2006.
To illustrate Equation 3.5, which gives the present value o f a future sum promised, suppose th a t an
individual is offered the sum o f $100 000 to be received after 5 years. I f the relevant interest rate is 5 per
cent per annum, compounded annually, the present value o f this promised sum is:
(1 + /广
_ $100 000
一
（1.05)5
$100 000
_ 1.276281563
=$78352.62
DISCOUNTING
process by which,
through the operation
of interest, a future
sum is converted to
its equivalent present
value
That is, looking ahead 5 years to the receipt o f this promised sum o f $100000, it is w orth, in todays
terms, only $78 352.62. The logic underlying this result is th a t i f one wished to set aside money today to
accumulate a sum o f $100000 in 5 years* tim e, the am ount needed to be set aside today is $78352.62.
A fte r 5 years, this sum w ill accumulate to $78 352.62 x (1.05)5 = $100 000. Clearly, all o ther things being
equal, the longer the w aiting period— th a t is, the later the promised sum is to be received— the lower is
the value today.
The process by which a future sum is converted to its equivalent present value is called discounting.
This process is illustrated in Table 3.2, which shows the present value o f $100 000 to be received at selected
future dates, discounted using an interest rate o f 5 per cent per annum.
Again, the effect o f compound interest becomes more pronounced when the num ber o f periods is
large. A promise to be paid $100000 in 50 years* tim e is w o rth only $8720.37 in todays terms i f the
discount rate is 5 per cent per annum.
TABLE 3.2 Present value of $100000 at 5 per cent per annum
Number of years to wait
Calculation
Present value ($)
1
$100000/1.05
95 238.10
2
$100000/(1.05)2
90702.95
3
$100000/(1.05)3
86383.76
4
$100000/(1.05)4
82270.25
C hapter three T he
time value of m o n e y : a n introduction to financial mathematics
Table 3.2 continued
Number of years to wait
Calculation
Present value ($)
5
$100000/(1.05)5
78352.62
10
$100000/(1.05)10
61391.33
20
$100000/(1.05)2°
37688.95
50
$100000/(1.05)so
8720.37
3 .4 .3 1 Nominal and effective interest rates
Many financial contracts specify th a t a loan shall be repaid by a series o f payments made on various future
dates, rather than by a lum p sum at the end o f a single tim e period. For example, a so-called interestonly loan requires payments o f interest at regular intervals followed by the repayment o f the principal in
a lum p sum on the loan’s m a tu rity date.
In m ost loans, the interest rate specified is a nom inal in terest rate, which is an interest rate where
interest is charged more frequently than the tim e period specified in the interest rate. To sim plify
matters, we assume th a t interest is charged (and therefore compounded) on the same dates as payments
are required.4 Examples o f nom inal interest rates are: 15 per cent per annum w ith quarterly payments,
and 1.5 per cent per quarter w ith m on thly payments.
Where a nom inal interest rate is used in a loan contract, a convention is needed to decide how an
interest rate quoted fo r one tim e period w ill be applied to a different tim e period. The convention adopted
is to take a simple ratio. So, fo r example, *15 per cent per annum payable quarterly* means th a t interest
w ill be charged each quarter at the rate o f 3.75 per cent per quarter— th a t is, the annual rate o f 15 per
cent is simply scaled down to one-quarter o f this rate because there are fo ur quarters in a year. Similarly,
*1.5 per cent per quarter payable m o n th ly * means th a t interest w ill be charged each m on th at 0.5 per cent
per m onth because a m on th is one-third o f a quarter and one-third o f 1.5 is 0.5.
Conversely, an effective in terest rate is one where the frequency o f charging (payment) does match
the tim e period specified by the interest rate. Examples o f effective interest rates are: 15 per cent per
annum w ith annual payments and 0.5 per cent per m onth w ith m on thly payments. W hile few financial
contracts specify an effective interest rate, i t is an im p o rta n t concept because it provides a consistent
basis on which to compare interest rates. This use is illustrated later in Example 3.8.
From the lender s view point i t is preferable to have interest paid more frequently, all other things
being equal. To illustrate th is fact, suppose th a t a bank is w illin g to lend $100 000 fo r 1 year at 15 per cent
per annum on an in te re s t only, basis b u t has the choice o f receiving either annual or quarterly interest
payments. Thus, the bank faces a choice between the cash inflows shown in Table 3.3.
INTEREST-ONLY LOAN
loan in which the
borrower is required
to make regular
payments to cover
interest accrued but is
not required to make
payments to reduce
the principal. On the
maturity date of the
loan, the principal is
repaid in a lump sum
N O M IN A L INTEREST
RATE
quoted interest
rate where interest
is charged more
frequently than the
basis on which
the interest rate is
quoted. The interest
rate actually used to
calculate the interest
charge is taken as
a proportion of the
quoted nominal
rate. Note: The term
'nominal interest rate7
also has another
meaning (see Section
3.4.4)
TABLE 3.3 Cash inflows at 15 per cent per annum
EFFECTIVE INTEREST
RATE
Cash inflow at Hme t
At f = 1 quarter
Annual interest
Quarterly interest
4
A t t = 2 quarters
A " = 3 quarters
At f = 4 quarters
$0
$0
$0
$115000
$3750
$3750
$3750
$103750
This assumption is relaxed in Section 3.8.
interest rate where
interest is charged at
the same frequency
as the interest rate is
quoted
I f we sim ply add up the two streams o f cash flows shown in Table 3.3 we would, o f course, find that
both to ta l $115000 but, as we explained earlier, this procedure is n o t valid because i t involves adding
cash flows th a t occur on different dates. Because earlier cash inflows are preferred to later cash inflows,
the quarterly interest stream is w o rth more to the bank. I t is w o rth more because the early* cash inflows
o f $3750 can be re-lent to earn fu rth e r interest later in the year.
Exactly how much more valuable the quarterly stream w ill prove to be w ill depend on the level o f
interest rates during the year, b u t because interest rates are always positive, the bank cannot lose by
accepting the quarterly payments rather than the annual payment.
An im p o rta n t special case can be developed by assuming th a t during the coming year the bank can
continue to lend money at 3.75 per cent per quarter. Thus the firs t quarterly inflow o f $3750 can be
re-lent fo r the rem aining three quarters, generating fu rth e r quarterly interest payments o f 0.0375 x
$3750 = $140.63, together w ith the repayment o f $3750 at the end o f the fo u rth quarter. A quarterby-quarter analysis is shown in Figure 3.1.
As shown in Figure 3.1, taking in to account the future opportunities fo r re-lending, the bank can
secure a to ta l cash inflow, at the end o f the fo u rth quarter, o f $115 865.06, which fo r the bank is clearly
preferable to a cash in flo w (on the same date) o f only $115 000. In effect, w ith interest paid quarterly, the
bank has earned at an annual rate o f retu rn given by:
$115 865.06 - $100 000
$100 000
» 15.865%
Cash flows re-lent at 3.75 per cent per quarter
0
1
2
$3 750.00
1—
3
4
$3 750.00
$3 750.00
$103 750.00
,► $ 140.63
$ 140.63
$
3 890.63
$ 145.90
$
4 036.53
$
4 187.90
Quarters
$3 890.63
1----------- ►
$4 036.53
$115 865.06
W ith only an annual interest payment, the bank would have had to specify an interest rate o f 15.865
per cent per annum to equal this rate o f return. Therefore, this example has established that there is a
sense in which the nom inal interest rate o f 15 per cent per annum, which is payable quarterly, is equivalent
to an effective interest rate o f 15.865 per cent per annum, payable annually.
But the sum o f $115865 is simply the future sum that would result from lending $100000 to earn
compound interest at the rate o f 3.75 per cent per quarter for four quarters. This is easily seen by noting that:
$100000 x (1.0375)4 = $100000 x 1.158 65 = $115865
Generalising from this example, i f a lender advances a principal o f P and specifies a nom inal interest
rate o f; per period, w ith interest payments required every subperiod, and there are m subperiods in every
period, then the future sum at the end o f one period is given by:
The effective interest rate i per period is:
. S -P
i = -----P
p { x+ i )
P
~p
C hapter THREE T he TIME VALUE OF MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
therefore
Equation 3.6 is the form ula fo r calculating the effective interest rate zper period fo r a nom inal interest
rate;, compounding m times per period. The use o f this form ula is illustrated in Examples 3.7 and 3.8.
Example 3.7
Calculate the effective annual interest rates corresponding to 12 per cent per annum, compounding:
a) semi-annually
6
b) quarterly
c) monthly
d) daily.
SOLUTION
Using Equation 3.6, the calculations are shown in Table 3.4.
TABLE 3.4
Compounding frequency
Calculation
Effective annual interest rate (%)
(a) Semi-annually
(1.06)2- 1
12.3600
(b) Quarterly
(1.03)4 - 1
12.5509
(c) M onthly
( l. 〇l ) 12- l
12.6825
(d) Daily
(1.000 328 767)365- l
12.7475
These calculations illustrate the fact that, all other things being equal, more frequent compounding
produces a higher effective interest rate.
Example 3.8
Lake Developments Ltd wishes to borrow money and is offered its choice of the following nominal
interest rates:
a) 15.00 per cent per annum, payable annually
b) 14.50 per cent per annum, payable semi-annually
c) 14.00 per cent per annum, payable quarterly
d) 13.92 per cent per annum, payable monthly.
Which of these nominal interest rates provides the lowest cost of finance in terms of the corresponding
effective annual interest rate?
SOLUTION
Using Equation 3.6, the effective annual interest rates are:
a) /= 15 per cent per annum
b) / = (1.0725)2 - 1 = 1 5 . 0 2 6 per cent per annum
c) / = (1.035)4 - 1 = 14.752 per cent per annum
d) / = (1.01 16)12 - 1 = 14.843 per cent per annum.
Thus option (c), which is a nominal interest rate of 14.00 per cent per annum with quarterly
compounding, provides the lowest effective annual interest rate.
6
In some problems it is necessary to fin d out w hat nom inal interest r a te ,m u s t be charged in order to
achieve a target effective interest rate, z. Answering a problem o f this type requires th a t Equation 3.6 be
rearranged so th a t; appears on the left-hand side o f the equation. This is shown below. Equation 3.6 is:
1
+
丄
m
Adding 1 to b oth sides, and raising to the power 1/m:
( l + /)1/m = l + 丄
m
Subtracting 1 from b oth sides, and m u ltip lyin g by m:
7 = /7?[(l + /)1/m- l ]
3.7
The use o f this form ula is illustrated in Example 3.9.
Example 3.9
A financial institution raises funds from several different types of deposits but all its loans to borrowers
require monthly repayments. The effective annual interest rate that it pays depositors is 7.5 per cent
per annum. To cover its other costs and make a profit, the institution adds a margin of 3 per cent per
annum. Therefore, its target effective interest rate is 10.5 per cent per annum. W hat nominal annual
interest rate must it charge borrowers?
6
SOLUTION
Using Equation 3.7, the nominal annual interest rate is:
/ = m[(l + i)]^m- 1]
= 12W.10511/ 12- 1]
= 1 2 x 0.008355155
= 1 0% per annum
The financial institution would need to charge a nominal annual interest rate of 10 per cent on the
loans it makes.
3.4.41 Compound interest: two special cases and
a generalisation
In this section we discuss real interest rates, continuous interest rates and geometric rates o f return. To
understand the remainder o f the chapter, knowledge o f these issues is not required, so some readers may
wish to o m it this section.
Special case no. 1: the real interest rate
REAL INTEREST RATE
interest rate after
taking out the effects
of inflation
N O M IN A L INTEREST
RATE
interest rate before
taking out the effects
of inflation. Note: the
term 'nominal interest
rate' also has another
meaning (see Section
3.4.3)
A real in te re st rate is an interest rate after taking out the effects o f infla tion . Hence, the word Veal1
in this context is used in the same sense as i t is used in phrases such as ‘real GDP’ and ‘real wages’. An
interest rate before taking out the effects o f in fla tio n is usually referred to as a nom inal in terest rate.
The phrase ‘nom inal interest rate’ in this context should n o t be confused w ith its use in Section 3.4.3.
In th a t section, the phrase N om inal interest rate* referred to an interest rate where the frequency o f
payment o r compounding did n ot match the basis on which the interest rate was quoted.
Suppose th a t a representative basket o f goods th a t a consumer m ig ht buy costs $500 today. I f the
in fla tio n rate in the coming year is expected to be 20 per cent per annum, the price o f the basket at the end
o f the year is expected to be $500 x 1.2 = $600. Suppose also th a t a lender currently has $2000 th a t w ill
be lent at a nom inal interest rate fo r 1 year. By lending this sum the lender forgoes the consumption now
o f four representative baskets o f goods. I f a real interest rate o f 5 per cent per annum is to be achieved,
C hapter three T he
time value of m o n e y : a n introduction to financial mathematics
then the lender requires th a t at the end o f the year the sum generated w ill be sufficient to purchase
4 x 1.05 = 4.2 baskets o f goods— th a t is, the sum required in 1 year is:
4.2
baskets x $600 per basket = $2520
Therefore, the nom inal annual interest rate required is:
$2520 - $2000
$2000
=26%
Generalising from this example, let:
B = the price today o f a representative basket o f goods
P = principal
p = expected in fla tio n rate
z* = required real interest rate
z = nom inal interest rate
^
^
Thus the lender forgoes consumption o f — baskets today, to be able to consume ~ ^ +
baskets in
a years tim e. The expected price o f one basket in a years tim e is B(1 + p ). Therefore, the sum required in
p
1 years tim e is —(1 + i*) x B(1 + p). Therefore, the nom inal interest rate required is:
i = ^ ------------------------------P
On sim plifying, this gives:
3.8
/ = (1 + i*) (1 + / ? ) - l
Equation 3.8 shows the lin k w ith the idea o f compounding: the nom inal interest rate i is n o t sim ply
the sum o f the real interest rate i* and the expected in fla tio n rate p t b u t rather is in the form o f the real
interest rate compounded, by the expected in fla tio n rate. Rearranging Equation 3.8 gives:
3.9
l + P
Equation 3.9 gives the real interest rate corresponding to a nom inal interest rate z i f the expected
infla tion rate is p. Expansion o f Equation 3.9 gives the result:
•氺 .
•幸
i = i- p - p i
士
i- v
That is, the real interest rate i* is not simply the difference between the nom inal interest rate i and the
expected infla tion rate p. However, where the rates are ^m a ir, pi* w ill also be small and the approximation
i* ^ i - p w ill be close. The calculation o f a real interest rate is illustrated in Example 3.10.
E xample 3.10
If the inflation rate is expected to be 2 0 per cent per annum and the nominal interest rate is 30 per
cent per annum, calculate the corresponding real interest rate.
SOLUTION
Using Equation 3.9:
r = 上^ - 1
1 +P
1.30
= ---------l
1.20
.
=8.33% per annum
6
Special case no. 2: continuous interest rates
CONTINUOUS INTEREST
method of calculating
interest in which
interest is charged so
frequently that the time
period between each
charge approaches
zero
As we showed in Section 3.4.3, the more frequently compounding occurs, the higher is the effective
interest rate, other things being equal. In the lim itin g case, compounding becomes so frequent th a t the
tim e period between each interest charge approaches zero. This is know n as continuous in terest and it
can be shown th a t continuous interest is an example o f exponential growth. Using continuous interest,
the fu tu re sum S is
S
where
3.10
= P eJn
S = future sum
P = principal
j = continuously compounding interest rate per period
n = number o f periods
e = 2.71828182846
The calculation o f a future sum using continuous interest is illustrated in Example 3.11.
E xample 3.11
If the interest rate is 12 per cent per annum, compounding continuously, how much will a principal of
$ 1 0 0 0 0 0 be worth after 1 year? After 2 years?
SOLUTION
Using Equation 3.10, the future sum after 1 year is:
S = Pein
=$100000
x e (012) ( 1)
=$100000
X
1.127496852
=$112 749.69
Again using Equation 3.10, the future sum after 2 years is:
S = Pein
x e (012)( 2)
=$100000 x e 0-24
=$100000
=$127124.92
The effective interest rate th a t results from continuous compounding is found by setting n equal to 1
period and solving:
. S -P
i = -----P
_ Pef - P
—
i h
where
P
Kill
i = effective interest rate per period
j = continuously compounding interest rate per period
e = 2.71828182846
The calculation o f an effective annual interest rate th a t is equivalent to a continuously compounding
interest rate is illustrated in Example 3.12.
命
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
E xample 3.1!
W hat is the effective annual interest rate corresponding to a nominal interest rate of 12 per cent per
annum, compounding continuously?
SOLUTION
Using Equation 3.11, the effective annual interest rate / is given by:
/=
- 1
= e°-,2 - l
= 1 2 .7 4 9 6 9 % per annum
Of course, this is the interest rate implicit in Example 3.1 1.
Although continuous compounding is rarely used in loan contracts, i t is frequently used in other
contexts. In particular, academic studies o f security prices often assume th a t returns compound
continuously between the dates on which the prices are observed. Consider the security prices P〇, Px and
P2 observed on dates 0 ,1 and 2 respectively. These dates are assumed to be equally spaced. For example,
the prices may be observed at weekly intervals. Assuming th a t returns accrue continuously through time,
we can apply Equation 3.10 to assert th a t in the firs t week:
P i = P〇eri
and in the second week:
P2 = P\eri
where r1 is the continuously compounding weekly rate o f retu rn in the firs t week and r2 is the continuously
compounding weekly rate o f retu rn in the second week.
Solving fo r r1 and r2 gives:
n = in (P i/P 〇 )
and
r2 = in {P2/P l )
where in means logarithm to the base e (usually referred to as the natural logarithm ). More generally, we
can w rite th a t the rate o f retu rn in period t is:
rt = £n {P t/P t-i)
An expression o f the fo rm £n (P t/P t-i) is called a lo g p ric e re la tiv e and, when calculated this way, r t
is called a logarithm ic rate o f retu rn or a continuous rate o f return.
There are two reasons fo r choosing to measure rates o f retu rn in this way. First, the correct way to
compound logarithm ic rates o f return is sim ply to add them. Thus, fo r example:
LOG PRICE RELATIVE
That is:
natural logarithm of
the ratio of successive
security prices.
Implicitly, it is assumed
that prices have
grown (or decayed)
in a continuous
fashion between
the two dates on
which the prices are
observed. Also known
as a logarithmic
rate of return and a
P2 = P0eri+r2
continuous rate of
return
P2 = P\er2
But
P\ = P〇 eri
Substituting, we find:
P2 = P〇 en er2
The last equation shows that, using logarithm ic rates o f return, the to ta l rate o f retu rn over the
two tim e periods is sim ply the sum o f the rates o f retu rn in each o f the tw o constituent periods. Thus
calculations such as finding an average rate o f retu rn are simpler when using logarithm ic rates o f return.
命
B usiness finance
As discussed in Section 3.4.5, i t is not valid to add rates o f retu rn i f they are measured using the simple
a rith m e tic1d efin itio n that:
The second reason fo r using logarithm ic rates o f retu rn is a statistical one. The greatest loss an investor
can suffer is when the security price falls to zero. Using the simple arithm etic definition, the rate o f return
associated w ith this event is - 1 — th a t is, the rate o f retu rn is -1 0 0 per cent. Using logarithm ic rates o f
return, the same event w ill register as a rate o f retu rn o f - 〇〇. Given th a t there is no upper lim it to the
rate o f retu rn th a t m ight be achieved, i t follows th a t while arithm etic rates o f retu rn fa ll in the range
-1 to +〇〇, logarithm ic rates o f retu rn fa ll in the range - 〇〇to +〇〇. Thus, w hile the statistical d istribution
th a t describes logarithm ic rates o f retu rn might have the convenient property o f symmetry, and thus
might fo llo w the norm al d istribution, arithm etic rates o f retu rn w ill not be sym metric and thus cannot be
norm ally distributed.
A generalisation: geometric rates of return
GEOMETRIC RATE OF
RETURN
average of a sequence
of arithmetic rates of
return, found by a
process that resembles
compounding
Compound interest is a special case o f a geom etric rate o f return. In the case o f compound interest, the
interest rate is the same in each period. In the more general case o f geometric rates o f return, the rate o f
retu rn can be different in each period. W hile the sum invested is s till subject to the compounding process,
the rate at which compounding occurs w ill differ from period to period.
Suppose th a t $1000 is invested fo r 4 years and each year the investm ent earns a different rate o f
return, as follows:
•
•
•
•
In
In
In
In
Year 1: 10 per cent per annum
Year 2: 5 per cent per annum
Year 3: 8 per cent per annum
Year 4 :1 5 per cent per annum.
The value o f this investm ent therefore grows as follows:
1 A t the
2 A t the
3 A t the
4 A t the
end o f Year 1: $1000.00
end o f Year 2: $1100.00
end o f Year 3: $1155.00
end o f Year 4: $1247.40
x 1.10 = $1100.00
x 1.05 = $1155.00
x 1.08 = $1247.40
x 1.15 = $1434.51.
O f course, this result could have been found more quickly and conveniently by calculating, in one step:
$1000 x 1.10 x 1.05 x 1.08 x 1.15 = $1434.51
W ritin g the calculation in this way emphasises the sim ilarity between compound interest and the
more general case o f geometric rates o f return.
I t is natural to ask: w hat annual compound interest rate would have produced the same result? In
other words, w hat single rate o f retu rn zper year would need to be earned in each o f the 4 years, to produce
the same future sum? To answer this question we need to solve:
$1000 x 1.10 x 1.05 x 1.08 x 1.15 = $1000(1 + 〇 4
th a t is,
i = [(1.10)(1.05)(1.08)(1.15)]1/4_ i
=(1.434 S l) 1^ - !
=9.440% per annum
In fact, i in this calculation is the mean (or average) geometric rate o f return. I t is the rate o f return
which, i f earned in every period, and allowing fo r the effects o f compounding, would produce the same
outcome as th a t actually observed. In the general case, the mean geometric rate o f retu rn is:
i = [ ( l + r i ) ( l + r2) . . . ( l + 〇 ] V " - l
where
命
rk = the rate o f retu rn in period k
/c = 1, 2,
n
n = the num ber o f completed periods
K1H
CHAPTER THREE T he TIME VALUE 〇F MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
I f the rate o f retu rn is calculated each period from security prices P〇, Pl
t
then:
Pk ~ Pk-\
Pk-l
Pk
Pk-l
Substituting in Equation 3.13 gives:
3.14
It is im p o rta n t to understand th a t the mean rate o f retu rn is not (rx + r2 + ... + rn)/ri— th a t is, i t is not
correct simply to sum the rates o f retu rn and divide by the number o f periods. This fact is illustrated in
Example 3.13.
E xample 3.1
An investment of $ 1 0 0 0 0 0 produces rates of return as follows:
In Year
In Year
In Year
In Year
1:
2:
3:
4:
a
a
a
a
gain of 10 per cent
loss of 5 per cent
loss of 8 per cent
gain of 3 per cent
Calculate the value of the investment at the end of the fourth year and calculate the mean annual
rate of return.
SOLUTION
The value of the investment at the end of the fourth year is:
$ 1 0 0 0 0 0 x 1.10 x 0.95 x 0.92 x 1.03 = $ 9 9 0 2 4 .2 0
Using Equation 3.14, the mean annual rate of return is:
_ /$ 9 9 0 2 4 .2 0 \1/4
—V $100000
)
1
一
= -0.002 448
= -0.2 448%
This small negative mean rate of return is consistent with the outcome that the final value ($99024.20)
is less than the sum invested ($ 1 0 0 0 0 0 )— that is, the investment has produced a loss after 4 years.
Note that the incorrect calculation of the mean as:
10% - 5 % - 8 % + 3 %
4
=0%
clearly gives a nonsensical answer because in this example the mean rate of return must be negative.5
5
Note that we are discussing here the correct measurement of p a s t returns. We are not discussing the forecasting of fu tu re
returns.
B usiness finance
3.5
LEARNING
OBJECTIVE 2
Value, as at any date,
contracts involving
multiple cash flows
Valuation of contracts with multiple
cash flows
3.5.1 | Introduction
Many loan contracts stipulate th a t more than one cash flow is required to repay the loan. For example, a
housing loan may require m on thly repayments over a period o f 20 years— a to ta l o f 240 repayments. In
this section we consider the valuation o f contracts th a t involve m ultiple cash flows. We do n o t assume
th a t the am ount or tim in g o f the cash flows follows any particular pattern. Some im p o rta n t special cases
involving equal amounts at equally spaced tim e intervals are considered in Section 3.6.
3.5_2| Value additivity
W hile i t is not valid to add cash flows th a t occur at different times, i t is valid to add cash flows th a t occur at
the same tim e. Therefore, i f a contract requires cash payments to be made on, say, 1 A p ril and 1 May, we
should n o t sim ply add these cash flows.
However, i f we firs t value the 1 A p ril cash flow as i f i t were to occur on 1 May, we could then add the
two cash flows, since one is actually a May cash flow and the other has, so to speak, been converted to the
equivalent o f a May cash flow. Alternatively, we could firs t value the 1 May cash flow as i f it were to occur
on 1 A p ril; sum m ation o f these tw o cash flows then provides the to ta l value o f the tw o cash flows as at 1
A pril. For th a t m atter we could choose any date at all, value the two cash flows as i f they were to occur on
that date, and thus produce a valuation as at th a t date.
To im plem ent this approach we need to decide how we can value, as at any given date, a cash flow that
occurs on some earlier or later date. For example, we need to decide how a 1 A p ril cash flow can be valued
as at 1 May. The answer is provided by the interest rate. Using our knowledge o f compound interest we
can use Equation 3.4 to carry forw ard in tim e (‘accumulate’）the value o f any cash flow, provided we know
the interest rate to use. Similarly, we can use Equation 3.5 to carry backward in tim e (‘discount’) the
value o f any cash flow i f we know the interest rate to use. The process o f valuation as at any given date is
illustrated in Example 3.14.
Example 3.14
On 1 February 2 0 1 4 you sign a contract that entitles you to receive two future cash flows, as follows:
On 1 February 2016: $ 1 0 0 0 0
On 1 August 2017: $6 00 0
Assuming that the relevant interest rate is 5 per cent per annum (effective), value this contract as at:
a) 1 February 2 0 14
b) 1 February 2 0 16 and
c) 1 August 2017.
The following time line shows the timing of the cash flows in this problem.
t= 0 years
I
1
1 February 2014
t= 2 years
I
1
1 February 2016
$10000
t= 3.5 years
I
1
1 August 2017
$6000
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
SOLUTION
a) Valuation as at 1 February 2 0 14
Both cash flows must be discounted to 1 February 2014. This requires that the $ 1 0 0 0 0 to be
received on 1 February 2016 be discounted for 2 years and the $6 0 0 0 to be received on 1 August
20 1 7 be discounted for 3.5 years. The equation we need to use in each case is Equation 3.5. The
valuation as at 1 February 2 0 1 4 is:
$10000
°
$6000
(1.05)2 + (1.05)3.5
= $9070.2948+ $5058.1151
= $ 1 4 128.41
Because this valuation is made as at the start of the contract, Va is called the present value of the
contract.
b) Valuation as at 1 February 20 1 6
The cash flow of $ 6 0 0 0 on 1 August 2 0 1 7 must be discounted for 1.5 years to calculate an
equivalent amount as at 1 February 2016. Therefore, the valuation as at 1 February 2 0 1 6 is:
$6000
Vb = $10000 +
PRESENT VALUE OF A
CONTRACT
the value today
that is equivalent to
the stream of cash
flows promised in a
financial contract
(1 .0 5 )15
= $ 1 0 0 0 0 + $5576.57
$15 576.57
c) Valuation as at 1 August 2 0 1 7
The cash flow of $ 1 0 0 0 0 on 1 February 2 0 16 must be accumulated for 1.5 years to calculate an
equivalent amount as at 1 August 2017. The equation we need to use is Equation 3.4. Therefore, the
valuation as at 1 August 2 0 1 7 is:
^ = $1 〇〇〇〇(1.〇5)15 + $6000
=$10759.30 +$6000
= $16759.30
Because 1 August 2 0 1 7 is the date of the final cash flow of the contract, Vc is called the terminal
value of the contract.
In Example 3.14, the three valuations VQf Vb and Vc are all valuations o f the same financial contract.
They d iffer because the date o f valuation differs. There should, therefore, be logical connections between
the three valuations. For example, the contracts present value (Vai the valuation as at 1 February 2014)
should be the same as taking the contracts term inal value (Vct the valuation as at 1 August 2017) and
discounting fo r 3.5 years. In fact, the mathematics underlying the valuation process guarantees this
result, as the follow ing calculation confirms:
Vc
(1.05)3*5
$16759.30
(1.05)3*5
=$14128.41
=Va
In effect, the valuation process consists o f using compound interest to discount and accumulate cash
flows to calculate value equivalents at a common date. The valuation as at th a t date is then found sim ply
by adding the value equivalents fo r th a t date.
TERMINAL VALUE OF A
CONTRACT
the value, as at the
date of the final cash
flow promised in a
financial contract, that
is equivalent to the
stream of promised
cash flows
3 .5 .3 1 Formula development: valuation as at any date
Where a cash flow o f C dollars occurs on a date t, the value o f th a t cash flow as at a valuation date t* is
given by:
V r = Ct( l +
I f date t* occurs after date t, then t* is greater than t and, in Equation 3.15, the power (t* - t) is
positive, and the equation correctly indicates th a t an accumulation o f Ct is required. Conversely, i f date
t* occurs before date t, then t* is less than t and, in Equation 3.15, the power (t* - t) is negative, and the
equation correctly indicates th a t a discounting o f Ct is required.
Where there is more than one cash flow to be valued, the to ta l value o f the contract is the sum o f
the values o f each cash flow. The calculation o f a contracts value at various dates is illustrated in
Example 3.15.
E xample 3.15
Confirm that Equation 3.15 is correct by using it to recalculate the valuations made in Example 3.14.
In each case, / = 5 per cent per annum, C 2 = $ 1 0 0 0 0 and C3 5 = $6000. The valuation date t * ,
however, differs in each case.
SOLUTION
a)
Valuation as at 1 February 20 1 4
In this case, t* = 0. Using Equation 3.15:
V〇= $ 10 0 0 0 (1,05)°-2 + $ 6 0 0 0 (1.05)°-3-5
= $ 10 0 0 0 11.05 厂2 + $ 6 0 0 0 (1 _05 广3 5
= $10000
$6000
(1.05)2
(1.05)3"5
= $ 9 0 7 0 . 2 9 4 8 + $5058.1151
= $ 1 4 1 2 8 .4 1
= Va as calculated in Worked example 3.14
b)
Valuation as at 1 February 2016
In this case, t* = 2. Using Equation 3.15:
V2 = $ 10 0 0 0 (1.05)2-2 + $6 0 0 0 (1,05)2-3-5
= $ 10 0 0 0 (1.05)0 + $ 6 0 0 0 (1.05 广1 5
= $10000+ ^ 〇
(1.05)1-5
= $ 1 0 0 0 0 + $5 576.57
= $ 1 5 576.57
=
c)
as calculated in Worked example 3.14
Valuation as at 1 August 2 0 17
In this case, t* = 3.5. Using Equation 3.15:
V3 5 = $10 0 0 0 (1,05)3-5- 2 + $ 6 0 0 0 (1.05)3-5- 3-5
= $ 10 0 0 0 (1.05)1 5 + $6 0 0 0 (1.05)°
= ($ 10 0 0 0 x 1.075 92 9 83) + $6 00 0
= $ 1 6 7 5 9 .3 0
= Vc as calculated in Worked example 3.14
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
3 .5 .4 1 Measuring the rate of return
When there are m ultiple cash flows in an investm ent, there are also m ultiple tim e periods. Inevitably
the question arises: For a given set o f cash flows extending over tw o or more tim e periods, how can we
measure the rate o f retu rn per period? There are a num ber o f d ifferent answers to this question, b ut the
answer most frequently offered is to employ a measure know n as the internal rate o f return. In this
section we outline this method. I t is discussed in greater detail in Section 5.4.2.
First, however, we review the measurement o f the rate o f retu rn over a single period. Consider a oneperiod investm ent th a t costs $1000 and promises a cash inflo w o f $1120 a year later. Such an investm ent
would usually be described sim ply as a 1-year loan o f $1000 at an interest rate o f 12 per cent per annum.
We would infer th a t the interest rate is 12 per cent per annum by observing th a t the interest component
o f the cash flow after 1 year is $120, so the interest rate is $120/$1000 = 12 per cent. This is, o f course,
the result given by the simple defin itio n o f *rate o f return* in Equation 3.1. Equally, we could have said
that the rate o f return is the value o f r th a t solves the follow ing equation:
$1120
-$1000 = 0
The calculation $1120/(1 + r) is the present value o f $1120 using a discount rate o f r. On solving this
equation we would, o f course, fin d th a t r = 0.12, or 12 per cent.
The advantage o f th in kin g about the rate o f retu rn in this way is th a t we can readily see how to extend
this approach to the case o f many cash flows and tim e periods. Consider the follow ing investm ent. An
in itia l investm ent o f $1000 is made and, as before, a cash flow o f $1120 is to be received after 1 year but,
in addition, a fu rth e r cash flow o f $25 is to be received 2 years after making the in itia l investm ent. In
tabular form , the cash flows o f this investm ent are shown in Table 3.5.
TABLE 3.5
Year
Cash flow ($)
0
-1 0 0 0
1
+ 1120
2
+ 25
Obviously this investm ent promises a rate o f retu rn o f more than 12 per cent per annum, since the
firs t cash inflo w alone is sufficient to produce a rate o f retu rn o f 12 per cent per annum. As an investor,
however, we would prefer the $25 inflo w to have been promised fo r Year 1 rather than Year 2. Had this
occurred, the cash inflow after 1 year would be $1145, representing a rate o f retu rn o f 14.5 per cent per
annum. P utting these observations together, the investm ent s annual rate o f retu rn m ust be more than
12 per cent, b u t less than 14.5 per cent.
The internal rate o f return measure proposes th a t the rate o f retu rn in this case is the value o f r th a t
satisfies the follow ing equation:
$1120
$25
1+ r
(1 + r)2
-$1000 = 0
The term $25/(1 + r)2 can be thought o f as the present value o f $25, discounted fo r 2 years at the rate r
per annum. Solving this equation, we find r = 14.19 per cent per annum.6 We can confirm this result by
noting that:
$1120
1.1419
$25
-$1000
(1.1419)2
= $980.821438 + $19.172 725 - $1000
= -$ 0 .0 0 5 8 3 6
«$0
6
In this particular case, r can be found by solving the resulting quadratic equation. In more general cases, numerical methods
are usually required.
B usiness finance
The figure o f 14.19 per cent falls w ith in the range o f 12 per cent to 14.5 per cent, as suggested earlier
by our in tu itiv e reasoning.
Where there are n cash inflow s Ct (where t = 1,
n), follow ing an in itia l cash outflow o f C〇, the
internal rate o f return is th a t value (or values) o f r th a t solves the equation:7
c.
,
c2
r\
1+ r
(1 + r)2
I ••• l
Cn
(1 + r)1
or
X：
Ct t
3.6
LEARNING
OBJECTIVE 3
Distinguish between
different types of
a 门nuity and calculate
their present value and
future value
AN N U ITY
series of cash flows,
usually of equal
amount, equally
spaced in time
Co = 0
3.16
A n n u itie s
3.6.1 I Definition and types of annuity
In Section 3.5 we explained how to analyse contracts th a t require more than one cash flow to be paid.
We considered a general case th a t can be used to deal w ith a wide range o f contracts. There is, however, a
special case th a t is found in a large num ber o f financial contracts and hence requires fu rth e r discussion.
This is the case o f the annuity.
An annuity is a series o f cash flows, usually o f equal amount, equally spaced in tim e. Thus, fo r example,
$500 paid each m onth fo r a year is an annuity. Similarly, $600 per week fo r 12 weeks is an annuity; so is
$20 000 per annum fo r 10 years. Annuities are involved in many personal loans and commercial loans,
and in certain kinds o f financial instrum ents such as bonds.
In itia lly we consider fo ur types o f annuity: ordinary annuity, annuity-due, deferred annuity and
ordinary perpetuity.
The o rd in a ry annuity
ORDINARY ANNUITY
annuity in which the
time period from the
date of valuation to
the date of the first
cash flow is equal
to the time period
between each
subsequent cash flow
Like many annuities, the cash flow pattern o f the ordinary annuity consists o f equal amounts, equally
spaced in tim e. The distinguishing characteristic o f the ordinary annuity is that the tim e period fro m the
date o f valuation to the date o f the firs t cash flow is equal to the tim e period between each subsequent
cash flow.
Diagrammatically, the cash flow pattern o f the ordinary annuity, using six cash flows as an example, is:
0
1
2
3
4
5
6
$C
$C
$C
$C
$C
$C
AN NUITY-DUE
annuity in which the
first cash flow is to
occur 'immediately'
(i.e. on the valuation
date)
The annuity-due
The distinguishing feature o f the annuity-due is th a t the firs t cash flow occurs on the valuation
date 一 th a t is, immediately.
Diagrammatically, the cash flow pattern o f the annuity-due, using six cash flows as an example, is:
DEFERRED AN N U ITY
annuity in which
the first cash flow
is to occur after a
time period that
exceeds the time
period between each
subsequent cash flow
0
1
2
3
4
5
$C
$C
$C
$C
$C
$C
The deferred annuity
The distinguishing feature o f the deferred annuity is th a t the firs t cash flow is to occur after a tim e
period th a t exceeds the tim e period between each subsequent cash flow.
7
If the cash flows are produced by a bond, it is conventional to call the internal rate of return the bonds y ie ld -to -m a tu rity (or
'yield1for short). For further discussion, see Sections 4.4 and 4.7. The Microsoft Excel* function IRR uses numerical methods
to calculate the internal rate of return for a given initial outlay and set of cash flows.
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
Diagrammatically, the cash flow pattern o f the deferred annuity, using as an example six cash flows,
the firs t to occur after three tim e periods, is:
0
1
2
3
4
$C
5
$C
6
$C
7
$C
8
$C
$C
The ordinary perpetuity
The ordinary perpetu ity is an ordinary annuity w ith the special feature th a t the cash flows are to
continue forever.8
Diagrammatically, the cash flow pattern o f the ordinary perpetuity is:
0
1
2
3
4_____________
$C
$C
$C
$C ----------------- >
where the arrows indicate continuing forever.
3 .6 .2 1 Formula development: present value of an ordinary annuity
The form ula fo r the present value o f an ordinary annuity is one th a t we w ill use frequently. This form ula
can then be adapted to apply to the other types o f annuity.
The cash flow pattern o f an ordinary a nnuity o f n cash flows o f C dollars each is shown below:
0
1 2
$C
3
$C
$C
n -1
n
$C
$C
The present value P o f this stream o f cash flows is given by the sum o f the present values o f the
individual cash flows:
C
P-
+ i
C
C
C
C
( i + iy
( i + iy
( l + i) " - 1
( l + i) n
K IH
where z = the interest rate per period.
M u ltip lyin g both sides o f Equation 3.17 by (1 + 〇 gives:
n/1
.x ^
P(1 + z) = C +
C
+ /
C
C
C
( l + i)2
( l + 〇n_2
( l + i) n~l
B f lU
Subtracting Equation 3.17 from Equation 3.18, we fin d th a t all terms on the right-hand side cancel
out, except the last term o f Equation 3.17 and the firs t term o f Equation 3.18, giving:
P (l + / ) - P = C -
C
(1 + 0 "
C
Pi = C-
(1 + i)n
which, on rearrangement gives:
P.
C
1
(1 + ^
I t is often convenient to consider an annuity o f $1 per period— th a t is, we set C = 1 and Equation 3.19
becomes:
P = A(n, i)
(i + 0n
Equation 3.20 is the form ula fo r the present value o f an ordinary a nnuity consisting o f n cash
flows, each o f $1 per period. The functional notation A{ny i) is sim ply a shorthand way o f referring to
8
We could, of course, also consider the categories p e rp e tu ity -d u e and d eferred p e rp e tu ity but have not done so because the
purpose at this stage is simply to introduce the idea of a perpetuity, as distinct from an annuity of finite life.
ORDINARY PERPETUITY
ordinary annuity with
the special feature that
the cash flows are to
continue forever
this equation.9 Values o f A(n, 〇 fo r different values o f n and i are provided in Table 4 o f Appendix A.
The valuation o f ordinary annuities is illustrated in Example 3.16.
Example 3.
Find the present value of an ordinary annuity of $ 5 0 0 0 per annum for 4 years if the interest rate is
8 per cent per annum by:
a) using a calculator to discount each individual cash flow
b) using a calculator to evaluate the formula given in Equation 3.19
c) using the Microsoft Excel® function PV (rate, nper, pmt)
d) using Table 4 of Appendix A to evaluate the formula given in Equation 3.20.
SOLUTION
a)
Discounting each individual cash flow:
P= —
+
C
+
i + ； (i
=$5000
1.08
C
+
+/)2
C
(i +/]3
$5000
$5000
$5000
(1.08)2
(1.08)3
(1.08)4
(i +/)4
=$4629.6296 + $4286.6941 + $3969.1612 + $3675.1493
= $16560.63
b)
Using Equation 3.19:
$5000
0.08
(1.08)4
$ 5 0 0 0 x3 .3 1 2 122 684
$16560.63
c) Using the Microsoft Excel® function PV (rate, nper, pmt):
The Microsoft Excel® function PV returns -1 x the present value of an ordinary annuity. The
required inputs are the interest rate (as a decimal), the number of periods and the amount of each
cash flow. Using a Microsoft Excel® spreadsheet, we find that-PV(0.08, A, 5000) = $16560.63.
d) Using Table 4 of Appendix A:
P= CA[n, i)
=$5000 x 3.3121
=$16560.50
Except for the relatively small rounding error when using Table 4 of Appendix A, the four answers
are identical.
3.6.31 Formula development: present values of annuities-due,
deferred annuities and o rdinary perpetuities
Present value of an annuity-due
The cash flow pattern o f an annuity-due w ith n cash flows o f C dollars each is shown below:
0
$C
9
1
$C
2
3
$C
n -2
$C
$C
n -1
$C
The notation
sometimes read as 'A angle n at rate i \ is also used to indicate this equation. There is no special significance
in this notation: it is simply a different convention. Mathematically, the functional notation A {n ,i) serves equally well.
C hapter three T he
time value of m o n e y : a n introduction to
It is im p o rta n t to be aware th a t in an annuity-due consisting o f n cash flows, there are only {n - 1)
tim e periods involved.10
Inspecting the annuity-due diagram, i t is clear th a t an annuity-due o f n cash flows is sim ply an
immediate cash flow plus an ordinary a nnuity o f (n - 1) cash flows. The present value o f an annuity-due
is therefore:
P = C + -4
i 1
^
13.21
( l + £•广 1
or
13.22
P = C[1 + y 4 ( n - l, 〇l
where
P = present value
C = cash flow per period
z = interest rate per period
n = num ber o f cash flows
The valuation o f annuities-due is illustrated in Example 3.17.
E xample 3.17
Kathy's rich uncle promises her an allowance of $ 1 0 0 0 0 per month, starting today, with a final
payment to be made 6 months from today. If the interest rate is 0.5 per cent per month, what is the
present value of the promised allowance?
SOLUTION
Kathy has been promised seven payments of $ 1 0 0 0 0 with the first being due immediately. Thus,
she has been promised $ 1 0 0 0 0 today, plus an o rd in a ry annuity of six payments. This is the logic
embodied in Equation 3.21. Using this equation with n set equal to 7, gives:
p= c + ^ [ i - - L _ ]
= $10000+ i M ° ° [ l
0.005
= $ 1 0 0 0 0 + $ 10000
0.005
(1.005)7-1
1
(1.005)6
= $ 1 0 0 0 0 + $58 963.84
=$ 68 963.84
Present value of a deferred annuity
The cash flow pattern o f a deferred annuity is as follows:
0
1 2
k -1
k
k+1
k + n -2
k + n -1
$C
$C
$C
$C
In this case, there are n cash flows and the firs t cash flow occurs on date k. To find the present value o f
this series o f cash flows, imagine th a t the valuation was to be made as at date (k - 1) instead o f date zero.
Looking ahead from date ( k - 1 ) , the cash flow pattern is th a t o f an ordinary a nnuity o f n cash flows. Thus,
at date (/c - 1), the present value is given by the present value o f an ordinary annuity:
10 This is frequently a source of confusion. For an ordinary annuity, it makes no difference whether n is defined as the number
of cash flows or the number of time periods, since these are equal. For an annuity-due, we must choose whether to use
n to represent the number of cash flows or the number of time periods. We have chosen to develop the formula with n
representing the number of cash flows.
c
Pk-l
1
3.23
(1 + i) n
where
_ 丄= the present value at date (/c - 1)
To s h ift the valuation date back from date (k - 1) to date zero, we sim ply discount the value given by
Equation 3.23 fo r (k - 1) periods. Thus the required form ula is:
」 ____C
P=
(1 + 〇fc_1 i
3.24
(1 + i) n
or
C
P=
A{n, i)
3.25
(1 + 〇fc_1
where
C = cash flow per period
z = interest rate per period
n = num ber o f cash flows
k = num ber o f tim e periods u n til the firs t cash flow
Alternatively, the present value o f a deferred a nnuity can be found by firs t im agining th a t cash flows
are to occur on all (k + n - 1 ) dates. The present value o f such a stream is, o f course, given by the present
value o f an ordinary annuity consisting o i (k + n - 1) cash flows. The effect o f the deferral period is
accounted fo r by subtracting the present value o f the firs t (k - 1) h is s in g 1cash flows, because these cash
flows w ill n o t occur. That is:
present value o f an
p =
present value o f an
ordinary annuity of
less
(k-\- n - l ) cash flows
ordinary annuity o f
(A: - 1) cash flows
That is:
C !_
1
i
( l + i) k+n- \
c 1
1
i
3.26
= C[A(k+ n - l J ) - A ( k - l , i ) ]
The valuation o f deferred annuities is illustrated in Example 3.18.
Example 3.
Jason will be starting a 6-month live-in training course in 4 months, time. His father, Sam, has promised
him a living allowance of $ 2 0 0 0 per month to help support him during this time. If the simple interest
rate is 9 per cent per annum, payable monthly, how much money will Sam need to set aside today to
finance Jason's allowance?
SOLUTION
Sam needs to set aside the present value of the promised allowance. The allowance is an annuity of
six payments, the first payment to be made 4 months from today.
Diagrammatically, the cash flows are:
0
1
2
3
4
$2000
5
6
$2000
7
$2000
8
$2000
9
$2000
$2000
Using the logic developed in this section, we can approach this problem in two stages. First, w hen
v ie w e d from the s ta n d p o in t o f d ate 3, the cash flows form an ordinary annuity of six payments. W e
therefore value this stream, as at date 3, using Equation 3.19, which gives the present value of an
ordinary annuity. Second, we find the value as at date zero by discounting for three periods. The
calculations are shown below. Note that the interest rate is 0.09/1 2 = 0.75 per cent per month.
G h APTER THREE T he TIME VALUE OF MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
As at date 3 the value is:
$2000
0.0075
(1.0075)°
$11 691.195 260
As at date zero, the value is thus:
p _ $11 691.195 260
(1.0075)3
=$11 432.04
This is, of course, the logic embodied in Equation 3.24, as we now show. In this case, n = 6,
k = 4 and /' = 0.09/1 2 = 0.75 per cent per month. Using Equation 3.24:
n
1
(1+/)
C
k-]
(1
$2000
1
0.0075
(1.0075)°.
(1.0075) r
1
x $ 2 0 0 0 x5 .8 4 5 59763
1.022 669172
=$11 691.195260
~
1.022 669172
= $11432.04
Alternatively, using Equation 3.26, and again using n = 6 , k = 4 and / = 0.75 per cent per month,
the required sum is:
c
!
i L
1
( i+ ^ ' J
$2000 i
0.0075 L
C
,
1
i
i
(1.0075)9 J
$2000 ,
0.0075 L
1
( i. 〇〇75)3 J
=($2000 x 8.671 5 76 42 3)-($ 20 00 x 2.955 556 237)
= $ 17343.1 5 2 9 -$ 5 9 1 1 .1125
= $11432.04
Present value of an ord ina ry perpetuity
The cash flow pattern o f an ordinary perpetuity o f C dollars per period is shown below:
0
1
2
3
4
5
---------------------------------------------------------------►
$C $C $C $C $ C --------------------►
The ordinary p erpe tu ity is an ordinary annuity where the num ber o f cash flows n becomes in d e fin ite ly
large. Therefore, to fin d its present value, we need to consider the form ula fo r the present value o f an
ordinary annuity and allow n to become indefinitely large. Thus the problem is to value:
P = lim —
(1 + i) n
Because the interest rate z is positive, (1 + i)n becomes ind efin itely large as n becomes ind efin itely
1
large. This means th a t (丄 +
becomes very small because the denom inator o f this fraction becomes
very large. In the lim it, the value o f this fraction approaches zero and thus the present value o f an ordinary
p erpetuity is:11
C
3.27
where
C = cash flow per period
i = interest rate per period
The valuation o f ordinary perpetuities is illustrated in Example 3.19.
E xample 3.19
A government security promises to pay $3 per annum forever. If the interest rate is 8 per cent per
annum and a payment of $3 has just been made, how much is the security worth?
SOLUTION
Using Equation 3.27:
$3
0.08
=$37.50
The value of the security is $37.50.
3 .6 .4 ! Future value of annuities
I t is frequently necessary to calculate the value o f an annuity as at the date o f the final cash flow. Such a
calculation is required if, fo r example, regular savings are being made towards a target fu tu re sum.
To derive the form ula fo r the future value o f an ordinary annuity, we use a two-stage process. First,
the present value o f the annuity is calculated. Second, the future value is calculated by accumulating the
present value fo r the n periods from the valuation date to the date o f the final cash flow. In effect we
use the compound interest form ula S = P(1 + i)n where, in this case, P is given by the present value o f an
ordinary annuity. That is:
1
(1 + i) n
(1 + i) n
= f [ ( i + On - i ]
3.28
I f C = $1, Equation 3.28 may be w ritte n as:12
S(n, i) = (1 + 〇 n-1
i
3.29
Values o f S(«, z) fo r different values o f n and i are given in Table 3 o f Appendix A. Alternatively, the
M icrosoft Excel4 fu nctio n - FV(rate, nper, pm t) m aybe used. The FV fu nctio n returns the value o f- 1 x the
future value o f an ordinary annuity, where 'rate* means the interest rate as a decimal, 'nper* means the
number o f periods and pint* means the am ount o f each periodic cash flow. The calculation o f the future
value o f an annuity is illustrated in Example 3.20.
11
• _
. . .
c
Similarly, it is a simple matter to show that the present value of a perpetuity-due is C + —, and the present value of a deferred
1 C
i
perpetuity, where the first cash flow occurs after k periods, i s ------- -- x
(1
+
i)K
12 The notation
can also be used.
CHAPTER THREE T he TIME VALUE 〇F MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
Example 3.20
Starting with his next monthly salary payment, Harold intends to save $ 2 00 each month. If the interest
rate is 8.4 per cent per annum, payable monthly, how much will Harold have saved after 2 years?
SOLUTION
The monthly interest rate is 8.4/12 = 0.7 per cent. Using Equation 3.28, Harold's savings will
amount to:
s = y [ii+ - r - i]
= ^ ° ° f(1.007)24- l l
0.007 L'
J
= $ 2 0 0 x2 6 .0 3 4 9 2 5 07
=$5206.99
Alternatively, using Microsoft Excel®, we find that - FV(0.007, 24, 200) = $5206.99.
We could use this two-stage approach to derive formulae fo r the future values o f annuities-due and
deferred annuities. In practice, however, i t is usually ju s t as easy to apply this approach using the numbers
o f the particular problem. As we said at the sta rt o f this chapter, rather than learning a lis t o f formulae, i t is
preferable to learn the approach and then apply th is approach to the particular problem. This is illustrated
in Example 3.21.
Example 3.21
Harold's sister Janice can also save $ 2 0 0 per month, but whereas Harold takes 1 month to save his
first $200, Janice will start by setting aside $ 2 0 0 immediately. With an interest rate of 0.7 per cent
per month, how much will she have in 2 years' time? Reconcile this amount with the savings achieved
by Harold in the previous example.
SOLUTION
This problem requires the future value of an annuity-due. W e first calculate the present value, then
accumulate this amount for 24 months:
Step 1
n
^
C
1
(1 + /)
$200.
$200
0.007
(1.007)24
$4604.321 714
Step 2
S=P(1 +/)n
=$4604.321 714(1.007)24
=$5443.43
Janice is thus able to save $5443.43 after 2 years, compared with Harold's savings of $5206.99.
That is, Janice will save $236.44 more than Harold. Logically, this amount should equal the future
value of the initial $ 2 0 0 Janice set aside at the start, accumulated for 24 months at 0.7 per cent per
month. This is in fact the case, because $ 2 00 x (1.007)24 = $236.44.
6
B usiness finance
3.7
LEARNING
OBJECTIVE 4
Apply your knowledge
of annuities to solve
a range of problems,
including problems
involving principaland-interest loan
contracts
Principal-and-interest loan contracts
Basic features of the contract
An im p o rta n t application o f annuities is to loan contracts, where the principal is gradually reduced by a
series o f equal repayments. This type o f loan is often called a prin cipal-an d-in terest loan or a credit
foncier loan. M any commercial loans, consumer loans and housing loans are in this category. The promised
repayments form an annuity and the present value o f the repayments is equal to the loan principal.
Therefore, i f the promised future repayments are made on tim e the debt should reduce gradually during
the loan term , so th a t when the final promised repayment is made the debt should be extinguished. This
pattern is illustrated in Example 3.22.
Example 3.22
On 31 December 2014, Pennant Ltd borrows $ 1 0 0 0 0 0 from Z N A Bank. Annual repayments are
required over 5 years at a fixed interest rate of 11.5 per cent per annum. How much is each annual
repayment? Show the year-by-year record of the loan account for the 5 years ended 31 December
2019.
SOLUTION
PRIN CIPAL-AND INTEREST LOAN
loan repaid by a
sequence of equal
cash flows, each of
which is sufficient
to cover the interest
accrued since the
previous payment and
to reduce the current
balance owing.
Therefore, the debt
is extinguished when
the sequence of cash
flows is completed.
Also known as a credit
fonder loan
The annual repayments of C dollars form an ordinary annuity with a present value of $ 100000. Using
Equation 3.19:
$100000
C
=
0.115
(1.115 广
C x 3.649 877 84
So
c=
$100000
_ 3.649 877 847
=$27398.18
The annual repayment required is $27398.1 8.
Alternatively, we could use the Microsoft Excel® function PMTjrate, nper, pv). Using the spreadsheet,
we find that -PM T(0.115,5, 100000) returns $27398.1 8.
The year-by-year record o f the loan account is shown in Table 3.6.
TABLE 3.6
Entry
Date
31 December 2014
31 December 2015
31 December 2016
31 December 2017
Principal borrowed
interest 0.115 x $100000.00 = $11500.00
Balance owing
$100000.00
$111500.00
Less repayment $27398.18
$84101.82
Arfrf interest 0.115 x $84101.82 = $9671.71
$93 773.53
Less repayment $27398.18
$66375.35
AcW interest 0.115 x $66375.35 = $7633.17
$74008.52
Less repayment $27398.18
$46610.34
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
Table 3.6 continued
Date
Entry
31 December 2018
31 December 2019
Balance owing
interest 0.115 x $46610.34 = $5360.19
$51970.53
Less repayment $27398.18
$24572.35
^ i n t e r e s t 0.115 x $24572.35 = $2825.83
$27398.18
Less repayment $27398.18
$0.00
The year-by-year record shows th a t annual repayments o f $27398.18 are just sufficient to repay the
loan over the 5-year term .
3 .7 .2 1 Principal and interest components
As shown by the loan account in Example 3.22, the required repayments are ju s t sufficient to extinguish
the debt at the required date. This is achieved by a series o f repayments, each o f which is sufficient to cover
interest accrued since the previous repayment and to reduce the principal. As the principal decreases, so
also does the interest accruing and thus, as tim e passes, a larger p roportion o f each repayment goes to
reducing the principal. The principal and interest components o f the repayments in Example 3.22 are
shown in Table 3.7.
TABLE 3.7
Year ended 31 December
Interest component ($)
Principal component ($)
Repayment ($)
2015
11500.00
15898.18
27398.18
2016
9671.71
17726.47
27398.18
2017
7633.17
19765.01
27398.18
2018
5 360.19
22037.99
27398.18
2019
2825.83
24572.35
27398.18
This pattern is more marked where the num ber o f repayments to be made is large. This is shown in
Example 3.23.
Example 3.23
Phantom Ltd borrows $1 0 0 0 0 0 at an interest rate of 1 1.5 per cent per annum, repayable by equal
monthly instalments over 2 0 years. Calculate the principal and interest components of the first and
last repayments.
SOLUTION
In this example, the monthly interest rate is 0 .1 1 5 /1 2 = 0 .0 0 9 5 8 3 3 3 3 and the loan term is
20 x 12 = 2 40 months. W e use Equation 3 .19 to calculate the monthly repayment:
$ 1 0 0 0 0 0 = --------- ---------0.009583 333
1-
________ 1________
(1.009583 333)240
= C x 93.77084022
continued
continued
So
c=
$100000
~ 93.770 840 22
= $1066.43
The interest accrued during the first month of the loan is 0 .0 0 9 5 8 3 333 x $ 1 0 0 0 0 0 = $958.33.
Therefore, when the first monthly repayment of $ 1066.43 is made, $958.33 (or nearly 90 per cent of
the repayment) is required to meet the interest accrued during the first month and only $108.10 (just
over 10 per cent of the repayment) is available to reduce the principal. At the end of the loan term
this pattern is reversed. Only a small amount of interest will accrue during the last month, so almost
the whole of the final monthly repayment will be available to reduce the principal. The component
of principal in the final repayment is $ 1 0 6 6 .4 3 / 1 .0 0 9 5 8 3 333 = $1056.31; therefore, the interest
component is only $10.1 2. One aspect of this pattern is that the balance owing decreases slowly in
the early stages of repayment, but decreases rapidly as the maturity date is approached. This pattern
is considered in more detail in the next section.
3 .7 .3 ] Balance owing at any given date
The balance owing at any given date is the present value o f the then rem aining repayments. We explained
earlier how the principal is the present value o f all promised repayments. O f course, the principal is
sim ply the balance owing at the tim e the loan is made. Similarly, the balance owing at any given date is
the present value o f the repayments s till to be made as at th a t date. The calculation o f the balance owing
on a loan is illustrated in Example 3.24.
E xample 3.24
Consider again Phantom Ltd's loan of $ 1 0 0 0 0 0 at an interest rate of 1 1.5 per cent per annum,
repayable by equal monthly instalments over 20 years. As shown in Example 3.23, the required
monthly repayment is $1066.43. W hat is the balance owing when:
a) one-third of the loan term has expired?
b) two-thirds of the loan term has expired?
SOLUTION
a) The loan term is 2 4 0 months. Therefore, when one-third (or 80 months) of this term has expired,
160 monthly repayments are still to be made. The balance owing at the end of month 80 is the
present value of the then remaining 16 0 repayments:
$1066.43
0.009583 333
(1.009583 333)*160.
= $87087.85
b) When two-thirds (or 160 months) of the loan term has expired, 80 monthly repayments still have
to be made. Therefore, the balance owing at the end of month 160 is:
$1066.43
________1________ ■
0.009583 333
(1.009583 333)80.
=$59394.64
C hapter three T he
time value of m o n e y : a n introduction t o financial mathematics
In the previous section we explained that, in these types of loans, the balance owing reduces
slowly at first and more rapidly towards the end of the loan term. This pattern is clearly evident in this
example. When one-third of the loan term has expired, the balance owing is still more than $ 8 7 0 0 0
out of an original loan of $ 1 0 0 0 0 0 . That is, the passing of one-third of the loan term has seen the
principal fall by less than 13 per cent. When two-thirds of the loan term has expired, only about
4 0 per cent of the debt has been repaid. A more detailed presentation of this pattern is provided in
Figure 3.2.
Figure 3.2 Balance owing as a loan is repaid
o
o
o
o
o
o
o
o
0
9
8
7
6
5
4
3
o o o - $ lM O
cr)
.E
9UUDID
CQ
10
220 200
180
160
140
120 100
80
60
40
20
Months remaining
3 .7 .4 1 Loan term required
In some applications it is necessary to solve fo r the required loan term n given the principal, interest rate
and periodic repayment. For example, in order to plan future expenditure, a borrow er may wish to know
when an existing loan w ill be repaid. Solving fo r the loan term requires us to rearrange Equation 3.19 so
th a t n appears on the left-hand side:
C
(i + 0"
c
(1 + i) n
( i + O77
c
C -P i
and therefore:
n = log[C/(C-P/)]
i 〇g (i + 〇
_
_
E E 3
Logarithms to any base (such as base 10 or base e) w ill give the correct answer. The calculation o f a
required loan term is illustrated in Example 3.25.
A
B usiness finance
E xample 3.25
One year ago, Canberra Fruit Ltd borrowed $ 7 5 0 0 0 0 at an interest rate of 12 per cent per annum.
The loan is being repaid by monthly instalments of $ 1 6 6 8 3 .3 4 over 5 years. As a result of making
the promised repayments over the past year, the balance owing is now $ 6 33 532 .48 . The company
can now afford repayments of $ 2 0 0 0 0 per month and the company manager wishes to know when
the loan will be repaid if repayments are increased to that level. The manager also wishes to know
the amount of the final repayment.
SOLUTION
Using Equation 3.30:
n _ log [C /(C -P i]
lo g (l + /)
_ log { $ 2 0 0 0 0 / [ $ 2 0 0 0 0 - ($633 5 3 2.481(0.011]}
=
log(l.Ol)
_ lo g ( $ 2 0 0 0 0 / $ l3 6 6 4 .6 7 5 2 )
=
l〇g(i. 〇 i)
_ log (1 .4 6 3 6 2 7 9 1 )
=
log(l.Ol)
Using 'common' logarithms (logarithms to the base 10):13
= 0 .1 6 5 4 3 0 6 8 2
0 .0 0 4 321 373
= 3 8 .2 8 2
months
The loan will be repaid after a further 39 months; for the first 38 months the repayment will be
$ 2 0 0 0 0 per month, while the last (39th) repayment will be a smaller amount. The amount of the last
repayment must be such that the present value of all 39 repayments equals the balance owing of
$633 532.48. Using R to represent the amount of the last repayment, we therefore require that:
$ 6 3 3 5 3 2 .4 8 =
$20000
0.01
R
(1.01)38
(1.01)39
= $ 6 2 9 69 3 .2 6 6 1 + —
(1.01)39
$ 3 8 3 9 .2 1 3 9 =
R
(1.01)39
which gives R = $5659.47.
The amount of the last (39th) repayment is $5659.47.
3 .7 .5 1 Changing the interest rate
VARIABLE INTEREST
RATE LOAN
loan where the
lender can change
the interest rate
charged, usually in
line with movements
in the general level
of interest rates in the
economy
In some loan contracts, usually called variable in terest rate loans, the interest rate can be changed at any
tim e by the lender, although, in practice, changes are norm ally made only when there has been a change in
the general level o f interest rates in the economy. Such a change may be signalled or caused by the Reserve
Bank o f Australia changing the cash rate. In Australia, many housing loans, and many commercial loans,
are in this category. Typically, the parties to the contract w ill at the outset agree on a notio na l loan term —
say, 15 years fo r a housing loan— and the lender w ill then require a regular repayment th a t is calculated as
i f the current interest rate is fixed fo r 15 years. If, as is always the case, the general level o f interest rates
subsequently changes, the interest rate charged on the loan w ill then be changed. The lender w ill then set
the new required repayment, which w ill be calculated as i f the new interest rate is fixed fo r the remaining
13
令
Use of natural logarithms (logarithms to the base e) must give the same answer. In this case the calculation is
n = 0.380918223/0.00995033 = 38.282.
C hapter THREE T he TIME VALUE OF MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
loan term. Alternatively, the lender may allow the borrower to continue m aking the same repayment and,
instead, alter the loan term to reflect the new interest rate.14 O f course, a com bination o f b oth responses
is also a possibility. These choices are illustrated in Example 3.26.
E xample 3.26
Three years ago Andrew and Jane borrowed $ 8 0 0 0 0 , repayable by equal monthly instalments over
15 years. At the time they borrowed the money, the interest rate was 9.6 per cent per annum calculated
monthly. Following standard procedures, the lender correctly calculated the required monthly payment
to be $840.21. Andrew and Jane have made all repayments on time and the balance owing is now
$71 685.05. The general level of interest rates has been rising and the lender has now decided
to increase the interest rate to 10.8 per cent per annum calculated monthly. What will be the new
monthly repayment if the loan term is to remain unchanged? If, instead, the monthly repayment is left
at $840.21, by how many months will the loan term increase?
SOLUTION
The new monthly repayment C must be set so that the present value, calculated using the ne w interest
rate, of the remaining 144 repayments equals the balance outstanding of $71 685.05. The new
interest rate is 10.8 per cent per annum or 0.9 per cent per month. Therefore, using Equation 3.19:
$ 7 1 6 8 5 .0 5 = — ^
1 --------- — 0.009 L
(1.009)144.
= 80.531 669 39 C
C = $890.15
The new repayment is $890.15 per month.
Alternatively, if the loan term is extended, and the monthly repayment is left at $840.21, the new
loan term may be found using Equation 3.30:
n
log [C /(C -P f)]
log(l + /)
log {$8 40.21/[$840.21 -($71 685.05)(0.009)]}
log( 1.009)
_ log(4.307785 068)
=
log( 1.009)
=162.998 months
w 163 months
The remaining loan term is now 163 months, which is 19 months longer than the 144 'expected7
at the time of the interest rate increase.
LEARNING
OBJECTIVE 5
Distinguish between
simple and general
annuities and make
basic calculations
involving general
annuities
SIMPLE A N N U IT Y
3.8
G eneral annuities
In our discussion o f annuities, the frequency o f compounding has coincided w ith the frequency o f the
cash flows. An a nnuity w ith this feature is called a sim ple annuity. For example, we have considered
cases where interest is calculated and charged annually, and the borrow er is required to make annual
repayments. In practice, however, this is n ot always the case. Situations arise where loan repayments are
required more frequently, o r less frequently, than interest is charged (compounded). An a nnuity w ith this
feature is called a general annuity.
14 Note, however, that if the interest rate is increased to a level where the monthly repayment is less than the monthly interest
accruing (that is, C < P i), then the loan term becomes infinite. In these circumstances lenders will usually require a higher
monthly repayment.
annuity in which the
frequency of charging
interest matches the
frequency of payment
GENERAL A N N U IT Y
annuity in which the
frequency of charging
interest does not
match the frequency
of payment; thus,
repayments may be
made either more
frequently or less
frequently than interest
is charged
In a general annuity, the frequency o f compounding does n o t match the frequency o f repayment.
There are thus two cases to consider:
a
b
The frequency o f compounding is greater than the frequency o f repayment. For example, a loan contract
may specify an interest rate o f 8 per cent per annum, compounding quarterly, b u t repayments are
made annually.
The frequency o f compounding is less than the frequency o f repayment. For example, a loan contract may
specify an interest rate o f 8 per cent per annum, compounding quarterly, b u t repayments are made
m onthly.
In b oth cases, to solve the problem we need firs t to adjust the specified interest rate to an interest rate
where the compounding frequency matches the repayment frequency.15 This adjustm ent is made using
the concept o f the effective interest rate th a t we discussed in Section 3.4.3. This concept was summarised
in Equation 3.6, which we reproduce below:
/
. \
m
/=(1 +m)
where
_1
i = the effective interest rate per period
j = the nom inal interest rate, compounding m times per period
Note th a t in this equation the tim e dimension o f z is fo r a longer period than the tim e dimension o f
m ight be an interest rate per quarter.
I t is convenient to restate Equation 3.6 in terms o f an interest rate zs, fo r the shorter tim e period, and an
interest rate zL, fo r the longer tim e period. That is, Equation 3.6 is rew ritten as:
j/m . For example, z m ig ht be an interest rate per annum while
3.31
where m = the num ber o f ‘short’ periods in one ‘long’ period.
The use o f Equation 3.31 is illustrated in Examples 3.27 and 3.28.
E xample 3.27
Use Equation 3.31 to express 8 per cent per annum, compounding quarterly, as:
a) an effective annual interest rate
b) an effective monthly interest rate.
SOLUTION
a) In this case, interest is compounding quarterly and we wish to calculate an equivalent interest rate
in which compounding occurs annually. Thus we are required to calculate iL,
where is = 0.08/4 = 0.02, and m = 4. Using Equation 3.31:
彳=(1 + 'S )m _ 1
= (1.02)4 -1
= 0 .0 8 2 4 3 2 16
« 8 .2 4 3 % perannum
b) In this case, interest is compounding quarterly and we wish to calculate an equivalent interest rate
in which compounding occurs monthly. Thus we are required to calculate is,
where iL = 0.08/4 = 0.02 and m = 3. Using Equation 3.31:
0.02 = (1 + /s)3 - l
/s = (1 .0 2 )1/ 3 _ l
= 0 .0 0 6 6 2 2 71
« 0 .6 6 2 % per month
15 Alternatively, an adjustment can be made to the repayment amount. However, when using a calculator it is generally easier to
adjust the interest rate.
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
Example 3.28
A loan is currently being repaid by repayments of $ 5 5 0 0 0 at the end of each quarter. The interest
rate is 8 per cent per annum. The borrower wishes to change to a monthly repayment schedule that
will pay oft the loan by the same maturity date. Calculate the amount of each monthly repayment.
SOLUTION
The repayment schedule for a typical quarter is shown in Figure 3.3.
:igure 3.3 Monthly and quarterly repayments
i
:l
3 me)nths
$c
$C
$55 000
$C
As shown in Figure 3.3, it is proposed to replace each end-of-quarter cash flow of $ 5 5 0 0 0 with
three end-of-month cash flows of C dollars each. Interest is charged quarterly at a nominal rate of
8 per cent per annum— that is, the effective qfuarter/y interest rate is 2 per cent per quarter. As shown
in Example 3.27 (b), the equivalent effective m onthly interest rate is 0.662 271 per cent per month.
Equating the present values of the quarterly and monthly cash-flow streams gives:
$55 000 =
1.02
C
(1.006622 71 )3
1.006622 71
Note, however, that although we have included the calculation of (1.006622 71 )3 in this
expression, this calculation should by definition equal 1.02 (see the calculation in Example 3.27 (b)
for clarification). Therefore, we need to solve:
$55 000 =
1.02
which gives
C
L _
0.006622 71 L
1 '
1.02.
C = $ 1 8 2 1 2 .4 5
Therefore, monthly repayments of $1 8 2 1 2 .4 5 will pay the loan off at the same maturity date as
quarterly repayments of $ 5 5 0 0 0 . Note that 3 x $18 212.45 = $5 46 37.3 5, which is slightly less
than the quarterly repayment of $5 5 0 0 0 . This difference reflects the present-value effect of making
monthly repayments earlier than the quarterly repayments they replace.
B usiness finance
SUMMARY
• Financial managers frequently make decisions that
involve the time value of money. This chapter covered
the major tools of financial mathematics needed
to support these decisions. These tools include
calculating rates of return, present values and future
values, and defining and applying interest rates,
including simple interest and compound interest.
• The definition and valuation of various streams of
cash flows were considered in detail, with the present
value of an ordinary annuity being used as the basis
for dealing with several related problems. Annuity
applications, including interest-only loans and
principal-and-interest loans, were also discussed.
• A wider class of problems, in which interest is
charged either more frequently or less frequently
than cash flows occur, was also discussed.
• Throughout the chapter, emphasis was placed on
developing a sound understanding to support the
use of the various formulae that were derived.
KEY TERMS
accumulation 34
annuity 50
annuity-due 50
cash flow 29
compound interest 33
continuous interest 42
debt 30
deferred annuity 50
discounting 36
effective interest rate 37
financial contract 29
future sum 32
general annuity 63
geometric rate of return 44
interes卜
only loan 37
interest rate 30
log price relative 43
nominal interest rate 3 7 , 40
ordinary annuity 50
ordinary perpetuity 51
present value 32
present value of a contract 47
principal 31
principal-and-interest loan 58
rate of return 29
real interest rate 40
simple annuity 63
simple interest 31
terminal value of a contract 47
time value of money 30
variable interest rate loan 62
SELF-TEST PROBLEMS
1 Andrew borrowed $ 6 0 0 0 and repaid the loan 60 days later by a single payment of $6250. What is the
implied annual simple interest rate?
2 Angela deposits $ 5 0 0 0 today in a bank account that pays interest annually at the rate of 8 per cent. She
then makes 10 more deposits of $ 1 0 0 0 each at annual intervals.
a) How much does she have when she has made the last deposit?
b) If Angela wished to accumulate the same sum by making a single deposit now, what amount would she
need to deposit?
3
Geoff and Gail wish to borrow $ 7 5 0 0 0 to be repaid by equal monthly instalments over 25 years. The
nominal annual interest rate is 9.9 per cent.
a) What is the effective annual interest rate?
b) What is the amount of the monthly repayment?
Solutions to self-test problem s ore a v a ila b le in A p p e n d ix B.
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66
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
1
[LO 1] Explain the difference(s) between an interest rate and a rate of return.
2
[LO 1] Distinguish between simple interest and compound interest.
3
[LO 1] In financial mathematics, the symbol P can stand for 'present value', 'price' or 'prin cipa l’，but all
three terms really hove the some meaning. Discuss.
4
[ L O llT h e term 'nominal interest rate' has two different meanings. Explain these two meanings,
distinguishing carefully between them.
5
[LO 1] Rotes o f return should be multiplied, not added. Is this true? Why, or why not?
6
[LO 2] Given a required rote o f return, a set o f cash inflows can be valued os at any date, and the later is
the valuation date the higher the value. Is this true? Why, or why not?
7
[LO 3] Distinguish between an annuity-due and a deferred annuity.
8
[LO 4] In any variable interest rote loon, it is possible that the interest rate con be increased to a level where
the loan term becomes infinite unless the periodic repayment is increased. Explain how this can occur, and
relate your answer to the characteristics of Equation 3.30.
9
[LO 5] Distinguish between a simple annuity and a general annuity.
CHAPTER THUEE REVIEW
QUESTIONS
PROBLEMS
1
Simple interest earned [LO 1]
Nicholas deposits $2 0 0 0 in a bank fixed deposit for 6 months at an interest rate of 13.25 per cent per
annum. How much interest will he earn?
2
Simple interest earned [LO 1]
If Nicholas reinvests the $2000, plus the interest earned (see Problem 1), for a further 6 months, again at
13.25 per cent per annum, how much interest will he earn in this second 6-month period?
3
Implied simple interest rate [LO 1]
Jane borrowed $ 1 0 0 0 0 and repaid the loan 30 days later by a single payment of $10400. What is the
implied annual simple interest rate?
4
Calculating the loan term [LO 1]
Mary borrowed $7250 at an annual simple interest rate of 15.50 per cent. She repaid the loan by paying a
lump sum of $7394.70. What was the loan term?
5
Calculating the lump sum repayment [LO 1]
On 2 April 2014, Paradise Pencils Ltd borrows $2 00 000 , repaying in a lump sum on 16 M ay 2014. The
interest rate is 9.55 per cent per annum. How much is the lump sum repayment?
6
Simple interest earned (harder) [LO 1]
On 5 February 2014, Financial Solutions Ltd deposits $ 3 0 0 0 0 0 with Second Street Bank at a simple interest
rate of 4.4 per cent per annum. The maturity date of the deposit is 5 M ay 2014. Calculate the amount of
interest the deposit will earn.
7
Present value [LO 1]
Jupiter Mining Ltd promises to pay $ 5 0 0 0 0 0 in 90 days' time. Taking into account the company’s credit
standing, the market interest rate for a loan period of 90 days is 10.65 per cent per annum. How much can
Jupiter Mining borrow?
8
Simple and compound interest [LO 1]
a) What will be the accumulated value, at the end of 10 years, of $1000 invested in a savings account that
pays 8 per cent per annum? Assume that no withdrawals are made from the savings account until the end
of the tenth year. What is the interest component of the accumulated value?
b) Assume that interest is withdrawn every year. What will be the total interest earnings at the end of the tenth
year? W hy does this amount differ from the interest earned in Problem 8 (a)?
67
Compound interest earned [LO 1]
If you invest $ 6 5 0 0 0 for 3 years at 14.7 per cent per annum (interest payable annually), how much will you
have at the end of the 3 years?
Compound interest earned [LO 1]
If you invest $ 8 7 0 0 0 at 7.35 per cent per annum (interest paid annually), how much will you have:
a) at the end of 3 years?
b) at the end of 6 years?
Compound interest earned (harder) [LO 1]
Frank has invested $ 1 0 0 0 0 for 10 years at 12.4 per cent per annum. He has to pay tax on the interest
income each year.
a)
Calculate the value of the investment at the end of the tenth year if his tax rate is:
i) 45 per cent per annum
ii) 30 per cent per annum
iii) 15 per cent per annum
iv) zero per annum.
b)
Rework your answer to (a)(i) if, instead of having to pay tax each year, Frank must pay in tax 45 per cent
of the accumulated interest at the end of the tenth year. Which tax system is better for him? W h y?
Compound interest earned [LO 1】
Philip invests $ 1 7 2 0 0 at an interest rate of 2.5 per cent per quarter. How much is the investment worth after
2 years?
Compound interest earned [LO 1】
Rhiannyn invests $ 2 5 0 0 0 at an interest rate of 0.6 per cent per month. How much is the investment worth after
3 years?
Present value [LO 1]
Calculate the following present values:
a) $1 00 0 payable in 5 years if the interest rate is 12 per cent per annum
b) $ 1000 payable in 10 years if the interest rate is 12 per cent per annum
c) $1000 payable in 5 years if the interest rate is 6 per cent per annum
d) $ 1 6 2 0 5 payable in 1 year if the interest rate is 1.5 per cent per month
e) $1 million payable in 4 0 years if the interest rate is 15 per cent per annum
f)
$1 million payable in 100 years if the interest rate is 15 per cent per annum.
Compound interest [LO 1]
Neeta Stoves Ltd borrows $8 00 0 repayable in a lump sum after 1 year. The interest rate agreed to is
described as ' 15.0 per cent per annum, calculated monthly’. How much is the repayment?
Implied compound interest rate [LO 1]
What is the annual interest rate (compound) implied by each of the following future values (FV), present values
(PV) and terms (/):
a) FV = $9 20 00; PV = $8 20 00; f = 2 years
b) FV = $1 6 0 4 6 0 0 ; PV = $1 50 0 0 0 0 ; f= 4 years
c) FV = $ 2 0 0 0 0 0 0 ; PV = $ 1 3 0 7 6 0 0 ; t = 3 years
d) FV = $ 1 0 0 0 0 0 0 0 ; PV = $ 6 0 0 0 0 0 0 ; t = 6 years
e) FV = $ 1 0 0 0 0 0 0 0 ; PV = $ 6 0 0 0 0 0 0 ; f = 5.5 years?
Effective annual interest rate [LO 1]
What is the effective annual interest rate corresponding to each of the following nominal interest rates:
a) 18 per cent per annum, payable half-yearly
b) 18 per cent per annum, payable monthly
c) 18 per cent per annum, payable fortnightly
d) 1 8 per cent per annum, payable daily
e) 18 per cent per annum, payable continuously?
C hapter THREE T he TIME VALUE 〇F MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
Effective annual interest rate [LO 1]
What is the effective annual interest rate corresponding to each of the following nominal interest rates:
a) 7.5 per cent per annum, payable half-yearly
b) 7.5 per cent per annum, payable monthly
c) 7.5 per cent per annum, payable fortnightly
d) 7.5 per cent per annum, payable daily
e) 7.5 per cent per annum, payable continuously?
19
Effective annual interest rate [LO 1]
Jerm Ltd buys a bank bill for $91 107 and sells it 5 4 days later for $93 323. What annual effective interest
rate did Jerm Ltd earn?
20
Simple interest and effective annual interest rate [LO 1]
Liana Ltd bought a bank bill on 7 January 2012 for $976 751 and sold it on 3 March 2012 for $98761 8.
a) What simple interest rate did Liana Ltd earn?
b) What annual effective interest rate did Liana Ltd earn?
21
Calculating the effective annual interest rate [LO 1]
On 16 January 201 2, an investor lent a sum of money to be repaid, with interest, on 1 1 March 2012. The
interest rate was 6.15 per cent and was quoted on a simple interest basis. What effective annual interest rate
did the investor earn?
22
CHAPTER THUEE REVIEW
18
Effective annual interest rate (harder) [LO 1]
Rock Solid Ltd sells, on credit, goods to the value of $8465.95 to University Garden Supplies Ltd. Rock Solid
offers a discount of half of 1 per cent for payment within 7 days; otherwise, payment must be made on or
before the thirtieth day. What is the effective annual interest rate implicit in the discount being offered? State
any assumptions you make.
23
Effective annual interest rate (harder) [LO 1]
Since 1 August 201 2, W ing Yin's investment policy has been to lodge fixed (term) deposits at her local bank.
The bank pays interest on the maturity date of a deposit and the interest rate is expressed as an annual simple
interest rate. When a deposit matures, W ing Yin's policy is to re-lodge the whole sum (principal and interest)
immediately for a further period. She chooses the term of each deposit according to her assessment of the
interest rates available at that time. W ing Yin's decisions to date are as follows:
Date
Decision
1 August 2012
8-month deposit at 9.15 per cent per annum
1 April 2013
6-month deposit at 8.45 per cent per annum
1 October 2013
10-month deposit at 8.16 per cent per annum
Calculate, as at 1 August 2014, the effective annual interest rate W ing Yin has earned since she began this
policy. (Assume that all months are of equal length.) Briefly explain each step.
24
Nominal interest rate [LO 1]
A retail chain operates its own credit provision system for customers. Company policy is to set a nominal
annual interest rate, and to charge interest monthly. To cover its costs and make a return on capital, the
company has a target effective interest rate of 19.5 per cent per annum. What nominal annual interest rate
should it set?
25
Nominal interest rate [LO 1]
If the real interest rate is 10 per cent per annum, and the expected inflation rate is 25 per cent per annum,
what should be the nominal interest rate?
26
Nominal interest rate (harder) [LO 1]
George is intending to lend money to his nephew to help him set up a new business. The loan will be
made now, and is to be repaid in a lump sum after 3 years. George wishes to earn a real interest rate of
3.5 per cent per annum. He expects the inflation rate in the coming year to be 10 per cent but believes that it
will fall steadily thereafter to 6 per cent in the following year and to 4 per cent in the third year. What annual
interest rate should George set on the loan?
69
27
Nominal interest rate (harder) [LO 1]
Grose Paterson Bank Ltd is intending to lend money to a client. The loan is to be repaid in a lump sum after 7
years. The bank's required real rate of return is 3 per cent per annum. The bank expects the inflation rate in
the coming year to be 8 per cent per annum, falling to 5 per cent per annum the following year and 4 per cent
per annum thereafter. What annual interest rate should the bank set?
28
Real annual rate of return [LO 1]
In Xanadu, the consumer price index (CPI) stood at 147.6 on 1 January 2010. O n that date, SBF Ltd invested
$ 5 0 0 0 0 for 4 years at an interest rate of 11.4 per cent per annum (compound). On 1 January 2 0 14 the CPI
stood at 193.8. What real annual rate of return has SBF earned?
29
Log price relative [LO 1]
An investor purchases 1000 shares at $5.50 per share on 31 M ay 2014. Over the next 6 months the investor
notes down the price of the share at the end of each month. The result is shown below:
End o f June
$5.85
End of July
$6.12
End o f August
$5.75
End o f September
$5.75
End o f October
$6.44
End of November
$6.60
There were no dividends paid in this period. Calculate, for each month, the log price relative, using
natural (base e) logarithms. What does the sum of the log price relatives represent? Compare this sum to
^n($6.60/$5.50). Explain.
30
Average annual rate of return [LO 1]
Matthew bought an apartment for $3 64 000 . After 4 years he estimates that its value has changed as follows:
In Year 1: an increase of 7 per cent
In Year 2: an increase of 2 7 per cent
In Year 3: a decrease of 5 per cent
In Year 4: an increase of 1 1 per cent.
How much is it worth now? What is the average annual rate of return?
31
Present value [LO 1]
What is the present value (at 7 per cent per annum) of a contract that provides for the following three
payments to be made:
After 6 months: $7601
After 2.5 years: $9900
After 7 years: $1 8 5 2 2 ?
32
Present and future values [LO 1]
A company is entitled to receive a cash inflow of $8 00 0 in 2 years7 time and a further cash inflow of $ 1 4 0 0 0
in 5 years' time. If the interest rate is 8.5 per cent per annum, how much is this stream of cash inflows worth:
a) today
b) in 5 years7 time.
33
Internal rate of return [LO 1]
An investment costs $ 5 0 0 0 0 and generates cash inflows of $ 4 0 0 0 0 after 1 year and $ 3 0 0 0 0 after 2 years.
Show that the internal rate of return on this investment is approximately 27.2 per cent per annum.
34
Valuation of cash flows at any date [LO 2]
A contract will produce cash inflows on 4 different dates. These cash inflows are: $1 0 0 0 after 1 year, $8000
after 3 years, $ 1 2 0 0 0 after 7 years and $ 1 0 0 0 0 after 10 years. The required rate of return is 8.5 per cent
per annum.
a) Calculate the present value.
b) Calculate the value as at the start of Year 1.
C hapter three T he
time value of m o n e y : a n introduction to finan c ial mathematics
d) Calculate the value as at the start of Year 7.
e) Calculate the terminal value.
f) What is the relationship between these successive valuations?
35
Valuing different types of annuity [LO 3]
Consider an annuity of 6 cash flows of $5 00 0 payable annually. If the interest rate is 7 per cent per annum,
what is the value of this annuity today if the first cash flow is to be paid:
a) immediately
b) in 1 year’s time
c) in 4 years' time?
36
Annuities [LO 3]
Today is Stanley's 55th birthday. He plans to retire on his 65th birthday and wants to put aside the same sum
of money every birthday (starting today) up to and including his 65th birthday. He then wants to be able to
withdraw $ 1 0 0 0 0 every birthday (starting with his 66th) up to and including his 85th birthday. He believes
that an interest rate of 10 per cent per annum is a reasonable estimate. How much does he need to put aside
each birthday?
37
O rdinary perpetuities [LO 3]
How much money would be needed to establish a permanent scholarship paying $1 00 0 at the end of each
year, if money can be invested at 8 per cent per annum?
38
CHAPTER THREE REVIEW
c) Calculate the value as at the start of Year 3.
O rdinary perpetuities (harder) [LO 3]
Kevin Oldfellow attended Unicorn High School in the 1960s. After leaving school, Kevin established an
advertising agency that proved to be highly successful. Kevin is now very wealthy and wishes to establish a
fund that will provide a perpetual scholarship scheme to support students at Unicorn High. At the initiation
of the scheme Kevin will award six scholarships— one each to students currently in Years 7 to 12 inclusive.
These students keep these scholarships until they leave the school. In subsequent years, one scholarship will be
awarded every year to a student entering the school at Year 7 and that student keeps the scholarship through
to Year 12. Kevin has sought advice from the school and has been told that it costs about $6 00 0 to keep a
student at Unicorn High for 1 year.
The current long-term nominal interest rate is 6 per cent per annum. The long-term real interest rate is
estimated to be 2.5 per cent per annum. Kevin has been advised that it will cost him $ 6 3 6 0 0 0 to set up the
scheme. However, Kevin is not convinced, arguing that, 'The current inflation rate is about 3.5 per cent per
annum. If this continues then it won't be long before the real value of a scholarship will not be enough to keep
a student at the school for a year. Surely this has to be factored into the calculation somehow'. Kevin has
approached you for advice.
a) What is the logic behind the advice that a fund of $ 6 3 6 0 0 0 would be sufficient? Show your calculations.
b) Suppose that for the next 5 years the annual inflation rate continues to be 3.5 per cent and the annual
interest rate continues to be 6 per cent. What will be the real value of an annual scholarship payment after
5 years?
c) What amount would you advise Kevin to put into the scholarship fund? Explain.
d) Assuming that the forecasts in (b) are correct, show how the amount in the fund and the amount of each
scholarship would evolve over the first 2 years.
39
Deferred perpetuities [LO 3]
A pine plantation returns nothing to its owner in the first 2 years. In the following 2 years, the returns are
$ 1 0 0 0 0 0 and $1 50 000 , respectively, and after that the return is $ 2 0 0 0 0 0 per year in perpetuity. All returns
are in cash and occur at year end.
a) What is the present value of the constant return stream at the beginning of the fifth year if the returns can be
invested at 8 per cent per annum?
b) What is the current present value of the whole return stream at the same required rate of return?
40
Deferred perpetuities [LO 3]
What is the present value of a perpetual cash inflow of $1 00 0 received at the end of each year, the first inflow
occurring 2 years from now, if the interest rate is 5 per cent per annum? This cash flow can be produced by
investing $ 1 0 0 0 0 in a business this year and $6 00 0 next year. What is the present value of the investment?
Is it profitable?
71
B usiness finance
41
Calculating principal and interest repayments [LO 4]
Luke borrows $ 8 0 0 0 0 0 from a bank to set up a medical practice. He agrees to pay a fixed interest rate of
10.2 per cent per annum (calculated monthly) and to repay by equal monthly instalments over 10 years.
Calculate the monthly repayment. By how much does Luke's first repayment reduce the principal? If the loan is
paid off as planned, by how much will the lost repayment reduce the principal?
42
Calculating principal outstanding [LO 4]
After making 21 monthly repayments, Luke (see Problem 41) inherits a large sum of money and decides to
repay the (remaining) loan. When the twenty-second repayment is due he asks for the payout figure. How
much should it be?
43
Calculating the loan term [LO 4]
John decides that he desperately needs a new Italian suit priced at $1999. He borrows the money and agrees
to pay $71.07 each month at an interest rate of 16.8 per cent per annum, payable monthly. For how long will
he be making repayments?
44
Annual rate of return [LO 4]
What is the approximate annual rate of return on an investment with an initial cash outlay of $ 1 0 0 0 0 and net
cash inflows of $2 77 0 per year for 5 years?
45
Nom inal interest rate and effective interest rate [LO 4 】
Warren Cameron buys a boat for $30000, paying $5 00 0 deposit. The remainder is borrowed from the
Goodfriend Loan Co. to be repaid by 15 monthly payments of $2027.50 each. What is the monthly interest
rate being charged? What is the nominal annual interest rate? What is the effective annual interest rate?
46
Calculating the loan term [LO 4 】
Anne Hopewell has just borrowed $ 7 0 0 0 0 to be repaid by monthly repayments over 20 years at an interest
rate of 18 per cent per annum. Based on this information, the monthly repayment is approximately $1 08 0 but
Anne intends to make higher monthly repayments. She asks you how long it will take to repay the loan if the
amount she pays per month is:
a) $1100
b) $1200
c) $1500.
47
Annuities [LO 4]
Layla borrows $5 00 00, repayable in monthly instalments over 10 years. The nominal interest rate is
12 per cent per annum. What is the monthly repayment? After 3 years have passed, the lender increases
the interest rate to 13.5 per cent per annum and Layla is given the choice of either increasing the monthly
repayment or extending the term of the loan. What would be the new monthly repayment? What would be
the new loan term?
48
Annuities [LO 4]
Exactly a year ago, Stephen and Lan Kuan borrowed $ 1 5 0 0 0 0 from a bank, to be repaid in equal monthly
instalments over 25 years at an interest rate of 7.8 per cent per annum. Today, the bank told them that it was
introducing a monthly fee of $10 but they could continue to repay the loan by making their current monthly
payments. However, Stephen and Lan Kuan are worried because if they do this, the loan will take longer to
repay. They have asked you to calculate how much longer it will take to repay the loan.
49
Effective annual interest rate, repayments and loan terms [LO 4 】
Don and Jenny wish to borrow $180000, to be repaid over a period of 20 years by monthly instalments.
The interest rate (nominal) is 7.8 per cent per annum. The first payment is due at the end of the first month.
a) Calculate the effective annual interest rate.
b) Calculate the amount of the monthly repayment if the same amount is to be repaid every month for the
period of the loan.
c) Suppose, instead, that the lender agrees that Don and Jenny will repay $1 10 0 per month for the first 12
months, then $ 1 2 5 0 per month for 出e 12 months after that, then $X per month thereafter. Assuming that
the term is to stay at 20 years, how much is $X?
d) Alternatively, suppose that Don and Jenny decide to repay $2 50 0 per month from the time the money is
borrowed until it is repaid. How long would it take to repay the loan? What would be the amount of the
final payment?
72
C hapter THREE T he TIME VALUE 〇F MONEY: AN INTRODUCTION TO FINANCIAL MATHEMATICS
Repayments and loan terms [LO 4 】
Peter borrowed $ 8 0 0 0 0 0 to refit his fishing trawler. The loan requires monthly repayments over 15 years.
When he borrowed the money the interest rate was 13.5 per cent per annum, but 18 months later the bank
increased the interest rate to 15.0 per cent per annum, in line with market rates. The bank tells Peter he can
increase his monthly repayment (so as to pay off the loan by the originally agreed date) or he can extend the
term of the loan (and keep making the same monthly repayment). Calculate:
a) the new monthly repayment if Peter accepts the first option
b) the extra period added to the loan term if Peter accepts the second option.
51
Calculating repayments [LO 4]
Wahroonga Furniture Ltd (WFL) is planning a large sale of its stock of lounge suites and dining tables. As part
of its marketing, WFL will offer customers loans of up to $1 00 00, with no repayment required during the first
6 months. The customer then makes equal monthly repayments. The total loan term (including the first 6 months)
is 2 years. The effective interest rate that WFL requires on the loans is 12 per cent per annum. What monthly
repayment must WFL charge on a loan of $ 1 0 0 0 0 ?
52
Simple and general annuities [LO 5]
A simple annuity of $ 3 00 per quarter is to be replaced by annual payments (the payments to be made at the
end of each year). What will be the annual payments if the nominal interest rate is 6 per cent per annum?
CHAPTER THREE REVIEW
50
REFERENCES
Crapp, H. & Marshall, J., Money Market Maths, Allen &
Unwin, Sydney, 1986.
M artin, P. & Burrow, M ., Applied Financial Mathematics,
Prentice-Hall, Sydney, 1991.
Knox, DM., Zima, P. & Brown, R.L., Mathematics of Finance,
2nd edn, M cG raw-H ill, Sydney, 1999.
73
CHAPTER FOUR
Applying the time
value of money
.
to security
.
valuation
CHAPTER CONTENTS
ED
Introduction
75
Financial asset valuation under certainty
75
Valuation of shares
76
HH
Valuation of debt securities
80
BH
Interest rate risk
81
m
m
The term structure of interest rates
82
EB
The default-risk structure of interest rates
89
BE1
Other factors affecting interest rate structures
91
Appendix 4.1 Duration and immunisation
97
LEARNING OBJECTIVES
After studying this chapter you should be able to:
命
1
understand how assets are valued under conditions of certainty
2
use the tools of financial mathematics to value equity securities
3
explain the main differences between the valuation of ordinary shares based on dividends and on
Gamings
4
use the tools of financial mathematics to value debt securities
5
explain the nature of interest rate risk
6
understand the theories that are used to explain the term structure of interest rates
7
understand the effect of default risk on interest rates
8
apply the concept of duration to immunise a bond investment.
C hapter four A pplying
the time value of m o n e y to security valuation
In Chapter 1 we discussed b riefly the im p o rta n t concept o f the tim e value o f money. In Chapter 3 we
presented some mathematical tools useful in analysing problems involving the tim e value o f money.
In particular, we showed how promised streams o f future cash flows can be valued, provided th a t the
required rate o f retu rn is known.
In this chapter we apply these tools to the valuation o f debt and equity securities. In itia lly we
assume th a t the security s fu tu re cash flows are know n w ith certainty. Later in the chapter we introduce
uncertainty, b ut only in a lim ite d way. A more form al and detailed treatm ent o f u ncertainty is given in
Chapter 6.
4.2
Financial asset valuation under certainty 1
The benefits o f owning an asset are the present and future consumption opportunities attributable to
it. For a financial asset, these benefits are in the form o f cash. For example, an investor who holds a
government bond u n til m a tu rity receives cash in the form o f interest payments during the bonds life
and, at m aturity, in the fo rm o f the payment o f the face value. In the case o f shares, the investor receives
cash in the form o f dividends and, on sale o f the shares, in the form o f the price obtained fo r the shares.
A decision to buy an asset implies a simultaneous decision to forgo current consumption. It is assumed
that, at any time, investors prefer more consumption to less consumption, other things being equal.
Application o f this principle between tw o points in tim e implies that, other things being equal, earlier
cash inflows are preferred to later cash inflows. As explained in Chapter 3, these observations may be
summarised by the phrase ‘money has a tim e value’.
To review this principle, suppose th a t a person is given the choice o f receiving $100 now or $100 in
1 years time. A rational person w ill always choose to receive the cash immediately, even i f there is no
desire to consume immediately. The reason, o f course, is th a t the earlier cash flow can be invested. This
w ill enable even greater consum ption later. I f the interest rate is 12 per cent per annum, the investor
(consumer) in this example can invest fo r 1 year the immediate cash flow o f $100, and at the end o f
the year have $112 available fo r consumption. Clearly $112 o f consum ption is preferable to $100 o f
consumption. In this example the cash flows were, in effect, a g ift. Suppose, however, th a t the investor
is offered the chance to buy the rig h t to receive $100 in 1 years tim e. W hat is the m axim um price the
investor should offer fo r th is right? We have just seen th a t $100 is ‘w o rth ’ $100 x 1.12 = $112 in 1 year’s
time. The rig h t to receive $100 in 1 years tim e is therefore w o rth at present:
=
LEARNING
OBJECTIVE 1
Understand how
assets are valued
under conditions of
certainty
$100
1.12
$89.29
The am ount $89.29 is referred to as the present value o f $100 to be received in 1 years tim e i f the
discount rate is 12 per cent per annum. Therefore, the interest rate has tw o functions: it is the rate at
which present sums can be converted to equivalent future sums, and i t is also the rate at which promised
future sums can be converted to equivalent present values. Therefore the value o f a financial asset is
not simply the sum o f the cash th a t it generates in future periods. For example, a financial asset that
generates returns o f $100 at the end o f each o f the next 5 years is n o t w o rth $500 today. I t is n o t valid
to add together cash flows th a t occur at different times. However, adding together present values is valid
because each value relates to the same tim e, the present.
Where there are many cash flows from the same asset, the present value o f the asset is the sum o f the
present values o f every future cash flow. The present value o f the asset is calculated using the relevant
interest rate. I f the cash flows are certain to occur, as we assume here, then the relevant interest rate is
the risk-free interest rate, Tr. Thus:
P〇 =
1
1+
7 + —(l +^ rf—2)2 + . . . +
—
^
(1 + rf)n
In this section we review some of the results explained in Chapter 3. Readers familiar with this material may safely omit this
section.
令
A
B usiness finance
or
p〇 = t ^
ED
y
where
P〇 = present value o f the asset
Ct = dollar return (cash flow) at tim e t
n = term o f the investm ent
= risk-free interest rate per tim e period
t = 1, 2,
n
Suppose th a t an asset returns $100 per annum fo r 5 years and th a t an investor requires an annual
interest rate o f 3.6 per cent as compensation fo r forgoing current consumption. Substituting in
Equation 4.1 we find that:
$100
$100
$100
$100
$100
1 + 0.036
(1 + 0 .0 3 6 ) 2
(1 + 0.036”
（1 + 0 .0 36)4
(1 -f 0 .0 3 6 )5
n
= $ 9 6 ,5 2 5 + $93,171 + $89,933 + $86,808 + $83,792
= $ 4 5 0 ,2 2 9
Therefore, this investor would be prepared to pay $450.23 fo r the asset. In summary, a financial asset
is valued in a w orld o f certainty by discounting the known future cash flows at the risk-free interest rate,
thus compensating investors fo r th e ir preference fo r current consumption.
4.3
LEARNING
OBJECTIVE 2
Use the tools of
financial mathematics
to value equity
securities
4.3.1 [V aluation of shares assuming certainty
I f future cash flows are known w ith certainty, Equation 4.1 can be used to value shares.2 The periodic
cash flows from an investm ent in shares are called dividends. Unless liqu id atio n o f the company is
contemplated, the dividends are assumed to continue indefinitely. Therefore, Equation 4.1 may be
rew ritten as:
DIVIDENDS
periodic distributions,
usually in cash, by
a company to its
shareholders
Valuation of shares
D,
p 〇
= J2
4.2
(1 + rf Y
where D t = dividend per share in period t
The appropriate discount rate remains the risk-free interest rate, because under conditions o f certainty
investors require the same rate o f return on all assets.
I t m ig h t appear th a t Equation 4.2 ignores a second potential source o f retu rn from an investm ent in
shares— th a t is, the capital gain from selling the shares at a price greater than the price at which they were
purchased. This impression is incorrect. Suppose th a t an individual purchases shares w ith the inte n tio n
o f selling them in 5 years* time. Equation 4.2 may be expanded as follows:
Dt
p〇 = E
r=l (1 + rf )[
Ps
(1 + r /)5
4.3
where P5 = share price at the end o f the fifth year
The capital gain (or loss) is the difference between P5 and P〇
. The price o f the shares when they are sold
is the discounted value o f all future dividends from Year 6:
〇〇
作
2
令
= Z
Dt
t=6 (1 + r/ 广 5
4.4
The discussion that follows is directed towards the valuation of ordinary shares. Preference shares are another form of
equity capital. The valuation of preference shares is discussed in Chapter 14 and the distinction between ordinary shares and
preference shares is discussed in detail in Section 10.7.2.
C hapter four A
pplying the time value of m o n e y to security valuation
+
I
I
-
E
5 3E
W
x
Substituting Equation 4.4 in to Equation 4.3:
5
(
D/
-f/
+/
which is Equation 4.2.
Therefore, where a company is assumed to have an in fin ite life, the current m arket price o f its shares
can be expressed as the present value o f an in fin ite stream o f dividends. Even in a m arket where investors
are seeking capital gains, the valuation form ula remains the same.
4 .3 .2 1 Valuation of shares under uncertainty
Valuing a security under uncertainty is d iffic u lt and, in general, few ( if any) people can consistently expect
to reach a better valuation than that given by the current m arket price. This statement is discussed fu lly
in Chapter 16. However, the statement is unhelpful i f the company is n ot traded on a stock exchange,
because there is then no current m arket price to observe. Moreover, to say th a t the best estimate o f a
shares ^true* value is its current m arket price provides no insight in to the factors th a t give a share its
value. In this section, some o f the fundam ental factors determ ining a share s value are considered.
Where there is uncertainty, investors require compensation in the form o f a higher promised rate of
return. Equation 4.2 becomes:
p 〇= H
g (D ')
(i +
where E(Dt ) = expected dividend per share in period t
ke = required rate o f return on the shares
The appropriate value o f ke is determ ined using the concept o f the o p p o rtu n ity cost o f capital.
The ‘true ’ or economic cost o f investing in a particular security is the retu rn forgone on the next best
alternative. For a risky security, this return is greater than the return on the risk-free security (r^). In
short, ke > r,. The am ount by which ke exceeds r^is often referred to as the security s risk premium.
Further, the riskier the security being considered, the higher the risk premium w ill be and the higher
ke w ill be. D eterm ination o f exactly how much higher ke should be requires a measurement o f risk* and a
theory lin kin g th a t measure to required rates o f return. These theories are developed in Chapter 7.
A t this p o in t we assume th a t all investors reach the same assessment o f risk, and therefore apply the
same o p p ortu nity cost o f capital (discount rate) to the same expected dividend stream, therefore a rriving
at the same price fo r the company s shares. It may seem unrealistic to assume th a t everyone has the same
expectations. However, at the tim e o f making a financial decision, it may be reasonable fo r the company s
management to assume th a t its assessment o f the likely impact o f th a t decision on the company s share
price w ill prove to be correct. I f this is so, then management should act as i f it is realistic to assume that
everyone has the same expectations.
The simplest assumption to make when estim ating a share s value is th a t the company w ill m aintain
in perpetuity the current dividend per share, D 〇
. In this case the estimate is:3
P〇
A)
ke
The use o f Equation 4.6 is shown in Example 4.1.
3
This formula treats the dividends as an ordinary perpetuity. For further details, see Section 3.6.
♦
B usiness finance
Example 4.1
Rankine Ltd is currently paying a dividend of 90 cents per share. If investors expect this dividend
to be maintained and require a rate of return of 15 per cent on the investment, what is the value of
Rankine's shares?
SOLUTION
The value of Rankine's shares is calculated as follows:
$0.90
0.15
$ 6.00
G rowth in dividends
I t is usually more realistic to assume th a t a company s dividend per share w ill change. For example, it may
be assumed th a t the dividend per share w ill grow at a constant rate. In this case, the estimated value is:
p 〇
= J2
Q〇( l + g ) f
(1 + ke)1
where g = expected grow th rate in dividend per share
Where k e is greater thang and the grow th in dividends is assumed to continue indefinitely, Equation 4.7
can be w ritte n as:4
A ) ( l+ g )
P〇
k e -g
One approach to estim ating g is to calculate the past grow th rate in dividend per share and use this as
the estimate o f the expected grow th rate. This is shown in Example 4.2.
Example 4 .：
Assume that for the past 10 years the growth rate in Rankine Ltd's dividend per share has been 10 per cent
per annum. Assume further that this growth rate is expected to be maintained indefinitely. The latest
dividend per share was 90 cents and was paid yesterday. What is the value of Rankine's shares?
SOLUTION
Using Equation 4.8, the value of Rankine’s shares is:
D〇
(l+ g )
P〇 -
k e -g
$0.90 x 1.1
0 .1 5 -0 .1 0
$19.80
4
The terms in Equation 4.7 form an infinite geometric series, with a common factor (or ratio) between each term of,
-8 . Provided that - 1 < + 8
• there will be a limiting sum equal to the first term of the series, divided by
1 ke
\
ke
(1 - the common ratio). That is:
P
〇 \ ke
、
1 K}
D〇(l + g )
k e-g
1 + kt>
A)(l +g)
ke-g
■+ ke
If ke < g , the model breaks down. Under these circumstances: -
命
■ke
>
1 and there is no limiting sum (P0
).
〇〇
C hapter four A pplying
the time value of m o n e y to security valuation
A second approach to estim ating g is to assume th a t the grow th in dividend per share is related to
the company s retained earnings and to the rate o f retu rn on those earnings. I f the company retains a
constant p roportion b o f its earnings each year and reinvests those earnings at a constant rate r, then
g = hr, and Equation 4.8 can be rew ritten:
If Rankine Ltd retains 4 0 per cent of its earnings each year (jb = 0.4), and these earnings are reinvested
to earn a 25 per cent rate of return (r = 0.25), what is the value of Rankine's shares?
SOLUTION
The value of Rankine’s shares, using Equation 4.9, is as follows:
p _ $0.90 x [1 + (0.4 x 0.25)]
0
一 ^ 0 . 1 5 - ( 0 . 4 x 0.25)^
=$19.80
The assumption th a t the past grow th rate is expected to be m aintained indefinitely is unlikely to be
realistic, particularly where the company has been experiencing a relatively high growth rate. We m ight
therefore assume th a t the current grow th rate w ill be m aintained fo r several years before falling to a level
expected to be sustained indefinitely. This is shown in Example 4.4.
Example 4.4
Assume that the growth rate will remain at its current level of 10 per cent per annum (gf^ for only
a further 3 years, and is then expected to fall to 6 per cent per annum (g) and remain at that level
indefinitely. W hat is the share price today?
SOLUTION
This complication is easily handled by first using Equation 4.8 to estimate the value of the shares as at
the end of the third year. The value of the shares today is given by the present value of this estimate,
plus the present value of the dividends to be paid in the first 3 years. The value of Rankine's shares is
calculated as follows:
p
0
D〇
l i + g ,) , P〇
(i ^ g ') 2 , Poll + g ,)3 ,
(i + M
(i + M
_ $ 0 .9 0 X 1.10
1.15
2
(l + M
$ 0 .9 0 X (1.10)2
+
(1.15)2
+
3
1 _ :: P 〇
( i + g 'l 3(i+ g l
(l + M
3
(b-gl
$ 0 .9 0 x (1.10 )3
1
$ 0 .9 0 x (1.10)3 x (1.06)
(1.15 )3
+ (1.15)3 X
(0 .1 5 -0 .0 6 )
= $ 1 1 .7 5
Comparing the previous tw o examples, the reduction in the expected dividend grow th rate after Year 3
has resulted in a reduction in the value o f the shares from $19.80 to $11.75. This highlights the sensitivity
o f the share value to estimates o f the future grow th rate in dividend per share.
The formulae used to estimate a share value may also be used to estimate the required rate o f retu rn on
a company s shares, given th e ir current m arket price. This application is discussed fu rth e r in Chapter 14.
4 .3 .3 | Share valuation and the price-earnings ratio
The ratio o f a company s share price to its earnings per share— th a t is, its price-earnings ratio _ is often
used by security analysts to estimate the value o f the company s shares.5 To illustrate this m ethod o f
5
m
LEARNING
OBJECTIVE 3
Explain the main
differences between
the valuation of
ordinary shares based
on dividends and on
earnings
A discussion of the use of the price-earnings ratio to value shares is contained in most texts on investments. See, for example,
Brailsford, Heaney and Bilson (2011, pp. 386-93) and Bodie, Kane and Marcus (2011, pp. 601-9).
命
B usiness finance
valuation, we again use the example o f Rankine Ltd, and assume th a t Rankines current earnings per
share is $2.25. Assume also th a t an analyst estimates th a t the appropriate price-earnings ratio fo r the
company is 9.0. Therefore, the value o f each share is estimated at $20.25— th a t is, $2.25 x 9.0. This
estimate would then be compared w ith the current market price to determine whether the shares are
overvalued or undervalued.
However, this leaves unanswered the question: How does an analyst estimate the appropriate priceearnings ratio? In m ost cases where analysts use this m ethod o f valuation, the appropriate price-earnings
ratio is determ ined in a way th a t can best be described as judgm ental— th a t is, no form al model is used
b ut the analyst tries to take into account the factors considered to be relevant.
Two im p o rta n t factors are risk and grow th opportunities. The riskier the analyst believes the
investm ent to be, the lower the appropriate price-earnings ratio. To see this, imagine th a t an analyst is
try in g to value two companies th a t are equivalent in all respects, including th e ir current and expected
earnings, except th a t one company is riskier than the other. Because investors dislike risk, other things
being equal, the company th a t is riskier w ill be less attractive to investors and w ill thus have a lower value.
Since both companies have the same earnings, the ratio o f price to earnings w ill be lower fo r the riskier
company.
The other im p o rta n t factor is grow th opportunities. I f an analyst believes a company has substantial
opportunities fo r growth, a high price-earnings ratio w ill be assigned. In this case the current earnings
level is likely to be surpassed in the future, thereby ju stifyin g a price today th a t appears ‘h igh’ relative to
current earnings. O ther factors likely to be considered include the price-earnings ratios o f companies in
the same industry, and prospects fo r the ind ustry and the economy as a whole.
4.4
LEARNING
OBJECTIVE 4
Use the tools of
financial mathematics
to value debt securities
As we saw in Section 4.3, the returns on an investm ent in shares are dividends and capital gains. In the
case o f an investm ent in debt securities (frequently called bonds or debentures), the returns are usually
in the fo rm o f interest payments and the repayment o f the face value or principal on the m a tu rity date.
As has been explained fo r shares, i f all securities offer certain returns, each security s o p p o rtu n ity cost o f
capital is the risk-free interest rate (or yield) r^. Therefore, i f future cash flows are know n w ith certainty,
rf \s the appropriate discount rate to apply. Equation 4.1 is rew ritten fo r bonds as follows:
n
deben tu res)
d e b t s e c u ritie s issued
w ith a m e d iu m o r lo n g
te rm to m a tu rity
COUPONS
fix e d in te re s t p a y m e n ts
m ade on bonds a nd
d e b e n tu re s
Valuation of debt securities
F
Q
P〇 == E
t=\ (1 + rf y
(1 + rf )n
interest payment (often called coupon payment or just coupon) at tim e i
F = face value (principal repayment) at m aturity, which is date n
n = num ber o f periods to m a tu rity
risk-free interest rate (yield)
rf =
The use o
where
Example 4.5
Suppose that Rankine Ltd borrows by issuing 3-year bonds with a face value of $100, and a coupon
interest rate of 10 per cent. The cash flows to a bond holder will be interest (/coupon,) payments of
$ 1 0 per year for 3 years, followed by payment of $ 1 0 0 at the end of the third year. If the required
rate of return is also 10 per cent per year, what is the value of Rankine’s bonds?
SOLUTION
The value of the bonds is given by Equation 4.10:
D
0
$10
$10
$10
$100
1.1
( l. l) 2
( l. l) 3
( l. l) 3
=$9.091 +$8.26 4+ $7.513+ $75.131
= $
100.00
C hapter four A
pplying the time value of m o n e y to security valuation
Once a bond has been issued— th a t is, sold by the borrower to the lender— its promised future cash
flows are fixed. Ownership o f the bond entitles the owner to receive from the issuer a fixed schedule
o f future cash flows. I f the m arket interest rate changes, it w ill affect the attractiveness o f the bond to
potential investors. I f m arket interest rates decrease, the bond w ill become more attractive; i f m arket
interest rates increase, the bond w ill become less attractive. O f course, this w ill cause bond prices to
change. A decrease (increase) in m arket interest rates w ill cause an increase (decrease) in the prices of
existing bonds. This is illustrated in Example 4.6.
Example 4.6
Suppose that immediately after Rankine's debt contract is agreed, conditions in the debt market
change and the required rate of return falls to 8 per cent per annum. Rankine must still make interest
payments of $1 0 each year, but investors now require a return of 8 per cent per annum. W hat is the
value of Rankine’s bonds now?
SOLUTION
Again applying Equation 4.10, the security is now valued more highly, as follows:6
$10
$10
^
$10
(
$100
0 = h O S + (1.08 )2 + (1 .0 8 )3 + (1.08)3
= $ 1 0 5 ,1 5 4
Similarly, if the required rate of return had risen from 10 per cent to 12 per cent, the price would
have fallen as follows:
$10
$10
$10
$100
TTTi + (i.i2)2 + (1.12)3 + (i.i2)3
$ 9 5 .1 9 6
4.5
Interest rate risk
Example 4.6 shows th a t when interest rates change, so do bond prices. The possibility o f unforeseen price
changes means th a t a bond is risky— its future value is uncertain. Thus, even i f a bond is risk-free in the
sense th a t the borrower is certain to make the promised cash payments, it is risky in the sense th a t the
bond holder (lender) can suffer unforeseen losses i f interest rates increase.
When interest rates increase, bond prices fall. For the investor in bonds this is a capital loss, and
therefore in this respect the increase in interest rates is undesirable. A benefit m ust be set against that
loss: the interest receipts can be reinvested at the new, higher rate o f interest. The opposite occurs when
interest rates fall. Investors make capital gains b ut interest receipts can be reinvested only at the new
lower rate. These effects are know n as the price effect and the reinvestment effect and are always o f opposite
sign fo r a given change in m arket interest rate. The price effect and the reinvestm ent effect are both
sources o f interest rate risk. The net effect fo r the investor depends on the size o f the interest rate change
and on the period fo r which the bond is held. Appendix 4.1 outlines a m ethod th a t an investor may use to
obtain some protection against interest rate risk.
A t any given tim e, the m arket-determ ined interest rate (or yield) on a bond w ill depend on the features
o f that bond. Two features th a t are usually particularly im p o rta n t to m arket participants are the term o f
the security and the risk o f the borrower defaulting on the promised payments. The connection between
By convention, bonds in Australia are assumed to have a face value of $100, but in practice bond face values are much
higher—often in the millions o f dollars. Therefore, bond prices per $100 of face value are usually taken to more than two
decimal places. We follow the Australian convention and use three decimal places.
m
LEARNING
OBJECTIVE 5
Explain the nature of
interest rate risk
B usiness finance
Finance
in
ACTION
O N GUARD AGAINST A BOND FALL__________________________
In an article published in 2013, financial journalist Christopher Joye reminds readers of interest
rate risk, which flows from the connection between interest rates and bond prices.
TERM STRUCTURE OF
INTEREST RATES
relationship between
interest rates and term
to maturity for debt
securities in the same
risk class
Bond traders have been making out like bandits since the global financial crisis. A portfolio of
Australian government bonds with maturities longer than 10 years has delivered annual total
returns of over 12 per cent since December 20 07 .
Yet the preconditions for the mother-of-all bond market reckonings are sliding into place.
This contingency, which A M P ’s Shane Oliver believes is a 'significant risk’， could result in
wiping more than $ 6 0 billion off Aussie bond values, with steep capital losses.
To properly understand these risks, one needs to appreciate how extraordinary current
circumstances are. W hen doing so, it helps to keep in mind a key principle: bonds that pay
fixed, as opposed to variable, rates have prices that are inversely related to external interest
rates.
If you invested in a bond paying an annual fixed coupon of, say, 3 per cent, and market
interest rates surge to 5 per cent, that bond would be worth substantially less than when you
bought it. The converse is also true: if market rates decline ... it would be worth more.
This is why Australian government bond prices have soared since 20 07 : market yields
have fallen sharply as global central banks have floored policy rates close to zero and printed
unprecedented amounts of money to fund public and private debt.
Source: 7On guard against a bond fall', Christopher Joye, The Australian Financial Review, 5 January 2013, p. 39.
DEFAULT-RISK
STRUCTURE OF
INTEREST RATES
relationship between
default risk and
interest rates
term and interest rates is called the term stru ctu re o f in te re st rates, while the connection between
default risk and interest rates is called the d efau lt-risk stru ctu re of in te re st rates. These are now
considered.
4.6
LEARNING
OBJECTIVE 6
Understand the
theories that are used
to explain the term
structure of interest
rates
ZERO-COUPON BONDS
(zero s)
bonds that pay only
one cash flow, the
payment at maturity
The term structure of interest rates
4.6.1 | W h a t is the term structure?
To consider the effect o f a bonds term on its interest rate, all other factors need to be held constant.
Thus, to elim inate the effect o f differences in default risk, the term structure o f interest rates is usually
studied by focusing on government bonds since all such bonds have the same risk o f default (assumed to
be zero).
The least complicated measure o f the term structure o f interest rates is the m arket yield on a
government bond th a t pays no interest during its life, b ut pays a fixed sum at m aturity. Such a bond is
known as a zero-coupon bond (often abbreviated just to a zero).
The price o f a zero w ith a face value o f F dollars and a term o f n years is simply:
P〇= ( T ^ f
where zn is the yield on the zero, often known as the zero rate fo r a term o f n. The term structure o f
interest rates is the set o f zero rates zv z2, ... zn. In practice, except fo r terms o f 6 m onths or less, zerocoupon bonds are relatively rare. However, there are coupon-paying bonds and it is possible to estimate
the underlying zero rates from the prices o f coupon-paying bonds. The Reserve Bank o f Australia has
made such estimates fo r the Australian m arket. Four examples are shown in Figure 4.1.
As shown in Figure 4.1, the shape and level o f the term structure can vary w idely over tim e. For
example, i t may be steeply upward sloping, as i t was on 27 June 1994, or almost flat, as i t was on 19 July
2006, or gently downward sloping, as i t was on 27 November 2007.
G h APTER FOUR A
ure 4.1 The term structure
pplying
THE TIME VAUJE OF MONEY TO SECURITY VALUATION
Australia: various dates
12 . 00 %
—
10. 00 %
d
--------- 19-Jul-06
d
8 .00 %
oJ
a>
OJOZ
6 .00 %
P 0 !
D
如SE
4.00%
— 27-Jun-94
——— 27-Nov-07
一 广
......
7-Jan-09
LU
2 .00 %
0.00%
0.00
2.00
4.00
6.00
8.00
10.00
12.00
Term to maturity (years)
Source: Based on estimates available from the Reserve Bank of Australia website.
4 .6 .2 1 Using the term structure to price a bond
I f we know — or have estimated— the current term structure o f zero rates, in principle it is easy to calculate
the price o f any coupon-paying bond. This process is illustrated in Example 4.7. When we have the prices,
we can then calculate the corresponding yields. These calculations are shown in Example 4.8.
Example 4.7
Suppose that the face value of every bond is $ 100 and the current zero rates for terms of 1 ,2 and 3
years are 7 .0 , 8.0 and 8.5 per cent per annum respectively. W hat are the prices of: a 1-year bond
paying annual coupons of 5 per cent, a 2-year bond paying annual coupons of 9 per cent and a
3-year bond paying annual coupons of 7.5 per cent per annum?
SOLUTION
In a year's time, the 1-year bond will make a single payment of $105, consisting of $ 1 0 0 face value
and $5 of coupon interest. The required rate of return on a 1-year investment is 7.0 per cent per
annum. The price of the bond is therefore
D
$105
r = ------1.07
=$98.131
The 2-year bond will pay $9 after 1 year and $1 09 after 2 years. In effect, this coupon-paying
bond can be decomposed into two zero-coupon bonds. The first is a 1-year zero which pays $9 and
the second is a 2-year zero that pays $109. Because we know the 1-year and 2-year zero rates, we
know how to price these constituent zero-coupon bonds. The price of the 2-year bond is the sum of
the two constituents.
D
$9
$109
1.07
(1.0812
p = ------- +
*
=$101.861
Extending the same logic to the 3-year bond, its price is
P:
$ 7 .5 0
_______
$7.5 〇 + $ 1 〇7.5 〇
1.07 + (1.08)2
$97.602
(1.085)J
B usiness finance
Given the price o f a coupon-paying bond, its in te rn a l rate o f return, know n as the bonds yield, can be
calculated. For fu rth e r details, see Sections 3.5.4 and 5.4.2.
Example 4.8
What are the yields on the three bonds described in Example 4.7?
SOLUTION
For the 1-year bond, the yield is the value of r which solves the following equation:
$98,131 = $ 1 0 5 0 0
1+r
We know from the previous example that the solution to this equation is r = 7.0 per cent per annum.
For the 2-year bond, yield is the value of r which solves the following equation:
$101,861
l^
+ $10900
n + r|2
This equation is solved when r is approximately 7.957 per cent per annum.
For the 3-year bond, yield is the value of r which solves the following equation:
$ 9 7 ,6 0 2
$ 7 .5 0
$ 7 .5 0
$ 1 0 7 .5 0
1 + r + (1 + r ) 2 +
(1 + r)3
This equation is solved when r is approximately 8.438 per cent per annum.
Note that the 2-year and 3-year yields are close to, but not equal to, the corresponding zero rates.
YIELD CURVE
graph of yield to
maturity against bond
term at a given point
in time
The pattern o f yield against term is called the yield curve. Data fo r the Australian yield curve at 10
different dates are given in Table 4.1.
TABLE 4.1 Australian yield curve data
Term to maturity
Date of yield curve
3 months
6 months
2 years
5 years
10 years
June 1998
4.93
4.98
5.18
5.38
5.58
June 2000
5.87
5.96
5.89
6.05
6.16
June 2002
5.21
5.32
5.44
5.78
5.99
June 2004
5.61
5.65
5.34
5.67
5.87
June 2006
6.09
6.16
5.78
5.78
5.79
June 2008
7.81
8.04
6.97
6.69
6.59
June 2009
3.25
3.30
3.90
5.10
5.56
June 2010
4.89
5.01
4.57
4.97
5.33
June 2011
4.99
5.10
4.75
4.89
5.16
June 2012
3.49
3.41
2.40
2.49
3.00
Source: Compiled from Reserve Bank of Australia data (www.rba.gov.au). See tables Interest Rates and Yields— Money
Market and Capital Market Yields— Government Bonds. For 1998 and 2000 yields for 3(6) months are issue yields for
13-(26)-week Treasury notes. From 2002 to 201 2 these yields are yields for 90-(l 80)-day bank accepted bills. Yields for 2,
5 and 10 years are bond yields.
Like the closely related concept o f the term structure, yield curves can have a wide range o f shapes.
For example, the yield curve in Australia was upward sloping in June 2002 and June 2009 b ut m ostly
downward sloping in June 2012. Typical yield curve shapes are illustrated in Figure 4.2.
C hapter four A pplying
the time value of m o n e y to security valuation
Figure 4.2 Alternative yield curves
4 .6 .3 1 Term structure theories: expectations and liquidity (risk)
premium
Obviously the term structure at any given tim e is no accident. Presumably, participants in the debt
markets do n ot set the interest rate for, say, a term o f 2 years7 w ith o u t in some way considering the
1-year and 3-year interest rates. In other words, the interest rate fo r a particular term w ill be determ ined
by the m arket in the context o f interest rates fo r other terms. The exact id e n tity o f the factors th a t explain
the term structure is controversial, w ith different theories proposing different mechanisms. There is,
however, broad agreement th a t expectations o f the future course o f interest rates are central to explaining
the term structure.
The core o f the e x p e c ta tio n s th e o ry o f the term structure is th a t interest rates are set such that
investors can expect, on average, to achieve the same retu rn over any future period, regardless o f the term
o f the zero-coupon bond in which they invest. For example, suppose th a t in the current term structure
the interest rate fo r a 2-year term to m a tu rity is 8 per cent per annum, while the interest rate fo r a 3-year
term to m a tu rity is 9 per cent per annum. Suppose, fu rthe r, th a t $1000 is invested fo r 3 years. A fte r 3
years, the investor w ill have $1000 x (1.09)3 = $1295.03. Alternatively, suppose the same investor invests
$1000 fo r 2 years. A fte r 2 years, the investor w ill have $1000 x (1.08)2 = $1166.40. I f the investor can
re-lend this sum fo r the th ird year at an interest rate o f 11.028 per cent per annum, then at the end o f the
th ird year the investor w ill have $1166.40 x 1.11028 = $1295.03, which is the same as the retu rn from
the 3-year investm ent. This is shown in Figure 4.3.
Figure 4.3 Return from the 3-year investment
0
1
2
3 years
<<--------------------------------------------- 9% p . a . --------------------------------------------- >
< --------------8% p.a. -----------------------------1.028% p .a .----------------------------->
As shown in Figure 4.3, the current term structure is 8 per cent per annum fo r a term o f 2 years and
9 per cent per annum fo r a term o f 3 years. According to expectations theory, the factor th a t explains the
7
For ease of exposition, in this section we use the term interest rate for a term of n years* to mean the yield per annum on a
zero-coupon bond with a term o f n years.
EXPECTATIONS THEORY
of the term structure is
that interest rates are
set such that investors
in bonds or other
debt securities can
expect, on average,
to achieve the same
return over any future
period, regardless of
the security in which
they invest
B usiness finance
current term structure is the m arkets expectation th a t the 1-year interest rate on the day 2 years from
now w ill be 11.028 per cent per annum. In th a t case investors w ill earn 9 per cent per annum over the
coming three years, regardless o f whether they invest fo r three years, by:
a
b
buying the 3-year bond today; or
buying the 2-year bond today and buying a 1-year bond in 2 years* time.
Therefore, the expectation o f the future interest rate determines today s term structure.
This process is extended in Figure 4.4. Suppose th a t today s 1-year interest rate is 6.5 per cent per
annum. Then the m arket m ust expect next years 1-year interest rate to be 9.521 per cent per annum,
because (1.08)2 = 1.065 x 1.095 21 = 1.1664. The economic interpretatio n is th a t the same return is
expected over the next 2 years, regardless o f whether an investor:
a
b
buys a 1-year bond today and buys a fu rth e r 1-year bond in 1 years tim e; or
buys the 2-year bond today.
Figure 4.4 Return from the 3-year investment (extended)
years
- 9% p.a.
8% p.a.
-6.5% p .a .-
-> < r
-11.028% p.a.
9.521% p.a.-
-11.028% p.a.
As a final illu stratio n o f the expectations mechanism, consider again the in fo rm a tio n shown in
Figure 4.4 and imagine th a t there is an investor who intends to lend $1000 fo r a 2-year period. Consider
the follow ing three ways in which such an investm ent could be made:
a
b
c
Buy the 2-year bond now and hold i t u n til i t matures. A t the end o f the 2-year period, this
investm ent w ill have accumulated to $1000 x (1.08)2 = $1166.40.
Buy a 1-year bond now and, after 1 year, reinvest in a fu rth e r 1-year bond, which is then held u n til
m aturity. A t the end o f the 2-year period, this investm ent is expected to have accumulated to
$1000 x 1.065 x 1.095 21 = $1166.40.
Buy the 3-year bond now and sell i t after 2 years. A t the end o f the 2-year period, th is investm ent is
expected to be w o rth $1000 x (1.09)3/1 .1 10 28 = $1166.40.
As these calculations show, the expected outcome is the same, regardless o f the investm ent strategy.
The m arket has set today s term structure in such a way th a t it reflects the m arkets expectations o f the
future course o f interest rates.
To formalise our discussion o f expectations theory, we w ill use the notation zt t+k to mean the interest
rate per annum fo r a period beginning on date t and ending on date t + k. For example, z3 4 means the
interest rate fo r the year starting 3 years from now and ending 4 years from now. We make the follow ing
assumptions:
a
b
fu tu re 1-year interest rates (zx 2, z2 3, and so on) are known w ith certainty8
there are no transaction costs.
Given these assumptions, com petition in the bond m arket w ill result in a term structure th a t ensures
th a t the sum to which a dollar accumulates over n years i f invested at today s long-term interest rate z 〇n
m ust equal the sum to which it accumulates over n years when invested in the sequence o f present and
future 1-year interest rates z12, z2 3, . . . , zn_^ n. As a consequence, an investor who wants to invest for, say,
10 years is indifferent between investing in a 10-year bond and investing in a sequence o f 1-year bonds
over the next 10 years. Hence, today s 2-year interest rate, z〇2, is determ ined from today s 1-year interest
rate and the 1-year interest rate in a years time. That is,
(1 + z 〇 ,2)2 = (1 + 2〇 .i)(l +<2l ，2)
命
8
Alternatively, we could assume that investors are risk neutral. The concept of risk neutrality is explained in Section 7.3.
C hapter four A
pplying the time value of m o n e y to security valuation
Similarly, today s 3-year interest rate, z 〇3, is determ ined from today s 1-year interest rate, the 1-year
interest rate in a years tim e and the 1-year interest rate in the year after that. That is,
(1 + 2 〇,3)3 = (1 + z 〇，i ) ( l + 2 1?2)(1 + 之 2,3)
Generalising, fo r any given term o f t years, today s t-year interest rate z〇t is set by the m arket such that:
(1 + 20，f ) ’ = (1 + 20，1)(1 + 21，2)(1 +
Q j
) . . . (1 + 2 f- l ，f )
Rearranging this equation, today’s t-year interest rate z 〇t is given by:
z〇 ,t = [(1 + 2〇a ) x (1 + z i, 2) x (1 + z 2,3) x ... x (1 + z M .f) ]1/r- l
E U I
Thus, in our earlier discussion, using Equation 4.11 gives the 2-year interest rate as:
z 〇,2 = (1.065 x 1.095 21)1/2- 1
= 8% oer annum
and the 3-year interest rate is:
z〇,3 = (1.065 x 1.095 21 x 1.11028)1/3 - 1
= 9% per annum
The essence o f expectations theory is th a t the term structure is determ ined by investors’ expectations
o f short-term rates w ith in the m a tu rity o f the competing long-term security.9 Expectations theory can
help to reconcile the existence o f the differing shapes o f the term structures shown in Figure 4.1 and the
yield curves shown in Figure 4.2.
In general, an upward-sloping term structure implies th a t investors expect future short-term interest
rates to increase.10 In th a t case, investors are n ot prepared to invest in long-term securities unless the
yield is greater than th a t on short-term securities, because otherwise the investors would be better o ff
investing in short-term securities and reinvesting the proceeds at m aturity.
In general, a downward-sloping term structure implies th a t investors expect future short-term
interest rates to decrease— th a t is, investors are prepared to purchase long-term securities yielding less
than short-term securities because they expect th e ir retu rn to be no larger i f they adopted an investm ent
strategy requiring continual reinvestm ent in short-term securities. In short, i f expectations about the
level o f future short-term rates change, then actual long-term yields on existing securities w ill tend to
adjust in the same direction.
A fla t term structure means th a t investors expect future short-term interest rates to be the same as
the current short-term rate. Consequently, the long-term rates w ill equal the short-term rates.11
Commentators on the expectations theory o f the term structure have suggested th a t interest rates are
not formed solely on the basis o f expectations. For example, the liquidity prem ium (risk prem ium )
theory suggests th a t although expectations are a foundation fo r the term structure, there is in addition
a premium due to uncertainty about the future level o f interest rates. Suppose, fo r example, th a t an
investor has an investm ent target o f $10000 to be achieved in 2 years* tim e — th a t is, the investm ent
horizon is 2 years. The easiest and safest way to achieve this target is to invest today the present value o f
$10000, where the present value is calculated using todays 2-year zero rate. Alternatively, the investor
could invest the same sum today fo r 1 year at today s 1-year interest rate and, when this investm ent
matures in 1 years tim e, reinvest the proceeds fo r a fu rth e r year. O f course, this reinvestm ent is made at
next years 1-year interest rate, which today is n ot known. Hence, the outcome o f this alternative is risky,
whereas the previous approach is risk-free.12 This fact is illustrated in Example 4.9.
LIQUIDITY PREMIUM
( r is k p r e m i u m )
THEORY
of the term structure
is that although
future interest rates
are determined
by investors'
expectations, investors
require some reward
(liquidity premium) to
bear the increased risk
of investing long term
INVESTMENT HORIZO N
the particular future
date on which an
investor intends to
liquidate (sell) their
investment
It is convenient to think of short-term rates as determining long-term rates, but in fact the market determines all rates
simultaneously.
10 That this is not always the case may be seen from the following example. If the current term structure is: 1 year: 6 per cent;
9
2 years: 10 per cent; and 3 years: 11 per cent, then the 1-year interest rate, 1 year hence, is expected to b e :--------- 1 = 14.15%
( l. ll) 3
(I.IO)2
while the 1-year interest rate, 2 years hence, is expected to be: —------ - 1 = 13.03%.
l 〇6
11 This result holds even if there is a large difference in the number of bonds outstanding with different maturities. One of the
implications of the expectations theory is that interest rates are independent of the relative supply of bonds across the range
of maturities.
12 A third possibility would be to buy today a 3-year bond and sell it after 2 years, at which time it has become a 1-year bond. The
price obtained at the end of 2 years will depend on the 1-year interest rate at the time of the sale. Because this interest rate is
not known today, the price that will be achieved is also unknown today—that is, the investment is risky.
令
Example 4 .9
Freya wishes to have $ 1 0 0 0 0 in 2 years7 time. The current interest rate on a 2-year zero-coupon
bond is 7.5 per cent per annum and Freya decides to invest in this bond.
a) How much should Freya invest today? How much will she have after 2 years have passed?
b) The current interest rate on a 1-year zero-coupon bond is 6.5 per cent per annum. It turns out that
during the coming year interest rates fall steeply and at the end of the year the interest rate on a
1-year zero-coupon bond is only 4.2 per cent per annum. If Freya had chosen to invest the same
amount in 2 sequential 1-year investments, how much would she have after 2 years have passed?
c) The current interest rate on a 3-year zero-coupon bond is 8 per cent per annum. It turns out that
the 1-year interest rate at the end of 2 years is 9.5 per cent per annum. If Freya had chosen to
invest the same amount in a 3-year bond and then sell that bond after 2 years, how much would
she have after 2 years have passed?
SOLUTION
a) Freya should invest today the present value of $ 1 0 0 0 0 at today's 2-year interest rate. The amount
to invest is therefore $ 1 0 0 0 0 / (1 .075)2, which equals $8653.33.
• That is, Freya will today pay $8653.33 for a 2-year zero-coupon bond with a face value of
$10000.
• This investment is guaranteed to produce $ 1 0 0 0 0 after 2 years because on the bond's maturity
in 2 years7 time, the face value of $ 1 0 0 0 0 will be paid to Freya.
b) After 1 year, Freya will have $8653.33 x 1.065, which is equal to $9215.80. Reinvesting this
amount for a further year at 4.2 per cent per annum produces a final amount of $9 215.80 x
1.042, which is equal to $9602.86. Freya therefore does not achieve her target of $1 00 00.
c) The face value of the 3-year zero-coupon bond must be $8653.33 x (1.08)3, which is equal to
$1 09 00.7 0. At the end of the second year, the bond has become a 1-year bond and the interest
rate at that time is 9.5 per cent per annum. Therefore, the price of the bond when it is sold is
$1 0900.70/1.095, which equals $9954.98. Freya therefore does not achieve her target of
$10000.
As Example 4.9(a) illustrates, an investor who buys a zero-coupon bond w ith a term to m a tu rity that
matches the investm ent horizon is guaranteed to achieve th e ir target. As Examples 4.9(b) and 4.9(c)
illustrate, a different choice may lead to the target n ot being achieved. In other cases, the target could
be exceeded. For example, in p a rt (c), i f the 1-year interest rate at the end o f the second year had been
anything lower than 9.007 per cent Freya would have ended up w ith more than $10 000 at the end o f the
th ird year.13 In other words, any choice other than investing in the m aturity-m atching bond involves risk:
the target m ig ht be exceeded or i t m ight n o t be achieved. To induce an investor to depart from investing
in the m aturity-m atching bond w ill require a higher interest rate— th a t is, a risk prem ium . In Freyas
case, she w ould require a higher interest rate on either the 1-year or the 3-year bonds. However, proponents
o f the liq u id ity (risk) prem ium theory believe that, in general, the investm ent horizons o f bond investors
(lenders) are shorter than the investm ent horizons o f bond issuers (borrowers).14 Therefore, on balance,
the prem ium tends to be higher, the longer the term o f the bond, causing an upward bias in the term
structure. Such a bias w ill tend to cause yield curves to be upward sloping.
This means th a t compared w ith the yield curves th a t would be observed i f only expectations mattered,
an upward-sloping yield curve w ill become steeper, a downward-sloping yield curve w ill become less steep
(or perhaps even fla t o r upward-sloping) and a fia t yield curve w ill become upward sloping.15
4 .6 .4 | Empirical evidence
The empirical evidence on the theories we have discussed presents a rather complex picture. In the
US, Fama (1984), McCulloch (1987) and Richardson, Richardson and Sm ith (1992) found evidence
13 Because $10 900.70/1.09007 is equal to $10 000.
14 Proponents could, for example, point to the fact that investors rarely lodge fixed deposits at a bank with a term exceeding
5 years. But banks often offer mortgage loans with terms of 20 or 30 years.
15 In June 2009 the yield curve was steeply upward sloping. This yield curve is consistent with short-term interest rates having
been reduced by central banks to stimulate growth in response to the global financial crisis. Higher yields for longer term
securities are consistent with expectations of increasing future short-term interest rates and an increase in the risk premium.
C hapter four A pplying
the time value of m o n e y to security valuation
supporting the existence o f a premium. But Longstaff (2000) found no evidence o f a prem ium at the
very short end o f the yield curve. The evidence in Australia is also mixed. In a test at the short end o f
the term structure (90-day interest rates, compared w ith 180-day interest rates), Tease (1988) found
that the data quite strongly supported the expectations theory in various forms. Similarly, studies by
Robinson (1998), and Young and Fowler (1990) found support fo r the expectations theory using 90-day
and 10-year interest rates. However, studies by Alles (1995) and Heaney (1994), in both cases using more
thorough statistical analyses, found little support fo r the expectations theory. In a study o f 14 countries,
Beechey, Hjalmarsson and Osterholm (2009) found that, consistent w ith the expectations hypothesis,
in 10 countries (including Australia) the m arket appeared to set short-term interest rates and long-term
interest rates simultaneously. However, fo r all 10 o f these countries there appeared to be risk premiums,
suggesting th a t expectations alone do n o t determine the term structure.
4 .6 .5 1 Inflation and the term structure
One issue yet to be considered is the relationship between the in fla tio n rate and the term structure o f
interest rates. In general, we w ould expect lenders to require the nom inal interest rate to compensate
them fo r expected in fla tio n .16 Therefore, the higher the expected in fla tio n rate, the higher w ill be the
observed nom inal interest rate. As a consequence, i f the in fla tio n rate is expected to increase over
tim e, the nom inal interest rate on sh ort-term bonds w ill also be expected to increase over tim e.
According to the expectations th eo ry we w ill therefore see an upward-sloping yield curve. In addition,
unexpected changes in the in fla tio n rate are also like ly to have an im pact on the term structure. Such
unexpected changes w ill cause a change in the level o f interest rates. As explained earlier, the p ossibility
o f such changes gives rise to interest rate risk, and the liq u id ity prem ium th eo ry suggests th a t this in
tu rn w ill give rise to the tendency fo r interest rates on long-term bonds to be higher than those on
short-term bonds.
4.7
The default-risk structure of interest rates
As explained in Section 4.3.2, the presence o f uncertainty causes the o p p o rtu n ity cost o f capital to exceed
the risk-free interest rate. For debt o f a given term , the higher the m arkets assessment o f the p robability
o f default, the higher w ill be kdi the required rate o f return (or expected yield) on the debt. However,
because debtholders rank ahead o f shareholders, it is expected th a t the required rate o f retu rn on a
company s debt w ill be less than the required rate o f return on its shares. In short, fo r any given company,
rf <kd <ke.
Similarly, fo r debt o f a given term and fo r a given company, the required rate o f return, kd, w ill be less
than the yield to m aturity, r, where yield to m a tu rity is the rate o f retu rn earned by an investor i f the
company does n o t default. This relationship is shown in Example 4.10.
Services have existed fo r many years th a t supply ratings on the Quality* o f debt securities issued by
both public and private sector borrowers. There is evidence to suggest th a t there is a high correlation
between these ratings and the p robability o f default and i t is n o t surprising, therefore, th a t the yields are
related to the quality rating.
In Australia, ratings are supplied by Fitch Ratings (www.fitchratings.com .au), M oody s Investors
Service (www.moodys.com.au) and by Standard & Poors (w w w .standardandpoors.com .au). Issuers
o f long-term debt are rated by M oody s on a 21-point scale, ranging from Aaa (of the highest quality,
w ith m inim al credit risk) down to C (typically in default, w ith little prospect fo r recovery o f principal or
interest).17 The inform a tion in Table 4.2 is indicative o f the ratings supplied by M oody s.
16 See Equation 3.7 and the discussion in Section 3.4.4.
17 Standard & Poors rates issuers o f long-term debt on a 23-point scale ranging from AAA (extremely strong capacity to pay
interest and repay principal) to D (the borrower is expected to fail to pay all or substantially all of its obligations as they come
due). Fitch uses a 21-point scale, ranging from AAA (exceptionally strong capacity for payment of financial commitments)
to D (has entered into bankruptcy filings, administration, receivership, liquidation or other formal winding-up procedure, or
which has otherwise ceased business). All three companies also rate short-term debt. Both Fitch and Standard & Poors use an
8-point scale, while Moody’s uses a 4-point scale.
LEARNING
OBJECTIVE 7
Understand the effect
of default risk on
interest rates
|www j
Example 4 . 1 0
Bonds issued by the Red Vines Company mature in 1 year's time with a maturity value of $110.
There is no cash flow during the year. Investors believe that there is a 90 per cent chance that the full
payment of $ 1 10 will be made and a 10 per cent chance that no payment will be made. Calculate:
a) the price of Red Vines' bonds
b) the yield to maturity of the bonds.
SOLUTION
a)
The expected payment at the end of the year is 0.90 x $ 1 1 0 + 0 . 1 0 x $ 0 = $99. Assuming that the
market requires an expected rate of return, kd, of 10 per cent on these bonds, they will have a price of:
=$90
b)
The yield, r, is therefore found by solving:
$ 9 0 = ili
〇
1+ r
Therefore, the yield to maturity is:
$110 ,
r = ----------1
$90
=
22 . 22 %
That is, an investor who purchases the bonds for $9 0 and holds them to maturity will earn a rate
of return of 22.22 per cent per annum if Red Vines does not default.
TABLE 4.2 Moody's ratings for long-term <obligations of selected Australian
companies and government entities
Aaa
Aa
Aal
Of the highest quality; minimal credit risk
Government o f Australia
New South Wales Treasury Corporation
Treasury Corporation o f Victoria
Western Australian Treasury Corporation
High quality; subject to very low credit risk
Queensland Treasury Corporation
South Australian Government Financing Authority
Tasmanian Public Finance Corporation
Aa2
Australia and New Zealand Banking Group Ltd
Australian Rail Track Corporation Ltd
Commonwealth Bank of Australia
Macquarie University
Rabobank Australia Ltd
National Australia Bank Ltd
University o f Newcastle (Australia)
Westpac Banking Corporation
Aa3
Toyota Finance Australia Ltd
A
Upper-premium grade; subject to low credit risk
A1
BHP Billiton Ltd
HSBC Bank Australia Ltd
SPI Electricity Pty Ltd
Suncorp-Metway Ltd
A2
AMP Group Finance Services Ltd
Bendigo and Adelaide Bank Ltd
Macquarie Bank Ltd
Telstra Corporation Ltd
Westfield Group
A3
Baa
Baal
Coca-Cola Am atil Ltd
Heritage Bank Ltd
Jemena Ltd
Members Equity Bank Pty Ltd
Rio Tinto Ltd
Volkswagen Financial Services Australia Ltd
Wesfarmers Ltd
Woolworths Ltd
Subject to moderate credit risk; medium grade; may possess certain speculative characteristics
Bank of Queensland Ltd
Brambles Ltd
C hapter four A pplying
the time value of m o n e y to security valuation
Table 4.2 continued
Baa2
Baa3
Dexus Property Group
Victoria Teachers Mutual Bank
Alcoa of Australia Ltd
Brisbane A irport Corporation Pty Ltd
Goodman Group
Origin Energy Ltd
Ansell Ltd
Lend Lease Group
Premier Finance Trust Australia
Transurban Finance Company Pty Ltd
Woodside Petroleum Ltd
Amcor Ltd
Envestra Ltd
Leighton Holdings Ltd
Sydney A irport Finance Company Pty Ltd
Boral Ltd
Newcrest M ining Ltd
Qantas Airways Ltd
Ba
Speculative elements; subject to substantial credit risk
Bal
Ba2
Ba3
Aus drill Ltd
Fortescue Metals Group Ltd
B
Speculative; subject to high credit risk
B1
B2
B3
Barminco Holdings Pty Ltd
Atlas Iron Ltd
Cristal Mining Australia Ltd
Caa
Of poor standing; subject to very high credit risk
Investec Bank (Australia) Ltd
Nufarm Ltd
Genesee & Wyoming Australia Pty Ltd
Caal
Caa2
Caa3
Ca
C
Highly speculative; in or very near default; some prospect of recovery of principal and interest
Typically in default; little prospect for recovery of principal or interest
Source: www.moodys.com, accessed 9 September 2013.
4.8
O ther factors affecting interest rate
structures
Yield differentials on securities may also result from differences in m arketability— th a t is, the investors
ability to convert the securities in to cash w ith o u t a price penalty. O ther things being equal, an investor w ill
buy a security o f low m arketability only i f the yield is greater than th a t on a security o f high m arketability.
For example, a life insurance company would usually require a higher interest rate to lend mortgage funds
to a company than to lend the same am ount by purchasing the company s debt securities th a t are traded
in an active m arket. Similarly, it is conceivable th a t tax effects w ill give rise to differences in yields on
bonds.
Finally, we refer briefly to the relationship between the yield on bonds and the required rate o f retu rn
on ordinary shares. In Section 4.3, we suggested th a t the required rate o f return on ordinary shares may
be expressed as the rate o f discount th a t equates the present value o f the expected future dividends w ith
the current m arket price o f the shares. Clearly, i f dividends are expected to grow over tim e, the required
rate o f return on an investm ent in ordinary shares w ill be greater than the current dividend yield (D 〇/P 〇).
Therefore, it is n ot valid to directly compare the yields on debt securities w ith the dividend yields on
ordinary shares. N ot surprisingly, the evidence suggests th a t the required returns on ordinary shares
exceed those on debt securities.18 This evidence is consistent w ith the idea th a t investors require a higher
expected rate o f return to invest in ordinary shares than to invest in, say, debentures because ordinary
shareholders are exposed to greater risk. Their risk exposure is greater because ordinary shareholders
are the residual claimants on the cash flows o f the company. Therefore, th e ir returns are the firs t to be
affected by a dow nturn in the company s prospects and, in the event o f the company being wound up,
ordinary shareholders have the last claim on its assets.
18 For international evidence, see Dimson, Marsh and Staunton (2003) and for Australian evidence, see Brailsford, Handley and
Maheswaran (2008) and Brailsford, Handley and Maheswaran (2012).
命
B usiness finance
SUMMARY
• Financial assets such as bonds and shares can be
valued by discounting their future cash flows to
present values and summing these present values.
The discount rate used is the required rate of return
or opportunity cost of capital.
• If the future cash flows from an asset are certain,
the required rate of return will reflect only the
effect of time on the value of money.
• If the future cash flows are uncertain, investors
will also require compensation for risk and the
rate will be increased by the inclusion of a risk
premium.
• The value of an ordinary share is the present value
of a dividend stream that can, in principle, continue
forever. The calculation of a share’s value can be
simplified by assuming that dividends are constant
or grow at a constant rate over time. Shares can
also be valued using the company’s current earnings
and a price-earnings ratio. The value of this ratio
depends mainly on risk and expected growth in
namings.
• Debt securities (bonds) are priced by discounting
their future coupon interest payments and face
value. For any company, the interest rate required by
lenders will be less than the required rate of return
on the company’s ordinary shares. The price of a
debt security is inversely related to the interest rate
required by investors.
• Interest rates at any given time will usually be different
for different terms to maturity. This pattern is known
as the term structure of interest rates. Expectations
of future interest rates, together with a risk premium
have been suggested as explanations of the shape
of the term structure.
• The interest rate or yield on debt also depends on
the probability that the borrower will default.
KEY TERMS
bonds (or debentures) 80
coupons 80
default-risk structure of interest rates
dividends 76
duration 98
expectations theory 85
82
immunisation 97
investment horizon 87
liquidity premium (risk premium) theory
term structure of interest rates 82
yield curve 84
zero-coupon bonds 82
87
SELF-TEST PROBLEMS
1 Richards Ltd pays annual dividends on its ordinary shares. The latest dividend was 75 cents per share
and was paid yesterday. Dividends are expected to grow at 8 per cent per annum for the next 2 years,
after which a growth rate of 4 per cent per annum will be maintained indefinitely. Estimate the value of
one share if the required rate of return is 14 per cent per annum.
2 A government bond with a face value of $ 1 00 and a coupon interest rate of 1 1 per cent per annum
matures in 3 years7 time. Interest payments occur twice each year and a payment has just been made.
If the current market yield on the bond is 13 per cent per annum, what is the current price of the bond?
3 The current interest rates (yields) on zero-coupon government bonds are as follows:
Interest rate [%
13.90
11.70
10.50
Assume that the term structure can be explained purely by expectations of future interest rates, and
therefore there is no liquidity (or risk) premium. Calculate the expected 1-year rates for the next 2 years.
Solutions to self-test problems are available in Appendix B.
92
C hapter
four
A pplying
the time value of m o n e y to security valuation
1
[LO 1] Assuming certainty, the rates o f return on a ll financial assets w ill be identical. Outline why this
statement is correct and indicate the factors on which this market rate of return depends.
2
[LO 2] The valuation o f a share using the dividend growth model is very sensitive to the forecast o f the
dividend growth rate. This feature is a serious limitation on its usefulness to a share analyst. Discuss.
3
[LO 3] A company's share price reflects the discounted value o f either its future dividends or its future
earnings. Discuss.
4
[LO 4] W h y are bond prices and yields inversely related? Doesn't a higher yield make a bond more
attractive to investors and hence make it worth more, not less?
5
[LO 5] Government bonds are not riskless. Do you agree with this statement? W h y?
6
[LO 6] Differences between the current yields on different bonds con be explained by their relative riskiness
7
[LO 6] What is the term structure of interest rates? Discuss the various theories that try to explain the term
structure of interest rates.
8
[LO 6 】Given an upward-sloping term structure, it is preferable for a company to raise debt by issuing shortterm debt securities. Discuss.
9
[LO 6 】 If the term structure is downward sloping, does this mean that liquidity preferences are not having
any influence on interest rates?
10
[L0 7] How can both the Government of Australia and the Treasury Corporation of Victoria have a credit
rating of A a a? Wouldn't the Treasury Corporation of Victoria have a higher credit risk than the Australian
government?
11
[LO 8] What is 'immunisation7? (See Appendix 4.1, Introduction.) How may duration matching help? What
are the problems of duration matching?
and different terms to maturity. Discuss.
cA
PROBLEMS
1
Valuation under certainty [LO 1]
A promise to pay $ 1 0 0 0 0 in 4 years' time is certain to be kept. If the risk-free rate for a 4-year term is 5 .5 per
cent per annum, what is the value of this promise today? Do we know what the value will be in a year's time?
W hy or why not?
2
Valuation of shares [LO 2]
Assume that today is the last day of 2014. Rednip Ltd is expected to pay annual dividends of 64 cents in
2015 (Year 1). Assume that this dividend is expected to grow at an annual rate of 10 per cent and investors
require a rate of return of 20 per cent per annum.
a) Estimate Rednip Ltd's share price today.
b) What is Rednip Ltd's share price expected to be at the end of 2 0 1 5 ?
3
Valuation of shares [LO 2]
The required rate of return on the shares in the companies identified in (a) to (c) below is 15 per cent per
annum. Calculate the current share price in each case.
a) The current earnings per share of Zero Ltd are $1.50. The company does not reinvest any of its earnings,
which are expected to remain constant.
b) Speedy Ltd's current dividend per share is 80 cents. This dividend is expected to grow at 5 per cent per
annum.
c) Reduction Ltd's current dividend per share is 60 cents. The dividend of the company has been grow­
ing at 12 per cent per annum in recent years, a rate expected to be maintained for a further 3 years.
It is envisaged that the growth rate will then decline to 5 per cent per annum and remain at that level
indefinitely.
CHAPTER F O U R REVIEW
QUESTIONS
4
Required rate of return on a bond [LO 4]
A 10 per cent $ 1 00 government bond that pays interest annually, and currently is 5 years from maturity, is
selling for $103.29. What is the required rate of return (yield) on this bond? What is the implied real interest
rate if the expected inflation rate is 5 per cent per annum?
5
Valuation of bonds [LO 4]
A 12 per cent $ 1 00 government bond pays coupon interest twice yearly and matures in 5 years7 time. The
current market yield on the bond is 10 per cent per annum. If a coupon payment has just been made, what is
the current price of the bond?
6
Bond prices and interest rate changes [LO 5]
Consider two 1 2 per cent $100 government bonds that differ only in that one matures in 2 years7 time and the
other in 5 years7 time. Both bonds are currently selling for $1 00 and pay coupon interest annually.
a) What will be the price of each bond, given an immediate fall in the required yield to 10 per cent per
annum?
b) What will be the price of each bond, given an immediate increase in the required yield to 14 per cent per
annum?
c) Explain the relative price movements in response to interest rate changes as evidenced by parts (a) and (b).
7
Bond prices and interest rate changes [LO 5]
Welshpool Investments Ltd has a portfolio of 5 bonds (A, B, C, D and E). Their terms to maturity are 2, 3, 5,
10 and 25 years respectively. Each of the bonds has a coupon interest rate of 8 per cent per annum and a
yield of 6 per cent per annum and each has just made a coupon payment. All 5 bonds pay annual coupons.
a) Calculate the price of each bond.
b) Re-calculate the price of each bond if the required yield on each bond increases to 7 per cent per annum.
c) Comparing your answers to (a) and (b), what patterns are evident? Explain.
8
Using the term structure to price a bond [LO 6]
The government currently has on issue zero-coupon bonds with terms of 1, 2 and 3 years. Their yields are,
respectively, 6, 9 and 10 per cent per annum. The government proposes to issue a 3-year bond paying
annual coupons and wishes to issue the bond at a price close to its face value of $100. To two decimal
places, what coupon interest rate should the government choose?
9
Expectations theory of the term structure [LO 6]
The current risk-free zero-coupon interest rates are as follows:
1
6.00
2
6.50
3
6.90
4
7.20
5
7.40
a) Assume that the term structure can be explained purely by expectations of future interest rates, and there­
fore there is no liquidity or risk premium. Calculate the expected 1-year interest rates for the next 4 years.
b) Explain why it is not possible in this market for the 6-year zero-coupon interest rate to be 6 per cent per
annum.
10
Liquidity premium theory of the term structure [LO 6 】
The current zero-coupon interest rates for terms of 4 and 5 years are 8.4 and 8.5 per cent per annum
respectively. Jane Chan wishes to invest today and has an investment horizon of 4 years. Specifically, her
target is to have $ 1 0 0 0 0 0 in 4 years' time. She is considering two investment strategies: (i) buying the 4-year
bond and (ii) investing the amount calculated for the first strategy but instead buying the 5-year bond and
selling the bond after 4 years have passed.
CHAPTER FOUR APPLYING THE TIME VALUE 〇F MONEY TO SECURITY VALUATION
b) Suppose Jane decides to implement strategy (ii). What 1-year interest rate on the horizon date will see Jane
exceed her target?
c) How would proponents of the expectations hypothesis interpret this result? How would proponents of the
liquidity premium hypothesis interpret this result?
11
Pricing with default risk [LO 7]
Waverton Foundry Ltd has just issued a 1-year zero-coupon bond with a face value of $ 1 0 0 0 0 0 0 0 . It is
known that there is a 3 per cent chance that the company will default on this payment and that, if it does,
investors in the bond will receive nothing. The market requires an expected rate of return of 8.6 per cent per
annum.
a) How much is the bond issue worth today? What is the implied promised yield?
b) Suppose instead that, in the event of default, there is a 2 per cent chance that investors would receive
$ 7 0 0 0 0 0 0 and a 1 per cent chance that they would receive nothing. How much is the bond issue worth
today? What is the implied promised yield? Compare this with your answer to (a) and comment.
12
Duration and interest rate elasticity [LO 8]
Consider the following four bonds:
Bond
Term to maturity (years)
Coupon rate [% p.a.)
A
2
10
B
3
12
C
3
10
D
3
8
芝
C H A P T EF
R oan HEVIE
a) How much will Jane need to invest today if she implements strategy (i)?
Each bond has a face value of $100 and the current yield is 9 per cent per annum. All bonds pay annual
coupons.
a) Calculate the current price of each bond.
b) Calculate the duration of each bond. (See Appendix 4.1.)
c) Calculate what the price of each bond would be if the market interest rate increased to 11 per cent per
annum.
d) What would be the percentage capital loss on each bond?
13
Duration and immunisation [LO 8]
An investor is considering the purchase of a 10-year bond that pays a single annual interest payment at the
rate of 10 per cent. The bond's face value is $1 00 0 and its current price is $1 134.19. Determine whether the
investor can ensure a particular rate of return over a 7-year time horizon. (See Appendix 4.1
14
Duration and immunisation [LO 8]
If you wish to 'lock in’ the current yield of 8.5 per cent per annum for 3 years, which of the following bonds
should you invest in?
Coupon rate (% p.a.) 1
Bond
Term to maturity (years)
A
2.0
10
B
3.0
10
C
3.5
10
D
4.0
10
E
4.0
18
Each bond has a face value of $100. Assume that coupon payments are made at the end of each year.
95
B usiness finance
REFERENCES
Alles, L, 'Time varying risk premium and the predictive
power of the Australian term structure of interest rates ’，
/Accounf/ng one/ F/'nance, November 1995, pp. 7 7 —96.
Beechey, M w Hjalmarsson, E. & Osterholm, P., Testing
the expectations hypothesis when interest rates are near
integrated', Journal of Banking and Finance, M ay 2009,
pp. 9 3 4 -4 3 .
Bodie, Z., Kane, A. & Marcus, A.J., Investments, 9th edn;
M cG raw-H ill, N ew York, 20 1 1 .
Brailsford, Tw Heaney, R. & Bilson, C., Investments, 4th edn,
Cengage, M elbourne, 20 11 .
Brailsford, T., Handley, J.C. & Maheswaran, K.,
'Re-examination of the historical equity risk premium
in Australia7, Accounting and Finance, M arch 20 08 ,
pp. 7 3 -9 7 .
96
Fama, E.F., 'Term premiums in bond returns', Journal of
Financial Economics, December 1984, pp. 5 2 9 -4 6 .
Heaney, R., 'Predictive power of the term structure in
Australia in the late 1980s: a note', Accounting and Finance,
M a y 1994, pp. 3 7 -4 6 .
Longstaff, F.A., The term structure of very short-term rates:
new evidence for the expectations hypothesis', Journal of
Financial Economics, December 20 00 ,
pp. 3 9 7 -4 1 5 .
Macaulay, Fw Some Theoretical Problems Suggested by the
Movements of Interest Rates, Bond Yields and Stock Prices in
the US Since 1856, N ational Bureau o f Economic Research,
N ew York, 1938.
McCulloch, J., 'The monotonicity o f the term structure: a
closer look', Journal of Financial Economics, M arch 1987,
pp. 1 8 5 -9 2 .
Brailsford, T.; Handley, J.C. & Maheswaran, K., 'The
historical equity risk premium in Australia: post-GFC and
128 years o f da ta', Accounting and Finance, M arch 20 12 ,
pp. 2 3 7 -4 7 .
Richardson, M ., Richardson, P. & Smith, T., 'The monotonicity
of the term structure: another look', Journal of Financial
Economics, M arch 1992, pp. 9 7 -1 0 5 .
Cox, J.C., Ingersoll, J.E. & Ross, S.A., 'Duration and the
measurement o f basis risk', Journal of Business, January
1979, pp. 5 1 -6 1 .
Robinson, E.S., 'The term structure of Australian interest rates:
tests of the expectations hypothesis', Applied Economics
Letters, July 1998, pp. 4 6 3 -6 7 .
Dimson, E., Marsh, P.R. & Staunton, M ., 'G loba l evidence
on the equity risk premium', Journal of Applied Corporate
Finance, Fall 2 0 0 3 , pp. 2 7 -3 8 .
Tease, W.J., The expectations theory of the term structure of
interest rates in Australia7, The Economic Record, June 1988,
pp. 1 2 0 -7 .
Elton, EJ. & Gruber, M J ., Modern Portfolio Theory and
Investment Analysis, 5th edn, John W ile y and Sons,
N ew York, 1995.
Young, I. & Fowler, D., 'Some evidence on the term structure
of interest rates: how to find a black cat when it's not there',
Accounf/’ng one/ F/nance, M a y 1990, pp. 2 1 -6 .
A ppendix 4 .1
A p p e n d ix
命
D uration
a n d im m u n isatio n
Duration and immunisation
Introduction
In S ection 4.5 it w as sh ow n that h old ers o f b o n d s are su bject to in terest rate risk. A change in th e level
o f interest rates affects b o th the m arket price o f an existing b o n d an d th e in terest rate at w hich in terest
receipts can be reinvested. For exam ple, an increase in in terest rates m eans an im m ed ia te capital loss to
holders o f b o n d s becau se th e price o f th eir secu rities w ill fall. H ow ever, th ere is th en th e o p p o r tu n ity to
reinvest in terest receipts at th e h igh er in terest rate. The reverse applies i f in terest rates fall.
The possib ility o f ch a n g in g in terest rates p resen ts difficulties fo r in vestors. Su ppose, fo r exam ple,
that an in vestor w ishes to h ave a target su m o f m o n e y in 3 years* tim e. The challenge is to c h o o s e a b o n d
LEARNING
OBJECTIVE 8
Apply the concept of
duration to immunise a
bond investment
in vestm en t that w ill achieve th is target, regardless o f in terest rate changes du ring the 3 years. A strategy
to achieve such an ob jectiv e is called
im m unisation.
If p ossib le, the in vestor sh ou ld bu y a 3-year b o n d
that m akes n o in terest p a ym en ts (k n ow n as c o u p o n s) du ring its life. Such secu rities are usually called
z e r o -co u p o n b o n d s .19 The in v e s to r k n ow s w ith certain ty the price o f the b o n d at th e en d o f th e 3 years
because th e b o n d w ill th en b e w o rth exactly its face value, as it m atu res at th at tim e. Since there are n o
cou p on in terest paym en ts, th e in vestor also has n o d ou b ts arising fr o m u n certain ty a b ou t the in terest rate
that w ill b e earn ed o n rein vested cou p on s. Th erefore, the in vestor k n ow s p recisely w hat th e in vestm en t
IM M U N IS A TIO N
strategy designed
to achieve a target
sum of money at a
future point in time,
regardless of interest
rate changes
w ill b e w orth at the en d o f th e 3 years, an d thus ach ievem en t o f the target is guaranteed. The p rob lem
is that alth ough z e r o -c o u p o n b o n d s exist, c o u p o n b o n d s are m u ch m ore co m m o n . Im m u n isation u sing
cou p on -p a y in g b o n d s is m ore difficu lt to achieve.
A tech n iqu e certain to im m u n ise an in v estm en t in c ou p on -p a y in g b o n d s against all p ossib le changes
in in terest rates has n ever b e e n achieved. H ow ever, there is a tech n iq u e th at w ill im m u n ise a b o n d
in vestm ent in a relatively sim ple en v iro n m e n t in w hich the yield curve is fiat, b u t m a y m ake a single
parallel sh ift up o r d o w n .20 This tech n iq u e is b a sed o n th e co n c e p t o f b o n d d u ra tion an d its origin s can be
traced to research u n derta k en b y M acaulay (1 9 3 8 ).
Bond duration
M acaulay realised th at a b o n d payin g a lo w c o u p o n rate is in a sen se a lon ger* in v estm en t th an a h igh er
c o u p o n b o n d w ith the sam e term to m aturity. For exam ple, con sid er tw o 5-y ear b o n d s , b o th o f w h ich
have a face value o f $ 1 0 0 0 , pay in terest annually an d are cu rren tly p riced to yield 10 p er cen t p er annum .
They differ, h ow ever, in that o n e has a c o u p o n rate o f 5 p e r cen t per an n u m and the o th e r a c o u p o n rate
o f 15 p er cen t p er annum .
The cash flow s and th eir p resen t values are sh ow n in Table A 4.1.
Table A 4 .1
5% coupon cash flow
Present value
15% coupon cash flow
Present value
($)
t$)
($)
($)
1
50
45.45
150
136.36
2
50
41.32
150
123.97
3
50
37.57
150
112.70
50
34.15
150
102.45
5
50
31.05
150
93.14
5
1000
620.92
1000
620.92
Year
4
Total
8 1 0 .4 6
1189.54
19 With zero-coupon bonds, an investor receives no regular interest payments during the bonds life. A zero-coupon bond is
purchased at a discount from its face value and it is either held to maturity, when the investor receives the face value, or sold
before maturity at a price determined in the market.
20 For a discussion of techniques appropriate to several, more complex, environments, see Elton and Gruber (1995).
令
T h erefore, th e price o f the 5 per cen t c o u p o n b o n d is $ 8 1 0 .4 6 and th e price o f th e 15 p er cen t cou p on
b o n d is $ 1 1 8 9 .5 4 . For th e lo w -c o u p o n b o n d , th e face value p a ym en t ($ 1 0 0 0 ) represents a b ou t 77 per cent
o f its p rice (becau se $ 6 2 0 .9 2 /$ 8 1 0 .4 6 = 0 .7 7 ). For the h ig h -c o u p o n b o n d , th e face value represents
on ly a b o u t 52 p er cen t o f its p rice ($ 6 2 0 .9 2 / $ l 1 8 9 .5 4 ~ 0 .5 2 ). Conversely, the first in terest paym en t
con trib u tes on ly a b ou t 5.6 p er cen t to the value o f th e lo w -c o u p o n b o n d ($ 4 5 .4 5 /$ 8 1 0 .4 6 = 0 .0 5 6 ) bu t
c on trib u tes nearly 11 .5 p er cen t to the value o f th e h ig h -c o u p o n b o n d ($ 1 3 6 .3 6 /$ 1 1 8 9 .5 4 = 0 .1 1 5 ). It is
clear th a t the lo w -c o u p o n b o n d brin gs returns to th e in vestor later in its life, relative to the h ig h -co u p o n
b on d . In this sense, the lo w -c o u p o n b o n d is longer*.
DURATION
M acaulay p r o p o s e d that this tim in g feature cou ld be in co rp o ra te d in to a d u r a t io n m easure by
measure of the
time period of an
investment in a bond
or debenture that
incorporates cash
flows that are made
prior to maturity
w eigh tin g th e n u m ber o f p eriod s that w ill elapse b e fo r e a cash flo w is received b y th e fraction o f the
b o n d s p rice th at the p resen t value o f th at cash flo w represents. In this w ay th e tim e p e r io d is w eigh ted by
th e ‘relative im p o rta n ce ’ o f the cash flo w that w ill occu r at th at tim e.
Table A 4 .2 sh ow s th e calculation o f d u ra tion fo r the tw o b o n d s discu ssed above.
T able A 4 . 2
鲁
~ 'f
Time
5% coupon weight
Weight x time
15% coupon weight
Weight x time
1
4 5 .4 5 /8 1 0 .4 6 = 0 .0 5 6 0 8
0.056 08
1 3 6 .3 6 /1 1 8 9 .5 4 = 0 .1 1 4 6 3
0.1 14 63
2
4 1 .3 2 /8 1 0 .4 6 = 0 .0 5 0 9 8
0.101 96
1 2 3 .9 7 /1 1 8 9 .5 4 = 0 .1 0 4 2 2
0.208 44
3
3 7 .5 7 /8 1 0 .4 6 = 0 .0 4 6 3 6
0.139 08
1 1 2 .7 0 /1 1 8 9 .5 4 = 0 .0 9 4 7 4
0.2 84 22
4
3 4 .1 5 /8 1 0 .4 6 = 0 .0 4 2 1 4
0.168 56
1 0 2 .4 5 /1 1 8 9 .5 4 = 0 .0 8 6 1 3
0.344 52
5
3 1 .0 5 /8 1 0 .4 6 = 0 .0 3 8 3 1
0.191 55
9 3 .1 4 /1 1 8 9 .5 4 = 0 .0 7 8 3 0
0.391 50
5
6 2 0 .9 2 /8 1 0 .4 6 = 0 .7 6 6 1 3
3.830 65
6 2 0 .9 2 /1 1 8 9 .5 4 = 0 .5 2 1 9 8
2.609 90
T otal = d u ra tion
4 .4 8 7 88
3.9 5 3 21
As su ggested earlier, the du ration o f the lo w -c o u p o n b o n d (4 .4 8 8 years) is lon g er th an the du ration
o f th e h ig h -c o u p o n b o n d (3 .9 5 3 years). D u ration an d term to m a tu rity are equal on ly fo r a z e r o -co u p o n
b on d . The du ration o f a co u p o n -p a y in g b o n d is always less th an its term to m aturity.
The steps u sed to calculate d u ra tion
D are
su m m arised in th e form u la:
rm 〇) if
D = f
A4.1
台 卜 。J
w here
Ct = cash flo w (c o u p o n in terest o r p rin cip al) at tim e
PV(Ct) = p resen t value
t
o f Ct
Q
~ (i + 0 f
N ow
P
〇
= price o f the b o n d
_ y -
Q
,
" t t (i + 0 f
w here
Pn
(1 +
Ct = c o u p o n in terest at tim e t
Pn = face value pa ym en t at m atu rity
z = required yield p er p e rio d
n = n u m ber
o f p eriod s to m atu rity
E qu ation A 4 .1 can be rew ritten in its m ore usual form :
y ' Ct x t
D：
f t i (1 + 〇r
f
Q
r t i (1 + iY
A4.2
A ppendix 4 .1
D uration
Example A4.2 includes a duration calculation th a t follows Equation A4.2. First, however, we provide
a b rie f mathematical analysis to h ig hligh t the importance o f the duration measure. Readers who are n ot
interested in this analysis can o m it this section.
Duration and interest elasticity
As explained in Section 4.4, i f interest rates increase (decrease), then bond prices decrease (increase).
When there is a change in interest rates, all bond prices respond in the opposite direction, b u t they do
not all respond to the same extent. In other words, different bonds have different interest elasticities. It
is im p orta nt fo r a bond investor to know the interest elasticity o f the bond because this w ill be a good
indicator o f the interest rate risk being borne.
The n otio n o f elasticity is prom inent in economics. Perhaps the best known example is the price
elasticity o f demand fo r a particular good. This is expressed as follows:
QdP
where
rj = price elasticity o f demand
P = price o f the good
Q = q uantity o f the good demanded
^
= derivative o f q ua ntity demanded w ith respect to price
Price elasticity indicates the response o f the q ua ntity demanded to a change in price.
W hat m atters fo r a bond investor is the interest elasticity o f the bond price; in other words, what
matters is the response o f the bond price to a change in the interest rate. The elasticity E is given by:
i dP〇
E:
A4.3
P〇 d i
The form ula fo r bond price is:
Ci
P〇
Pn
Cn
C2
(1 +
(i + v
i) n
(1 + /广
and therefore:
Q
2C2
(1 + 0 2
(1 + i f
dP〇
di
~
(-1
'
f
2 〇2
nCn
(1 + 〇2
(1 + i) n
C\
\\-\- i ) \ l + i
nPn
nCn
(l + i) ^ 1 (l + O^
.
1
nPn
( l + i) n
Substituting in to Equation A4.3:
E
^ i \ f
l
\ f
C{
2C2
nCn
nPn
(1 + i y
(1 -f i) n
(1 + i) n
：
P〇 I \ l + i )
D
.1 + /
\ l + i
A4.4
where duration, D, is as defined in Equation A4.2.
Equation A4.4 shows th a t the interest elasticity o f a bonds price is proportional to its duration. The
longer the duration, the greater (in the sense o f being more negative) is the interest elasticity. For example,
i f the interest rate is 10 per cent per annum and the duration is 4.5 years, the interest elasticity is:
3.10
( 1r 10
,
.
：-0.409
(4.5)
,
a n d im m unisation
I f the duration is 9 years, the interest elasticity is:
/0.10、
E
V I . 10,
⑼
- 0 .8 1 8
Duration and bond price changes
Given th a t duration is related to interest elasticity, it follows th a t i t is possible to use duration to work
out the approximate percentage price change th a t w ill occur fo r a given change in interest rate. Using
Equations A4.3 and A4.4:
i dP〇 = _ f
P〇 d i
~
D
VI
I t follows that:
dP〇 _
f
\
P〇" ~ ~ V l T /
Ddi
Therefore, fo r 'small* discrete changes in interest rates and bond prices we have the follow ing
approxim ation:
AP〇
(it
DAi
A4.5
An application o f Equation A4.5 is shown in Example A4.1.
Example A 4 .1
Consider the 5-year 15 per cent coupon bond priced to yield 10 per cent per annum. As shown in
Tables A4.1 and A4.2, the price of this bond is $1 189.54 (per $1 0 0 0 face value) and its duration
is 3.953 years. What is the percentage price change if the interest rate falls to 9.5 per cent per
annum?
SOLUTION
In this case the interest rate change is -0.5 per cent = -0.005. Equation A4.5 gives the approximate
answer as:
1
V I . 10
0.01797
(3.953)(-0.005)
In other words, the result will be a capital gain of approximately 1.797 per cent. (The exact answer
is close to 1.819 per cent.)
Duration and immunisation
Suppose th a t the yield curve is flat, b ut i t may make a parallel s h ift up or down. If, at the tim e o f a
parallel sh ift, an investor is holding a bond whose duration matches the rem aining investm ent period, the
investm ent is im m unised against the s h ift— th a t is, the investm ent w ill achieve at least the target yield,
notw ithstanding the yield shift. This can be seen in Example A4.2.
Managing risk by matching Macaulay s duration to the investm ent horizon is an im p o rta n t idea but
the procedure we have described has a num ber o f lim ita tion s. In particular, it is im p o rta n t to investigate
w hat happens i f there is more than one yield s h ift during the investm ent period. Consider again
Example A4.2 and suppose th a t the yield had shifted down to 8 per cent imm ediately after date 0.0, but
then shifted up to 12 per cent just before date 3.0 (the end o f the investm ent period). In th a t case, the
investor w ill hold 1.229 37 bonds after 3 years have passed, b ut the price w ill be only $1022.578 per bond,
which gives a value o f 1.229 37 x $1022.578 = $1257.127. This falls short o f the target o f having at least
$1275.312.
A ppendix 4 .1
D uration
Example A4.2
Suppose that there is a flat yield curve at an interest rate of 10 per cent per annum. An investor wishes
to lock in7 this yield for a 3-year investment period. Bond A has a term of 3.4 years, a face value of
$1000, a coupon rate of 7 per cent and pays interest annually. Table A4.3 shows the calculation of
Bond A 7s duration using Equation A4.2.
n
$2877.402
Duration = —---------------
$958,161
=3.003 years
Table A4.3 Bond A
Time (years)
Cash flow ($)
Present value of cash flow ($)
Time
x present value ($)
0.4
70
67.382
26.953
1.4
70
61.256
85.758
2.4
70
55.687
133.649
3.4
1070
773.836
2631.042
958.161
2877.402
Total
According to the immunisation strategy, Bond A should provide an immunised investment because
its duration matches the investment period— that is, an investment of $958,161 in Bond A will be
worth at least $958,161 x ( l. l) 3 = $127 5.31 2 in 3 years7 time, regardless of an interest rate shift.
To demonstrate this, it is assumed that:
a) immediately after buying Bond A, the yield curve makes a parallel shift from 10 per cent to 8 per
cent, and remains at that level for the next 3 years
b) as each coupon interest payment is received, the investor reinvests in— that is, buys more of— the
same bond
c) bonds and dollars are infinitely divisible, thereby allowing the investor to purchase or sell any
fraction of Bond A.
After 0.4 years have passed, the investor receives a coupon payment of $70. The bond is now a
3-year bond. The yield curve has shifted down to 8 per cent, so the price of one bond is then:
$70
$70
$1070
hOS + (1.08)2 + (1.08)3
=$974,229
Therefore, the investor can purchase the fraction 70.00 /97 4.2 29 of one bond. This fraction is
0.071 852, so the investor now holds 1.071 852 bonds. After 1.4 years, the investor receives a further
coupon payment of $70 per bond; therefore the cash received is $70 x 1.071 852 = $75.0296. The
bond is now a 2-year bond and its price is:
$70
$1070
L08 + (1.08)2
=$982,167
The investor can now purchase a further 75 .02 9 6 / 9 8 2 .1 6 7 = 0 .0 7 6 3 9 of a bond. This type of
cycle is repeated after 2.4 years and the investment in bonds is then sold after 3 years. Table A4.4
summarises the progress of the investment.
continued
a n d im m unisation
continued
Table A4.4
Date = investment period expired (years)
Item
0.0
0.4
M
2.4
3.0
3.40000
3.00000
2.00000
1.00000
0.40000
70.00000
75.02960
80.37700
958.16100
974.22900
982.16700
990.74100
Bonds purchased (no.)
1.00000
0.07185
0.07639
0.08113
N il
No. of bonds held
1.00000
1.07185
1.14824
1.229 37
1.22937
958.16100
1044.22700
1127.76400
1217.98700
1275.54900
Bond term remaining (years)
Coupon interest received ($)
Price o f one bond ($)(fl)
Value o f bonds held ($)
N il
Nil
1037.56300
(°) Present value of remaining cash flows per $ 1000 face value. Yield used is 10 per cent per annum for the price at date
zero. Yield used is 8 per cent per annum for prices calculated after date zero.
As can be seen in the bottom right-hand corner of the table, the sum received from the sale after
3 years is $1275.549. This amount exceeds the target sum after 3 years of $ 1 27 5.31 2 and the
investment has therefore achieved the target rate of return of at least 10 per cent per annum.
What if the interest rate had risen to 12 per cent (instead of falling to 8 per cent)? In that case, the
progress of the investment would be as shown in Table A4.5.
Table A4.5
Date = investment period expired (years)
Item
0.0
Bond term remaining (years)
Coupon interest received ($)
3.40000
Nil
0.4
3.00000
1.4
2.000 00
2.4
1.00000
3.0
0.40000
70.00000
75.56880
81.34680
958.16100
879.90800
915.49700
955.35700
Bonds purchased (no.)
1.00000
0.07955
0.08255
0.08515
No. of bonds held
1.00000
1.07955
1.16210
1.24725
1.24725
958.16100
949.905 00
1063.89700
1191.56500
1275.40600
Price o f one bond ($)(a)
Value o f bonds held ($)
N il
1022.57800
N il
Present value of remaining cash flows per $ 1000 face value. Yield used is 10 per cent per annum for the price at date
zero. Yield used is 12 per cent per annum for prices calculated after date zero.
Again, therefore, the investment has achieved the target yield of 10 per cent per annum,
notwithstanding the shift in yield after the investment was made.
In principle, this problem can be solved easily. W hen the yield changes, so too does the duration o f
the bond held. W hen the yield shifts on the firs t occasion, the investor should change the bond holding
so that, once again, duration matches the investm ent period. The investor is then imm unised against
the next yield shift. This is simple in principle b ut in practice there are difficulties because it implies that
a rebalancing o f the investm ent— buying and selling bonds— is needed every tim e the duration o f the
investm ent changes. Because duration is a function o f the current yield and future coupon payments, this
means th a t a bond transaction is needed every tim e the yield shifts, and every tim e a coupon payment is
received. This can be costly and cumbersome.
Only a fla t yield curve subject to parallel shifts has been considered. It may be shown th a t i f a sloped
yield curve shifts in parallel fashion the investor s till matches duration and investm ent period, b ut the
duration form ula is slightly more complex. I f a sloped yield curve shifts in some non-parallel way then the
im m unisation strategy w ill depend on the type o f non-parallel s h ift assumed to occur. For an example,
see the article by Cox, Ingersoll and Ross (1979).
▼
CHAPTER CONTENTS
ED
Introduction
104
m
The discounted cash flow methods compared
108
m
The capital-expenditure process
104
EB
Other methods of project evaluation
118
BH
Methods of project evaluation
104
Project evaluation and real options analysis
123
LEARNING OBJECTIVES
After studying this chapter you should be able to:
1
explain the importance of each of the steps in the capital-expenditure process
2
outline the decision rules for each of the main methods of project evaluation
3
explain the advantages and disadvantages of the main project evaluation methods
4 explain why the net present value method is preferred to all other methods
5
understand the relationship between economic value added (EVA) and net present value (NPV)
6
understand the relationship between real options, managerial flexibility and firm value.
B usiness finance
Introduction
In Chapter 1 we described the p rim ary financial functions o f a financial manager as raising funds and
allocating them to investm ent projects so as to maximise shareholders’ wealth. In this chapter, we
consider how such projects should be selected to ensure the m axim isation o f shareholders’ wealth.
The term investment project is interpreted very broadly to include any proposal to outlay cash in the
expectation th a t future cash inflow s w ill result. There is, therefore, a wide range o f such projects. These
include proposals fo r the replacement o f plant and equipment, a new advertising campaign, research and
development activities, and proposals to take over competing firm s.
In th is book, investm ent and financing decisions are discussed in the order in which they are usually
considered in practice. In general, management w ill firs t examine the alternative investm ent projects
available to it. A fte r the acceptability o f these projects has been determined, management w ill, i f
necessary, set about raising the funds to im plem ent them. It is logical, therefore, to discuss the evaluation
and selection o f proposed investm ent projects before discussing the methods o f financing them. In this
chapter, we examine the principles and methods o f project evaluation. In Chapter 6, the application o f
these principles and methods is discussed.
The evaluation and selection o f investm ent projects is only one element o f the capital-expenditure
process. Before discussing the methods o f project evaluation, therefore, we outline the capital-expenditure
process.
5.2
LEARNING
OBJECTIVE 1
Explain the importance
of each of the steps in
the capital-expenditure
process
*
LEARNING
OBJECTIVE 2
Outline the decision
rules for each of the
main methods of
project evaluation
^0^
The capital-expenditure process
Capital-expenditure management involves the planning and control o f expenditures incurred in the
expectation o f deriving future economic benefits in the fo rm o f cash inflows. Consider the follow ing
possible proposals: a m anufacturer is considering b uilding a new plant; an airline is considering the
replacement o f several o f its aircraft; a pharmaceutical company is considering a new research and
development program. Each proposal involves m aking current outlays in the expectation o f future cash
inflows and, therefore, each can be analysed as a capital-expenditure proposal. This is the case even though,
fo r example, the costs o f research and development are usually recognised fo r accounting purposes as
expenses in the period in which they are incurred.
Capital expenditures are very im p o rta n t fo r a company because freq ue n tly the am ounts o f m oney
involved are large and th e ir effects extend w ell in to the fu tu re . A fte r capital expenditures have
been made, i t is lik e ly th a t th e ir effects w ill continue fo r some tim e as m any projects are n o t easily
m odified. I f there is e ithe r no second-hand m arket or, at best, o nly a <th in , m arket fo r capital assets,
management may have to abandon a project i f i t proves to be unprofitable. Because o f the longevity
and frequent irre v e rs ib ility o f many investm ents, they are lik e ly to com m it a company to a p articula r
technology and to have a considerable influence on the p a tte rn o f its fu tu re operating cash flows.
The im portance o f these decisions, therefore, can extend w ell beyond the period in w hich the in itia l
capital outlay is made.
The tasks involved in the capital expenditure process, as well as the associated outcomes from their
im plem entation, are outlined in Table 5.1.
5.3
Methods of project evaluation
In th is section we consider the evaluation and selection o f investm ent projects. F irst, we consider
the net present value and the in te rn a l rate o f re tu rn m ethods, w hich were explained in a one-period
se ttin g in Chapters 2 and 3. We then consider o the r m ethods th a t have been employed in project
evaluation.
C hapter five Project
evaluation : principles a n d methods
TABLE 5.1 Tasks and outcomes of the capital expenditure process
|
Tasks
Outcomes
Stage 1
Generation of
investment
proposals
Systematic processes are established to
ensure members of the organisation may
contribute ideas to enhance firm value
Incentives may be provided to reward
employees who contribute ideas
Investment proposals are forwarded
to management
- employees dealing in production
processes w ill typically
contribute ideas relating
to eliminating operating
inefficiencies
- proposals by upper-level
managers w ill mostly relate to
wider issues such as product
development or expansionary
opportunities
Stage 2
Evaluation
and selection
of investment
proposals
Data about each investment proposal are
•
collected. Data include:
一 a description of the proposal
- the reasons for its adoption
- estimates of amount and tim ing of cash
inflows and outflows
- an estimate o f the time u ntil the proposal
w ill come into operation and the economic
life o f the proposal once it is adopted
All proposals are then evaluated using
standard uniform procedures to ensure that
assessments are conducted objectively
The economic evaluation of the projects
is conducted using a variety o f techniques
(discussed in Section 5.3) that take into
account the risk of the net cash flows that are
expected to be delivered by the project
A list o f recommended projects
is prepared by responsible
management
Stage 3
Approval
and control
of capital
expenditures
A capital expenditure budget is prepared that •
details the estimated capital expenditure
requirements on new and existing projects
over the next few years:
- a short-term budget is prepared that
relates to a period ranging from, say,
6 months to 2 years
- a longer-term budget is also prepared that
provides forecasts of cash requirements
over the next 2 to 5 years
Processes are established to ensure that the
project is properly managed and monitored.
These processes typically include:
- the appointment of a project manager
responsible for the implementation of
the project and the preparation of regular
progress reports
一 the establishment of a realistic timetable
for implementation of the project
- the establishment of a separate
account for each project to ensure that
expenditures are readily observed
Systematic processes are
established that enable the firm to
effectively manage and m onitor the
implementation o f new projects
continued
B usiness finance
Table 5.1 continued
Tasks
Stage 4
Post­
completion
audit of
investment
projects
•
•
Outcomes
Projects are regularly re-evaluated via a postcompletion audit to ensure that each project is
meeting the expectations o f the firm
The audit w ill identify where cash flows are
significantly different from budget forecasts
and possible reasons for such differences
•
•
In itial investment decisions may be
improved as those responsible for
investment proposals are aware that
they w ill be audited
Improvements in the operating
perform 芑nee of projects
facilitated as new inform ation is
regularly provided to managers
Unsuccessful projects are identified
at the earliest possible time—
leading to their abandonment and
subsequent savings to the firm
M any methods are used to evaluate and compare investm ent projects. The methods outlined in this
section are those th a t surveys o f business practice suggest are used most frequently. They are o f two basic
types:
a
b
the discounted cash flow methods, such as the internal rate o f return and net present value
methods, which discount a projects estimated cash flows to allow fo r the magnitude and tim in g o f
the cash flows
the non-discounted cash flow methods, such as the accounting rate o f retu rn and payback period
methods.
Figure 5.1 shows some results from different surveys o f chief financial officers in the US, Australia and
Canada. In all three countries, net present value and internal rate o f retu rn are easily the m ost popular,
followed by payback period.
Figure 5.1 Selected project evaluation methods used by surveyed chief financial
officers!0)
80.00%
70.00%
<
- ui 60.00%
、
!/>
50.00%
40.00%
30.00%
f i
20 .00 %
s<
^0 o 10.00 %
0.00%
Internal rate
of return
Net present
value
Payback
period
Accounting rate Real options
of return
analysis
(a) The aggregated percentage exceeds 100 per cent because most respondents use more than one method of project evaluation
Sources: Graham, J.R. & Harvey, C.R., 'The theory and practice of corporate finance: Evidence from the field7, Journal
of Financial Economics, May 2001, pp. 187-243; Coleman, L., Maheswaran, K. & Pinder, S.; 'Narratives in managers'
corporate finance decisions', Accounting & Finance, September 2010, pp. 6 0 5 -3 3 ; Baker, H., Dutta, S. & Saadi, S.,
'Management views on real options in capital budgeting', Journal of Applied Finance, February 2011, pp. 18-29.
C hapter five Project
evaluation : principles a n d methods
In this chapter i t is assumed in itia lly th a t investm ent projects are independent. Two projects are said
to be independent i f the acceptance o f one project does n o t preclude the acceptance o f the other project.
Two conditions are necessary fo r two or more projects to be classified as independent:
•
•
It m ust be technically feasible to undertake one o f the projects, irrespective o f the decision made
about the other project(s).
The net cash flows from each project m ust be unaffected by the acceptance or rejection o f the other
project(s).
An example o f independent investm ent projects is where an e n tity is considering whether to
purchase new machinery fo r its factory and whether to commission a new advertising campaign. As
these investments are independent, management can make an accept/reject decision on each investm ent
w itho ut considering its relationship to other investments. Problems caused by the existence o f projects
that are n ot independent are considered in Section 5.4.3.
INDEPENDENT PROJECT
a project that may be
accepted or rejected
without affecting
the acceptability of
another project
DISCOUNTED CASH
FLOW (DCF) METHODS
5.3.1 I Discounted cash flow methods
It can be seen from Figure 5.1 th a t the two m ost frequently employed discounted cash flow (DCF)
m ethods are the net present value and internal rate o f retu rn methods.The net presen t value (NPV)
o f a project is equal to the difference between the present value o f its net cash flows and its in itia l cash
outlay.1 Assuming a cash outlay at the beginning o f the projects life, and a series o f net cash flows in the
following periods, the net present value o f the project is calculated as follows:
which can be w ritte n more conveniently as:
npv
=
y
^
c, ?- c 〇
(1 + k)(
+ — ^
(1 + r)
(1 + r)2
+
+
(1 + r)n
5.3
This can be w ritte n more conveniently as:
n
Ct
Q = E
t=\ (1 + r )'
5.4
where C〇= the in itia l cash outlay on the project
Ct = net cash flow generated by the project at tim e t
n = the life o f the project
r - the internal rate o f return
1
2
NET PRESENT VALUE
(N P V )
the difference between
the present value of
the net cash flows
from an investment
discounted at the
required rate of
return, and the initial
cash outlay on the
investment
5.2
where C〇= the in itia l cash outlay on the project
Ct = net cash flow generated by the project at tim e t
n = the life o f the project
k = required rate o f retu rn
The in tern al rate of retu rn (IRR) o f a project is the rate o f return th a t equates the present value o f
its net cash flows w ith its in itia l cash outlay.2 Assuming a cash outlay at the beginning o f the projects life
and a series o f net cash flows in the follow ing periods, the internal rate o f retu rn is found by solving fo r
r in the follow ing equation:
C〇 = - ^ -
methods which
involve the process of
discounting a series of
future net cash flows to
their present values
The cash flows could be discounted and/or compounded to equivalent values at any point in time. It is usual to discount
the cash flows to the present; hence the use of the term n e t p r e se n t value. An alternative would be to calculate a n et terminal
value. This is equal to the difference between the accumulated value of the net cash flows generated by a project, and the
accumulated value of the initial cash outlay. Use of the net terminal value method gives the same decision as for the net
present value method.
Other terms used to describe the same concept include ‘the DCF return on investment’，‘yield’ and ‘the marginal efficiency of
capital’.
INTERNAL RATE OF
RETURN (IRR)
the discount rate
that equates the
present value of an
investment’s net cash
flows with its initial
cash outlay; it is the
discount rate at which
the net present value is
equal to zero
5.4
The discounted cash flo w methods
com pared
The assumed objective o f a company is to maximise shareholders* wealth. Consistent w ith this objective,
projects should be accepted only i f they are expected to result in an increase in shareholders’ wealth.
Therefore, the m ethod o f project evaluation m ust be consistent w ith m axim ising shareholders* wealth.
O ther things being equal, this w ill occur where a project generates more cash, rather than less cash, and
generates cash sooner, rather than later. The ability o f the net present value and interna l rate o f return
methods to result in decisions th a t are consistent w ith this objective is considered in the follow ing
sections.
5.4.1 | Net present value
The net present value o f a project is found by discounting the projects future net cash flows at the
required rate o f return and deducting from the resulting present value the in itia l cash outlay on the
project. Therefore:
n
npv
=J2
t= l
Ct
(1 + 吖
-C o
5.5
Where the investment outlays occur over more than one period, C〇in Equation 5.5 refers only to the
in itia l cash outlay. A ll subsequent outlays are included in the calculation o f the net cash flows o f future
periods. O f course, this may result in subsequent negative net cash flows in addition to the in itia l cash outiay.
Management should select projects w ith a positive net present value and reject projects w ith a negative
net present value. The am ount o f any positive net present value represents the imm ediate increase in
the company s wealth th a t w ill result from accepting the project— th a t is, a positive net present value
means th a t the projects benefits are greater than its cost, w ith the result th a t its im plem entation w ill
increase shareholders1wealth. Conversely, projects th a t have a negative net present value would reduce
shareholders’ wealth.
The m agnitude o f a projects net present value depends on the projects cash flows and the rate used to
discount those cash flows. I t follows th a t the estim ation o f a projects future cash flows is an im p o rta n t
step in project evaluation. This involves deciding w hat cash flow data are relevant fo r project evaluation
and then estim ating those data. W hile both aspects are im p orta nt, the mechanics o f estim ation, which is
the job o f engineers, m arket research analysts and others, is beyond the scope o f this book. We focus on
the firs t aspect— th a t is, the principles involved in defining and measuring project cash flows.
There are essentially tw o approaches to measuring a projects net cash flows. The most popular
m ethod is to forecast the expected net p ro fit from the project and adjust i t fo r non-cash flow items, such
as depreciation. The second method, and the approach used in this book, is to estimate net cash flows
directly. The cash inflow s w ill comprise receipts from the sale o f goods and services, receipts from the sale
o f physical assets, and other cash flows. Cash outflows include expenditures on materials, labour, indirect
expenses fo r m anufacturing, selling and adm inistration, inventory and taxes. W hile the measurement o f
a projects net cash flows may seem to be straightforw ard, there are some aspects th a t w arrant fu rth e r
consideration. These are discussed in Chapter 6.
In addition to estim ating a projects future cash flows, i t is also necessary to estimate the life o f the
project and determine the required rate o f retu rn to be used in discounting the cash flows. The correct
discount rate to apply is the o p p o rtu n ity cost o f capital.3 This is the rate o f retu rn required on the next
3
Estimation of the required rate of return, or discount rate, is discussed in Chapter 14. It is sufficient at this stage to point out
that the required rate of return is simply the rate of return that a project must generate in order to justify raising funds to
undertake it. Where there is perfect certainty about the outcome of an investment, the risk-free rate, such as the current yield
on government securities of the same maturity as the investment, is the appropriate discount rate. However, where there
is uncertainty about the outcome of the investment, a risk-adjusted required rate of return must be used. Throughout the
remainder of the book we will use the term req u ired rate o f retu rn to indicate the discount rate used in discounted cash flow
calculations.
C hapter five Project
evaluation : principles a n d methods
best— th a t is, forgone— alternative investment. I f the net cash flows have been estimated on an after-tax
basis, then, to be consistent, the appropriate required rate o f retu rn is the after-tax rate. The measurement
o f the required rate o f retu rn is considered in Chapter 14.
Example 5.1 illustrates the application o f the net present value method.
Example 5.1
Bruce Barry is considering an investment of $ 9 0 0 0 0 0 in a project that will return net cash flows
of $5 09 000 , $ 4 5 0 0 0 0 and $ 4 0 0 0 0 0 at the end of Years 1, 2 and 3, respectively. Assuming a
required rate of return of 10 per cent per annum, what is the net present value of the project?
SOLUTION
The net present value may be calculated as shown in Table 5.2.
TABLE 5.2 Calculating a project’s net present value (NPV)
Year
Net cash flows ($ ) !
0
(900 000 )⑷
Discount factor at 10%
Present value ($)
(900000)
1
509000
0.909 09
462 727 (扮
2
450000
0.826 45
371901^)
3
400000
0.751 31
300 526 (幻
235154
NPV ($)
^T h e amount in brackets represents the initial cash outlay.
^T he sum of $ 4 6 2 7 2 7 + $371 901 + $ 3 0 0 5 2 6 = $1 135 154 is the maximum amount the company
would be prepared to pay for the project if the required rate of return is 10 per cent per annum.
A t a discount rate o f 10 per cent per annum, the project has a positive NPV o f $235154 and is
therefore acceptable.
This m ethod is consistent w ith the company’s objective o f m axim ising shareholders’ wealth. I f a
company implements a project th a t has a positive net present value, the company w ill be more valuable
than before it undertook the project, and therefore, other things being equal, the to ta l m arket value o f
the company s shares should increase im m ediately by the same am ount as the net present value o f the
new project. In other words, the company is undertaking a project th a t has a net present value in excess
o f th a t necessary to leave its share price unchanged. This was shown form ally in Chapter 2 using Fishers
Separation Theorem.
In summary, the decision rule fo r the net present value m ethod is as follows:
Accept a project i f its net presen t value is positive when the p ro je cts net cash flows are discounted a t
the required rate o f return.
5 .4 .2 1 Internal rate of return
The internal rate o f return fo r a project is the rate o f return th a t equates the present value o f the projects
net cash flows w ith its in itia l cash outlay. This means th a t Equation 5.4 can be rew ritten as follows:
Ct
c〇 = 0
From Equation 5.6, the internal rate o f retu rn is the discount rate th a t results in a zero net present
value. However, the interna l rate o f retu rn is n o t only the discount rate th a t causes the net present value
o f the projects cash flows to be zero. It also represents:
... the highest rate o f interest an investor could afford to pay, w ithout losing money, i f a ll the funds to
finance the investm ent were borrowed, an d the loan (principal an d accrued in terest) w as repaid by using
the cash proceeds from the investm ent a s they were earn ed.4
Even i f the investm ent outlays occur in more than one period, C〇in Equation 5.6 refers only to the
in itia l cash outlay. Any subsequent investm ent outlays are subtracted from the cash flows o f future
periods, which suggests th a t some o f the net cash flows in Equation 5.6 m aybe negative. The effect on the
interna l rate o f retu rn o f negative net cash flows in subsequent periods is discussed later in this section.
If, as is usual in practice, the projects net cash flows in each period are n o t equal, the internal rate o f
retu rn can be found only by tria l and error— th a t is, by varying the discount rate u n til the present value
o f the cash flows is equal to the investm ent outlay. I f this process shows th a t the present value o f the net
cash flows is greater than the in itia l cash outlay, then some higher discount rate should make them equal,
and vice versa.
A fte r the interna l rate o f return has been measured, the acceptability o f an investm ent project is
determ ined by comparing the internal rate o f return r w ith the required rate o f retu rn k. Any project w ith
r > k should be accepted and any project w ith r < k should be rejected.
Example 5.2 illustrates the application o f the internal rate o f retu rn method.
Example 5.2
If we take the cash flows of Example 5.1, the project's internal rate of return may be calculated using
Equation 5.3 as follows:
Cn =
C l
〇
d - )
_
+
C2
d
+ r
+
)2
C3
( l + r
)3
Thus:
$900 0 0 0 - $509000 + $450000 + $_400000
By trial and error, r = 25 per cent.5 If the required rate of return is, say, 15 per cent, the project’s
internal rate of return of 25 per cent exceeds the required rate of return and the project is acceptable.
The use o f this method, therefore, appears to be consistent w ith the company s objective o f m aximising
shareholders* wealth. I f the required rate o f retu rn is the m inim um return th a t investors demand on
investments then, other things being equal, accepting a project w ith an internal rate o f return greater
than the required rate should result in an increase in the price o f the company s shares.
M ultiple and indeterminate internal rates of return
In Example 5.2 the investm ents cash flows consisted o f an in itia l cash outlay, followed by a series o f
positive net cash flows. In such cases a unique positive internal rate o f retu rn w ill usually exist.
In certain circumstances, however, it is possible fo r the present value o f the future net cash flows to be
equal to the in itia l cash outlay at more than one discount rate— th a t is, a project may have more than one
internal rate o f return. A necessary condition fo r m ultiple internal rates o f retu rn is th a t one or more o f
the net cash flows in the later years o f a projects life m ust be negative. The presence o f negative net cash
flows in the later years o f a projects life is n o t a sufficient condition fo r m ultiple interna l rates o f return.
In many cases, negative cash flows in the later years o f a projects life are consistent w ith there being only
one internal rate o f re tu rn .6
4
5
6
See Bierman and Smidt (1993).
In practice, a financial calculator may be used to calculate the internal rate of return and eliminate the time-consuming
computations involved in the trial-and-error process. Alternatively, the ^RR1function in Microsoft Excel® might also be used.
Descartes* rule of signs states that there can be as many positive roots for 1 + r as there are changes in the sign of the cash
flows. Therefore, if, after the initial cash outlay, the net cash flows are always positive, there will be at most one positive root
for l + r, and consequendy only one for r itself. However, two sign changes in the cash flow can result in two positive values
for 1 + r, so there may also be two positive values for r. For example, if the two positive values for 1 + r are +1.1 and +1.3,
there will be two positive values for r: 10 per cent and 30 per cent. In the remainder of this section we use the term in tern al
rate o f retu rn to mean p o sitiv e in te rn al r a te o f retu rn .
C hapter five Project
evaluation : principles a n d methods
While, in practice, there is little likelihood o f the occurrence o f m ultiple internal rates o f return, i t is
im p orta nt to recognise th a t there are circumstances where m ultiple internal rates do occur. Such a set o f
circumstances is illustrated in Example 5.3.
E xample 5.3
Consider an investment project with the cash flows shown in Table 5.3.
TABLE 5.3 Project cash flows
Year
Cash flow
0
-14545 620
1
34182 000
2
-20000 000
An example of where such a cash flow pattern may occur is where a mining company is obliged,
after completion of its mining operations, to restore the mine site to its original condition. If we solve
for the internal rate of return of this project, then we find that its net present value is zero at both
10 per cent and 25 per cent— that is, the project has two internal rates of return. The project's net
present value profile, which plots the project's net present value as a function of the required rate of
return, is shown in Figure 5.2.
Figure 5.2 Net present value profile showing two internal rates of return
The number o f internal rates o f retu rn is lim ite d to the number o f sign reversals in the cash flow
stream. In this case there are tw o sign reversals, which is a necessary, b u t n o t sufficient, condition fo r two
internal rates o f return. Three sign reversals is a necessary condition fo r three rates, and so on. Hence, the
number o f cash flow sign reversals corresponds to the maximum, b ut n ot necessarily the actual, number
o f internal rates o f return.
It may be argued th a t m ultiple rates are not a problem because the project may be abandoned at the
beginning o f the second year, thereby avoiding the subsequent negative cash flow, and also the m ultiple
internal rate o f return problem. I f the project is term inable and has a positive residual value, a unique
internal rate o f return may be calculated. However, in some cases, abandonment o f the project may n ot
be feasible because it may involve substantial abandonment costs in the early years o f operation, or there
may be a legal obligation to continue the project fo r a num ber o f years.
In addition to the problem o f m ultiple internal rates o f return, it is possible fo r an investm ent project
to have no internal rate o f return. For example, a project w ith the follow ing pattern o f cash flows:
-$80 000, +$100 000, -$5 0 000, has no internal rate o f return.
6
^
B usiness finance
Projects w ith a cash flow stream th a t results in either m ultiple internal rates o f return, or no internal
rate o f return, are likely to be rare in practice, b ut the possibility o f such occurrences does exist. In what
follows, it is assumed th a t a projects cash flow pattern results in a unique internal rate o f return.
In summary, the decision rule fo r the internal rate o f retu rn m ethod is:
Accept a project i f it h as a unique in ternal rate o f return th at is g reater than the required rate o f return.
5 .4 .3 1 Choosing between the discounted cash flow methods
Independent investments
LEARNING
OBJECTIVE 3
Explain the
advantages and
disadvantages of
the main project
evaluation methods
For independent investments, both the IRR and NPV methods o f investm ent evaluation lead to the same
accept/reject decision, except fo r those investments where the cash flow patterns result in either m ultiple
interna l rates o f retu rn or no internal rate o f return. In other words, i f a project has an internal rate o f
retu rn greater than the required rate o f return, the project w ill also have a positive net present value
when its cash flows are discounted at the required rate o f retu rn — th a t is, NPV > 0 when r > k, NPV < 0
when r < k, and NPV = 0 when r = k. This is always true, provided th a t the projects cash flows consist o f
one or more periods o f cash outlay followed only by positive net cash flows. Such a project is referred to
as a conventional project and the net present value profile o f such a project is illustrated in Figure 5.3.
Figure 5.3 shows th a t the higher the discount rate, the lower is the net present value. The intercept o f the
net present value profile w ith the horizontal axis occurs at the p o in t where k = r, which is the interna l rate
o f return because i t is the discount rate at which the net present value is zero.
Figure 5.3 Net present value profile for a conventional project
Figure 5.3 shows th a t at a required rate o f retu rn o f k1} the net present value is positive and r >
k1} while at a required rate o f retu rn o f k2 the net present value is negative and r < /c2. I f management
has to decide whether to accept or reject an independent investm ent project, then b o th the internal
rate o f retu rn m ethod and the net present value m ethod w ill give results consistent w ith m axim ising
shareholders’ wealth.
M utually exclusive investments
So far it has been assumed th a t investm ent projects are independent, which means th a t management
can make an accept/reject decision about each project w ith o u t considering its relationship w ith other
C hapter five Project
evaluation : principles a n d methods
projects. In this section, we allow fo r the fact th a t investm ent projects may be interdependent. In this
case, the expected benefits fro m one project are affected by a decision to accept or reject another project.
In the extreme case, where the expected cash flows from a project w ill completely disappear i f another
project is accepted, or i t is technically impossible to undertake the proposed project i f another project is
accepted, the projects are said to be m utually exclusive. For example, i f a company owns land on which
it can build either a factory o r a warehouse, then these tw o projects are m utually exclusive. I f a decision
is made to b uild the factory, the company is unable to build the warehouse. A nother example o f m utually
exclusive projects is i f different types o f equipment can be used to manufacture the same product. The
choice o f one type o f equipm ent autom atically leads to the rejection o f the other.In the remainder o f
this section the discounted cash flow methods w ill be evaluated, assuming th a t investm ent projects are
m utually exclusive. Where management has to select from m utually exclusive projects it is necessary to
rank the projects in order o f acceptability. This means th a t i t is necessary to determ ine w hether it makes
any difference to project selection i f projects are ranked according to th e ir internal rates o f retu rn or th eir
net present values.
First, we consider in Example 5.4 whether the interna l rate o f retu rn or net present value methods
should be used to evaluate m utually exclusive investments.
E xample 5.4
Consider the mutually exclusive investments, A and B, in Table 5.4.
TABLE 5.4
Project 1 Cash outlay ($)
Net cash flow 1 year after the year
of outlay ($)
IRR (%)
N P V @ 10%($)
A
-1
+10
900
8.09
B
-100000
+200000
100
81818.18
The internal rate o f retu rn m ethod ranks a 900 per cent retu rn on $1 ahead o f a 100 per cent return
on $100000. A t a required rate o f retu rn o f 10 per cent, both investments are w o rth undertaking, but
if a choice has to be made between the tw o investments, then investm ent B w ith the larger net present
value is to be preferred. This is because B adds more to the company s value than A. The net present value
method w ill ensure th a t the value o f the company is maximised, whereas the use o f the internal rate
o f return m ethod w ill n o t ensure th a t result. I t is apparent, therefore, th a t the internal rate o f return
and net present value methods can rank m utually exclusive investm ent projects differently. This is now
explained.
Ranking mutually exclusive investments
Although both projects in Example 5.4 had the same life, the in itia l cash outlays were different. However,
even if the in itia l cash outlays and the projects* lives had been the same, i t is s till possible th a t the internal
rate o f return and net present value methods would rank m utually exclusive investments differently. This
is illustrated by Example 5.5.
In Example 5.5, the difference in ranking is caused by differences in the magnitude o f the net cash
flows. In addition to differences in ranking caused by differences in the cash flow streams, the interna l
rate o f retu rn and net present value methods may give a different ranking where the investm ent projects
have unequal lives.
It may be concluded, therefore, that:
… any difference in the m agnitude or tim ing o f the cash flows m ay cause a difference in the ranking o f
investm ent projects using the internal rate o f return an d net presen t value methods.
MUTUALLY EXCLUSIVE
PROJECTS
alternative investment
projects, only one
of which can be
accepted
Example 5.5
Two projects, C and D, have the same initial cash outlays and the same lives but different net cash
flows, as shown in Table 5.5.
What are the internal rates of return and net present values for projects C and D?
SOLUTION
Table 5.6 shows the internal rates of return and the net present values at a required rate of return of
10 per cent for projects C and D.
TABLE 5 .6
Internal rate of return (%) Net present value ($)
Project
C
40
119008
D
50
105 785
Both projects have a positive net present value and an internal rate of return greater than the
required rate of return and are therefore acceptable in their own right. In other words, if the projects
are independent, both should be implemented. However, if the projects are mutually exclusive and
therefore must be ranked, the two methods give different rankings. In this case using the net present
value method, C is preferred to D, while using the internal rate of return method, D is preferred to C.
This is illustrated in Figure 5.4, which shows the net present value profiles fo r tw o projects, E and
F. Assume, as in Example 5.5, th a t the tw o projects have the same cash outlay and lives, and that the
pattern o f net cash flows results in the net present value profiles shown in Figure 5.4. In this case, the
net present value profiles o f the two projects intersect. A t a discount rate o f rv or at any other discount
rate less than r2, the net present value o f E is greater than the net present value o f F, w hile at a discount
rate o f r3, or at any other discount rate greater than r2, the net present value o f F is greater than the net
present value o f E.7
On the other hand, it has already been shown th a t the interna l rate o f retu rn is found where the net
present value is zero and, using this rule, Project F is ranked ahead o f Project E because its internal rate o f
return, r5, is greater than r4, which is the internal rate o f retu rn o f E.8 In this case, the tw o methods can
provide management w ith different rankings o f projects E and F.
7
For projects such as those in Table 5.5 with the same initial cash outlay, r2 is found by equating the present values of projects
E and F as follows:
PVe = Y 7.
8
Ce,
(1 + r2) f
c,：t
-E
；
,= 1 (1 +
厂2 )
In this instance, r2 = 18.89 per cent. This means that if the required rate of return is less than 18.89 per cent, the internal rate
of return and net present value methods result in conflicting rankings.
Remember that discounting of the net cash flows at the internal rate of return will result in a net present value of zero.
Therefore:
n
〇= E
Q
( l + r)f
-C 〇
C hapter five Project
evaluation : principles a n d methods
Figure 5.4 Net present value profiles for projects E and F
Like Example 5.5, Figure 5.4 shows th a t even where tw o m utually exclusive projects have the same
in itia l outlays and the same lives, a difference in the projects* rankings may s till occur as a result o f the
projects’ different tim e patterns o f net cash flows. Therefore, fo r m utually exclusive investm ent projects,
the net present value m ethod is superior to the internal rate o f retu rn method, because it always gives a
wealth-maximising decision.
Figure 5.5 Net present value profiles for projects G and
Even where the projects are m utually exclusive, the tw o methods could 5deld consistent rankings i f
the patterns o f the projects* net cash flows result in net present value profiles th a t do n o t intersect. This
is illustrated in Figure 5.5. In this case, the net present value o f Project G at a discount rate o f is greater
than the n et present value o f Project H. This is consistent w ith the internal rate o f retu rn m ethod as r3,
the interna l rate o f retu rn o f Project G, is greater than r2, the internal rate o f retu rn o f Project H.
However, because o f the possibility th a t the internal rate o f retu rn m ethod may give an incorrect
ranking o f m utually exclusive investm ent projects, the net present value m ethod is preferred.
The incremental internal rate of return approach to ranking
mutually exclusive investments
The internal rate o f return m ethod can be adapted so th a t i t provides a correct ranking o f m utually
exclusive projects. This is shown in Example 5.6.
Example 5.6
The cash flows for two projects, I and J, are shown in Table 5.7. Are projects I and J acceptable?
TABLE 5.7
"
Cash flows ($)
Project
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
I
-45 000
13 500
13500
13500
13500
13 500
J
-30000
9150
9150
9150
9150
9150
SOLUTION
If the required rate of return is 8 per cent per annum, both projects are acceptable using either the net
present value or the internal rate of return method, as shown in Table 5.8.
TABLE 5.8
Project
Internal rate of return (%)
Net present value ($)
I
15.2
8902
J
15.9
6533
If the two projects are mutually exclusive, then, using the net present value method, Project I is
preferred to Project J, while using the internal rate of return method, Project J is preferred to Project I.
The incremental cash flows from choosing Project I (the project with the lower internal rate of return)
rather than Project J (the project with the higher internal rate of return) are presented in Table 5.9.
These cash flows may be assigned to the notional project 1 minus J’.
TABLE 5.9 Cash flows for notional project
Year
1 minus } ' ($)
0
-15000
1
4350
2
4350
3
4350
4
4350
5
4350
C hapter five Project
evaluation : principles a n d methods
The internal rate of return of this notional project is 13.8 per cent. As this internal rate of return
is greater than the required rate of return of 8 per cent, the notional project should be accepted.
Accepting the notional project 7I minus J7 is equivalent to accepting Project I in preference to Project J.
This is the ranking given by the net present value method.
The possibility o f conflict between the interna l rate o f retu rn and net present value methods may
therefore be avoided by the use o f this ‘increm ental internal rate o f retu rn ’ approach. It results in a
ranking o f m utually exclusive projects th a t is consistent w ith the net present value method. However,
the net present value m ethod is simpler and is more obviously consistent w ith the objective o f wealth
maximisation, which is expressed in absolute dollar term s rather than in percentage terms.
5 .4 .4 1 Benefit-cost ratio (profitability index)
Research shows th a t some chief financial officers use the p ro fita b ility index m ethod o f project
evaluation. In this m ethod, instead o f showing the net present value as an absolute am ount, the
present value o f the n et cash flows is divided by the in itia l cash outlay to give a b e n e fit-c o st ra tio or
p ro fita b ility index.A b e n e fit-co st ratio fo r the project in Table 5.2 is calculated as follows:
Benefit-cost ratio =
present value o f net cash flows
5.7
initia l cash outlay
_ $1 135154
$900 000
m
LEARNING
OBJECTIVE 4
Explain why the net
present value method
is preferred to all other
methods
BENEFIT-COST RATIO
index calculated by
dividing the present
value of the future
net cash flows by the
initial cash outlay
(also known as a
profitability index)
= 1 .2 6
Using the benefit-cost ratio, the decision rule is to accept projects w ith a benefit-cost ratio greater than
1, and to reject projects w ith a benefit-cost ratio less than 1. Clearly, projects w ith benefit-cost ratios
greater than 1 w ill have positive net present values, and those w ith benefit-cost ratios less than 1 w ill have
negative net present values. In the above example, the net present value is $235154 and the benefit-cost
ratio is 1.26. Both methods therefore indicate th a t the project is acceptable and, in general, b oth methods
w ill give the same accept/reject decision fo r independent projects.
However, the benefit-cost ratio provides no info rm a tio n additional to th a t already provided by the
NPV method. Thus, there is little p o in t in using this method. In addition, the benefit-cost ratio can result
in a ranking o f m utually exclusive projects th a t differs from the ranking th a t would result from using the
NPV method. This is shown in Example 5.7.
LEARNING
OBJECTIVE 2
Outline the decision
rules for each of the
main methods of
project evaluation
Example 5.7
Consider the mutually exclusive investments projects in Table 5.10.
TABLE 5.10 Ranking projects using the benefit-cost ratio
Project K
Project L
Present value of net cash flows ($)
260000
100000
Initial cash outlay ($)
180000
50000
80000
50000
260 000
100 000
180 000
1.44
50 000
2.00
Net present value
Benefit-cost ratio =
In this case, although the net present value of Project L is less than the net present value of Project K,
the benefit-cost ratio of L is greater than that of K.
命
B usiness finance
Therefore, i f the b e n e fit-co st ra tio is used i t may result in management p re fe rrin g projects
w ith low er net present values. The b e n e fit-co st ra tio m ust therefore be rejected as a ranking
technique because i t can provide incorrect rankings o f m u tu a lly exclusive projects. Research
indicates th a t the p o p u la rity o f the p ro fita b ility index to managers relative to o the r p roject evaluation
techniques is low. Further, survey evidence9 suggests th a t the technique tends to be used by managers
who face a shortage o f funds available to invest in w ealth-enhancing projects. Faced w ith such
constraints, managers have to decide on the m ix o f acceptable projects th a t should be funded in order
to m axim ise the w ealth created fo r the firm . This process, know n as capital rationing, is discussed in
Section 6.8.
5.5
O ther methods of project evaluation
In Figure 5.1, there were two m ajor non-discounted cash flow methods employed by the companies
surveyed. They are the accounting rate o f retu rn and the payback methods. These methods are frequently
employed in conjunction w ith the discounted cash flow methods o f project evaluation.
The accounting rate of return
ACCOUNTING RATE OF
RETURN
earnings from an
investment expressed
as a percentage of the
investment outlay
There are many ways to calculate the accounting rate o f return or retu rn on investm ent. The most
popular methods are those th a t express a projects average annual earnings as a percentage o f either the
in itia l investm ent or the average investm ent in the project. That is:
average annual earnings
Va =
100
------------------------------------------------------------ X ------- %
initia l investment in a project
average annual earnings
1
100
ra = --------------------------------------------------- x ----- %
average investment in a project
1
5.8
■
5.9
PAYBACK PERIOD
the time it takes
for the progressive
accumulated net cash
flows generated by an
investment to equal the
initial cash outlay
Payback period
The payback period is the tim e it takes fo r an e n tity to recover a projects in itia l cash outlay. For example,
the payback period o f a machine th a t costs $300000 and has net cash flows o f $100000 per annum
is 3 years. Sections 5.5.1 and 5.5.2 show th a t the accounting rate o f retu rn and payback methods are
in fe rio r to the net present value method.
5.5.1 | Accounting rate of return
LEARNING
OBJECTIVE 2
Outline the decision
rules for each of the
main methods of
project evaluation
Essentially, the accounting rate o f retu rn is the earnings from a project, usually after deducting both
depreciation and income tax, expressed as a percentage o f the investm ent outlay. I t is compared w ith a
required rate o f retu rn or cut-off rate to determine the project s acceptability. I f the accounting rate o f
return is greater than the required rate o f return, the project is acceptable; i f i t is less than the required
rate o f return, the project is unacceptable.
The accounting rate o f retu rn has many variants. We w ill calculate only three o f these. To calculate
these variants o f the accounting rate o f return, management m ust firs t estimate:
a
b
9
the average annual earnings to be generated by a project. This is calculated by d ivid in g the to ta l
net p ro fit from the project by the num ber o f years d urin g w hich the p ro fit is expected to be
received.
the investm ent outlay on the project. This is equal to either its in itia l investm ent outlay, including
additional and permanent w orking capital requirements, or the average capital employed in the
For surveys of capital budgeting practices, see Burns and Walker (2009).
C hapter five Project
evaluation : principles a n d methods
project. The average capital employed on a project is calculated either as the average book value
o f the investment, or more frequently as the average o f the capital invested in the project at the
beginning and the end o f its life.
The methods o f calculating the accounting rate o f retu rn are illustrated in Example 5.8.
E xample 5.8
Assume that a company is considering an investment project that costs $ 1 0 0 0 0 0 0 0 and generates
returns in Years 1 ,2 and 3 as shown in Table 5.11.
6
TABLE 5.11 Data for calculating the accounting rate of return
Item___________ I
Year 2
Year 3
2000000
3000000
4000000
10000000
7000000
4900000
31 December
7000000
4900000
3430000
Average
8500000
5 950000
4165 000
Earnings (after depreciation
and income tax) ($)
Year 1_____
|
Average
3000000
Book value ($)(a)
1 January
6205 000
^Assuming that depreciation is calculated at 30 per cent on the reducing balance.
Using these data, the following accounting rates of return may be calculated:
a) Accounting rate of return based on the initial investment is:
$3000000 =3〇%
$10000000
b) Accounting rate of return based on the average book value is:
$3 000000 = 48%
$6205000
c)
Accounting rate of return based on average investment as measured by the average of the capital
invested at the beginning and the end of the project's life is:
$3 000000
=44.68%
$ 10 000000+ $3 430000
Each variant yields a different rate of return. For example, if the rate of return is calculated by
dividing average annual earnings by the a verage investment outlay, then the project's rate of return
would be much higher than if it had been calculated by dividing average annual earnings by the
in itia l investment outlay.
There are two fundam ental problems w ith using the accounting rate o f return, irrespective o f the way
it is defined. First, it is arbitrary. This is because i t is based on accounting earnings rather than cash flows.
As a result, factors such as the depreciation m ethod employed and the m ethod o f valuing inventories
w ill have a substantial bearing on the measurement o f earnings and therefore on the accounting rate o f
return. Second, i t ignores the tim in g o f the earnings stream. Equal weight is given to the earnings in each
year o f the projects life. This problem is illustrated in Example 5.9.
LEARNING
OBJECTIVE 3
Explain the
advantages and
disadvantages of
the main project
evaluation methods
E xample 5.9
A company is considering two projects, M and N. Both projects cost $ 1 000 00 at the beginning of
the first year and have a life of 5 years. The residual value of each project at the end of the fifth year
is zero. The earnings for each project are shown in Table 5.12.
TABLE 5.12
Annual earnings ($)
Project
Outlay ($1
Year 1
Year 2
Year 3
Year 4
Year 5
Total
M
100000
2500
5000
10000
15000
17500
50000
N
100000
17500
15000
10000
5000
2500
50000
The average rate of return for each project is:
$50 00 0/5
$10000
$ 10 00 00 /2
$50000
100%
0^ 0/
1
Project M has increasing earnings while Project N has decreasing earnings. However, both result
in the same total earnings, and therefore the same average annual earnings. Consequently, both
projects are regarded as equally acceptable if the accounting rate of return method is used. However,
the two projects are not equally acceptable because the earnings from Project N are received earlier
than the earnings from Project M. Intuition would suggest, therefore, that Project N is preferable to
Project M.
The accounting rate o f retu rn fails to reflect the advantages th a t earlier returns have over later returns.
As a result, this m ethod ranks projects w ith the same in itia l outlay, life and to ta l earnings equally, even
though the projects1patterns o f earnings may be different. In addition, i f projects w ith the same in itia l
outlay and to ta l earnings have different lives, the accounting rate o f retu rn m ethod w ill automatically
favour projects w ith short lives. However, there is no reason w hy such projects should necessarily prove
to be the m ost profitable projects.
Because o f its significant shortcomings, the accounting rate o f retu rn m ethod should n o t be used to
evaluate investm ent projects. However, as we observed earlier, in practice the accounting rate o f return is
often used in conjunction w ith the discounted cash flow methods. Because external financial analysts use
earnings (profit) to assess a company s performance, management may wish to ensure th a t projects are
acceptable according to both accounting and discounted cash flow criteria.
5 .5 .2 1 Payback period
The payback period is the tim e it takes fo r the in itia l cash outlay on a project to be recovered from the
projects net cash flows. I t is calculated by summing the net cash flows from a project in successive years
u n til the to ta l is equal to the in itia l cash outlay. This is illustrated in Table 5.13.
TABLE 5.13 Calculation of payback period
Project Q
Year
Initial cash outlay ($)
0
100000
Project R
Net cash flow ($)
Initial cash outlay ($)
Net cash flow ($)
100000
1
20000
20000
2
30000
40000
C hapter five Project
evaluation : principles a n d methods
Table 5.1 3 continued
Project Q
Year
Initial cash outlay ($)
Project R
Net cash flow ($)
Initial cash outlay ($)
Net cash flow ($)
3
30000
40000
4
20000
10000
5
70000
10000
Total
170000
120000
Payback
period
4 years
3 years
To decide whether a project is acceptable, its payback period is compared w ith some maximum
acceptable payback period. A project w ith a payback period less than the m axim um w ill be accepted, while
a project w ith a payback period greater than the m axim um w ill be rejected.
An im p o rta n t question is: W hat length o f tim e represents the correct, payback period as a standard
against which to measure the acceptability o f a particular project? In practice a m axim um payback period
is set, which is inevitably arbitrary, and may be from , say, 2 to 5 years. A ll projects w ith a payback period
greater than this m axim um are rejected.
Calculation o f the payback period takes in to account only the net cash flows up to the p o in t where they
equal the investm ent outlay. The calculation o f the payback period ignores any net cash flows after that
point. As a result, the payback m ethod o f evaluation discriminates against projects w ith long gestation
periods and large cash flows late in th e ir lives.
The payback period is n o t a measure o f a project s pro fitab ility. I f the m ost profitable projects were
always those th a t recovered the investm ent outlay in the shortest period o f tim e, then current assets
such as inventory and accounts receivable would yield higher returns than non-current assets, and noncurrent assets w ith short lives would yield higher returns than non-current assets w ith long lives. Mere
recovery o f the outlay on a project yields no p ro fit at all. I f there is a p ro fit on the project i t m ust be due
to additional cash flows after the investm ent outlay has been recovered. Therefore, the m ajor weakness
o f the payback m ethod is its failure to take account o f the magnitude and tim in g o f all o f a projects cash
inflows and outflows.
Why then is payback popular as a m ethod o f investm ent evaluation? As was shown in Figure 5.1,
many companies around the w orld use payback in conjunction w ith other methods. One reason fo r its
popularity is th a t i t provides in fo rm a tio n on how long funds are likely to be com m itted to a project.
Managers who prefer projects w ith short payback periods are interested in how soon the funds invested in
a project w ill be recouped and hence this m ethod provides managers w ith inform a tion th a t w ill facilitate
th eir preparation o f cash flow budgets, thereby enabling them to better manage the liq u id ity o f the firm .
Another reason is th a t the near-term cash flows considered in calculating the payback period are regarded
as more certain than later cash flows. As a result, insistence on a short payback period is a simple b u t
imprecise way o f controlling fo r risk.
5 .5 .3 1 Economic value added (EVA)
In Section 5.5.1, i t was noted th a t the accounting rate o f retu rn m ethod is often used in addition to
the discounted cash flow methods because financial analysts generally use accounting inform a tion to
assess performance year by year. To overcome the problems o f measuring the accounting rate o f return
discussed in Section 5.5.1, the economic value added (EVA) approach to measuring performance was
introduced by consulting firm s in the US.10
10 Economic value added (EVA) is the term used by the US consulting firm Stern-Stewart. This firm has been instrumental in
popularising this measure of performance.
LEARNING
OBJECTIVE 2
Outline the decision
rules for each of the
main methods of
project evaluation
m
LEARNING
OBJECTIVE 5
Understand the
relationship between
economic value added
(EVA) and net present
value (NPV)
B usiness finance
Accounting p ro fit is calculated as the difference between revenues and expenses fo r a reporting
period. One o f the costs incurred by a company th a t is n o t deducted in calculating p ro fit is the company s
required rate o f return. To calculate the EVA o f an investm ent, i t is sim ply a m atter o f deducting from
accounting earnings the p ro fit required from the investm ent, calculated as the required rate o f return
m ultiplie d by the capital invested in the project. Thus, using Example 5.9, i f the required rate o f return is
10 per cent, then the returns generated in Years 1, 2 and 3 would be as shown in Table 5.14.
TABLE 5.14
Year 1
Year 2
Year 3
2000
3000
4000
700
490
$2300
$3510
Earnings (after depreciation and income tax) ($)
Capital charge:
Am ount invested x 10% ($)
1000(fl)
Economic value added (EVA)
$1000
In Year 1, the amount invested in the project is $10000, therefore the capital charge is $10000 x 10% = $1000.
The EVA in Table 5.14 shows the addition to the company s wealth created by the investment. If
the accounting rate o f retu rn were equal to the required rate o f return, then EVA would be zero. EVA,
therefore, provides management w ith a simple rule: invest only i f the increase in earnings is sufficient to
cover the required rate o f return.
EVA makes the required rate o f retu rn an im p o rta n t element in measuring the performance o f an
investm ent. The manager o f a plant can improve EVA either by increasing earnings or by reducing the
capital employed. Therefore, there is an incentive fo r managers to id e n tify underperform ing assets and
dispose o f them.
Note th a t this approach to measuring EVA does n ot measure present value. However, it can be shown
th a t the present value o f a stream o f future EVAs fo r an investm ent is equal to the net present value of
the investm ent. The EVA in each period is equal to the net cash flow plus or m inus the change in the value
o f the investm ent less the required rate o f return. Thus:
5.10
E V A ^ C ^ il-I^ -k l^
where Ct = net cash flow in Year t
I t = value o f the investm ent at the end o f Year t
= value o f the investm ent at the end o f Yeart
k = required rate o f return
However, there are tw o special cases:
a
b
In Year 0, EVA0 = C〇+ J〇because there is no capital charge u n til Year 1.
A t the end o f the project, the investm ent in the project (Jt) is zero because the investm ent is
liquidated and therefore EVAt = Ct - (1 + k) 1 ^ .
Therefore, the present value o f a stream o f EVAs is:
EVA〇
EVAi
EVA2
1+ k
(1 + k ) 2
EVAT. y
EVAt
{ l + k )T~l ( l + k )T
BB1
where EVA0 = C〇+ J〇
EVA1 = C1 + I 1 - ( l + k) I 0
EVA2 = C2 + 12 - (1 + /c)
£ \^ 4 了_1 = C t_i + 1"了_1 (1 + /c) 1了_2
EVAj = CT - (1 + /c) I T-1
W hen these values are substituted in to Equation 5.11, we fin d th a t all the I terms cancel out, leaving:
C〇 ^ - g j - + — ^
1 + fc
(1 + k f
+ .,,+
£ r-i
(l + k f - 1
_C
t
(1 + k ) T
= NPV
That is, the discounted stream o f EVAs is the same as the NPV o f the investment.
C hapter five Project
5.6
evaluation : principles a n d methods
Project evaluation and real options
analysis
A key message o f this chapter has been th a t discounted cash flow techniques, such as NPV and IRR,
provide the m ost accurate, and m ost popular, approach to project evaluation. However, we know th a t
these techniques are answering a very specific question about the lin k between a project and wealth
creation th a t may n o t be the question we should be m ost interested in. For example, NPV analysis
provides us w ith an estimate o f the wealth created fo r the firm now zfthe firm were to imm ediately invest
in the project. That is, the approach treats projects as now-or-never prospects— whereas we know th a t in
reality managers often have significant fle xib ility in how they manage a project (including when to begin
it). In addition, NPV is lim ite d to a yes-or-no analysis; fo r example, i t im p lic itly gives no recognition to
the fact that, after a project has begun, managers may intervene in the project as circumstances develop.
Obviously, this significantly understates the role o f managers.
These lim ita tion s o f NPV analysis can, in principle, be dealt w ith using an approach known as
real options analysis. The follow ing section explains how real options analysis differs from standard
discounted cash flow techniques and describes some o f the evidence th a t suggests that, despite its
apparent usefulness, it is used by relatively few financial managers.11
5 .6 .1 1 Real options analysis
Consider the follow ing scenario: substantial o il reserves have just been discovered in Sydney Harbour
and the government has called fo r bids fo r the rig h t to extract the oil. Comprehensive geological reports
estimate th a t there are 40 m illio n barrels o f o il th a t could be extracted. Owing to the unique environm ent
in which the o il is located, and the need to ensure that any disturbance to the environm ent fro m the
invasive extraction process is remedied, the present value o f the expected cost o f extraction is relatively
high, at $80 per barrel. The long-run expected sales price o f the o il is estimated to be $70 per barrel in
present value terms. How much would an investor bid fo r the rig h t to extract oil? Standard NPV analysis
would suggest that no rational investor would bid a positive amount fo r the extraction rig h t as the project
has a negative NPV w ith each barrel o f o il extracted decreasing wealth by $10.
W hat is wrong w ith this analysis? I t ignores the fact th a t the successful bidder fo r the project obtains
the right, b u t n o t the obligation, to commence operations. That is, the successful bidder has the option to
extract the oil. Based upon current expectations o f available technology, cost structures and revenues i t is
at present unprofitable to extract the o il and the option would n o t be imm ediately taken up. However, it
is n ot d ifficu lt to th in k o f circumstances th a t may result in the project having a positive NPV. For example,
new technology may be developed to substantially reduce the cost o f extraction or the long-run expected
sales price o f o il m ig ht increase. Either way, the successful bidder has purchased the rig h t to exploit any
advantageous change in circumstances.
Throughout this chapter it has been im p lic itly assumed th a t the problem facing management is
lim ited to accepting or rejecting a project fo r immediate im plem entation. In reality o f course, th is is
rarely the case. Managers can often choose when to im plem ent a project and can influence the way an
ongoing project is managed. These choices* faced by management are often referred to as real option s
and problems may arise when the value o f options created (or destroyed) by management decisions is not
accounted fo r during the project evaluation stage.
Some common examples o f real options include:
•
O ption to delay investm ent— this option is linked to the a b ility o f the firm to ‘w ait and see’ and
collect more inform a tion about the project th a t may alter the final decision. This option is especially
valuable to a firm where the level o f uncertainty surrounding a project is high. W hen a firm finally
commits to a project, it is giving up the o pp o rtu n ity to collect more info rm a tio n about the project,
and hence, it is often argued, the NPV o f a project m ust n o t only be positive, b ut be great enough to
compensate the firm fo r the value o f the fle xib ility i t is giving up.
11 For an excellent and accessible discussion of the importance of incorporating real options into project evaluation see Dixit
and Pindyck (1995).
LEARNING
OBJECTIVE 6
Understand the
relationship between
real options,
managerial flexibility
and firm value
REAL OPTIONS
ANALYSIS
method of evaluating
an investment
opportunity that
accounts for the
value associated with
managers having
flexibility in their
decisions about when
to invest, how to
manage the investment
and when to divest
themselves of the
investment asset
REAL OPTIONS
the flexibility that
a manager has in
choosing whether to
undertake or abandon
a project or change
the way a project is
managed
B usiness finance
•
•
•
O ption to expand operations— when a firm firs t enters a m arket i t quite often does so on
unprofitable terms. That is, firm s w ill quite w illin g ly enter in to a project th a t has a negative NPV.
One explanation fo r this seemingly irra tion al behaviour is th a t by gaining a presence in the market,
the firm is able to acquire valuable expansion options th a t would otherwise be unavailable. An
example o f this type o f behaviour was the intro du ction o f V irg in Blue Airlines to the Australian
m arket. In itia lly the airline provided only seven daily Brisbane-Sydney return flights. However,
follow ing the collapse o f Ansett Airlines (the second largest domestic carrier in Australia at the
tim e), V irg in Blue found itse lf in a position where it could rapidly expand to fill the void le ft by
Ansett.
O ption to abandon operations— once a firm makes the decision to proceed w ith a project, it
generally retains the rig h t to abandon operations and sell o ff the assets dedicated to the project at
th e ir salvage value. A t the outset, o f course, the firm does n o t expect to make use o f (or exercise)
this option, b u t i t is im p orta nt th a t it has the a bility to do so i f m arket conditions were to move
significantly against the project. This does not, however, im p ly th a t the firm w ill abandon operations
as soon as a project becomes unprofitable, since by doing so the firm gives up the a bility to remain in
the m arket were conditions to change back in the project’s favour.
Once we accept the notion th a t managerial fle x ib ility is valuable, ide ntifyin g real options is relatively
straightforw ard. The d ifficult p art is to tr y to then value them. A discussion o f the general principles
underlying option pricing, as well as a more detailed discussion o f real options analysis, is provided
in Chapter 18.
W hile finance academics have been very enthusiastic about the possible im plications o f real options
analysis fo r financial managers, the international evidence in Figure 5.1 suggests th a t the actual usage of
the technique has been relatively low over an extended tim e interval beginning at the tu rn o f the century.
So who is using real options analysis and why are they doing so? In a survey o f the capital budgeting
practices o f Fortune 1000 companies in the US, Block (2007) reports th a t users o f the technique tended
to be concentrated in industries such as technology, energy and u tilitie s, where sophisticated analysis*
was a standard part o f running the business. In a sim ilar survey o f Canadian firm s, Baker, D utta and
Saadi (2011) report th a t the most popular reasons cited fo r using real options analysis were that the
approach assists management in form ing th e ir strategic vision, fo r the firm while allowing fo r the impact
o f managerial fle x ib ility in the analysis. Also o f interest are the factors th a t impede the im plem entation o f
real options analysis. Block (2007) finds th a t the m ost frequently cited reason fo r avoiding the technique
is *[a] lack o f top management support*. Baker, D utta and Saadi (2011) provide a helpful glimpse at the
reason behind th a t lack o f support: th e ir respondent sample nominates a 'lack o f expertise or knowledge*
as the m ost significant reason fo r not using the approach.
C hapter five Project
evaluation : principles a n d methods
Of the two discounted cash flow methods of investment
evaluation, we recommend the net present value
method because it is consistent with the objective of
maximising shareholders' wealth. It is also simple to
use and gives rise to fewer problems than the internal
rate of return method. W e have shown that where
mutually exclusive projects are being considered, the
internal rate of return method may result in rankings
that conflict with those provided by the net present
value method. In addition, we have shown that even
if investment projects are independent, it is possible
that a project's pattern of cash flows may give rise to
multiple internal rates of return, or to no internal rate
of return at all.
If the net present value method is adopted, the
rules for making correct investment decisions are
straightforward:
• Calculate each project's net present value, using
the required rate of return as the discount rate.
•
If the projects are independent, accept a project
if its net present value is greater than zero, and
reject it if its net present value is less than zero.
• If the projects are mutually exclusive, accept
the project with the highest net present value,
provided that it is greater than zero.
• In practice, companies often use one method of
project evaluation in conjunction with other methods.
For example, one of the discounted cash flow methods
may be used to measure a project's profitability, but
the payback period may also be used, either as a
check on liquidity effects or as a means of monitoring
the project's cash flows against expectations.
• Whereas the evaluation methods considered
throughout the chapter tend to treat projects as
'now-or-never7 prospects, and ignore the ability of
management to intervene in an ongoing project,
real options analysis considers the value associated
with managerial flexibility.
KEY TERMS
accounting rate of return 1 18
benefit-cost ratio 117
discounted cash flow (DCF) methods
independent project 107
internal rate of return (IRR) 107
107
mutually exclusive projects 113
net present value (NPV) 107
payback period 118
real options 123
real options analysis 123
SELF-TEST PROBLEMS
The management of a company is considering an investment of $1 8 0 0 0 0 in a project that will generate
net cash flows of $101 80 0 at the end of the first year, $ 9 0 0 0 0 at the end of the second year and
$ 8 0 0 0 0 at the end of the third year. Assuming a required rate of return of 10 per cent per annum,
calculate the project's net present value.
Calculate the internal rate of return for the investment in Question 1.
Calculate the benefit-cost ratio for the investment in Question 1.
Solutions to self-test problems are available in Appendix B.
QUESTIONS
1
[LO 1 ] Outline the four steps in the capital-expenditure process.
2
[LO 2 】What factors does the required rate of return of a project reflect?
3
[LO 2] Compare the internal rate of return and net present value methods of project evaluation. Do these
methods always lead to comparable recommendations? If not, why not?
4
[LO 2] Distinguish between independent and mutually exclusive investment projects.
5
[LO 3] Evidence suggests that financial managers use more than one method to evaluate investment projects.
Comment on this statement.
C H A P T E R FIVE R E V I E W
SUMMARY
B usiness finance
6
[ L 0 3 ] The internal rate o f return m ethod o f p ro je c t evaluation is easier to use because it avoids the need to
calculate a re q u ire d rate o f return. C o m m e n t o n th is s ta te m e n t.
7
[L O 3 ]
W h a t p ro b le m s a r e a s s o c ia te d w ith th e use o f th e a c c o u n tin g r a te o f re tu rn m e th o d f o r th e
e v a lu a tio n o f in v e s tm e n t p ro p o s a ls ? W h y m ig h t m a n a g e rs b e a ttr a c te d to its use?
8
9
[L O 4 ] Even w here projects are independent, the uncritical use o f the internal rate o f return m ethod can
seriously m islead management. D iscuss.
[L O 4
】D e m o n s tra te ,
fo r in d e p e n d e n t in v e s tm e n t p ro je c ts , th a t th e in te rn a l ra te o f re tu rn a n d n e t p re s e n t
v a lu e m e th o d s o f e v a lu a tio n y ie ld id e n tic a l d e c is io n s . S p e c ify a n y a s s u m p tio n s y o u m a k e .
10
[LO 4 ] U s in g th e N P V p r o file te c h n iq u e , e x p la in w h y th e IRR a n d N P V ru le s w ill a lw a y s re s u lt in th e s a m e
a c c e p t o r r e je c t d e c is io n f o r in d e p e n d e n t p ro je c ts .
11
12
[LO 4 The p a y b a c k p e rio d m ethod o f p ro je c t evaluation is b ia se d a g a in st projects w ith lo n g e r
developm ental lives, even w here they ultim ately generate g re a t value fo r the firm. Discuss.
[L 0 5 ]
A s th e p re s e n t v a lu e o f a stre a m o f EVAs f o r a n in v e s tm e n t is th e s a m e a s its n e t p re s e n t v a lu e , w h y
d o a n a ly s ts use EVA?
13
[L O 6 ] T h e re is s o m e e v id e n c e th a t w h e n m a n a g e rs e v a lu a te p ro je c ts , th e y s y s te m a tic a lly e m p lo y d is c o u n t
ra te s th a t e x c e e d th e ris k -a d ju s te d r e q u ire d ra te o f re tu rn . H o w is th is o b s e r v a tio n c o n s is te n t w ith th e n o tio n
th a t re a l o p tio n s a r e im p o r ta n t in p r o je c t e v a lu a tio n ?
14
[L O 6 ] Real options analysis prom ises to be a ve ry p o w e rfu l to o l fo r fin a n c ia l m anagers. D e s c rib e th e
e v id e n c e c o n c e r n in g th e p o p u la r ity o f th e a p p r o a c h — re la tiv e to d is c o u n te d c a s h f lo w t e c h n iq u e s — a n d
s u g g e s t p o s s ib le re a s o n s f o r th e se resu lts.
cA
1
PROBLEMS
Discount rates, IRR and N P V analysis [LO 2]
A s s u m e th a t y o u a re a s k e d to a n a ly s e th e fo llo w in g th re e p ro je c ts :
A
-2 0 0 0 0 0
20000
20000
20000
20000
220000
B
-2 0 0 0 0 0
52760
52760
52760
52 760
52760
C
-2 0 0 0 0 0
一
一
一
一
322100
C o n s tru c t a s p re a d s h e e t, a n d a s s o c ia te d g ra p h s , th a t w ill e n a b le y o u to a n a ly s e th e im p a c t o f d iffe re n t d is c o u n t
ra te s o n th e N P V o f a p r o je c t as w e ll a s c a lc u la te th e IRR fo r a p r o je c t (a n e x a m p le is p r o v id e d in F ig u re 5 .2 ).
a)
R a nk th e th re e p ro je c ts a s s u m in g th e a p p r o p r ia te d is c o u n t ra te is:
i) 6 p e r c e n t p e r a n n u m
b)
2
ii)
10 per cent per annum
iii)
15 p e r ce n t p e r a n nu m .
C a lc u la te th e IRR fo r e a c h o f th e p ro je c ts , th e n ra n k th e m .
IRR and N P V analysis for independent projects [LO 2]
T he fo llo w in g in v e s tm e n t p ro p o s a ls a re in d e p e n d e n t. A s s u m in g a r e q u ire d ra te o f re tu rn o f 1 0 p e r c e n t, a n d
u s in g b o th th e in te rn a l ra te o f re tu rn a n d n e t p re s e n t v a lu e m e th o d s , w h ic h o f th e p ro p o s a ls a r e a c c e p ta b le ?
C a s h f lo w ($ )
126
P ro p o s a l
Year 0
Year 1
Year 2
A
-4 0 0 0 0
8000
48000
B
-4 0 0 0 0
42000
C
-4 0 0 0 0
48000
C hapter five Project
evaluation : principles a n d methods
U s in g th e fo llo w in g d a ta , c a lc u la te th e :
a)
a c c o u n tin g ra te o f re tu rn
b)
p a y b a c k p e rio d
c)
in te rn a l ra te o f re tu rn
d)
n e t p re s e n t v a lu e .
P ro je c t co st:
$100000
E stim a te d life :
5 y e a rs
E s tim a te d re s id u a l v a lu e :
$20000
A n n u a l n e t c a sh f lo w :
$30000
R e q u ire d ra te o f re tu rn :
10%
U se th e s tra ig h t-lin e m e th o d o f d e p r e c ia tio n in y o u r c a lc u la tio n s .
H o w w o u ld y o u r a n s w e rs d iff e r if th e n e t c a s h flo w s w e r e a s fo llo w s ?
Y e a r 1:
$30000
Year 2:
$40000
Year 3:
$60000
Year 4 :
$20000
Year 5:
$50000
C H A P T E R FIVE R E V I E W
A c c o u n tin g ra te o f r e tu r n , p a y b a c k p e r io d , IRR a n d N P V [L O 2 ]
A c c o u n tin g r a te o f re tu r n a n d p a y b a c k p e r io d [L O 3 ]
U s in g th e f o llo w in g d a ta , c a lc u la te :
a)
th e a c c o u n tin g ra te o f re tu rn
b)
th e p a y b a c k p e r io d .
P ro je c t co st:
$40000
E stim a te d p r o je c t life :
5 y e a rs
E stim a te d re s id u a l v a lu e :
$8000
A n n u a l a c c o u n tin g p r o fit
(e q u a l to a n n u a l n e t c a s h in flo w ):
$ 12000
Use th e s tra ig h t-lin e m e th o d o f d e p r e c ia tio n in y o u r c a lc u la tio n s .
H o w w o u ld y o u r a n s w e rs to (a) a n d (b) d iffe r if th e e s tim a te d d o lla r re tu rn s w e r e a s fo llo w s ?
Year 1
$12000
Year 2
$16000
Year 3
$24000
Year 4
$20000
Year 5
$8000
IRR a n d N P V a n a ly s is [L O 4 ]
E ach o f th e fo llo w in g m u tu a lly e x c lu s iv e in v e s tm e n t p ro je c ts in v o lv e s a n in itia l c a sh o u tla y o f $ 2 4 0 0 0 0 . T he
e s tim a te d n e t c a s h flo w s fo r th e p ro je c ts a re a s fo llo w s :
C a s h f lo w ($)
P ro je ct
1
140000
20000
2
80000
40000
3
60000
60000
4
20000
100000
5
20000
180000
127
B usiness finance
T he c o m p a n y 's re q u ire d ra te o f re tu rn is 1 1 p e r ce n t.
C o n s tru c t a s p re a d s h e e t, a n d a s s o c ia te d g ra p h s , th a t w ill e n a b le y o u to a n a ly s e th e im p a c t o f d iffe re n t
d is c o u n t rates o n th e N P V o f a p r o je c t as w e ll as c a lc u la te th e IRR fo r a p ro je c t. W h a t is th e N P V a n d IRR fo r
b o th p ro je c ts ? W h ic h p r o je c t s h o u ld b e c h o s e n ? W h y ?
6
N P V and IRR analysis for mutually exclusive projects [LO 4 】
A c o m p a n y w is h e s to e v a lu a te th e fo llo w in g m u tu a lly e x c lu s iv e in v e s tm e n t p ro p o s a ls :
P ro p o s a l
a)
A
-97400
34000
34000
34000
34000
34000
B
-63200
24000
24000
24000
24000
24000
C a lc u la te e a c h p r o p o s a l’s n e t p re s e n t v a lu e a n d in te rn a l ra te o f re tu rn . A s s u m e th e re q u ire d ra te o f re tu rn is
8 p e r ce n t.
b)
H o w w o u ld y o u e x p la in th e d iffe re n t ra n k in g s g iv e n b y th e n e t p re s e n t v a lu e a n d in te rn a l ra te o f re tu rn
m e th o d s?
7
N P V a n d IRR a n a ly s is [L O 4 】
You h a v e b e e n a s k e d to e v a lu a te th e f o llo w in g in v e s tm e n t p ro p o s a ls :
C a s h f lo w ($ )
P ro p o s a l
Year 0
Year 1
A
100000
-140000
60000
B
-12000
24000
-20000
Year 2
C a lc u la te th e n e t p re s e n t v a lu e (a s s u m in g a re q u ire d ra te o f re tu rn o f 1 2 p e r cen t) a n d th e in te rn a l ra te o f
re tu rn fo r e a c h p ro je c t. E x p la in y o u r results.
REFERENCES
Baker, H., Dutta, S. & Saadi, S., 'M anagem ent views on real
options in capital budgeting', Journal of A pplied Finance,
February 2 0 1 1 , pp. 1 8 -2 9 .
Dixit, A.K. & Pindyck, R.S., 'The options approach to capital
investment7, Harvard Business Review, M ay-June 1995,
pp. 1 0 5 -1 5 .
Bierman, H. Jr & Smidt, S., The Capital Budgeting Decision:
Economic Analysis of Investment Projects, 8th edn, M acmillan
Company, N ew York, 1993.
Graham, J.R. & Harvey, C.R., 'The theory and practice of
corporate finance: evidence from the field', Journal of
Financial Economics, May-June 2 0 0 1 , pp. 1 8 7 -2 4 3 .
Block, S., 'Are "real options” actually used in the real world?'
The Engineering Economist, 2 0 0 7 , pp. 2 5 5 -6 7 .
W alker, E.D., Introducing project management concepts
using a jewelry store robbery7, Decision Sciences Journal of
Innovative Education, Spring 2 0 0 4 , pp. 6 5 -9 .
Burns, R.M. & W a lk e r,」•，'C apital budgeting surveys: The
future is now ', jo u m a / o f >App//ec/ 尸 /nance, 2 0 0 9 , pp. 7 8 -9 0
Coleman, L , Maheswaran, K. & Pinder, S., 'N arratives in
managers7 corporate finance decisions', Accounting and
Finance, September 2 0 1 0 ; pp. 6 0 5 -3 3 .
128
▼
CHAPTER CONTENTS
m
H H
I n t r o d u c tio n
130
A n a ly s in g p r o je c t ris k
149
A p p lic a t io n o f th e n e t p r e s e n t v a lu e m e th o d
130
D e c is io n - tr e e a n a ly s is
153
T a x is s u e s in p r o je c t e v a lu a t io n
134
QQj
Q u a lit a t iv e f a c t o r s a n d th e s e le c tio n
o f p r o je c ts
156
P r o je c t s e le c tio n w it h r e s o u r c e c o n s tr a in ts
157
C o m p a r in g m u tu a lly e x c lu s iv e p r o je c ts t h a t
h a v e d if f e r e n t liv e s
139
H H
D e c id in g w h e n to r e t ir e ( a b a n d o n ) o r
r e p la c e a p r o je c t
146
LEARNING OBJECTIVES
A f te r s tu d y in g th is c h a p t e r y o u s h o u ld b e a b le to :
1
e x p la in th e p r in c ip le s u s e d in e s t im a tin g p r o je c t c a s h f lo w s
2
e x p la in th e e ffe c ts o f t a x e s o n p r o je c t c a s h flo w s
3
c o m p a r e m u t u a lly e x c lu s iv e p r o je c ts t h a t h a v e d if f e r e n t liv e s
4
d e t e r m in e w h e n to r e t ir e ( a b a n d o n ) o r r e p la c e a s s e ts
5
e x p la in h o w s e n s itiv ity a n a ly s is , b r e a k - e v e n a n a ly s is a n d s im u la t io n a s s is t in a n a ly s in g p r o je c t r is k
6
u s e d e c is io n - tr e e a n a ly s is to a n a ly s e s e q u e n tia l d e c is io n s
7
e x p la in th e r o le o f q u a lit a t iv e f a c t o r s in p r o je c t s e le c tio n
8
e x p la in th e e ffe c ts o f r e s o u r c e c o n s t r a in ts o n p r o je c t s e le c tio n .
B usiness finance
Introduction
In C h a p te r 5, m e th o d s o f p ro je c t e v a lu a tio n w e re discussed a n d th e reasons f o r u s in g th e n e t p re s e n t
va lu e m e th o d o f p ro je c t e v a lu a tio n w e re o u tlin e d . H o w e ve r, in C h a p te r 5 i t was a ssu m ed t h a t a p ro je c ts
cash flo w s a n d th e d is c o u n t ra te a p p lic a b le to th o s e cash flo w s w e re b o th k n o w n . In p ra c tic e , a p ro je c t s
cash flo w s a n d re q u ire d ra te o f r e tu r n are n o t k n o w n w it h c e rta in ty b u t m u s t be e s tim a te d . In o th e r
w o rd s, p ra c tic a l p ro je c t e v a lu a tio n in v o lv e s im p o r t a n t issues c o n c e rn in g th e e s tim a tio n o f cash flo w s an d
ris k . These a n d o th e r issues are th e s u b je c t o f th is c h a p te r. In p a rtic u la r, th e m a tte rs c o n s id e re d in th is
c h a p te r in c lu d e :
•
th e a p p lic a tio n o f th e n e t p re s e n t v a lu e m e th o d , in c lu d in g th e e s tim a tio n o f cash flo w s
•
u s in g th e n e t p re s e n t v a lu e m e th o d to solve p ro b le m s , such as c o m p a rin g p ro je c ts w it h d iffe re n t
liv e s a n d a sse t-re p la ce m e n t de cisio ns
•
th e a p p lic a tio n o f te c h n iq u e s t h a t a llo w m an ag ers to analyse th e r is k o f p ro je c ts
•
th e in flu e n c e o f q u a lita tiv e fa c to rs o n th e s e le c tio n o f in v e s tm e n t p ro je c ts
•
th e p ro b le m s associated w it h u s in g th e n e t p re s e n t v a lu e m e th o d w h e re co m p a n ie s are assu m ed to
have o n ly lim ite d access to reso urce s.1
6.2
LEARNING
OBJECTIVE 1
Explain the principles
used in estimating
project cash flows
A pp lica tio n of the net present value
method
A n y a p p lic a tio n o f th e n e t p re s e n t va lu e m e th o d re q u ire s e s tim a te s o f p ro je c t cash flo w s . This s e c tio n
discusses issues t h a t are im p o r t a n t in d e fin in g th e re le v a n t cash flo w s.
6.2.1 | Estimation of cash flows in project evaluation
Issues t h a t a rise in d e fin in g th e re le v a n t cash flo w s in c lu d e th e :
•
tre a tm e n t o f fin a n c in g charges
•
in c lu s io n o f in c re m e n ta l cash flo w s
•
im p o rta n c e o f e x c lu d in g s u n k costs
•
tre a tm e n t o f a llo c a te d costs
•
tre a tm e n t o f a p ro je c ts re s id u a l value
•
t im in g o f th e cash flo w s
•
tr e a tm e n t o f in fla tio n .
These issues are discussed in tu r n .
Financing charges
C o m pa nie s s h o u ld use th e re q u ire d ra te o f r e tu r n to d is c o u n t a p ro je c ts n e t cash flo w s . The re q u ire d rate
o f r e tu r n is th e r e tu r n t h a t is s u ffic ie n t to co m p e n sa te s h a re h o ld e rs a n d d e b th o ld e rs f o r th e resources
c o m m itte d to th e p ro je c t. I t in clu d e s b o th in te re s t p a id to d e b th o ld e rs a n d re tu rn s to sha reh old ers.
T h ere fore, fin a n c in g charges such as in te re s t a n d d iv id e n d s s h o u ld n o t be in c lu d e d in th e c a lc u la tio n o f a
p ro je c ts n e t cash flo w s . The in c lu s io n o f fin a n c in g charges in a p ro je c t s n e t cash flo w s a n d in th e d is c o u n t
ra te w o u ld re s u lt in d o u b le c o u n tin g .
Incremental cash flows
In c a lc u la tin g a p ro je c t s n e t cash flo w s , i t is th e in c re m e n ta l n e t cash flo w s t h a t are im p o r ta n t. A n a n a ly s t
s h o u ld in c lu d e
all cash flo w s
t h a t change i f th e p ro je c t is u n d e rta k e n . W h e n d e c id in g w h e th e r a p a rtic u la r
ite m s h o u ld be in c lu d e d , th e a n a ly s t is in te re s te d in th e an sw e rs to tw o q u e s tio n s :
1
The effects of taxes on discount rates are discussed in Chapter 14.
C hapter six T he
application of project evaluation methods
cash ite m ?
a
Is i t a
b
W ill th e a m o u n t o f th e ite m
change i f
th e p ro je c t is u n d e rta k e n ?
I f th e an sw e r to b o th q u e s tio n s is ‘yes’，th e n th e ite m is an in c re m e n ta l cash flo w . I f th e a n sw e r to
e ith e r q u e s tio n is ‘n o ’，th e n th e ite m is irre le v a n t to th e an alysis. F o r e xa m p le , assum e t h a t a c o m p a n y
is re c e iv in g $ 4 0 0 0 0 p e r yea r fr o m r e n tin g a p o r tio n o f its fa c to ry , a n d t h a t i t is c o n s id e rin g u s in g th a t
space to m a n u fa c tu re a p ro d u c t t h a t w i ll r e tu r n n e t cash flo w s o f $ 1 0 0 0 0 0 p e r year. In t h is case, $ 1 0 0 000
o ve rsta tes th e n e t cash flo w s f r o m th e p ro d u c t b y an a m o u n t o f $ 4 0 0 0 0 ; th e cash in flo w fo rg o n e because
a p o r tio n o f th e fa c to ry w ill n o t be re n te d . The in c re m e n ta l n e t cash flo w in th is case is $ 6 0 0 0 0 p e r
year. The p rin c ip le o f in c lu d in g o n ly in c re m e n ta l cash flo w s m a y seem sim p le , b u t i t s o m e tim e s in v o lv e s
d iffic u ltie s such as id e n tify in g s u n k costs a n d a llo c a te d costs.
Sunk costs
Suppose t h a t th e S p ilt O il C o m p a n y has s p e n t $ 2 0 m illio n e x p lo rin g a p a r tic u la r area w ith o u t success.
H a rv e y M ills , th e g e o lo g is t w h o o r ig in a lly id e n tifie d th a t area as p o te n tia lly va lu a b le , argues t h a t th e
co m p a n y s h o u ld spe nd a n o th e r $5 m illio n to d r ill an a d d itio n a l w e ll because: ‘I f w e d o n ’t, th e $ 2 0 m illio n
th a t we have a lre a d y s p e n t w i ll be lost*. M r M ills s a rg u m e n t is in c o rre c t because th e $ 2 0 m illio n is a sunk
SUNK COST
cost.
cost that has already
been incurred and
is irrelevant to future
decision making
S u n k costs are p a s t o u tla y s a n d s h o u ld be ig n o re d in m a k in g de cisio n s a b o u t w h e th e r to c o n tin u e a
p ro je c t o r to te rm in a te it . In t h is case, th e $ 2 0 m illio n has a lre a d y b e en s p e n t. T his fig u re w i ll n o t change
i f th e p ro je c t is c o n tin u e d o r a b a n d o n e d . A llo w in g s u n k costs to in flu e n c e d e cisio n s can lead to t h r o w in g
good m o n e y a fte r b a d 1. R egardless o f w h e th e r $2 o r $2 0 m illio n has a lre a d y be en s p e n t, d e cisio n s o n
w h e th e r to c o n tin u e a p ro je c t s h o u ld be based o n ly o n e xp ected
future costs
a n d b e n e fits .
Allocated costs
C om panies o fte n a llo ca te costs such as re n t, p o w e r, w a te r, research a n d d e v e lo p m e n t, he ad o ffic e costs,
tra v e l an d o th e r ove rh e a d costs to t h e ir d iv is io n s . T h ere fore, w h e n th e p r o fita b ilit y o f a p ro je c t is
e stim a te d , th e costs a ttr ib u te d to th e p ro je c t m a y in c lu d e a share o f th e se a llo c a te d costs. The a n a ly s t
s h o u ld re m e m b e r t h a t w h e n a p ro je c t is b e in g eva lu ated , o n ly in c re m e n ta l cash flo w s s h o u ld be in c lu d e d .
In som e cases, im p le m e n tin g an a d d itio n a l p ro je c t m a y re s u lt in s ig n ific a n tly h ig h e r o v e rh e a d costs, b u t
in o th e r cases a n y increase m a y be n e g lig ib le . W h e n e s tim a tin g p ro je c t cash flo w s , a n y a llo c a te d costs
s h o u ld be e x a m in e d c a re fu lly to d e te rm in e w h e th e r th e y w o u ld change i f th e p ro je c t w e re to go ahead. I f
th e y w o u ld n o t change th e y s h o u ld be exclud ed.
Residual value
W h e n a p ro je c t is te rm in a te d , i t is lik e ly t h a t a p o r tio n o f th e in it ia l c a p ita l o u tla y w ill be recovered. This
is o fte n te rm e d th e p ro je c ts
residual value.
A p ro je c ts re s id u a l va lu e w ill be th e d isp o sa l va lu e o f th e
p ro je c ts assets, less a n y d is m a n tlin g a n d re m o v a l costs associated w it h th e te r m in a tio n o f th e p ro je c t.
Timing of the cash flows
In som e cases, fin a n c ia l c a lc u la tio n s are based o n th e precise t im in g o f th e re le v a n t cash flo w s . F o r
exam ple, such p re c is io n is s ta n d a rd p ra c tic e w h e n c a lc u la tin g th e va lu e o f m a rk e ta b le d e b t s e c u ritie s
such as b o n d s a n d b a n k b ills . In the se cases, b o th th e a m o u n t a n d th e t im in g o f th e cash flo w s are k n o w n .
H o w eve r, w h e n an in v e s tm e n t p ro je c t is e va lu a te d , th e m a g n itu d e o f th e cash flo w s is ra re ly k n o w n b u t
m u s t be e s tim a te d , u s u a lly w it h som e degree o f e rro r. S im ila rly , th e t im in g o f cash flo w s can ra re ly be
e s tim a te d p re c is e ly a n d th e s im p lify in g a s s u m p tio n t h a t n e t cash flo w s are rece ive d a t th e e n d o f a p e rio d
is u s u a lly a d o p te d . T his a s s u m p tio n reduces th e c o m p le x ity o f th e n e t p re s e n t v a lu e c a lc u la tio n s w ith o u t
causing a m a rk e d decrease in th e ir re lia b ility , a n d i t is th e a s s u m p tio n a d o p te d in th e re m a in d e r o f th is
cha pter.
Inflation and project evaluation
The A u s tra lia n e co n o m y has a t tim e s e xp e rie n ce d p ro lo n g e d p e rio d s o f in fla tio n . D u rin g a p e rio d
o f in fla tio n th e re is an in crea se in th e g e n e ra l le v e l o f p rice s a n d hence a fa ll in th e p u rc h a s in g p o w e r
o f m oney. There are tw o a p pro ache s to in c o rp o ra tin g th e e ffe cts o f in fla t io n in to p ro je c t e v a lu a tio n .
RESIDUAL VALUE
disposal value of
a project's assets
less any dismantling
and removal costs
associated with the
project's termination
B o th ap pro ache s, a p p lie d c o n s is te n tly , w ill g ive th e sam e n e t p re s e n t value . B o th re q u ire th e a n a ly s t to
e s tim a te th e f u tu r e ra te o f in fla tio n .
O ne a p p ro a ch in v o lv e s m a k in g e s tim a te s o f cash flo w s t h a t are based o n a n tic ip a te d p rice s d u rin g
each y e a r o f a p ro je c ts life , a n d d is c o u n tin g th o s e cash flo w s a t th e n o m in a l re q u ire d ra te o f r e tu rn . In
th is case, th e e s tim a te d n e t cash flo w s fr o m a p ro je c t in , say, its f o u r t h y e a r o f o p e ra tio n are based on
th e p ric e s e xp ected in t h a t f o u r t h year. The presence o f in fla t io n th e re fo re m akes th e jo b o f e s tim a tin g
n e t cash flo w s m o re d iffic u lt, esp e cia lly i f p rice s are e xp e cte d to increase a t a ra p id ra te . The use o f th e
nominal re q u ire d
ra te o f r e tu r n m ea ns t h a t th e d is c o u n t ra te re fle c ts th e m a rk e ts e x p e c ta tio n s a b o u t th e
ra te o f in fla tio n . I f i t is e xp e cte d t h a t th e ra te o f in fla t io n w ill increase in th e fu tu re , th e n m a rk e t pressure
s h o u ld le a d to an increase in th e n o m in a l re q u ire d ra te o f r e t u r n o n an in v e s tm e n t. T h e re fo re , o b serve d
n o m in a l ra te s o f r e tu r n have b u ilt in to th e m e xp ected f u tu r e in fla t io n rates. T his a p p ro a ch is c o n s is te n t,
in t h a t n e t cash flo w s based o n a n tic ip a te d f u tu r e p ric e le vels are d is c o u n te d a t th e n o m in a l re q u ire d rate
o f r e tu r n , w h ic h also has b u ilt in to i t e xp ected in fla t io n rates.
The o th e r a p p ro a ch in v o lv e s e s tim a tin g th e n e t cash flo w s w ith o u t a d ju s tin g th e m f o r a n tic ip a te d
changes in p rice s, a n d d is c o u n tin g th o se cash flo w s a t th e
real re q u ire d
ra te o f re tu rn . In o th e r w o rd s, th e
n e t cash flo w s are e s tim a te d u s in g e x is tin g (c o n s ta n t) prices. To be c o n s is te n t i t is n e cessa ry to d is c o u n t
the se n e t cash flo w s a t th e real re q u ire d ra te o f re tu rn , w h ic h excludes e xp e cte d in fla tio n .
E xa m p le 6.1 illu s tra te s t h a t th e tw o approaches, a p p lie d c o n s is te n tly , g ive th e sam e re s u lt.
Example 6.1
A s s u m e th a t a n in v e s tm e n t o f $ 1 0 0 0 is e x p e c te d to g e n e r a te c a s h flo w s o f $ 5 0 0 , a t c o n s ta n t p ric e s ,
a t th e e n d o f e a c h o f 3 y e a rs . A s s u m e a ls o th a t p ric e s a r e e x p e c te d to in c re a s e a t th e ra te o f 1 0 p e r
c e n t p e r a n n u m a n d th a t th e n o m in a l r e q u ire d ra te o f re tu rn is 1 5 p e r c e n t p e r a n n u m . W h a t is th e
p r o je c t's n e t p re s e n t v a lu e ?
SOLUTION
U s in g th e firs t a p p r o a c h , th e n e t p re s e n t v a lu e o f th e in v e s tm e n t is a s fo llo w s :
$]〇〇〇| $500 (1.10 ) f $ 5 0 0 (1 .10)2 ( $ 5 0 0 (1 .10)3
1.15
(1.15)2
(1.15 )3
= $ 1 0 0 0 = $550 + ^
+
1.15
1.3225
1 .5 209
= $ 3 73
U s in g th e s e c o n d a p p r o a c h , th e n e t c a s h f lo w o f $ 5 0 0 p e r a n n u m a t c o n s ta n t p ric e s is d is c o u n te d
a t th e re a l r e q u ire d ra te o f re tu rn . A s d is c u s s e d in S e c tio n s 1 . 5 . 4 a n d 3 . 4 . 4 , th e re a l ra te m a y b e
e x p re s s e d in te rm s o f th e n o m in a l ra te a s fo llo w s :
1+p
w h e re
i* = th e
re a l ra te o f re tu rn p e r a n n u m
/ = th e n o m in a l ra te o f re tu rn p e r a n n u m
p = th e a n t ic ip a t e d ra te o f in fla tio n p e r a n n u m
T h e re fo re :
1.10
= 4 .5 5 %
T he n e t p re s e n t v a lu e is th e n c a lc u la te d a s fo llo w s :
$500
$500
$500
1 .0 455
(1.0455)2
(1 .0 4 5 5 )3
-$ 1 0 0 0 + J 5 0 ^ + J 5 0 ^ + J 5 0 ^
1.0455
= $373
1.0931
1.1428
C hapter six T he
application of project evaluation methods
In su b se q u e n t exam ples, th e f ir s t a p p ro a ch to in c o rp o ra tin g th e e ffe c t o f in fla t io n in to p ro je c t
e v a lu a tio n is g e n e ra lly a d o p te d . U n lik e th e second ap p ro a ch , i t can be re a d ily a p p lie d w h e re th e a n a ly s t
w ishes to in c o rp o ra te d iffe re n t rates o f change in p rice s f o r d iffe re n t c o m p o n e n ts o f a p ro je c ts cash flo w s.
F o r exam ple, th e ra te o f change in wage rates m a y be fo re c a s t to be d iffe re n t fr o m th e ra te o f change
in ra w m a te ria ls prices. In a d d itio n , th e seco nd a p p ro a ch re q u ire s re lia b le e s tim a te s o f th e a n tic ip a te d
ra te o f in fla tio n , w h ic h m a y be d iff ic u lt to o b ta in . T h e re fo re , th e f ir s t a p p ro a ch is easier to h a n d le in
practice.
6 .2 .2 1 Illustration of cash-flow information in project evaluation
The cash flo w in fo r m a tio n t h a t s h o u ld be c o m p ile d f o r p ro je c t e v a lu a tio n is illu s tra te d in E xa m p le 6.2.
Example 6.2
T he F ra n k S to n e C o m p a n y is c o n s id e r in g th e in tr o d u c tio n o f a n e w p ro d u c t. G e n e r a lly , th e c o m p a n y 's
p ro d u c ts h a v e a life o f a b o u t 5 y e a rs , a fte r w h ic h th e y a r e d e le te d fro m th e r a n g e o f p ro d u c ts th a t
th e c o m p a n y sells. T he n e w p r o d u c t re q u ire s th e p u rc h a s e o f n e w e q u ip m e n t c o s tin g $ 4 0 0 0 0 0 0 ,
in c lu d in g f r e ig h t a n d in s ta lla tio n c h a rg e s . T h e u se fu l life o f th e e q u ip m e n t is 5 y e a rs , w ith a n e s tim a te d
re s id u a l v a lu e o f $1 5 7 5 0 0 0 a t th e e n d o f th a t p e r io d .
T he n e w p r o d u c t w ill b e m a n u fa c tu re d in a f a c t o r y a lr e a d y o w n e d b y th e c o m p a n y . T h e fa c to r y
o r ig in a lly c o s t $1 5 0 0 0 0 0 to b u ild a n d h a s a c u r r e n t re s a le v a lu e o f $ 3 5 0 0 0 0 0 , w h ic h s h o u ld
re m a in f a ir ly s ta b le o v e r th e n e x t 5 y e a rs . T h is f a c t o r y is c u r r e n tly b e in g re n te d to a n o th e r c o m p a n y
u n d e r a le a s e a g r e e m e n t th a t h a s 5 y e a rs to ru n a n d p r o v id e s f o r a n a n n u a l re n ta l o f $ 1 5 0 0 0 0 .
U n d e r th e le a s e a g re e m e n t, th e F ra n k S to n e C o m p a n y c a n c a n c e l th e le a s e b y im m e d ia te ly p a y in g
th e le ssee c o m p e n s a tio n e q u a l to 1 y e a r 's re n ta l p a y m e n t.
It is e x p e c te d th a t th e p r o d u c t w i ll in v o lv e th e c o m p a n y in s a le s p r o m o tio n e x p e n d itu re s th a t w ill
a m o u n t to $ 5 0 0 0 0 0 d u r in g th e firs t y e a r th e p r o d u c t is o n th e m a rk e t. A d d it io n s to c u r r e n t a sse ts w ill
re q u ire $ 2 2 5 0 0 0 a t th e c o m m e n c e m e n t o f th e p r o je c t a n d a r e a s s u m e d to b e fu lly r e c o v e r a b le a t th e
e n d o f th e fifth y e a r.
T h e n e w p r o d u c t is e x p e c te d to g e n e r a te n e t o p e r a tin g c a s h flo w s a s fo llo w s :
Y e a r 1: $ 2 0 0 0 0 0 0
Year 2 : $ 2 5 0 0 0 0 0
Year 3: $3 2 5 0 0 0 0
Year 4 : $ 3 0 0 0 0 0 0
Year 5 : $ 1 5 0 0 0 0 0
It is a s s u m e d th a t a ll c a s h flo w s a r e re c e iv e d a t th e e n d o f e a c h y e a r a n d th e r e q u ire d ra te o f re tu rn
is 1 0 p e r c e n t p e r a n n u m . W h a t is th e n e t p re s e n t v a lu e o f a d d in g th e n e w p ro d u c t?
SOLUTION
T he s o lu tio n to th is e x a m p le is se t o u t in T a b le 6 . 1 .
TABLE 6.1 Cash flow information for adding the new product
C ash
Item
1.
I n it ia l o u tla y
2.
Sale o f e q u ip m e n t
Year 0
Year 1
flows ($，_
Year 2
Year 3
Year 4
Year 5
(4000)
1575
continued
B usiness finance
T a ble 6.1
3.
continued
Factory
The cost and the
c u rre n t resale value o f
th e fa c to ry are b o th
irre le v a n t
(a) Cancel lease
(150)
(b) N e t cash flo w
forgo ne due to re n t
forgone
(150)
4.
M a rk e t research o u tla y
(500)
5.
A d d itio n s to cu rre n t
assets
6.
(150)
(150)
(150)
(225)
(150)
225
N e t cash flow s fro m
operations:
Year 1: $2 000 000
2000
Year 2: $ 2 5 0 0 000
2500
Year 3: $ 3 2 5 0 0 0 0
3250
Year 4: $ 3 0 0 0 0 0 0
3000
Year 5: $ 1 5 0 0 0 0 0
T otal
1500
(4375)
1350
2350
3100
2850
3150
1.000 00
0.909 09
0.826 45
0.751 31
0.683 01
0.620 92
Present value o f n e t cash flow s
(4375)
1227.3
1942.1
2329.1
1946.6
1955.9
N e t pre sen t value
$5026
D is c o u n t fa c to r a t 10%
O n th e b a s is o f th is q u a n tita tiv e a n a ly s is th e c o m p a n y s h o u ld a d d th e n e w p r o d u c t to its p r o d u c t
lin e .
6.3
Tax issues in project evaluation
So fa r in o u r d iscu ssio n o f a lte rn a tiv e m e th o d s o f p ro je c t e v a lu a tio n w e have o u tlin e d th e reasons fo r
LEARNING
OBJECTIVE 2
Explain the effects
of taxes on project
cash flows
p r e fe r r in g th e use o f th e n e t p re s e n t va lu e m e th o d . H o w e ve r, th e e ffe cts o f taxes have so fa r b e en ig n o re d .
The e ffe c ts o f taxes are c o n sid e re d in th is se ctio n .
6.3.1 | Effect of taxes on net cash flows
I f th e re w e re n o taxes, th e m a g n itu d e a n d t im in g o f a p ro je c ts cash in flo w s a n d o u tflo w s w o u ld be th e
o n ly re le v a n t cash flo w in fo r m a tio n f o r p ro je c t e v a lu a tio n p u rp o se s. H o w e ve r, u n d e r th e p ro v is io n s o f th e
Income TaxAssessmentAct 1936} ta x is assessed o n th e ta x a b le in c o m e o f in d iv id u a ls a n d com p an ies. Taxable
in co m e is th e d iffe re n c e b e tw e e n gross in c o m e a n d c e rta in a llo w a b le d e d u c tio n s s p e c ifie d in th e A c t. In c o m e
ta x pa yab le is g e n e ra lly c a lc u la te d as a pe rce n ta g e o f ta x a b le in co m e . In c o m e ta x is a m a jo r cash o u tflo w
f o r m o s t co m p a n ie s a n d its e ffe c t s h o u ld be co n sid e re d to g e th e r w it h o th e r cash in flo w s a n d o u tflo w s .
The ta x re la tin g to a p ro je c t s h o u ld be tre a te d as a cash o u tflo w w h e n th e ta x is p a id . F o r exa m ple, i f
^0^
ta x w ere u s u a lly p a id a t th e en d o f th e y e a r fo llo w in g th e ye a r o f in c o m e , th e n a 1 2 -m o n th la g w o u ld be
C hapter six T he
application of project evaluation methods
a p p ro p ria te f o r c a lc u la tin g a fte r-ta x n e t cash flo w s . H o w e ve r, f o r ease o f c a lc u la tio n , w e assum e t h a t ta x
is p a id w h e n th e associated cash in flo w is received.
A p ro je c ts a fte r-ta x n e t cash flo w s f o r each p e rio d m a y be c a lc u la te d as:
A fte r-ta x n e t cash flo w = n e t cash flo w b e fo re ta x x (1 - tc)
m
w h ere tc = s ta tu to r y c o m p a n y in c o m e ta x ra te 2
H ow ever, th is e q u a tio n ig n o re s th e e ffe c t o f th e ta x d e d u c tib ility o f expenses t h a t do n o t in v o lv e a cash
o u tflo w . In p a rtic u la r, d e p re c ia tio n o f n o n -c u rre n t assets, e x c lu d in g la n d an d, in som e cases, b u ild in g s ,
is an a llo w a b le d e d u c tio n f o r in c o m e ta x p u rp o se s. D e p re c ia tio n is n o t it s e lf a n o u tflo w o f cash, b u t th e
fa ct th a t d e p re c ia tio n is d e d u c tib le f o r ta x p u rp o se s reduces th e in c o m e ta x th a t w o u ld o th e rw is e be
payable— a n d in c o m e ta x is d e fin ite ly a cash o u tflo w . The h ig h e r is th e d e p re c ia tio n charge, th e lo w e r
is th e in co m e ta x payable b y th e co m p a n y a n d hence th e h ig h e r w ill be th e c o m p a n y s a fte r-ta x n e t cash
flow . This increase in a fte r-ta x n e t cash flo w s is re p re s e n te d b y th e ta x savings o n d e p re c ia tio n , w h ic h is
calcula ted as fo llo w s :
6.2
Tax savings o n d e p re c ia tio n = d e p re c ia tio n x tc
T herefore, th e a fte r-ta x n e t cash flo w s g e n e ra te d b y an in v e s tm e n t p ro je c t m a y be c a lc u la te d b y
s u m m in g E q u a tio n s 6.1 a n d 6 .2 as fo llo w s :
A fte r - ta x n e t cash flo w = n e t cash flo w x (1 - tc)
+ d e p re c ia tio n
x tc
6.3
E xam p le 6.3 illu s tra te s th e a p p lic a tio n o f E q u a tio n 6.3.
Example 6.3
A p ro je c t's b e fo re -ta x n e t c a s h f lo w is e x p e c te d to b e $ 1 0 0 0 0 0 p e r a n n u m . F o r ta x p u rp o s e s th e
d e p r e c ia tio n c h a r g e is $ 1 0 0 0 0 p e r a n n u m a n d th e c o m p a n y in c o m e ta x ra te is 3 0 c e n ts in th e d o lla r .
The a fte r-ta x n e t c a s h f lo w is c a lc u la te d a s fo llo w s :
After-tax net cash flow = $ 1 0 0 000(1 - 0 . 3 0 ) + $ 1 0 0 0 0 (0.30)
= $ 7 0 0 0 0 + $7000
=$77000
The e ffe c t o f d e p re c ia tio n o n p ro je c t cash flo w s is m o re co m p le x th a n E xa m p le 6.3 suggests because
th e Income Tax A ssessm en t A ct a llo w s tw o m e th o d s o f c a lc u la tin g d e p re c ia tio n : th e straight-line (or prime-
cost) method a n d th e reducing-balance (or dim inishing-value) method. I f th e re d u cin g -b a la n ce m e th o d is
used, th e a llo w a b le d e p re c ia tio n ra te is g e n e ra lly tw ic e th e s tra ig h t-lin e ra te .3
The d e p re c ia tio n charge c a lc u la te d f o r ta x p u rp o se s m a y b e a r n o re la tio n s h ip to t h a t ca lcu la te d f o r
fin a n c ia l r e p o rtin g p u rp o s e s . F o r exa m ple, a co m p a n y m a y use th e s tra ig h t-lin e m e th o d f o r re p o rtin g
p u rpo ses a n d th e re d u c in g -b a la n c e m e th o d f o r in c o m e ta x p u rp o se s. S tra ig h t-lin e d e p re c ia tio n in v o lv e s
a llo c a tin g th e asse ts co st in e q u a l a m o u n ts o v e r its e s tim a te d u s e fu l life . T h a t is, g iv e n th e a sse ts in it ia l
cost, C, a n d its e s tim a te d u s e fu l life o f n years, th e s tra ig h t-lin e d e p re c ia tio n charge in each ye a r o f th e
assets life is C /n .4SF o r e xa m p le , i f an asset costs $ 1 0 0 0 0 0 a n d has a 1 0 -y e a r life , th e a n n u a l d e p re c ia tio n
charge is $ 1 0 0 0 0 0 / 1 0 = $ 1 0 0 0 0.
2
3
4
As discussed in Section 14.3, under the imputation system that exists in Australia, a company's effective tax rate may be less
than the statutory tax rate and in most cases it is appropriate for the effective tax rate to be used.
For eligible assets purchased after 10 May 2006, the allowable depreciation rate using the reducing-balance method is
twice the straight-line rate. For assets purchased prior to that date, the allowable depreciation rate using the reducingbalance method is 1.5 times the straight-line rate. Taxpayers have at times been able to claim an investment allowance that
is essentially an additional depreciation deduction—for example, as part of its economic stimulus package announced in
2009, the Australian Government permitted small businesses to claim a one-off additional 50 per cent tax deduction on the
purchase of eligible new assets or the improvement of eligible existing assets. Assets that qualified for the allowance were
basically those that could be depreciated for tax purposes.
This contrasts with the method of calculating depreciation for financial reporting purposes. In accounting, the straight-line
depreciation charge is:
(C -S )/n
where C = initial cost
S = estimated residual value or scrap value
n = estimated useful life in years
B usiness finance
Example 6.4
Table 6.2 shows the calculation of the present value of the tax effects associated with depreciation
and disposal of an asset that costs $100000, has an estimated useful life of 5 years and a
disposal value of $7776 at the end of the fifth year. The company income tax rate is 30 per cent
and the after-tax discount rate is 10 per cent per annum. Table 6.2 shows that the reducing-balance
method should be preferred because it results in a higher present value of tax savings and net sale
proceeds.
TABLE 6.2 Tax effects of depreciation and sale of an asset
-
I
Depreciation method
-------------------------------------------------------------------- ------------------------------Straight lin e ^
—
Reducing balance⑹
($)
Present
value of
tax savinqs
and
proceeds
of sale, net
of tax ($)
40000
12 000
10909
4959
24000
7200
5 950
6000
4508
14400
4320
3 246
20000
6000
4098
8640
2592
1770
20000
6000
3 726
5184
1555
966
End of
year
Present
value
factor
1
0.90909
20000
6000
5454
2
0.82645
20000
6000
3
0.75131
20000
4
0 .6 8 3 0 1
5
0.62092
Disposal
Allowable
Tax
depreciation savings^
expense ($)'
($)
Present
value of
tax savings
and
proceeds
Allowable
of sale, net depreciation
of tax ($)
expense ($)
Tax
savings
—
7 7 7 6 (b )
—
4828
7776
—
4828
—
7776
—
—
0
—
—
—
—
(2332)
(1448)
—
—
一
26124
一
value
G ain on
sale
Tax on
0
0
gain
T o ta l
_
一
27669
(a) Straight-line depreciation is charged at a rate of 20 per cent of acquisition cost, and reducing-balance depreciation
is charged at a rate of 40 per cent of the written-down value.
(b) It is assumed that at the end of Year 5 the asset is sold for $7776. Under the reducing-balance method of
depreciation, this is equal to the written-down value at the end of Year 5 and there is no gain or loss on sale.
Consequently, there is no tax effect on the $7776. The present value of the cash inflow is calculated in the usual
way and equals $7776 x (0.620 92) = $4828. Under the straight-line method of depreciation, as the whole of the
asset's acquisition cost has been written off for tax purposes by the end of Year 5, the $7776 received at that time
is regarded as a gain on sale for tax purposes, and increases tax payable by $2332. The present value of this tax
payment is $ 1448.
(c) Tax savings are equal to allowable depreciation expenses x 0.30.
C hapter six T he
In c o n tra s t, re d u c in g -b a la n c e d e p re c ia tio n in v o lv e s c h a rg in g a fix e d
amount)
percentage
application of project evaluation methods
(ra th e r th a n a fix e d
o f th e asse ts w r itte n - d o w n (o r a d ju s ta b le ) v a lu e in each year. The a sse ts w r itte n - d o w n value
is equal to its cost o r o th e r v a lu e (such as a re v a lu e d a m o u n t) less a c c u m u la te d d e p re c ia tio n , w h e re
a ccu m u la te d d e p re c ia tio n is eq u a l to th e s u m o f th e d e p re c ia tio n charges in p re v io u s years. In c o m p a ris o n
w ith s tra ig h t-lin e d e p re c ia tio n , th e re d u cin g -b a la n ce m e th o d o f d e p re c ia tio n re s u lts in la rg e r d e p re c ia tio n
charges in th e e a rly years o f a n a s s e ts life a n d s m a lle r charges in la te r years. T h ere fore, co m p a re d w ith
th e s tra ig h t-lin e m e th o d , re d u c in g -b a la n c e d e p re c ia tio n re s u lts in lo w e r taxes a n d h ig h e r a fte r-ta x cash
flo w s in th e e a rly years. The t o t a l in c o m e ta x p a id is n o t re d u ce d b y u s in g th e re d u cin g -b a la n ce m e th o d .
H ow ever, a p o r tio n o f th e ta x payable is p o s tp o n e d in th e e a rly years o f th e p ro je c ts life . G ive n t h a t a
d o lla r to d a y is w o r th m o re th a n a d o lla r in a y e a rs tim e , i t fo llo w s t h a t th e use o f th e re d u cin g -b a la n ce
m e th o d is g e n e ra lly a d va n ta g e o u s to an asset’s ow ne r.
The a fte r-ta x cash flo w s a sso cia te d w it h o w n e rs h ip o f a d e p re cia b le asset also d e p e n d o n th e
re la tio n s h ip b e tw e e n th e a s s e ts d isp o sa l v a lu e a n d its w r itte n - d o w n value. I f th e d isp o sa l va lu e is eq ua l
to th e w r itte n - d o w n va lu e , th e n sale o f th e asset has n o e ffe c t o n ta x p a id b y th e seller. H o w e ve r, i f th e
tw o values d iffe r, th e re are tw o p o s s ib ilitie s :
a
The asse ts d isp o sa l v a lu e is less th a n it s w r itte n - d o w n value
Suppose t h a t an asset is s o ld f o r $ 1 0 0 0 0 0 b u t its w r itte n - d o w n va lu e is $ 2 5 0 00 0. The d iffe re n c e o f
$ 1 5 0 0 0 0 is reg ard ed as a loss o n sale, w h ic h is ta x d e d u c tib le . I f t c = 0 .3 0 , th e ta x sa vin g o n th e loss
o f $ 1 5 0 0 0 0 is $ 1 5 0 0 0 0 x 0 .3 0 = $ 4 5 0 0 0. T his ta x s a vin g is tre a te d as a cash in flo w , so th e n e t a fte r ­
ta x proceeds are $ 1 4 5 0 0 0.
The asset s d is p o s a l va lu e is m o re th a n its w r itte n - d o w n value
b
Suppose t h a t an asset is s o ld f o r $ 3 0 0 00 0, w h ic h is $ 5 0 0 0 0 m o re th a n its w r itte n - d o w n va lu e . In
th is case th e g a in o n sale o f $ 5 0 0 0 0 is re g ard ed as re c o v e ry o f d e p re c ia tio n d e d u c tio n s t h a t w ere
p re v io u s ly cla im e d . T h e re fo re , th e g a in is ta xa b le b u t th e ta x m a y be d e fe rre d b y d e d u c tin g th e g a in
fro m th e w r itte n - d o w n v a lu e o f a re p la c e m e n t asset o r o th e r de p re cia b le assets.5 I f th e g a in is ta xe d
im m e d ia te ly , th e n e t sale pro cee ds are $ 3 0 0 0 0 0 - $ 5 0 0 0 0 x 0 .3 0 = $ 2 8 5 0 0 0 .
The ta x e ffe cts o f th e s tra ig h t-lin e a n d re d u cin g -b a la n ce m e th o d s are co m p a re d in E xa m p le 6.4.
6 .3 .2 1 Illustration of cash-flow information in project evaluation
with taxes
E a rlie r in th is c h a p te r w e co n s id e re d th e c a s h -flo w in fo r m a tio n t h a t s h o u ld be c o m p ile d f o r p ro je c t
e va lu a tio n . E xam p le 6.5 illu s tra te s h o w taxes s h o u ld be in c o rp o ra te d in to th e c o m p ila tio n o f cash flo w s.
E xample 6.5
The C la r e n d o n C o m p a n y is c o n s id e r in g th e in tr o d u c tio n o f a n e w p r o d u c t. G e n e r a lly , th e c o m p a n y 's
p ro d u c ts h a v e a life o f a b o u t 5 y e a rs , a fte r w h ic h th e y a r e d e le te d fro m th e ra n g e o f p ro d u c ts th a t
th e c o m p a n y sells.
T he n e w p r o d u c t r e q u ire s th e p u rc h a s e o f n e w e q u ip m e n t c o s tin g $ 6 0 0 0 0 0 , in c lu d in g f r e ig h t
a n d in s ta lla tio n c h a rg e s . T h e u s e fu l life o f th e e q u ip m e n t is 5 y e a rs , w ith a n e s tim a te d r e s id u a l v a lu e
o f $ 2 3 6 5 0 0 a t th e e n d o f th a t p e r io d . T h e e q u ip m e n t w ill b e d e p r e c ia te d fo r ta x p u rp o s e s b y th e
r e d u c in g - b a la n c e m e th o d a t a ra te o f 2 0 p e r c e n t p e r a n n u m .
T he n e w p r o d u c t w ill b e m a n u fa c tu re d in a f a c t o r y a lr e a d y o w n e d b y th e c o m p a n y . T h e f a c t o r y
o r ig in a lly c o s t $ 2 0 0 0 0 0 to b u ild a n d h a s a c u rre n t re s a le v a lu e o f $ 5 0 0 0 0 0 , w h ic h s h o u ld re m a in
f a ir ly s ta b le o v e r th e n e x t 5 y e a rs . T h is f a c t o r y is c u rre n tly b e in g re n te d to a n o th e r c o m p a n y u n d e r
a le a s e a g r e e m e n t th a t h a s 5 y e a r s to ru n a n d p r o v id e s f o r a n a n n u a l re n ta l o f $ 2 0 0 0 0 . U n d e r th e
continued
5
Replacement decisions are discussed in Section 6.5.2.
continued
le a s e a g r e e m e n t th e C la r e n d o n C o m p a n y c a n c a n c e l th e le a s e b y p a y in g th e le sse e c o m p e n s a tio n
e q u a l to 1 y e a r 's re n ta l p a y m e n t. T h is a m o u n t is n o t d e d u c tib le fo r in c o m e ta x p u rp o s e s .
It is e x p e c te d th a t th e p r o d u c t w ill in v o lv e th e c o m p a n y in s a le s p r o m o tio n e x p e n d itu re s , w h ic h w ill
a m o u n t to $ 6 0 0 0 0 d u r in g th e firs t y e a r th e p r o d u c t is o n th e m a rk e t. T h is a m o u n t is d e d u c tib le fo r
in c o m e ta x p u rp o s e s in th e y e a r in w h ic h th e e x p e n d itu re is in c u rre d .
A d d it io n s to c u rre n t a sse ts w ill re q u ire $ 3 2 0 0 0
a t th e c o m m e n c e m e n t o f th e p r o je c t a n d a re
a s s u m e d to b e fu lly r e c o v e r a b le a t th e e n d o f th e fifth y e a r.
T he n e w p r o d u c t is e x p e c te d to g e n e r a te n e t o p e r a tin g c a s h flo w s (b e fo re d e p r e c ia t io n a n d in c o m e
ta x ) a s fo llo w s :
•
Y e a r 1: $ 3 0 0 0 0 0
•
Year 2: $ 3 7 5 0 0 0
•
Year 3: $ 4 9 0 0 0 0
•
Year 4: $ 4 5 0 0 0 0
•
Year 5 : $ 2 2 5 0 0 0
It is a s s u m e d th a t a ll c a s h flo w s a r e re c e iv e d a t th e e n d o f e a c h y e a r a n d th a t in c o m e t a x is p a id
a t th e e n d o f th e y e a r in w h ic h th e in flo w o c c u rre d .
T h e c o m p a n y in c o m e t a x ra te is 3 0 c e n ts in th e d o lla r . T h e c o m p a n y h a s a r e q u ire d ra te o f re tu rn
o f 1 0 p e r c e n t a fte r ta x .
T h e s o lu tio n to th is e x a m p le is se t o u t in T a b le 6 . 3 .
SOLUTION
TABLE 6 . 3
C a s h - flo w in f o r m a tio n f o r th e e v a lu a tio n o f th e p u r c h a s e o f
n e w e q u ip m e n t
After-tax cash flows
Item
Year 0
1. I n itia l o u tla y
2. D e p re c ia tio n
Year
Year 1
Year 2
；
Year 3 j Year 4
Year 5
(600000)
Writtendown
value ($)
Depreciation
1
600000
20
120000
36000
—
36000
—
—
—
—
2
480000
20
96000
28800
—
—
28800
—
—
—
3
384000
20
76800
23040
—
—
—
23 040
—
—
4
307200
20
61440
18432
—
—
—
—
18432
—
5
245 760
20
49152
14746
—
—
—
—
—
14746
( %) ( $ )
Tax
savings at
30c in $
3. S ale o f e q u ip m e n t
Sale
$236500
W ritten-down value
$196608
Gain on sale
$39892
Tax on gain at 30%
$11968
Total proceeds
$236500
-$ 1 1 9 6 8
—
—
—
—
—
224532
C hapter six T he
T able 6 .3
application of project evaluation methods
continued
4. Factory
—
—
—
—
—
The cost and th e c u rre n t resale value o f the
fa c to ry are b o th irre le v a n t
a.
Cancel lease
b.
N e t cash flo w forgone due to re n t
(2 0 0 0 0 )
forgone
$20000 ( 1 -0 .3 0 )
5.
—
(1 4 0 0 0 ) (1 4 0 0 0 ) (1 4 0 0 0 ) (1 4 0 0 0 )
(1 4 0 0 0 )
—
(4 2 0 0 0 )
(32 000)
—
—
_
—
32000
Market research outlays
O u tla y
$60000
Less n e t ta x savings a t 30%
$18000
$42000
6. Addition to current assets
______ ______________________________
7. Net cash flows from operations after
deducting company income tax
Year 1: $ 3 0 0 0 0 0
(1 - 0 .3 0 )
—
210000
—
—
—
—
Year 2: $ 3 7 5 0 0 0
(1 - 0 .3 0 )
—
—
262500
—
—
—
Year 3: $ 4 9 0 0 0 0
(1 - 0.30)
—
—
—
343000
—
—
Year 4: $ 4 5 0 0 0 0
(1 - 0 .3 0 )
—
—
—
—
315000
—
Year 5: $ 2 2 5 0 0 0
(1 - 0 .3 0 )
—
—
—
—
—
157500
-6 5 2 0 0 0
190000
277300
352040
319432
414778
0.90909 0.82645 0.75131 0.68301
0.62092
218176
257544
Total
D iscoun t fa c to r a t 10%
Present value o f n e t cash flow s
1.0000
-6 5 2 000
172727
229173
264493
N et present value = $ 4 9 0 1 1 4
O n th e b a s is o f th is q u a n tita tiv e a n a ly s is , th e n e w p r o d u c t s h o u ld b e m a n u fa c tu re d .
6.4
C om paring mutually exclusive projects
that have different lives
In C h a p te r 5 w e c o m p a re d m u t u a lly e xclu sive p ro je c ts t h a t h a d th e sam e life . In p ra c tic e , m a n a g e m e n t
w ill fr e q u e n tly have to c o m p a re m u tu a lly e x c lu s iv e p ro je c ts t h a t ha ve d iffe re n t e c o n o m ic liv e s . Such
p ro je c ts w i ll o fte n in v o lv e e q u ip m e n t t h a t is o f d iffe re n t q u a lity a n d th e re fo re also o f d iff e r e n t cost.
Suppose t h a t a coffee sh o p can b u y e ith e r a T it a n co ffe e m a k e r w it h a life o f 3 yea rs o r th e h ig h e r
q u a lity , m o re e xp e n sive , V u lc a n co ffe e m a k e r w it h a lif e o f 5 yea rs to p e r fo r m th e sam e jo b . B o th
coffee m a ke rs ge n e ra te th e sam e cash in flo w s , so one w a y to co m p a re th e m w o u ld be to c a lc u la te th e
p re s e n t v a lu e o f th e cash o u tflo w s f o r each o f th e m . S uppose t h a t th e p re s e n t v a lu e o f cash o u tflo w s
is $ 4 0 0 0 f o r th e T ita n a n d $ 5 0 0 0 f o r th e V u lc a n . T h is does n o t n e c e s s a rily m e a n t h a t th e T it a n s h o u ld
be p re fe rre d . I f th e T it a n is p u rc h a s e d , i t w i ll have to be re p la c e d 2 years e a rlie r th a n th e V u lc a n .
The a lte rn a tiv e s are n o t d ir e c tly c o m p a ra b le because th e d iffe re n c e in liv e s m e a n s t h a t th e y in v o lv e
d iffe re n t f u tu r e cash flo w s , w h ic h have n o t b e e n co n s id e re d . O n e s o lu tio n w o u ld be to assum e t h a t th e
V u lc a n is s o ld a fte r 3 years. H o w e v e r, th e d is p o s a l v a lu e m a y n o t re fle c t it s v a lu e in use, a n d i t is u s u a l
LEARNING
OBJECTIVE 3
Compare mutually
exclusive projects that
have different lives
B usiness finance
to m a ke o th e r a s s u m p tio n s a b o u t w h a t w i ll h a p p e n a t th e e n d o f th e u s e fu l liv e s o f th e e q u ip m e n t.
CONSTANT CHAIN
C o n s id e r th e fo llo w in g tw o ap pro ache s:
OF REPLACEMENT
ASSUMPTION
may be used to
evaluate mutually
exclusive projects of
unequal lives; in this
case, each project
is assumed to be
replaced at the end of
its economic life by an
identical project
a
I t m a y be assum ed t h a t th e co m p a n y w ill re in v e s t in a p ro je c t t h a t is id e n tic a l to t h a t w h ic h is
b
S pe cific a s s u m p tio n s m a y be m ade a b o u t th e re in v e s tm e n t o p p o r tu n itie s t h a t w ill be com e ava ila ble
c u r r e n tly b e in g a n alysed. T his is k n o w n as th e
con stan t chain o f replacem ent assum ption,
in th e fu tu re .
The second ap p ro a ch is th e m o re re a lis tic a n d c o u ld be im p le m e n te d w h e re th e fu tu r e in v e s tm e n t
o p p o r tu n itie s are k n o w n . H o w e ve r, in p ra c tic e th is a p p ro a ch is d iff ic u lt to im p le m e n t unless m anagers
have co n sid e ra b le fo re s ig h t. T h ere fore, th e f ir s t a p p ro a ch is o fte n used. T his a p p ro a ch is illu s tra te d in
E xa m p le 6.6.
E xample 6 .6
A s s u m e th a t a c o m p a n y is c o n s id e r in g th e p u rc h a s e o f t w o d iffe r e n t p ie c e s o f e q u ip m e n t, A a n d B,
th a t w i ll p e rfo rm th e s a m e ta s k a n d g e n e r a te th e s a m e c a s h in flo w s . T h e re fo re , A a n d B c a n b e
c o m p a r e d o n th e b a s is o f th e ir c a s h o u tflo w s . T he in fo r m a tio n in T a b le 6 . 4 re la te s to A a n d B.
TABLE 6.4 Cash outflows for equipment
In itia l a n d o p e r a tin g costs ($ )
E q u ip m e n t
Year 0
Year 1
A (life 1 year)
15 000
6000
B (life 3 years)
20000
10000
Year 2
Year 3
10000
10000
A s s u m in g a r e q u ire d ra te o f re tu rn o f 1 0 p e r c e n t p e r a n n u m f o r b o th p ie c e s o f e q u ip m e n t, c a lc u la te
th e p re s e n t v a lu e s o f th e costs o f A a n d B.
SOLUTION
T he p re s e n t v a lu e s o f th e co sts o f A a n d B a r e a s fo llo w s :
PV of costs for A = $ 15 000 + $ 6 〇〇〇
1.1
= $ 20 45 5
PV of costs for B = $20 000 + $ 10 000
n . i) 3
0.1
=$ 44 869
If m a n a g e m e n t c o m p a re s th e se fig u re s , th e n in v e s tm e n t in E q u ip m e n t A w o u ld a p p e a r to b e m o re
d e s ir a b le . H o w e v e r, th is c o m p a r is o n is in v a lid b e c a u s e it ig n o re s th e fa c t th a t A a n d B h a v e d iffe re n t
live s. To m a k e a v a lid c o m p a r is o n it is a s s u m e d th a t a t th e e n d o f b o th th e firs t a n d th e s e c o n d y e a rs
E q u ip m e n t A w o u ld b e p u rc h a s e d a g a in . If E q u ip m e n t A w e r e r e p la c e d a t th e e n d o f Y e a rs 1 a n d 2
w ith th e s a m e e q u ip m e n t (a c h a in o f re p la c e m e n t), th e co sts w o u ld b e as s h o w n in T a b le 6 . 5 .
TABLE 6.5 Costs for chain of replacement over 3i years
In itia l a n d o p e r a tin g costs ($)
E q u ip m e n t
Year 0
Year 1
Year 2
A
15 000
15000
15 000
6000
6000
6000
21000
21000
6000
A
T otal
15 000
Year 3
C hapter SIX T he APPLICATION 〇F PROJECT EVALUATION METHODS
In th is c a s e ,
DV/ ,
‘ f
A ⑴
識
$21000
$21000
for A = $ 15 0 0 0 + ------------- + -----------
PVof costs
1.1
( l.l) 2
$6000
( l. l) 3
= $ 5 5 954
B a s e d o n th is c o m p a r is o n o v e r 3 y e a rs , th e p re s e n t v a lu e o f th e co sts f o r A ( $ 5 5 9 5 4 ) is g r e a te r
th a n th e p re s e n t v a lu e o f th e co sts f o r B ( $ 4 4 8 6 9 ) a n d , th e re fo re , B s h o u ld b e p u rc h a s e d .
In th e re m a in d e r o f th is s e c tio n i t is assum ed t h a t m a n a g e m e n t a d o p ts th is a p p ro a ch a n d t h a t each
p ro je c t is re p lic a te d o v e r th e years. A v a lid c o m p a ris o n o f tw o cha in s o f re p la c e m e n t can be m ade o n ly
w h e n b o th cha in s are o f e q u a l le n g th . T his c o m p a ris o n can be ach ie ved in tw o ways:
a
S uppose t h a t P ro je c t A has a life o f 6 years a n d P ro je c t B has a life o f 9 years. I f A is u n d e rta k e n
th re e tim e s a n d B tw ic e , th e re p la c e m e n t c h a in s w i ll be o f eq ua l le n g th — t h a t is, 18 years. In th is
exam ple, 18 is th e lo w e s t c o m m o n m u ltip le o f 6 a n d 9, so th is a p p ro a ch is u s u a lly called th e
common multiple method. A lth o u g h
lowest
th e use o f th is m e th o d c o rre c tly ra n k s m u tu a lly e xclusive p ro je c ts
w ith d iffe re n t live s, i t can be cu m b e rso m e . F o r e xa m p le , tw o p ro je c ts w ith liv e s o f 1 9 a n d 21 years,
resp ective ly, have a lo w e s t c o m m o n m u ltip le o f 3 9 9 years a n d th e cash flo w s f o r each o f these
3 9 9 years w o u ld have to be d is c o u n te d to a p re s e n t value,
b
A less c o m p le x a p p ro a c h , w h ic h ra n k s p ro je c ts id e n tic a lly to th e lo w e s t c o m m o n m u ltip le m e th o d ,
is to assum e t h a t b o t h c h a in s c o n tin u e in d e fin ite ly . In t h is case th e ‘le n g th s ’ o f th e c h a in s are
^ q u a r in th e sense t h a t th e y are b o th in fin it e . T his m e th o d is k n o w n as th e constant chain of
replacement in perpetuity method. I f th e N P V o f each re p la c e m e n t p ro je c t is N d o lla rs a n d th e life
o f each p ro je c t is n yea rs, th e n th e c o n s ta n t c h a in o f re p la c e m e n t is e q u iv a le n t to re c e iv in g a
cash in flo w o f N d o lla rs a t tim e s 0, n, 2rz, 377, a n d so o n , fo re v e r. T h e re fo re , th e N P V o f th e c h a in
c o n sists o f N d o lla rs a t t im e 0 p lu s a p e r p e tu ity o f N d o lla rs pa yab le a t n, 2n, 3n, a n d so on.
T h ere fore:
N
NPV = N +
N
(1 + k )n
(1 + k)
1
N
(1 +
2n
1
k)n
(1 +
k)2n
1
N
1
( l + k )n j
.
k)n
+ k)n- l
(1 +
N
(1
The n e t p re s e n t v a lu e o f th e in fin it e ch a in , N P V ^ , is th e re fo re :
層
一
6.4
。
w h e re N P V 〇 = n e t p re s e n t v a lu e o f each re p la ce m e n t.
A v a r ia n t o f t h is m e th o d is th e
equivalent annual value m ethod.
th e q u e s tio n : W h a t a m o u n t, to be re ce ive d each y e a r f o r
p re s e n t v a lu e o f a p ro je c t w h o s e life is
value (E A V ),
n years?
n yea rs,
T his m e th o d in v o lv e s a n s w e rin g
is e q u iv a le n t to re c e iv in g th e n e t
T his a m o u n t, w h ic h is k n o w n as th e
equivalent annual
is c a lc u la te d f o r each p ro je c t. The p ro je c t w it h th e h ig h e r E A V is p re fe rre d to th e p ro je c t
w it h th e lo w e r EAV, p ro v id e d t h a t b o th p ro je c ts have th e sam e r is k , a n d th e re fo re th e sam e re q u ire d
ra te o f re tu rn .
The s tre a m o f EAVs o v e r
a n n u ity is g iv e n by:
n years
is an o rd in a ry a n n u ity a n d th e re fo re th e n e t p re s e n t v a lu e o f th e
EQUIVALENT A N N U A L
VALUE METHOD
involves calculating
the annual cash flow
of an annuity that has
the same life as the
project and whose
present value equals
the net present value
of the project
or:
(1 + k )n
NPV = EAV
〇
k
T herefore:
NPV
〇
EAV =
(1 W
7
k
The re la tio n s h ip b e tw e e n th e c o n s ta n t c h a in o f re p la c e m e n t a n d E A V m e th o d s is s tra ig h tfo rw a rd .
A ssu m e t h a t a p ro je c t is re p lic a te d in d e fin ite ly . The p re s e n t v a lu e o f an in f in it e s tre a m o f EAVs is:
EAV
PV--
k
NPV
〇
(1 + k )n
1
■NPV 〇
1
(1 w
NPVq
(1 + k )u
(1 + k )r
NPVoo
T h a t is, th e p re s e n t v a lu e o f an in fin it e s tre a m o f EAVs is e q u a l to th e n e t p re s e n t v a lu e o f th e c o n s ta n t
c h a in o f re p la c e m e n t in p e rp e tu ity . T h e re fo re , i f th e n e t p re s e n t v a lu e o f th e in fin it e c h a in
c a lcu la te d , th e n th e E AV can be fo u n d b y m u ltip ly in g
NPV^ b y
NPV^ has been
th e re q u ire d ra te o f r e t u r n — t h a t is, th e
E A V is g iv e n by:
6.6
EAV=kNPV(X
The c o n s ta n t c h a in o f re p la c e m e n t a n d e q u iv a le n t a n n u a l va lu e m e th o d s are illu s tr a te d in E xa m p le 6.7.
Example 6.7
S u p p o s e th a t tw o a sse ts, A a n d B, a r e m u tu a lly e x c lu s iv e p ro je c ts a n d h a v e th e c h a r a c te r is tic s s h o w n
in T a b le 6 . 6 .
TABLE 6.6 Characteristics of two mutually exclusive projects
C a sh in flo w s ($ )
A sset
Life ( Y r s ) , In itia l cash
Year 1
Year 2
Year 3
Year 4
Year 5
o u tla y ($ )
A
3
10000
10000
23000
25 000
—
—
B
5
30000
12000
15000
25 000
30000
30000
It is a ls o a s s u m e d th a t th e r e q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m fo r b o th p ro je c ts . W h ic h
a s s e t s h o u ld b e p u rc h a s e d ?
C hapter SIX T he APPLICATION OF PROJECT EVALUATION METHODS
SOLUTION
The n e t p re s e n t v a lu e o f A s s e t A a t tim e z e r o is:
N PVAo = -$ 1 0 0 0 0 . ^
00 +
1.1
+ $25000
( l. l) 2
( l.l) 3
= $ 3 6 8 8 2 .0 4
T he n e t p re s e n t v a lu e o f A s s e t B a t tim e z e r o is:
md' / d
NPVBr, =
$12000 $15000 $25000 $30000 $30000
-$30000 + ----------+
-------- + ------------------------- — + -------
广
1.1
( i . i )2
( i . i )3
( i . i )4
( i . i )5
=$51 206.70
U s in g E q u a tio n 6 . 4 , th e n e t p re s e n t v a lu e s o f th e in fin ite c h a in s o f re p la c e m e n t a re :
NPVAX
= ($36 882.04)
(1^ —
=$148 308.14
N P V B 〇c = ($51
2 0 6 .7 0 )-^ — '
=$135081.98
T h e re fo re , A s s e t A s h o u ld b e a c c e p te d , n o tw ith s ta n d in g th a t its n e t p re s e n t v a lu e (o v e r its 3 -y e a r
life ) is less th a n th e n e t p re s e n t v a lu e o f A s s e t B (o v e r its 5 - y e a r life ).
U s in g E q u a tio n 6 . 5 , th e e q u iv a le n t a n n u a l v a lu e m e th o d , it is fo u n d th a t:
$36 882.04
EAVA =
" '1
1
(1 H -0 .1 0 )3
0.10
$14830.81
$51 206.70
EAVb
T T T Z Z r ^ r
(1 + 0 . 1 0 ) 5
a io
$13508.20
T h e re fo re , A s s e t A s h o u ld b e c h o s e n b e c a u s e its E A V is g r e a te r th a n th a t o f A s s e t B. A lte r n a tiv e ly ,
th e e q u iv a le n t a n n u a l v a lu e s c o u ld h a v e b e e n c a lc u la te d fro m th e n e t p re s e n t v a lu e s o f th e in fin ite
c h a in s o f r e p la c e m e n t ( N P V ^ ) u s in g E q u a tio n 6 . 6 , E AV = fc N P V ^ a s fo llo w s :
EAVA=
(0.1)($148 308.14
=$14830.81
EAVB= (0.1)($135081.98
=$13508.20
T hese resu lts a r e id e n tic a l to th o s e o b ta in e d u s in g E q u a tio n 6 . 5 .
In s u m m a ry , th e resu lts fo r A s s e t A s h o w th a t a n in v e s to r w o u ld b e in d iffe r e n t b e tw e e n re c e iv in g
p a y m e n ts o f $ 3 6 8 8 2 . 0 4
e v e r y 3 y e a rs , o r a s in g le p a y m e n t o f $ 1 4 8 3 0 8 . 1 4
p a y m e n ts o f $ 1 4 8 3 0 . 8 1
fo re v e r. T h e c o r r e s p o n d in g a m o u n ts fo r A s s e t B a r e $ 5 1 2 0 6 . 7 0 e v e ry
5 y e a rs , $ 1 3 5 0 8 1 . 9 8
now , or annual
n o w , o r $ 1 3 5 0 8 . 2 0 a n n u a lly f o r e v e r . 〇f th e se th re e p a ir s o f fig u re s , th e
s e c o n d a n d th ird p a ir s a d ju s t f o r th e u n e q u a l live s o f th e a sse ts, a n d b o th s h o w th a t A s s e t A s h o u ld
b e p re fe rre d .
B usiness finance
E xa m p le 6 .8 p ro v id e s a m o re d e ta ile d illu s t r a t io n o f th e c o n s ta n t c h a in o f re p la c e m e n t m e th o d .
E xample 6 .8
A s s u m e t h a t M a d is o n C o m p a n y , w h ic h o p e ra te s a fle e t o f tru c k s , is c o n s id e r in g r e p la c in g th e m w ith
a n e w m o d e l. T h e d a t a in T a b le 6 . 7 a r e a v a ila b le f o r th e o ld a n d th e n e w tru c k s .
TABLE 6.7 Data for old and new trucks
Item
O ld tru cks
N e w tru c k s
1. N e t cash flow s
$45 000 p.a.
$ 5 0 0 0 0 p.a.
2. E s tim a te d life
2 years
4 years
3. D isposal value:
(a) at pre se n t
$10000
(b) in 4 years, tim e
N il
$10000
4. Cost o f new tru cks
$60000
5. R equired rate o f re tu rn (real)
10% p.a.
10% p.a.
M a n a g e m e n t is c o n s id e r in g tw o p r o p o s a ls :
a)
R e p la c e th e o ld tru c k s n o w a n d a s s u m e th a t th e n e w tru c k s a r e o p e r a te d f o r 4 y e a r s a n d r e p la c e d
in p e rp e tu ity .
b)
R e p la c e th e o ld tru c k s in 2 y e a r s ' tim e a n d a s s u m e th a t th e n e w tru c k s a r e o p e r a te d f o r 4 y e a rs
a n d r e p la c e d in p e rp e tu ity .
W h ic h o f th e se p r o p o s a ls s h o u ld m a n a g e m e n t a c c e p t?
SOLUTION
O b v io u s ly th e re a r e o th e r a lte r n a tiv e s th a t m a n a g e m e n t c o u ld c o n s id e r, su ch a s r e p la c in g th e p re s e n t
tru c k s in 1 y e a r ’s tim e o r r e p la c in g th e o ld tru c k s n o w a n d th e n e w o n e s in 2 y e a r s ' tim e . H o w e v e r,
it is a s s u m e d th a t th e se p o s s ib ilitie s h a v e b e e n c o n s id e r e d a n d r e je c te d b y m a n a g e m e n t. It is a ls o
a s s u m e d th a t th e re a r e n o e x p e c te d im p ro v e m e n ts in tru c k d e s ig n th a t w o u ld m a k e th e n e w tru c k
o b s o le te .
P ro p o s a ls (a) a n d (b) w ill th e re fo r e b e e v a lu a te d a s s u m in g a c o n s ta n t c h a in o f re p la c e m e n t. T he
p r o p o s a l w ith th e la r g e r n e t p re s e n t v a lu e , p r o v id e d th a t it is g r e a te r th a n z e r o , w ill b e a c c e p te d , o th e r
th in g s b e in g e q u a l. In th e f o llo w in g e v a lu a tio n th e n e t p re s e n t v a lu e f o r a s in g le tru c k is c a lc u la te d . If
th e re a r e 1 0 tru c k s in th e fle e t, th e n th e n e t p re s e n t v a lu e s o f th e t w o p r o p o s a ls w ill b e m u ltip lie d b y
1 0 to f in d th e ir to ta l n e t p re s e n t v a lu e s .
a)
R e p la c e th e o ld tru c k s n o w , o p e r a te th e n e w tru c k s f o r 4 y e a r s a n d r e p la c e th e m in p e rp e tu ity .
T h e n e t p re s e n t v a lu e o f a n e w tru c k is:
NPV0 = - $ 6 0 0 0 0
+ $50000
(1 + 0 . 1 0 ) 4
0.10
$10000
( i.i) 4
= - $ 6 0 0 0 0 + $ 1 5 8 4 9 3 .2 7 + $6 8 3 0 .1 3
= $ 1 0 5 3 2 3 .4 0
T h e p re s e n t v a lu e o f a n in fin ite c h a in o f th e s e tru c k s is th e re fo re :
NPV 〇 〇 = ($ 1 0 5 3 2 3 .4 0 )
= $ 3 3 2 265
O ' 1/
C hapter s ix T he
application of project evaluation methods
In a d d itio n , a t th e s ta rt o f th is c h a in M a d is o n C o m p a n y re c e iv e s a c a s h in flo w o f $ 1 0 0 0 0 fro m
th e d is p o s a l o f th e o ld tru c k . T h e re fo re , th e total n e t p re s e n t v a lu e is:
$332265 + $10000 = $342265
b)
R e p la c e th e o ld tru c k s in 2 y e a r s ' tim e , o p e r a te th e n e w tru c k s f o r 4 y e a rs , a n d r e p la c e th e m in
p e rp e tu ity .
A s in th e p re v io u s c a lc u la tio n , N P V 00= $ 3 3 2 2 6 5 . H o w e v e r, th e firs t o f th e c h a in o f n e w tru c k s is
n o w p u rc h a s e d a t Y e a r 2 in s te a d o f a t Y e a r 0 a s p re v io u s ly . A s a re su lt, NPV 〇
〇m u st b e d is c o u n te d
to Y e a r 0 :
$332 265
(I.” 2
=$274 599.17
In a d d itio n , M a d is o n C o m p a n y o b ta in s th e n e t p re s e n t v a lu e o f o p e r a tin g th e o ld tru c k s f o r th e
firs t 2 y e a rs . T h is is g iv e n b y :
$45 000
$45 000
i. i
( i.i) 2
=$78 099.17
The total n e t p re s e n t v a lu e is th e re fo re :
$ 2 7 4 5 9 9 .1 7 + $ 7 8 0 9 9 .1 7 = $ 3 5 2 6 9 8 .3 4
T he n e t p re s e n t v a lu e o f P ro p o s a l (b) is g r e a te r th a n th e n e t p re s e n t v a lu e o f P ro p o s a l (a) a n d
m a n a g e m e n t s h o u ld r e p la c e th e o ld tru c k s in 2 y e a r s 7 tim e .
Chain of replacement methods and inflation
C h a in o f re p la c e m e n t m e th o d s re ly o n th e a s s u m p tio n t h a t each p ro je c t w ill, a t th e e n d o f its life , be
replaced b y an id e n tic a l p ro je c t— t h a t is, each re p la c e m e n t w i ll c o st th e sam e a m o u n t, g e n e ra te th e sam e
cash flo w s , a n d la s t f o r th e sam e tim e . C learly, i f th e re is in fla tio n , fu tu r e costs a n d cash flo w s w ill n o t be
exp ected to re m a in th e sam e in n o m in a l te rm s , b u t th e y m a y re m a in th e sam e in re a l te rm s . To e n sure
t h a t in fla t io n is tre a te d c o n s is te n tly , a ll cash flo w s a n d th e re q u ire d ra te o f r e t u r n s h o u ld g e n e ra lly be
expressed in re a l te rm s w h e n a c h a in o f re p la c e m e n t m e th o d is use d .6
Is the chain of replacement method realistic?
A possible p ro b le m w ith th e c o n s ta n t c h a in o f re p la c e m e n t m o d e l is t h a t i t em p lo ys u n re a lis tic a s s u m p tio n s
a b o u t th e re p la c e m e n t assets in th e ch a in , n a m e ly th a t th e assets a n d th e services th e y p ro v id e are
id e n tic a l in e ve ry respect. These a s s u m p tio n s are u n re a lis tic . H o w eve r, th e fa c t t h a t th e re p la ce m e n ts
m ay be m a n y years in th e fu tu re , a n d th e fa c t t h a t t h e ir cash flo w s w ill be d is c o u n te d to a p re s e n t value,
reduces th e im p a c t o f m a k in g such u n re a lis tic a s s u m p tio n s . I t m a y be even m o re u n re a lis tic to assum e th a t
m a n a g e m e n t has s u ffic ie n t fo re s ig h t to be able to p re d ic t such fa c to rs as th e c a p ita l o u tla y, n e t cash flo w s ,
life a n d re s id u a l value o f re p la ce m e n t assets. H o w eve r, i f such in fo r m a tio n is available, i t is n o t a d iffic u lt
m a tte r to in s e rt in to th e a n alysis th e re p la c e m e n t o f an e x is tin g asset w it h an asset o f im p ro v e d d e sig n .7
The m e th o d s discussed in th is se ctio n are v e ry u s e fu l b u t som e p o in ts s h o u ld be n o te d . F irs t, i t is n o t
necessary to use the se m e th o d s in a ll cases w h e re p ro je c ts have d iffe re n t lives. F o r in d e p e n d e n t p ro je c ts , th e
n e t p re se n t value m e th o d a u to m a tic a lly a llo w s f o r a n y such diffe re nce s. The d iffe re n t lives p ro b le m , arises
o n ly f o r m u tu a lly e xclusive p ro je cts. Second, i t is p a rtic u la rly im p o r ta n t, w h e n u s in g c h a in o f re p la ce m e n t
m e th o d s, to be c o n s is te n t in th e tre a tm e n t o f in fla tio n . T h ird , in m a n y cases m u tu a lly exclusive p ro je c ts w ill
in v o lv e th e same b e n e fits (cash in flo w s ) b u t d iffe re n t costs (cash o u tflo w s ). In these cases th e cash in flo w s
can be ig n o re d a nd th e a lte rn a tiv e s can be co m p a re d o n th e basis o f th e ir cash o u tflo w s , as in E xam p le 6.3.
6
7
For a discussion of this issue and presentation of a nominal version of the constant chain of replacement model, see Faff and
Brailsford (1992).
Brown and Davis (1998) highlight the real options that are ignored in using the constant chain of replacement model. For a
discussion of real options, see Chapters 5 and 18.
B usiness finance
continued
SOLUTION
If th e m a c h in e is p u rc h a s e d , u s e d fo r o n ly 1 y e a r a n d th e n s o ld , its n e t p re s e n t v a lu e w o u ld b e as
fo llo w s :
吟
-$ 2 〇
o〇
〇+ $I ^ 2
1
+ i l ^
1.1
1.1
= $ 5 455
If th e m a c h in e is u se d f o r 2 y e a rs a n d th e n s o ld , th e n e t p re s e n t v a lu e w o u ld b e a s fo llo w s :
NPV2 = - $ 2 0 0 0 0
+
$12000
$11500
$14000
i.i
( i . i )2
( i . i r
$11 983
S im ila rly , n e t p re s e n t v a lu e s c a n b e c a lc u la te d b a s e d o n use f o r 3 , 4 a n d 5 y e a r s . H o w e v e r , th e se
n e t p re s e n t v a lu e s c a n n o t b e c o m p a r e d , b e c a u s e th e y a r e b a s e d o n d iffe r e n t liv e s . A s w e n o te d in
S e c tio n 6 . 4 , th is d iff ic u lt y c a n b e o v e r c o m e b y a s s u m in g a c o n s ta n t c h a in o f r e p la c e m e n t. If it is
a s s u m e d th a t th e m a c h in e is r e p la c e d e v e r y y e a r in p e rp e tu ity , th e n e t p re s e n t v a lu e w ill b e a s fo llo w s :
NPV(1,〇〇 ) = $5 4 5 4 .5 5
(1 1 )
( l- l) - l
=$60000
If th e m a c h in e is r e p la c e d e v e r y s e c o n d y e a r in p e rp e tu ity , th e n e t p re s e n t v a lu e w ill b e a s fo llo w s :
NPV(2/X)) = $ 1 1 9 8 3 .4 7
,2
( i.ir
= $69048
T h e n e t p re s e n t v a lu e s , a s s u m in g th a t th e m a c h in e is r e p la c e d in p e rp e tu ity , a t th e e n d o f th e th ir d ,
fo u rth a n d fifth y e a rs , re s p e c tiv e ly , a r e a s fo llo w s :
NPV[3, ) = $ 1 7 6 9 3 .4 6
(1 .1 )
3
〇〇
= $ 7 1 148
NPV
〇
〇
) =
(1 -1 )4
'
$ 1 9 9 4 7 -41
= $ 6 2 92 6
NPV(5o〇) = $22 0 5 8 .5 4
(1 .1 )
5
= $ 5 8 190
T h e se resu lts s h o w th a t th e m a c h in e s h o u ld b e r e p la c e d a fte r 3 y e a rs . In g e n e r a l th e d e c is io n ru le
is to c h o o s e th e re p la c e m e n t fr e q u e n c y th a t m a x im is e s th e p r o je c t's n e t p re s e n t v a lu e f o r a p e rp e tu a l
c h a in o f r e p la c e m e n t, o r th a t m a x im is e s its e q u iv a le n t a n n u a l v a lu e .
Non-identical replacement
Suppose t h a t a m a c h in e is p h y s ic a lly s o u n d b u t te c h n ic a lly ob solete. W h e n th e m a c h in e is replaced,
its re p la c e m e n t w ill be o f a n e w d e sig n t h a t m a y have th e sam e ca p a c ity b u t costs less to op era te . The
q u e s tio n is: W h e n s h o u ld th e o ld m a c h in e be d isca rd e d in fa v o u r o f th e n e w one? The s o lu tio n in v o lv e s tw o
steps. F irs t, th e o p tim u m re p la c e m e n t fre q u e n c y f o r th e n e w m a c h in e is d e te rm in e d u s in g th e m e th o d
illu s tra te d in E xa m p le 6.1 0. Second, th e e q u iv a le n t a n n u a l va lu e o f th e n e w m a c h in e a t it s o p tim u m
re p la c e m e n t fre q u e n c y is c o m p a re d w it h th e n e t p re s e n t va lu e o f c o n tin u in g to o p e ra te th e o ld m a ch in e ,
C hapter s ix T he
application of project evaluation methods
as s h o w n in E xam p le 6.9. The d e c is io n ru le is t h a t th e cha n g e o ve r s h o u ld be m ade w h e n th e n e t p re s e n t
value o f c o n tin u in g to o p e ra te th e o ld m a c h in e f o r one m o re y e a r is less th a n th e e q u iv a le n t a n n u a l v alue
o f th e n e w m a ch in e .
6.6
Analysing project risk
The e ffe c t o f r is k o n th e v a lu e o f a p ro je c t is n o r m a lly in c lu d e d in th e e v a lu a tio n b y u s in g a re q u ire d ra te
o f re tu r n t h a t re fle c ts th e r is k o f th e p ro je c t. H o w e ve r, th e c a lc u la te d n e t p re s e n t v a lu e is o n ly an e s tim a te
th a t relies o n foreca sts o f th e p ro je c ts cash flo w s . In p ra c tic e the se fo re ca sts w ill, a lm o s t c e rta in ly , t u r n
o u t to be in c o rre c t, p e rh a p s because th e v o lu m e o f sales tu r n s o u t to be m o re o r less th a n expected,
th e p ric e o f th e p ro d u c t is h ig h e r o r lo w e r th a n expected, o r o p e ra tin g costs d iffe r fr o m th e fo re ca st.
Therefore, in m a n y cases m a n a g e rs a n a ly s in g p ro p o s e d p ro je c ts w ill ne ed to a n sw e r q u e s tio n s such as:
•
W h a t are th e k e y v a ria b le s t h a t are lik e ly to d e te rm in e w h e th e r th e p ro je c t is a success o r a fa ilu re ?
•
H o w fa r can sales fa ll o r costs increase b e fo re th e p ro je c t loses m on ey?
LEARNING
OBJECTIVE 5
Explain how sensitivity
analysis, break­
even analysis and
simulation assist in
analysing project risk
M an ag ers can use v a rio u s te c h n iq u e s to a n s w e r the se a n d o th e r re la te d q u e s tio n s . The te c h n iq u e s we
discuss are s e n s itiv ity an alysis, bre a k-e ve n a n a lysis a n d s im u la tio n .
6 .6 .1 1 Sensitivity analysis
A p ro je c ts cash flo w s a n d re q u ire d ra te o f r e tu r n are u s u a lly s p e c ifie d as cb e s t e stim a te s* o r exp ected
values1 an d th e re s u ltin g n e t p re s e n t value , o fte n re fe rre d to as th e
best e s tim a te o r e xp e cte d va lu e .
Sensitivity an alysis
base-case net present value, is
also a
in v o lv e s assessing th e e ffe c t o f changes o r e rro rs
SENSITIVITY ANALYSIS
in th e e s tim a te d v a ria b le s o n th e n e t p re s e n t v a lu e o f a p ro je c t. T his is a ch ie ved b y c a lc u la tin g n e t p re s e n t
analysis of the effect
of changing one or
more input variables
to observe the effects
on the results
values based o n a lte rn a tiv e e s tim a te s o f th e va ria b le s. F o r in sta n ce , m a n a g e m e n t m a y w is h to k n o w th e
e ffe ct o n n e t p re s e n t va lu e i f a p ro je c ts n e t cash flo w s are e ith e r 20 p e r c e n t less th a n , o r 20 p e r ce n t
g re a te r th a n , th o se e s tim a te d . K n o w le d g e o f th e s e n s itiv ity o f n e t p re s e n t va lu e to changes o r e rro rs in
th e va ria b le s places m a n a g e m e n t in a b e tte r p o s itio n to decide w h e th e r a p ro je c t is to o r is k y to accept.
A lso , i f m a n a g e m e n t k n o w s t h a t th e n e t p re s e n t va lu e is s e n s itiv e to changes in p a r tic u la r v a ria b le s , i t
can e xa m in e th e e stim a te s o f the se v a ria b le s m o re th o ro u g h ly , o r c o lle c t m o re d a ta in an e f f o r t to reduce
e rro rs in fo re ca stin g .
A s s u m in g t h a t a ll v a ria b le s in th e a n a lysis are u n c e rta in , a s im p le e xa m p le o f s e n s itiv ity a n alysis
in vo lve s th e fo llo w in g steps:
a
P essim istic, o p tim is tic a n d e xp ected e s tim a te s are m ad e f o r each v a ria b le .
b
N e t p re s e n t va lu e is ca lcu la te d u s in g th e e xp ected e s tim a te s f o r e v e ry v a ria b le exce pt one, th e value
fo r w h ic h is, in t u r n , its o p tim is tic a n d p e s s im is tic e s tim a te . This p ro c e d u re is re p e a te d u n t il a n e t
p re s e n t va lu e has been ca lcu la te d u s in g an o p tim is tic a n d p e s s im is tic e s tim a te f o r each v a ria b le , in
c o m b in a tio n w it h th e e xp ected values o f th e o th e r v a ria b le s.
C
The d iffe re n c e b e tw e e n th e o p tim is tic a n d p e s s im is tic n e t p re s e n t values is ca lcu la te d f o r each
va ria b le . A s m a ll d iffe re n c e b e tw e e n th e n e t p re s e n t value s suggests t h a t th e p ro je c ts n e t p re s e n t
value is in s e n s itiv e to changes o r e rro rs in t h a t v a ria b le . A la rg e d iffe re n c e b e tw e e n th e n e t p re s e n t
values suggests th e o p p o s ite .
F o r exa m ple, suppose t h a t in a p ro je c t in v o lv in g th e use o f a n e w m a c h in e , th e re are o n ly fiv e u n c e rta in
variab les: sales p rice , v a ria b le cost, sales v o lu m e , fix e d o p e ra tin g costs a n d th e life o f th e m a c h in e . In th is
case, e ig h t n e t p re s e n t v a lu e c a lc u la tio n s are m ade, u s in g th e d a ta in p u ts s h o w n in T able 6 .1 0 . The s y m b o l
O in d ic a te s th e o p tim is tic v a lu e o f th e v a ria b le , P in d ic a te s th e p e s s im is tic va lu e o f th e v a ria b le , a n d E
in d ic a te s th e e xp ected va lu e o f th e v a ria b le .
The a p p lic a tio n o f s e n s itiv ity a n a lysis to p ro je c t e v a lu a tio n in a case such as t h a t s h o w n in Table 6.1 0
is illu s tra te d in E xam p le 6.1 1.
The use o f s e n s itiv ity a n a lysis in v o lv e s som e p ro b le m s . O ne is t h a t fr e q u e n tly i t is d iff ic u lt to
sp e cify p re c is e ly th e re la tio n s h ip b e tw e e n a p a r tic u la r v a ria b le a n d n e t p re s e n t value . I f th e assum ed
re la tio n s h ip is based o n p a s t o u tco m e s, th e re is alw ays th e p o s s ib ility t h a t th is re la tio n s h ip m a y n o t
h o ld in th e fu tu re . I t is f u r t h e r c o m p lic a te d b y re la tio n s h ip s b e tw e e n th e v a ria b le s . F o r e xa m p le , i t is
TABLE 6.10 Combinations of variable values for sensitivity analysis
Estim ates
(i)
Sales price
0
P
E
E
E
Variable cost
E
E
〇
P
Sales vo lu m e
E
E
E
Fixed o p e ra tin g
E
E
E
E
(v ii)
(v iii)
(ix )
(x)
E
E
E
E
E
E
E
E
E
E
E
E
〇
P
E
E
E
E
E
E
E
E
〇
P
E
E
E
E
E
E
E
E
〇
P
(iii)
N
(v)
M
costs
M ach in e life
E xample 6.11
A s s u m e th a t a m a n a g e r is c o n s id e r in g w h e th e r to p u rc h a s e a n e w m a c h in e th a t c o sts $ 5 0 0 0 0 0 . It
is a s s u m e d th a t th e re a r e o n ly fiv e u n c e rta in v a r ia b le s : sa le s p r ic e , v a r ia b le c o s t, s a le s v o lu m e , fix e d
o p e r a tin g co sts a n d th e life o f th e n e w m a c h in e . T he sa le s p r ic e is e x p e c te d to b e $ 7 0 p e r u n it, th e
v a r ia b le c o s t is e x p e c te d to b e $ 4 8 p e r u n it, s a le s v o lu m e is e x p e c te d to b e 1 5 0 0 0 u n its p e r a n n u m ,
w ith fix e d o p e r a tin g co sts o f $ 2 0 0 0 0 0 d u r in g a n e x p e c te d life o f 1 0 y e a rs . A ll o th e r v a r ia b le s a re
e x p e c te d to re m a in c o n s ta n t d u r in g th e m a c h in e 's life . T h e r e q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r
annum .
T he e x p e c te d a n n u a l n e t c a s h flo w s a r e ( $ 7 0 - $ 4 8 ) x 1 5 0 0 0 - $ 2 0 0 0 0 0 = $ 1 3 0 0 0 0 , a n d th e
b a s e -c a s e n e t p re s e n t v a lu e is:
Base-case N P V =
-$500 000 + $ 130 000 — 1 J
0.1
=$298 794
T he in fo r m a tio n n e e d e d f o r th e s e n s itiv ity a n a ly s is is s h o w n in T a b le 6 .1 1, w h ic h p re s e n ts :
•
f o r e a c h u n c e rta in v a r ia b le , e x p e c te d (c o lu m n 1), o p tim is tic (c o lu m n 2 ) a n d p e s s im is tic (c o lu m n 3 )
e s tim a te s
•
th e n e t p re s e n t v a lu e (c o lu m n 4 ) w h e n o n e o f th e u n c e rta in v a r ia b le s is set a t its o p tim is tic e s tim a te
•
th e n e t p re s e n t v a lu e (c o lu m n 5 ) w h e n o n e o f th e u n c e rta in v a r ia b le s is se t a t its p e s s im is tic e s tim a te
a n d e a c h o f th e o th e r v a r ia b le s is set a t its e x p e c te d v a lu e
a n d e a c h o f th e o th e r v a r ia b le s is set a t its e x p e c te d v a lu e
•
in c o lu m n 6, th e d iffe re n c e b e tw e e n c o lu m n s 4 a n d 5, w h ic h is fr e q u e n tly c a lle d th e 'r a n g e o f th e
n e t p re s e n t v a lu e ’ .
T a b le 6 .1 1 s h o w s th a t th e e s tim a te o f n e t p re s e n t v a lu e is m o re s e n s itiv e to c h a n g e s in s a le s p ric e
th a n to c h a n g e s in th e o th e r u n c e rta in v a r ia b le s . In a d d it io n , it s h o w s th a t if th e p e s s im is tic e s tim a te
o f e ith e r s a le s p r ic e o r s a le s v o lu m e o c c u rs , th e p u rc h a s e o f th e m a c h in e w i ll g e n e r a te a n e g a tiv e n e t
p re s e n t v a lu e .
B e fo re d e c id in g to p u rc h a s e th e n e w m a c h in e , m a n a g e m e n t is th e re fo re lik e ly to g a th e r m o re
in fo r m a tio n o n s a le s p r ic e a n d s a le s v o lu m e in a n e ffo r t to m in im is e fo r e c a s tin g e rro rs . In c o n tra s t,
th e v a lu e o f a d d itio n a l d a ta a b o u t th e m a c h in e 's v a r ia b le co sts, fix e d o p e r a tin g c o sts a n d u s e fu l life
is r e la tiv e ly s m a ll. T he p r o je c t is still a c c e p ta b le , b a s e d o n th e p e s s im is tic v a lu e s f o r th o s e v a r ia b le s ,
a n d th e re fo re th e c o m p a n y is u n lik e ly to m a k e a lo ss o n th e p r o je c t e v e n if th e s e v a r ia b le s h a v e b e e n
in c o r r e c tly e s tim a te d .
C hapter six T he
application of project evaluation methods
TABLE 6.11 Sensitivity analysis of the purchase of a new machine, based on
optimistic and pessimistic estimates of the values of each variable
V a r ia b le
E x p e cte d
O p tim is tic
P essim istic
⑴
⑵
(31
NPV:
NPV:
o p tim is tic
p e s s im is tic
e s tim a te ($1 ⑹ e s tim a te
.
(4)
($)⑹
R ange o f
N P V ($ )
(5 )
—1 6 T
Sales price $
70
76
63
(i) 8 5 1 8 0 5
(ii) 3 4 6 3 8 6
1198191
Variable
48
46
50
(iii) 4 8 3 1 3 1
(iv) 1 1 4 4 5 7
368674
15 000
17000
12500
(v) 5 6 9 1 5 5
(vi) 3 9 1 5 7
608312
200000
190000
205000
(v ii) 3 6 0 2 3 9
(v iii) 2 6 8 0 7 1
92169
10
12
9
(ix) 385 780
(x) 248 673
137107
cost $
Sales volum e
Fixed
operating
costs $
Life o f
machine
(years)
The figures in lower case Roman numerals in these columns indicate the net present value calculation that corresponds
to the input shown in Table 6.10.
in a p p ro p ria te to e xa m in e th e e ffe c t o n n e t p re s e n t va lu e o f a 20 p e r c e n t re d u c tio n in sales v o lu m e
w ith o u t re c o g n is in g t h a t lo w e r sales v o lu m e m a y also m e a n t h a t th e s e llin g p ric e is lo w e r th a n expected.
A llo w in g f o r these in te rd e p e n d e n c ie s w i ll c o m p lic a te th e an alysis. A n o th e r p ro b le m is t h a t th e te rm s
‘o p tim is tic ’ a n d ‘p e s s im is tic ’ are su b je c t to in te r p r e ta tio n , a n d th e re s u lts m a y be s o m e w h a t a m b ig u o u s.
F o r exa m ple, th e m a rk e tin g d e p a rtm e n t’s ‘o p t im is t ic ’ sales fo re ca sts m a y be so o p tim is tic t h a t th e y are
v ir t u a lly u n a ch ie va b le , w h ile a n o th e r d e p a rtm e n ts o p t im is t ic , e s tim a te s o f o th e r v a ria b le s m a y be m o re
co n se rva tive .
6 .6 .2 1 Break-even analysis
B r e a k - e v e n a n a ly s is is a f o r m o f s e n s itiv ity an alysis. S e n s itiv ity a n a lysis g e n e ra lly in v o lv e s fin d in g
BREAK-EVEN ANALYSIS
answ ers to *w ha t if* q u e s tio n s such as: W h a t w ill be th e n e t p re s e n t v a lu e o f th e p ro je c t i f sales are 10 p e r
analysis of the
amounts by which
one or more input
variables may change
before a project
ceases to be profitable
cen t less th a n expected? In b re a k-e ve n a n alysis th e q u e s tio n is tu r n e d a ro u n d , in t h a t th e m a n a g e r asks:
H o w p o o r can sales v o lu m e be co m e b e fo re th e p ro je c t loses m o n e y? The b re a k-e ve n p o in t is th e sales
v o lu m e a t w h ic h th e n e t p re s e n t va lu e is zero. B reak-even a n a lysis is illu s tra te d in th e fo llo w in g e xa m ple
b y re -e x a m in in g th e in fo r m a t io n in E xa m p le 6.11.
Example 6.12
F or e a c h o f th e fiv e u n c e rta in v a r ia b le s , th e n e t p re s e n t v a lu e is c a lc u la te d u s in g th e e x p e c te d v a lu e s
o f th e o th e r fo u r v a r ia b le s , w ith th e v a lu e s o f th e fifth v a r ia b le b e in g th e o n e th a t re su lts in th e n e t
p re s e n t v a lu e b e in g z e ro . T h e resu lts f o r a ll v a r ia b le s a r e s h o w n in T a b le 6 .1 2 w ith th e resu lts f o r s a le s
v o lu m e a ls o b e in g s h o w n in F ig u re 6 . 1 .
T he n e t p re s e n t v a lu e o f p u r c h a s in g th e m a c h in e w ill b e p o s itiv e if th e e x p e c te d v a lu e s o f th e o th e r
fo u r u n c e rta in v a r ia b le s a r e a c h ie v e d a n d th e s a le s p r ic e is g r e a te r th a n o r e q u a l to $ 6 7 . S im ila rly ,
th e n e t p re s e n t v a lu e o f p u r c h a s in g th e m a c h in e w ill b e p o s itiv e if th e e x p e c te d v a lu e s o f th e o th e r fo u r
u n c e rta in v a r ia b le s a r e a c h ie v e d a n d s a le s v o lu m e is 1 2 7 9 0 o r m o re un its.
continued
B usiness finance
continued
TABLE 6.12 Breat:-even analysis of the purchase of a
new rnachine
Variable
Expected
Break even
Sales p rice $
70
67
V ariable cost $
48
51
15000
12 790
Fixed o p e ra tin g costs $
200000
248627
Life o f m achine (years)
10
6
Sales volum e
6 .6 .3 1 Simulation
S e n s itiv ity a n alysis in v o lv e s c h a n g in g one v a ria b le a t a tim e a n d e x a m in in g th e e ffe cts o f th e changes
SIMULATION
analysis of the effect
of changing all of the
input variables whose
values are uncertain to
observe the effects on
the results
夺
o n th e p r o f it a b ilit y o f a p ro je c t. O n th e o th e r h a n d ,
sim ulation
a llo w s a m a n a g e r to c o n s id e r th e effects
o f c h a n g in g a ll th e v a ria b le s w h ose values are u n c e rta in . The f ir s t ste p in a s im u la tio n is to id e n tify th e
re le v a n t v a ria b le s a n d to s p e c ify th e p ro b a b ility d is tr ib u tio n o f each v a ria b le . F o r e xa m p le , in th e case
o f th e pu rcha se o f th e n e w m a c h in e in E xam p le s 6 .1 1 a n d 6 .1 2 , th e v a ria b le s c o u ld in c lu d e s e llin g p rice ,
v a ria b le cost, sales v o lu m e , fix e d o p e ra tin g costs a n d th e u s e fu l life o f th e m a ch in e . The second step
is to s p e c ify a n y re la tio n s h ip s b e tw e e n th e va ria b le s. F o r exa m ple, a h ig h e r sales v o lu m e m a y re s u lt in
C hapter s ix T he
application of project evaluation methods
econom ies o f scale in p r o d u c tio n a n d d is tr ib u tio n , w h ic h s h o u ld be re fle c te d in th e v a ria b le costs. The
t h ir d step in v o lv e s u s in g a c o m p u te r to s im u la te th e p ro je c t s cash flo w s . E sse n tia lly, th e p ro c e d u re is as
fo llo w s:
a
b
The c o m p u te r selects value s ra n d o m ly fr o m th e d is tr ib u tio n o f each o f th e sp e cifie d v a ria b le s,
In th e f ir s t ru n o f th e s im u la tio n th e c o m p u te r calcula tes values f o r th e p ro je c ts cash flo w s f o r each
year.
C
The re s u lts o f th e f ir s t r u n are s to re d a n d a n e w s e t o f values is cho sen a n d used in th e seco nd ru n
o f th e s im u la tio n , w h ic h gives f u r t h e r re su lts t h a t are also sto re d . T his p ro c e d u re is re p e a te d a t le a s t
one h u n d re d an d p e rh a p s th o u s a n d s o f tim e s .
d
The re s u lts o f a ll th e in d iv id u a l ru n s are c o m b in e d to p ro d u ce a p r o b a b ility d is tr ib u tio n f o r th e
p ro je c ts cash flo w s.
S im u la tio n is a p o te n tia lly va lu a b le to o l t h a t a llo w s m an ag ers to analyse m a n y aspects o f th e ris k s
associated w it h a p ro je c t. I t is g e n e ra lly used fo r la rge p ro je c ts w h e re th e size o f th e in v e s tm e n t can ju s t if y
th e cost o f d e v e lo p in g th e s im u la tio n m o d e l. W h ile s p e c ify in g th e m o d e l can be tim e c o n s u m in g , once i t
has been d e ve lo p e d i t is re la tiv e ly easy to e xa m in e th e e ffe cts o f c h a n g in g th e p r o b a b ility d is tr ib u tio n f o r
one o r m o re va ria b le s. H o w e ve r, users o f th e te c h n iq u e s h o u ld rea lise it s lim ita tio n s . These in c lu d e th e
fo llo w in g :
•
S im u la tio n is a te c h n iq u e f o r p ro ce ssin g in fo r m a tio n a n d p re s e n tin g th e re s u lts o f t h a t p ro ce ssin g
in a p a rtic u la r way. T h e re fo re , th e re s u lts o f a s im u la tio n c a n n o t be a n y m o re re lia b le th a n th e in p u t
d a ta a n d th e m o d e l t h a t spe cifie s th e re la tio n s h ip s b e tw e e n v a ria b le s. P ro v id in g re a lis tic e s tim a te s
o f th e p ro b a b ility d is tr ib u tio n s f o r th e v a ria b le s a n d o f th e re la tio n s h ip s b e tw e e n th e v a ria b le s can
be v e ry d iffic u lt.
•
S im u la tio n re s u lts can be d iff ic u lt to in te r p r e t. The o u t p u t fr o m th e s im u la tio n co n sists o f a
p ro b a b ility d is tr ib u tio n f o r th e p ro je c ts cash flo w s f o r each ye a r o f its life . H o w s h o u ld a m a n a g e r
use th is data? The o b v io u s f ir s t ste p is to use th e m e a n o r e xp e cte d fo re c a s t cash flo w s f o r each y ea r
to e s tim a te th e p ro je c ts n e t p re s e n t v alue . The n e x t ste p m ig h t be to use o th e r p o ssib le v alue s fo r
th e cash flo w s to calcula te a d is tr ib u tio n o f n e t p re s e n t values. Suppose t h a t the se steps are c a rrie d
o u t a n d th e re s u lts s h o w t h a t th e e xp ected n e t p re s e n t va lu e o f a p ro je c t is $2 m illio n , b u t th e re is
a 20 p e r c e n t p ro b a b ility t h a t th e a c tu a l n e t p re s e n t v a lu e w ill be n e g a tive . D iffe r e n t in d iv id u a ls are
lik e ly to have d iffe re n t o p in io n s a b o u t w h e th e r th e p ro je c t s h o u ld be accepted— t h a t is, s im u la tio n
does n o t p ro v id e an u n a m b ig u o u s a c c e p t/re je c t sig n a l f o r p ro je c ts .
•
S im u la tio n focuses o n th e to t a l r is k o f a p ro je c t a n d ig n o re s th e p o s s ib ility t h a t m u c h o f th is
ris k m ig h t be re m o v e d b y d iv e rs ific a tio n . As discussed in S e ctio n 7.5, i t is th e s y s te m a tic o r n o n d iv e rs ifia b le r is k o f a p ro je c t t h a t is im p o r t a n t in d e te rm in in g its re q u ire d ra te o f r e tu rn .
In s u m m a ry, s im u la tio n is a p o te n tia lly va lu a b le te c h n iq u e f o r a n a ly s in g th e ris k s a sso cia te d w ith a
p ro je c t, b u t users s h o u ld be aw are o f it s lim ita tio n s .
6.7
Decision-tree analysis
M a n a g e m e n t is s o m e tim e s faced w it h th e ne ed to e va lu a te a lte rn a tiv e s in v o lv in g a
sequence o f
d e cisio n s
ove r tim e . D e c is io n -tre e a n a lysis p ro v id e s a m eans o f e v a lu a tin g such d e cisio ns. The d e c is io n -tre e
a p pro ach takes in to a c c o u n t th e p ro b a b ility o f v a rio u s e ve n ts o c c u rrin g a n d th e e ffe c t o f th o s e eve nts
o n th e expected n e t p re s e n t v a lu e o f a p ro je c t. D e c is io n -tre e a n a lysis uses th e c o n c e p t o f ‘ro ll-b a c k ’ to
eva lu ate a lte rn a tiv e d e cisio n s. T his is illu s tra te d in E xa m p le 6 .1 3 .8
This ap p ro a ch to e v a lu a tin g a sequence o f d e cisio n s re la tin g to an in v e s tm e n t in a r is k y p ro je c t is
o p e ra tio n a l f o r o u r s im p le exa m p le . I t has th e ad van ta ge t h a t i t forces m a n a g e m e n t to c o n s id e r fu tu re
in v e s tm e n t d e cisio n s w h e n m a k in g c u rre n t in v e s tm e n t de cisio n s. H o w e ve r, th e c o m p le x ity o f d e c is io n tre e analysis is in crea sed c o n s id e ra b ly since a d d itio n a l a lte rn a tiv e s , such as a llo w in g f o r a m e d iu m -s iz e d
p la n t a n d a m e d iu m le vel o f d e m a n d , are in c lu d e d in th e d e c is io n process.
8
For a simple discussion of decision-tree analysis, see Levin, Kirkpatrick and Rubin (1992).
m
LEARNING
OBJECTIVE 6
Use decision-tree
analysis to analyse
sequential decisions
B usiness finance
Example 6.13
T he m a n a g e m e n t o f a V ic to r ia n - b a s e d c o m p a n y is c o n s id e r in g th e p r o p o s e d c o n s tru c tio n o f a p la n t to
m a n u fa c tu r e its p ro d u c ts in C h in a . In itia lly , m a n a g e m e n t is fa c e d w ith th e c h o ic e o f c o n s tru c tin g e ith e r
a la r g e o r a s m a ll p la n t. If it c o n s tru c ts a la r g e p la n t, th e in itia l o u tla y w ill b e $ 2 m illio n , w h e r e a s if
it c o n s tru c ts a s m a ll p la n t, th e in it ia l o u tla y w ill b e $1 m illio n . If a s m a ll p la n t is c h o s e n , m a n a g e m e n t
w ill r e c o n s id e r its d e c is io n a fte r 2 y e a rs . A t th a t tim e , m a n a g e m e n t m a y , if it b e lie v e s th a t fu rth e r
e x p a n s io n is w a r r a n t e d , e x p a n d th e s m a ll p la n t to a c h ie v e th e s a m e c a p a c ity a s a la r g e p la n t. The
e x p a n s io n w ill c o s t $ 1 . 2 5 m illio n .
T he c o m p a n y h a s e s tim a te d th e e x p e c te d n e t c a s h flo w s to b e g e n e r a te d b y a la r g e p la n t, a s m a ll
p la n t a n d a n e x p a n d e d p la n t o n th e b a s is o f a tw o - w a y c la s s ific a tio n o f d e m a n d : h ig h d e m a n d a n d
lo w d e m a n d . T h e se e x p e c ta tio n s a r e s u m m a ris e d in T a b le 6 . 1 3 .
TABLE 6.13 Expected net cash flows for different plants
and levels of demand
P o s s ib ilitie s
E x p e c te d n e t c a sh f lo w p .a . ($ m )
Large p la n t, h ig h dem and
0.8000
Large p la n t, lo w dem and
0.1000
Sm all p la n t, h ig h dem and
0.4000
Sm all p la n t, lo w dem and
0.3500
Expanded p la n t, h ig h dem and
0.5000
Expanded p la n t, lo w dem and
0.0750
M a n a g e m e n t h a s a ls o e s tim a te d th e p r o b a b ilit y o f a c h ie v in g e ith e r h ig h d e m a n d o r lo w d e m a n d
d u r in g th e p r o je c t's 1 0 - y e a r life . It h a s e s tim a te d th e lik e lih o o d o f h ig h d e m a n d t h r o u g h o u t th e p ro je c t's
life to b e 0 . 6 , th e p r o b a b ilit y o f a c h ie v in g h ig h d e m a n d f o r th e firs t 2 y e a rs a n d lo w d e m a n d fo r
th e re m a in in g 8 y e a rs to b e 0 . 2 , a n d th e p r o b a b ilit y o f lo w d e m a n d th r o u g h o u t th e p ro je c t's life to
b e 0 . 2 . T he p r o b a b ilit ie s a n d th e e x p e c te d n e t c a s h flo w s a r e s h o w n in F ig u re 6 . 2 in th e fo rm o f a
decision tree.
T he s q u a re s in F ig u re 6 . 2 re p re s e n t d e c is io n p o in ts a n d th e s m a ll c irc le s re p re s e n t c h a n c e e v e n ts
th a t m a y o c c u r d u r in g th e life o f th e p r o je c t. T he b a s e o f a d e c is io n tre e is th e b e g in n in g , D e c is io n
p o in t 1. Its b ra n c h e s b e g in a t th e firs t c h a n c e e v e n t. E a ch c h a n c e e v e n t p r o d u c e s tw o o r m o re p o s s ib le
o u tc o m e s , s o m e o f w h ic h le a d to o th e r c h a n c e e v e n ts a n d / o r s u b s e q u e n t d e c is io n p o in ts .
T h e o p tim u m s e q u e n c e o f d e c is io n s is d e te r m in e d u s in g a ro llb a ck p r o c e d u r e , w h ic h m e a n s th a t
th e m o s t d is ta n t d e c is io n — in th is c a s e , th e d e c is io n w h e th e r to e x p a n d th e s m a ll p la n t — is e v a lu a te d
firs t. E a c h a lte r n a tiv e is e v a lu a te d o n th e b a s is o f its e x p e c te d n e t p re s e n t v a lu e . T h e r e q u ir e d ra te o f
re tu rn is a s s u m e d to b e 9 p e r c e n t p e r a n n u m .
Decision 2: Whether to expand the small plant
EXPAND:
r,
N P V = 0 .7 5 [$0 .5 m )
1
i
(1+0.0918
0.09
[1
+ 0.25($0.075m)
1
1
(1+0 .0 9)8
- $ 1.25m
0.09
=$929355
D O N O T EXPAND:
「
NPV= 0.75 ($0.4m)
$2 144 743
1-
1
1
[1
(1 +0.09)8
+ 0.25($0.035m)
0.09
1
1
|1 +0.09)8
0.09
C hapter s ix T he
Demand
level
Expected
cash flo w
P robability
- Years 0 -2
Demand
level
P rob ab ility
—
application of project evaluation methods
Expected
cash flo w
Years 3 - 1 0
0 . 7 5 --------- $0.8rr
0.8
$0.8m
0 .25 ---------- $0.1n
0.2
$0.1 r
0.8
1.0
$0.1 m
0.75
$0.5m
0.25
$0.075m
0.75
$0.4m
0.25
$0.35m
1.0
$0.35m
$0.4m
Small
plant
($lm)
0.2
$0.35rr
T h e re fo re , th e o p tim u m c h o ic e is n o t to e x p a n d th e s m a ll p la n t a t th e e n d o f th e s e c o n d y e a r.
T he r o llb a c k m e th o d s im p lifie s th e e v a lu a tio n b y e lim in a tin g th e a lte r n a tiv e o f b u ild in g a s m a ll p la n t
a n d th e n e x p a n d in g it a fte r 2 y e a rs . O n c e m a n a g e m e n t k n o w s w h a t it o u g h t to d o if fa c e d w ith th e
e x p a n s io n d e c is io n , it c a n 'r o ll b a c k 7 to t o d a y 's d e c is io n . T h is d e c is io n is w h e th e r to b u ild a la r g e
p la n t o r a s m a ll p la n t to b e o p e r a te d f o r 1 0 y e a rs .
Decision 1: Construct either a large plant or a small plant and operate for 10 years
LAR G E PLANT:
( 1 + 0 .0 9 〆
Expected NPV = 0 .8 ($0 .8 m )
0 .0 9
■ 0 .8 [0 .7 5 ($ 0 .8 m )
(1 + 0 . 0 9 广
(1 .0 9 )
-2
0 .0 9
-0 .2 5 ($ 0 .1 m )
(1 + 0 . 0 9
广
(1 .0 9 )-2]
0 .0 9
1
-0 .2 0 ($ 0 .1 m )
(1 + 0 . 0 9 )
10
- $2m
0 .0 9
$ 1 5 8 3 0 0 0 (to the nearest thousand dollars)
continued
B usiness finance
continued
S M A L L PLA N T:
Expected NPV = 0 .8 ($0 .4 m )
(1 + 0 . 0 9 卜
0 .0 9
+ 0 .0 8 [$ 2 1 4 4 743 (1 .0 9 )-2 ]
1
•0 .2 ($ 0 .3 5 m )
(1 + O .Q 9 )10
■$lr
0 .0 9
= $ 1 4 5 6 0 0 0 (to the nearest thousand dollars)
In th is c a s e th e e x p e c te d n e t p re s e n t v a lu e o f b u ild in g a la r g e p la n t e x c e e d s th a t o f b u ild in g a s m a ll
p la n t.
6.8
LEARNING
OBJECTIVE 7
Explain the role of
qualitative factors in
project selection
Q ualitative factors and the selection
of projects
A f te r th e q u a n tita tiv e a n alysis has been co m p le te d , m a n a g e m e n t has to decide w h ic h p ro je c ts to
im p le m e n t. W h ile th e a im is to m a x im is e s h a re h o ld e rs , w e a lth , i t does n o t ne ce ssa rily f o llo w t h a t p ro je c t
s e le c tio n d e cisio n s s h o u ld be g u id e d o n ly b y th e re s u lts o f th e q u a n tita tiv e an alysis. M a n a g e m e n t s h o u ld
also c o n s id e r a n y q u a lita tiv e fa c to rs t h a t m a y a ffe c t th o s e p ro je c ts .
E s s e n tia lly , q u a lita tiv e fa c to rs are th o se t h a t m a n a g e m e n t w o u ld lik e to in c lu d e in th e q u a n tita tiv e
an alysis b u t is u n a b le to in c lu d e because th e y are d iffic u lt, i f n o t im p o s s ib le , to m ea sure in d o lla rs . F o r
th is rea son th e y are assessed separately, a fte r th e q u a n tita tiv e a n a lysis o f th e a lte rn a tiv e s has been
co m p le te d .
Q u a lita tiv e fa c to rs m a y p la y a v it a l ro le in p ro je c t se le ctio n . F o r e xa m p le , suppose t h a t q u a n tita tiv e
a n a lysis sho w s t h a t i t is che ap er f o r a tr a n s p o r t c o m p a n y to c o n tin u e u s in g som e o ld tru c k s f o r a n o th e r
ye a r ra th e r th a n re p la c in g th e m no w . H o w e ve r, m a n a g e m e n t m a y decide to replace th e o ld tru c k s n o w
because o f q u a lita tiv e fa c to rs such as th e de sire to m a in ta in a m o d e rn im a ge f o r th e c o m p a n y a n d th e
im p ro v e d s a tis fa c tio n , a n d c o n s e q u e n tly th e im p ro v e d p ro d u c tiv ity , o f th e d riv e rs re s u ltin g fr o m th e
c o m fo rt o f th e n e w tru c k s .
Som e f u r t h e r exa m ples o f q u a lita tiv e fa c to rs t h a t m a y a ffe c t m a n a g e m e n ts d e cisio n s a b o u t p ro je c ts
are:
•
The in tr o d u c tio n o f la b o u r-s a v in g m a c h in e ry m a y be d e fe rre d (p e rh a p s in d e fin ite ly ) because o f
u n io n o p p o s itio n , even th o u g h o n th e basis o f th e q u a n tita tiv e a n a lysis th e p ro p o s a l to in tro d u c e
th e m a c h in e ry has a n e t p re s e n t v a lu e g re a te r th a n zero.
•
T w o m u tu a lly e xclu sive in v e s tm e n ts m a y have n e t p re s e n t values t h a t are a lm o s t eq ua l, b u t one
re q u ire s m u c h m o re m a n a g e m e n t s u p e rv is io n , o r th e use o f som e o th e r scarce h u m a n resource. The
use o f th is scarce reso urce in v o lv e s an o p p o r tu n ity cost th a t, w h ile re co g n ise d b y m a n a g e m e n t, is
d iff ic u lt to q u a n tify . T h e re fo re , ra th e r th a n a tte m p tin g to m ea sure th e o p p o r tu n it y co st o f u s in g th e
scarce h u m a n resources, m a n a g e m e n t m a y s im p ly select th e p ro p o s a l t h a t i t b e lie ve s w ill use fe w e r
o f th o s e resources, o th e r th in g s b e in g equal.
I t is e s s e n tia l t h a t such q u a lita tiv e fa c to rs be c o n sid e re d b e fo re s e le c tin g a p ro je c t. H o w eve r, th e
re c o g n itio n o f q u a lita tiv e fa c to rs is n o t a g e n e ra l p re s c rip tio n f o r ig n o r in g o r re d u c in g th e im p o rta n c e
o f th e q u a n tita tiv e a n a lysis. As a ll fa c to rs c a n n o t be in c o rp o ra te d in to th e q u a n tita tiv e an alysis, a
c o m p a ris o n o f a lte rn a tiv e in v e s tm e n t p ro p o s a ls is in c o m p le te w ith o u t an asse ssm en t o f th e po ssib le
e ffe cts o f th e q u a lita tiv e fa c to rs . Ind e e d , th e in flu e n c e o f q u a lita tiv e fa c to rs m a y be s u ffic ie n tly im p o r ta n t
to cause m a n a g e m e n t to select p ro p o sa ls w ith lo w e r c a lc u la te d n e t p re s e n t values.
C hapter SIX T he APPLICATION 〇F PROJECT EVALUATION METHODS
6.9
Project selection with resource
constraints
So fa r i t has been a ssu m ed t h a t m a n a g e m e n t is w illin g a n d able to accept a ll in d e p e n d e n t in v e s tm e n t
p ro je c ts th a t have a n e t p re s e n t v a lu e g re a te r th a n zero an d, i f m u tu a lly e xclusive p ro je c ts are b e in g
com pared, th o se p ro je c ts w it h th e h ig h e s t p o s itiv e n e t p re s e n t value. H o w e ve r, so m e tim e s a c o m p a n y s
LEARNING
OBJECTIVE 8
Explain the effects of
resource constraints on
project selection
m anagers be lie ve t h a t th e y are p re v e n te d fr o m u n d e rta k in g a ll acceptable p ro je c ts because o f a sho rta ge *
o f fu n d s .
C apital ration in g
is th e te rm used to de scrib e such a s itu a tio n . I t m a y be c la s s ifie d f u r t h e r in to
in te rn a l (o r ‘s o f t ’）c a p ita l ra tio n in g a n d e x te rn a l (o r ‘h a rd ’）c a p ita l ra tio n in g .
Internal capital rationing
occurs w h e n m a n a g e m e n t lim it s th e a m o u n t t h a t can be in v e s te d in n e w
p ro je c ts d u rin g som e s p e c ifie d tim e p e rio d . There are seve ral reasons w h y m a n a g e m e n t m a y im p o s e a li m it
o n c a p ita l e x p e n d itu re . O n e is t h a t m a n a g e m e n t is c o n s e rv a tiv e a n d has a p o lic y o f fin a n c in g a ll p ro je c ts
fro m in te r n a lly g e n e ra te d cash because i t is u n w illin g to b o rro w . S im ila rly , m a n a g e m e n t m a y be u n w illin g
to issue m o re shares because o f p o ssib le e ffe cts o n th e c o n tro l o f th e com p an y. A lte rn a tiv e ly , im p o s in g
c a p ita l e x p e n d itu re lim it s can be a w a y o f m a in ta in in g fin a n c ia l c o n tro l. F o r e xa m p le , in a la rg e com p an y,
m anagers m a y a tte m p t to e x p a n d t h e ir d iv is io n s b y p ro p o s in g m a n y n e w p ro je c ts , som e o f w h ic h o n ly
appear to
be p ro fita b le because th e cash flo w fo re ca sts are v e ry o p tim is tic . To a v o id th is p ro b le m , to p
m a n a g e m e n t m a y delegate a u t h o r ity f o r c a p ita l e x p e n d itu re d e cisio n s to d iv is io n a l m an ag ers, b u t re ta in
o ve ra ll c o n tro l b y g iv in g each d iv is io n a c a p ita l e x p e n d itu re lim it . The a im is to fo rce each d iv is io n a l
m an ag er to decide w h ic h o f th e p o ssib le p ro je c ts re a lly s h o u ld be a d op te d.
A n o th e r p o s s ib ility is t h a t i t m a y be d e sira b le to li m i t th e ra te a t w h ic h a c o m p a n y exp an ds because o f
th e o rg a n is a tio n a l d iffic u ltie s in h e re n t in h ir in g a n d t r a in in g m a n y a d d itio n a l s ta ff. M a n a g e m e n t m a y be
con cern ed t h a t ra p id e x p a n s io n w ill le a d to in e ffic ie n c y a n d h ig h e r costs. To a v o id th e se p ro b le m s i t m a y
lim it th e n u m b e r o f n e w p ro je c ts t h a t are im p le m e n te d . In th is case, a c a p ita l e x p e n d itu re li m i t is used to
im p ose th e d e sire d r e s tr ic tio n , b u t i t is n o t
capital t h a t
is th e scarce resource. R a th e r, th e scarce resource
is m a n a g e m e n t tim e , a n d th e re a l c o n ce rn is t h a t th is c o n s tra in t m a y re s u lt in s u p e rv is io n p ro b le m s .
External capital rationing occu rs
w h e n th e c a p ita l m a rk e t is u n w illin g to s u p p ly th e fu n d s necessary
to fin a n ce th e p ro je c ts t h a t a c o m p a n y s m a n a g e m e n t w ishes to u n d e rta k e . I n th is case, th e c o m p a n y
has p ro je c ts t h a t o ffe r p o s itiv e n e t p re s e n t value s b u t c a n n o t raise, a t a co st t h a t m a n a g e m e n t con sid ers
acceptable, th e fu n d s necessary to fin a n c e th e m . T h is s itu a tio n can o ccu r i f fin a n c ia l in te rm e d ia rie s are
sub je ct to c o n tro ls such as lim it s o n th e v o lu m e o r g r o w th ra te o f t h e ir le n d in g . H o w e ve r, i t is d iffic u lt
to see w h y i t s h o u ld o ccu r in d e re g u la te d fin a n c ia l m a rk e ts . A n y c o m p a n y t h a t has a p ro je c t exp ected
to be p ro fita b le s h o u ld be able to o b ta in th e necessary c a p ita l, n o m a tte r h o w s m a ll its c a p ita l b u d g e t.
F or exam ple, suppose t h a t a s m a ll com p an y, w h ic h p la n s to in v e s t n o m o re th a n , say, $ 5 0 0 0 0 in th e
c u rre n t year, discove rs an in e x p e n s iv e w a y o f e x tra c tin g g o ld fr o m th e oceans. R a is in g c a p ita l to b u ild th e
e x tra c tio n p la n t s h o u ld n o t be a p ro b le m .
E m p iric a l evidence suggests t h a t c a p ita l r a tio n in g is m o re lik e ly to re s u lt fr o m e x p e n d itu re lim it s
im p o se d b y m a n a g e m e n t o f its o w n v o lit io n th a n fr o m an u n w illin g n e s s o f th e c a p ita l m a rk e t to s u p p ly
fu n d s (P ike 1 9 8 3 ). I f m a n a g e m e n ts de cisio n s re s u lt in th e re je c tio n o f p ro je c ts w it h p o s itiv e n e t p re s e n t
values, th e n m a n a g e m e n t is a d o p tin g a p o lic y in c o n s is te n t w it h th e o b je c tiv e o f m a x im is in g th e m a rk e t
value o f th e c o m p a n y ’s shares. I f c a p ita l ra tio n in g is e s s e n tia lly an in te r n a l ‘p ro b le m ’, i t m ig h t a p p e a r th a t
th e s o lu tio n s h o u ld be sim p le . M a n a g e m e n t s h o u ld re m o ve th e c o n s tra in ts so t h a t a ll p o s itiv e n e t p re s e n t
value p ro je c ts can be im p le m e n te d . In som e cases, th is does occur. F o r e xa m p le , in cases w h e re c a p ita l
e x p e n d itu re lim it s are used to m a in ta in fin a n c ia l c o n tro l, th e lim it s are lik e ly to be fle x ib le , a n d a d d itio n a l
fu n d s w ill be p ro v id e d i f a p ro fita b le in v e s tm e n t o p p o r tu n ity arises u n e xp e cte d ly.
H o w eve r, as discussed above, c a p ita l e x p e n d itu re lim it s m a y be im p o s e d f o r v a lid reasons t h a t do
n o t re fle c t a sh o rta g e o f c a p ita l. R a th e r, th e re a l c o n s tra in t m a y be a s h o rta g e o f o th e r resources such
as m a n a g e m e n t tim e . T h e re fo re , c a p ita l r a tio n in g can be a real p h e n o m e n o n a n d m an ag ers m a y ne ed to
choose th e set o f p ro je c ts t h a t m a x im is e s n e t p re s e n t value , s u b je c t to a reso urce c o n s tra in t. O n th e o th e r
ha n d , i f e x te rn a l c a p ita l r a tio n in g e xists, a tte m p ts to m a x im is e n e t p re s e n t value , su b je c t to a c a p ita l
e x p e n d itu re lim it , in v o lv e a n in h e re n t c o n tra d ic tio n . The p ro b le m is t h a t a p ro je c ts n e t p re s e n t va lu e
is ca lcula ted u s in g a re q u ire d ra te o f r e tu r n , b u t th e existe nce o f an e x te rn a l l i m i t o n th e a v a ila b ility
o f c a p ita l im p lie s t h a t once th e li m it is reached, th e re q u ire d ra te o f r e tu r n is in fin ite . In th e fo llo w in g
CAPITAL RATIO NING
a condition where
a firm has limited
resources available for
investment
d iscu ssio n , th e re fo re , i t w ill be assu m ed t h a t c a p ita l r a tio n in g e xists o n ly because o f in te r n a lly im p o s e d
c o n s tra in ts . A m a n a g e r a tte m p tin g to ‘m a x im is e , th e m a rk e t value o f th e c o m p a n y ’s shares w it h in these
s e lf-im p o s e d c o n s tra in ts s h o u ld calcula te th e n e t p re s e n t value o f each p ro je c t b y d is c o u n tin g its cash
flo w s a t th e re q u ire d ra te o f re tu rn , a n d th e n choose th e c o m b in a tio n o f p ro je c ts t h a t m a xim ise s n e t
p re s e n t v a lu e . The fo llo w in g e xa m p le illu s tra te s th is ap pro ach.
E xample 6.14
S u p p o s e th a t a c o m p a n y is c o n s id e r in g th e p r o p o s a ls lis te d in T a b le 6 . 1 4 . A s s u m e th a t it h a s a c a p it a l
e x p e n d itu re lim it o f $ 6 0 0 0 0 0 , a ll p ro je c ts a r e in d e p e n d e n t, th e p ro je c ts a r e n o t d iv is ib le a n d it is n o t
e n v is a g e d th a t a n e x p e n d itu re lim it w ill e x is t in fu tu re y e a rs .
TABLE 6.14 Ranking of projects under capital rationing
Project
Initial cash outlay ($)
Net present value ($)
A
200000
28000
B
200000
20000
C
200000
15 000
D
200000
35 000
E
400000
45 000
F
400000
22000
M a n a g e m e n t m u st f in d th e c o m b in a tio n o f p ro je c ts th a t m a x im is e s n e t p re s e n t v a lu e , s u b je c t to th e
e x p e n d itu re lim it o f $ 6 0 0 0 0 0 .
SOLUTION
In th is e x a m p le , e x a m in a tio n o f a ll p o s s ib le o u tc o m e s s h o w s th a t th e la rg e s t n e t p re s e n t v a lu e w ill b e
a c h ie v e d b y th e c o m b in a tio n o f P ro je cts D, A a n d B. T h is c o m b in a tio n resu lts in a n e t p re s e n t v a lu e
o f $ 8 3 0 0 0 . B y c o m p a r is o n , th e n e x t b e s t a lte r n a tiv e , a c o m b in a tio n o f P ro je cts D a n d E, resu lts in
a n e t p re s e n t v a lu e o f $ 8 0 0 0 0 . A s a re s u lt o f th e e x p e n d itu re lim it, e v e n th o u g h P ro je c ts C , E a n d
F h a v e p o s itiv e n e t p re s e n t v a lu e s , th e c o m p a n y is u n a b le to im p le m e n t th e m th is y e a r . W it h o u t th e
e x p e n d itu r e lim it, a ll th e p ro je c ts s h o w n in T a b le 6 . 1 4 c o u ld h a v e b e e n a c c e p te d a n d th e to ta l n e t
p re s e n t v a lu e w o u ld h a v e b e e n $ 1 6 5 0 0 0 in s te a d o f $ 8 3 0 0 0 .
In re a lity , ra n k in g o f in v e s tm e n t p ro je c ts w h e re th e re is c a p ita l r a tio n in g is m u c h m o re co m p le x
because o f th e la rg e n u m b e r o f in v e s tm e n t a lte rn a tiv e s g e n e ra lly a va ila b le to a co m p a n y. To f in d s o lu tio n s
to such p ro b le m s , m a th e m a tic a l p ro g ra m m in g m o d e ls have b e en de velope d.
W e n o w r e tu r n to th e e a rlie r p o in t t h a t th e im p o s itio n o f c a p ita l r a tio n in g b y m a n a g e m e n t can p re v e n t
th e m a x im is a tio n o f s h a re h o ld e rs ’ w e a lth . C a p ita l r a tio n in g is n o t in th e s h a re h o ld e rs ’ b e s t in te re s t i f
p ro je c ts w it h p o s itiv e n e t p re s e n t values are rejected . In E x a m p le 6 .1 4 , P ro je cts C, E a n d F, w ith p o s itiv e
n e t p re s e n t values t o t a llin g $ 8 2 00 0, are re je cte d because o f a c a p ita l c o n s tra in t. U n less th e c o m p a n y faces
a re a l c o n s tra in t, such as a s h o rta g e o f p e rs o n n e l, o r ra p id e x p a n s io n in v o lv e s excessive r is k , m a n a g e m e n t
s h o u ld raise th e fu n d s necessary to fin a n c e the se p ro je c ts b y re d u c in g d iv id e n d s , b o rro w in g , is s u in g m o re
shares o r som e c o m b in a tio n o f the se a ctio n s.
C hapter six T he
application of project evaluation methods
This c h a p te r h a s d is c u s s e d s e v e ra l im p o r ta n t a s p e c ts
c h a in
o f p r o je c t e v a lu a tio n , b e g in n in g w ith th e e s tim a tio n o f
th e e q u iv a le n t a n n u a l v a lu e o f e a c h p r o je c t. T hese
of
re p la c e m e n t
m e th o d
or
by
c a lc u la tin g
c a s h flo w s .
m e th o d s a ls o p r o v id e a c o n v e n ie n t w a y o f a n a ly s in g
•
a s s e t r e p la c e m e n t d e c is io n s .
In e s tim a tin g c a s h flo w s , f in a n c in g c h a rg e s s h o u ld
b e e x c lu d e d , a s to o s h o u ld a llo c a te d costs a n d su n k
•
•
W h ile
th e e ffe c ts o f ris k c a n
be
in c o r p o r a t e d
in
p r o je c t e v a lu a tio n b y u s in g a ris k -a d ju s te d d is c o u n t
costs. C o n v e rs e ly , a ll in c re m e n ta l c a s h flo w s m ust b e
in c lu d e d . T he c o r r e c t tre a tm e n t o f in fla tio n re q u ire s
ra te , th e re a r e s e v e ra l m e th o d s o f p r o je c t a n a ly s is
th a t c a s h flo w s a n d th e r e q u ir e d ra te o f re tu rn b e
th a t c a n b e u se fu l in d e s c r ib in g ris k a n d p r o v id in g
d e fin e d in a c o n s is te n t m a n n e r.
m a n a g e rs w ith in fo r m a tio n a b o u t th e ris k o f a p r o je c t.
In d iv id u a ls a n d firm s a r e
T he m e th o d s d is c u s s e d in th e c h a p te r a r e s e n s itiv ity
r e q u ire d to p a y in c o m e
ta x e s to th e g o v e rn m e n t. H e n c e , it is im p o r ta n t th a t
a n a ly s is ,
p r o je c t e v a lu a tio n m e th o d s ta k e in to a c c o u n t ite m s
D e c is io n -tre e
th a t q u a lif y as a s s e s s a b le in c o m e a n d
e v a lu a tin g s e q u e n tia l d e c is io n s w h e r e p r o b a b ilit ie s
q u a lify
as
a llo w a b le
d e d u c tio n s .
An
ite m s th a t
in c re a s e
b re a k -e v e n
a n a ly s is
a n a ly s is
can
be
and
a
s im u la tio n .
u se fu l
to o l
fo r
c a n b e a tta c h e d to th e p o s s ib le o u tc o m e s .
in
a s s e s s a b le in c o m e resu lts in a h ig h e r ta x p a y m e n t,
T he c h a p te r
w h ile a n in c re a s e in a llo w a b le d e d u c tio n s re su lts in
•
P ro je c ts
th a t
a re
a ls o
p r o v id e d
a
d is c u s s io n
o f th e
im p o r ta n c e o f c o n s id e r in g q u a lita tiv e fa c to rs in p r o je c t
a lo w e r t a x p a y m e n t.
m u tu a lly
e x c lu s iv e
and
have
d iffe re n t liv e s c a n b e c o m p a r e d u s in g th e c o n s ta n t
e v a lu a tio n , a n d c o n c lu d e d w ith a d is c u s s io n o f th e
e ffe c ts o f re s o u rc e c o n s tra in ts o n p r o je c t e v a lu a tio n .
KEY TERMS
b re a k -e v e n a n a ly s is
c a p ita l r a tio n in g
re s id u a l v a lu e
151
131
s e n s itiv ity a n a ly s is
157
c o n s ta n t c h a in o f re p la c e m e n t a s s u m p tio n
e q u iv a le n t a n n u a l v a lu e m e th o d
s im u la tio n
140
su n k co st
141
149
152
131
SELF-TEST PROBLEMS
A c o m p a n y is c o n s id e r in g th e p u rc h a s e o f e q u ip m e n t c o s tin g $ 8 4 0 0 0 , w h ic h w ill p e r m it it to re d u c e its
e x is tin g la b o u r co sts b y $ 2 0 0 0 0 a y e a r fo r 1 2 y e a rs . T h e c o m p a n y e s tim a te s th a t it w ill h a v e to s p e n d
$ 2 0 0 0 e v e r y 2 y e a rs o v e r h a u lin g th e e q u ip m e n t. The e q u ip m e n t m a y b e d e p r e c ia te d f o r t a x p u rp o s e s
b y th e s tr a ig h t-lin e m e th o d , o v e r a 1 2 -y e a r p e r io d . T he c o m p a n y ta x ra te is 3 0 c e n ts in th e d o lla r a n d th e
a fte r-ta x c o s t o f c a p it a l is 1 0 p e r c e n t p e r a n n u m . A s s u m in g a ll c a s h flo w s , in c lu d in g ta x p a y m e n ts , a r e
m a d e a t th e e n d o f e a c h y e a r, s h o u ld th e c o m p a n y p u rc h a s e th e e q u ip m e n t?
T he m a n a g e m e n t o f th e T M T C o m p a n y is c o n s id e r in g p u r c h a s in g a n e w m a c h in e a n d it h a s g a th e r e d th e
f o llo w in g d a ta :
a)
The c a s h n e e d e d to p u rc h a s e th e n e w m a c h in e is $ 6 4 0 0 0 .
b) The re s id u a l v a lu e a n d a n n u a l c a s h o p e r a tin g e x p e n s e s fo r th e n e x t 5 y e a rs a r e e s tim a te d to be:
R e sid u a l v a lu e a t e n d
A n n u a l ca sh o p e r a tin g
Year
o f y e a r ($ )
e xp e n se s ($ }
1
50000
11000
2
40000
13000
3
30000
18000
4
23000
24000
5
3500
28000
C H A P T E R SIX R E V I E W
SUMMARY
B usiness finance
c)
N o cha ng es in residual values o r a n n u a l cash o p e ra tin g expenses a re exp ected .
d) The re q u ire d rate o f return is 15 per cent pe r annum .
e) The effects o f c o m p a n y in com e ta x m a y be ig n o re d .
W h a t is the o p tim u m re p la ce m e n t p o lic y fo r this m achine?
3
The m a n a g e m e n t o f A B C T ra n sp o rt Ltd, w h ic h is e n g a g e d in interstate tra n s p o rt, is c o n s id e rin g the
re p la c e m e n t o f its pre sen t fle e t o f 1 0 CB sem i-trailers w ith six A Z F lexivans. A su rve y has re ve a le d the
fo llo w in g estim ates o f costs, a n d so on, p e r vehicle:
CB s e m i-tra ile rs
R em aining life
E stim ate s
3 years
A Z F le x iv a n s
E stim ates
E stim ate d life
5 years
1
Residual value:
A t th e p re se n t tim e
$5 000
Cost
$70000
In 3 years’ tim e
$1000
A n n u a l n e t cash flow s
$40000
A n n u a l n e t cash flow s
$30000
Residual value a fte r
$5 000
5 years’ o p e ra tio n
O th e r in fo r m a tio n is a s fo llo w s :
•
N e t c a s h flo w s a r e to b e r e g a r d e d a s re c e iv e d a t th e e n d o f e a c h y e a r.
•
T he r e q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m .
S h o u ld m a n a g e m e n t:
a)
re ta in th e C B s e m i-tra ile rs f o r 3 y e a rs a n d th e n re p la c e th e m w ith A Z F le x iv a n s ?
b)
re p la c e th e C B se m i-tra ile rs w ith th e A Z F le x iv a n s n o w ?
Solutions to self-test problems ore available in Appendix B.
QUESTIONS
1
[LO 1! A p r o p e r ty d e v e lo p m e n t c o m p a n y p la n s to d e m o lis h th e b u ild in g o n a site th a t it a lr e a d y o w n s , a n d
th e n b u ild a c o n v e n ie n c e sto re . W h ic h o f th e f o llo w in g ite m s s h o u ld b e in c lu d e d a s in c re m e n ta l c a s h flo w s
w h e n th e p r o je c t is e v a lu a te d :
2
a)
th e m a rk e t v a lu e o f th e p r o p e r ty
b)
th e c o s t o f d e m o lis h in g th e o ld b u ild in g
c)
th e co st o f n e w w a te r a n d e le c tric p o w e r c o n n e c tio n s in s ta lle d 3 m o n th s a g o
d)
a p o rtio n o f th e c o s t o f le a s in g c a rs use d b y th e c o m p a n y 's e x e c u tiv e s
e)
m o n e y th a t ha s a lr e a d y b e e n s p e n t o n a rc h ite c tu ra l c o n c e p t p la n s fo r th e n e w b u ild in g ?
[L O 1] E x p la in th e re la tio n s h ip b e tw e e n
nominal a n d real d is c o u n t ra te s . O u t lin e its a p p lic a t io n to p r o je c t
e v a lu a tio n in th e c o n te x t o f a n in fla t io n a r y e c o n o m y .
3
[LO 1] L e a v in g a s id e th e e ffe c t o f ta x e s , w h ic h o f th e f o llo w in g ite m s s h o u ld b e c o n s id e r e d in th e in itia l
o u tla y o n a n e w m a c h in e f o r p r o je c t e v a lu a tio n p u rp o s e s ? G iv e re a s o n s .
a)
T he d is p o s a l v a lu e o f th e o ld m a c h in e , w h ic h is $ 6 0 0 0 .
b) T he $ 4 0 0 c o s t o f in s ta llin g th e n e w m a c h in e .
4
5
c)
A d d it io n a l in v e s tm e n t o f $ 1 0 0 0 0 in c u rre n t assets th a t w ill b e re q u ire d .
d)
C o sts o f $ 3 0 0 0 re c e n tly in c u rre d in a sse ssin g th e s u ita b ility o f th e n e w m a c h in e .
[L O 2 】It
doesn't matter whether the straight-line method or reducing-balance method o f depreciation is
used since the total tax b ill over the life o f the project is the some. C o m m e n t o n th is s ta te m e n t.
[LO 3 】 O u t lin e tw o m e th o d s o f s o lv in g p r o je c t e v a lu a tio n p ro b le m s w h e r e th e p ro je c ts u n d e r c o n s id e r a tio n
d o n o t h a v e c o m m o n te r m in a l d a te s .
160
C hapter six T he
[L O 3 ] D e fin e th e te rm 'm u tu a lly e x c lu s iv e p r o je c ts ' a n d p r o v id e a s im p le e x a m p le . O u tlin e a n d ju s tify th e
b a s ic n e t p re s e n t v a lu e ru le a p p lic a b le to th e m . H o w s h o u ld th is ru le b e m o d ifie d w h e n such p ro je c ts h a v e
u n e q u a l live s?
7
[L O 4 ] H o w s h o u ld th e o p tim u m life o f a p r o je c t b e d e te rm in e d ?
8
[L O 4 ] D is tin g u is h b e tw e e n re p la c e m e n t d e c is io n s a n d re tire m e n t d e c is io n s .
9
[L O 5 ]
10
[L O 5 ] O u tlin e th e w e a k n e s s e s o f s e n s itiv ity a n a ly s is .
Sensitivity analysis may be used to identify the variables that ore most important for a project's
success. D iscuss.
11
[LO 5 ]
12
[L 0 5 ]
Simulation is only useful for large-scale investment projects. D iscuss.
Simulation is extremely valuable because it is useful in refining cash flow forecasts and it avoids the
need to estimate a project's required rote o f return. D o y o u a g r e e w ith th e se c la im s ? G iv e re a s o n s f o r y o u r
a n s w e r.
13
[LO 8 ] D is tin g u is h b e tw e e n in te rn a l a n d e x te rn a l c a p it a l r a tio n in g . G iv e e x a m p le s o f e a c h .
14
[L0 8]
a)
O u tlin e p o s s ib le re a s o n s fo r th e im p o s itio n b y m a n a g e m e n t o f c a p ita l ra tio n in g . D o e s th e im p o s itio n o f
b)
If a c o m p a n y is s u b je c t to c a p ita l ra tio n in g , d o e s th is m a k e a n y d iffe re n c e to p r o je c t e v a lu a tio n u s in g th e
C H A P T E R SIX R E V I E W
6
application of project evaluation methods
in te rn a l c a p ita l r a tio n in g im p ly th a t m a n a g e m e n t is f a ilin g to m a x im is e s h a re h o ld e rs 7 w e a lth ?
n e t p re s e n t v a lu e m e th o d ? G iv e re a so n s.
CA
PROBLEMS
1
Application of the N P V method [LO 1]
The fu rn itu re d iv is io n o f P la y fu rn Ltd, a p ro fita b le , d iv e rs ifie d c o m p a n y , p u rc h a s e d a m a c h in e 5 y e a rs a g o
fo r $ 7 5 0 0 0 . W h e n it w a s p u rc h a s e d th e m a c h in e h a d a n e x p e c te d use ful life o f 1 5 y e a rs a n d a n e s tim a te d
v a lu e o f z e ro a t th e e n d o f its life . T h e m a c h in e c u rre n tly h a s a m a rk e t v a lu e o f $ 1 0 0 0 0 . T he d iv is io n
m a n a g e r re p o rts th a t he c a n b u y a n e w m a c h in e fo r $ 1 6 0 0 0 0 (in c lu d in g in s ta lla tio n ) w h ic h , o v e r its 1 0 -y e a r
life , w ill re su lt in a n e x p a n s io n o f sa le s fro m $ 1 0 0 0 0 0 to $1 1 0 0 0 0 p e r a n n u m . In a d d itio n , it is e s tim a te d th a t
th e n e w m a c h in e w ill re d u c e a n n u a l o p e r a tin g costs fro m $ 7 0 0 0 0 to $ 5 0 0 0 0 . If th e r e q u ire d ra te o f re tu rn is
1 0 p e r c e n t p e r a n n u m , s h o u ld P la y fu rn b u y th e n e w m a c h in e ?
2
Application of the N P V method [LO 1]
T he T w o-B it M in in g C o m p a n y h a s c o n s tru c te d a to w n a t B ig B o re , n e a r th e site o f a ric h m in e ra l d is c o v e r y
in a re m o te p a r t o f A u s tr a lia . T he to w n w ill b e a b a n d o n e d w h e n m in in g o p e ra tio n s c e a s e a fte r a n e s tim a te d
1 0 -y e a r p e r io d . T he fo llo w in g e s tim a te s o f in v e s tm e n t costs, sa le s a n d o p e r a tin g e x p e n s e s re la te to a p r o je c t to
s u p p ly B ig B o re w ith m e a t a n d a g ric u ltu r a l p ro d u c e o v e r th e 1 0 -y e a r p e r io d b y d e v e lo p in g n e a r b y la n d .
a)
In v e s tm e n t in la n d is $ 1 0 m illio n , fa rm b u ild in g s $ 2 0 0 0 0 0 0 a n d fa rm e q u ip m e n t $ 4 0 0 0 0 0 0 . T he la n d
is e x p e c te d to h a v e a re a lis a b le v a lu e o f $ 5 0 0 0 0 0 0 in 1 0 y e a rs ' tim e . T he re s id u a l v a lu e o f th e b u ild in g s
a fte r 1 0 y e a rs is e x p e c te d to b e $ 5 0 0 0 0 0 . T he fa rm e q u ip m e n t ha s a n e s tim a te d life o f 1 0 y e a rs a n d a
z e r o re s id u a l v a lu e .
b)
In ve stm e n t o f $ 2 5 0 0 0 0 0 in c u rre n t assets w ill b e re c o v e re d a t th e te rm in a tio n o f th e v e n tu re .
c)
A n n u a l c a s h sales a r e e s tim a te d to b e $ 2 4 . 8 m illio n .
d)
A n n u a l c a s h o p e r a tin g costs a r e e s tim a te d to b e $ 2 2 m illio n .
Is th e p ro je c t p r o fita b le , g iv e n th a t th e r e q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m ?
3
Application of the N P V method [LO 1]
A s o ftw a re p r o v id e r b u y s b la n k B lu -ra y D V D s a t $ 5 5 0 p e r h u n d re d a n d c u rre n tly uses 2 m illio n D V D s p e r y e a r.
The m a n a g e r b e lie v e s th a t it m a y b e c h e a p e r to m a k e th e D V D s ra th e r th a n b u y th e m . D ire c t p r o d u c tio n costs
(la b o u r, m a te ria ls , fu e l) a r e e s tim a te d a t $ 2 . 5 0 p e r D V D . T he e q u ip m e n t n e e d e d w o u ld c o s t $ 3 m illio n . T he
e q u ip m e n t s h o u ld la s t fo r 1 5 y e a rs , p r o v id e d it is o v e rh a u le d e v e ry 5 y e a rs a t a c o s t o f $ 2 5 0 0 0 0 e a c h tim e .
The o p e r a tio n w ill re q u ire a d d itio n a l c u rre n t assets o f $ 4 0 0 0 0 0 . The c o m p a n y 's r e q u ire d ra te o f re tu rn
is 1 2 p e r c e n t. E v a lu a te th e p ro p o s a l.
161
B usiness finance
4
Application of the N P V method [LO 1]
O z z ie N a tio n w id e In d u strie s Ltd is a la r g e c o m p a n y w ith in te re sts in m in in g , s h ip b u ild in g , e n te rta in m e n t, fo o d
p ro c e s s in g a n d in te rs ta te fr e ig h t h a u la g e . Its fo o d p ro c e s s in g d iv is io n is in v e s tig a tin g th e p o s s ib ility o f a d d in g
m a n d a rin -fla v o u re d y o g h u r t to its c u rre n t ra n g e o f b a n a n a , s tr a w b e r r y a n d a p p le . C u rre n tly , a ll fla v o u rs a re
s o ld a t a p ric e o f $ 1 . 5 0 p e r c a rto n a n d sa le s a re e ve n th ro u g h o u t th e y e a r. O z z ie re c e n tly h ir e d M e lb o u r n e
M a r k e t R e se a rch Ltd to s u rv e y co n s u m e rs to ju d g e th e lik e ly p o p u la r ity o f th e n e w fla v o u r. The r e p o r t c o s t
$ 4 0 0 0 0 a n d s u g g e s te d th a t th e c o m p a n y s h o u ld b e a b le to sell 4 0 0 0 0 0 c a rto n s o f th e n e w fla v o u r n e x t y e a r,
a n d 8 0 0 0 0 0 in e a c h o f th e f o llo w in g 2 y e a rs . A fte r th a t tim e , th e fa d fo r m a n d a r in fla v o u r is e x p e c te d to
h a v e run its c o u rs e . O z z ie 's c o s tin g d e p a rtm e n t h a s a d v is e d th a t th e in c re m e n ta l c o s t o f p ro d u c tio n is $ 1 . 2 0
p e r c a rto n . O z z ie 's sales d e p a rtm e n t h a s a d v is e d th a t it is e s s e n tia l th a t a ll fla v o u rs in th e ra n g e s h o u ld b e
so ld a t th e s a m e p ric e . O z z ie 's e n g in e e rs h a v e a d v is e d th a t th e re is n o s p a re p ro d u c tio n c a p a c ity a lth o u g h
th e re is p le n ty o f s p a re flo o r s p a c e in th e fa c to ry . T h e y h a v e a ls o a d v is e d th a t y o g h u r t p ro c e s s in g m a c h in e s
h a v e a p r o d u c tio n c a p a c ity o f 4 0 0 0 0 0 c a rto n s p e r a n n u m a n d th a t th e c o s t o f o n e m a c h in e , fu lly in s ta lle d ,
is $ 2 3 0 0 0 0 . O z z ie 's fin a n c e d iv is io n ha s a d v is e d th a t th e c o m p a n y 's re q u ire d ra te o f re tu rn (n o m in a l) is
e s tim a te d to b e 1 5 p e r c e n t p e r a n n u m . T he m a c h in e s h a v e a life o f 3 y e a rs a n d a t th a t p o in t h a v e o n ly a
s c ra p v a lu e , w h ic h is e s tim a te d to b e o n ly $ 1 0 0 0 0 . H o w e v e r, th is a m o u n t u s u a lly o n ly ju st c o v e rs th e costs o f
re m o v in g th e m a c h in e fro m th e fa c to ry .
O z z ie 's p r o je c t a n a ly s t h a s re c o m m e n d e d a g a in s t p r o c e e d in g w ith th e n e w fla v o u r, b a s in g this
r e c o m m e n d a tio n o n a n e t p re s e n t v a lu e a n a ly s is . T he n e t c a s h in flo w s w e r e fo re c a s t to b e $ 1 2 0 0 0 0 in th e
firs t y e a r, a n d $ 2 4 0 0 0 0 in th e s e c o n d y e a r a n d th e th ird y e a r. T he in itia l o u tla y w a s $ 5 0 0 0 0 0 . T he N P V w a s
c a lc u la te d as:
K(m/ $ 1 2 0 0 0 0
$240000
$240000
N P V = --------------- + -------------------1-$ 5 0 0 0 0 0
1.1 50 5
1 .1 5 15
1 .1 5 2-5
一
$ 2 4 2 64
The p r o je c t a n a ly s t's re p o r t c o n ta in e d th e u su al r a n g e o f s e n s itiv ity a n a ly s e s a n d s u p p o rtin g d is c u s s io n a n d
d o c u m e n ta tio n b u t th is c a lc u la tio n w a s th e c e n tra l result.
You h a v e b e e n a s k e d to r e v ie w th e p r o je c t a n a ly s t’s w o r k a n d re p o r t o n a n y e rro rs y o u d e te c t. P ro v id e
re a s o n s. Ig n o re ta x . N o te th a t it is n o t n e c e s s a ry to re d o th e a n a ly s is , o r to s u g g e s t h o w th e a n a ly s is m ig h t b e
e x te n d e d . Y o u r ta s k is to id e n tify e rro rs .
5
Application of the N P V method [LO 1]
T he B e rtie H a m ilto n F is h in g C o m p a n y (BHF) p u rc h a s e d a tr a w le r 6 y e a rs a g o fo r $ 4 2 0 0 0 0 . A t th e tim e
it w a s p u rc h a s e d , th e t r a w le r h a d a use ful life o f 1 0 y e a rs . If BHF w e r e to re ta in th is b o a t, it is a n tic ip a te d
th a t u ltra s o n ic d e te c tio n e q u ip m e n t w o u ld h a v e to b e in s ta lle d in th e s e c o n d -la s t y e a r o f its life a t a c o s t o f
$ 4 0 0 0 0 . H o w e v e r, th e C o m m e rc ia l T ra w le r C o m p a n y (CT) ha s re c e n tly la u n c h e d a fa ste r, co m p u te r-a s s is te d
tr a w le r th a t BHF is c o n s id e rin g a s a re p la c e m e n t. T his tr a w le r w ill c o s t $ 6 0 0 0 0 0 b u t w ill n e e d im m e d ia te
re fittin g to s u it th e p u rc h a s e r's s p e c ific a tio n s a t a n a d d itio n a l c o s t o f $ 1 5 0 0 0 . It h a s a n e x p e c te d use ful life o f
1 2 y e a rs .
If p u rc h a s e d , th e n e w tr a w le r is lik e ly to in c re a s e c a s h o p e r a tin g costs b y $ 1 0 p e r to n n e o f fish , w h ic h
c u rre n tly sells f o r $ 3 0 p e r to n n e . H o w e v e r, fu tu re c a tc h e s a re lik e ly to in c re a s e s ig n ific a n tly b y 6 0 0 0 to n n e s in
th e firs t y e a r, a n d the n a t a ra te o f 1 0 0 0 to n n e s p e r a n n u m , s ta b ilis in g a t 1 2 0 0 0 to n n e s fro m Y e a r 7 o n w a r d .
O w in g to in te n s iv e u s a g e , it is e x p e c te d th a t to w a r d s th e e n d o f th e fifth y e a r th e n e w tr a w le r w ill re q u ire a
m in o r e n g in e o v e rh a u l a t a c o s t o f $ 3 0 0 0 0 . P a rt o f th e p u rc h a s e a g re e m e n t a ls o in v o lv e s a m a in te n a n c e
c o n tra c t w ith C T c o v e rin g th e nets a n d t r a w lin g a p p a ra tu s , w h ic h w ill c o s t BHF $ 1 2 0 0 0 , p a y a b le a t th e e n d
o f e v e r y fo u rth y e a r.
A s a c o m p e titiv e stra te g y, C T o ffe rs a n o p tio n a l fin a n c in g p a c k a g e fo r u p to 8 0 p e r c e n t o f th e in v o ic e p ric e
o n a n y b o a t. T h e ra te o f in te re s t o n th is a m o u n t is 1 2 p e r c e n t p e r a n n u m , w ith th e firs t p a y m e n t d e fe rre d
1 y e a r. If th e fin a n c in g p a c k a g e is a d o p te d , BHF m ust u n d e rta k e to sell th e tr a w le r b a c k to C T in 1 2 y e a rs '
tim e fo r $ 5 0 0 0 0 . BHF e s tim a te s th a t th e c u rre n t s e c o n d -h a n d p r ic e o f its p re s e n t tr a w le r is o n ly $ 1 4 0 0 0 0 . It is
e s tim a te d th a t th e n e w tr a w le r c a n b e s o ld f o r $ 1 0 0 0 0 0 a t th e e n d o f its use fu l life . T h e c o m p a n y 's n o m in a l
re q u ire d ra te o f re tu rn is 3 0 p e r ce n t.
a)
E stim a te th e n e t c a s h f lo w (N C F ) a t th e b e g in n in g o f Y e a r 1.
bj
E stim a te th e N C F in Y e a r 4 .
C hapter six T he
M a n a g e m e n t b e lie v e s th a t re la tiv e to to d a y 's p ric e s , th e a v e r a g e in fla tio n ra te is e x p e c te d to b e 8 p e r c e n t
p e r a n n u m o v e r th e n e x t 1 2 y e a rs . W h a t is th e Y e a r 3 in fla tio n -a d ju s te d N C F ?
d)
E stim a te th e a p p r o p r ia te d is c o u n t ra te to p e rfo rm a n N P V a n a ly s is in re a l te rm s.
Application of the N P V method [LO 1]
A c o m p a n y m ust c h o o s e b e tw e e n tw o m a c h in e s . M a c h in e A costs $ 5 0 0 0 0 a n d th e a n n u a l o p e r a tin g
e x p e n s e s a re e s tim a te d to b e $ 2 0 0 0 0 , w h ile M a c h in e B costs $ 8 5 0 0 0 a n d ha s e s tim a te d a n n u a l o p e r a tin g
e x p e n s e s o f $ 1 5 0 0 0 . B o th m a c h in e s h a v e a 1 0 -y e a r life a n d w ill h a v e a z e ro re s id u a l v a lu e .
a)
The c o m p a n y h a s a r e q u ire d ra te o f re tu rn o f 1 0 p e r c e n t p e r a n n u m . W h ic h m a c h in e s h o u ld it p u rc h a s e ?
b)
R e w o rk th e p ro b le m fo r a 7 p e r c e n t r e q u ire d ra te o f re tu rn .
Application of the N P V method [LO 1]
A c o m p a n y is c o n s id e rin g th e p u rc h a s e o f e q u ip m e n t c o s tin g $ 1 2 5 0 0 0 th a t w ill p e rm it it to re d u c e its e x is tin g
la b o u r costs b y $ 2 0 0 0 0 a y e a r f o r 1 2 y e a rs . T h e c o m p a n y e s tim a te s th a t it w ill h a v e to s p e n d $ 3 0 0 0 e v e r y
2 y e a rs o v e rh a u lin g th e e q u ip m e n t. T h e re q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m . A s s u m in g a ll c a s h
flo w s a re m a d e a t th e e n d o f e a c h y e a r, s h o u ld th e c o m p a n y p u rc h a s e th e e q u ip m e n t?
Explaining the effects of taxes on project cash flows [LO 2 】
The F o u r a n d S ix S tore s Pty Ltd is c o n s id e rin g lo c a tin g a n o th e r o u tle t in a n e a s te rn s u b u rb o f M e lb o u r n e .
C H A P T E R SIX R E V I E W
c)
application of project evaluation methods
Estim ates o f sales a n d o p e r a tin g e x p e n s e s h a v e b e e n m a d e a n d a n e s tim a te d p r o fit a n d loss s ta te m e n t fo r
the n e w s to re d r a w n u p . T he p r o fit a n d loss s ta te m e n t fo r Y e a r 1 is th o u g h t to b e re p re s e n ta tiv e o f e a c h o f
th e 1 0 y e a rs o f th e e x p e c te d life o f th e n e w F o u r a n d S ix s to re . T he in itia l o u tla y to c o n s tru c t th e s to re is
$ 4 0 0 0 0 0 0 , w h ile th e o u tla y n e c e s s a ry to sto ck th e s to re is $ 2 0 0 0 0 0 0 . T h e e s tim a te d s ta te m e n t o f fin a n c ia l
p e rfo rm a n c e fo r th e n e w s to re fo r Y e a r 1 is s h o w n in th e fo llo w in g ta b le :
Revenue
Less sales re tu rn s, discou nts
4000000
400 000
3 600000
N et revenue
O pe ra ting expenses
Cost o f goods sold
1600000
A d m in is tra tio n costs
600000
D e pre ciatio n
360000
In te re st
240000
2800000
N e t p ro fit before tax
800000
Tax (30% tax rate)
240000
N e t p ro fit a fte r tax
560000
E stim ate th e p ro je c t's a n n u a l a fte r-ta x c a s h flo w .
Explaining the effects of taxes on project cash flows [LO 2]
A ll- N ig h t C o ffe e S h o p s Ltd is a su cce ssful p r o fita b le c o m p a n y o p e r a tin g s e v e ra l d o z e n c o ffe e sh o p s th ro u g h o u t
th e m e tro p o lita n a r e a o f M e lb e r r a . H o w e v e r, th e s h o p in th e s u b u rb o f B u rn a b y h a s n o t b e e n w e ll p a tro n is e d ,
g e n e ra tin g a b e fo re -ta x n e t c a sh f lo w o f o n ly $ 5 0 0 0 0 in th e p a s t y e a r. T he B u rn a b y s h o p b e g a n tr a d in g
2 y e a rs a g o in p re m is e s le a s e d fro m C B D Ltd. T he le a s e is a b o u t to e x p ir e a n d A ll- N ig h t w ill n o t re n e w it.
A c o m p e tito r, B ra z il C o ffe e S h o p s Ltd, h a s o ffe re d to b u y th e fix tu re s a n d fittin g s a n d th e e q u ip m e n t in th e
B u rn a b y s h o p fo r $ 4 0 0 0 0 0 . A ll- N ig h t ha s a g r e e d to th is fig u re , e ve n th o u g h it is $ 3 0 0 0 0 0 less th a n th e c o s t
o f th e fix tu re s a n d fittin g s a n d th e e q u ip m e n t 2 y e a rs a g o . A s s u m e th a t:
a)
fo r ta x p u rp o s e s th e fix tu re s a n d fittin g s a n d th e e q u ip m e n t w e re d e p r e c ia te d o n a s tra ig h t-lin e b a s is a t
b)
th e a fte r-ta x c o m p a n y ta x ra te is 3 0 p e r ce n t.
10 pe r cent pe r annum
W h a t is th e a fte r-ta x n e t ca sh f lo w (fo r Y e a r 2 ) a ttr ib u ta b le to A ll- N ig h t's B u rn a b y sh o p ?
163
10
Explaining the effects of taxes on project cash flows [LO 2 】
It doesn't matter whether the straight-line or reducing-balance method o f depreciation is used, since the total tax
bill over the life o f the project is the same. D iscuss th e v a lid ity (o r o th e rw is e ) o f this s ta te m e n t in th e c o n te x t o f
th e fo llo w in g e x a m p le :
A s s e t co st (n o w )
$10000
A sset life
5 years
Residual value (in 5 years)
$4700
A n n u a l n e t cash in flo w be fore ta x
$6000
S tra ig h t-lin e d e p re cia tio n rate (per an nu m )
10%
Reducing-balance de p re cia tio n rate (per a n nu m )
20%
C om pany incom e ta x rate
30%
Cost o f cap ital
11
10% p.a.
Explaining the effects of taxes on project cash flows [LO 2]
A c o m p a n y is c o n s id e r in g p u rc h a s in g a n e w m a c h in e a t a c o s t o f $ 9 0 0 0 0 0 to re p la c e a m a c h in e p u rc h a s e d
6 y e a rs a g o f o r $1 m illio n . T h e d is p o s a l v a lu e o f th e o ld m a c h in e is $ 2 5 0 0 0 0 a n d th e a c c u m u la te d
d e p r e c ia tio n , w h ic h h a s b e e n a llo w e d fo r ta x p u rp o s e s , is $ 6 0 0 0 0 0 . B oth m a c h in e s w ill h a v e s im ila r o u tp u ts
a n d w ill p r o d u c e w o r k o f id e n tic a l q u a lity . T he e s tim a te d y e a r ly costs o f o p e r a tin g e a c h m a c h in e a re as
fo llo w s :
O ld m a c h in e ($)
N e w m a c h in e ($ ) 1
Wages
225 000
75 000
D e pre ciatio n
100000
225000
Supplies, repairs, po w e r
65 000
30000
Insurance and m iscellaneous
36000
20000
426000
350000
B oth m a c h in e s h a v e a n e s tim a te d re m a in in g life o f 4 y e a rs , a t w h ic h tim e b o th m a c h in e s w ill h a v e a n
e s tim a te d d is p o s a l v a lu e o f $ 9 0 0 0 0 . A s s u m e th a t:
a)
th e a fte r-c o m p a n y -ta x c o s t o f c a p ita l is 1 0 p e r c e n t p e r a n n u m
b)
th e o p e r a tin g co sts o f th e o ld m a c h in e a n d th e n e w m a c h in e a r e in c u rre d a t th e e n d o f e a c h y e a r
c)
th e c o m p a n y in c o m e ta x ra te is 3 0 ce n ts in th e d o lla r.
S h o u ld th e c o m p a n y p u rc h a s e th e n e w m a c h in e ?
12
Mutually exclusive projects with different lives [LO 3]
T h e m a n a g e m e n t o f H a r b o u r F e rrie s Ltd is c o n s id e rin g th e re p la c e m e n t o f its e x is tin g fle e t o f s ix ste a m fe rrie s
w ith th re e h y d ro fo ils . T he fo llo w in g e s tim a te s o f costs, a n d so o n , fo r e a c h vesse l h a v e b e e n c a lc u la te d :
I S te a m fe rrie s
E stim ate d re m a in in g life
E stim ates
5 years
E stim a te d scrap value:
N ow
$50000
In 5 years’ tim e
$10000
A n n u a l n e t cash flow s
$100000
H y d ro fo ils
E stim ate s
Cost
$500000
E stim ate d life
10 years
E stim ate d scrap value:
In 5 years’ tim e
$200000
In 10 years’ tim e
$100000
A n n u a l n e t cash flow s
$200000
C hapter six T he
application of project evaluation methods
a v a ila b le in 5 y e a rs 7 tim e . T he fo llo w in g e stim a te s o f costs, a n d so o n , p e r h o v e rc ra ft h a v e b e e n p r o v id e d b y
th e m a n u fa c tu re r:
H o v e rc ra ft
E stim ate s
Cost
$600000
E stim ated life
15 years
E stim ate d disposal value:
$200000
A fte r 5 years* o p era tion
$50000
A fte r 15 years* op e ra tio n
$250000
A n n u a l n e t cash flow s
C H A P T E R SIX R E V I E W
M a n a g e m e n t is a ls o a w a r e o f th e d e v e lo p m e n t o f h o v e rc ra ft, w h ic h th e m a n u fa c tu re r e s tim a te s w ill b e
It is c o n s id e re d th a t tw o o f th e n e w h o v e rc ra ft w ill b e a d e q u a te to c a r r y th e e s tim a te d n u m b e r o f p a s s e n g e rs .
O th e r in fo rm a tio n is a s fo llo w s :
•
M a n a g e m e n t c a n n o t fo re s e e a n y fu rth e r d e v e lo p m e n ts b e y o n d th e h o v e rc ra ft.
•
T he a n n u a l n e t c a s h flo w s a r e re c e iv e d a t th e e n d o f e a c h y e a r.
•
T he c o m p a n y 's re q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m .
You a re re q u ire d to a d v is e m a n a g e m e n t w h e th e r it s h o u ld :
a)
re p la c e th e stea m fe rrie s w ith h y d ro fo ils n o w , a n d re p la c e th e la tte r w ith h o v e rc ra ft in 5 y e a r s ' tim e
b)
re ta in th e ste a m fe rrie s fo r 5 y e a rs , a n d th e n re p la c e th e m w ith h o v e rc ra ft
c)
re p la c e th e stea m fe rrie s w ith h y d ro fo ils n o w , a n d re p la c e th e la tte r w ith h o v e rc ra ft in 1 0 y e a r s 7 tim e .
O th e r a lte rn a tiv e s a re n o t to b e c o n s id e re d .
13
Mutually exclusive projects with different lives [LO 3]
H e rm e s Pty Ltd o p e ra te s a c o u r ie r s e rv ic e . A n e w v a n is r e q u ire d to m e e t th e in c re a s e d d e m a n d fo r the
c o m p a n y ’s s e rv ic e s . T he c h o ic e h a s b e e n n a r r o w e d d o w n to th re e v a n s , A , B a n d C , e a c h c o s tin g $ 1 0 0 0 0 0 .
N e t c a s h f lo w e s tim a te s a r e as fo llo w s :
N e t c a sh f lo w e stim a te s ($)
Year
Van A
VanB
Van C
1
$47000
$48000
$47000
2
$50000
$40000
$48000
3
$50000
$40000
$48000
4
$58000
$52000
$55000
5
0
$42000
0
20%
20%
20%
$30795
$32881
$26801
Required rate o f re tu rn
NPV
By d is c o u n tin g e a c h n e t c a s h flo w , s h o w th a t th e n e t p re s e n t v a lu e o f V a n A h a s b e e n c a lc u la te d p ro p e rly .
W h ic h v a n s h o u ld b e p u rc h a s e d ? G iv e re a so n s.
16 5
14
Mutually exclusive projects with different lives [LO 3]
The m a n a g e m e n t o f H u n te r A ir Ltd is c o n s id e rin g th e re p la c e m e n t o f its e x is tin g fle e t o f seve n A 6 1 6 a ir c r a ft
w ith th re e B 7 2 7 a ir c r a ft. T he fo llo w in g e s tim a te s fo r e a c h a ir c r a ft h a v e b e e n c a lc u la te d :
A 6 1 6 a ir c r a ft
E stim ate d re m a in in g
E stim ates
5 years
B 7 2 7 a e ro p la n e s
Estim ates
Cost
$ 5 00 m illio n
E stim ated life
10 years
life
E stim ated scrap value
N ow
$50 m illio n
E stim ate d disposal
value
In 5 years’ tim e
A n n u a l n e t cash flow s
$10 m illio n
$100 m illio n
In 5 years’ tim e
$200 m illio n
In 10 years’ tim e
$100 m illio n
A n n u a l n e t cash flow s
$200 m illio n
M a n a g e m e n t is a ls o a w a r e o f th e d e v e lo p m e n t o f th e C 8 9 8 , w h ic h th e m a n u fa c tu re r e s tim a te s w ill
b e a v a ila b le in 5 y e a rs 7 tim e . T h e fo llo w in g e s tim a te s fo r a C 8 9 8 a ir c r a ft h a v e b e e n p r o v id e d b y th e
m a n u fa c tu re r.
I C 8 9 8 a ir c r a ft
E stim ates
Cost
$600 m illio n
E stim a te d life
15 years
E stim ate d disposal value
A fte r 5 years’ op e ra tio n
$200 m illio n
A fte r 15 years’ op e ra tio n
$50 m illio n
A n n u a l n e t cash flow s
$250 m illio n
It is c o n s id e re d th a t t w o o f th e n e w C 8 9 8 a ir c r a f t w ill b e a d e q u a te to c a r r y th e e s tim a te d n u m b e r o f
p a s s e n g e rs . O th e r in fo rm a tio n is a s fo llo w s :
i)
M a n a g e m e n t c a n n o t fo re s e e a n y fu rth e r d e v e lo p m e n ts b e y o n d th e C 8 9 8 a ir c r a ft.
ii)
T he a n n u a l n e t c a sh flo w s a re re c e iv e d a t th e e n d o f e a c h y e a r.
iii) T he c o m p a n y 's a fte r-ta x c o s t o f c a p ita l is 1 0 p e r c e n t p e r a n n u m .
iv) T he c o m p a n y 's ta x ra te is 3 0 cen ts.
v)
T he A 6 1 6 a ir c r a f t a re a s s u m e d to b e fu lly d e p re c ia te d .
vi) S tra ig h t-lin e d e p r e c ia tio n m a y b e a ss u m e d .
You a re re q u ire d to a d v is e m a n a g e m e n t w h e th e r it s h o u ld :
a)
re p la c e th e A 6 1 6 a ir c r a ft w ith B 7 2 7 a ir c r a ft n o w , a n d re p la c e th e la tte r w ith C 8 9 8 a ir c r a f t in
5 y e a r s ' tim e
b)
re ta in th e A 6 1 6 a ir c r a ft fo r 5 y e a rs , a n d th e n re p la c e th e m w ith C 8 9 8 a ir c r a ft
c)
re p la c e th e A 6 1 6 a ir c r a ft w ith B 7 2 7 a ir c r a ft n o w , a n d re p la c e th e la tte r w ith C 8 9 8 a ir c r a f t in
1 0 y e a r s ' tim e .
O th e r a lte rn a tiv e s a r e n o t to b e c o n s id e re d .
15
Mutually exclusive projects with different lives [LO 3]
S p e e d y Pty Ltd o p e ra te s a s u b u rb a n d o c u m e n t d e liv e r y bu sin e ss. It is c o n s id e rin g th e r e p la c e m e n t o f a 2 -to n n e
tru c k w ith a 3 -to n n e tru c k . D e ta ils o f th e re s p e c tiv e v e h ic le s a re a s fo llo w s :
C hapter six T he
Rem aining life
5 years
Residual value:
N ow
$6000
In 4 years
$0
C H A P T E R SIX R E V I E W
3 -to n n e tru c k
E stim ates
2 -to n n e tru c k
application of project evaluation methods
E stim ates
E stim ate d life
6 years
Cost
$25 000
Residual value a fte r 6 years’
op e ra tio n
$2000
D e pre ciatio n (allow able fo r tax
$4000 p.a.
purposes)
W ritte n -d o w n value (fo r ta x
$7500 (before
purposes)
ta xa tio n )
D e pre ciatio n (fo r ta x purposes)
$1200 p.a.
N et cash flo w (before ta x a tio n )
$ 1 2 0 0 0 p.a.
N e t cash flo w
$ 2 0 0 0 0 p.a.
O th e r in fo rm a tio n is a s fo llo w s :
i)
N e t c a s h flo w s a re to b e r e g a r d e d a s re c e iv e d a t th e e n d o f e a c h y e a r.
ii)
T he e ffe c tiv e a fte r-ta x c o s t o f c a p ita l is 1 0 p e r c e n t p e r a n n u m .
iii) T he c o m p a n y in c o m e ta x ra te is 3 0 c e n ts in th e d o lla r.
M a n a g e m e n t is c o n s id e rin g th e fo llo w in g a lte rn a tiv e s :
a)
R e p la c e th e 2 -to n n e tru c k w ith th e 3 -to n n e tru c k n o w .
b)
R e p la c e th e 2 -to n n e tru c k w ith th e 3 -to n n e tru c k in 5 y e a r s ' tim e .
A ll o th e r a lte rn a tiv e s m a y b e ig n o r e d . A d v is e m a n a g e m e n t as to w h ic h a lte rn a tiv e it s h o u ld a d o p t, a n d ju s tify
y o u r a n a ly s is .
16
Replacement decision [LO 4]
A c o m p a n y is c o n s id e r in g th e in s ta lla tio n o f a n e w m a c h in e a t a c o s t o f $ 6 0 0 0 0 to re p la c e a m a c h in e
p u rc h a s e d 7 y e a rs a g o f o r $ 1 0 0 0 0 0 . T he d is p o s a l v a lu e o f th e o ld m a c h in e is $ 1 5 0 0 0 . B oth m a c h in e s w ill
h a v e s im ila r o u tp u ts a n d w ill p ro d u c e w o r k o f id e n tic a l q u a lity . T he e s tim a te d y e a r ly costs o f o p e r a tin g e a c h
m a c h in e a re as fo llo w s :
O ld m a c h in e ($ )
Wages
N e w m a c h in e ($ ) 1
15000
5 000
Supplies, repairs, pow er
5000
3 000
Insurance and m iscellaneous
2000
3000
22000
11000
T otal
Both m a c h in e s h a v e a n e s tim a te d re m a in in g life o f 3 y e a rs , a t w h ic h tim e b o th m a c h in e s w ill h a v e a n
e s tim a te d d is p o s a l v a lu e o f $ 5 0 0 0 . A s s u m e th a t:
a)
th e re q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m
b) th e o p e r a tin g costs o f th e o ld m a c h in e a n d th e n e w m a c h in e a r e in c u rre d a t th e e n d o f e a c h y e a r.
S h o u ld th e c o m p a n y p u rc h a s e th e n e w m a c h in e , o r c o n tin u e to o p e r a te th e o ld o n e ?
17
Replacement decision [LO 4]
T he m a n a g e m e n t o f N e w W o r ld A irlin e s is c o n s id e rin g th e re p la c e m e n t o f its p re s e n t fle e t o f 1 0 p is to n e n g in e
p la n e s w ith fiv e tu rb o p ro p s . A s u rv e y ha s re v e a le d th e f o llo w in g e s tim a te s o f costs, a n d so o n , p e r p la n e :
Piston e n g in e
R em aining life
Residual value:
E stim ates
5 years
T u rb o p ro p
E stim ate s
Life
5 years
Cost
$3430000
j
167
I P iston e n g in e
E stim ates
T u rb o p ro p
E stim ate s
A t p resent tim e
$10000
In 2 years’ tim e
$5 000
In 5 years’ tim e
$0
A fte r 2 years’ o p e ra tio n
30% o f purchase price
$100000
A fte r 5 years’ o p e ra tio n
5% o f purchase price
A n n u a l n e t cash flow s
a)
A n n u a l n e t cash flow s
$1000000
Residual value:
S h o u ld re p la c e m e n t b e u n d e rta k e n n o w o r in 5 y e a r s 7 tim e ?
Im m e d ia te ly a fte r th e d e c is io n ha s b e e n re a c h e d , m a n a g e m e n t is in fo rm e d o f a s u p e rje t th a t w ill b e c o m e
a v a ila b le in 2 y e a r s ' tim e . T he e stim a te s fo r th e n e w p la n e a re :
S u p e rje t
Estim ates
Cost
$4500000
A n n u a l n e t cash in flo w s
$1200000
Life
5 years
Residual value a fte r
3% o f purchase price
5 years’ o p e ra tio n
It is c o n s id e re d th a t fo u r o f th e n e w s u p e rje ts w ill b e a d e q u a te to c o v e r th e e s tim a te d p a s s e n g e r lo a d .
O th e r in fo r m a tio n is as fo llo w s :
•
M a n a g e m e n t c a n n o t fo re s e e a n y fu rth e r d e v e lo p m e n ts b e y o n d th e s u p e rje t.
•
A n n u a l n e t c a s h flo w s a r e a s s u m e d to b e re c e iv e d a t th e e n d o f e a c h y e a r.
•
T he r e q u ir e d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m ,
b)
S h o u ld m a n a g e m e n t:
i) re ta in th e p is to n e n g in e p la n e s fo r 5 y e a rs a n d re p la c e th e m w ith su p e rje ts
ii) re p la c e th e m im m e d ia te ly w ith tu rb o p ro p s , o p e ra te th e m fo r 5 y e a rs , a n d th e n re p la c e th e m w ith
s u p e rje ts
iii) re p la c e th e m n o w w ith tu rb o p ro p s , o p e ra te th e m fo r 2 y e a rs , a n d th e n re p la c e th e m w ith su p e rje ts
iv) re ta in th e p is to n e n g in e p la n e s fo r 2 y e a rs a n d th e n re p la c e th e m w ith s u p e rje ts?
O th e r re p la c e m e n t d a te s a re n o t to b e c o n s id e re d .
18
Replacement decision [LO 4]
A .B . Pty Ltd is c u rre n tly o p e r a tin g a s u b u rb a n ta x i-tru c k b u sin e ss. It is c o n s id e rin g th e re p la c e m e n t o f a
1 .5
to n n e v e h ic le w ith a 2 to n n e v e h ic le . D e ta ils o f th e re s p e c tiv e v e h ic le s a re a s fo llo w s :
I 1 .5 -to n n e v e h ic le
R em aining life
Estim ates
4 years
Residual value:
N ow
$4000
2 -to n n e v e h ic le
Estim ates
E stim ate d life
7 years
Cost
$15000
Residual value a fte r
$1000
7 years’ op e ra tio n
In fo u r years
A n n u a l n e t cash flo w
$0
$6000
N e t cash flo w
$10000
C hapter SIX T he APPLICATION 〇F PROJECT EVALUATION METHODS
•
N e t ca sh flo w s a r e to b e re g a r d e d as re c e iv e d a t th e e n d o f e a c h y e a r.
•
T he re q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m .
M a n a g e m e n t is c o n s id e rin g th e f o llo w in g a lte rn a tiv e s :
a)
re p la c e th e 1 .5 to n n e v e h ic le w ith th e 2 to n n e v e h ic le n o w
b)
re p la c e th e 1 .5 to n n e v e h ic le w ith th e 2 to n n e v e h ic le in 4 y e a r s 7 tim e .
A ll o th e r a lte rn a tiv e s m a y b e ig n o r e d .
A d v is e m a n a g e m e n t a s to w h ic h a lte r n a tiv e it s h o u ld a d o p t, a n d ju s tify y o u r a n a ly s is .
19
Retirement decision [LO 4 】
P ulp a n d P a p e r Ltd h a s ju st p la n te d p in e tre e s a t a c o s t o f $ 1 2 0 0 0 p e r h e c ta re o n 5 0 0 h e c ta re s o f la n d , w h ic h
it p u rc h a s e d fo r $ 4 0 0 0 0 0 . T he tre e s a r e e x p e c te d to g r o w r a p id ly a n d th e c o m p a n y 's e s tim a te s o f th e n e t
fu tu re v a lu e o f th e c u t tim b e r a re :
T im e o f h a rv e s t e n d
N e t fu tu re v a lu e ($ p e r
o f year
h e c ta re )
2
17320
3
20000
4
22360
5
24495
6
26450
C H A P T E R SIX R E V I E W
O th e r in fo rm a tio n is as fo llo w s :
T he re q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m a n d ta x e s c a n b e ig n o r e d .
a)
C a lc u la te th e o p tim u m tim e to h a rv e s t th e c r o p o f tre e s. A s s u m e th a t th e v a lu e o f th e c le a re d la n d in c re a s e s
a t a ra te o f 1 0 p e r c e n t p e r a n n u m .
b)
E stim a te th e n e t p re s e n t v a lu e o f th e p ro je c t, a s s u m in g s a le o f th e la n d a fte r th e tre e s a re h a rv e s te d . N o te
a n y a s s u m p tio n s y o u m a k e .
20
Replacement decision [LO 4]
A c o m p a n y is c o n s id e r in g th e re p la c e m e n t o f a n o ld m a c h in e w ith a n e w m a c h in e . T he o ld m a c h in e w a s
p u rc h a s e d a y e a r a g o f o r $ 1 2 5 0 0 . A d d it io n a l in fo r m a tio n re la tin g to th e se m a c h in e s (cash flo w s a re in
n o m in a l term s) is a s fo llo w s :
E stim ates
O ld m a c h in e ($)
Item
N e w m a c h in e ($)
M a rk e t value (now )
$7000
$5000
Service life (w hen
6 years
5 years
$0
$1000
purchased)
Residual value in 5 years’
tim e
Cash op e ra tin g receipts
-
$500 p.a. in excess o f o ld
m achine
T he re a l re q u ire d ra te o f re tu rn is 1 0 p e r c e n t p e r a n n u m , a n d th e a n tic ip a te d in fla tio n ra te is 1 0 p e r c e n t p e r
a n n u m . C a lc u la te th e n e t p re s e n t v a lu e o f r e p la c in g th e o ld m a c h in e w ith th e n e w m a c h in e .
169
21
Sensitivity analysis [LO 5]
M a n a g e m e n t o f R id e Ltd is c o n s id e rin g th e p o s s ib ility o f m a n u fa c tu rin g a n e w m o to ris e d g o lf b u g g y . The
in itia l o u tla y f o r th e n e w p la n t to m a n u fa c tu re th e v e h ic le is $1 m illio n . T h e s ta ff o f R id e Ltd h a v e p r o v id e d th e
f o llo w in g e s tim a te s fo r th e p ro je c t:
Estim ates
Item
P essim istic
Sales (u n its )
S elling price ($)
Fixed o p e ra tin g costs p e r a n n u m ($)
M o s t lik e ly
O p tim is tic
3000
3500
4000
750
800
850
100000
90000
80000
25
24
23
4
5
6
Variable o p e ra tin g costs pe r a n nu m
per u n it o f sales ($)
Life o f the p la n t (years)
A s s u m in g a re q u ire d ra te o f re tu rn o f 1 0 p e r c e n t, c o n d u c t a s e n s itiv ity a n a ly s is . W h a t a re th e m a jo r
u n c e rta in tie s if th e p r o je c t is u n d e rta k e n ?
22
Break-even analysis [LO 5]
T he m a n a g e r o f A ls p o rts Ltd is c o n s id e rin g a p la n to m a n u fa c tu re a lu m in iu m b a s e b a ll b a ts. E q u ip m e n t to
m a n u fa c tu re th e b a ts w ill c o s t $ 8 5 0 0 0 0 a n d is e x p e c te d to h a v e a use ful life o f 3 y e a rs . F ix e d costs a re
e s tim a te d to b e $ 8 0 0 0 0 p e r a n n u m a n d th e b a ts a r e e x p e c te d to sell fo r $ 4 0 e a c h , w h ile v a r ia b le costs w ill
b e $ 2 8 p e r b a t. A b o u t 5 0 0 0 0 0 b a s e b a ll b a ts a re s o ld e a c h y e a r a n d A ls p o rts h a s a re q u ire d ra te o f re tu rn o f
1 0 p e r c e n t. C a lc u la te th e b re a k -e v e n sales v o lu m e .
23
Decision-tree analysis [LO 6]
P asha B u lk e r Ltd is c o n s id e rin g p r o d u c in g a n e w p ro d u c t. It e x p e c ts th a t th e p r o d u c t w ill h a v e a life o f
1 0 y e a rs , b y w h ic h tim e th e m a rk e t f o r th e p r o d u c t w ill b e s a tu ra te d a n d fh e assets n e c e s s a ry to p ro d u c e it
w ill b e s o ld . T h e c o m p a n y is u n c e rta in a s to w h e th e r th e p r o d u c t s h o u ld b e m a n u fa c tu re d o n a la r g e s c a le
in a la r g e p la n t, o r o n a s m a ll s c a le in a s m a ll p la n t. If th e c o m p a n y c h o o s e s a s m a ll p la n t, it w o u ld c o n s id e r
e x p a n d in g th e p la n t a fte r 3 y e a rs .
T he c o m p a n y e s tim a te s th a t th e re is a 5 0 p e r c e n t p r o b a b ilit y th a t a h ig h le ve l o f d e m a n d w ill b e a tta in e d
o v e r th e 1 0 y e a rs d u r in g w h ic h th e p r o d u c t w ill b e m a rk e te d , a 2 5 p e r c e n t p r o b a b ilit y th a t d e m a n d w ill b e
h ig h d u rin g th e firs t 3 y e a rs a n d th e n d r o p to a lo w le ve l o v e r th e s u c c e e d in g 7 y e a rs , a n d a 2 5 p e r c e n t
p r o b a b ilit y th a t a lo w le ve l o f d e m a n d w ill p e rs is t o v e r th e e n tire 1 0 y e a rs .
T he f o llo w in g ta b le in d ic a te s th e e x p e c te d a n n u a l n e t c a s h flo w s a n d re s id u a l v a lu e s a s s o c ia te d w ith e a c h
s c a le o f p ro d u c tio n a n d le ve l o f d e m a n d :
I P o s s ib ilitie s
A n n u a l n e t c a sh f lo w ($ )
R e sid u a l v a lu e ($ ) 1
Large p la n t, h ig h dem and
500000
500000
Large p la n t, lo w dem and
150000
200000
Sm all p la n t, h ig h dem and
200000
200000
Sm all p la n t, lo w dem and
150000
100000
Expanded p la n t, h ig h dem and
300000
400000
Expanded p la n t, lo w dem and
100000
150000
T he in itia l c o s t a s s o c ia te d w ith th e c o n s tru c tio n o f a la r g e p la n t is $ 2 m illio n , a n d th a t a s s o c ia te d w ith a
sm a ll p la n t is $1 m illio n . T he e x p e c te d c o s t o f e x p a n d in g fro m a s m a ll p la n t to a la r g e p la n t a fte r 3 y e a rs is
$1 m illio n . T h e c o m p a n y 's re q u ire d ra te o f re tu rn o f 1 2 p e r c e n t p e r a n n u m is re le v a n t fo r a ll a lte rn a tiv e s .
a)
W h ic h p o lic y s h o u ld th e c o m p a n y p u rsu e ?
b)
Is it lik e ly th a t th e s a m e d is c o u n t ra te w ill b e a p p r o p r ia te fo r a ll a lte rn a tiv e s ? G iv e re a so n s.
C hapter six T he
application of project evaluation methods
Brown, C. & Davis, K., 'O ptions in mutually exclusive
projects of unequal lives', Quarterly Review of Economics
and Finance, Special Issue 1998, pp. 5 6 9 -7 7 .
Levin, R.I., Kirkpatrick, C.A. & Rubin, D.S., Quantitative
Approaches to Management, 8th edn, M cG raw-Hill, N ew
York, 1992, pp. 2 3 1 -7 .
Faff, R. & Brailsford, T., 'The constant chain of replacement
model and inflation', Pacific Accounting Review, December
1992, pp. 4 5 -5 8 .
Pike, R.J., The capital budgeting behaviour and corporate
characteristics of capital-constrained firms', Journal of
Business Finance and Accounting, W inter 1983, pp. 6 6 3 -7 .
C H A P T E R SIX R E V I E W
REFERENCES
171
CHAPTER CONTENTS
m
R e tu rn a n d ris k
EB
T h e in v e s to r 's u t ilit y fu n c tio n
m
T h e ris k o f a s s e ts
3
7
I n t r o d u c t io n
6
7
9
7
m
g g
3
7
ED
EB
P o r t f o lio t h e o r y a n d d iv e r s if ic a t io n
179
T h e p r ic in g o f r is k y a s s e ts
190
A d d it io n a l f a c t o r s t h a t e x p la in re tu rn s
19 7
P o r t f o lio p e r f o r m a n c e a p p r a is a l
19 8
LEARNING OBJECTIVES
A f t e r s tu d y in g th is c h a p t e r y o u s h o u ld b e a b le to :
1
u n d e r s ta n d h o w r e tu r n a n d r is k a r e d e f in e d a n d m e a s u r e d
2
u n d e r s ta n d th e c o n c e p t o f r is k a v e r s io n b y in v e s to rs
3
e x p la in h o w d iv e r s if ic a t io n r e d u c e s ris k
4
e x p la in th e c o n c e p t o f e f f ic ie n t p o r t f o lio s
5
u n d e r s ta n d th e im p o r t a n c e o f c o v a r ia n c e b e t w e e n re tu rn s o n r is k y a s s e ts in d e t e r m in in g th e r is k o f a
p o r t f o lio
6
e x p la in th e d is tin c t io n b e t w e e n s y s te m a tic a n d u n s y s te m a tic r is k
7
e x p la in w h y s y s te m a tic ris k is im p o r t a n t to in v e s to rs
8
e x p la in th e r e la t io n s h ip b e t w e e n re tu rn s a n d ris k p r o p o s e d b y th e c a p it a l a s s e t p r ic in g m o d e l
9
u n d e r s ta n d th e r e la t io n s h ip b e t w e e n th e c a p it a l a s s e t p r ic in g m o d e l a n d m o d e ls t h a t in c lu d e a d d i t i o n a l
fa c to r s
1 0 e x p la in th e d e v e lo p m e n t o f m o d e ls t h a t in c lu d e a d d i t i o n a l f a c to r s
11
d is tin g u is h b e t w e e n a lt e r n a t iv e m e th o d s o f a p p r a is in g th e p e r f o r m a n c e o f a n in v e s tm e n t p o r t f o lio .
C hapter seven Risk
a n d return
Introduction
A fin a n c ia l d e c is io n ty p ic a lly in v o lv e s r isk . F o r e x a m p le , a c o m p a n y t h a t b o r r o w s m o n e y f a c e s th e r is k
th a t in t e r e s t r a t e s m a y c h a n g e , a n d a c o m p a n y t h a t b u ild s a n e w f a c t o r y f a c e s th e r i s k t h a t p r o d u c t s a l e s
m a y b e lo w e r th a n e x p e c te d . T h e se a n d m a n y o t h e r d e c is io n s in v o lv e fu t u r e c a s h flo w s t h a t a r e risk y .
In v e s t o r s g e n e r a lly d is lik e r i s k , b u t th e y a re a ls o u n a b le to a v o id it. Th e v a lu a t io n f o r m u la e fo r s h a r e s a n d
d e b t s e c u r itie s o u tlin e d in C h a p t e r 4 sh o w e d t h a t th e p ric e o f a r is k y a s s e t d e p e n d s o n i t s e x p e c t e d fu tu r e
c a s h flo w s, th e tim e v a lu e o f m o n e y , a n d r isk . H o w ev e r, little a t t e n t i o n w a s p a id to th e c a u s e s o f r i s k o r to
h o w r is k s h o u ld b e d e fin e d a n d m e a s u r e d .
T o m a k e e ffe c tiv e fin a n c ia l d e c is io n s , m a n a g e r s n e e d to u n d e r s t a n d w h a t c a u s e s r is k , h o w i t s h o u ld
b e m e a s u r e d a n d th e e ffe c t o f r is k o n th e r a te o f r e t u r n r e q u ir e d b y in v e s t o r s . T h e se i s s u e s a r e d is c u s s e d
in t h is c h a p te r u s in g th e fr a m e w o r k o f p o r t f o lio th e o r y , w h ic h s h o w s h o w in v e s t o r s c a n m a x im is e th e
e x p e c te d r e tu r n o n a p o r t f o lio o f r is k y a s s e t s fo r a g iv e n le v e l o f r isk . Th e r e la t io n s h ip b e t w e e n r is k a n d
e x p e c te d r e tu r n is fir s t d e s c r ib e d b y th e c a p it a l a s s e t p r ic in g m o d e l (C A P M ), w h ic h lin k s e x p e c t e d r e t u r n
to a sin g le so u r c e o f r is k , a n d s e c o n d , b y m o d e ls t h a t in c lu d e a d d it io n a l f a c t o r s to e x p la in r e t u r n s .
To u n d e r s ta n d th e m a t e r ia l in t h is c h a p t e r i t i s n e c e s s a r y to u n d e r s t a n d w h a t is m e a n t b y re tu rn a n d
risk. T h e re fo re , w e b e g in b y d i s c u s s i n g t h e s e c o n c e p ts .
7.2
Return and risk
The re tu r n o n a n in v e s t m e n t a n d th e r i s k o f a n i n v e s t m e n t a r e b a s ic c o n c e p t s in fin a n c e . R e tu r n o n a n
in v e s t m e n t is th e fin a n c ia l o u t c o m e f o r th e in v e sto r . F o r e x a m p le , i f s o m e o n e i n v e s t s $ 1 0 0 in a n a s s e t
a n d s u b s e q u e n t ly s e lls t h a t a s s e t f o r $ 1 1 1 , th e d o lla r retu rn is $ 1 1 . U su a lly a n i n v e s t m e n t s d o lla r r e t u r n is
L E A R N IN G
O B JEC TIVE 1
U nde rstand h o w return
c o n v e r te d to a ra te o f retu rn b y c a lc u la tin g th e p r o p o r t io n o r p e r c e n ta g e r e p r e s e n t e d b y th e d o lla r r e tu r n .
a n d risk are defined
F o r e x a m p le , a d o lla r r e t u r n o f $ 1 1 o n a n in v e s t m e n t o f $ 1 0 0 is a r a t e o f r e t u r n o f $ 1 1 / $ 1 0 0 , w h ic h is
a n d m easured
0 .1 1 , o r 1 1 p e r c e n t. In th e r e m a in d e r o f t h is c h a p t e r th e w o rd re tu rn is u s e d to m e a n ra te o f re tu rn .
R isk is p r e s e n t w h e n e v e r i n v e s t o r s a r e n o t c e r ta in a b o u t th e o u t c o m e s a n in v e s t m e n t w ill p r o d u c e .
S u p p o s e , h o w e v e r, t h a t in v e s t o r s c a n a t ta c h a p r o b a b ility t o e a c h p o s s ib le d o lla r r e t u r n t h a t m a y o ccu r.
In v e sto r s c a n t h e n d r a w u p a p r o b a b ility d is tr ib u t io n f o r th e d o lla r r e t u r n s fr o m th e in v e s t m e n t .
A p ro b ab ility d istrib u tio n is a l is t o f th e p o s s ib le d o lla r r e t u r n s f r o m th e in v e s t m e n t t o g e t h e r w ith th e
p r o b a b ility o f e a c h r e tu r n . F o r e x a m p le , a s s u m e t h a t th e p r o b a b ilit y d is t r ib u t io n in T a b le 7 .1 i s a n
i n v e s t o r s a s s e s s m e n t o f th e d o lla r r e t u r n s
t h a t m a y b e re c e iv e d f r o m h o ld in g a s h a r e in a c o m p a n y fo r
1 year.
TABLE 7.1
D o lla r re tu rn , Rt ($ )
P ro b a b ility , P,
9
0.1
10
0 .2
11
0 .4
12
0 .2
13
0 .1
S u p p o s e th e in v e s t o r w is h e s to s u m m a r is e t h is d is t r ib u t io n b y c a lc u la tin g tw o m e a s u r e s , o n e to
r e p r e s e n t th e s iz e o f th e d o lla r r e t u r n s a n d th e o t h e r to r e p r e s e n t th e r i s k in v o lv e d . Th e s iz e o f th e d o lla r
r e t u r n s m a y b e m e a s u r e d b y th e e x p e c t e d v a lu e o f th e d is t r ib u t io n . Th e e x p e c t e d v a lu e E (R ) o f th e d o lla r
r e t u r n s is g iv e n b y th e w e ig h te d a v e r a g e o f all th e p o s s ib le d o lla r r e t u r n s , u s i n g th e p r o b a b ilit ie s a s
w e ig h t s — t h a t is:
E (R ) = ($ 9 ) (0 .1 ) + ( $ 1 0 ) ( 0 .2 ) + ($ 1 1 ) (0 .4 ) + ($ 1 2 ) (0 .2 ) + ( $ 1 3 ) (0 .1 )
=
$11
In general, the expected return on an investment can be calculated as:
w h ic h c a n b e w r it t e n a s fo llo w s:
n
E{R) = Y ^ R iP i
i= l
The c h o ic e o f a m e a s u r e f o r r is k is l e s s o b v io u s . In t h is e x a m p le , r i s k is p r e s e n t b e c a u s e a n y o n e o f
fiv e o u t c o m e s ($ 9 , $ 1 0 , $ 1 1 , $ 1 2 o r $ 1 3 ) m ig h t r e s u lt fr o m th e i n v e s t m e n t . I f th e i n v e s t o r h a d p e r fe c t
fo r e s ig h t , th e n o n ly o n e p o s s ib l e o u tc o m e w o u ld b e in v o lv e d , a n d th e r e w o u ld n o t b e a p r o b a b ility
d i s t r ib u t io n t o b e c o n s id e r e d . T h is s u g g e s t s t h a t r i s k is r e la t e d to th e d is p e r s io n o f th e d is tr ib u t io n . The
VARIANCE
m easure of variability;
the m ean of the
squared deviations
from the m ean or
expected value
m o r e d i s p e r s e d o r w id e s p r e a d th e d is tr ib u t io n , th e g r e a t e r th e r is k in v o lv e d . S t a t i s t i c i a n s h a v e d e v e lo p e d
a n u m b e r o f m e a s u r e s to r e p r e s e n t d is p e r s io n . T h e se m e a s u r e s in c lu d e th e r a n g e , th e m e a n a b s o lu t e
d e v ia tio n a n d th e v a r ia n c e . H o w e v e r, it is g e n e r a lly a c c e p te d t h a t in m o s t in s t a n c e s t h e
i t s s q u a r e r o o t, th e
stan d ard deviation,
a) is
variance
(o r
th e m o s t u s e f u l m e a s u r e . A c c o rd in g ly , t h is m e a s u r e o f
d i s p e r s io n is th e o n e w e w ill u s e to r e p r e s e n t th e r is k o f a s in g le in v e s t m e n t . T h e v a r ia n c e o f a d is tr ib u t io n
STANDARD DEVIATION
o f d o lla r r e t u r n s is th e w e ig h te d a v e r a g e o f th e s q u a r e o f e a c h d o lla r r e t u r n s d e v ia tio n f r o m th e e x p e c te d
square root of the
d o lla r r e t u r n , a g a in u s i n g th e p r o b a b ilit ie s a s th e w e ig h ts . F o r th e s h a r e c o n s id e r e d in T a b le 7 .1 , th e
varian ce
v a r ia n c e is:
cr2 = (9-11)2(0.1) + (10-11)2(0.2) + (11-11)2(0.4) + (12-11)2(0.2) + (13 - 11)2(0.1)
= 1.2
In g e n e r a l th e v a r ia n c e c a n b e c a lc u la te d a s:
〇2 -
[/?, -£(/?)]2p, + [R2 - E ( R ) Y P 2 + ... + [/?„-£(/?)]2p„
w h ic h c a n b e w r it t e n a s fo llo w s:
n
o2 = J 2 ^ R' ~ E(R^ 2pi
i= l
In t h is c a s e th e v a r ia n c e is 1 .2 s o th e s t a n d a r d d e v ia tio n is:
a = \/L 2
= $ 1 .0 9 5
In t h e s e c a lc u la tio n s w e h a v e u s e d d o lla r r e t u r n s r a t h e r t h a n r e t u r n s m e a s u r e d in th e fo r m o f a ra te .
T h is is b e c a u s e i t is g e n e r a lly e a s ie r to v is u a lis e d o lla r s t h a n r a t e s , a n d b e c a u s e i t a v o id s c a lc u la tio n s w ith
a la r g e n u m b e r o f z e r o s fo llo w in g th e d e c im a l p o in t . H o w e v e r, th e r e is n o d iffe r e n c e in s u b s t a n c e , a s m a y
b e s e e n f r o m r e w o r k in g th e e x a m p le u s i n g r e t u r n s in r a te fo r m . I f th e s u m in v e s t e d is $ 1 0 0 , th e n a d o lla r
r e tu r n o f $ 9 , f o r e x a m p le , is a r e t u r n o f 0 .0 9 w h e n e x p r e s s e d a s a ra te . T a b le 7 .2 sh o w s r a t e s o f r e t u r n t h a t
c o r r e s p o n d to th e d o lla r r e t u r n s in T a b le 7 .1 .
TABLE 7.2
R etu rn,
P ro b a b ility , P,
0 .0 9
0 .1
0 .1 0
0 .2
0 .1 1
0 .4
0 .1 2
0 .2
0 .1 3
0 .1
U s i n g r a t e s , th e e x p e c t e d r e t u r n E (R ) is:
E (R ) = (0 .0 9 ) (0 .1 ) + (0 .1 0 ) (0 .2 ) + ( 0 .1 1 ) ( 0 .4 ) + (0 .1 2 ) (0 .2 ) + (0 .1 3 ) (0 .1 )
=
0.11
= 11%
C hapter seven Risk
The v a r ia n c e o f r e t u r n s is:
a 2 = (0.09-0 .1 1 )2(0.1) + (0 .1 0 -0 .1 1 )2(0.2) + (0.11-0 .1 1 )2(0.4) + (0 .1 2 -0 .1 1 )2(0.2)
+ ( 0 . 1 3 - 0 . 1 1 ) 2( 0 . 1 )
= 0 .0 0 0 12
The s t a n d a r d d e v ia tio n o f r e t u r n s is t h e r e fo r e :
ct=
v/0.00012
= 0 .0 1 0 9 5
= 1 .0 9 5 %
It is o ft e n a s s u m e d t h a t a n i n v e s t m e n t s d is t r ib u t io n o f r e t u r n s fo llo w s a n o r m a l d is tr ib u t io n . T h is
is a c o n v e n ie n t a s s u m p t i o n b e c a u s e a n o r m a l d is t r ib u t io n c a n b e fu lly d e s c r ib e d b y i t s e x p e c t e d v a lu e
a n d s t a n d a r d d e v ia tio n . T h e r e fo re , a n i n v e s t m e n t s d is t r ib u t io n o f r e t u r n s c a n b e fu lly d e s c r ib e d b y i t s
e x p e c te d r e t u r n a n d r is k . A s s u m i n g t h a t r e t u r n s fo llo w a n o r m a l p r o b a b ility d is tr ib u t io n , th e t a b le o f
a r e a s u n d e r th e s t a n d a r d n o r m a l c u rv e (s e e T a b le 5 o f A p p e n d ix A ) c a n b e u s e d t o c a lc u la te th e p r o b a b ility
th a t th e in v e s t m e n t w ill g e n e r a t e a r e tu r n g r e a t e r t h a n o r l e s s t h a n a n y s p e c ifie d r e tu r n . F o r e x a m p le ,
s u p p o s e t h a t th e r e t u r n s o n a n in v e s t m e n t in C o m p a n y A a r e n o r m a lly d is tr ib u t e d , w ith a n e x p e c t e d
r e tu r n o f 1 3 p e r c e n t p e r a n n u m a n d a s t a n d a r d d e v ia tio n o f 1 0 p e r c e n t p e r a n n u m . S u p p o s e a n in v e s t o r
in th e c o m p a n y w ish e s to c a lc u la te th e p r o b a b ilit y o f a l o s s — t h a t is , th e in v e s t o r w is h e s to c a lc u la te th e
p r o b a b ility o f a r e tu r n o f l e s s th a n z e r o p e r c e n t. A r e t u r n o f z e r o p e r c e n t is 1 .3 s t a n d a r d d e v ia t io n s b e lo w
th e e x p e c te d r e t u r n (b e c a u s e 0 .1 3 / 0 .1 0 = 1 .3 ). F ig u r e 7 .1 illu s t r a t e s t h is c a s e . Th e s h a d e d a r e a r e p r e s e n t s
th e p r o b a b ility o f a lo s s . Th e ta b le o f a r e a s u n d e r th e s t a n d a r d n o r m a l c u r v e (T a b le 5, A p p e n d ix A o r th e
N O R M S D IS T f u n c tio n in M ic r o s o ft E x c e l*) in d ic a t e s t h a t th e p r o b a b ility o f a l o s s o c c u r r in g is 0 .0 9 6 8 o r
a lm o s t 9 .7 p e r c e n t.
T o h ig h lig h t th e i m p o r t a n c e o f th e s t a n d a r d d e v ia tio n o f th e r e t u r n d is tr ib u t io n , a s s u m e t h a t th e
s a m e in v e s t o r a ls o h a s th e o p p o r t u n it y o f in v e s t in g in C o m p a n y B w ith a n e x p e c t e d r e t u r n o f 1 3 p e r c e n t
a n d a s t a n d a r d d e v ia tio n o f 6 .9 1 p e r c e n t. Th e p r o b a b ility d i s t r ib u t io n s o f th e r e t u r n s o n in v e s t m e n t s in
c o m p a n ie s A a n d B a re s h o w n in F ig u r e 7 .2 .
B o th in v e s t m e n t s h a v e t h e s a m e e x p e c t e d r e tu r n b u t, o n th e b a s i s o f th e d is p e r s io n o f th e r e t u r n s ,
a n in v e s t m e n t in C o m p a n y A (w ith a s t a n d a r d d e v ia tio n o f 1 0 p e r c e n t) is r is k ie r t h a n a n in v e s t m e n t in
C o m p a n y B (w ith a s t a n d a r d d e v ia tio n o f 6 .9 1 p e r c e n t).
S u p p o s e t h a t th e in v e s t o r d e c id e s t h a t a r e t u r n o f z e r o p e r c e n t o r l e s s i s u n s a t is f a c t o r y . A r e tu r n
o f z e r o p e r c e n t o n a n in v e s t m e n t in C o m p a n y B is 1 .8 8 s t a n d a r d d e v ia tio n s b e lo w th e e x p e c t e d r e tu r n
(b e c a u se 0 . 1 3 / 0 .0 6 9 1 = 1 .8 8 ). Th e p r o b a b ilit y o f t h is o c c u r r in g is 0 .0 3 . T h e r e fo re , th e p r o b a b ilit y t h a t
a n in v e s t m e n t in o n e o f t h e s e c o m p a n ie s w ill g e n e r a t e a n e g a tiv e r e t u r n is 3 p e r c e n t fo r C o m p a n y B
c o m p a r e d w ith 9 .7 p e r c e n t f o r C o m p a n y A . H o w e v e r, w h e n th e i n v e s t o r c o n s id e r s r e t u r n s a t th e u p p e r
e n d o f th e d i s t r ib u t io n s i t i s fo u n d t h a t a n i n v e s t m e n t in C o m p a n y A o f f e r s a 9 .7 p e r c e n t c h a n c e o f a
a n d return
B usiness finance
Figure 7.2
RISK-AVERSE INVESTOR
an investor who
dislikes risk and who
will only choose a
risky investment if the
expected return is high
enough to compensate
for bearing the risk
retu rn in excess o f 26 per cent, compared w ith only a 3 per cent chance fo r an investm ent in Company
B. In summ ary the p robability o f both very low returns and very high returns is much greater in the
case o f Company A. The fact th a t the investor is more uncertain about the retu rn from an investm ent in
Company A does n o t mean th a t the investor w ill necessarily prefer to invest in Company B. The choice
depends on the investors a ttitude to risk.
A lternative attitudes to risk and the effects o f risk are considered in the next section, which can safely
be o m itte d by readers who are prepared to accept th a t investors are generally risk averse. Risk aversion
does not mean th a t an investor w ill refuse to bear any risk at all. Rather i t means th a t an investor regards
risk as something undesirable, b ut which may be w o rth tolerating i f the expected retu rn is sufficient to
compensate fo r the risk. Therefore, a ris k -a v e rs e in v e s to r would prefer to invest in Company B because
A and B offer the same expected return, b u t B is less risky.
7.3
LEARNING
OBJECTIVE 2
Understand the
concept of risk
aversion by investors
RISK-NEUTRAL
INVESTOR
an investor who
neither likes nor
dislikes risk
RISK-SEEKING
INVESTOR
an investor who
likes risk and who
will choose a risky
investment even if the
expected return is less
than the expected
return on a less risky
investment
The investor’s utility function
Consider the decision to invest in either Company A or Company B. As discussed in Section 7.2, both
companies offer the same expected return, b ut differ in risk. A preference fo r investing in either Company
A or Company B w ill depend on the investors a ttitude to risk. An investor may be risk averse, risk
neutral o r risk seeking. A risk-averse investor attaches decreasing u tility to each increm ent in wealth; a
risk -n eu tral in vestor attaches equal u tility to each increm ent in wealth; while a risk -seek in g investor
attaches increasing u tility to each increm ent in wealth. Typical u tility -to -w e a lth functions fo r each type
o f investor are illustrated in Figure 7.3.
The characteristics o f a risk-averse investor w arrant closer examination, as risk aversion is the
standard assumption in finance theory. Assume th a t a risk-averse investor has wealth o f $ W* and has the
o p p o rtu n ity o f p articipating in the follow ing game: a fa ir coin is tossed and i f it falls tails (probability 0.5),
then $1000 is won; i f i t falls heads (probability 0.5), then $1000 is lost. The expected value o f the game is
$0 and it is, therefore, described as a *fair game*. Would a risk-averse investor participate in such a game?
I f he or she participates and wins, wealth w ill increase to $(PV* + 1000), b ut i f he or she loses, wealth w ill
fall to $(PV* - 1000). The results o f this game are shown in Figure 7.4.
The investors current level o f u tility is U2. The investors u tility w ill increase to U3 i f he or she wins
the game and w ill decrease to [7Xin the event o f a loss. W hat is the expected u tility i f the investor decides
to participate in the game? There is a 50 per cent chance th a t his or her u tility w ill increase to U3, and a
50 per cent chance th a t i t w ill decrease to Uv Therefore, the expected u tility is 0 . 5 ^ + 0.5U3. As shown
in Figure 7.4, the investors expected u tility w ith the gamble (0.5U1 + 0.5U3) is lower than the u tility
obtained w ith o u t the gamble (U2). As it is assumed th a t investors maximise th e ir expected u tility , a riskaverse investor would refuse to participate in this game. In fact, a risk-averse investor may be defined as
C hapter seven Risk
a n d return
ure 7.3 Utility-to-wealth functions for different types of investors
Risk seeking
Risk neutral
IM
ln
ir
un
Wealth (W )
1
someone who would n ot participate in a fa ir game. Similarly, it can be shown th a t a risk-neutral investor
would be indifferent to participation, and a risk-seeking investor would be prepared to pay fo r the rig h t
to participate in a fa ir game.
Now consider the preferences o f a risk-averse investor w ith respect to an investm ent in either
Company A or Company B. As we have seen, the expected retu rn from each investm ent is the same but
the investment in A is riskier. An investm ent in A offers the possibility o f making either higher returns
or lower returns, compared w ith an investm ent in B. However, from Figure 7.2, the increased spread o f
returns above the expected retu rn tends to increase expected u tility . But this increase w ill be outweighed
by the decrease in expected u tility resulting from the greater spread o f returns below the expected return.
Therefore, the risk-averse investors expected u tility would be greater i f he or she invests in B.
As both investments offer the same expected return, the risk-averse investors choice implies th a t the
increased dispersion o f returns makes an investm ent riskier. This suggests th a t the standard deviation
o f the return distribu tio n may be a useful measure o f risk fo r a risk-averse investor. Similarly, it can be
argued th a t the risk-neutral investor would be ind iffe re nt between these tw o investments. For any given
amount to be invested, such an investor w ill always choose the investm ent th a t offers the higher return,
命
B usiness finance
irrespective o f the relative risk o f other investm ents— th a t is, the standard deviation is ignored. The risk­
seeking investor would choose to invest in A. I f a given am ount is to be invested, and the investor has
the choice o f two investments th a t offer the same expected return, the risk-seeking investor w ill always
choose the investm ent w ith the higher risk.
An investors preferences regarding expected retu rn and risk can be illustrated using indifference
curves. For a given am ount invested, an indifference curve traces out all those combinations o f expected
return and risk th a t provide a particular investor w ith the same level o f u tility . Because the level o f
u tility is the same, the investor is indifferent between all points on the curve. A risk-averse investor has
a positive attitude towards expected retu rn and a negative a ttitude towards risk. By this, we mean th a t a
risk-averse investor w ill prefer an investm ent to have a higher expected retu rn (for a given risk level) and
lower risk (for a given expected return).
Risk aversion does not mean th a t an investor w ill refuse to bear any risk at all. Rather it means th a t an
investor regards risk as something undesirable, b u t which may be w o rth tolerating i f the expected return
is sufficient to compensate fo r the risk. In graphical terms, indifference curves fo r a risk-averse investor
m ust be upward sloping as shown in Figure 7.5.
The risk-re tu rn coordinates fo r a risk-averse investor are shown in Figure 7.5 fo r three investments— A,
B and C. I t is apparent that this investor would prefer Investment B to Investment A, and would also prefer
Investment B to Investment C. This investor prefers a higher expected return at any given level o f risk (compare
investments B and A) and a lower level o f risk at any given expected return (compare investments B and C).
However, this investor would be indifferent between investments A and C. The higher expected return on
investm ent C compensates this investor exactly fo r the higher risk. In addition, fo r a given expected return
the expected u tility o f a risk-averse investor falls at an increasing rate as the dispersion o f the distribution
o f returns increases. As a result, the rate o f increase in expected return required to compensate for every
increment in the standard deviation increases faster as the risk becomes larger. Note that indifference curves
for a risk-averse investor are n ot only upward sloping, but also convex, as shown in Figure 7.5.
So far we have concentrated on the characteristics and behaviour o f a risk-averse investor. However,
there are instances where individuals behave in a way contrary to risk aversion. For example, a risk-averse
person w ill never purchase a lo tte ry ticket, as the expected value o f the gamble is less than the price o f
the ticket. However, many individuals whose current level o f wealth is quite low relative to the lo tte ry
prize are prepared to purchase lo tte ry tickets because, w hile only a small outlay is required, there is the
small chance o f achieving a relatively large increase in wealth. In decisions th a t involve larger outlays,
risk aversion is much more likely. As the financial decisions considered in this book generally involve
Figure 7.5
Increasing utility
|
0)
EIRB) = EIRC)
J
I
肌
)
°C
aA = aB
Risk (o)
C hapter seven Risk
a n d return
large investments and small rates o f retu rn (at least relative to w inning a lo tte ry prize), i t is assumed
throughout that investors behave as i f they are risk averse.
7.4
The risk of assets
I f investors, expectations o f the returns from an investm ent can be represented by a norm al probability
distribution, then the standard deviation is a relevant measure o f risk fo r a risk-averse investor. I f two
investments offer the same expected return, b ut differ in risk, then a risk-averse investor w ill prefer
the less risky investm ent. Further, it has been shown th a t a risk-averse investor is prepared to accept
higher risk fo r higher expected return, w ith the result th a t the required retu rn on a particular investm ent
increases w ith the investors perception o f its risk.
The standard deviation o f the retu rn from a single investm ent is a relevant measure o f its riskiness
in cases where an individual is considering the investm ent o f all available funds in one asset. However,
it is exceptional to lim it investm ents in this way. M ost people invest in a num ber o f assets; they may
invest in a house, a car, th e ir human capital and numerous other assets. In addition, where they invest
in shares, i t is likely th a t they w ill hold shares in a num ber o f companies. In other words, people typically
invest th e ir wealth in a p o rtfolio o f assets and w ill be concerned about the risk o f th e ir overall p ortfo lio .
This risk can be measured by the standard deviation o f the returns on the p o rtfo lio . Therefore, when an
individual asset is considered, an investor w ill be concerned about the risk o f th a t asset as a component o f
a p o rtfo lio o f assets. W hat we need to know is how individual p o rtfo lio components (assets) contribute
to the risk o f the p o rtfo lio as a whole. An apparently plausible guess would be th a t the co ntribu tion
o f each asset is p ro p o rtio n a l to the assets standard deviation. However, p o rtfo lio theory, w hich is
discussed in the next section, shows th a t this guess turns o ut to be alm ost always incorrect.
7.5
PORTFOLIO
combined holding of
more than one asset
Portfolio theory and diversification
m
Portfolio theory was in itia lly developed by M arkow itz (1952) as a norm ative approach to investm ent
choice under uncertainty.1 Two im p o rta n t assumptions o f p o rtfo lio theory have already been discussed.
These are:
a
The returns from investments are norm ally distributed. Therefore, two parameters, the expected
return and the standard deviation, are sufficient to describe the d istrib u tio n o f returns.2
b Investors are risk averse. Therefore, investors prefer the highest expected retu rn fo r a given standard
deviation and the lowest standard deviation fo r a given expected return.
Given these assumptions, it can be shown th a t i t is rational fo r a utility-m axim isin g investor to hold
a well-diversified p o rtfo lio o f investments. Suppose th a t an investor holds a p o rtfo lio o f securities. This
investor w ill be concerned about the expected retu rn and risk o f the p ortfolio. The expected retu rn on a
portfolio is a weighted average o f the expected returns on the securities in the p ortfolio. Let E(Rt) be the
expected return on the zth security and E(Rp) the expected retu rn on a p o rtfo lio o f securities. Then, using
the n otation introduced earlier:
n
E(R„) = ^ 2 w iE(Ri)
i= \
where
= the proportion o f the to ta l current m arket value o f the p o rtfo lio constituted by the current
m arket value o f the zth security— th a t is, it is the ‘w eight’ attached to the security
n = the number o f securities in the p ortfo lio
Calculation o f the expected return on a p o rtfo lio is illustrated in Example 7.1.
1
2
For a more extensive treatment, see Markowitz (1959).
Other parameters may exist if the distribution is non-normal. In this case it is assumed that investors base decisions on
expected return and standard deviation and ignore other features such as skewness.
LEARNING
OBJECTIVE 3
Explain how
diversification reduces
risk
Example 7.1
A s s u m e th a t th e re a r e o n ly t w o s e c u ritie s (1 a n d 2 ) in a p o r tf o lio a n d E(R}) = 0 . 0 8 a n d E(/?2) =
〇• 1 2 .
A ls o a s s u m e th a t th e c u r r e n t m a rk e t v a lu e o f S e c u rity 1 is 6 0 p e r c e n t o f th e to ta l c u rre n t m a rk e t v a lu e
o f th e p o r tf o lio (th a t is, w 1 = 0 . 6 a n d w 2 = 0 . 4 ) . T h e n :
E(/?p) = ( 0 . 6 ) ( 0 .0 8 ) + ( 0 . 4 ) ( 0 .1 2 )
= 0 . 0 9 6 o r 9 .6 %
Example 7.1 illustrates the fact th a t the expected retu rn on a p o rtfo lio is sim ply the weighted average
o f the expected returns on the securities in the p ortfo lio . However, the standard deviation o f the return
on the p o rtfo lio (c p) is not sim ply a weighted average o f the standard deviations o f the securities in the
p ortfo lio . This is because the riskiness o f a p o rtfo lio depends n ot only on the riskiness o f the individual
securities b ut also on the relationship between the returns on those securities. The variance o f the return
on a p o rtfo lio o f two securities is given by:
#
=
4 cr| + 2
Cov(/?卜 i?2)
where Cov(Rv R2) = the covariance between the returns on securities 1 and 2
The covariance between the returns on any pair o f securities is a measure o f the extent to which the
returns on those securities tend to move together or covary*. This tendency is more commonly measured
using the correlation coefficient p, which is found by dividing the covariance between the returns on
the tw o securities by the standard deviations o f th e ir returns. Therefore, the correlation coefficient for
securities 1 and 2 is:
Pi,2 =
Cov(/?i,/?2)
7.3
The correlation coefficient is essentially a scaled measure o f covariance and it is a very convenient
measure because it can only have values between +1 and -1 . I f the correlation coefficient between the
returns on two securities is +1, the returns are said to be perfectly positively correlated. This means th a t
i f the retu rn on security z is ^ ig h 1(compared w ith its expected level), then the retu rn on se curity; w ill,
unfailingly, also be ‘high’ （
compared w ith fts expected level) to precisely the same degree. I f the correlation
coefficient is -1 , the returns are perfectly negatively correlated; high (low) returns on security i w ill always
be paired w ith low (high) returns on security A correlation coefficient o f zero indicates the absence of
a systematic relationship between the returns on the tw o securities. Using Equation 7.3 to substitute for
the covariance, Equation 7.2 can be expressed as:
=
w \ 〇\ -f- W2 O 2 + 2 W \W 2 P \ 2 (J \ (T2
7.4
As may be seen from Equation 7.4, the variance o f a p o rtfo lio depends on:
a
b
c
the com position o f the p o rtfo lio — th a t is, the p roportion o f the current m arket value o f the
p o rtfo lio constituted by each security
the standard deviation o f the returns fo r each security
the correlation between the returns on the securities held in the p ortfo lio .
The effect o f changing the composition o f a p o rtfo lio o f tw o securities is illustrated in Example 7.2.
7.5.1 I Gains from diversification
Example 7.2 shows th a t some portfolios enable an investor to achieve simultaneously higher expected
retu rn and lower risk; fo r example, compare portfolios (d) and (f) in Figure 7.6. It should be noted th a t
Portfolio (d) consists o f both securities, whereas Portfolio (f) consists o f only Security 1— th a t is, Portfolio
(d) is diversified, whereas Portfolio (f) is not. This illustrates the general principle th a t investors can gain
from diversification.
C hapter seven Risk
a n d return
E xample 7.2
A n in v e s to r w is h e s to c o n s tru c t a p o r tf o lio c o n s is tin g o f S e c u rity 1 a n d S e c u rity 2 . T h e e x p e c te d re tu rn s
o n th e tw o s e c u ritie s a r e E(R}) = 8 % p .a . a n d E(R2) = 1 2 % p .a . a n d th e s ta n d a r d d e v ia tio n s a re
= 2 0 % p .a . a n d a 2 = 3 0 % p .a . T he c o r r e la tio n c o e ffic ie n t b e tw e e n th e ir re tu rn s is p ] 2 = - 〇.5. The
in v e s to r is fre e to c h o o s e th e in v e s tm e n t p r o p o r tio n s w ] a n d w 2/ s u b je c t o n ly to th e re q u ire m e n ts th a t
+ w 2 = 1 a n d th a t b o th
a n d vv2 a r e p o s itiv e .3 T h e re is n o lim it to th e n u m b e r o f p o r tfo lio s th a t
m e e t th e se re q u ire m e n ts , s in c e th e re is n o lim it to th e n u m b e r o f p r o p o r tio n s th a t sum to 1. T h e re fo re ,
a re p re s e n ta tiv e s e le c tio n o f v a lu e s is c o n s id e r e d fo r W ]：
0 , 0 . 2 , 0 . 4 , 0 . 6 , 0 . 8 a n d 1.
U s in g E q u a tio n 7 . 1 , th e e x p e c te d re tu rn o n a tw o -s e c u rity p o r tf o lio is:
E(/?p) = w .E iR ,) + w 2E(R2)
= w ^ O .0 8 ) +
w
2( 0 . 1 2 )
U s in g E q u a tio n 7 . 4 , th e v a r ia n c e o f th e re tu rn o n a tw o -s e c u rity p o r tf o lio is:
ap =
=
+ w^ + 2w 1vv2Pir2a l °2
w2(〇.20)2
+ w2(0.30)2 + 2Wl w2(-0.5)(0.20)(0.30)
= 0.04w^ + 0.09w^ - 0.06W] vv2
T he s ta n d a rd d e v ia tio n o f th e p o r tf o lio re tu rn s is fo u n d b y ta k in g th e s q u a re r o o t o f a . E a ch p a ir o f
p r o p o r tio n s is n o w c o n s id e r e d in tu rn :
a)
w 1 = 0 and w 2 = 1
q /y
= (o .〇
8 i( o ) + ( o .i
2 )⑴
= 0 . 1 2 o r 1 2 % p .a .
〇
p = (〇.〇4)(0)2 + (0.09)(1)2 -(0.06)(0)(1)
o2
p = 0.09
〇
b)
p - 0.30 or 30% p.a.
W! = 0 . 2 a n d w 2 = 0 . 8 E(Rp) = ( 0 . 0 8 ) ( 0 . 2 ) + ( 0 . 1 2 ) ( 0 . 8 ) = 0 . 1 1 2 o r 1 1 . 2 % p .a .
o2
p = (0.04)(0.2)2 + (0.09)(0.8)2 -(0.06)(0.2)(0.8)
o2
p = 0.0496
.-.〇 p = 0.2227 or 22.27% p.a.
c)
d)
W l = 0 . 4 a n d w 2 = 0 . 6 E[Rp) = ( 0 . 0 8 ) ( 0 . 4 ) + ( 0 . 1 2 ) ( 0 . 6 ) = 0 . 1 0 4 o r 1 0 . 4 % p .a .
〇
p = (〇.〇4)(0.2)2 + (0.09)(0.6)2 -(0.06)(0.4)(0.6)
〇
p = 0.0244
〇
p = 0.1562 or 15.62% p.a.
W l = 0 . 6 a n d w 2 = 0 . 4 E(/?p) = ( 0 . 0 8 ) ( 0 . 6 ) + ( 0 . 1 2 ) ( 0 . 4 ) = 0 . 0 9 6 o r 9 . 6 % p .a .
〇
l = (0.04)(0.6)2 + (0.09)(0.4)2 -(0.06)(0.6)(0.4)
=0.0144
= 0.12 or 12% p.a.
e)
vvt
= 0 . 8 a n d w 2 = 0 . 2 E(/?p) = ( 0 . 0 8 ) ( 0 . 8 ) + ( 0 . 1 2 ) ( 0 . 2 ) = 0 . 0 8 8 o r 8 .8 % p .a .
a2
p = (0.04)(0.8)2 + (0.09)(0.2)2 - (0.06)(0.8)(0.2)
=0.0196
〇
p = 0.14 or 14% p.a.
continued
3
Negative investment proportions would indicate a short sale', which means that the asset is first sold and later purchased.
Therefore, a short-seller benefits from price decreases.
^0^
B usiness finance
continued
f)
vvt
= 1 . 0 a n d w 2 = 0 E(/?p) = ( 0 . 0 8 ) ( 1 ) + ( 0 .1 2 ) ( 0 ) = 0 . 0 8 o r 8 % p .a .
〇l = (〇
.〇
4 ) ( l) 2
+ (0 .0 9 )(0 )2 - ( 0 . 0 6 ) ( l) ( 0 )
〇
p = 0.04
〇
p = 0.20 or 20% p.a.
T h e se re su lts a r e s u m m a ris e d in T a b le 7 . 3 .
TA B LE 7 .3
P o rtfo lio
(a)
(b)
(Cl
(d)
(e)
(f)
Proportion in Security 1 (Wj)
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
Proportion in Security 2 (w2)
1.0000
0.8000
0.6000
0.4000
0.2000
0.0000
Expected return E (Rp)
0.1200
0.1120
0.1040
0.0960
0.0880
0.0800
Standard deviation a
0.3000
0.2227
0.1562
0.1200
0.1400
0.2000
R e a d in g a c ro s s T a b le 7 .3 , th e in v e s to r p la c e s m o re w e a lth in th e lo w -re tu rn S e c u rity 1 a n d less in
th e h ig h -re tu rn S e c u rity 2 . C o n s e q u e n tly , th e e x p e c te d re tu rn o n th e p o r tfo lio d e c lin e s w ith e a c h step.
T he b e h a v io u r o f th e s ta n d a rd d e v ia tio n is m o re c o m p lic a te d . It d e c lin e s o v e r th e firs t fo u r p o rtfo lio s ,
re a c h in g a m in im u m v a lu e o f 0 . 1 2 0 0 w h e n Nv! = 0 . 6 , b u t th e n rises to 0 . 2 0 0 0 a t th e sixth p o r tfo lio ,
w h ic h co n sists e n tire ly o f S e c u rity 1 .4 T his is a n im p o rta n t fin d in g a s it im p lie s th a t so m e p o rtfo lio s
LEARNING
OBJECTIVE 4
Explain the concept of
efficient portfolios
w o u ld n e v e r b e h e ld b y risk-a ve rse in ve sto rs. F or e x a m p le , n o risk-a ve rse in v e s to r w o u ld c h o o s e P o rtfo lio
(e) b e c a u s e P o rtfo lio (d) o ffe rs b o th a h ig h e r e x p e c te d re tu rn a n d a lo w e r ris k th a n P o rtfo lio (e). P o rtfo lio s
th a t o ffe r th e h ig h e s t e x p e c te d re tu rn a t a g iv e n le ve l o f risk a re re fe rre d to a s 'e ffic ie n t’ p o rtfo lio s . T he
d a ta in T a b le 7 . 3 a re p lo tte d in F ig u re 7 . 6 .
A s c a n b e se e n fro m F ig u re 7 .6 , p o r tfo lio s (e) a n d (f) a r e n o t e ffic ie n t.
■
E n J P9p9dx
ai
uj
4
me minimum value of the standard deviation actually occurs slightly beyond Portfolio (d) at proportions Wj = 0.6333, and
= 0.3667. The standard deviation for this portfolio is 0.11.92% p.a. and its expected return is 9.48% p.a.
w2
C h apter
The magnitude o f the gain from diversification is closely related to the value
coefficient, p12- To show the importance o f the correlation coefficient, securities
considered. This tim e, however, the investm ent proportions are held constant at
and different values o f the correlation coefficient are considered. Portfolio variance is
=
o f the correlation
1 and 2 are again
= 0.6 and w2 = 0.4
given by:
o ^ C T j - f 1〇2 〇 2 + 2 W \ W 2 p \ , 2 ^ \ ^ 2
= (0.6)2(0.20)2 + (0.4)2(0.30)2 + 2(0.6)(0.4)pi,2(0.20)(0.30)
=0.0144 + 0.0144 + 0.0288pi,2
(Tp = ^/0.0288 + 0.0288^! 2
a
Pi,2 = +1.00
(Tp = x/0.0288 4-0.0288pi,2
CTp = 0.2400
b
Pi,2 = +0.50
CTp = ^/0.0288 + 0.0288/), i2
(Tp = 0.2079
c
Pi,2 = 0.00
〇
"p = ^0.0288 + 0.0288^1^
CTp = 0.1697
d
Pi,2 = -0.50
(Tp = ^ 0 .0 2 8 8 + 0.0288p1<2
(Tp = 0.1200
e
Pi,2 = -1.00
(Tp = ^0.0288 + 0.0288/?,,2
(Tp = 0
These results are summarised in Table 7.4.
TABLE 7.4 Effect of correlation coefficient on portfolio standard deviation
C o r r e la tio n c o e ffic ie n t
P i
S ta n d a rd d e v ia tio n
2= + l.
〇
〇
Pi 2 = +0.50
P i 2
=
p i 2
=
〇
.〇
〇
0 .2 4 0 0
0.2 0 7 9
0 .1 6 9 7
-0 .5 0
0.1 2 0 0
P i 2 = - 1 .0 0
0 .0 0 0 0
Table 7.4 shows three im p o rta n t facts about p o rtfo lio construction:
a
b
Combining two securities whose returns are perfectly positively correlated (that is, the correlation
coefficient is +1) results only in risk averaging, and does n ot provide any risk reduction. In th is case
the p ortfo lio standard deviation is the weighted average o f the two standard deviations, which is
(0.6)(0.20) + (0.4)(0.30) = 0.2400.
The real advantages o f diversification result from the risk reduction caused by com bining securities
whose returns are less than perfectly positively correlated.
s e ven
Risk
a n d return
B usiness finance
C
The degree o f risk reduction increases as the correlation coefficient between the returns on the two
securities decreases. The largest risk reduction available is where the returns are perfectly negatively
correlated, so the tw o risky securities can be combined to form a p o rtfo lio th a t has zero risk (<Jp = 0).
By considering different investm ent proportions w 1 and w 2, a curve sim ilar to th a t shown in Figure 7.6
can be plo tte d fo r each assumed value o f the correlation coefficient. These curves are shown together in
Figure 7.7.
Figure 7.7
I t can be seen th a t the lower the correlation coefficient, the higher the expected re tu rn fo r any given
level o f risk (or the lower the level o f risk fo r any given expected return). This shows th a t the benefits o f
diversification increase as the correlation coefficient decreases, and when the correlation coefficient is -1 ,
risk can be elim inated completely. The significance o f the dotted lines in Figure 7.7 is th a t a risk-averse
investor would never hold combinations o f the two securities represented by points on the dotted lines.
A t any given level o f correlation these combinations o f the tw o securities are always dom inated by other
com binations th a t offer a higher expected retu rn fo r the same level o f risk.
7 .5 .2 1 Diversification with multiple assets
LEARNING
OBJECTIVE 5
Understand the
importance of
covariance between
returns on risky assets
in determining the risk
of a portfolio
^0^
W hile the above discussion relates to the tw o-security case, even stronger conclusions can be drawn fo r
larger portfolios. To examine the relationship between the risk o f a large p o rtfo lio and the riskiness o f
the individual assets in the p ortfo lio , we sta rt by considering tw o assets. Using Equation 7.2, the p ortfo lio
variance is:
ojj = W y〇 i
+ U/2〇2 + ^ w l W 2C 〇v (R \ , R 2 )
C hapter seven Risk
a n d return
The variances and covariances on the right-hand side of this equation can be arranged in a matrix as follows:
1
1
2
C ov(R
C〇v(i?2,i?1)
2
v
R 2)
°2
W ith two assets the variances and covariances form a 2 x 2 m atrix; three assets w ill result in a
3 x 3 m atrix; and in general w ith n assets there w ill be ann x n m atrix. Regardless o f the num ber o f assets
involved, the variance-covariance m a trix w ill always have the follow ing properties:
The m atrix w ill contain a total o f n2 terms. O f these terms, n are the variances o f the individual assets
and the remaining (n2 - n) terms are the covariances between the various pairs o f assets in the portfolio,
b The two covariance terms fo r each pair o f assets are identical. For example, in the 2 x 2 m a trix above,
a
C o v (R v R 2) = C o v (R 2>^ i )-
c
Since the covariance term s fo rm identical pairs, the m atrix is sym metrical about the m ain diagonal,
which contains the n variance terms.
Remember th a t the significance o f the variance-covariance m atrix is th a t it can be used to calculate
the p ortfo lio variance. The p o rtfo lio variance is a weighted sum o f the terms in the m atrix, where the
weights depend on the proportions o f the various assets in the p ortfolio.
The firs t property o f the m a trix listed above shows th a t as the number o f assets increases, the number
o f covariance terms increases much more rapidly than the number o f variance terms. For a p o rtfo lio o f
n assets there are n variances and {n2 - n) covariances in the m atrix. This suggests th a t as a p o rtfo lio
becomes larger, the effect o f the covariance terms on the risk o f the p o rtfo lio w ill be greater than the
effect o f the variance terms.
To illustrate the effects o f diversification and the significance o f the covariance between assets, consider
a portfolio o f n assets. Assume th a t each o f these assets has the same variance {cr\). Also assume, initially,
that the returns on these assets are independent— that is, the correlation between the returns on the assets
is assumed to be zero in all cases. I f we form an equally weighted p o rtfo lio o f these assets, the proportion
invested in each asset w ill be (1/n). Given the assumption o f zero correlation between all the asset returns,
the covariance terms w ill all be zero, so the variance o f the p ortfo lio w ill depend only on the variance terms.
Since there are n variance term s and each such term is
the variance o f the p o rtfo lio w ill be:
7.5
aP
Equation 7.5 shows that as n increases, the p o rtfo lio variance w ill decrease and as n becomes large,
the variance o f the p o rtfo lio w ill approach zero; th a t is, i f the returns between all risky assets were
independent, then i t would be possible to elim inate all risk by diversification.
However, in practice, the returns between risky assets are not independent and the covariance
between returns on most risky assets is positive. For example, the correlation coefficients between the
returns on company shares are m ostly in the range 0.5 to 0.7. This positive correlation reflects the fact
that the returns on m ost risky assets are related to each other. For example, i f the economy were growing
strongly we would expect sales o f new cars and construction o f houses and other buildings to be increasing
strongly. In turn, the demand fo r steel and other b uilding materials would also increase. Therefore, the
profits and share prices o f steel and b uilding m aterial manufacturers should have a tendency to increase
at the same tim e as the p ro fits and share prices o f car manufacturers and construction companies.
To reflect the relationships among the returns on individual assets, we relax the assumption th a t
the returns between assets are independent. Instead, we now assume th a t the correlation between the
returns on all assets in the p o rtfo lio is p*. I f the p o rtfo lio is again equally weighted, the p o rtfo lio variance
w ill now be equal to the sum o f the variance terms shown in Equation 7.5, plus (n2 - n) covariance terms
2
where each such term w ill be
T
+ ( 1 ~ n )p^
p*a^- Therefore, the variance o f the p o rtfo lio w ill be:
7.6
40V
B usiness finance
Equation 7.6 illustrates an im p o rta n t result: w ith identical positively correlated assets, risk cannot be
completely eliminated, no m atter how many such assets are included in a p ortfolio. As n becomes large,
(1/n) w ill approach zero so the firs t term in Equation 7.6 w ill approach zero, b ut the second term w ill
approach p*G^; th a t is, the variance o f the p o rtfo lio w ill approach
which is the covariance between
the returns on the assets in the p ortfolio. Thus, the positive correlation between the assets in a p ortfolio
imposes a lim it on the extent to which risk can be reduced by diversification.
In practice, the assets in a p o rtfo lio w ill n ot be identical and the correlations between the assets
w ill d iffer rather than being equal as we have assumed. However, the essential results illustrated in
Equation 7.6 remain the same— th a t is, in a diversified p o rtfo lio the variances o f the individual assets w ill
contribute little to the risk o f the p ortfo lio . Rather, the risk o f a diversified p o rtfo lio w ill depend largely
on the covariances between the returns on the assets. For example, Fama (1976, pp. 245-52) found that
in an equally weighted p o rtfo lio o f 50 random ly selected securities, 90 per cent o f the p o rtfo lio standard
deviation was due to the covariance terms.
7 .5 .3 1 Systematic and unsystematic risk
LEARNING
OBJECTIVE 6
Explain the distinction
between systematic
and unsystematic risk
UNSYSTEMATIC
( d iv e r s if ia b l e ) RISK
that component of
total risk that is unique
to the company and
may be eliminated by
diversification
SYSTEMATIC (MARKETRELATED OR N O N DIVERSIFIABLE) RISK
that component of
total risk that is due to
economy-wide factors
As discussed in Section 7.5.2, i f we diversify by combining risky assets in a p o rtfo lio , the risk o f the
p o rtfo lio returns w ill decrease. Diversification is most effective i f the returns on the individual assets are
negatively correlated, b u t i t s till works w ith positive correlation, provided th a t the correlation coefficient
is less than +1. We have noted that, in practice, the correlation coefficients between the returns on
company shares are m ostly in the range 0.5 to 0.7. We also noted th a t this positive correlation reflects the
fact th a t the returns on the shares o f m ost companies are economically related to each other. However,
the correlation is less than perfect, which reflects the fact th a t much o f the va riab ility in the returns on
shares is due to factors th a t are specific to each company. For example, the price o f a company’s shares
may change due to an exploration success, an im p o rta n t research discovery or a change o f chief executive.
Over any given period, the effects o f these company-specific factors w ill be positive fo r some companies
and negative fo r others. Therefore, when shares o f different companies are combined in a p ortfo lio , the
effects o f the company-specific factors w ill tend to offset each other, which w ill, o f course, be reflected in
reduced risk fo r the p ortfolio. In other words, p a rt o f the risk o f an individual security can be eliminated
by diversification and is referred to as unsystem atic risk or diversifiable risk. However, no m atter
how much we diversify, there is always some risk th a t cannot be elim inated because the returns on all
risky assets are related to each other. This p art o f the risk is referred to as sy stem atic risk or nondiversifiable risk. These tw o types o f risk are illustrated in Figure 7.8.
igure 7.8
C hapter seven Risk
a n d return
Figure 7.8 shows th a t m ost unsystematic risk is removed by holding a p o rtfo lio o f about 25 to 30
securities. In other words, the returns on a well-diversified p o rtfo lio w ill n ot be significantly affected by
the events that are specific to individual companies. Rather, the returns on a well-diversified p o rtfo lio
w ill vary due to the effects o f market-wide or economy-wide factors such as changes in interest rates,
changes in tax laws and variations in com m odity prices. The systematic risk o f a security or p o rtfo lio w ill
depend on its sensitivity to the effects o f these market-wide factors. The d istin ction between systematic
and unsystematic risk is im p o rta n t when we consider the risk o f individual assets in a p o rtfo lio context,
which is discussed in Section 7.5.4, and the pricing o f risky assets, which is discussed in Section 7.6.
7 .5 .4 | The risk of an individual asset
The reasoning used above can be extended to explain the factors th a t w ill determine the risk o f an
individual asset as a component o f a diversified portfolio. Suppose th a t an investor holds a p o rtfo lio o f
50 assets and is considering the addition o f an extra asset to the p ortfolio. The investor is concerned
w ith the effect that this extra asset w ill have on the standard d e la tio n o f the p ortfo lio . The effect is
determined by the p o rtfo lio proportions, the extra assets variance and the 50 covariances between
the extra asset and the assets already in the portfolio. As discussed above, the covariance terms are the
dom inant influence— th a t is, to the holder o f a large p o rtfo lio the risk o f an asset is largely determined
by the covariance between the retu rn on th a t asset and the retu rn on the holders existing p ortfolio. The
variance o f the return on the extra asset is o f little importance. Therefore, the risk o f an asset when it is
held in a large p o rtfo lio is determ ined by the covariance between the return on the asset and the return
on the portfolio. The covariance o f a security z w ith a p o rtfo lio P is given by:
The holders o f large p ortfo lio s o f securities can s till achieve risk reduction by adding a new security
to their portfolios, provided th a t the returns on the new security are n o t perfectly positively correlated
w ith the returns on the existing p ortfo lio . However, the increm ental risk reduction due to adding a new
security to a p o rtfo lio decreases as the size o f the p o rtfo lio increases and, as shown in Figure 7.8, the
additional benefits from diversification are very small fo r portfolios th a t include more than 30 securities
(Statman 1987).
I f investors are well diversified, th e ir portfolios w ill be representative o f the m arket as a whole.
Therefore, the relevant measure o f risk is the covariance between the retu rn on the asset and the return
on the m arket or Cov(Ri}RM). The covariance can then be scaled by dividing it by the variance o f the return
on the m arket th a t gives a convenient measure o f risk, the b e ta factor, j3{) o f the asset— th a t is, fo r any
asset z, the beta is:
Cov(i?/, Rm)
Beta is a very useful measure o f the risk o f an asset and i t w ill be shown in Section 7.6.2 th a t the
capital asset pricing model proposes th a t the expected rates o f retu rn on risky assets are directly related
to th e ir betas.
Value Line (w w w .valueline.com ) is a US website based on the Value Line Investm ent Survey and
contains inform a tion to help determine a share s level o f risk.
LEARNING
OBJECTIVE 7
Explain why
systematic risk is
important to investors
BETA
measure of a security’s
systematic risk,
describing the amount
of risk contributed
by the security to the
market portfolio
^w w ^J
VALUE AT RISK (VaR)-AN O TH ER WAY OF LOOKING AT RISK
Finance
Since the m id -1990s, a new measure o f risk exposure has become popular. This measure
was developed by the investment bank J.P. M organ and is known as value at risk (VaR).5 It is
defined as the worst loss that is possible under normal market conditions during a given time
period. It is therefore determined by w hat are estimated to be normal market conditions and
by the time period under consideration. For a given set o f market conditions, the longer the
IN A C T IO N
continued
5
*
7.7
Cov{Ri,Rp) = pip(Tiap
。
*
A detailed examination of value at risk is provided by Jorion (2006), while an excellent online resource for those interested in
the topic is provided at www.gloria-mundi.com.
B usiness finance
continued
VALUE AT RISK
tim e h o r iz o n th e g r e a t e r is th e v a lu e a t ris k . T h is m e a s u re o f r is k is b e in g in c r e a s in g ly u s e d b y
worst loss possible
under normal market
conditions for a given
time horizon
c o r p o r a t e tr e a s u r e r s , fu n d m a n a g e r s a n d f in a n c ia l in s titu tio n s a s a s u m m a r y m e a s u r e o f th e to ta l
r is k o f a p o r t f o lio .
To illu s tra te h o w v a lu e a t ris k is m e a s u re d , s u p p o s e th a t $ 1 5 m illio n is in v e s te d in s h a re s in
G r a d s t a r ts Ltd. S h a re s in G r a d s ta r ts h a v e a n e s tim a te d re tu rn o f z e r o a n d a s ta n d a r d d e v ia tio n
o f 3 0 p e r c e n t p e r a n n u m . 6 T h e s ta n d a r d d e v ia tio n o n th e in v e s tm e n t o f $ 1 5 m illio n is th e re fo r e
$ 4 . 5 m illio n . S u p p o s e a ls o t h a t re tu rn s f o llo w a n o r m a l p r o b a b ilit y d is tr ib u tio n . T h is m e a n s th a t th e
t a b le o f a r e a s u n d e r th e s t a n d a r d n o r m a l c u r v e (see T a b le 5 o f A p p e n d ix A , o r th e N O R M S D IS T
fu n c tio n in M ic r o s o f t E xcel® ) c a n b e u s e d to c a lc u la te th e p r o b a b ilit y th a t th e re tu rn w ill b e g r e a t e r
th a n a s p e c ifie d n u m b e r. S u p p o s e a ls o th a t a b n o r m a lly b a d m a r k e t c o n d itio n s a r e e x p e c te d 5 p e r
c e n t o f th e tim e . T h e t a b le o f a r e a s u n d e r th e s t a n d a r d n o r m a l c u r v e in d ic a te s t h a t th e re is a 5 p e r
c e n t c h a n c e o f a lo ss o f g r e a t e r th a n $ 7 . 4 0 2 5 m illio n p e r a n n u m . T h is f ig u r e is e q u a l to 1 . 6 4 5
m u ltip lie d b y th e s t a n d a r d d e v ia tio n o f $ 4 . 5 m illio n . A s s h o w n in F ig u re 7 . 9 , th e v a lu e a t ris k o f
th e in v e s tm e n t in G r a d s t a r ts is th e re fo r e $ 7 . 4 0 2 5 m illio n p e r a n n u m .
Figure 7.9 Value of Gradstarts Ltd
!l!
2 >
OJd
-e
_Q
S u p p o s e t h a t $ 1 0 m illio n is a ls o in v e s te d in s h a re s in C u r z o n C r e a t iv e Id e a s Ltd . T h e s e
C u r z o n C r e a t iv e Id e a s s h a re s h a v e a n e s tim a te d re tu rn o f z e r o a n d h a v e a s t a n d a r d d e v ia t io n
o f 2 0 p e r c e n t p e r a n n u m . T h e s t a n d a r d d e v ia t io n o n th e in v e s tm e n t o f $ 1 0 m illio n is th e r e f o r e
$ 2 m illio n p e r a n n u m . It is a g a in a s s u m e d t h a t re tu rn s f o ll o w a n o r m a l p r o b a b il it y d is t r ib u t io n
a n d t h a t a b n o r m a lly b a d m a r k e t c o n d it io n s a r e e x p e c t e d 5 p e r c e n t o f th e tim e . A s im ila r
c a lc u la t io n to t h a t f o r G r a d s t a r ts p r o v id e s a v a lu e a t r is k o f th e in v e s tm e n t in C u r z o n C r e a t iv e
Id e a s o f $ 2 m illio n m u lt ip lie d b y 1 . 6 4 5 o r $ 3 . 2 9 m illio n p e r a n n u m .
T h e b e n e fits o f d iv e r s if ic a t io n m a y b e d e m o n s tr a te d b y c a lc u la t in g th e v a lu e a t r is k o f a
p o r t f o lio c o m p r is in g a $ 1 5 m illio n in v e s tm e n t in G r a d s t a r t s a n d a $ 1 0 m illio n in v e s tm e n t in
C u r z o n C r e a t iv e Id e a s . T h e w e ig h t o f th e in v e s tm e n t in G r a d s t a r t s is $ 1 5 m illio n o f $ 2 5 m illio n
o r 0 . 6 o f t h e p o r t f o lio . T h e w e ig h t o f th e in v e s tm e n t in C u r z o n C r e a t iv e Id e a s is 0 . 4 . S u p p o s e
t h a t th e c o r r e la t io n b e tw e e n th e re tu rn s o n th e s h a re s is 0 . 6 5 . U s in g E q u a t io n 7 .4 , th e v a r ia n c e
o f th e re tu r n s o n th e p o r t f o lio is:
a 2= ( 0 . 6 ) 2 ( 0 . 3 ) 2 + ( 0 .4 ) 2 ( 0 . 2 ) 2 + 2 ( 0 . 6 ) ( 0 . 4 ) ( 0 . 3 ) ( 0 . 2 ) ( 0 . 6 5 )
= 0 .0 5 7 5 2
T h e s ta n d a r d d e v ia tio n o f p o r t f o lio re tu rn s , a , is th e r e fo r e 0 . 2 3 9 8 3 3 o r 2 3 . 9 8 3 3 p e r c e n t
a n d th e s ta n d a r d d e v ia tio n o n th e in v e s tm e n t is $ 2 5 m illio n x 0 . 2 3 9 8 3 3 = $ 5 . 9 9 5 8 m illio n .
T h e v a lu e a t ris k o f th e p o r t f o lio is $ 5 . 9 9 5 8 m u ltip lie d b y 1 . 6 4 5 o r $ 9 . 8 6 3 1
6
m illio n p e r a n n u m .
It is usual in calculating value at risk to assume an expected return of zero. This is a reasonable assumption where the
expected return is small compared with the standard deviation of the expected return.
C hapter seven Risk
T h e t o t a l v a lu e a t r is k o f t h e in d iv id u a l in v e s tm e n ts in G r a d s t a r t s a n d C u r z o n C r e a t iv e Id e a s
w a s $ 7 . 4 0 2 5 m illio n p lu s $ 3 . 2 9 m illio n o r $ 1 0 . 6 9 2 5 m illio n p e r a n n u m . T h e d if f e r e n c e
b e tw e e n t h a t a m o u n t a n d th e v a lu e a t r is k o f th e p o r t f o lio o f $ 9 . 8 6 3 1
m illio n is d u e to th e
b e n e fits o f d iv e r s if ic a t io n . If, h o w e v e r , th e re tu rn s o n th e s h a re s o f th e t w o c o m p a n ie s w e r e
p e r fe c t ly c o r r e la t e d , th e v a lu e a t r is k o f th e p o r t f o lio w o u ld e q u a l th e v a lu e a t r is k f o r th e
in v e s tm e n t in G r a d s t a r t s p lu s th e v a lu e a t r is k o f th e in v e s tm e n t in C u r z o n C r e a t iv e Id e a s .
V a R is a t e c h n iq u e t h a t is c o m m o n ly u s e d b y f in a n c ia l in s titu tio n s t o m o n it o r t h e ir e x p o s u r e
to lo s s e s t h r o u g h a d v e r s e c h a n g e s in m a r k e t c o n d it io n s . A p e r t in e n t e x a m p le o f th e u s e o f V a R
is p r o v id e d b y th e J a n u a r y 2 0 0 4 a n n o u n c e m e n t o f a $ 3 6 0 m illio n f o r e ig n e x c h a n g e lo s s b y
th e N a t io n a l A u s t r a lia B a n k . W h i l e a n in d e p e n d e n t in v e s t ig a t io n b y P r ic e w a t e r h o u s e C o o p e r s
a ttr ib u t e d m o s t o f th e b la m e f o r th e lo s s to d is h o n e s t y o n th e p a r t o f th e c u r r e n c y t r a d e r s
in v o lv e d a n d th e la c k o f s u it a b le c o n t r o l m e c h a n is m s in p la c e to u n c o v e r s u c h b e h a v io u r , th e
r e p o r t a ls o m a d e s o m e in te r e s t in g c o m m e n ts o n th e b a n k ’s u s e o f V a R . T h e N a t i o n a l A u s t r a lia
B a n k 's b o a r d o f d ir e c t o r s h a d a u t h o r is e d a V a R m a r k e t r is k e x p o s u r e lim it o f $ 8 0 m illio n p e r
d a y f o r th e b a n k in g g r o u p a s a w h o le . T h is lim it w a s d i v id e d b e t w e e n t h e v a r io u s d iv is io n s o f
th e b a n k . T h e c u r r e n c y o p t io n s d e s k h a d a V a R lim it o f $ 3 . 2 5 m illio n p e r d a y . T h is lim it w a s
p e r s is te n tly b r e a c h e d o v e r th e 1 2 -m o n th p e r io d p r i o r to th e a n n o u n c e m e n t o f th e $ 3 6 0 m illio n
lo s s . In r e la t io n to th e im p le m e n t a t io n o f a f la w e d V a R s y s te m th e P r ic e w a t e r h o u s e C o o p e r s
r e p o r t c o m m e n te d th a t:
... m a n a g e m e n t h a d little c o n fid e n c e in the VaR num bers d u e to systems a n d d a ta issues,
a n d e ffe ctive ly ig n o re d VaR a n d o th e r lim it breaches. There w a s n o sense o f u rg e n c y in
resolving the VoR c a lc u la tio n issues w h ic h h o d been a p ro b le m fo r a p e rio d o f tw o o r
m ore ye a rs.7
7 .5 .5 1 The efficient frontier
When all risky assets are considered, there is no lim it to the num ber o f portfolios th a t can be formed,
and the expected return and standard deviation o f the retu rn can be calculated fo r each p ortfo lio . The
coordinates fo r all possible p ortfo lio s are represented by the shaded area in Figure 7.10.
Figure 7.10
j E n
s '
UJ
J
Qj
p a p a d x
LIJ
Risk (a)
7
See PricewaterhouseCoopers (2004, p. 4).
a n d return
B usiness finance
Only portfolios on the curve between points A and B are relevant since all portfolios below this curve
yield lower expected return and/or greater risk. The curve AB is referred to as the efficient frontier and it
includes those portfolios that are efficient in that they offer the m aximum expected return for a given level
o f risk. For example, Portfolio 1 is preferred to an internal p oint such as Portfolio 3 because Portfolio 1 offers
a higher expected return fo r the same level o f risk. Similarly, Portfolio 2 is preferred to Portfolio 3 because
it offers the same expected return for a lower level o f risk. No such <dominance, relationship exists between
efficient portfolios— that is, between portfolios whose risk-re tu rn coordinates plot on the efficient frontier.
Given risk aversion, each investor w ill want to hold a p ortfo lio somewhere on the efficient frontier.
Risk-averse investors w ill choose the p o rtfo lio th a t suits th e ir preference fo r risk. As investors are a diverse
group there is no reason to believe th a t they w ill have identical risk preferences. Each investor may therefore
prefer a different p oint (portfolio) along the efficient frontier. For example, a conservative investor would
choose a p ortfo lio near p o in t A while a more risk-tolerant investor would choose a p ortfo lio near p oint B.
In summary, the m ain points established in this section are that:
diversification reduces risk
the effectiveness o f diversification depends on the correlation or covariance between returns on the
individual assets combined into a p o rtfo lio
C the positive correlation th a t exists between the returns on m ost risky assets imposes a lim it on the
degree o f risk reduction th a t can be achieved by diversification
d the to ta l risk o f an asset can be divided in to two parts: systematic risk th a t cannot be elim inated by
diversification and unsystematic risk th a t can be elim inated by diversification
e the only risk th a t remains in a well-diversified p o rtfo lio is systematic risk
f fo r investors who diversify, the relevant measure o f the risk o f an individual asset is its systematic
risk, which is usually measured by the beta o f the asset
g risk-averse investors w ill aim to hold p ortfolios th a t are efficient in th a t they provide the highest
expected retu rn fo r a given level o f risk.
a
b
The concepts discussed in this section can be extended to model the relationship between risk and
expected return fo r individual risky assets. This extension o f p o rtfo lio theory is discussed in Section 7.6
and we discuss below an alternative technique to measuring risk th a t focuses on the maximum dollar
losses th a t would be expected during norm al trading conditions.
7.6
The pricing of risky assets
Section 7.5 focused on investm ent decision making by individuals. We now s h ift the focus from the
behaviour o f individuals to the pricing o f risky assets and we introduce the assumption th a t investors can
also invest in an asset th a t has no default risk. The return on this risk-free asset is the risk-free interest
rate, R^. Typically, this is regarded as the interest rate on a government security, such as Treasury notes.
We continue to assume th a t all investors in a particular m arket behave according to p o rtfo lio theory,
and ask: How would prices o f individual securities in th a t m arket be determined? In tu itive ly, we would
expect risky assets to provide a higher expected rate o f retu rn than the risk-free asset. In other words, the
expected retu rn on a risky asset could be viewed as consisting o f the risk-free rate plus a premium fo r risk,
and this prem ium should be related to the risk o f the asset.
However, as discussed in Section 7.5.3, part o f the risk o f any risky asset— unsystematic risk — can be
eliminated by diversification. It seems reasonable to suggest that in a competitive market, assets should be
priced so that investors are not rewarded fo r bearing risk that could easily be eliminated by diversification.
On the other hand, some risk — systematic risk— cannot be eliminated by diversification so it is reasonable
to suggest that investors w ill expect to be compensated fo r bearing that type o f risk. In summary, in tu itio n
suggests that risky assets w ill be priced such that there is a relationship between returns and systematic risk.
The remaining question is: W hat sort o f relationship w ill there be between returns and systematic risk? The
work o f Sharpe (1964), Lintner (1965), Fama (1968) and Mossin (1969) provides an answer to this question.8
8
Although we have referred to the pricing5of assets, much of this work deals with expected returns, rather than asset prices.
However, there is a simple relationship between expected return and price in that the expected rate of return can be used to
discount an assets expected net cash flows to obtain an estimate of its current price.
7 .6 .1 1 The capital market line
W ith the opp ortu nity to borrow and lend at the risk-free rate, an investor is no longer restricted to
holding a p o rtfo lio th a t is on the efficient fro n tie r AB. Investors can now invest in combinations o f risky
assets and the risk-free asset in accordance w ith th e ir risk preferences. This is illustrated in Figure 7.11.
N
%
◦s
C J n oJ
L
U
p a p a d x
L
U
Risk [a)
The line R^T represents p o rtfo lio s th a t consist o f an investm ent in a p o rtfo lio o f ris k y assets T
and an investm ent in the risk-free asset. Investors can achieve any com bination o f ris k and re tu rn on
the line RrT by investing in the risk-free asset and P o rtfo lio T. Each p o in t on the line corresponds to
different p ro po rtio ns o f the to ta l funds being invested in the risk-free asset and P o rtfo lio T. However,
it would n o t be ratio na l fo r investors to hold p o rtfo lio s th a t p lo t on the line RjT, because they can
achieve higher returns fo r any given level o f risk by com bining the risk-free asset w ith o the r p o rtfo lio s
th a t p lo t above T on the efficient fro n tie r (AB). This approach suggests th a t investors w ill achieve the
best possible re tu rn fo r any level o f ris k by holding P o rtfo lio M rather th an any other p o rtfo lio o f risky
assets.
The line R^MN is tangential at the p o in t M to the efficient fro n tie r (AB) o f portfolios o f risky assets.
This line represents p ortfo lio s that consist o f an investm ent in Portfolio M and an investm ent in the
risk-free asset. Points on the line to the le ft o f M require a positive am ount to be invested in the risk-free
asset— that is, they require the investor to lend at the risk-free rate. Points on the line to the rig h t o f
M require a negative am ount to be invested in the risk-free asset— th a t is, they require the investor to
borrow at the risk-free rate.
It is apparent th a t the line R^MN dominates the efficient fro n tie r AB since at any given level o f risk a
portfolio on the line offers an expected return at least as great as th a t available from the efficient fro n tie r
(curve AB). Risk-averse investors w ill therefore choose a p o rtfo lio on the line R^MN— th a t is, some
combination o f the risk-free asset and Portfolio M. This is true fo r all risk-averse investors who conform
to the assumptions o f p o rtfo lio theory. The portfolios th a t m ig ht be chosen by three investors are shown
in Figure 7.11. Having chosen to invest in Portfolio M, each investor combines this risky investm ent w ith
a position in the risk-free asset. In Figure 7.11, Investor 1 w ill invest p a rtly in Portfolio M and p a rtly in
the risk-free asset. Investor 2 w ill invest all funds in Portfolio M , while Investor 3 w ill borrow at the risk­
free rate and invest his or her own funds, plus the borrowed funds, in Portfolio M . A fo u rth strategy, n o t
shown in Figure 7.11, is to invest only in the risk-free asset. This is the least risky strategy, whereas the
strategy pursued by Investor 3 is the riskiest.
B usiness finance
MARKET PORTFOLIO
portfolio of all risky
assets, weighted
according to their
market capitalisation
CAPITAL MARKET LINE
efficient set of
all portfolios that
provides the investor
with the best
possible investment
opportunities when
a risk-free asset is
available. It describes
the equilibrium riskreturn relationship for
efficient portfolios,
where the expected
return is a function of
the risk-free interest
rate, the expected
market risk premium
and the proportionate
risk of the efficient
portfolio to the risk of
the market portfolio
I f all investors in a particular m arket behave according to p o rtfo lio theory, all investors hold Portfolio
M as at least a p art o f th e ir to ta l p o rtfo lio .9 In turn, this implies th a t Portfolio M m ust consist o f all risky
assets. In other words, under these assumptions, a given risky asset, X, is either held by all investors as
part o f Portfolio M or it is n o t held by any investor. In the la tte r case, Asset X does n o t exist. Therefore,
Portfolio M is often called the m arket portfolio because it comprises all risky assets available in the
m arket. For example, i f the to ta l m arket value o f all shares in Company X represents 1 per cent o f the
to ta l m arket value o f all assets, then shares in Company X w ill represent 1 per cent o f every investors
to ta l investm ent in risky assets.
The line R^MN is called the capital m arket line because i t shows all the to ta l portfolios in which
investors in the capital m arket m ight choose to invest. Since investors w ill choose only efficient portfolios,
it follows th a t the m arket p o rtfo lio is predicted to be efficient* in the sense th a t it w ill provide the
m axim um expected retu rn fo r th a t particular level o f risk. The capital m arket line, therefore, shows the
trade-off between expected return and risk fo r all efficient portfolios. The equation o f the capital m arket
line is given b y:10
' E(Rm ) - R f 、
E(Rp) = Rf +
where
〇
7.8
M is the standard deviation o f the retu rn on the m arket Portfolio M
The slope o f this line is 丑( 只以)—
and this measures the m arket price o f risk. It represents the
additional expected retu rn th a t investors would require to compensate them fo r in cu rring additional
risk, as measured by the standard deviation o f the p ortfolio.
7 .6 .2 |T h e Capital Asset Pricing Model (CAPM) and the
security market line
LEARNING
OBJECTIVE 8
Explain the
relationship between
returns and risk
proposed by the
capital asset pricing
model
A lthough the capital m arket line holds fo r efficient portfolios, it does n o t describe the relationship between
expected return and risk fo r individual assets or inefficient portfolios. In equilibrium , the expected return
on a risky asset (or inefficient p ortfo lio ), z, can be shown to be:11
f E(R M) - R f \
E(R i) = Rf + f
^
f j Cow(Rh RM)
where
7.9
= the expected retu rn on the zth risky asset
C ov(R j} Rm) = the covariance between the returns on the zth risky asset and the m arket p o rtfo lio
9 This ignores the extreme case of investors who hold only the risk-free asset.
10 The fact that Equation 7.8 is the equation for the capital market line can be shown as follows: let Portfolio p consist of an
investment in the risk-free asset and the market portfolio. The investment proportions are w f in the risk-free asset and
w M = 1 - W fin the market portfolio. Therefore, Portfolio p is, in effect, a two-security portfolio and its expected return is
given by:
£(Kp) = w R f + (1 -
w f ) E (RM)
and the variance of its return is:
+
By definition,
a2P
_ w)2〇
2m + 2My(! -
= 0 so the variance reduces to:
= ^ ~ wf)Z〇
2M
Therefore:
(Tp = ( l - Wf)crM
Since the expected return and standard deviation of Portfolio p are linear functions of w^, it follows that R f M in Figure 7.11
is a straight line. This result is not specific to portfolios consisting of the risk-free asset and Portfolio M: rather it applies to a ll
portfolios that include the risk-free asset.
The equation for a straight line can be expressed as y = m x + c where m is the slope of the line and c is the intercept on the
y axis. Referring to Figure 7.11, it can be seen that:
n
c = Rr
」
and
m =
E (R M - R f )
--------- —
O 'M
Therefore, the equation for the line rf M N is Equation 7.8.
11 This is a purely mathematical problem. For a derivation see Levy and Sarnat (1990) or Brailsford and Faff (1993).
C hapter seven Risk
a n d return
Equation 7.9 is often called the CAPM equation. An equivalent version is given in Equation 7.11. The
CAPM equation shows th a t the expected return demanded by investors on a risky asset depends on
the risk-free rate o f interest, the expected retu rn on the m arket p ortfo lio , the variance o f the retu rn on
the m arket p ortfolio, and the covariance o f the return on the risky asset w ith the retu rn on the market
portfolio.
The covariance term Cov(Rj} RM) is the only explanatory factor in the CAPM equation specific to
asset z. The other explanatory factors (R厂，£(RM) and c r^) are the same, regardless o f which asset z. is being
considered. Therefore, according to the CAPM equation, i f tw o assets have different expected returns, this
is because they have different covariances w ith the m arket p ortfo lio . In other words, the measure o f risk
relevant to pricing a risky asset is Cov(Rif RM)t the covariance o f its returns w ith returns on the m arket
portfolio, as this measures the contribution o f the risky asset to the riskiness o f an efficient p ortfolio. In
contrast, fo r the efficient p o rtfo lio itse lf the standard deviation o f the p o rtfo lio s return is the relevant
measure o f risk (see Figure 7.11).
As discussed in Section 7.5.4, the measure o f risk fo r an investm ent in a risky asset i is often referred
to as its beta factor,
where:
Cov(i?/, Rm)
Pi
7.10
Because Cov(Rj} RM) is the risk o f an asset held as part o f the m arket p ortfo lio , while crM is the risk (in
terms o f variance) o f the m arket p ortfolio, it follows th a t J3f measures the risk o f i relative to the risk o f
the market as a whole. Using beta as the measure o f risk, the CAPM equation can be rew ritten:
£( r ) = v
z p (r m)
-
〜
]
HD
When graphed, Equation 7.11 is called the security m arket line and is illustrated in Figure 7.12.
■
graphical
representation of the
capital asset pricing
model
ure 7.12 Security market line
Security
market
line
b / )CJ n 4J
UJ
a}
p a p a d x
LU
0.5
SECURITY MARKET LINE
1.0
1.5
Risk (A)
The significance o f the security m arket line is that in equilibrium each risky asset should be priced so that
it plots exactly on the line. Equation 7.11 shows that according to the capital asset pricing model, the expected
return on a risky asset consists o f two components: the risk-free rate o f interest plus a premium for risk.
The risk premium for each asset depends on the assets beta and on the market risk premium [E(RM) - Rr].
B usiness finance
The betas o f individual assets w ill be distributed around the beta value o f the market portfolio, which is l . 12
A risky asset w ith a beta value greater than 1 (that is, higher risk) w ill have an expected return greater than
E(Rm), while the expected return on a risky asset w ith a beta value o f less than 1 (that is, lower risk) w ill be
less than E(RM). Assuming that the risk-free rate o f interest is 10 per cent and the m arket risk premium
[E(Rm) is 5 per cent, the expected return on risky Asset 1 w ith a beta value o f 0.5 w ill be 12.5 per cent.
The expected return on risky Asset 2 w ith a beta value o f 1.5 w ill be 17.5 per cent.
The capital asset pricing model applies to individual assets and to portfolios. The beta factor fo r a
p o rtfo lio p is simply:
^
_
Cov (Rp ,R m)
Pp
一
Z2^
7.12
where Cov(R yRM) = the covariance between the returns on p o rtfo lio p and the m arket p ortfo lio .
Equation 7.12 is sim ply Equation 7.10 rew ritten in term s o f a p o rtfo lio pt instead o f a particular
asset i. Fortunately there is a simple relationship between a p o rtfo lio s beta (J3p) and the betas o f the
individual assets th a t make up the p ortfo lio . This relationship is:
n
0p = Y l
7.13
i= \
where n = the num ber o f assets in the p ortfo lio
= the proportion o f the current m arket value o f p o rtfo lio p constituted by the zth asset
Equation 7.13 states th a t the beta factor fo r a p o rtfo lio is sim ply a weighted average o f the betas o f
the assets in the p o rtfo lio .13 One useful application o f Equation 7.13 is to guide investors in choosing
the investm ent proportions
to achieve some target p ortfo lio beta, /3p. An im p o rta n t special case is to
construct such a p o rtfo lio using only the m arket p o rtfo lio (J3 = 1) and a position in the risk-free asset
(J3 = 0). In this case, investors place a pro po rtio n wM o f th e ir to ta l funds in the m arket p ortfolio, and a
p roportion Wr = (1 - wM) in the risk-free asset. Using Equation 7.13, the target beta is given by:
P p
=
wf 0 f
+
w m
P m
Substituting /3f= 0 and j3 m = 1 gives:
wM=^*p
and W f r = l- J3*
For example, if / ^ = 0.75, investors should invest 75 per cent o f their funds in the m arket portfolio and
lend 25 per cent o f their funds at the risk-free rate. I f
= 1.3, investors should borrow an amount equal to
30 per cent o f their own investment funds and invest the total amount (130 per cent) in the market portfolio.
12 Since
Cov (/?,, R m)
P i = ----------5-------we have
_ C o v (/?a/ ,/? a/)
13 Our discussion has omitted the steps between Equations 7.12 and 7.13. For the interested reader, these steps are as follows.
Since:
R P = ^ 2 WjRj
/=i
it follows that:
C o v (R r , R m ) =
Cov
5 3 ^/C 〇v(/?„ R m)
/=i
Substituting in Equation 7.12:
(^i =
=
i=i
i=l
WiCov (/?,, Rm)
Wi(3i
C hapter seven Risk
a n d return
7 .6 .3 1 Implementation of the CAPM
Use o f the CAPM requires estim ation o f the risk-free interest rate,
the systematic risk o f equity, fie and
the m arket risk premium, E(RM) - Rf：
. Each o f these variables is discussed in turn.
The risk-free interest rate (Rfj
The assets closest to being risk free are government debt securities, so interest rates on these securities are
norm ally used as a measure o f the risk-free rate. However, as discussed in Section 4.6.1, unless the term
structure o f interest rates is flat, the various government securities w ill offer different interest rates. The
appropriate risk-free rate is the current yield on a government security whose term to m a tu rity matches
the life o f the proposed projects to be undertaken by the company. Since these activities undertaken by
the company typically provide returns over many years, the rate on long-term securities is generally used.
The share's systematic risk [jSJ
The betas o f securities are usually estimated by applying regression analysis to estimate the follow ing
equation from tim e series data:
Ri t = a i + ^ iRM + eit
where ^ = a constant, specific to asset z
eit = an error term
Equation 7.14 is generally called the m arket model. Its relationship to the security m arket line can
MARKET MODEL
time series regression
of an asset's returns
be readily seen by rew riting Equation 7.11 as follows:
E (R )= R f + ^ E (R M) - A R f
7.15
Therefore, the m arket m odel is a counterpart (or analogue) o f Equation 7.15. The magnitude o f the
betas th a t result from using this model when i t is applied to returns on shares is illustrated in Table 7.5,
which contains a sample o f betas fo r the shares o f selected listed companies. The values are calculated
using ordinary least squares (OLS) regression.
TABLE 7.5 Betas of selected Australian listed companies calculated using daily
share price and index data for the period January 2009 - December 2013
N am e o f com pany
M a in in d u s tria l a c tiv ity
Beta
ANZ Banking Group
Banking
1.16
Amcor
Packaging
0.75
BHP Billiton
Minerals exploration, production and
processing
1.32
Coca-Cola Amatil
Food, beverage and tobacco
0.41
Fairfax Media
Media
1.16
Harvey Norman
Retailing
1.03
QBE Insurance
Insurance
0.95
Woolworths
Food and staples retailing
0.46
The m arket model, as specified in Equation 7.14, is often used to obtain an estimate o f ex-post
systematic risk. To use the m arket model, it is necessary to obtain tim e series data on the rates o f return
on the share and on the m arket p o rtfo lio — th a t is, a series o f observations fo r both Rit and RMt is needed.
However, when using the m arket model, choices m ust be made about two factors. First, the model may be
estimated over periods o f different length. For example, data fo r the past 1, 2 ,3 or more years may be used.
Five years o f data are commonly used, but the choice is somewhat arbitrary. Second, the returns used in
the m arket model may be calculated over periods o f different length. For example, daily, weekly, monthly,
quarterly or yearly returns may be used. Again this choice is subject to a considerable degree o f judgment.
From a statistical perspective, it is generally better to have more rather than fewer observations,
because using more observations generally leads to greater statistical confidence. However, the greater the
num ber o f years o f data th a t are used, the more likely i t is th a t the company s riskiness w ill have changed.
This fact highlights a fundam ental problem o f using the m arket model. The m arket model provides a
measure o f how risky a company s equity was in the past. W hat we are seeking to obtain is an estimate of
future risk. Therefore, the choice o f both the number o f years o f data and the length o f the period over
which returns are calculated involves a trade-off between the desire to have many observations and the
need to have recent and consequently more relevant data.14
The market risk premium [E{RM] - Rf]
The m arket p o rtfo lio specified in the CAPM consists o f every risky asset in existence. Consequently, it
is impossible in practice to calculate its expected rate o f retu rn and hence impossible to also calculate
the m arket risk premium. Instead, a share m arket index is generally used as a substitute fo r the m arket
p ortfolio. As the rate o f retu rn on a share m arket index is highly variable from year to year, it is usual
to calculate the average retu rn on the index over a relatively long period. Suppose th a t the average rate
o f return on a share m arket index such as the All-Ordinaries Accum ulation Index over the past 10 years
was 18.5 per cent per annum. I f this rate were used as the estimate o f E(RM) and today s risk-free rate is
8.5 per cent, the m arket risk prem ium [E(RM) - R^\ would be 10 per cent.
A problem w ith using this approach is th a t the estimate o f ^ re fle c ts the m arkets current expectations
o f the future, whereas E(RM) is an average o f past returns. In other words, the two values may n ot match,
and some unacceptable estimates may result. For example, [E(RM) - RJ estimated in this way may be
negative i f the rate o f in fla tio n expected now, which should be reflected in
is greater than the realised
rate o f in fla tio n during the period used to estimate E(RM).
A better approach is to estimate the market risk prem ium directly, over a relatively long period. For
example, Ibbotson and Goetzmann (2005) compare the returns on equities w ith the returns on bonds
in the US between 1792 and 1925 and report an average difference o f approximately 3.8 per cent per
annum. The Credit Suisse Global Investment Returns Yearbook provides an annual update o f m arket risk
premiums across 20 countries. The 2013 yearbook authored by Dimson et al. (2013) reports that over the
113 years from 1900 to 2012 the average prem ium in the US was 5.3 per cent per annum. Over the same
period, the country w ith the lowest premium was Denmark, at 2.7 per cent per annum, and the country
w ith the highest premium was Australia, at 6.4 per cent per annum. Brailsford, Handley and Maheswaran
(2012) provide sim ilar estimates fo r Australia. They report that, over the 128 years from 1883 to 2010, the
premium was approximately 6.1 per cent per annum. Using a shorter tim e period during which the quality
o f the data is higher, they estimate th a t the premium from 1958 to 2010 was also 6.1 per cent per annum.
However, estim ating the m arket risk premium directly also has some problems. R itte r (2002) uses
the example o f Japan at the end o f 1989 to illustrate th a t historical estimates can result in nonsensical
numbers. He notes th a t estim ating the m arket risk prem ium at the end o f 1989 using historical data
starting when the Japanese stock m arket reopened after W orld War II would have provided a m arket risk
premium o f over 10 per cent per annum. The Japanese economy was booming, corporate profits were
high and average price-earnings (P-E) ratios were over 60. I t was considered th a t the cost o f equity for
Japanese companies was low. However, it is n ot possible fo r the cost o f equity to be low and the market
risk premium to be high. O f course, it is possible fo r the historical m arket risk premium to be high and the
expected m arket risk prem ium (and therefore the expected cost o f equity capital) to be low.
In an im p o rta n t theoretical paper, Mehra and Prescott (1985) showed th a t a long-term risk premium
such as th a t found in the US, Canada, the UK and Australia cannot be explained by standard models o f
risk and return. This fin ding has led to arguments th a t historical measures o f the risk prem ium are subject
to errors in th e ir measurement. For example, Jorion and Goetzmann (1999) argue th a t estimates o f the
m arket risk premium based solely on data obtained from the US w ill be biased upwards sim ply as a result
14 For a discussion of the issues associated with calculating systematic risk from historical data, see Brailsford, Faff and Oliver
( 1997) .
C hapter seven Risk
of the outperformance o f the US m arket relative to other equity markets over the tw e ntie th century.
Others, such as Heaton and Lucas (2000), argue th a t increased opportunities fo r p o rtfo lio diversification
mean th a t the m arket risk prem ium has fallen.
These concerns have led to new techniques being employed to estimate the m arket ris k prem ium .
Fama and French (2002), among others, use the dividend g ro w th m odel and conclude th a t the m arket
risk prem ium is now o f the order o f 1 per cent per annum . Claus and Thomas (2001) use forecasts by
security analysts and conclude th a t the m arket risk prem ium is approxim ately 3 per cent per annum.
Duke U niversity and CFO magazine have conducted a qua rte rly survey o f chief financial officers since
1996 (see w w w .cfosurvey.org). The average estimated ris k prem ium fo r the US over th a t tim e has
been approxim ately 4 per cent per annum . For the fo u rth quarter o f 2013, when asked how much
they expect returns in the equity m arket in the US to exceed the returns on governm ent bonds over
the next 10 years, the average response was 3.6 per cent per annum . In summary, the d isp a rity o f
estimates o f the m arket risk prem ium is considerable, ranging from 1 to in excess o f 6 per cent per
annum.
a n d return
卜， |
7 .6 .4 | Risk, return and the CAPM
The d istin ction between systematic and unsystematic ris k is im p o rta n t in explaining why the CAPM
should represent the ris k -re tu rn relationship fo r assets such as shares. This issue was discussed in
Section 7.5.3 b ut is reiterated here because o f its importance in understanding the CAPM. The returns
on a company s shares may vary fo r many reasons: fo r example, interest rates may change, or the
company may develop a new product, attract im p o rta n t new customers or change its chief executive.
These factors can be divided in to tw o categories: those related only to an individual company (companyspecific factors) and those th a t affect all companies (m arket-wide factors). As the shares o f different
companies are combined in a p o rtfo lio , the effects o f the company-specific factors w ill tend to cancel
each other out; this is how diversification reduces risk. However, the effects o f the m arket-wide factors
w ill remain, no m atter how many d ifferent shares are included in the p o rtfo lio . Therefore, systematic
risk reflects the influence o f m arket-wide factors, w hile unsystematic risk reflects the influence o f
company-specific factors.
Because unsystematic risk can be elim inated by diversification, the capital m arket w ill n o t reward
investors fo r bearing this type o f risk. The capital m arket w ill only reward investors fo r bearing risk that
cannot be elim inated by diversification— th a t is, the risk inherent in the m arket p ortfo lio . There are
cases when, w ith hindsight, we can id e n tify investors who have reaped large rewards from taking on
unsystematic risk. These cases do n ot im p ly th a t the CAPM is invalid: the model sim ply says th a t such
rewards cannot be expected in a competitive market. The reward fo r bearing systematic risk is a higher
expected retu rn and, according to the CAPM, there is a simple linear relationship between expected
return and systematic risk as measured by beta.
A d d itio n a l factors that explain returns
In 1977 Richard Roll published an im p o rta n t article th a t pointed out th a t while the CAPM has strong
theoretical foundations, there is a range o f difficulties th a t researchers face in testing i t empirically. For
example, in testing fo r a positive relationship between an assets beta and realised returns, a researcher
first needs to measure the correlation between the assets returns and the returns on the m arket p ortfolio.
The m arket p o rtfo lio theoretically consists o f all assets in existence and is therefore unobservable in
practice— im plying th a t ultim ately the CAPM itse lf is untestable.
Aside from the problems associated w ith testing fo r a relationship between estimates o f beta and
realised returns, voluminous empirical research has shown th a t there are other factors th a t also explain
returns. These factors include a company s dividend yield, its price-earnings (P-R) ratio, its size (as
measured by the m arket value o f its shares), and the ratio o f the book value o f its equity to the m arket
value o f its equity. This last ratio is often called the company s book-to-m arket ratio. In a detailed study,
Fama and French (1992) show th a t the size and book-to-m arket ratio were dom inant and th a t dividend
yield and the price-earnings ratio were n o t useful in explaining returns after allowing fo r these more
dom inant factors.
LEARNING
OBJECTIVE 9
Understand the
relationship between
the capital asset
pricing model and
models that include
additional factors
B usiness finance
In another im p o rta n t paper, Fama and French (1993) tested the follow ing three-factor model of
expected returns:
£(Rit) - Rf, = Pm [E{Rm ) - Rf,} + j3 iS £(SMBt) + J3m £(H M Lt)
LEARNING
OBJECTIVE 10
Explain the
development of
models that include
additional factors
B
In Equation 7.16, the firs t factor is the m arket risk premium, which is the basis o f the CAPM discussed
earlier in this chapter. The next factor, SMB, refers to the difference between the returns o f a diversified
p o rtfo lio o f small and large companies, while H M L reflects the differences between the returns o f a
diversified p o rtfo lio o f companies w ith high versus low book-to-m arket values. j3iM, j3jS and j3jH are the
risk parameters reflecting the sensitivity o f the asset to the three sources o f risk. A ll three factors were
found to have strong explanatory power. Brailsford, Gaunt and O b rie n (2012) found th a t in Australia,
over the period 1982 to 2006, all three factors provided strong explanatory power.
I t is possible th a t both the size and book-to-m arket ratio factors m ig ht be explicable by risk. For
example, Fama and French (1996) argue th a t smaller companies are more likely to default than larger
companies. Further, they argue th a t this risk is likely to be systematic in th a t small companies as a group
are more exposed to default during economic downturns. As a result, investors in small companies w ill
require a risk premium. Similarly, Zhang (2005) argues th a t companies w ith high book-to-m arket ratios
w ill on average have higher levels o f physical capacity. Much o f this physical capacity w ill represent excess
capacity during economic dow nturns and therefore expose such companies to increased risk.
However, as discussed in detail in Chapter 16, the relationship between these additional factors and
returns may n o t be due to risk. Further, Carhart (1997) added a fo u rth factor to the three described in
Equation 7.16 to explain returns earned by m utual funds. In an earlier paper, Jegadeesh and Titm an
(1993), using US data from 1963 to 1989, identified better perform ing shares (the winners) and poorer
perform ing shares (the losers) over a period o f 6 months. They then tracked the performance o f these
shares over the follow ing 6 months. On average, the biggest winners outperform ed the biggest losers by
10 per cent per annum. When Carhart added this m om entum effect to the three-factor model, he found
th a t it too explained returns. Unlike the size and book-to-m arket ratio factors, it is d iffic u lt to construct
a simple risk-based explanation fo r this factor.
W hile the CAPM is clearly an incomplete explanation o f the relationship between risk and returns,
it is im p o rta n t to note th a t it is s till widely applied. This p o in t is perhaps best demonstrated by the
Coleman, Maheswaran and Pinder (2010) survey o f the financial practices adopted by senior financial
managers in Australia. Financial managers employ asset pricing models to estimate the discount rate
used in project evaluation techniques such as the net present value approach. Coleman, Maheswaran
and Pinder reported that more than twice as many respondents used the trad ition al single-factor CAPM
compared w ith models th a t used additional factors.
7.8
LEARNING
OBJECTIVE 11
Distinguish between
alternative methods
of appraising the
performance of an
investment portfolio
S
Portfolio perform ance appraisal
A fundam ental issue th a t faces investors is how to measure the performance o f th e ir investm ent p ortfolio.
To illustrate the problem, assume th a t an investor observes th a t during the past 12 m onths, his or her
p o rtfo lio has generated a return o f 15 per cent. Is this a good, bad or indifferent result? The answer to
that question depends, o f course, on the expected return o f the p o rtfo lio given the p o rtfo lio s risk. That
is, in order to answer the question, we need a measure o f the risk o f the investors p o rtfo lio , and then
compare its performance w ith the performance o f a benchmark p o rtfo lio o f sim ilar risk. However, even
after accounting fo r the specific risk o f the p ortfo lio , the performance o f a p o rtfo lio may d iffer from that
o f the benchmark fo r four reasons:
•
•
Asset allocation. Investors m ust decide how much o f th e ir wealth should be allocated between
alternative categories o f assets such as corporate bonds, government bonds, domestic shares,
international shares and property. This decision w ill ultim ately affect the performance o f the
p o rtfo lio because in any given period a particular asset class may outperform other asset classes on a
risk-adjusted basis.
M arket timing. In establishing and adm inistering a p ortfo lio , investors need to make decisions
about when to buy and sell the assets held in a p ortfo lio . For example, investors m ig h t choose to
C hapter seven Risk
•
•
move out o f domestic shares and in to corporate bonds or alternatively sell the shares o f companies
that operate in the telecomm unication ind ustry and invest these funds in the shares o f companies
operating in the retail industry. Clearly, the performance o f a p o rtfo lio w ill be affected by an
investors success in selling assets before th e ir prices fall and buying assets before th e ir prices rise.
Security selection. Having made a decision about the desired m ix o f different asset classes w ith in a
portfolio, and when that desired m ix should be implemented, investors m ust then choose between
many different individual assets w ith in each class. For example, having determined th a t they wish
to hold half o f th e ir p o rtfo lio in domestic shares, investors m ust then decide which o f the more than
2000 shares listed on the Australian Securities Exchange they should buy. The a rt o f security selection
requires the investors to id e n tify those individual assets th a t they believe are currently underpriced
by the m arket and hence whose values are expected to rise over the holding period. Similarly, if
investors believe th a t any o f the assets held in the p o rtfo lio are currently overpriced, they would sell
these assets so as to avoid any future losses associated w ith a reduction in th e ir m arket value.
Random influences. Ultim ately, investing is an uncertain a ctivity and in any given period the
performance o f a p o rtfo lio may n o t reflect the skills o f the investor who makes the investm ent
decisions. That is, good decisions m ig ht yield poor outcomes and poor decisions m ight yield good
outcomes in what we would label as ‘bad luck’ or ‘good luck’, respectively. Over enough time, though,
we would expect the influence o f good luck and bad luck to average out.
We now consider four comm only used ways o f measuring the performance o f a p ortfo lio . Each o f these
measures has a different approach to try in g to determine the ‘expected’ performance o f the benchmark
portfolio in order to determ ine whether the p ortfo lio has met, exceeded or failed to meet expectations.
Simple benchmark index
This is probably the m ost comm only used approach to appraising the performance o f a p o rtfo lio and
involves a simple comparison between the p o rtfo lio s retu rn and the retu rn on a benchmark index that
has (or is assumed to have) sim ilar risk to the p o rtfo lio being measured. For example, a well-diversified
portfolio o f domestic shares m ig h t be benchmarked against the S&P/ASX 200 Index, which measures
the performance o f the shares in the 200 largest companies listed on the Australian Securities Exchange.
The advantages associated w ith using this approach to performance appraisal are th a t it is easy to
implement and to understand. The main problem w ith this approach is th a t i t implies th a t the risk o f the
portfolio is identical to the risk o f the benchmark index, whereas, w ith the exception o f so-called passive
funds, which are specifically established to m im ic (or track) the performance o f benchmark indices, this
w ill rarely be the case.
The Sharpe ratio
The Sharpe ratio, developed by W illiam Sharpe15, is a measure o f the excess retu rn o f the p o rtfo lio per
u n it o f total risk and is calculated using the follow ing formula:
where fp is the average re tu rn achieved on the p o rtfo lio over the tim e period, 7y is the average risk-free
rate o f return over the same tim e period and crp is the standard deviation o f the returns on the p ortfo lio
over the tim e period and is a measure o f the to ta l risk o f the p ortfo lio . I f the Sharpe ratio o f the investors
p ortfo lio exceeds the Sharpe ratio o f the m arket p ortfolio, then the investors p o rtfo lio has generated a
greater excess return per u n it o f to ta l risk and hence is regarded as exhibiting superior performance to
the m arket p ortfolio. Conversely, i f the p o rtfo lio s Sharpe ratio is less than th a t o f the m arket p ortfo lio
then the p o rtfo lio has generated less excess return per u n it o f to ta l risk than the m arket p o rtfo lio and the
p ortfo lio can be seen as having underperform ed th a t benchmark.
15 See Sharpe (1966).
a n d return
B usiness finance
The rationale behind the use o f the Sharpe ratio is best demonstrated by considering the ratios links
w ith the ris k -re tu rn trade-off described by the capital m arket line discussed in section 7.6.1. Consider
Figure 7.13, which illustrates the risk and retu rn profile fo r a superannuation fu nd s p o rtfo lio relative to
the m arket p ortfolio.
Note from Figure 7.13 that the superannuation fu nd s p ortfo lio has generated a lower rate o f return
than the m arket p o rtfo lio but has also generated a lower level o f to ta l risk. That is, while fp is less than
is also less than
The key point, however, is th a t the realised excess retu rn per unit o f risk
is higher fo r the fu nd s p o rtfo lio compared w ith the m arket p o rtfo lio and hence the fu n d s p ortfo lio is
regarded as having exhibited superior performance. This is illustrated in Figure 7.13 by the fu nd s p ortfolio
p lo ttin g above the capital m arket line. I f the fu nd s p o rtfo lio had generated a lower excess retu rn per u n it
o f risk than the m arket p ortfo lio , then i t would have plotted below the capital m arket line and this would
have im plied th a t the p o rtfo lio had underperformed the benchmark on a to ta l risk-adjusted basis.
Note th a t the Sharpe ratio assumes th a t in determ ining the risk-adjusted performance o f a p ortfo lio
the appropriate measure o f risk is to ta l risk. Following on from our discussion earlier in the chapter, it is
clear th a t to ta l risk is an appropriate measure only when we are dealing w ith well-diversified portfolios
rather than individual assets or undiversified portfolios.
The Treynor ratio
The Treynor ratio, named after Jack T re yn o r16, is a measure th a t is related to the Sharpe ratio of
performance measurement, in th a t it measures excess returns per u n it o f risk, b ut differs in th a t it
defines risk as non-diversifiable (or systematic) risk instead o f to ta l risk. I t can be calculated using the
follow ing form ula:
P
p
where Op and fr are the returns on the p o rtfo lio and the risk-free asset as defined earlier, and f3P is slu
estimate o f the systematic risk o f the p o rtfo lio over the period in which the returns were generated,
as measured by beta and defined in Section 7.6.2. As w ith the Sharpe ratio, insights in to the rationale
behind the use o f the Treynor ratio are provided by considering the lin k between ris k and expected
retu rn — b u t this tim e, instead o f considering the trade-off fo r efficient portfolios im plied by the capital
16 See Treynor (1966).
C hapter seven Risk
market line, we tu rn instead to the security m arket line, which applies to individual assets and inefficient
portfolios. In Figure 7.14 we compare the ex-post systematic risk and excess returns o f a superannuation
fund relative to the m arket p o rtfo lio over the same period o f time.
Recall th a t the security m arket line is sim ply the graphical representation o f the CAPM. The slope
o f the security m arket line describes the extra return, in excess o f the risk-free rate, th a t is expected for
each additional u n it o f systematic risk (as measured by beta) and is w hat we have previously defined as
the m arket risk premium
The slope o f the line th a t intersects the realised systematic risk and
return o f the funds p o rtfo lio is in tu rn the Treynor ratio. Hence, the decision rule used in assessing the
performance o f a p o rtfo lio using this technique requires a comparison o f the Treynor ratio calculated fo r
the p ortfolio over a specified interval w ith the market risk prem ium generated over th a t same interval.
Example 7.3 illustrates the three approaches to p o rtfo lio appraisal discussed above.
E xample
7.3
An investor holds a portfolio that consists of shares in 15 companies and wants to assess the
performance using a simple benchmark index as well as calculating the portfolio's Sharpe and Treynor
ratios. She estimates the parameters shown in Table 7.6 for the financial year ended 30 June 2014.
TABLE 7.6
Realised return
(% p.a.)
Standard deviation of returns
(a) (% p.a.)
Systematic risk
estimate (p)
Portfolio
13
30
1.2
S&P/ASX 200 share
price index
11
20
1.0
Government bonds
5
0
0
Based solely on the benchmark index approach, the portfolio appears to have performed well in
that it has generated an additional 2 per cent return above the proxy for the market (S&P/ASX 200).
a n d return
A s d is c u s s e d e a r lie r , h o w e v e r, th is a s s e s s m e n t fa ils to a c c o u n t fo r d iffe re n c e s in th e ris k p ro file s o f th e
tw o p o r tfo lio s .
T h e S h a r p e r a t io is e s tim a te d u s in g E q u a tio n 7 . 1 7 f o r b o th th e in v e s to r's p o r tf o lio a n d th e A S X 2 0 0
a s fo llo w s :
5 = ^
(7 P
1 3 -5
SPortfolio
•
30
~
1 1 -5
^ASX 200
20
0.27
= 0.30
A s th e S h a r p e r a t io f o r th e p o r tf o lio is less th a n th a t o f th e S & P /A S X 2 0 0 , th e in v e s to r c o n c lu d e s
th a t th e p o r tf o lio h a s u n d e r p e r fo rm e d th e m a rk e t o n a ris k -a d ju s te d b a s is . A p o s s ib le p r o b le m w ith
th is c o n c lu s io n is th a t, a s d e s c r ib e d a b o v e , th e S h a rp e r a t io a ssu m e s th a t th e r e le v a n t m e a s u re o f
ris k fo r th e in v e s to r is to ta l ris k , a s m e a s u re d b y th e s ta n d a r d d e v ia tio n o f re tu rn s . T h is is n o t th e c a s e
w h e r e , f o r e x a m p le , th e p o r tf o lio o f s h a re s re p re s e n ts o n ly o n e c o m p o n e n t o f th e in v e s to r’s o v e r a ll
set o f assets.
T h e T re y n o r ra tio s f o r th e p o r tf o lio a n d f o r th e A S X 2 0 0 a r e m e a s u re d a s fo llo w s :
rp -'rf
Pp
1 3 -5
1.2
1Portfolio
T
'A S X 200
•
6.67
1 1 -5
1.0
6
N o te th a t th e T re y n o r r a t io f o r th e S & P /A S X 2 0 0 is s im p ly e q u a l to th e m a rk e t ris k p re m iu m o f 6 p e r
c e n t. A s th e T re y n o r r a tio o f th e p o r tf o lio e x c e e d s th is a m o u n t th e in v e s to r c o n c lu d e s th a t th e p o r tf o lio
h a s o u tp e r fo r m e d th e m a rk e t o n a s y s te m a tic ris k -a d ju s te d b a s is . W e c a n r e c o n c ile th is re s u lt w ith th e
s e e m in g ly c o n t r a r y re su lts p r o v id e d b y th e S h a rp e r a t io b y a c k n o w le d g in g th a t s o m e o f th e p o r tf o lio
ris k th a t is a c c o u n te d fo r in th e S h a rp e r a tio m a y a c tu a lly b e d iv e r s ifie d a w a y o n c e w e a c c o u n t fo r
th e o th e r asse ts in th e in v e s to r's p o r tf o lio . T h e re fo re , in th is c a s e , th e T re y n o r r a t io p r o v id e s th e m o re
s u ita b le a s s e s s m e n t o f th e p e r fo r m a n c e o f th e p o r tf o lio re la tiv e to th e m a rk e t g e n e r a lly , as it c o n s id e rs
o n ly th a t ris k th a t c a n n o t b e e lim in a te d b y d iv e r s ific a tio n .
Jensen’s alpha
Jensens alpha is a measure pioneered by Michael Jensen17 and relies on a m ulti-pe rio d analysis o f the
performance o f an investm ent p o rtfo lio relative to some proxy fo r the m arket generally. Recall that
the CAPM suggests th a t the relationship between systematic risk and retu rn is fu lly described by the
follow ing equation:
E iR ^ R f+ m R ^ -R f)
The CAPM is an ex-ante single-period model, in the sense th a t it is concerned w ith the returns that
m ig ht be expected over the next tim e period. Its conclusion is relatively simple: the retu rn in excess o f
the risk-free rate th a t we expect any asset i to generate is determ ined only by the level o f systematic risk
reflected in the assets fi. We compute Jensens alpha by im plem enting an ex-post m ulti-period regression
analysis o f the returns on the p o rtfo lio and the returns on the m arket and ask the question: Is there
any evidence o f systematic abnormal retu rn performance th a t cannot be explained by the p o rtfo lio s
systematic risk? The regression equation estimated is as follows:
rP ，t _ r f ，
t= a P +
[rM,r_ rfA + e t
where
t and
are the returns from the p ortfo lio , the risk-free asset and the proxy fo r the m arket
p o rtfo lio th a t have been observed in period t. /3P is an estimate o f the p o rtfo lio s beta over the entire
period in which returns were collected. Qp is an estimate o f Jensens alpha and reflects the incremental
17 See Jensen (1968 & 1969).
C hapter seven Risk
a n d return
performance o f the p o rtfo lio after accounting fo r the variation in p o rtfo lio returns th a t can be explained
by market-wide returns.
I f 〇 tp is positive, and statistically significant, then this is an indication th a t the p o rtfo lio has
outperformed the market, on a risk-adjusted basis, and may be interpreted as evidence o f a p o rtfo lio
managers skill in managing the p ortfolio. Conversely, a statistically significant negative estimate o f
Qp m ight be interpreted as evidence th a t the p o rtfo lio managers actions in managing the p o rtfo lio are
actually destroying value!
There are many other techniques th a t have been developed by academics and practitioners to try
to assess the performance o f investm ent portfolios and each technique brings w ith it both advantages
and disadvantages over the alternative approaches.18 W hile much o f the preceding discussion has been
concerned w ith measuring the relative performance o f a p ortfolio, another issue facing managers and
investors is how much o f the performance o f a p o rtfo lio may be a ttributed to the different decisions made
by the investment manager. Specifically, as described at the beginning o f Section 7.8, an investor may be
concerned w ith how the performance has been affected by the managers decisions w ith respect to asset
allocation, market tim in g and security selection as well as the possible interactions between each o f these
decisions.
This
c h a p te r
d is c u s s e d
tw o
m a in
issues.
The
•
firs t,
S y s te m a tic
ris k
depends
on
th e
c o v a r ia n c e
b e tw e e n th e re tu rn s o n th e a sse t a n d re tu rn s o n th e
p o r tfo lio th e o ry , c o n c e rn s th e a p p r o a c h th a t c a n b e
use d b y ris k -a v e rs e in v e s to rs to s e c u re th e b e s t tr a d e ­
m a rk e t p o r tf o lio , w h ic h c o n ta in s a ll ris k y assets.
o ff b e tw e e n risk a n d re tu rn . S e c o n d , th e c h a p te r d e a lt
T he s y s te m a tic ris k o f a n a s s e t is u s u a lly m e a s u re d
in v o lv e s th e
b y th e a s se t's b e ta fa c to r, w h ic h m e a s u re s th e risk
r e la tio n s h ip b e tw e e n ris k a n d re tu rn in th e m a r k e t fo r
o f th e a s s e t re la tiv e to th e ris k o f th e m a rk e t as
ris k y assets.
a w h o le . R isk-a ve rse in v e s to rs w ill a im
w ith th e p r ic in g
•
o f ris k y a sse ts, w h ic h
T he e s s e n tia l m e s s a g e o f p o r tf o lio
d iv e r s ific a tio n
re d u c e s
ris k .
th e o ry
It is a ls o
is th a t
show n
h ig h e s t e x p e c te d re tu rn fo r a g iv e n le ve l o f risk.
th a t
T he set o f e ffic ie n t p o r tfo lio s fo rm s th e e ffic ie n t
th e e ffe c tiv e n e s s o f d iv e r s ific a tio n d e p e n d s o n th e
c o r r e la tio n o r c o v a r ia n c e
in d iv id u a l
b e tw e e n
assets c o m b in e d
in to
a
fro n tie r, a n d in a m a rk e t w h e r e o n ly ris k y assets
re tu rn s o n th e
p o r tf o lio .
a r e a v a ila b le , e a c h in v e s to r w ill a im to h o ld a
T he
g a in s fro m d iv e r s ific a tio n a r e la rg e s t w h e n th e re is
n e g a tiv e c o r r e la tio n b e tw e e n a s s e t re tu rn s , b u t th e y
p o r tf o lio s o m e w h e re o n th e e ffic ie n t fro n tie r.
•
th a n
p e rfe c t.
In p r a c tic e ,
th e
p o s itiv e
a n d e x p e c te d re tu rn f o r in d iv id u a l ris k y a sse ts. T he
is less
m a in re s u lt is th e C A P M , w h ic h p ro p o s e s th a t th e re
c o r r e la tio n
is a lin e a r r e la tio n s h ip b e tw e e n th e e x p e c te d ra te
th a t e xis ts b e tw e e n th e re tu rn s o n m o st ris k y assets
o f re tu rn o n a n a s s e t a n d its ris k a s m e a s u re d b y its
im p o s e s a lim it o n th e d e g r e e o f ris k r e d u c tio n th a t
c a n b e a c h ie v e d b y d iv e r s ific a tio n .
•
T he to ta l ris k o f a n a s s e t c a n b e d iv id e d in to tw o
b e ta fa c to r.
•
u n s y s te m a tic
ris k th a t re m a in s in a w e ll- d iv e rs ifie d
p o r tf o lio
is
s y s te m a tic ris k .
•
T he ris k o f a w e ll- d iv e rs ifie d
p o r tf o lio
can
be
m e a s u re d b y th e s ta n d a r d d e v ia tio n o f p o r tf o lio
re tu rn s .
H o w e v e r,
a n a ly s is
o f th e
fa c to rs
th a t
c o n trib u te to th is s ta n d a r d d e v ia tio n s h o w s th a t,
asset
re tu rn s
p r ic in g
a re
m o d e ls
lin e a r ly
p ro p o s e
re la te d
to
th a t
m u ltip le
fa c to rs ra th e r th a n th e s in g le m a rk e t fa c to r p ro p o s e d
ris k th a t can b e
e lim in a te d b y d iv e r s ific a tio n . It f o llo w s th a t th e o n ly
A lte r n a tiv e
e x p e c te d
p a rts : s y s te m a tic ris k th a t ca n n o t b e e lim in a te d b y
d iv e r s ific a tio n , a n d
In tro d u c tio n o f a ris k -fre e a s s e t a llo w s th e a n a ly s is to
b e e x te n d e d to m o d e l th e r e la tio n s h ip b e tw e e n ris k
still e x is t w h e n th e re is p o s itiv e c o r r e la tio n b e tw e e n
a s s e t re tu rn s , p r o v id e d th a t th e c o r r e la tio n
to h o ld
p o r tfo lio s th a t a r e e ffic ie n t in th a t th e y p r o v id e th e
b y th e C A P M .
•
A s s e s s m e n t o f th e
p e r fo r m a n c e
o f an
in v e s tm e n t
p o r tf o lio re q u ire s th e s p e c ific a tio n o f th e 'e x p e c t e d '
p e r fo r m a n c e o f a b e n c h m a r k p o r tfo lio .
An
e x c e lle n t s ite
w ith
r e la tin g to th is t o p ic is
a
w e a lth
of
in fo r m a tio n
vsww.wsharpe.com.
P ro fe s s o r
W illia m S h a rp e 's w o r k w a s r e c o g n is e d w ith a N o b e l
fo r in v e s to rs w h o d iv e rs ify , th e re le v a n t m e a s u re
P riz e in 1 9 9 0 . F in a n c ia l a d v is o r y in fo r m a tio n c a n a ls o
o f ris k f o r a n in d iv id u a l a s s e t is its s y s te m a tic risk.
b e fo u n d a t
www.moneysmart.gov.au.
18 See Chapter 24 of Bodie, Kane and Marcus (2013) for an excellent review of some of these alternative techniques, and a
comprehensive description of other issues faced when assessing portfolio performance.
CHAPTER SEVEN REVIEW
SUMMARY
B usiness finance
KEY TERMS
b e ta
187
c a p ita l m a rk e t lin e
m a rk e t m o d e l
s e c u rity m a rk e t lin e
193
s ta n d a rd d e v ia tio n
174
s y s te m a tic (m a rk e 卜
re la te d o r n o n -d iv e rs ifia b le )
195
m a rk e t p o r tfo lio
p o r tfo lio
192
192
ris k
179
186
u n s y s te m a tic (d iv e rs ifia b le ) ris k
ris k -a v e rs e in v e s to r
176
v a lu e a t ris k
ris k -n e u tra l in v e s to r
176
v a r ia n c e
ris k -s e e k in g in v e s to r
186
187
174
176
SELF-TEST PROBLEMS
1
A n in v e s to r p la c e s 3 0 p e r c e n t o f h is fu n d s in S e c u rity X a n d th e b a la n c e in S e c u rity Y. T he e x p e c te d
re tu rn s o n X a n d Y a r e 1 2 a n d 1 8 p e r c e n t, re s p e c tiv e ly . T he s ta n d a rd d e v ia tio n s o f re tu rn s o n X a n d Y
a r e 2 0 a n d 1 5 p e r c e n t, re s p e c tiv e ly .
a)
C a lc u la te th e e x p e c te d re tu rn o n th e p o r tfo lio .
b)
C a lc u la te th e v a r ia n c e o f re tu rn s o n th e p o r tfo lio a s s u m in g th a t th e c o r r e la tio n b e tw e e n th e re tu rn s o n
th e tw o s e c u ritie s is:
i) + 1 . 0
ii) + 0 . 7
iii) 0
iv) - 0 . 7
2
A n in v e s to r h o ld s a p o r tf o lio th a t c o m p ris e s 2 0 p e r c e n t X, 3 0 p e r c e n t Y a n d 5 0 p e r c e n t Z . T h e s ta n d a rd
d e v ia tio n s o f re tu rn s o n X, Y a n d Z a re 2 2 , 1 5 a n d 1 0 p e r ce n t, re s p e c tiv e ly , a n d th e c o r r e la tio n b e tw e e n
re tu rn s o n e a c h p a ir o f s e c u ritie s is 0 . 6 . P re p a re a v a r ia n c e - c o v a r ia n c e m a tr ix f o r th e se th re e s e c u ritie s a n d
use th e m a tr ix to c a lc u la te th e v a r ia n c e a n d s ta n d a rd d e v ia tio n o f re tu rn s f o r th e p o r tfo lio .
3
T he ris k -fre e r a te o f re tu rn is c u r r e n tly 8 p e r c e n t a n d th e m a rk e t ris k p re m iu m is e s tim a te d to b e
6 p e r c e n t. T h e e x p e c te d re tu rn s a n d b e ta s o f fo u r s h a re s a r e a s fo llo w s :
Expected return [%)
Beta
Carltown
13.0
0.7
Pivot
17.6
Forresters
14.0
i.i
Brunswick
10.4
0.4
I S h a re
丨
W h ic h sh a re s a re u n d e rv a lu e d , o v e r v a lu e d o r c o rre c tly v a lu e d b a s e d o n th e C A P M ?
Solutions to self-test problems are available in Appendix B.
t y
1
[LO 1]
QUESTIONS
F a rm e rs c a n in s u re th e ir c r o p s a g a in s t d a m a g e b y h a ils to rm s a t r e a s o n a b le ra te s . H o w e v e r , th e s a m e
in s u ra n c e c o m p a n ie s re fu s e to p r o v id e f lo o d in s u ra n c e a t a n y p r ic e . E x p la in w h y th is s itu a tio n e xists.
2
[LO 2]
Is ris k a v e rs io n a r e a s o n a b le a s s u m p tio n ? W h a t is th e re le v a n t m e a s u re o f ris k f o r a ris k -a v e rs e
in v e s to r?
204
C hapter seven Risk
[L O 3 i W h a t a r e th e b e n e fits o f d iv e r s ific a tio n to a n in v e s to r? W h a t is th e k e y fa c to r d e te r m in in g th e e x te n t
o f th e se b e n e fits ?
4
[LO 4 ] E x p la in e a c h o f th e f o llo w in g :
a)
th e e 仟
ic ie n t fro n tie r
b)
th e c a p ita l m a rk e t lin e
c)
th e s e c u rity m a rk e t lin e .
Risky assets con be combined to form a riskless asset. D iscuss.
5
[L O 5 ]
6
[L O 5 】Whenever
7
[L O 6 ]
an asset is added to a portfolio, the total risk o f the portfolio w ill be reduced p rovided the
returns o f the asset and the portfolio ore less than perfectly correlated. D iscuss.
Total risk can be decomposed into systematic and unsystematic risk. E x p la in e a c h c o m p o n e n t o f ris k ,
a n d h o w e a c h is a ffe c te d b y in c re a s in g th e n u m b e r o f s e c u ritie s in a p o r tfo lio .
8
[L O 7 】Diversification is certainly good for investors. Therefore, investors should be prepared to p ay a
premium for the shores o f companies that operate in several lines o f business. E x p la in w h y th is s ta te m e n t is
tru e o r fa ls e .
9
[L O 7 】M in c o Ltd, a la r g e m in in g c o m p a n y , p r o v id e s a s u p e r a n n u a tio n fu n d fo r its e m p lo y e e s . T he fu n d 's
m a n a g e r s a y s : 'W e k n o w th e m in in g in d u s try w e ll, so w e fe e l c o m fo r ta b le in v e s tin g m o s t o f th e fu n d in a
p o r tf o lio o f m in in g c o m p a n y s h a re s ’ . A d v is e M in c o ’s e m p lo y e e s o n w h e th e r to e n d o rs e th e fu n d ’s in v e s tm e n t
p o lic y .
C H A P T E R SEVEN! R E V I E W
3
a n d return
An important conclusion o f the CAPM is that the relevant measure o f an asset's risk is its systematic
risk. O u tlin e th e s ig n ific a n c e o f th is c o n c lu s io n fo r a m a n a g e r m a k in g f in a n c ia l d e c is io n s .
10
[L O 8 ]
11
[L O 8 】F o r in v e s to rs w h o a im to d iv e rs ify , s h a re s w ith n e g a tiv e b e ta s w o u ld b e v e r y u se fu l in v e s tm e n ts , b u t
such s h a re s a r e v e r y ra re . E x p la in w h y f e w s h a re s h a v e n e g a tiv e b e ta s .
12
[LO 8 ] C o m p a r e a n d c o n tra s t th e c a p it a l a s s e t p r ic in g m o d e l a n d m o d e ls th a t in c lu d e a d d itio n a l fa c to rs .
13
[L O 1 1 ] In w h a t s itu a tio n s w o u ld it b e a p p r o p r ia t e to use a s im p le b e n c h m a r k in d e x , such a s th e S & P /A S X
14
[L O ll]
2 0 0 s h a re p r ic e in d e x , to assess th e p e r fo r m a n c e o f a p o r tfo lio ?
When assessing the performance o f o set o f portfolios it does not really matter if you choose the
Shorpe ratio or the Treynor ratio to do so os both approaches account for the risk inherent in the portfolios.
D iscuss.
PROBLEMS
1
V a lu e a t r is k [L O 1 ]
C o n s id e r a p o r tfo lio c o m p ris in g a $ 3 m illio n in v e s tm e n t in O u tlo o k P u b lis h in g a n d a $ 5 m illio n in v e s tm e n t in
Russell C o m p u tin g . A s s u m e th a t th e s ta n d a rd d e v ia tio n s o f th e re tu rn s fo r sh a re s in the se c o m p a n ie s a r e 0 . 4
a n d 0 . 2 5 p e r c e n t p e r a n n u m re s p e c tiv e ly . A s s u m e a ls o th a t th e c o r r e la tio n b e tw e e n th e re tu rn s o n th e sh a re s
in these c o m p a n ie s is 0 . 7 . A s s u m in g a 1 p e r c e n t c h a n c e o f a b n o r m a lly b a d m a rk e t c o n d itio n s , c a lc u la te th e
v a lu e a t risk o f th is p o r tfo lio . S tate a n y a s s u m p tio n s th a t y o u m a k e in y o u r c a lc u la tio n s .
2
In v e s tm e n t a n d r is k [L O 2 ]
M r B o b N e il is c o n s id e r in g a 1 -y e a r in v e s tm e n t in sh a re s in o n e o f th e f o llo w in g th re e c o m p a n ie s .
•
C o m p a n y X: e x p e c te d re tu rn
= 1 5% w ith a s ta n d a rd d e v ia tio n o f 1 5%
•
C o m p a n y Y: e x p e c te d re tu rn
= 1 5 % w ith a s ta n d a rd d e v ia tio n o f 2 0 %
•
C o m p a n y Z : e x p e c te d re tu rn
= 2 0 % w ith a s ta n d a rd d e v ia tio n o f 2 0 %
R a n k th e in ve s tm e n ts in o r d e r o f p re fe re n c e fo r e a c h o f th e ca s e s w h e r e it is a s s u m e d th a t M r B o b N e il is:
a)
risk a v e rs e
b)
risk n e u tra l
c)
risk s e e k in g .
G iv e re a s o n s .
205
Portfolio standard deviation and diversification [LO 3]
The s ta n d a rd d e v ia tio n s o f re tu rn s o n assets A a n d B a r e 8 p e r c e n t a n d 1 2 p e r c e n t, re s p e c tiv e ly . A p o r tfo lio
is c o n s tru c te d c o n s is tin g o f 4 0 p e r c e n t in A s s e t A a n d 6 0 p e r c e n t in A sse t B. C a lc u la te th e p o r tfo lio s ta n d a rd
d e v ia tio n if th e c o r r e la tio n o f re tu rn s b e tw e e n th e tw o assets is:
a)
1
b)
0 .4
c)
0
d)
-1
G om m ^nt on y o u 「
a n s w e rs .
Expected return, variance and risk [LO 3]
You b e lie v e th a t th e re is a 5 0 p e r c e n t c h a n c e th a t th e s h a re p r ic e o f C o m p a n y L w ill d e c re a s e b y 1 2 p e r c e n t
a n d a 5 0 p e r c e n t c h a n c e th a t it w ill in c re a s e b y 2 4 p e r ce n t. F urther, th e re is a 4 0 p e r c e n t c h a n c e th a t th e
s h a re p r ic e o f C o m p a n y M w ill d e c re a s e b y 1 2 p e r c e n t a n d a 6 0 p e r c e n t c h a n c e th a t it w ill in c re a s e b y
2 4 p e r ce n t. T h e c o rre la tio n c o e ffic ie n t o f th e re tu rn s o n sh a re s in th e tw o c o m p a n ie s is 0 . 7 5 . C a lc u la te :
a)
th e e x p e c te d re tu rn , v a r ia n c e a n d s ta n d a rd d e v ia tio n fo r e a c h c o m p a n y 's sh a re s
b)
th e c o v a r ia n c e b e tw e e n th e ir return s.
Variance of return [LO 5]
A n in v e s to r p la c e s 4 0 p e r c e n t o f h e r fu n d s in C o m p a n y A 's sh a re s a n d th e r e m a in d e r in C o m p a n y B7s sha res.
T he s ta n d a rd d e v ia tio n o f th e re tu rn s o n A is 2 0 p e r c e n t a n d o n B is 1 0 p e r c e n t. C a lc u la te th e v a r ia n c e o f
re tu rn o n th e p o r tfo lio , a s s u m in g th a t th e c o r r e la tio n b e tw e e n th e re tu rn s o n th e tw o se c u ritie s is:
a)
+ 1 .0
b)
+ 0 .5
c) 〇
d)
-0 .5
Expected return, risk and diversification [LO 5 】
H a r r y Jo n e s h a s in v e s te d o n e -th ird o f his fu n d s in S h a re 1 a n d tw o -th ird s o f his fu n d s in S h a re 2 . H is
asse ssm en t o f e a c h in v e s tm e n t is as fo llo w s :
Item
S h a re
1
S h a re 2
Expected return (%)
15.0
21.0
Standard deviation (%)
18.0
25.0
Correlation between the
returns
0.5
a)
b)
W h a t a re th e e x p e c te d re tu rn a n d th e s ta n d a rd d e v ia tio n o f re tu rn o n H a r r y 's p o rtfo lio ?
R e c a lc u la te th e e x p e c te d re tu rn a n d th e s ta n d a rd d e v ia tio n w h e r e th e c o r r e la tio n b e tw e e n th e re tu rn s is
0 a n d 1 .0 , re s p e c tiv e ly .
c)
Is H a r r y b e tte r o r w o r s e o ff as a re su lt o f in v e s tin g in tw o s e c u ritie s ra th e r th a n in o n e se c u rity ?
Expected return, risk and diversification [LO 5]
A
12.5
40
1.00
0.20
0.35
B
16.0
45
0.20
1.00
0.10
C
20.0
60
0.35
0.10
1.00
C hapter seven Risk
a n d return
a)
P o rtfo lio 1 co n sists o f 4 0 p e r c e n t A s s e t A a n d 6 0 p e r c e n t A sse t B. C a lc u la te its e x p e c te d re tu rn a n d s ta n d ­
a r d d e v ia tio n .
b)
P o rtfo lio 2 co n sists o f 6 0 p e r c e n t A sse t A , 2 2 . 5 p e r c e n t A s s e t B a n d 1 7 .5 p e r c e n t A s s e t C . C a lc u la te its
e x p e c te d re tu rn a n d s ta n d a rd d e v ia tio n . C o m p a re y o u r a n s w e rs to (a) a n d c o m m e n t.
c)
P o rtfo lio 3 co n sists o f 4 . 8 p e r c e n t A s s e t A , 7 5 p e r c e n t A s s e t B a n d 2 0 . 2 p e r c e n t in th e risk-fre e asset.
C a lc u la te its e x p e c te d re tu rn a n d s ta n d a rd d e v ia tio n . C o m p a re y o u r a n s w e rs to (a) a n d (b) a n d c o m m e n t.
d)
P o rtfo lio 4 is a n e q u a lly w e ig h te d p o r tfo lio o f th e th re e ris k y assets A , B a n d C . C a lc u la te its e x p e c te d
re tu rn a n d s ta n d a rd d e v ia tio n a n d c o m m e n t o n the se results.
e)
P o rtfo lio 5 is a n e q u a lly w e ig h te d p o r tfo lio o f a ll fo u r assets. C a lc u la te its e x p e c te d re tu rn a n d s ta n d a r d
d e v ia tio n a n d c o m m e n t o n th e se results.
8
Expected return and systematic risk [LO 7 】
The e x p e c te d re tu rn o n th e /th a sse t is g iv e n b y:
E L R f+_ R
a)
M]-R
f 、
W h a t is th e e x p e c te d re tu rn o n th e /th a sse t w h e r e Rf = 0 . 0 8 , fi- = 1 . 2 5 a n d f(/?yvi) = 0 . 1 4 ?
b) W h a t is th e e x p e c te d re tu rn o n th e m a rk e t p o r tf o lio w h e r e E(Rj) = 0 . 1 1 ,
c)
9
= 0 . 0 8 a n d p y= 0 . 7 5 ?
W h a t is th e s y s te m a tic ris k o f th e /th a sse t w h e re E(Rt ) = 0 . 1 4 , ^ = 0 . 1 0 a n d E(RM) = 0 . 1 5 ?
Assessing diversification benefits [LO 7 】
CHAPTER SEVEN REVIEW
T h e re is a ls o a risk-fre e A s s e t F w h o s e e x p e c te d re tu rn is 9 . 9 p e r ce n t.
You a re a s h a re a n a ly s t e m p lo y e d b y a la r g e m u ltin a tio n a l in v e s tm e n t fu n d a n d h a v e b e e n s u p p lie d w ith th e
fo llo w in g in fo rm a tio n :
S ta n d a rd d e v ia tio n (%)
E x p e c te d re tu rn (%)
A sse t
BHZ Ltd
9
8
ANB Ltd
13
48
1
You a re a ls o to ld th a t th e c o r r e la tio n c o e ffic ie n t b e tw e e n th e re tu rn s o f th e tw o c o m p a n ie s is 0 . 8 . A c lie n t
c u rre n tly h a s a ll o f h e r w e a lth in v e s te d in B H Z s h a re s. S he w is h e s to d iv e r s ify h e r p o r tf o lio b y re d is trib u tin g h e r
w e a lth such th a t 3 0 p e r c e n t is in v e s te d in B H Z sh a re s a n d 7 0 p e r c e n t in A N B sh a re s.
a)
W h a t w ill b e th e e x p e c te d re tu rn o f th e n e w p o r tfo lio ?
b)
W h a t w ill b e th e s ta n d a rd d e v ia tio n o f re tu rn s fo r th e n e w p o rtfo lio ?
A fte r c o n s tru c tin g th e p o r tfo lio a n d r e p o r tin g th e results to y o u r c lie n t, she is q u ite u p se t, s a y in g , 7I th o u g h t
th e w h o le p u rp o s e o f d iv e r s ific a tio n w a s to re d u c e risk? Yet y o u h a v e ju st to ld m e th a t th e v a r ia b ility o f m y
p o r tfo lio h a s a c tu a lly b e e n in c re a s e d fro m w h a t it w a s w h e n I in v e s te d o n ly in B H Z ’ .
c)
P ro v id e a re s p o n s e to y o u r c lie n t th a t d e m o n s tra te s th a t th e n e w p o r tfo lio d o e s o r d o e s n o t re fle c t th e b e n e ­
fits o f d iv e rs ific a tio n . S h o w a ll n e c e s s a ry c a lc u la tio n s .
10
Portfolio weights systematic risk and unsystematic risk [LO 8 】
T he ta b le p ro v id e s d a ta o n tw o ris k y assets, A a n d B, th e m a rk e t p o r tf o lio M a n d th e ris k-fre e a sse t F.
Asset
E x p e c te d re tu rn (%)
A
A
10.8
324
60
48
0
B
15.6
60
289
96
0
M
14.0
48
96
80
0
F
6.0
0
0
0
0
A n in v e s to r w is h e s to a c h ie v e a n e x p e c te d re tu rn o f 1 2 p e r c e n t a n d is c o n s id e rin g th re e w a y s this m a y b e
done:
a)
in v e s t in A a n d B
b)
in v e s t in B a n d F
c)
in v e s t in M a n d F.
207
B usiness finance
F or e a c h o f th e se o p tio n s , c a lc u la te th e p o r tfo lio w e ig h ts r e q u ire d a n d th e p o r tfo lio s ta n d a rd d e v ia tio n . S h o w
th a t assets A a n d B a re p r ic e d a c c o r d in g to th e c a p ita l a sse t p r ic in g m o d e l a n d , in th e lig h t o f th is result,
c o m m e n t o n y o u r fin d in g s .
11
Portfolio performance appraisal [LO 11 ]
In 2 0 1 4 th e re tu rn o n th e F o rt K n o x Fund w a s 1 0 p e r ce n t, w h ile th e re tu rn o n th e m a rk e t p o r tfo lio w a s
1 2 p e r c e n t a n d th e risk-fre e re tu rn w a s 3 p e r ce n t. C o m p a ra tiv e sta tistics a r e s h o w n in th e ta b le b e lo w .
S ta tis tic
F o rt K n o x fu n d
S & P /A S X 2 0 0 sh a re
p r ic e in d e x
Standard deviation of return
15%
30%
Beta
0.75
1.00
C a lc u la te a n d c o m m e n t o n th e p e rfo rm a n c e o f th e fu n d u s in g th e fo llo w in g th re e a p p ro a c h e s :
a)
th e s im p le b e n c h m a rk in d e x
b)
th e S h a rp e ra tio
c)
th e T re y n o r ra tio .
REFERENCES
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2 0 0 2 , pp. 6 3 7 -5 9 .
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pedagogical use', Accounting a n d Finance, M a y 1993,
pp. 5 3 -6 0 .
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P ortfolio choice and asset prices: the
importance of entrepreneurial risk', Journal of Finance, June
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risk premium', A pril 2 0 0 5 , Yale ICF W orking Paper No.
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factors in Australia7, Australian Journal of Management,
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------ , Handley, J. & M aheswaran, K., The historical equity
risk premium in Australia: post-GFC and 128 years of data7,
Accounting and Finance, M arch 2 0 1 2 , pp. 2 3 7 -4 7 .
Carhart, M . M w 'O n persistence in mutual fund
performance', Journal of Finance, March 1997, pp. 5 7 -8 2 .
Claus, J. & Thomas, J., 'Equity premia as low as three per
cent? Evidence from analysts' earnings forecasts for domestic
and international stock markets7, Journal of Finance, O ctober
2 0 0 1 , pp. 1 6 2 9 -6 6 .
Coleman, L, M aheswaran, K. & Pinder, S., 'Narratives in
managers, corporate finance decisions', Accounting and
Finance, September 2 0 1 0 ; pp. 6 0 5 -3 3 .
Dimson, E., Marsh, P.R., Staunton, M . & G arthwaite, A.,
Credit Suisse G lobal Investment Returns Yearbook, Credit
Suisse A G Research Institute, Zurich, 20 1 3 .
Fama, E.F., 'Risk, return and equilibrium : some clarifying
comments', J o u rn o /o f F/nonce, M arch 1968, pp. 2 9 -4 0 .
-------, Foundations of Finance, Basic Books, N ew York,
1976.
------ & French, K.R., 'The cross-section of expected stock
returns', Journal of Finance, June 1 9 9 2 ; pp. 4 2 7 -6 5 .
------ , ------- , 'Common risk factors in the returns on stocks
and bonds', Journal of Financial Economics, February 1993,
pp. 3 -5 6 .
------ , ------- , 'M ultifactor explanations o f asset pricing
anomalies', Journal of Finance, March 1996, pp. 5 5 -8 4 .
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Jegadeesh, N . & Titman, S., 'Returns to buying winners and
selling losers: implications for market efficiency7, Journal of
Finance, 1993, pp. 6 5 -9 1 .
Jensen, M ., The performance of mutual funds in the period
1 9 4 5 -1 9 6 4 ', Jo u rn o /o f F/nonce, M a y 1 9 6 8 ; pp. 3 8 9 -4 1 6 .
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of investment portfolios', Journal of Business, April 1969,
pp. 1 6 7 -2 4 7 .
-------, 'C apital markets: theory and evidence7, Bell Journal
of Economics a n d M anagem ent Science, Autumn 1972,
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Value at Risk: The N e w Benchmark for Controlling
Market Risk, 3rd edn, M cG raw -H ill, Chicago, 2 0 0 6 .
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the twentieth century,/ Journal of Finance, June 1999,
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Levy, H. & Sarnat, M ., Capitol Investment a n d Financial
Decisions, 4th edn; Prentice-Hall, N ew Jersey, 1990,
pp. 3 1 9 -2 2 .
Lintner, J., ;The valuation of risk assets and the selection of
risky investments in stock portfolios and capital budgets',
Review of Economics and Statistics, February 1965,
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M arkow itz, H .M ., 'Portfolio selection', Journal of Finance,
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Investments, John W ile y & Sons, N ew York, 1959.
C hapter seven Risk
Sharpe, W.F., 'C apital asset prices: a theory of market
equilibrium under conditions of risk', Journal of Finance,
September 1964, pp. 4 2 5 -4 2 .
Mossin, Jw 'Security pricing and investment criteria in
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1969, pp. 7 4 9 -5 6 .
-------, 'Mutual fund performance', Journal of Business,
January 1966, pp. 1 1 9 -3 8
PricewaterhouseCoopers, Investigation into Foreign
Exchange Losses at the National Australia Bank, Melbourne,
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Statman, M ., 'H ow many stocks make a diversified
portfolio?', Joumcr/ o f F/ncmaa/ anc/ Gt/cmf/faf/Ve
September 1987, pp. 3 5 3 -6 3 .
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Treynor, J.L, 'H ow to rate management investment funds',
January 1966, Harvard Business Review, pp. 6 3 -7 5 .
Roll, R., 'A critique of the asset pricing theory's tests; Part 1:
On the past and potential testability of the theory', Journal of
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2 0 0 5 , pp. 6 7 -1 0 3 .
CHAPTER SEVEM REVIEW
Mehra, R. (& Prescott, E.C., 'The equity premium: a puzzle',
Journal of Monetary Economics, M arch 1985, pp. 1 4 5 -6 1 .
a n d return
209
CHAPTER CONTENTS
ED
I n t r o d u c t io n
21 1
EB
F in a n c ia l in t e r m e d ia r ie s
220
EQ
F in a n c ia l a g e n c y in s titu tio n s
215
ESI
In v e s tin g in s titu tio n s
224
LEARNING OBJECTIVES
A f t e r s tu d y in g th is c h a p t e r y o u s h o u ld b e a b le to :
1
u n d e r s ta n d th e f u n c tio n s o f a c a p it a l m a r k e t
2
d is tin g u is h b e t w e e n f in a n c ia l a g e n c y in s titu tio n s , f in a n c ia l in t e r m e d ia r ie s a n d in v e s tin g in s titu tio n s
3
4
5
id e n t if y a n d e x p la in th e r o le o f f in a n c ia l a g e n c y in s titu tio n s
o u t lin e th e r o le o f s e c u r it is a tio n
6
id e n t if y a n d e x p la in th e r o le o f in v e s tin g in s titu tio n s .
id e n t if y a n d e x p la in th e r o le o f f in a n c ia l in t e r m e d ia r ie s
Z
C hapter eight T he
capital market
■ jjJ ~ l^ tr o d u c tio n
In Chapters 5 and 6 we discussed the methods used to select a company s assets. The company also has
to decide how to finance those assets. Where w ill the money come from? Is the money needed fo r a long
time, or only a short time? Depending on the answers to these and related questions, the company w ill
enter in to different arrangements and different types o f financial assets w ill be created.
Financial a sse ts are legally enforceable claims to future cash flows. Bank deposits, trade creditors,
debt securities and shares are different types o f financial assets. The markets in which financial assets are
bought and sold are commonly referred to as financial markets and include the equity (share) market, the
bond m arket and the foreign exchange m arket. The financial markets in which companies raise long-term
funds are referred to collectively as the capital m arket. In this chapter we discuss the benefits o f having
a capital m arket and the m ajor features o f the Australian capital m arket, paying p articular attention to
the characteristics o f the im p o rta n t in stitu tio n s th a t participate in the market.
Over a given period an economic e n tity such as an individual, a company or an unincorporated business
w ill be either a ‘deficit u n it’ or a ‘surplus u n it’. A deficit u n it is one whose expenditure exceeds its income
for a particular period, whereas a surplus u n it is one whose income exceeds its expenditure fo r a particular
period. The financing process involves a flow o f funds from the surplus units to the deficit units.
I f a company wishes to grow, b ut does n o t generate sufficient funds interna lly to finance an increase
in its assets— th a t is, the company is a deficit u n it— it w ill need to finance the difference by drawing
on the funds held by surplus u nits.1 Surplus units may be households, businesses, governments or the
overseas sector.
The flow o f funds from surplus units to deficit units may be direct or indirect. A direct flow o f funds
may result solely from negotiation between the parties, or a financial in s titu tio n may be involved as an
adviser or underw riter.2 For example, when a company issues (that is, creates and sells) debt securities,
an investm ent bank may advise on and/or underw rite the issue.3 However, the funds w ill flow directly
from the purchasers o f the debt securities to the issuing company. D irect funding is more commonly used
where the borrower has a recognised credit rating and wishes to raise relatively large amounts.
Alternatively, the flow o f funds may be indirect— th a t is, i t occurs through financial interm e­
diaries, such as banks and finance companies. In this case the deficit u n it obtains funds from a
financial interm ediary th a t has borrowed the funds from surplus units. Interm ediated funding is
more commonly used where the credit risk o f the deficit u n it (the borrower) needs to be assessed, and
where the amounts fo r both borrowers and lenders are relatively small. Financial intermediaries have an
im portant role in facilitating the flow o f funds from surplus units to deficit units.
The number o f financial assets th a t are created in the overall financing process is an im p o rta n t
difference between direct and indirect financing. I f a company raises funds directly by, fo r example,
issuing a bond to an investor (lender), only one financial asset has been created. The bond is a financial
asset held by the investor and it is a lia b ility o f the company. In contrast, i f the investor deposits funds in a
bank, which then makes a loan to a company, two financial assets are created. The bank deposit is an asset
owned by the investor and the bank loan is an asset owned by the bank. Corresponding to these tw o assets
are two liabilities. The deposit is a lia b ility o f the bank and the bank loan is a lia b ility o f the borrower.
FINANCIAL ASSETS
assets such as shares,
bonds and bank
deposits, as distinct
from real assets
CAPITAL MARKET
market in which long­
term funds are raised
and long-term debt
and equity securities
are traded
FINANCIAL
INTERMEDIARY
institution that acts
as a principal in
accepting funds from
depositors or investors
and lending them to
borrowers
m
The capital m arket enables the suppliers o f funds (the surplus units) and the users o f funds (the deficit
units) to negotiate the conditions on which the funds w ill be transferred. Equity or share markets involve
1
2
3
Internally generated funds are discussed in Section 9.8.
Underwriting is discussed further in Section 8.2.2.
The activities of investment banks are discussed in Section 8.2.2. These institutions were generally referred to as merchant
banks until the early 1990s when the US term investment bank' was widely adopted in Australia. In this chapter we use the
latter term, except in cases where the historical context makes the earlier term appropriate.
LEARNING
OBJECTIVE 1
Understand the
functions of a capital
market
B usiness finance
ownership and usually a permanent transfer o f funds, w ith returns to shareholders contingent on the
future p ro fita b ility o f the company raising the funds. Debt markets usually involve a transfer o f funds fo r
a fin ite period, w ith predetermined promised returns to lenders. In the finance literature, equity and debt
markets together form the capital m arket.4
PRIMARY MARKET
market for new issues
of securities where
the sale proceeds go
to the issuer of the
securities
SECONDARY MARKET
market where
previously issued
securities are traded
EXCHANGE-TRADED
MARKET
market in which
trading takes place by
competitive bidding
on an organised
exchange
OVER-THE-COUNTER
MARKET
there is no organised
exchange and the
market consists of
financial institutions
that are willing
to trade with a
counterparty
Financial markets may be classified in several ways. For example, the d istinction between debt markets
and equity markets is based on the type o f financial asset th a t is traded in the market. Similarly, markets
fo r financial assets may be either prim ary m arkets, where financial assets are firs t sold by th e ir
originators, or secondary m arkets, where pre-existing financial assets are traded.
Prim ary markets are im p o rta n t because it is in these markets th a t a deficit u n it— fo r example, a
company— raises new funds to finance its investments. For example, a company may make a new share
issue or a new bond issue to finance the development o f a new m ine or the acquisition o f another business.
A transaction in the secondary m arket does n ot raise any new funds fo r the issuer o f the securities
th a t are traded. A ll th a t happens is a change o f ownership; the seller o f the security transfers, fo r a price,
ownership o f the security to the buyer. However, secondary markets are im p o rta n t because they provide
a way in which securities can be exchanged fo r cash— th a t is, they provide liquidity. The existence o f a
secondary m arket enables companies to raise long-term funds, even though individual suppliers o f funds
may be w illin g to provide funds only fo r much shorter terms. For example, a company may issue a 7-year
bond to an investor who wishes to invest fo r only 3 years. The investor is w illin g to buy the bond because
she knows that, after 3 years have passed, she w ill be able to sell the bond in the secondary m arket. In
this way, the existence o f an active secondary m arket facilitates capital raising in the p rim ary market.
W ith o u t an active secondary m arket, many investors would n o t participate in prim ary markets because
they require the fle xib ility to redeploy th e ir funds. The secondary m arket provides this flexibility.
A nother im p o rta n t d istin ction between different financial markets is based on the organisational
structure o f the markets. Indirect financing takes place through financial intermediaries, which raise
funds by issuing financial claims against themselves and use those funds to purchase financial assets,
most o f which cannot be traded in a secondary m arket. For example, a loan provided by a bank is often
retained as an asset o f th a t bank u n til it has been repaid. In contrast, the financial assets created through
direct financing are usually marketable securities. These securities may be traded through an organised
exchange or they may be traded in an over-the-counter market. In an exchange-traded m arket,
securities are traded through an organised exchange such as a stock exchange, where brokers carry out
d ie nts, instructions to buy or sell nom inated securities. In an over-the-counter m arket there is no
organised exchange and the m arket consists o f financial in s titu tio n s (dealers) who trade w ith clients
and w ith each other. The Australian capital m arket includes financial intermediaries and markets o f both
these types. Exchange-traded securities include shares, options on shares and futures contracts. Debt
securities, swaps and currency options are usually traded in over-the-counter markets.
Some features o f the financial system remain essentially constant over tim e while other features are
subject to change, which may be gradual or, in some cases, very rapid. For example, banks have had
a very im p o rta n t role in Australia since the firs t bank was established in 1817. However, the relative
importance o f banks has varied over tim e — many new banks have entered the market, a few banks have
failed and several have been acquired by other banks. The factors th a t can trigger significant changes in
the financial system include changes in regulation and technology, changes in the demand fo r different
form s o f funding and the effects o f financial crises.
The evolution and expansion o f the Australian financial markets in the last three decades were largely
an outcome o f the deregulation o f those markets in the 1980s. W hile the Australian financial markets
have been largely deregulated, this deregulation has n o t extended to the removal o f controls th a t serve
a prudential purpose. The p rim ary regulator o f Australia’s banks, insurance companies, superannuation
4
In practice, participants in the financial markets usually refer to the direct short-term debt market—that is, where loans are
for 12 months or less—as the m on ey m ark e t. The term c a p ita l m a r k e t is used to describe the direct long-term debt market.
C hapter eight T he
funds, credit unions and b uilding societies is the Australian Prudential Regulation A u th o rity (APRA,
www.apra.gov.au). In 1998, APRA took over prudential supervision functions from Australia’s central
ban k — the Reserve Bank o f Australia (RBA, www.rba.gov.au).
Arguably, the m ost im p o rta n t role fu lfille d by banking regulatory authorities is ensuring that
depositors* funds are adequately protected. One way o f protecting the interests o f depositors is to require
banks to m aintain an adequate level o f ‘capital’ （
fo r example, shareholders’ funds): the more capital a
bank has, the more it relies on its shareholders fo r funding and hence the less it relies on its depositors.
Therefore, the depositors are safer than they otherwise would be. I f a bank is judged by the regulator to
be carrying too much risk, it can be required to increase its capital, thus sh ifting more o f the cost o f risk­
bearing from the banks depositors to the banks shareholders.
In 1988, the Basel Committee on Banking Supervision established a set o f recommendations known
as the 1988 Capital Accord (or sim ply the Basel Accord). The Basel Committee was established by the Bank
fo r International Settlements (BIS, w w w .bis.org), which its e lf can be thought o f as a bank fo r central
banks. To illustrate one simple consequence o f the Basel Accord, a banks loan to a company would be
judged to be twice as risky as a loan secured by a firs t mortgage over fam ily-held real estate. Hence, twice
as much capital m ust be m aintained by the bank to protect the depositors.
Gup (2004) notes that during the period from 1980 to 1996, 133 o f the 181 member countries o f the
International M onetary Fund experienced serious banking sector problems, including those countries that
adopted the 1988 accord. Some o f the deficiencies o f the first set o f recommendations have been addressed
in a second accord, commonly referred to as Basel II, which provides a more comprehensive method by which
banks account for risk.5 The Basel II framework has applied in Australia from 1 January 2008.
The adequacy o f m any aspects o f bank regulation was called in to question by the global financial
crisis th a t began in m id-2007 when problems th a t o riginated in credit m arkets in the US became
widespread th ro ug h ou t the developed nations. This crisis saw tu rm o il in m any financial m arkets
during 2008 and 2009 and the failure or near-failure o f many financial in s titu tio n s in the US, the
UK and Europe. I t also involved unprecedented actions by central banks, financial regulators and
governments to restore confidence and s ta b ility in the financial system and to lim it the effects o f the
crisis on economic activity. In several stages beginning in December 2009 the Basel Com m ittee has
proposed fu rth e r refinem ents, inclu ding more detailed regulations aimed at increasing the q u a n tity
and q ua lity o f bank capital and strengthening bank liq u id ity . Together, these proposals have been
referred to as Basel III. In September 2012, APRA announced th a t the capital reform s w ould be
im plem ented on 1 January 2013 (APRA, 2012b). In May 2013 APRA stated th a t i t w ould introduce
changes to liq u id ity regulation based on Basel III in three stages on 1 January 2014, 1 January 2015
and 1 January 2018 (APRA, 2013b).
When the structure o f the financial system is viewed in terms o f the in s titu tio n s th a t operate w ith in
it, four main developments can be identified over the post-deregulation period— th a t is, from 1985 to
2005 (RBA March 2006). These developments are:
•
•
•
•
a significant increase in the importance o f banks
a decrease in the relative importance o f b uilding societies, credit unions, finance companies and
money m arket corporations
a significant increase in the share o f assets held through managed funds, particularly
superannuation funds
rapid growth in securitisation.
These developments, which typically occurred gradually, were followed by some much more rapid
changes associated w ith the global financial crisis. In Australia, the effects o f the financial crisis were less
severe than in the US, the U K and Europe b u t the effect on equity prices was comparable to the changes
experienced in other countries: from its peak in November 2007, the Australian stock m arket fell by more
than 50 per cent to a low in March 2009. O ther effects included a fu rth e r strengthening o f the dom inant
position held by banks and a significant reversal o f the previous grow th in securitisation. These, and other
developments, are discussed in Sections 8.2 to 8.4.
5
See Gup (2004) for a detailed discussion of the background to the introduction of Basel II and a critical analysis of its
recommendations •
capital market
CENTRAL BANK
a bank that controls
the issue of currency,
acts as banker to the
government and the
banking system and
sets the interest rate
for overnight cash
B usiness finance
Business funding
LEARNING
OBJECTIVE 2
Distinguish between
financial agency
institutions, financial
intermediaries and
investing institutions
FINANCIAL AGENCY
INSTITUTION
arranges or facilitates
the direct transfer of
funds from lenders to
borrowers
INVESTING
INSTITUTION
accepts funds
from the public
and invests them
in assets; includes
superannuation
funds, life insurance
companies and unit
trusts
AUTHORISED DEPOSIT­
TAKING INSTITUTION
a corporation that is
authorised under the
Banking Act 1959 to
accept deposits from
the public
Sections 8.2 to 8.4 outline the m ajor financial in s titu tio n s in the Australian capital m arket involved in
providing funds to companies. In stitu tio n s such as b uilding societies and credit unions, whose main
function is consumer lending, are n o t discussed. The financial in s titu tio n s we discuss can be divided into
three broad categories: financial agency institutio ns, financial intermediaries and investing institutions.
A financial agency in stitu tio n arranges or facilitates the direct transfer o f funds from lenders to
borrowers; typically, the funds are transferred from investors to companies. Companies usually obtain
the assistance o f a stockbroker or investm ent bank when they wish to raise capital externally. For
example, a broker or an investm ent bank may place a company s newly issued shares w ith in stitu tio n a l
clients. Stockbroking firm s and investm ent banks fu nctio n as agency in stitu tio n s and w ill receive a fee or
commission fo r arranging a transaction. Financial agency in s titu tio n s are discussed in Section 8.2.
A financial intermediary, such as a bank, provides funds as a principal— th a t is, a company that
borrows from a bank has an obligation to repay the bank, b u t it has no obligation to the banks depositors.
Similarly, a bank acts as a principal in its relationship w ith depositors who have claims against the bank;
depositors do n ot have claims against those who have borrowed from the bank. In contrast to agents,
whose earnings consist m ostly o f fees and commissions, financial intermediaries obtain a significant part
o f th e ir income from the in te re s t m argin,, which is the difference between the interest rates they charge
for loans and the rates they pay to depositors. M ost financial interm ediaries also charge various fees.
Companies w ith large funding requirements and high credit ratings are well placed to access debt
funds directly. Such companies can therefore raise m ost or all o f th e ir funding requirements w ith o u t the
services o f an interm ediary. However, m ost companies would fin d it either impossible or very expensive
to access debt funds directly, so these companies typically borrow from financial intermediaries. The
funds provided are sourced m ainly from depositors, so financial intermediaries have to provide services
th a t depositors find attractive. Financial intermediaries are discussed in Section 8.3.
Investing in stitu tio n s are sim ilar to financial intermediaries in th a t they accept funds from the
public and invest the funds in assets. However, there are im p o rta n t differences between them. Essentially,
financial intermediaries, such as banks, accept deposits and make loans. The m ajor roles o f investing
in s titu tio n s — which include superannuation funds, life insurance companies and u n it tru sts— are to
provide insurance and funds management. Funds placed w ith these in s titu tio n s are generally n ot in
the form o f deposits and, while some o f these in s titu tio n s do make loans, they also invest in shares,
debt securities, infrastructure assets and real estate, giving them a w ider spread o f assets than financial
intermediaries. Another difference is th a t the returns provided by investing in s titu tio n s usually depend
directly on the performance o f the assets held by them, whereas intermediaries have ‘fixed’ commitments
to depositors th a t m ust be m et even i f an unexpectedly high pro po rtio n o f borrowers fa il to repay th eir
loans. Investing in stitu tio n s are discussed in Section 8.4.
W hile Sections 8.2 to 8.4 discuss financial agency institutio ns, financial intermediaries and investing
in stitu tio n s, tw o qualifications should be noted. First, there are some entities th a t do n ot fit neatly
in to any one o f these three categories. In particular, despite the fact th a t securitisation vehicles do not
conform to our d e fin itio n o f ‘financial interm ediary’，we discuss securitisation in Section 8.3 because it
is a process widely used by financial intermediaries. Second, some o f the differences between these three
types o f in stitu tio n s have become less d istin ct in recent years. Many investing in s titu tio n s now offer
products, such as housing loans, th a t were previously provided almost exclusively by intermediaries. In
addition, there has been a considerable grow th in financial conglomerates th a t provide a wide range of
financial services. For example, many banks have funds management, stockbroking and life insurance
subsidiaries, while some life insurance companies have banking subsidiaries. These developments are
likely to continue. However, there are s till fundam ental differences between financial interm ediation,
the life insurance business and funds management. For example, the assets and liabilities o f a bank and
the risks involved in banking are quite different from those o f a life insurance company. Therefore, while
customers see a b lu rrin g o f previous distinctions, the differences between, say, banking and insurance
continue to be im p o rta n t to those involved in managing and regulating financial institutio ns.
A nother d ifficu lty arises from the terms used to refer to some institutio ns. In particular, the term
inve stm en t bank* is used despite the fact th a t these in s titu tio n s may n ot be au th orised deposit-taking
in stitu tio n s (ADIs) and are therefore n o t p erm itted to use the word ‘bank’ in th e ir title . On the other
C hapter eight T he
capital market
hand, many investm ent banks in Australia are the local wholesale m arket operations o f foreign banks.
In summary, activities described as ‘investm ent banking’ may be carried out by a bank or by a non-bank.
The to ta l assets o f the main types o f financial in s titu tio n s are shown in Table 8.1, which shows that
banks are by far the largest group o f in stitu tio n s in the Australian market, followed by life insurance
companies and superannuation funds. The grow th o f banks, life insurance companies and superannuation
funds, other managed funds and p articularly securitisation vehicles was relatively high in the period from
1990 to 2007, while the assets o f other ADIs and registered financial corporations grew more slowly.
Table 8.1 also shows th a t fo r some institutio ns, such as life insurance companies and superannuation
funds, the rate o f asset grow th has slowed since 2007, while fo r registered financial corporations, other
managed funds and securitisation vehicles, the value o f assets has fallen since 2007. Generally, these
differences between pre- and post-2007 conditions reflect the effects o f the global financial crisis.
TABLE 8.1 Assets of Australian financial institutions, $ billi on
r
Life in s u ra n c e
3 0 Ju n e |
A u th o ris e d
R e g iste re d
c o m p a n ie s a n d
O th e r
d e p o s it-ta k in g
fin a n c ia l
s u p e ra n n u a tio n
m anaged
in s titu tio n s
c o rp o ra tio n s
fu n d s
fu n d s
___
B a n ks (o th e r
O th e r
th a n RBA)
A D Is
.
G e n e ra l
in s u ra n c e
S e c u ritis a tio n
c o m p a n ie s
v e h ic le s
Total
1990
325.8
31.4
109.0
158.9
43.3
21.7
5.7
695.9
1995
437.9
27.4
95.6
241.1
57.7
38.9
9.8
908.3
2000
731.0
34.2
134.6
455.1
151.7
61.4
65.0
1633.0
2005
1363.5
49.2
166.7
662.9
243.0
105.1
184.5
2774.8
2006
1581.1
53.6
176.3
787.1
300.6
113.8
216.5
3228.9
2007
1876.9
59.3
222.8
1024.9
378.3
143.7
274.0
3980.0
2008
2324.1
64.6
251.4
997.0
352.7
137.2
239.2
4366.2
2009
2590.2
67.5
215.6
936.5
313.8
134.2
192.7
4450.5
2010
2613.2
73.0
168.6
1050.6
312.6
133.4
146.1
4497.6
2011
2733.2
82.2
171.2
1172.1
287.8
152.9
136.1
4735.6
2012
2964.9
68.7
154.0
1233.7
272.5
163.4
126.8
4984.0
2013
3103.0
66.8
155.5
1421.0
278.0
175.2
127.5
5327.0
Note: The figures for life insurance companies, superannuation funds and other managed funds have been consolidated by the Australian Bureau of
Statistics. They should not be compared with the figures in Tables 8.5, 8.6 and 8.7, which are unconsolidated.
Source: Table B1, Reserve Bank of Australia website, www.rba.gov.au.
8.2
Financial agency institutions
Financial agency in stitu tio n s are those th a t facilitate direct funding b u t do n o t themselves provide
the funds. These in stitu tio n s operate in the p rim ary markets to b ring together surplus units and
deficit units, and assist w ith the design o f appropriate contracts. They also operate in the secondary
markets. The m ain financial agency in stitu tio n s in Australia are stockbrokers and investm ent
banks.
LEARNING
OBJECTIVE 3
Identify and explain
the role of financial
agency institutions
8.2.1 I Brokers and the stock exchange
The trad ition al function o f the stock exchange (and o f stockbrokers) is to provide facilities fo r the trading
o f shares, bonds and other securities such as convertible notes, options and preference shares. As a result,
a stock exchange perform s three functions. First, i t mobilises savings. Because there are large numbers of
investors, issues o f securities can be fo r large sums. The presence o f a stock exchange allows companies to
issue debt or equity securities in relatively small units, and each surplus u n it can then invest its desired
amount. Second, it allocates resources. A stock exchange facilitates the allocation o f resources (savings)
among a large num ber o f competing investm ent opportunities. Third, it allows investments to be realised
through the sale o f securities— th a t is, i t provides investors w ith liquidity, and therefore the o pp ortu nity
to adjust th e ir portfolios. As explained earlier, the existence o f a liq u id secondary m arket encourages
investm ent in the p rim ary market.
Development of the Australian Stock Exchange
In 1987 the Australian Stock Exchange Ltd (ASX, www.asx.com.au) commenced business as a national
stock exchange form ed by amalgamating the six independent exchanges th a t previously operated in
the state capital cities. U n til 1998, the ASX was a company lim ite d by guarantee. However, follow ing
dem utualisation in 1998, i t became a company lim ite d by shares. In 2006 the ASX merged w ith the SFE
Corporation, the owner o f the Sydney Futures Exchange, resulting in an exchange group th a t operated
as the Australian Securities Exchange (ASX) u n til 1 August 2010 when it adopted the name ASX Group.
The ASX is a large and sophisticated m arket. A t the end o f 2012, more than 2000 companies had
equities listed on the exchange, w ith a to ta l m arket capitalisation o f $1335 billion. In th a t year, the
average daily value o f share trading was about $4 b illio n and more than $41 b illio n o f new equity capital
was raised during the year. By market capitalisation o f its listed entities, the ASX ranks te n th in the world;
by the value o f share trading, i t ranks tw e lfth .6
Other equity markets in Australia
There are two smaller stock exchanges in Australia: the Asia Pacific Stock Exchange and the National
Stock Exchange o f Australia.
•
•
The Asia Pacific Stock Exchange (www.apx.com .au), usually referred to as the APX, was started in
1997 and targets grow th-oriented companies based in Australia or elsewhere in the Asia-Pacific
region, including China. I t is owned by AIMS Financial Group.
The N ational Stock Exchange o f Australia (www.nsxa.com .au), usually referred to as the NSX, is
located in Newcastle and in 2013 had over 100 securities listed. I t is owned by its shareholders and
is its e lf listed on the ASX. It generally attracts smaller companies than the ASX because its listing
requirements are less demanding. For example, to lis t on the ASX a company m ust have at least
300 shareholders and a m arket capitalisation o f at least $10 m illion , whereas the NSX requires only
50 shareholders and a m arket capitalisation o f at least $500 000.
Australia also has other equity markets designed to meet the needs o f small and medium-sized
enterprises. These include the Australian Small Scale Offerings Board (www.assob.com.au) and the
CAPstart Private Equity M arket (w w w.capstart.com .au), which facilitate capital raising by small unlisted
companies.
Automation of trading
Since 1990, all shares have been traded electronically through systems th a t enable stockbrokers to trade
from term inals in th e ir offices; clients can place orders w ith online brokers using the internet. Visitors to
the stock exchanges can now view share prices and other inform ation, such as local and overseas m arket
indices, on video screens in the visitors* gallery. The ju n io r exchanges also use electronic trading and the
prices o f listed securities can be obtained from th e ir websites.
Table 8.2 provides some ASX m arket statistics fo r the period 1990 to 2012.
6
Ranks refer to the 53 members of the World Federation of Exchanges (www.world-exchanges.org).
C hapter eight T he
capital market
TABLE 8.2 ASX market statistics as at December, 1990-2012
Year
V a lu e o f A ll O r d in a r ie s s h a re , M a r k e t c a p ita lis a tio n d o m e s tic
p r ic e in d e x
e q u itie s ($ m illio n )
N u m b e r o f c o m p a n ie s w ith
e q u itie s liste d
1990
1280
139572
1136
1995
2203
329647
1178
2000
3155
670918
1406
2005
4709
1109596
1807
2006
5644
1390315
1908
2007
6421
1478651
2077
2008
3659
969046
2086
2009
4883
1403117
2043
2010
4847
1419001
2072
2011
4111
1168712
2079
2012
4665
1335 837
2056
Source: Compiled from Australian Stock Exchange Ltd, Fact Book 2001, 2001 and www.asx.com.au/research/market—
info/index.htm.
The role of the stockbroker
Traditionally, stockbrokers have played a leading role in the new-issues market. In the year to 31 December
2012, ASX-listed entities raised $41.2 b illio n in new equity capital compared w ith the 2010 and 2011
totals o f $56.5 b illio n and $47.8 b illio n respectively. The 2012 to ta l comprised $7.2 b illio n raised in in itia l
public offerings by newly listed entities and $34.0 b illio n raised by entities th a t were already listed (see
w w w .asx.co m .au /a bo ut/m a rke t-sta tistics.htm ). A company may m aintain a continuing relationship
w ith a stockbroking firm th a t advises it on the m ost appropriate means o f raising funds and the terms
o f a new issue o f securities. The same broker or an associated company may underw rite the issue, which
means th a t the broker or associated company agrees to subscribe to any p o rtio n o f the issue th a t is not
subscribed to by other investors during a given period. In addition, a broker may undertake to sell the issue,
mainly to the brokers clients and in s titu tio n a l investors. The larger stockbroking firm s also frequently
advise companies th a t are considering a merger or acquisition, and may assist w ith negotiations if the
merger or acquisition proceeds.
Many stockbroking firm s have extended th e ir services beyond those trad ition ally offered. O ther
services offered by brokers include advice on financial planning and superannuation, research and trading
of derivative securities (such as options), access to stock markets outside Australia and investments
in commercial bills and other money m arket assets.7 Although a stockbroking firm may provide these
services directly, they are usually provided through associated investm ent banks.
8 .2 .2 1 Investment banks
The role of investment banks
The term investm ent bank* has no official defin itio n in Australia. Rather, investm ent banks are identified
by the range o f financial services th a t they provide. Their m ain activities involve wholesale banking and
trading in the financial markets. The range o f activities is broad and includes financial interm ediation
(borrowing and lending), trading in securities, foreign exchange and derivatives, investm ent management,
7
Derivatives are discussed in Chapters 17 and 18 and commercial bills in Chapter 10.
Jw w ^J
provision o f corporate advisory services, u nd erw riting and stockbroking. Thus, unlike most banks and
other authorised deposit-taking in s titu tio n s (ADIs), investm ent banks have little involvem ent in retail
banking. Accordingly, they usually have m inim al dealings w ith individuals except perhaps as managers
o f funds such as cash management trusts or as advisers to a small number o f very wealthy individuals.
There is no <typical, investm ent bank because many o f them specialise in particular products and
services. However, as a group, investm ent banks focus on wholesale m arket operations, where they
deal w ith corporations, other financial institutio ns, governments and supranational bodies. Their main
functions can be outlined in four categories:
The wholesale banking operation provides a service to companies th a t wish to deposit tem porarily idle
cash balances, or to borrow funds fo r a short to m edium period,
b The investment management function involves managing the p ortfolios o f in s titu tio n a l investors and
an investm ent banks own u n it trusts. Part o f this fu nctio n is to direct funds to the new issues o f
Australian companies.
c The corporate financial advisory function involves providing advice to companies about raising
additional capital, or a merger or takeover, and the provision o f und erw riting facilities and
m arketing services fo r new issues. The u n d erw rite rs skills, contacts and knowledge o f the
capital m arket are expected to result in a higher price than i f the issuer attempted to m arket the
securities itself. In addition, the m arketing risk is assumed by the underw riter. I f the issue is
priced appropriately, the supply o f securities w ill match the demand. I f the issue is over-priced, the
u nderw riter w ill be le ft holding the unsold securities,
d Making a market in foreign exchange and derivative securities involves being w illin g to quote b oth a
price to buy and a price to sell in these m arkets— th a t is, this fu nctio n requires the investm ent bank
to be w illin g to deal on both sides o f the m arket at all times.
a
Regulation of investment banks
The regulatory provisions th a t apply to an investm ent bank w ill depend, at least in p art, on its structure
and the range o f services th a t it provides. An investm ent bank operating in Australia w ill be structured
either as an AD I or as a money m arket corporation. Those th a t are ADIs w ill be subject to the provisions
o f the Banking Act 1959 and to prudential supervision by APRA (w w w .a p ra .g o v .a u ). Investm ent banks
th a t are structured as money m arket corporations are n o t subject to prudential supervision, b ut are
required to register w ith, and provide statistical data to, APRA in accordance w ith the Financial Sector
(Collection of Data) Act 2001. Their name may n ot include the word ^ank*, but guidelines issued by APRA
in January 2006 allow registered money m arket corporations to use expressions such as 'merchant bank*
in relation to th e ir business. Because they are corporations, they are also regulated by the Australian
Securities and Investments Commission (ASIC, w w w .a s ic .g o v .a u ) and are subject to the same conduct
and disclosure regulations as other corporations.
As a provider o f financial advice or as a dealer in financial markets, an investm ent bank m ust have
an Australian Financial Services Licence issued by ASIC. In addition, m ost o f those th a t trade in the
financial markets are members o f the Australian Financial M arkets Association (AFMA, w w w .a fm a .
c o m .a u ). AFM A is an ind ustry association th a t represents the in s titu tio n s th a t operate in Australia’s
over-the-counter financial markets. It imposes a degree o f self-regulation through measures such as its
code o f conduct, codification o f m arket conventions and standardisation o f documentation.
Developments in Australian investment banking
A fte r the deregulation o f the banks in the 1980s, lending became a much less im p o rta n t activity o f money
m arket corporations, while other investm ent banking activities have grown considerably. Therefore, the
value o f th e ir assets and the associated m arket shares shown in Table 8.3 (see Section 8.3) are n o t good
measures o f the sectors importance. O ther measures, such as the value o f equity capital raised and fees
earned, are better indicators o f the importance o f investm ent banking. As noted above, investm ent banks
th a t engage in securities trading and u n d erw riting w ill usually be members o f AFM A. In 2013, AFM A
had more than 130 members and there are many investm ent banks th a t are n ot members o f AFMA.
These non-members do n o t trade in the financial markets and focus instead on activities such as advisory
services, investm ent and funds management.
Investm ent banking can involve inherent conflicts o f interest th a t m ust be managed i f they cannot
be avoided. These conflicts are m ost likely to arise in cases where the firm has a wide range o f activities
C hapter eight T he
including stockbroking, securities trading and u nderw riting. In such cases, investors and regulators may
be concerned th a t the broking analysts* recommendations on which shares to buy or sell may be influenced
by th e ir colleagues who are seeking to attract or retain business in u nd erw riting or corporate advisory
activities. Further, i f share trading undertaken by one section o f an investm ent bank is m otivated by
confidential inform a tion gathered by another section o f the bank, then the bank may be subject to a
charge o f insider trading. The standard approach to managing such conflicts o f interest is to employ
internal barriers— know n as inform a tion barriers or, more frequently, Chinese walls_ to lim it the flow
o f confidential client inform a tion between departments.
Concerns about the effectiveness o f Chinese walls were widely publicised in the US in 2001. One outcome
was that M errill Lynch agreed to pay a fine o f US$100 m illion because o f allegations th a t its broking analysts
issued overly optim istic reports on the shares o f companies that were clients o f its investment banking
operation. In Australia, ASIC took civil action against Citigroup in 2006 in the only recorded Australian case to
consider Chinese walls as a defence against insider trading (Overland and Li, 2012). Citigroup was successful
in defending the charges but the outcome o f the case highlights the importance o f m aintaining adequate
Chinese wall arrangements. In particular, the policies and procedures underpinning such arrangements
should be documented extensively, and understood and applied by employees. Some investment banks
avoid any exposure to inherent conflicts o f interest by restricting the scope o f th e ir activities. Firms that
take this approach focus on advisory services and do n ot engage in securities trading or underwriting.
Investment banks and the global financial crisis
The global financial crisis saw m ajor investm ent banks in the US experience severe stress. Bear Stearns
suffered a severe liq u id ity shortage in March 2008 and failure was avoided only when J. P. Morgan Chase
agreed to purchase Bear Stearns in a takeover facilitated by government authorities. By the end o f August
2008, the losses th a t had been recognised by financial in stitu tio n s w ritin g down the values o f assets
had accumulated to a global to ta l o f around US$500 billion. Pressure on the equity prices o f financial
institutions made it more d iffic u lt fo r banks to replenish th e ir depleted capital bases or to raise loan
funds from markets where lenders were unw illing to accept anything other than the lowest credit risks.
W ith th e ir higher leverage and exposures to impaired assets, investm ent banks experienced the greatest
pressure. O f the m ajor US investm ent banks, Lehman Brothers, w ith assets o f about $639 billion, faced
the m ost severe problems and when it was unable to raise urgently needed funding the company filed for
bankruptcy protection in September 2008— the largest ‘bank’ failure in US history.
The failure o f Lehman Brothers and the planned takeover o f M e rrill Lynch by the Bank o f America
would leave just two big investm ent banks: Goldman Sachs Group Inc. and Morgan Stanley. A week after
Lehman Brothers failed, the US central bank, the Federal Reserve, announced that, at a 9 pm meeting, its
Board o f Governors had approved applications delivered earlier th a t day by b oth firm s to become bank
holding companies— th a t is, firm s th a t own or control banks. The im plications o f this change o f status
included regulation by the Federal Reserve instead o f the Securities and Exchange Commission, lower
financial leverage, greater reliance on deposits from retail customers rather than borrow ing by issuing
bonds and probably less risk taking. A report by Bloomberg began:
The Wall Street that shaped the financial world for two decades ended last night, when Goldman Sachs
Inc. and Morgan Stanley concluded there is no future in remaining investment banks now that investors
have determined the model is broken.8
W hile the effects in Australia were less severe than in the US, the global financial crisis had significant
effects on investm ent banks in Australia. The Sydney-based investm ent bank Babcock & Brown (B&B),
which listed on the ASX in 2004 and had at its peak 28 offices worldwide and a m arket capitalisation in
excess o f $9 billion , became a victim o f the crisis when it failed in 2009. B&B had a leading role as an adviser
on structured finance including leases and securitisation, invested in real estate and infrastructure as a
principal and managed several satellite* funds th a t i t established. B&B relied heavily on short-term debt
to finance its holdings o f m ostly illiq u id assets, such as real estate and shareholdings in unlisted related
businesses. W ith financial markets disrupted and concerns about the high debt levels o f B&B and its
satellite funds, the company was unable to refinance its debt and was placed in voluntary adm inistration
in March 2009 and then in to liqu id atio n in August 2009. The Australian subsidiaries o f US and European
8
See Harper and Torres (2008).
capital market
B usiness finance
investm ent banks such as M e rrill Lynch and UBS reduced th e ir workforces to offset lower revenues.
As financial markets stabilised in 2009 and 2010, these and other investm ent banks were able to earn
substantial fees by arranging and u nd erw riting share issues fo r companies whose managers recognised
the need to reduce th e ir financial leverage.
8.3
LEARNING
OBJECTIVE 4
Identify and explain
the role of financial
intermediaries
Financial interm ediaries
Financial intermediaries borrow funds on th e ir own behalf and then lend the funds to another party.
The types o f financial intermediaries in the Australian capital m arket include banks, money m arket
corporations, finance companies, building societies and credit unions. Recent statistics on the assets o f
the financial interm ediaries th a t are im p o rta n t as lenders to businesses are shown in Table 8.3.
TABLE 8.3 Total assets of selected financial intermediaries ($ billion) and market
shares (percentage of total)
r
3 0 June
M o n e y m a rk e t
$ b illio n
F in a n c e c o m p a n ie s
c o rp o ra tio n s
B a n ks
%
$ b illio n
%
$ b illio n
,
Total
%
$ b illio n
1990
325.8
74.9
53.6
12.3
55.4
12.7
434.8
1995
437.9
82.1
51.2
9.6
44.4
8.3
533.5
2000
731.0
84.5
63.7
7.4
70.9
8.2
865.6
2005
1363.5
89.1
80.1
5.2
86.5
5.7
1530.1
2006
1581.1
90.0
79.0
4.5
97.3
5.5
1757.4
2007
1876.9
89.4
106.7
5.1
116.1
5.5
2099.7
2008
2324.1
90.3
121.9
4.7
129.5
5.0
2575.6
2009
2590.2
92.3
94.5
3.4
121.1
4.3
2805.8
2010
2613.2
93.9
64.8
2.3
103.9
3.7
2781.8
2011
2733.2
94.1
66.7
2.3
104.5
3.6
2904.5
2012
2964.9
95.1
49.1
1.6
104.9
3.4
3118.8
2013
3103.0
95.2
43.6
1.3
111.8
3.4
3258.5
Source: Table B1, Reserve Bank of Australia website, www.rba.gov.au.
8.3.1 | Banks
The to ta l assets o f financial in stitu tio n s in Australia are shown in Table 8.1. As can be seen from the table,
banks are the largest group o f financial in stitu tio n s in Australia. As at June 2013, th e ir assets accounted
directly fo r more than 58 per cent o f the assets held by all financial in stitu tio n s. However, this understates
the overall importance o f banks because many o f them also have interests in other financial institutio ns,
such as investm ent banks, finance companies, insurance companies, fund managers and stockbrokers.
Accordingly, banks— p articularly the larger ones— provide a wide range o f products and financial services
including funds management, insurance, und erw riting , security dealing and stockbroking. In many cases,
these activities are carried out through subsidiaries and affiliated businesses.
A m ajor part o f banking business is borrow ing from depositors and other investors and lending to a
wide range o f borrowers, including governments, businesses and consumers. Therefore, banks need to
offer services th a t attract both borrowers and depositors. The m ain attraction to borrowers is obvious:
access to debt capital. Banks are large lenders to the business sector, and in the 12-m onth period ended
C hapter eight T he
capital market
June 2013 accounted fo r more than 90 per cent o f commercial lending by interm ediaries.9 But banks offer
more than mere access to debt capital— they offer a wide range o f loans w ith different characteristics.
For example, there are short-term loans and long-term loans, secured loans and unsecured loans, fixedinterest rate loans and variable-interest rate loans, and domestic-currency loans and foreign-currency
loans. The most distinctive fo rm o f bank lending is the overdraft facility, which involves an arrangement
whereby borrowers may draw funds, at th e ir discretion, up to a specified lim it.
How do banks attract depositors? A n obvious answer is: by paying interest. But why would someone
deposit money in a bank, which then lends the money to a borrower, when the banks deposit interest
rate is almost certainly less than the interest rate charged to the borrower? In other words, why n o t lend
directly, instead o f going through the bank? The answer is that, in addition to paying interest, banks
provide valuable services to th e ir depositors, including:
•
•
•
•
•
Credit assessment. Banks typically have much greater expertise than depositors in assessing the
quality o f loan applicants, thus reducing default risk.
Credit enhancement. Partly by applying th e ir credit assessment skills, banks are able to offer low -risk
investments to depositors, even i f some o f the loans made by the bank are high risk.
Diversification. Banks reduce risk by lending to a much w ider variety o f borrowers than an individual
depositor could.10
Maturity transformation. Depositors often wish to lend fo r short periods (such as a few m onths or
a few years) whereas borrowers often wish to borrow fo r term s o f many years; banks make this
transform ation possible.
Transaction services. Banks assist depositors to receive and pay funds by (for example) cheques and
electronic transfers.11
In addition to m aking loans and meeting the needs o f depositors, banks also provide many other
services. These services include assisting clients to borrow from sources o ther than the bank by providing
guarantees, letters o f credit and b ill acceptances. O ther services assist clients in risk management and
involve market-related activities such as entering in to forw ard rate agreements, transacting in various
foreign-currency contracts and dealing in derivatives.
As at 11 October 2013, 69 banks were authorised to operate in Australia. O f these, 21 were
predominantly Australian owned, eight were subsidiaries o f foreign banks and 40 were branches
o f foreign banks. A foreign bank subsidiary is incorporated in Australia and m ust hold capital w ith in
Australia, whereas a foreign bank branch is essentially just a p art o f the parent bank th a t is authorised
to conduct banking business w ith in Australia. As discussed below, foreign bank branches are subject
to some restrictions th a t do n o t apply to subsidiaries o f foreign banks. Some foreign banks have both
a branch and a subsidiary in Australia. As from 1 July 1998, the responsibility fo r bank supervision
was transferred from the RBA to APRA. The RBA retains responsibility fo r m onetary policy and the
maintenance o f financial stability, including th a t o f the payments system— which is the cash, cheque and
electronic means by which payments are effected. As a result, the current regulatory structure requires
close cooperation between the RBA and APRA.
An a uth ority from APRA is required before a bank is perm itted to operate in Australia. APRA also
imposes a number o f other controls over banks, including m inim um capital requirements and asset
requirements. Banks are also required to provide APRA w ith extensive data on th e ir activities and
management systems. W hile subsidiaries o f foreign banks are subject to the same requirements as
locally owned banks, branches o f foreign banks are n ot subject to m inim um capital requirements in
Australia. However, such branches are effectively confined to operating in the wholesale m arket because
they are n ot perm itted to accept in itia l deposits o f less than $250000 from Australian residents and
non-corporate institutio ns. Therefore, a foreign bank th a t wishes to operate in the retail m arket m ust
establish a subsidiary in Australia.
Before the global financial crisis, the Australian government did n o t explicitly guarantee deposits in
Australian banks. As p art o f its response to the crisis, the government introduced an explicit guarantee
9
This percentage is derived from the Australian Bureau of Statistics publication L e n d in g F in an ce, A u str a lia , cat. no. 5671.0,
Table 3.
10 See Chapter 7 for a discussion of how diversification of a portfolio can reduce risk.
11 Banks are the major participants in the payments system in the settlement of cheques, which is conducted through exchange
settlement accounts at the RBA.
DEFAULT RISK
the chance that a
borrower will fail
to meet obligations
to pay interest and
principal as promised
B usiness finance
Finance
in
ACTION
GOVERNMENT GUARANTEE EXTENDED O N BANK DEPOSITS
P r io r to th e g lo b a l f in a n c ia l c ris is , b a n k d e p o s its in A u s t r a lia w e r e n o t g u a r a n t e e d , a lth o u g h
d e p o s it in s u r a n c e s c h e m e s w e r e c o m m o n in o t h e r c o u n tr ie s . F a c e d w ith a c ris is o f c o n fid e n c e in
la te S e p t e m b e r / e a r ly O c t o b e r 2 0 0 8 , m a n y g o v e r n m e n ts in c r e a s e d th e lim it o n th e a m o u n t o f
d e p o s its g u a r a n t e e d u n d e r th e s e s c h e m e s w h ile o th e rs w e n t fu r t h e r b y p r o v id in g a g u a r a n t e e
o v e r a ll d e p o s its , t y p ic a lly f o r a s e t p e r io d o f a r o u n d 2 y e a r s . S o m e g o v e r n m e n ts a ls o m o v e d to
p r o v id e a g u a r a n t e e o n w h o le s a le b o r r o w in g b y d e p o s it - ta k in g in s titu tio n s . W h il e m o s t A u s t r a lia n
in s titu tio n s r e m a in e d s o u n d a n d p r o f it a b le , th e A u s t r a lia n g o v e r n m e n t to o k s im ila r m e a s u re s
so t h a t A u s t r a lia n b a n k s a n d o fh e r d e p o s it - ta k in g in s titu tio n s w o u ld n o t b e d is a d v a n t a g e d
in te r n a tio n a lly . A n a r t ic le in T /ie A g e o u t lin e d th e g o v e r n m e n t's in itia tiv e s .
T h e G o v e r n m e n t w i l l g u a r a n t e e t h e $ 6 0 0 —$ 7 0 0 b i l l i o n d e p o s it s in A u s t r a lia n f i n a n c i a l
in s t it u t io n s in a m o v e t o s h o r e u p lo c a l c o n f id e n c e a n d p r o t e c t t h e n a t i o n ’ s in t e r n a t i o n a l
c o m p e t it iv e n e s s . D e c la r i n g t h a t t h e c o u n t r y is in 't h e e c o n o m ic e q u i v a le n t o f a r o l lin g
n a t io n a l s e c u r it y c r is is 7, [ P r im e M in is t e r ] K e v in R u d d h a s a ls o a n n o u n c e d t h a t a l l b o r r o w i n g
b y A u s t r a lia n b a n k s a n d o t h e r d e p o s it - t a k in g in s t it u t io n s f r o m o v e r s e a s w i l l b e g u a r a n t e e d .
T h e d e p o s it a n d le n d in g g u a r a n t e e s a r e u n p r e c e d e n t e d in A u s t r a lia n b a n k i n g h is t o r y
a n d a r e a n im m e d ia t e r e s p o n s e t o t h e d r a m a t i c m o v e s b y o t h e r c o u n t r ie s t o p r o p u p
t h e ir f a i l i n g f i n a n c i a l s y s te m s . . . . A u s t r a lia n b a n k s w e lc o m e d t h e G o v e r n m e n t 's m o v e s .
A u s t r a lia n B a n k e r s A s s o c i a t io n c h i e f e x e c u t iv e D a v id B e ll s a id A u s t r a lia n b a n k s w e r e w e ll
c a p it a l is e d b u t w e r e s till a f f e c t e d b y t h e s e iz u r e o f i n t e r n a t i o n a l f i n a n c i a l m a r k e ts . 'T h is
le v e ls t h e p l a y i n g f ie l d a n d a l lo w s A u s t r a lia n b a n k s t o c o m p e t e e q u a l l y a n d f a i r l y 7, h e
s a id .
Source: 'Rudd's $700 billion bank guarantee,/ Michelle Grattan and Vanessa O'Shaughnessy, The Age, 13 October 2008.
|w w w j
on deposits in banks and other AD Is.12 (See Finance in Action.) Some o f these guarantees were temporary
b u t the government continued to guarantee deposits o f up to $250 000 per person per ADI.
The Australian banking sector is dominated by fo ur m ajor banks, the AN Z Banking Group (www.
anz.com.au), the Commonwealth Bank o f Australia (w w w.com m bank.com .au), the N ational Australia
Bank (w w w .national.com .au) and Westpac Banking Corporation (www.westpac.com .au). These
banks accounted fo r 79 per cent o f the to ta l assets o f the Australian banking sector as at October 2013
(APRA 2013c). Each has a nationwide branch netw ork and provides a fu ll range o f banking services for
individuals as well as business customers b oth locally and overseas. O ther Australian-owned banks are
smaller and many are referred to as Regional banks’ because they originally had a regional base in one
state. M any o f these smaller banks, including the Bendigo and Adelaide Bank, Suncorp Bank and the Bank
o f Queensland, have since expanded to compete w ith the m ajor banks by achieving broader coverage of
the Australian market.
Historically, foreign-owned banks played only a m in o r role in the Australian financial system. However,
in recent years they have attracted increased a tte ntio n through measures such as attractive interest rates
paid on internet-based savings accounts. Foreign banks have also begun to compete more aggressively in
lending in Australia and at the end o f 2008 they held around 16 per cent o f overall Australian bank assets.
However, by the end o f October 2013, th e ir share o f bank assets had declined to 11.5 per cent (APRA
2013c).
Following the collapse o f the m ajor US firm Lehman Brothers in September 2008 and the failure
or near-failure o f many other financial institutio ns, there was a widespread loss o f confidence in the
solvency o f financial in stitu tio n s and the sta bility o f the global financial system. Governments in several
countries, including Australia, moved to restore confidence through measures th a t were in some cases
unprecedented. As m entioned above, in Australia one o f the m ajor changes was the announcement o f an
explicit government guarantee o f bank deposits.
12 For discussion of the guarantee measures, see Schwartz (2010).
C hapter eight T he
capital market
8 .3 .2 1 Money market corporations
The activities o f money m arket corporations (MMCs) were discussed in Section 8.2.2. Table 8.3 shows
that the assets o f these in stitu tio n s have declined from around 10 per cent o f the to ta l assets o f banks,
MMCs and finance companies in the mid-1990s to around 5 per cent from 2004 to 2008; they then fell
fu rth e r to only 1.3 per cent in 2013. As discussed in Section 8.2.2, the long-term decline reflects the
ongoing effects o f the deregulation o f the Australian financial system, whereby restrictions th a t applied to
banks were removed, allowing them to strengthen th e ir com petitive position at the expense o f non-bank
financial intermediaries. The more rapid decline over the 2008 to 2013 period coincides w ith the global
financial crisis and its afterm ath. Since MMCs are n o t authorised deposit-taking in s titu tio n s (ADIs) th eir
borrowings were not covered by the government guarantee announced in October 2008.
8 .3 .3 | Finance companies
Initially, finance companies were p rim a rily concerned w ith lending to individuals by providing instalm ent
credit for retail sales. In 1954 this accounted fo r 85 per cent o f finance company lending b ut by June
2010, lending to individuals accounted fo r only 27 per cent o f the to ta l assets o f finance companies.13
Finance companies grew rapidly during the period in which the Australian financial markets were
highly regulated. They offered a wide range o f financial services fo r companies, including instalm ent credit,
lease financing, inventory financing, discounting o f accounts receivable, mortgages and other commercial
loans. Their success was due largely to the regulatory constraints on th e ir natural competitors, the banks.
In fact, each o f the m ajor banks acquired a finance company subsidiary in order to gain access to markets
denied them by bank regulations.
The deregulation o f the banking sector in the 1980s removed much o f the competitive advantage
h itherto enjoyed by finance companies. As can be seen from Table 8.3, the assets o f finance companies
have grown at a much lower average rate than the assets o f banks over the period from 1995 to 2013 and
declined in dollar terms from 2008 to 2013. Many finance companies have become specialised in stitu tio n s
focusing on specific areas such as m otor vehicle finance or the financing o f machinery and equipment.
8 .3 .4 | Securitisation14
S e c u ritis a tio n is the process o f converting illiq u id assets such as bank loans in to tradable securities. In
a typical case, an originator o f financial assets— such as a bank th a t has provided a significant number
o f housing loans— sells a p o rtfo lio o f these loans to a specially created company or trust. This entity,
generally referred to as a securitisation vehicle or special purpose vehicle (SPV), finances its purchase
o f the loans by issuing tradable securities to investors using the underlying assets (the housing loans)
as collateral. I f these securities are long term they are generally referred to as asset-backed bonds, or i f
the loans involved are all mortgage loans over residential property, the securities may be referred to as
residential mortgage-backed securities (RMBS). I f the securities are short term — th a t is, th e ir term to
m aturity is less than a year— they may be referred to as asset-backed commercial paper (ABCP). The end
result is th a t securitisation allows a financial in s titu tio n to fund its lending indirectly through the capital
market instead o f by the trad ition al m ethod o f gathering deposits or borrow ing directly in its own name.
A traditional interm ediary assesses loan applications and provides funds to approved loan applicants.
One advantage claimed fo r securitisation is th a t it enables the credit assessment fu nctio n to be separated
from the funding function. That is, the lending in s titu tio n continues to assess loan applicants but, through
securitisation, the funds are provided by investors. One view is th a t this process enables in stitu tio n s to
specialise in either credit assessment or funding, depending on where th e ir expertise lies. A nother view
is that this separation may incur agency costs: the credit assessor may n o t bear the fu ll costs o f making
poor assessments.
The securitisation m arket in Australia has been dominated by securitisation o f residential mortgages
but the range o f assets that can be securitised also includes commercial mortgages, leases, trade receivables
13 See Reserve Bank of Australia, Table B10, www.rba.gov.au.
14 Facts related to the Australian securitisation market mentioned in this section are mostly drawn from Reserve Bank of
Australia (2004) pp. 48-56 and Debelle (2009).
LEARNING
OBJECTIVE 5
Outline the role of
securitisation
SECURITISATION
the process of making
assets marketable by
aggregating incomeproducing assets in a
pool and issuing new
securities backed by
the pool
B usiness finance
a n d m o to r v e h icle lo an s. A s s h o w n in Table 8.1, th e assets o f A u s tra lia n s e c u ritis a tio n ve h icle s g re w fro m
a ro u n d $ 1 0 b illio n in J u n e 1 9 9 5 to a p e a k o f $ 2 7 4 b illio n in J u n e 2 0 0 7 b u t th e n fe ll to $ 1 2 8 b illio n in
Ju n e 2 0 1 3 . D u rin g th e p e rio d o f ra p id g ro w th t h a t co m m e n ce d in th e 19 90 s, th e share o f re s id e n tia l
[ wwn^]
m o rtg a g e lo a n s fu n d e d th ro u g h s e c u ritis a tio n in cre a se d fr o m less th a n 10 p e r c e n t in th e la te 1990s
to a lm o s t 25 p e r c e n t in J u n e 2 0 0 7 (see D e b e lle 2 0 0 9 , p. 4 3 ). C u rre n t in fo r m a tio n a b o u t s e c u ritis a tio n
is p ro v id e d b y th e A u s tra lia n S e c u ritis a tio n F o ru m (ASF,
w w w .securitisation.com .au). The assets o f
A u s tra lia n s e c u ritis a tio n ve h icle s are s h o w n in Table 8.4.
TABLE 8.4 Assets of securitisation vehicles, $ million
O th e r
3 0 Ju n e
I
M o r tg a g e s
lo a n s a n d
Asse 卜
backed
O th e r
A ll o th e r
p la c e m e n ts
bonds
se cu ritie s
assets
Total assets
1990
4794
845
5734
1995
5358
1456
928
1229
894
9845
2000
41306
7905
8072
2515
5 216
65014
2005
146984
11293
12286
3972
9970
184505
2006
176288
11162
13738
2946
12327
216461
2007
215201
17319
18907
3025
19525
273977
2008
179669
19106
20997
2753
16715
239240
2009
142885
15346
15858
525
18104
192718
2010
115 794
11922
9229
0
8835
146073
2011
110666
13353
6983
255
4813
136070
2012
106495
13747
1556
0
5 024
12 6 8 2 2
2013
106156
14175
1374
0
5554
127259
Source: Table B19, Reserve Bank of Australia website, www.rba.gov.au.
The ra p id g ro w th in s e c u ritis a tio n u p to 2 0 0 7 can be a ttr ib u te d to tw o m a in fa c to rs . F irs t, th e d e m a n d
f o r h o u s in g fin a n c e in A u s tra lia re m a in e d s tro n g . Second, th e c o m p o s itio n o f le n d e rs in th e m o rtg a g e
m a rk e t changed, w it h m o rtg a g e o rig in a to rs t h a t s e c u ritis e a lm o s t a ll o f t h e ir lo a n s g a in in g a g ro w in g share
a fte r e n te rin g th e m a rk e t in th e 19 90 s (D e b e lle 2 0 0 9 , p p . 4 3 - 4 ) . The fa ll in th e assets o f s e c u ritis a tio n
vehicles a fte r 2 0 0 7 is a n o th e r o u tc o m e o f th e g lo b a l fin a n c ia l c ris is . A t tim e s d u r in g th is crisis, m a rk e ts
f o r asset-backed s e c u ritie s w e re e ffe c tiv e ly fro z e n , w ith m a n y sellers b u t n o b u ye rs, so th e re was li t t le i f
a n y tra d in g in s e c o n d a ry m a rk e ts . Issuance o f n e w s e c u ritie s d e c lin e d m a rk e d ly a n d in som e cases ceased
a lto g e th e r. W it h re p a y m e n ts o n th e u n d e rly in g lo a n s b e in g a p p lie d to a m o rtis e th e p r in c ip a l o f e x is tin g
s e c u ritie s a n d m in im a l issuance o f n e w s e c u ritie s , th e assets o f s e c u ritis a tio n veh icle s in e v ita b ly fe ll.
8.4
LEARNING
OBJECTIVE 6
Identify and explain
the role of investing
institutions
Investing institutions
The m a in in v e s tin g in s titu t io n s in A u s tra lia are life in s u ra n c e com p an ies, s u p e ra n n u a tio n fu n d s , p u b lic
u n it tr u s ts a n d ge n e ra l in s u ra n c e co m p a n ie s. A s n o te d e a rlie r, m a n y o f the se in s titu t io n s are o w n e d b y
b a n ks o r are m e m b e rs o f fin a n c ia l c o n g lo m e ra te s . There is also s ig n ific a n t o v e rla p b e tw e e n th e categories.
In p a rtic u la r, m a n a g e m e n t o f s u p e ra n n u a tio n fu n d s is a m a jo r a c tiv ity o f life in s u ra n c e com p an ies, so
m o s t o f th e assets h e ld b y the se co m p a n ie s are w it h in s u p e ra n n u a tio n fu n d s .
C hapter eight T he
8.4.1 | Insurance companies and superannuation funds
As s h o w n in Table 8.1, th e t o ta l assets o f ge ne ral in s u ra n c e co m p a n ie s are a ro u n d $ 1 7 5 b illio n , w h ic h
is a b o u t 3 p e r ce n t o f th e assets o f a ll A u s tra lia n fin a n c ia l in s titu tio n s . In A u s tra lia , m o s t o f th e g e ne ral
in su ra n ce b u sin ess in vo lve s p r o v id in g in s u ra n c e c o ve r f o r assets such as m o to r veh icle s a n d b u ild in g s
w h ere a n y losses are g e n e ra lly in c u rre d w it h in 12 m o n th s o f re c e iv in g th e p re m iu m . In s u ra n c e com p an ies
u s u a lly m a tc h th e d u ra tio n o f t h e ir assets w ith th e d u ra tio n o f t h e ir lia b ilitie s . T h e re fo re , w h ile g e ne ral
in su ra n ce com panies do m a k e som e lo n g -te rm in v e s tm e n ts , th e m a jo r ity o f t h e ir assets are s h o rt
te rm . This fa c to r, to g e th e r w it h t h e ir re la tiv e ly s m a ll size, m ea ns t h a t ge n e ra l in s u ra n c e co m p a n ie s are
n o t a m a jo r source o f c o m p a n y fin a n ce . Hence, in th is s e c tio n w e fo cu s o n life in s u ra n c e com p an ies
a n d s u p e ra n n u a tio n fu n d s , w h ic h m ake lo n g e r te r m in v e s tm e n ts . In s u ra n c e co m p a n ie s a n d m o s t
s u p e ra n n u a tio n fu n d s are re g u la te d b y A P R A , th e o n ly e x c e p tio n b e in g se lf-m a n a g e d s u p e ra n n u a tio n
fu n d s (SMSFs) w h ic h are re g u la te d b y th e A u s tra lia n T a x a tio n O ffice .
L ife in su ra n ce co m p a n ie s a n d s u p e ra n n u a tio n fu n d s are m a jo r sources o f co m p a n y fin a n ce .
These in s titu tio n s raise la rg e a m o u n ts as p re m iu m s a n d c o n trib u tio n s , w h ic h are la rg e ly lo n g -te rm
c o m m itm e n ts and, a cco rd in g ly, such in s titu t io n s te n d to a cq u ire lo n g -te rm assets such as shares issu e d b y
p u b lic com p an ies, an d b o n d s a n d o th e r fo rm s o f d e b t issu e d b y g o v e rn m e n ts a n d com p an ies. A u s tra lia s
s u p e ra n n u a tio n in d u s tr y has g ro w n ra p id ly since th e e a rly 19 90 s in resp on se to th e C o m m o n w e a lth
G o v e rn m e n t s s u p e ra n n u a tio n g u a ra n te e charge p o lic y , w h ic h a im s to p ro m o te u n iv e rs a l s u p e ra n n u a tio n
coverage. The g ro w th o f assets w it h in th e s u p e ra n n u a tio n s yste m is e xp e cte d to c o n tin u e , a lth o u g h th e
ra te o f g ro w th w ill be in flu e n c e d b y changes in g o v e rn m e n t p o lic y a n d flu c tu a tio n s in in v e s tm e n t re tu rn s .
Table 8.5 show s th e re c e n t g r o w th in b o th th e assets h e ld b y s u p e ra n n u a tio n fu n d s a n d th e to t a l n u m b e r
o f fu n d s .
TABLE 8.5 Assets and number of funds—superannuation funds
N u m b e r o f s u p e ra n n u a tio n e n titie s c la s s ifie d b y ty p e
P o o le d s u p e r­
P u b li 7 _
A s s e ts ~
3 0 Jun e ; ($ b illio n ) j C o r p o ra te
In d u s try
se cto r
R e ta il
S m a ll
a n n u a tio n trusts
Total
____ ：
_____________ ____：
___ ：
______ j
2000
484.2
3389
155
81
293
212538
164
216620
2005
751.4
962
90
43
228
296813
130
298266
2006
904.2
555
80
45
192
315924
123
316919
2007
1172.8
287
72
40
176
356309
101
356985
2008
1131.0
226
70
40
169
381413
90
382008
2009
1067.4
190
67
40
166
404131
82
404676
2010
1198.5
168
65
39
154
418928
79
419433
2011
1350.9
143
61
39
143
446597
77
447060
2012
1400.5
122
56
39
135
481538
67
481957
Source: Australian Prudential Regulation Authority, www.apra.gov.au, Annual Superannuation Bulletin, June 2006, June
2010 and June 2013a.
The la rge increase in to t a l s u p e ra n n u a tio n assets o v e r th e 7 years to J u n e 2 0 0 7 re fle c ts th e c o m b in e d
effects o f p o s itiv e n e t c o n tr ib u tio n flo w s — t h a t is, c o n trib u tio n s exceeded b e n e fits p a id — a n d s tro n g
in v e s tm e n t re tu rn s o n som e asset classes, p a r tic u la r ly A u s tra lia n e q u itie s , a fte r 2 0 0 2 . In th e years
im m e d ia te ly a fte r 2 0 0 7 , n e t c o n trib u tio n s re m a in e d p o s itiv e b u t fa lls in th e value s o f m a n y fin a n c ia l
assets, p a rtic u la rly e q u itie s , m e a n t t h a t t o ta l s u p e ra n n u a tio n assets d e c lin e d in 2 0 0 8 a n d 20 09 . Since
20 09 , th e assets h e ld b y s u p e ra n n u a tio n fu n d s have re su m e d t h e ir lo n g -te rm tre n d , g ro w in g b y 31 p e r
ce n t in th e 2 0 0 9 to 2 0 1 2 p e rio d .
capital market
The s ig n ific a n t increase in th e n u m b e r o f fu n d s o v e r th e p e rio d covered b y Table 8 .5 is due e n tire ly
to g r o w th in th e n u m b e r o f s m a ll fu n d s , m o s t o f w h ic h are SMSFs. The n u m b e r o f s m a ll fu n d s is
d is p ro p o rtio n a te ly h ig h re la tiv e to th e v a lu e o f t h e ir assets. To illu s tra te , a t 30 J u n e 2 0 1 2 s m a ll fu n d s
a cco u n te d f o r 9 9 .9 p e r c e n t o f th e to t a l n u m b e r o f fu n d s b u t o n ly 31 .5 p e r c e n t o f th e to t a l assets h e ld b y
s u p e ra n n u a tio n fu n d s (A P R A 2 0 1 3 c, Tables 1 a n d 9).
W h ile th e n u m b e r o f s m a ll fu n d s has g ro w n stro n g ly, Table 8.5 shows th a t th e n u m b e r o f fu n d s in o th e r
categories, p a rtic u la rly c o rp o ra te fu n d s , has d e clin e d d ra m a tic a lly in rece nt years. In la rge p a rt, th is decline
refle cts th e effects o f lic e n s in g re q u ire m e n ts th a t w ere phased in d u rin g a tra n s itio n a l p e rio d th a t ended on
30 J u n e 2 0 06 . The tru ste e s o f m a n y sta n d -a lo n e c o rp o ra te fu n d s chose n o t to seek a licence a n d th e m em bers
an d assets o f these fu n d s w ere tra n s fe rre d to o th e r fu n d s , p a rtic u la rly in d u s try fu n d s and re ta il fun ds.
The v a lu e o f assets h e ld b y s u p e ra n n u a tio n fu n d s o u ts id e life in su ra n ce co m p a n ie s is s h o w n in
Table 8.6. I t show s t h a t s u p e ra n n u a tio n fu n d s are la rge , a n d g ro w in g , in v e s to rs in th e shares o f A u s tra lia n
co m p a n ie s a n d in u n its in tru s ts . These assets ty p ic a lly a cco u n te d f o r a b o u t 45 p e r c e n t o f t o ta l fu n d assets
in th e la s t fe w years, co m p a re d w it h less th a n 3 0 p e r c e n t in 1 9 9 0 . These fig u re s , in c o n ju n c tio n w it h tho se
in Table 8.1, s h o w t h a t s u p e ra n n u a tio n fu n d s are p o te n tia lly th e la rg e s t in s titu t io n a l source o f e q u ity
c a p ita l f o r A u s tra lia n co m p a n ie s. O verseas assets m ad e u p 19 p e r c e n t o f to t a l assets in 2 0 1 3 com p are d
w ith 1 1 .4 p e r c e n t in 19 90 . S im ila rly , cash a n d d e p o s its m ade u p 1 6 .4 p e r c e n t o f t o t a l assets in 20 1 3 ,
co m p a re d w it h o n ly 1 0 .7 p e r c e n t in 19 90 . In c o n tra s t, th e d e b t-ty p e in v e s tm e n ts — lo a n s, p la ce m e n ts
a n d s h o r t- te rm s e c u ritie s — decreased fr o m a lm o s t 15 p e r c e n t o f t o ta l assets in 1 9 9 0 to 6 .7 p e r c e n t in
2 0 1 3 , w h ile in v e s tm e n ts in lo n g -te rm g o v e rn m e n t s e c u ritie s d e c lin e d fr o m 10 .1 p e r ce n t o f assets in
1 9 9 0 to o n ly 1.7 p e r c e n t in 2 0 1 3 . W h ile d e b t-ty p e in v e s tm e n ts have d e c lin e d as a pe rce n ta g e o f fu n d
assets, th e a b s o lu te size o f t h e ir asset p o o l is such t h a t s u p e ra n n u a tio n fu n d s re m a in a s ig n ific a n t source
o f d e b t fin a n c e , e ith e r d ire c tly o r in d ire c tly , f o r businesses. F o r exa m ple, th e in v e s tm e n t o f $7 9 b illio n in
s h o r t- te rm s e c u ritie s a t J u n e 2 0 1 3 w o u ld in c lu d e b ills o f exchange issu e d b y c o rp o ra te b o rro w e rs . A lso ,
th e cash a n d d e p o s its o f $ 2 2 7 b illio n h e ld in 2 0 1 3 w o u ld c o n s is t m o s tly o f d e p o s its in b a n ks, w h ic h co u ld
use the se d e p o sits to fu n d lo a n s, in c lu d in g lo a n s to com p an ies.
M a n a g e m e n t o f s u p e ra n n u a tio n fu n d s is a v e ry im p o r ta n t a c tiv ity o f life in s u ra n c e com p an ies:
as a t J u n e 2 0 1 2 , assets h e ld in s u p e ra n n u a tio n fu n d s a cco u n te d f o r o ve r 90 p e r c e n t o f th e assets o f
these c o m p a n ie s, c o m p a re d to a b o u t 65 p e r c e n t in 1 9 9 2 . D e s p ite th is h ig h p r o p o r tio n , th e re has been
TABLE 8.6 Assets held by superannuation funds outside life nsurancec:ompanies, $ million
3 0 June
L o n g -te rm
E q u itie s
C ash a n d
i Loans a n d
S h o rt-te rm
g o v e rn m e n t
a n d u n its in
Land a n d
O th e r
A ssets
d e p o s its
1 p la c e m e n ts
se cu ritie s
se c u ritie s
trusts
b u ild in g s
assets
o v e rs e a s
Total assets
1990
8629
4234
7703
8191
23 770
12668
6399
9226
80820
1995
11143
5375
8794
20632
56 715
11006
8 513
21094
143272
2000
23469
16138
19376
19877
144266
17294
21239
68065
329724
2005
57443
5 292
25134
21579
281691
32157
29159
114419
566874
2006
70102
5 756
27261
28032
352674
36602
33 499
147312
701236
2007
114270
7220
36197
29755
476461
48408
49917
184930
947 157
2008
1 1 5 561
7981
40124
27253
453015
56986
52829
179601
933 351
2009
137118
9035
46467
22819
401814
61589
53281
148678
880803
2010
13 8 2 2 0
10272
55 206
25885
463862
66687
61191
171437
992 760
2011
16 8 9 5 0
11148
50200
21254
542262
76685
64796
187637
1122934
2012
208998
11963
60872
20661
525960
86089
66136
201064
1181742
2013
227003
13 232
78924
22857
621688
96450
60984
262926
1384066
Source: Table B15, Reserve Bank of Australia website, wvsrw.rba.gov.au.
C hapter eight T he
capital market
TABLE 8.7 Assets held by life insurance companies—statutory funds, $ million
L o n g -te rm
3 0 Ju n e
(
C a sh a n d
Loan s a n d
S h o rt-te rm
d e p o s its
p la c e m e n ts
se cu ritie s
E q u itie s
g o v e rn m e n t a n d u n its in ; L a n d a n d
se cu ritie s
trusts
b u ild in g s
,
O th e r
A ssets
|
assets
o ve rse a s
Total assets
1990
2 680
10 701
5 347
14 265
24 415
13 397
6 217
8 401
85 422
1995
4 912
5 817
9 927
23 779
38 076
9 486
9 321
17 214
118 532
2000
7 015
8 819
14 040
24 093
78 477
7 474
17 608
32 953
190 478
2005
4 429
2 577
12 757
13 441
156 021
n.a.
n.a.
15 828
231 444
2006
4 777
4 396
11261
9 784
172 418
3105
21903
14 299
241 943
2007
5146
3 945
10 772
9 296
200 656
3 367
21 738
12 070
266 990
2008
4 643
3 975
8 771
9 405
173 943
2 710
20 814
11839
236 099
2009
7 816
3 594
10 349
7 091
149 238
1722
21 027
10 057
210 895
2010
7 261
2 337
9 821
7 066
165 534
1719
18 846
10 896
223 481
2011
8 464
2 284
6136
7 324
178 697
1829
18 765
11196
234 695
2012
11348
2 696
6 521
8 614
167 968
1871
21148
14 979
235 146
2013
12 034
1953
5 847
9 667
189 896
1520
19 303
14 986
255 206
Source: Table B1 4,
Reserve Bank of Australia website, www.rba.gov.au.
a s ig n ific a n t d e clin e in th e share o f t o ta l s u p e ra n n u a tio n assets h e ld b y life in s u ra n c e co m p a n ie s. T h e ir
share o f th e t o ta l s u p e ra n n u a tio n p o o l p eaked a t 4 4 p e r c e n t in 1 9 9 2 b u t d e c lin e d to less th a n 15 p e r ce n t
b y J u n e 2 0 1 2 (APR A, 2 0 1 2 a ). The assets o f life in s u ra n c e co m p a n ie s are s h o w n in Table 8.7.
W h ile th e d a ta in Table 8 .7 w ill la rg e ly re fle c t th e assets h e ld in s u p e ra n n u a tio n fu n d s m a n a g e d b y
life in su ra n ce com p an ies, th e re are som e n o tic e a b le d iffe re n ce s b e tw e e n th e d is tr ib u tio n s o f assets in
Tables 8.6 an d 8.7. C o m p a re d w it h th e s u p e ra n n u a tio n fu n d s o u ts id e life in s u ra n c e co m p a n ie s, based
on th e 2 0 1 3 fig u re s, th e life in s u ra n c e com p an ies have in v e s te d a h ig h e r p r o p o r tio n o f t h e ir assets
in d o m e s tic e q u itie s a n d tr u s ts (7 4 .4 p e r c e n t versu s 4 4 .9 p e r c e n t), a lo w e r p r o p o r tio n in cash an d
d e po sits (4 .7 p e r c e n t versu s 1 6 .4 p e r c e n t) a n d a lo w e r p r o p o r tio n in overseas assets (5 .9 p e r c e n t versus
19.0 p e r ce n t). Table 8 .7 sho w s t h a t life in s u ra n c e c o m p a n ie s are n o t la rg e le n d e rs to th e c o rp o ra te sector.
H is to ric a lly , m o s t o f t h e ir in v e s tm e n t in d e b t to o k th e fo r m o f g o v e rn m e n t d e b t se c u ritie s . H o w eve r,
h o ld in g s o f ‘o th e r assets’，w h ic h in c lu d e s d e b t s e c u ritie s issu ed b y n o n -g o v e rn m e n t b o rro w e rs , have
te n d e d to increase as t h e ir h o ld in g s o f lo n g -te rm g o v e rn m e n t s e c u ritie s have de clin e d . In c o n tra s t, lik e
s u p e ra n n u a tio n fu n d s o u ts id e life in s u ra n c e com p an ies, th e y are s ig n ific a n t s u p p lie rs o f e q u ity , w ith
shares a n d u n its in tru s ts g e n e ra lly c o n s titu tin g b e tw e e n 70 a n d 75 p e r c e n t o f t h e ir to t a l assets a t th e
end o f J u n e each ye a r fro m 2 0 0 6 to 2 0 1 3 .
W h e n assessing th e asset d is tr ib u tio n s s h o w n in Tables 8 .6 a n d 8.7, tw o q u a lific a tio n s s h o u ld be n o te d .
F irs t, th e in v e s tm e n t b y s u p e ra n n u a tio n fu n d s a n d life in s u ra n c e com p an ies in p r o p e r ty is c o n s id e ra b ly
g re a te r th a n suggested b y th e fig u re s s h o w n f o r 4la n d a n d b u ild in g s 1. M a n y o f the se in s titu t io n s in v e s t
in p ro p e rty b y p u rc h a s in g u n its in re a l esta te in v e s tm e n t tru s ts (R E IT s)15 m a in ly because th e y p re fe r
th e liq u id ity t h a t these tru s ts p ro v id e , p a r tic u la r ly i f th e t r u s t is lis te d o n a s to c k exchange. These
in v e s tm e n ts are in c lu d e d in th e fig u re s f o r ‘E q u itie s a n d u n its in tr u s t s ’. Second, th e ‘s to c k ，fig u re s s h o w n
in these ta b le s do n o t n e ce ssa rily p ro v id e an accu rate in d ic a tio n o f th e w a y in w h ic h
new m o n e y
flo w in g
in to s u p e ra n n u a tio n is in ve ste d . F o r exa m ple, as n o te d above, th e ta b le s s h o w t h a t e q u itie s a n d u n its
15 Real estate investment trusts (REITs) were traditionally referred to as property trusts, which could be listed or unlisted.
The term REIT was adopted in Australia in 2008. Where such trusts are listed on the ASX, they are referred to as A-REITs.
in tru s ts m a ke u p a la rg e a n d ty p ic a lly g ro w in g p r o p o r tio n o f th e assets o f s u p e ra n n u a tio n fu n d s and
life in s u ra n c e co m p a n ie s. In th e case o f s u p e ra n n u a tio n fu n d s o u ts id e life in s u ra n c e com p an ies, th is
asset class in cre a se d fr o m less th a n 30 p e r c e n t o f to t a l assets in 1 9 9 0 to ju s t o v e r 5 0 p e r c e n t o f to ta l
assets in 2 0 0 7 a n d has since s ta b ilis e d a t a b o u t 4 5 p e r ce n t. Thus, i t m ig h t seem t h a t th e p r o p o r tio n o f
s u p e ra n n u a tio n c o n trib u tio n s d ire c te d in to d o m e s tic e q u itie s pe ake d a ro u n d 2 0 0 6 -0 7 a n d th e n declin ed .
H o w eve r, th e values o f th e v a rio u s assets h e ld a t a n y tim e w ill re fle c t p a s t re tu rn s as w e ll as th e p a tte r n o f
n e w in v e s tm e n t. The r e tu rn s o n A u s tra lia n shares w e re u n u s u a lly h ig h fr o m 2 0 0 2 to 2 0 0 7 b u t n e g a tiv e in
2 0 0 8 a n d 20 0 9 . S pe cifica lly, th e S & P /A S X A ll O rd in a rie s share p ric e in d e x , w h ic h w as 3 1 6 3 .2 a t th e e n d o f
J u n e 2 0 0 2 , a lm o s t d o u b le d to reach 6 3 1 0 .6 a t th e e n d o f J u n e 2 0 0 7 a n d th e n fe ll to 3 9 4 7 .8 a t th e e n d o f
J u n e 2 0 0 9 . T h e re fo re , o v e r th e 2 0 0 2 to 2 0 0 9 p e rio d , a ty p ic a l fu n d c o u ld e x h ib it an in crea se in th e value
o f e q u itie s as a pe rce n ta g e o f it s to t a l assets u p to 2 0 0 7 , fo llo w e d b y a d e clin e , even i f th e p r o p o r tio n o f
n e w c o n trib u tio n s in v e s te d in each asset class re m a in e d c o n s ta n t o v e r tim e . The reverse can also occur:
fr o m J u n e 2 0 0 9 to J u n e 2 0 1 3 , th e S & P /A S X A ll O rd in a rie s share p ric e in d e x rose b y 21 p e r c e n t b u t o ve r
th e sam e p e rio d th e share o f t o t a l assets h e ld as e q u itie s a n d u n its in tru s ts fe ll m a rg in a lly fr o m 4 5 .6 to
4 4 .9 p e r c e n t.
U n it tr u s ts are a c o m m o n f o r m o f c o lle c tiv e in v e s tm e n t in w h ic h th e fu n d s o f in v e s to rs are p o o le d a n d
in v e s te d b y a p ro fe s s io n a l m a n a g e m e n t co m p a n y in a w id e ran ge o f in v e s tm e n ts , u s u a lly o f a specific
asset ty p e . F o r e xa m p le , th e re are R EITs, A u s tra lia n e q u ity tr u s ts a n d in te r n a tio n a l e q u ity tru s ts . These
a n d a v a r ie ty o f o th e r p o o le d in v e s tm e n ts are cla ssifie d as ‘m a n a g e d in v e s tm e n t sche m es’. The re g u la to ry
re g im e f o r the se in v e s tm e n ts is set o u t in th e
Managed Investments Act 1998.
I t spe cifie s t h a t m an ag ed
in v e s tm e n t schem es are to be o p e ra te d b y a sin g le R esponsible e n tity *, w h ic h m u s t be an A u s tra lia n
p u b lic c o m p a n y h o ld in g an a p p ro p ria te A u s tra lia n F in a n c ia l Services Licence. M o s t o f th e se re sp o n sib le
e n titie s are su b s id ia rie s o f b a n ks, in v e s tm e n t b a n k s o r in s u ra n c e co m p a n ie s. In v e s to rs place t h e ir m o n e y
in p o o le d in v e s tm e n ts to o b ta in a spre ad o f r is k a n d to o b ta in re tu rn s fr o m assets t h a t are to o exp en sive
f o r in d iv id u a ls to p u rcha se d ire c tly .
F o r som e in v e s to rs , tr u s ts m a y also be a ttra c tiv e f o r ta x reasons. In ge n e ra l, a t r u s t is n o t ta xe d
p ro v id e d t h a t i t d is trib u te s a ll o f its in c o m e to in v e s to rs . Each in v e s to r is th e n ta x e d o n th e in c o m e
th e y re ce ive d fr o m th e t r u s t . 16 T h ere fore, t r u s t in c o m e is a lm o s t in v a ria b ly d is tr ib u te d in f u ll w hereas a
co m p a n y can r e ta in a ll o r p a r t o f its p r o f it to fin a n c e exp a n sio n .
M a n y tr u s ts are o p e n -e n d fu n d s , w h ic h m ea ns t h a t n e w u n its m a y be cre a te d c o n tin u a lly as in v e s to rs
c o n trib u te a d d itio n a l cash. These tru s ts are u n lis te d a n d in v e s to rs p u rch a se a n d re d e e m u n its a t values,
c a lc u la te d d a ily b y th e fu n d m an ag er, based o n th e v a lu e o f th e assets h e ld b y th e t r u s t . The t r u s t m a y b u y
a d d itio n a l assets a t a n y tim e a n d m a y ne ed to se ll assets a t tim e s in o rd e r to m e e t re d e m p tio n req ue sts
fr o m e x is tin g in v e s to rs . In J u n e 2 0 1 3 , p u b lic u n it tr u s t s 17 in A u s tra lia h a d t o ta l assets o f $ 2 3 8 b illio n
a n d a f u r t h e r $2 5 b illio n w as h e ld b y cash m a n a g e m e n t tr u s ts (R eserve B a n k o f A u s tra lia , Table B l,
www.
rba.gov.au).
A w id e ran ge o f lis te d m a n a g e d in v e s tm e n ts (L M Is ) is also ava ila ble. A t th e e n d o f J u n e 2 0 1 3 , 2 0 4
m an ag ed in v e s tm e n ts w e re lis te d o n th e A S X a n d th e m a rk e t c a p ita lis a tio n o f the se e n titie s to ta lle d $ 1 63
b illio n . Based o n m a rk e t c a p ita lis a tio n a t t h a t tim e , th e la rg e s t c a te g o ry o f L M Is is re a l esta te in v e s tm e n t
tru s ts ($ 9 5 b illio n ) , fo llo w e d b y in fr a s tr u c tu r e fu n d s ($ 4 0 b illio n ) a n d lis te d in v e s tm e n t com p an ies
a n d tru s ts ($ 2 0 b illio n ) (A u s tra lia n S e cu ritie s E xchange,
w w w .asx.com .au/products/m anaged-funds/
m arket-update.htm .)
REITs a llo w in v e s to rs to acq uire an in te re s t in a p ro fe s s io n a lly m a n a g e d p o r tf o lio o f re a l estate. Some
R EITs in v e s t o n ly in a p a r tic u la r ty p e o f re a l esta te such as in d u s tr ia l (w a reho use s a n d fa c to rie s ), offices,
h o te ls o r re ta il (s h o p p in g ce n tre s, m a lls a n d cin e m a s). O th e rs are m o re d iv e rs ifie d a n d in v e s t in tw o o r
m o re o f th e se ty p e s o f re a l estate. There are also in te r n a tio n a l R EITs, w h ic h are lis te d o n th e A S X b u t
in v e s t in sp e cific o ffs h o re m a rk e ts such as th e US, E u ro p e o r Japan.
16 In many cases, the distributions from REITs are partly tax deferred, which means that investors do not pay tax on the taxdeferred component of the distribution until their holding in the trust is sold.
17 Public unit trusts are investment funds, excluding property and trading trusts, that are open to the Australian public.
C hapter eight T he
capital market
A R E IT lis te d o n th e A S X w i ll have one o f tw o s tru c tu re s :
•
a s ta n d -a lo n e t r u s t t h a t p ro v id e s in v e s to rs w it h e xp o su re o n ly to an u n d e rly in g p o r tf o lio o f real
estate assets; o r
•
a g ro u p c o n s is tin g o f a co m p a n y a n d one o r m o re re la te d tru s ts .
P a rtly because o f it s ta x a tio n tre a tm e n t, a s ta n d -a lo n e t r u s t is s u ita b le f o r h o ld in g a n d m a n a g in g a
p o r tfo lio o f assets t h a t p ro d u ce passive r e n ta l in c o m e f o r d is tr ib u tio n to in v e s to rs . P ro p e rty d e v e lo p m e n t
a n d /o r m a n a g e m e n t are u s u a lly b e tte r u n d e rta k e n b y a c o rp o ra te s tru c tu re r a th e r th a n a tr u s t. In a g ro u p
s tru c tu re , in c o m e -p ro d u c in g p ro p e rtie s w ill be h e ld b y th e tru s t(s ) w h ile an a sso cia te d c o m p a n y w i ll c a rry
o u t p ro p e rty d e v e lo p m e n t a n d /o r m a n a g e m e n t. The g ro u p w ill issue s t a p le d s e c u r it ie s c o m p ris in g a
STAPLED SECURITIES
share in th e c o m p a n y p lu s a u n it in each o f th e tru s ts . The te r m s ta p le d ' re fe rs to th e re q u ire m e n t t h a t
two or more legally
separate instruments,
typically an ordinary
share plus units in
one or more related
trusts, which cannot be
traded separately
th e tw o se c u ritie s m u s t be tra d e d to g e th e r as i f th e y w e re a s in g le s e cu rity.
In fra s tru c tu re fu n d s in v e s t in assets in v o lv e d in th e s u p p ly o f e s s e n tia l goods a n d services such as
p o r t fa c ilitie s , ra ilw a ys, t o ll roa ds, a irp o rts , c o m m u n ic a tio n fa c ilitie s , p o w e r lin e s a n d o il/g a s p ip e lin e s .
Some in fra s tru c tu re fu n d s in v o lv e a c o m p a n y /tru s t g ro u p th a t issues s ta p le d se c u ritie s . L ike REITs,
in fra s tru c tu re fu n d s g e n e ra lly receive a stab le in c o m e s tre a m a n d p a y re g u la r d is tr ib u tio n s to in v e s to rs .
In v e s to rs can also choose t o in v e s t b y b u y in g shares in a lis te d in v e s tm e n t co m p a n y (L IC ). T yp ica lly,
an LIC w ill in v e s t in a d iv e rs ifie d p o r tf o lio o f in v e s tm e n ts , o fte n c o n s is tin g o f th e shares o f a w id e range
o f o th e r com p an ies t h a t are also lis te d o n th e ASX. In v e s to rs th e re fo re achieve a d iv e rs ifie d p o r tf o lio
w ith o u t th e need to p e rs o n a lly select, b u y a n d m anage a la rg e n u m b e r o f in v e s tm e n ts . Som e LICs
specialise in p a rtic u la r typ e s o f assets such as in te r n a tio n a l shares, s m a ll co m p a n ie s o r g o ld co m p a n ie s, o r
th e y m a y focus on p a r tic u la r g e o g ra p h ic a l re g io n s such as E u ro p e o r A sia . In c o n tra s t to u n lis te d m an ag ed
in v e s tm e n ts , LICs are e s s e n tia lly clo sed -end , m e a n in g t h a t th e co m p a n y does n o t c o n tin u a lly issue n e w
shares o r cancel shares as s h a re h o ld e rs jo in a n d leave th e com pany. R a th e r, th e co m p a n y s shares are
tra d e d o n th e A S X in th e sam e w a y as o th e r lis te d shares, a n d th e size a n d t im in g o f a n y share issues o r
repurchases w ill be d e te rm in e d b y th e c o m p a n y s m anagers. The m a rk e t p ric e o f th e shares is d e te rm in e d
b y m a rk e t forces. The share p ric e w ill o fte n be s im ila r to th e m a rk e t va lu e o f th e L IC s assets b u t can be a t
a p re m iu m or, m o re o fte n , a t a d is c o u n t to th e n e t asset value.
The fa c t t h a t som e m a n a g e d in v e s tm e n ts are s tru c tu re d as a t r u s t w h ile o th e rs use a c o m p a n y
s tru c tu re creates im p o r t a n t ta x a tio n d iffe re n ce s. F o r exa m ple, i f a t r u s t m akes a p r o fit, th e e n tire p r o fit
w ill be passed o n to in v e s to rs as a d is tr ib u tio n a n d each in v e s to r w ill be ta x e d a t t h e ir in d iv id u a l rate. I f
a lis te d in v e s tm e n t co m p a n y m ake s th e sam e p r o fit, i t w ill p a y ta x a t th e co m p a n y ta x ra te o n t h a t p r o fit.
The a fte r-ta x p r o f it can th e n be d is tr ib u te d to sh a re h o ld e rs as a fra n k e d d iv id e n d .18
The A u s tra lia n c a p ita l m a rk e t is p a r t o f th e g lo b a l c a p ita l m a rk e t a n d f o r m a n y years th e re has b e en a
sizeable flo w o f fu n d s fro m overseas f o r in v e s tm e n t in A u s tra lia n com p an ies. These flo w s have c o m p ris e d
b o th e q u ity a n d d e b t, in c lu d in g e q u ity fu n d in g o f n e w v e n tu re s a n d f o r p o r tf o lio in v e s tm e n t. Some
A u s tra lia n com p an ies, p a r tic u la r ly v e ry la rge ones, b o rro w d ire c tly fr o m overseas, a n d b a n ks a n d o th e r
in te rm e d ia rie s have been v e ry a ctive in o b ta in in g fu n d s f r o m overseas. Because A u s tra lia n b a n ks ty p ic a lly
have h ig h c re d it ra tin g s , th e y are b e tte r p lace d to b o rro w overseas th a n m a n y com p an ies. The fu n d s
b o rro w e d b y th e in te r m e d ia ry are th e n le n t to c u sto m e rs.
W h ile sizeable fu n d s have flo w e d fr o m overseas f o r in v e s tm e n t in A u s tra lia n co m p a n ie s, A u s tra lia
has also been a s ig n ific a n t source o f fu n d s f o r in v e s tm e n t in fo re ig n com p an ies. F o r exa m p le , as s h o w n
in Table 8.6, A u s tra lia n s u p e ra n n u a tio n fu n d s have la rg e in v e s tm e n ts in overseas assets a n d the se
in v e s tm e n ts have a t tim e s exceeded 20 p e r c e n t o f th e fun ds* assets. The in flo w to , a n d o u tflo w o f c a p ita l
fro m , A u s tra lia is c o n s is te n t w it h in v e s to rs re c o g n is in g th e advantages o f d iv e rs ific a tio n , in c lu d in g th e
o p p o r tu n ity to in v e s t in in d u s trie s t h a t m a y n o t be p re s e n t in t h e ir d o m e s tic eco no m ies.
18 Franked dividends are discussed in detail in Section 11.4.1.
SUMMARY
•
A t a n y g iv e n tim e , s o m e e n titie s w ill h a v e su rp lu s
b y c o m p a n ie s to ra is e e q u ity a n d lo n g -te rm d e b t is
fu n d s (the 's u rp lu s u n its '), w h ile o th e rs w ill b e s e e k in g
c o n s id e re d in m o re d e ta il in C h a p te rs 9 a n d 1 0 .
fu n d s (the 'd e f ic it u n its '). A m a jo r ro le o f th e c a p it a l
m a rk e t is to tra n s fe r fu n d s fro m th e s u rp lu s u n its to
•
•
S e v e ra l
ty p e s
of
f in a n c ia l
in s titu tio n s
fo rm
an
im p o r ta n t p a r t o f th e c a p it a l m a rk e t. T h e se in c lu d e
th e d e fic it un its.
in s titu tio n s th a t o p e r a te a s a g e n ts (such a s b ro k e rs ),
The A u s tra lia n c a p ita l m a rk e t is la rg e , a c tiv e a n d w e ll
f in a n c ia l in te r m e d ia r ie s (such as b a n k s ) a n d in v e s to rs
re g u la te d a n d o ffe rs a w id e ra n g e o f o p tio n s fo r surp lu s
(such a s in s u ra n c e c o m p a n ie s a n d s u p e ra n n u a tio n
un its a n d d e fic it units. The use o f th e c a p ita l m a rk e t
fu n d s ).
KEY TERMS
a u th o ris e d d e p o s i 卜
ta k in g in s titu tio n
c a p ita l m a rk e t
c e n tra l b a n k
d e fa u lt ris k
214
211
in v e s tin g in s titu tio n
213
p r im a r y m a rk e t
e x c h a n g e -tra d e d m a rk e t
212
fin a n c ia l a g e n c y in s titu tio n
214
211
212
212
s e c o n d a ry m a rk e t
s e c u ritis a tio n
211
214
o v e r-th e -c o u n te r m a rk e t
22 1
fin a n c ia l assets
fin a n c ia l in te r m e d ia r y
212
223
s ta p le d s e cu ritie s
229
QUESTIONS
1
[L O 1
D is tin g u is h b e tw e e n d ir e c t f in a n c e a n d in te r m e d ia te d fin a n c e . D iscu ss w h y s o m e b o r r o w e r s m ig h t
p re fe r d ir e c t fin a n c e , w h ile o th e rs m ig h t p r e fe r in te r m e d ia te d fin a n c e .
2
[LO 1] W h y is th e e x is te n c e o f a s e c o n d a r y m a rk e t e x p e c te d to in c re a s e th e d e m a n d f o r s e c u ritie s is s u e d in
th e c o r r e s p o n d in g p r im a r y m a rk e t?
3
4
[ L O l ] W h a t a r e th e m a in d iffe re n c e s b e tw e e n a n e x c h a n g e -tr a d e d m a rk e t a n d a n o v e r-th e -c o u n te r m a rk e t?
[L O 2 ]
D is tin g u is h b e tw e e n f in a n c ia l a g e n c y in s titu tio n s , f in a n c ia l in te r m e d ia r ie s a n d in v e s tin g in s titu tio n s .
W h y is th e re s u ch a r a n g e o f in s titu tio n s in th e c a p it a l m a rk e t?
5
6
[L O 3 ] D iscu ss th e re la tiv e im p o r ta n c e o f th e f o llo w in g in s titu tio n s a s p r o v id e r s o f c o m p a n y fin a n c e :
a)
s to c k b ro k e rs
b)
in v e s tm e n t b a n k s
c)
banks
d)
fin a n c e c o m p a n ie s
e)
s u p e ra n n u a tio n fu n d s .
[L O 3 ] O u tlin e th e s e rv ic e s p r o v id e d b y fin a n c ia l in s titu tio n s , su ch a s s to c k b ro k e rs a n d in v e s tm e n t b a n k s , to
c o m p a n ie s w is h in g to ra is e fu n d s d ir e c t fro m th e c a p it a l m a rk e t.
7
[L O 3 ] W h a t d is tin c tio n s c a n b e m a d e b e tw e e n th e a c tiv itie s o f la r g e A u s tr a lia n b a n k s a n d in v e s tm e n t
banks?
8
[L O 3 ] In v e s tm e n t b a n k s c a n fa c e in h e re n t c o n flic ts o f in te re s t. E x p la in h o w th e se c o n flic ts o f in te re s t u s u a lly
a ris e . H o w c a n th e y b e m a n a g e d ?
9
[L O 3 ] D u rin g th e g lo b a l f in a n c ia l c ris is , a t le a s t o n e A u s tr a lia n - b a s e d in v e s tm e n t b a n k c o lla p s e d , w h ile
o th e rs , in c lu d in g th e s u b s id ia r ie s o f US a n d E u ro p e a n firm s , c o n tin u e d to o p e r a te b u t o n a s o m e w h a t s m a lle r
s c a le . O u tlin e th e m a in d iffe re n c e s th a t c o n trib u te d to th e se v e r y d iffe r e n t o u tc o m e s .
10
[L O 4 ] W h a t s e rv ic e s d o b a n k s o ffe r to d e p o s ito rs ?
11
[ L 0 4 ] W h a t s e rv ic e s d o b a n k s o ffe r to c o r p o r a te c lie n ts ?
C hapter eight T he
[LO 4
】W h a t
a re th e m a in r e g u la to r y d iffe re n c e s b e tw e e n a fo r e ig n b a n k s u b s id ia r y o p e r a tin g in A u s tr a lia
a n d a fo r e ig n b a n k b r a n c h o p e r a tin g in A u s tr a lia ? W h a t a r e th e m a in im p lic a tio n s o f th e se d iffe re n c e s ?
13
[LO 5 】The m a jo r b a n k s in A u s tr a lia s e c u ritis e o n ly a s m a ll p r o p o r tio n o f th e ir m o r tg a g e lo a n s , r e g io n a l
b a n k s m a k e g r e a te r use o f th is te c h n iq u e a n d s p e c ia lis t m o r tg a g e o r ig in a t o r s s e c u ritis e m o s t o f th e ir lo a n s .
E x p la in w h y th e se d iffe re n c e s e x is t.
14
[LO 6 ] E x p la in p o s s ib le re a s o n s f o r th e r a p id in c re a s e in th e n u m b e r o f s u p e r a n n u a tio n fu n d s in e x is te n c e as
w e ll a s th e to ta l assets h e ld b y th o s e fu n d s .
15
[LO 6 ] Institutional investors have a lw ays been m a jo r suppliers o f co m p a n y finance. D iscu ss th is s ta te m e n t
a n d e x p la in h o w th is f lo w o f fu n d s o c c u rs .
REFERENCES
Australian Bureau of Statistics, Lending Finance, Australia,
cat. no. 5 6 7 1 .0 , Table 3.
Australian Prudential Regulation Authority, Annual
Superannuation Bulletin, wvy^v.apra.gov.au, Commonwealth
of Australia, ACT, June 2 0 0 6 , June 2 0 0 9 and June 2 0 1 3 a .
September 2 0 0 8 . Available at w w w .blo om b erg.co m /a pps/
news?pid=2107 00 01 & sid=axaX5i4871 UO, 22 September
20 08 .
-------; li f e insurance industry overview 7, A PRA Insight, Issue
3, 20 12 a, pp. 1 8 -3 9 , w w w .apra.gov.au.
Investing in Australian Real Estate: A Guide for Global
Investors, King & W ood Mallesons, 2 0 1 3 . Available
at www.mallesons.com/Documents/Real_Estate_Real_
0pportunities% 20_0ct% 201 1_hyperlinks.pdf.
-------; Regulation Impact Statement: Implementing Basel III
Capital Reforms in Australia, September 2 0 1 2 b , w w w .a p ra .
gov.au.
O verland , 丄 & Li, K., 'Room for improvement: Insider trading
and Chinese w alls', Australian Business Law Review, 2 0 1 2 ,
pp. 2 2 3 -4 0 .
-------, Discussion Paper: Implementing Basel III Liquidity
Reforms in Australia, M a y 2 0 1 3 b , w w w .apra.gov.au.
Reserve Bank of Australia, 'Asset securitisation in Australia',
Financial Stability Review, September 2 0 0 4 , pp. 4 8 -5 6 .
-------, Monthly Banking Statistics, O ctober 2 0 1 3c.
Schwartz, C., 'The Australian Government Guarantee
Schemed Reserve Bank of Australia, Bulletin, M arch 2 0 1 0 ,
pp. 1 9 -2 6 .
Carew, E.; Fast M o n e y 4, Allen & Unwin, Sydney, 1998.
Debelle, G ., 'W hither securitisation?/, Reserve Bank of
Australia, Bulletin, December 2 0 0 9 , pp. 4 3 -5 3 .
Gup, B.E., The N e w Basel Capital Accord, Texere, N ew
York, 20 04 .
C H A P T E R EIGHT R E V I E W
12
capital market
Viney, C. & Phillips, P., Financial Institutions, Instruments and
Markets, 7th edn, M cG raw-H ill, Sydney, 20 12 .
Harper C. & Torres C., 'G oldm an, M organ Stanley bring
down curtain on an era' (Update 5), Bloomberg, 22
231
CHAPTER CONTENTS
I n t r o d u c t io n
T h e c h a r a c t e r is tic s o f o r d in a r y s h a re s
^ 0
P riv a te e q u it y
I^ Q
I n f o r m a tio n d is c lo s u r e
m
F lo a tin g a p u b lic c o m p a n y
g g■
g
m
S u b s e q u e n t is s u e s o f o r d in a r y s h a re s
252
E m p lo y e e s h a r e p la n s
265
In te r n a l fu n d s
266
M a n a g in g a c o m p a n y ’s e q u it y s tru c tu r e
268
LEARNING OBJECTIVES
m
A f te r s tu d y in g th is c h a p t e r y o u s h o u ld b e a b le to :
1
o u t lin e th e c h a r a c t e r is tic s o f o r d in a r y s h a re s
2
e x p la in th e a d v a n t a g e s a n d d is a d v a n t a g e s o f e q u it y a s a s o u r c e o f f in a n c e
3
o u t lin e th e m a in s o u rc e s o f p r iv a t e e q u it y in th e A u s t r a lia n m a r k e t
4
id e n t it y th e in f o r m a t io n t h a t m u s t b e d is c lo s e d w h e n is s u in g s e c u r itie s
5
o u t lin e th e p ro c e s s o f f lo a t in g a p u b lic c o m p a n y
6
d is c u s s a lte r n a tiv e e x p la n a t io n s f o r th e u n d e r p r ic in g o f in it ia l p u b lic o f f e r in g s
7
o u t lin e e v id e n c e o n th e lo n g - te r m p e r f o r m a n c e o f c o m p a n ie s t h a t a r e f lo a t e d
8
e x p la in h o w c o m p a n ie s r a is e c a p it a l t h r o u g h r ig h ts is s u e s , p la c e m e n ts , s h a r e p u r c h a s e p la n s a n d s h a r e
o p t io n s
9
o u t lin e th e d if f e r e n t ty p e s o f e m p lo y e e s h a r e p la n s
10
o u t lin e th e a d v a n t a g e s o f in te r n a l f u n d s a s a s o u r c e o f f in a n c e
11
o u t lin e th e e ffe c ts o f b o n u s is s u e s , s h a r e s p lits a n d s h a r e c o n s o lid a t io n s .
C hapter n in e S ources
of f in a n c e : equity
In th is c h a p te r a n d in C h a p te r 10, w e discuss m e th o d s b y w h ic h a c o m p a n y m a y fin a n c e its assets. In th is
c h a p te r we discuss e q u ity , C h a p te r 10 covers d e b t, a n d le a s in g is co n sid e re d in C h a p te r 15.
In th is cha pter, several w ays o f ra is in g e q u ity are co n sid e re d . The m a jo r ity o f e q u ity in A u s tra lia is
raised b y p u b lic co m p a n ie s a n d u n it tru s ts w it h shares, u n its a n d
stapled secu rities
lis te d o n a s to c k
exchange. I m p o r ta n t sources o f e q u ity f o r lis te d co m p a n ie s in c lu d e in it ia l p u b lic o ffe rin g s (IP O s) o f
primary raising, V ig hts* issues, share pu rcha se
o f w h ic h is a secondary raising o f c a p ita l. O th e r,
shares, w h ic h is an e xa m ple o f a
p la n s, p la ce m e n ts a n d
re in v e s tm e n t o f d iv id e n d s , each
less s ig n ific a n t sources
o f e q u ity in c lu d e share issues to em ployees, calls o n c o n tr ib u tin g shares a n d exercise o f c o m p a n y-issu e d
o p tio n s . In a d d itio n , th e use o f in te r n a l fu n d s as a source o f fin a n c e is discussed. E q u ity ra ise d b y is s u in g
o rd in a ry shares is an im p o r t a n t source o f fin a n c e f o r A u s tra lia n co m p a n ie s. The im p o rta n c e o f e q u ity
is illu s tra te d b y th e fa c t t h a t a t th e en d o f D e ce m b e r 2 0 1 3 , th e va lu e o f shares a n d o th e r e q u itie s lis te d
on th e A u s tra lia n S e cu ritie s E xchange (ASX) was $ 1 5 2 7 b illio n . 1 As s h o w n in Table 9.1 , e q u ity c a p ita l o f
a p p ro x im a te ly $ 3 1 5 b illio n was ra ise d th ro u g h th e issue o f shares a n d o th e r s e c u ritie s b y lis te d e n titie s
ove r th e 5 -ye a r p e rio d e n d in g 30 J u n e 20 13 .
TABLE 9.1 Listings and equity raisings by ASX-listed entities, financial year ended
30 June ($ billion)
2010
2011
2012
2013
1.9
11.4
35.6
10.2
9.9
Rights issues
28.5
23.2
7.4
8.1
4.0
Placements and share
42.0
28.6
10.1
12.8
19.2
15.0
10.2
7.8
9.3
6.9
2.1
2.4
2.1
2.4
2.3
0.5
0.7
0.2
0.1
0.1
90.0
76.5
63.2
42.9
42.4
【Type o f c a p ita l ra is in g
2009
Primary raisings
IPOs
Secondary raisings
purchase plans
R einvestm ent o f
dividends
Company-issued o p tio n s
and employee share
schemes
O thers
Total capital
Source: Australian Financial Markets Association, 2 0 1 3 Australian Financial Markets Report, February 2014, p. 55.
A m u ch s m a lle r b u t s t ill im p o r t a n t m a rk e t is th e p riv a te e q u ity m a rk e t, w h e re fin a n c e is ra ise d b y
is s u in g s e c u ritie s t h a t are n o t p u b lic ly tra d e d . P riv a te e q u ity in c lu d e s v e n tu re c a p ita l, w h ic h re fe rs to th e
fin a n c in g o f n e w v e n tu re s o r s ta rt-u p * com p an ies. B efo re d is c u s s in g th e ways in w h ic h co m p a n ie s raise
e q u ity, we o u tlin e th e fe a tu re s o f th e m a in ty p e o f e q u ity s e c u ritie s th e y issu e— t h a t is, o rd in a ry shares.
P reference shares, w h ic h are le g a lly e q u ity b u t also have som e o f th e c h a ra c te ris tic s o f d e b t, are discussed
in C h a p te r 10.
1
Australian Securities Exchange Limited, www.asx.com.au/about/historical-market-statistics.htm#End_of_month_values.
The figure quoted does not include the value of overseas-based equities listed on the ASX. There are also many private and
unlisted companies, most of which are much smaller than listed companies.
STAPLED SECURITIES
two or more legally
separate instruments,
typically an ordinary
share plus units in
one or more related
trusts, which cannot be
traded separately
B usiness finance
9.2
The characteristics of o rd in a ry shares
E q u ity is th e m o s t fu n d a m e n ta l f o r m o f c o rp o ra te fin a n c e because e v e ry co m p a n y m u s t raise som e e q u ity
LEARNING
OBJECTIVE 1
Outline the
characteristics of
ordinary shares
ORDINARY SHARES
securities that
represent an
ownership interest in a
company and provide
the owner with voting
rights. Holders of
ordinary shares have
a residual interest in
the net assets of the
issuing company and
are therefore exposed
to greater risk than
other classes of
investors
RESIDUAL CLAIM
b y is s u in g
ordinary sh ares.
A n o rd in a ry share gives th e h o ld e r o w n e rs h ip o f a p r o p o r tio n o f th e e q u ity
o f th e com p an y. I f a co m p a n y has 10 0 0 0 0 issu ed shares a n d an in v e s to r h o ld s 1 0 0 0 shares, th e in v e s to r
has an o w n e rs h ip in te re s t in 1 p e r c e n t o f th e n e t assets o f th e com pany. T h is does n o t m ea n t h a t th e
in v e s to r can exercise o w n e rs h ip rig h ts w it h re sp e ct to sp e cific assets o f th e com p an y. H o w eve r, w h e n
d iv id e n d s are p a id , o r i f th e co m p a n y is ta k e n o v e r b y a n o th e r com pany, o r is p lace d in t o liq u id a tio n , th e
in v e s to r has th e r ig h t to receive 1 p e r c e n t o f th e p a y m e n ts m ad e to o rd in a ry s h a re h o ld e rs.
P e rio d ica lly, a co m p a n y s d ire c to rs m a y decide to p a y d iv id e n d s to s h a re h o ld e rs an d, as discussed in
S e c tio n 4 .3 , th e va lu e o f an o rd in a ry share can be v ie w e d as th e p re s e n t va lu e o f exp ected f u tu r e d iv id e n d s .
The in te re s t h e ld b y s h a re h o ld e rs is a residual
claim
in th e sense t h a t s h a re h o ld e rs w ill receive d iv id e n d s
o n ly a fte r a co m p a n y has m e t its o b lig a tio n s to a ll o th e r c la im a n ts such as su p p lie rs , em ployees, le n d e rs
a n d g o v e rn m e n ts . S im ila rly , i f a c o m p a n y is placed in to liq u id a tio n , o rd in a ry s h a re h o ld e rs have a re s id u a l
c la im o n th e proceeds fr o m th e sale o f th e co m p a n y s assets. Because s h a re h o ld e rs are p a id la s t, th e y face
g re a te r r is k th a n o th e r in v e s to rs in a com pany. To com p en sate f o r th is ris k , in v e s to rs in o rd in a ry shares
exp ect a ra te o f r e tu r n t h a t is g re a te r th a n th e y c o u ld o b ta in b y le n d in g to th e com pany.
9.2.1 | Fully paid and partly paid shares
W h e n n e w shares are cre a te d a n d issu ed th e y w ill have a s ta te d issue p rice . T his p ric e m a y be payable in
claim to profit or
assets that remain
after the entitlements
of all other interested
parties have been met
has been p a id , shares are re fe rre d to as p a r tly p a id shares o r c o n trib u tin g shares. O nce th e t o ta l issue
CALL
p ric e has been p a id th e shares are f u lly p a id a n d th e h o ld e r c a n n o t be re q u ire d to c o n trib u te a n y m o re
notice given by a
company that the
holders of partly paid
shares must make an
additional contribution
of equity
LIMITED LIABILITY
legal concept that
protects shareholders
whose liability to meet
a company’s debts is
limited to any amount
unpaid on the shares
they hold
f u ll a t th e tim e th e shares are issu e d o r p a r t o f th e issue p ric e m a y be payable in it ia lly w it h th e balance to
be p a id in s u b se q u e n t in s ta lm e n ts , g e n e ra lly k n o v rn as calls. The a m o u n t a n d t im in g o f each
call
m a y be
sp e cifie d in it ia lly o r th e c o m p a n y s d ire c to rs m a y d e te rm in e th e m la te r. W h e re o n ly p a r t o f th e issue p rice
fu n d s to th e com pany, a lth o u g h th e y m a y be g iv e n th e o p p o r tu n it y to do so. A v e ry s im ila r s e c u rity th a t
has b e e n issu e d to in v e s to rs is ca lle d an in s ta lm e n t re c e ip t. C o n tr ib u tin g shares a n d in s ta lm e n t re ce ip ts
are discussed in d e ta il in S e ctio n 9.6 .3 .
9 .2 .2 ! Limited liability
W h ile s h a re h o ld e rs face g re a te r r is k th a n le n d e rs, t h e ir r is k is lim it e d in t h a t th e y e n jo y lim ited
liability.
This m ea ns t h a t a s h a re h o ld e r is n o t p e rs o n a lly lia b le f o r th e co m p a n y s de bts. In th e case o f a co m p a n y
lim ite d b y shares, th e lia b ilit y o f sh a re h o ld e rs is lim it e d to a n y a m o u n t u n p a id o n th e shares h e ld .2 F or
exa m ple, i f an in v e s to r purchases shares w it h an issue p ric e o f $ 2 .5 0 p e r share, t h a t are p a r tly p a id to
$1 .7 5 , th e in v e s to rs lia b ilit y f o r fu tu r e p a y m e n ts is lim it e d to 75 cen ts p e r share. C o n se q u e n tly, i f th e
c o m p a n y is placed in to liq u id a tio n a n d has in s u ffic ie n t cash to p a y its c re d ito rs , h o ld e rs o f its p a r tly p a id
shares can be re q u ire d to c o n trib u te u p to 75 cen ts p e r share to w a rd s th e p a y m e n t o f c re d ito rs . H o ld e rs
o f f u lly p a id shares w o u ld n o t be re q u ire d to m ake a n y c o n tr ib u tio n to w a rd s th e p a y m e n t o f c re d ito rs , so
th e m a x im u m a m o u n t th e y can lose is th e a m o u n t a lre a d y p a id to p u rch a se th e shares.
9 .2 .3 | No liability companies
The m a jo r ity o f com p an ies lis te d o n th e A S X are lim it e d lia b ilit y com p an ies, b u t th e re are also m a n y
m in in g co m p a n ie s th a t are re g is te re d as n o lia b ilit y co m p a n ie s. Such com p an ies m u s t in c lu d e th e w o rd s
*No L ia b ility * o r th e a b b re v ia tio n
lNV a t
th e e n d o f th e co m p a n y s na m e. These c o m p a n ie s ty p ic a lly have
p a r tly p a id shares on issue a n d can raise c a p ita l in stages b y c a llin g u p p a r t o f th e u n p a id c a p ita l. N o
lia b ilit y co m p a n ie s have tw o m a in fe a tu re s t h a t d is tin g u is h th e m fr o m o th e r ty p e s o f com p an ies. O ne
is t h a t th e y are re s tric te d to o p e ra tin g o n ly in th e m in in g in d u s try . The second fe a tu re is t h a t i f th e
c o m p a n y fa ils , sh a re h o ld e rs have n o lia b ilit y f o r th e co m p a n y s de bts. A c c o rd in g ly , h o ld e rs o f p a r tly *5
6
1
2
The advantages and disadvantages of limited liability are discussed in Lipton, Herzberg & Welsh (2010, p. 24). See also section
516 of the C o rp o ratio n s A c t 2 0 0 1 .
C hapter n in e S ources
of fin a n c e : equity
p a id shares issued b y a n o lia b ilit y c o m p a n y are n o t o b lig e d to p a y calls m ad e b y th e com pany. H o w eve r,
sha reh old ers w h o fa il to pay a ca ll f o r f e it t h e ir shares. N o lia b ilit y co m p a n ie s are ty p ic a lly in v o lv e d in
m in e ra l o r o il e x p lo ra tio n . T h e re fo re , th is second fe a tu re a llo w s sh a re h o ld e rs to re v ie w t h e ir in v e s tm e n t
in a ris k y v e n tu re w h e n a d d itio n a l fu n d s are b e in g ra ise d a n d gives th e m th e o p p o r tu n ity to a b a n d o n th e
in v e s tm e n t i f th e y be lie ve t h a t its p ro sp e cts are u n a ttra c tiv e .3
9.2.4|T he rights of shareholders
S hareholders in a lis te d co m p a n y have m a n y rig h ts , such as th e r ig h t to receive an a n n u a l re p o rt, to be
n o tifie d o f m e e tin g s a n d to a tte n d th o se m e e tin g s . In p ra ctice , m o s t o f these rig h ts are o f l i t t le im p o rta n c e
and, generally, th e re are ju s t th re e rig h ts t h a t are im p o r t a n t to sh a re h o ld e rs in lis te d com p an ies:
a
S ha reh old ers are e n title d to a p ro p o r tio n a l share o f a n y d iv id e n d t h a t is de cla red b y d ire c to rs ,
b
As p a rt ow n e rs o f th e com p an y, o rd in a ry s h a re h o ld e rs e x e rt a degree o f c o n tro l o v e r its m a n a g e m e n t
th ro u g h th e v o tin g rig h ts a tta c h e d to t h e ir shares. These rig h ts in c lu d e th e r ig h t to e le ct m e m b e rs
o f th e B o a rd o f D ire c to rs . The B oa rd, w h ic h is u s u a lly e lected a t th e A n n u a l G en eral M e e tin g , has
u ltim a te c o n tro l o ve r th e o p e ra tio n s o f th e com p an y. U su ally, sh a re h o ld e rs have one v o te f o r each
share h e ld .4 The r ig h t o f s h a re h o ld e rs to e le ct th e B o a rd o f D ire c to rs gives th e m som e c o n tro l o ve r
th e co m p a n y s o p e ra tio n s . H o w eve r, in p ra c tic e , t h e ir a b ility to exercise c o n tro l is lim it e d because
th e B oa rd o f D ire c to rs is g e n e ra lly able to m u s te r s u ffic ie n t vo te s, in c lu d in g p ro x ie s , to e n sure th a t
its m e m b e rs are re -e le cte d a t th e A n n u a l G e n e ra l M e e tin g .5
C
S ha reh old ers have th e r ig h t to sell t h e ir shares. This r ig h t can be exercised re a d ily in th e case o f
lis te d shares because th e shares can be s o ld th ro u g h th e s to c k exchange.
9 .2 .5 1 Advantages and disadvantages of equity as a source of
finance
E q u ity raised b y is s u in g o rd in a ry shares has im p o r ta n t advantages as a source o f fin a n ce :
•
A c o m p a n y is n o t
required to
pay d iv id e n d s to o rd in a ry sh a re h o ld e rs: p a y m e n t o f d iv id e n d s is a t
th e d is c re tio n o f d ire c to rs . T h ere fore, i f a c o m p a n y s u ffe rs a d e clin e in p r o fita b ilit y o r is s h o rt o f
cash, i t can o m it th e p a y m e n t o f d iv id e n d s w ith o u t a n y s e rio u s le g a l consequences. In c o n tra s t,
fa ilu re to pay in te re s t o n d e b t, o r delays in p a y in g in te re s t, w ill a lm o s t c e rta in ly have se rio u s legal
consequences a n d can u ltim a te ly le a d to a c o m p a n y b e in g p laced in to liq u id a tio n .
•
O rd in a ry shares do n o t have a n y m a t u r ity date, w h ic h m ea ns t h a t th e is s u in g c o m p a n y has
no o b lig a tio n to red ee m th e m .6 A g a in , in c o n tra s t, d e b t
must be
re p a id (o r *redeem ed,) w h e n
i t m a tu re s.
•
The h ig h e r th e p r o p o r tio n o f e q u ity in a co m p a n y s c a p ita l s tru c tu re , th e lo w e r is th e r is k th a t
le n d e rs w ill s u ffe r losses as a re s u lt o f th e b o rro w e r e x p e rie n c in g fin a n c ia l d iffic u lty . T h ere fore,
ra is in g e q u ity b y is s u in g o rd in a ry shares lo w e rs th e in te re s t ra te t h a t a c o m p a n y w ill have to pay
o n de bt.
W h ile e q u ity has im p o r t a n t advantages, i t also has som e disad vanta ges.
•
I f a co m p a n y issues m o re o r d in a r y shares to raise n e w c a p ita l, e x is tin g sh a re h o ld e rs w i ll have to
e ith e r o u tla y a d d itio n a l cash o r s u ffe r som e d ilu t io n o f t h e ir o w n e rs h ip a n d c o n tro l o f th e com pany.
3
4
5
6
Arguably, another feature of no liability (NL) companies is also important. Historically, NL companies had greater flexibility
than other companies to raise capital by issuing shares at a discount to their par value. When the C o rp o ratio n s A c t was
amended to abolish the par value concept from 1 July 1998, this advantage no longer existed. Subsequently, some NL
companies have converted to limited liability status and the number of new NL companies listing on the ASX has declined.
As at February 2014, only 68 of the 2140 companies listed on the ASX were NL companies (see www.asx.com.au/asx/
research/ASXListedCompanies.csv).
The voting rights of a company s shareholders must be specified in its constitution. For companies listed on the ASX, the form
of the voting rights is specified in Chapter 6 of the Exchange’s Listing Rules.
As many shareholders do not attend the Annual General Meeting, the right to vote by proxy is provided. Voting by proxy
involves a shareholder assigning to another person the right to vote on resolutions at the Annual General Meeting.
While ordinary shares have no maturity date and can, in principle, exist in perpetuity, companies are permitted to repurchase
their ovm shares, which leads to cancellation of those shares. Share buybacks are discussed in Chapter 11.
m
LEARNING
OBJECTIVE 2
Explain the
advantages and
disadvantages of
equity as a source of
finance
B usiness finance
B o rro w in g , o n th e o th e r h a n d , a llo w s fu n d s to be ra ise d w ith o u t such d ilu tio n . S m a ll sh a re h o ld e rs
m a y n o t be co n ce rn e d i f t h e ir in te re s t in a co m p a n y is d ilu te d , p ro v id e d th e n e w sh a re h o ld e rs pay a
f a ir p ric e f o r th e shares th e y o b ta in , b u t in v e s to rs w h o o w n a s ig n ific a n t p r o p o r tio n o f a com p an y's
shares m a y be u n w illin g to have t h e ir in te re s t d ilu te d .
•
The tra n s a c tio n costs o f ra is in g fu n d s b y is s u in g shares are u s u a lly h ig h e r th a n th e costs o f
b o rro w in g a s im ila r a m o u n t. O n e rea son is th a t, as discussed in S e ctio n 9.4, a share issue b y a p u b lic
co m p a n y o fte n re q u ire s a p ro s p e c tu s . Because o f th e v o lu m e o f in fo r m a tio n t h a t is u s u a lly p ro v id e d ,
a p ro s p e c tu s f o r a share issue ty p ic a lly ru n s to m o re th a n 1 0 0 pages a n d is c o s tly to p re pa re. A lso ,
share issues are o fte n u n d e r w r itte n : th is o fte n in v o lv e s a fee b e in g p a id to th e u n d e r w r ite r w h o
gu a ra n te e s to pu rcha se a n y shares n o t ta k e n u p b y in v e s to rs .
In o u t lin in g th e advan ta ge s a n d disad vanta ges o f e q u ity , ta x a tio n has n o t been m e n tio n e d because,
u n d e r th e A u s tra lia n ta x syste m , th e o v e ra ll ta x b u rd e n s o n d e b t a n d e q u ity are o fte n th e sam e fo r
A u s tra lia n re s id e n t in v e s to rs . A s discussed in S e ctio n 1 2 .5 .2 ，th e s yste m is e ith e r n e u tra l o r biase d
to w a rd s e q u ity d e p e n d in g o n th e in v e s to rs m a rg in a l ta x rate. F o r overseas in v e s to rs in A u s tra lia n
co m p a n ie s th e ta x b u rd e n o n e q u ity m a y be h ig h e r th a n th e ta x b u rd e n o n d e b t. T h e re fo re , in A u s tra lia ,
a n y ta x a tio n ad va n ta g e o r d isa d va n ta g e th a t m a y arise in a p a r tic u la r case de pe nd s o n th e circu m sta nce s
o f th e s h a re h o ld e r co n ce rn e d a n d is n o t an in h e re n t fe a tu re o f e q u ity as a source o f fin a n ce .
9.3
Private equity
M o s t o f th is c h a p te r covers e q u ity c a p ita l ra is in g b y com p an ies w h o se shares are lis te d a n d tra d e d p u b lic ly
LEARNING
OBJECTIVE 3
Outline the main
sources of private
equity in the
Australian market
o n a s to c k exchange. There is also a m u c h s m a lle r b u t s t ill v e ry im p o r ta n t p riv a te e q u ity m a rk e t. The te rm
p riv a te e q u ity * is o fte n used to de scrib e tw o d is tin c t typ e s o f in v e s tm e n t. The f ir s t ty p e is also k n o w n as
V e n tu re capital* a n d re fe rs to fu n d in g f o r s m a lle r a n d r is k ie r co m p a n ie s w it h p o te n tia l f o r s tro n g g ro w th .
F o r the se co m p a n ie s, p riv a te e q u ity can be m o re a ttra c tiv e th a n a s to c k exchange lis tin g . F o r exa m ple, th e
a m o u n t o f c a p ita l re q u ire d m a y be to o s m a ll to ju s t if y th e cost o f a share m a rk e t flo a t. A ls o , th e fu tu r e o f
th e v e n tu re — w h ic h a t th e e a rlie s t stage m a y be n o m o re th a n an id e a — m a y be to o u n c e rta in to a ttra c t
fu n d s f r o m a la rge n u m b e r o f in v e s to rs . The second ty p e is th e a c q u is itio n o f a lis te d p u b lic co m p a n y
b y a g ro u p o f in v e s to rs w h o p riv a tis e * th e co m p a n y so t h a t i t is d e lis te d fr o m th e s to c k exchange. Such
a c q u is itio n s u s u a lly in v o lv e a h ig h p r o p o r tio n o f d e b t fin a n c e a n d are c o m m o n ly k n o w n as leveraged
b u y o u ts (LB O s), w h ic h are discussed in S e ctio n 1 9 .7 .3 . The re m a in d e r o f th is s e c tio n focuses o n p riv a te
e q u ity fu n d in g f o r v e n tu re s o th e r th a n LBO s.
9.3.1 | W hat is private equity?
P riv a te e q u ity re fe rs to e q u ity s e c u ritie s t h a t are n o t p u b lic ly tra d e d . P riv a te e q u ity can be ra ised fr o m
v a rio u s sources in c lu d in g fa m ily m e m b e rs, frie n d s a n d ‘bu sin ess angels’，b u t th e m o re fo r m a l p riv a te
e q u ity m a rk e t in v o lv e s fu n d s b e in g c h a n n e lle d to businesses b y p riv a te e q u ity fu n d m an ag ers. P riva te
e q u ity fu n d in g can be d iv id e d in to fo u r ca te g o rie s:7
a
start-up fin a n c in g
f o r a b u sin ess less th a n 3 0 m o n th s o ld w h e re fu n d s are re q u ire d to de ve lo p th e
c o m p a n y ’s p ro d u c ts
b
expansion fin a n c in g
w h e re a d d itio n a l fu n d s are re q u ire d to m a n u fa c tu re a n d sell p ro d u c ts
c o m m e rc ia lly
c
d
turnaround fin a n c in g f o r a c o m p a n y in fin a n c ia l d iff ic u lt y
management buyout (M B O ) fin a n c in g w h e re a b u sin ess is p u rch a se d
b y its m a n a g e m e n t te a m w ith
th e assistance o f a p riv a te e q u ity fu n d .
Because p riv a te e q u ity is n o t p u b lic ly tra d e d , th e m a rk e t is illiq u id a n d in v e s to rs m u s t be p re p a re d to
c o m m it fu n d s f o r th e lo n g te rm , w ith p e rio d s o f 5 to 10 years b e in g ty p ic a l.
7
This four-category breakdown is provided by Connolly and Tan (2002).
C hapter NINE $ 〇URCES 〇F FINANCE: EQUITY
E n tre p re n e u rs a n d in v e s to rs in n e w v e n tu re s se e kin g s ta rt-u p fin a n c in g face th re e im p o r t a n t in fo r m a tio n
p ro b le m s .8
a
Information gaps: in fo r m a t io n
a b o u t th e va lu e o f th e v e n tu re is lik e ly to be in c o m p le te a n d v e ry
u n c e rta in .
b
Information asymmetry: im p o r t a n t
in fo r m a tio n is u s u a lly d is tr ib u te d u n e v e n ly b e tw e e n th e
p a rtie s , w h ic h is th e p ro b le m k n o w n as
in form ation asym m etry.
In p a rtic u la r, th e e n tre p re n e u r
w ill a lm o s t c e rta in ly have m o re accurate in fo r m a tio n th a n o u ts id e in v e s to rs a b o u t th e te c h n ic a l
o r s c ie n tific m e r it o f an id e a a n d o f th e te c h n o lo g y re q u ire d to e x p lo it th e idea. O n th e o th e r
ha n d , o u ts id e in v e s to rs m a y have m o re re a lis tic in fo r m a tio n a b o u t th e e co n o m ic v a lu e o f th e
idea. H o w eve r, p o te n tia l in v e s to rs in a n e w v e n tu re are n o t co n ce rn e d o n ly w ith th e va lu e o f
th e u n d e rly in g idea o r in v e n tio n . T hey also ne ed to assess th e s k ills a n d c o m m itm e n t o f th e
e n tre p re n e u r. Som e e n tre p re n e u rs have an accurate a p p re c ia tio n o f t h e ir o w n s k ills , a b ility an d
c o m m itm e n t, w h ile o th e rs te n d to be less re a lis tic .
C
Information leakage: th e re
is th e r is k t h a t o th e rs m a y a p p ro p ria te th e e n tre p re n e u r s idea. To
con vin ce p ro s p e c tiv e in v e s to rs t h a t a p ro p o s a l is va lu a b le , th e e n tre p re n e u r w ill have to p ro v id e
th e m w it h som e in fo r m a tio n a b o u t th e idea. U n fo rtu n a te ly , d is c lo s in g th is in fo r m a tio n m a y a llo w
som eone else to e x p lo it th e o p p o rtu n ity .
INFORMATION
ASYMMETRY
situation where all
relevant information
is not known by all
interested parties.
Typically, this
involves company
'insiders' (managers)
having more
information about the
company’s prospects
than 'outsiders'
(shareholders and
lenders)
The m a rk e t f o r n e w v e n tu re fin a n ce has som e u n iq u e fe a tu re s t h a t have d e velope d to m in im is e th e
effects o f these in fo r m a tio n p ro b le m s . The m a in such fe a tu re is t h a t fin a n c e f o r n e w v e n tu re s is n o rm a lly
p ro v id e d in stages ra th e r th a n as a sin g le lu m p sum . A lso , th e p ro v is io n o f fin a n c e a t each stage is g e n e ra lly
lin k e d to th e a ch ie ve m e n t o f m ile s to n e s , such as c o m p le tio n o f a p ro to ty p e o r successful o p e ra tio n o f a p ilo t
p la n t. A c h ie v e m e n t o f the se m ile s to n e s o r o th e r p e rfo rm a n c e b e n c h m a rk s h e lp s to reduce in fo r m a tio n
a s y m m e try in tw o ways. F irs t, i t p ro v id e s in v e s to rs w ith ta n g ib le evidence a b o u t th e v ia b ilit y o f th e
p ro je ct. Second, i t also p ro v id e s th e m w it h in fo r m a tio n a b o u t th e s k ill a n d a b ility o f th e e n tre p re n e u r.
P ro v id in g th e fin a n ce in stages is c le a rly sen sib le fr o m th e v ie w p o in t o f in v e s to rs . I f a p ro je c t is d e s tin e d
to fa il due to te c h n ic a l d iffic u ltie s , la c k o f c o n s u m e r d e m a n d o r h ig h m a n u fa c tu rin g costs, i t is b e tte r to
discove r these p ro b le m s b e fo re a ll th e fu n d s needed to c o m p le te th e p ro je c t have b e en c o m m itte d to it .
Staged fin a n c in g is also in th e in te re s t o f th e e n tre p re n e u r. F o r an e n tre p re n e u r w ith n o tra c k re c o rd o f
successful v e n tu re s , i t w ill be d iff ic u lt to co n vin ce o th e rs t h a t fu n d s in v e s te d in a n e w v e n tu re w ill be used
p ro fita b ly . F o r th e e n tre p re n e u r, ra is in g m o n e y fr o m o u ts id e in v e s to rs in th e e a rly stages o f a v e n tu re is
ge n e ra lly expensive. In th is c o n te x t, expensive* m eans t h a t th e e n tre p re n e u r w ill have to g ive u p a la rge
fra c tio n o f o w n e rs h ip to raise a r e la tiv e ly s m a ll a m o u n t o f c a p ita l. A c h ie v e m e n t o f each m ile s to n e reduces
u n c e rta in ty an d increases th e va lu e o f a p ro je c t. R a isin g fin a n c e in stages, a fte r m ile s to n e s have been
achieved, th e re fo re h e lp s th e e n tre p re n e u r to r e ta in g re a te r o w n e rs h ip th a n w o u ld o th e rw is e be th e case.
F in a lly, c o n s id e r th e p o s s ib ility t h a t release o f in fo r m a tio n to p ro s p e c tiv e in v e s to rs m a y le a d to
a p p ro p ria tio n o f th e e n tre p re n e u r s idea. The e n tre p re n e u r m a y seek p ro te c tio n b y a s k in g p ro s p e c tiv e
in v e s to rs to sig n c o n fid e n tia lity a g re e m e n ts w h e n th e y are g iv e n a co p y o f th e b u sin ess p la n . H o w eve r,
m a n y in v e s to rs re fu se to sig n such a g re e m e n ts because a le a k o f in fo r m a tio n fr o m a n y source can re s u lt
in c o s tly le ga l d isp u te s. I t is m o re im p o r t a n t to th e e n tre p re n e u r t h a t a p o te n tia l in v e s to r is h o n e s t a n d
can be tru s te d n o t to m isu se c o n fid e n tia l in fo r m a tio n . T h e re fo re , p riv a te e q u ity f u n d m an ag ers w ill t r y to
e sta b lish an d p ro te c t a re p u ta tio n f o r h o n e s ty a n d in te g rity .
There are m a n y p o te n tia l sources o f fin a n c e f o r a n e w v e n tu re . These sources in c lu d e th e e n tre p re n e u r s
p e rso n a l resources, p riv a te e q u ity fu n d s a n d fu n d s ra ise d b y an
in itial public offering
o f shares
associated w ith lis tin g o n a s to c k exchange. The s u ita b ility o f th e se a n d o th e r sources o f fin a n c e depends
o n th e v e n tu re s stage o f d e v e lo p m e n t. E v e ry v e n tu re is d iffe re n t a n d i t is im p o s s ib le to id e n tify a *life
cycle’ o f d e v e lo p m e n t stages t h a t a p p lie s to a ll n e w v e n tu re s . There are, h o w e ve r, som e id e n tifia b le
stages th a t w ill a p p ly in m a n y cases. M a n y v e n tu re s w ill b e g in w it h a research a n d d e v e lo p m e n t phase
8
Our discussion of these information problems is based on Smith and Smith (2000, pp. 27-8).
IN ITIAL PUBLIC
OFFERING
a company's first
offering of shares to
the public
B usiness finance
w h ic h , i f successful, w ill be fo llo w e d b y a s ta rt-u p phase w h e re th e e q u ip m e n t a n d p e rs o n n e l needed fo r
p ro d u c tio n are assem bled. I f th e p ro d u c t is accepted b y cu sto m e rs, th e v e n tu re m a y g ro w , p e rha ps v e ry
ra p id ly a t fir s t, a fte r w h ic h th e re w ill o fte n be p e rio d s o f s lo w e r g ro w th , m a t u r ity a n d p e rh a p s decline.
There m a y be n o cle ar d e m a rc a tio n p o in t b e tw e e n the se stages b u t in m a n y cases th e tr a n s itio n w ill
c o rre s p o n d to id e n tifia b le m ile s to n e s . In t u r n , th e re is o fte n a re la tio n s h ip b e tw e e n the se m ile s to n e s and
th e a v a ila b ility o f d iffe re n t sources o f fina nce .
A t th e research an d d e v e lo p m e n t stage th e e n tre p re n e u r w i ll u s u a lly re ly in it ia lly o n p e rso n a l
resources— t h a t is, savings, m o n e y t h a t can be b o rro w e d b y m o rtg a g in g th e fa m ily h o m e a n d p e rha ps
lin e s o f c re d it lin k e d to c re d it cards. U nless th e e n tre p re n e u r is v e ry w e a lth y , these resources m a y be
e x h a u ste d b e fo re th e v e n tu re is f u lly d e velope d a n d i t w ill u s u a lly be necessary to o b ta in fin a n c e fro m
o u ts id e rs such as fa m ily m e m b e rs, frie n d s , in d iv id u a ls k n o w n as ‘b u sin ess an ge ls’ a n d p riv a te e q u ity
fu n d s . O u ts id e fin a n c e ra ise d in th e e a rly stages o f a v e n tu re s d e v e lo p m e n t is n o r m a lly in th e fo r m o f
e q u ity — t h a t is, th e e n tre p re n e u r tra n s fe rs a share o f o w n e rs h ip to th e n e w in v e s to rs a n d th e re tu rn s to
the se in v e s to rs w ill d e p e n d d ire c tly o n th e success o r o th e rw is e o f th e v e n tu re .
9 .3 .4 1 Finance from business angels
B usiness angels are w e a lth y in d iv id u a ls p re p a re d to in v e s t in p ro je c ts t h a t are a t a n e a rly stage o f
d e v e lo p m e n t.9 The a m o u n ts in v o lv e d ty p ic a lly range fr o m te n s o f th o u s a n d s to h u n d re d s o f th o u s a n d s
o f d o lla rs p e r in v e s tm e n t. These in v e s to rs w ill o fte n p ro v id e th e fu n d s ne eded to de ve lo p a v e n tu re to
th e stage w h e re i t is p o ssib le to seek o u ts id e fin a n c e fr o m p riv a te e q u ity fu n d s , b a n ks a n d o th e r fin a n c ia l
in s titu tio n s . B usiness angels are g e n e ra lly p re p a re d to in v e s t in a v e n tu re f o r 5 to 10 years. M a n y o f th e m
have b u sin ess o r te c h n ic a l s k ills a n d a im to add v a lu e to a n e w v e n tu re b y p ro v id in g ad vice a n d e x p e rtis e
as w e ll as fin a n ce . T ra d itio n a lly th e m a rk e t has o p e ra te d in fo r m a lly o n th e basis o f c o n ta c ts a n d re fe rra ls.
H o w eve r, th e m a rk e t has re c e n tly been fo rm a lis e d b y th e d e v e lo p m e n t o f b u sin ess in tr o d u c tio n services
t h a t seek to m a tc h in v e s to rs w it h e n te rp ris e s t h a t need c a p ita l. Som e o f the se services s im p ly p ro v id e
in fo r m a tio n , w h ile o th e rs m a in ta in databases o f b o th in v e s to rs a n d c o m p a n ie s a n d a im to a c tiv e ly m a tc h
the se p a rtie s . Services o p e ra tin g in A u s tra lia in c lu d e Business A n g e ls P ty L td
(w w w .businessangels.com .
au) a n d th e A u s tra lia n S m a ll Scale O ffe rin g s B o a rd (w ww.assob.com .au).
Som e b u sin ess angels w ill in v e s t in p e rh a p s one p ro je c t p e r y e a r w h ile o th e rs w ill in v e s t in several.
M o s t r e s tr ic t t h e ir in v e s tm e n ts to in d u s trie s w h e re th e y u n d e rs ta n d th e te c h n o lo g y a n d to p ro je c ts
lo c a te d in t h e ir o w n g e o g ra p h ic a l area. A ty p ic a l e xa m p le is <J o h n ,, a 6 3 -y e a r-o ld c h a rte re d a c c o u n ta n t
w h o has m a d e 12 in v e s tm e n ts in 8 years as a f u ll- tim e e q u ity in v e s to r.10 H e p o in ts o u t t h a t th e e x p e rtis e
t h a t b u sin ess angels can p ro v id e is u s u a lly m o re im p o r t a n t th a n th e m o n e y th e y in v e s t. F in d in g m o n e y
is easy i f a bu sin ess is good. A n g e l in v e s to rs lo o k f o r a b u sin ess w it h a w eakness t h a t th e y can h e lp to
o ve rco m e so t h a t i t becom es a g o o d business. J o h n lo o k s f o r o p p o rtu n itie s in in d u s trie s w it h h ig h g ro w th
p o te n tia l. Because he does n o t w a n t h is m o n e y tie d u p f o r m o re th a n 5 years, he lo o k s f o r a co m p a n y
th a t can b e n e fit v e ry q u ic k ly fr o m re o rg a n is a tio n o r a d d itio n a l e x p e rtis e . Such co m p a n ie s are u s u a lly
s m a ll a n d have a g o o d idea, b u t la ck e x p e rtis e in m a n a g e m e n t, m a rk e tin g , m a n u fa c tu rin g o r d is tr ib u tio n .
J o h n w i ll in v e s t u p to $ 2 0 0 0 0 0 , re q u ire s a seat o n th e B o a rd a n d w ill sp e n d u p to h a lf a d a y each w eek
w o rk in g o n th e com p an y. F in a lly , he lo o k s f o r c o m p a n ie s t h a t can p ro v id e h ig h re tu rn s o n h is in v e s tm e n t
b y d e v e lo p m e n t to a stage w h e re th e c o m p a n y can be s o ld to o r m erg e w it h a la rg e r com pany, a ttra c t th e
in v o lv e m e n t o f a p riv a te e q u ity fu n d o r lis t o n a s to c k exchange.
9 .3 .5 1 Finance from private equity funds
The A u s tra lia n B u re a u o f S ta tis tic s (ABS) e s tim a te s t h a t $ 1 9 .8 b illio n was c o m m itte d to th e p riv a te e q u ity
m a rk e t a t 30 J u n e 2 0 1 3 , o f w h ic h $ 1 3 .8 b illio n was d ra w n d o w n , le a v in g $6 b illio n u n c a lle d .11 A c c o rd in g
to th e ABS, a t J u n e 2 0 1 3 a t o ta l o f 2 3 1 p riv a te e q u ity fu n d s o p e ra te d in A u s tra lia b y 1 2 2 v e n tu re c a p ita l
9 For a detailed discussion of this market in Australia, see Abernethy and Heidtman (1999).
10 This example is cited by Abernethy and Heidtman (1999, pp. 137-40). The remainder of this section relies heavily on that
source.
11 Australian Bureau of Statistics (2014).
C hapter n in e S ources
of fin a n c e : equity
m anagers h a d in v e s te d in 7 2 0 com p an ies. V e n tu re c a p ita l m an ag ers have tw o m a in roles: ra is in g m o n e y
fro m in v e s to rs a n d s e le c tin g s u ita b le co m p a n ie s in w h ic h to in v e s t th e c a p ita l. In A u s tra lia , in v e s to rs
in c lu d e s u p e ra n n u a tio n fu n d s , w h ic h are th e la rg e s t source o f fu n d s , w e a lth y in d iv id u a ls a n d ba nks.
W h ile these in v e s to rs have la rg e sum s ava ila ble, p riv a te e q u ity fu n d in g is n o t easy to o b ta in . A c c o rd in g
to th e ABS, th e 1 2 2 m anagers re v ie w e d 6 6 0 4 p o te n tia l n e w in v e s tm e n ts in th e fin a n c ia l yea r e n d in g
Ju n e 20 13 , f u r t h e r an alysis was c o n d u c te d o n 8 5 0 o f th o se a n d o n ly 76 w e re succe ssful in a ttra c tin g
in v e s tm e n t. D u rin g th a t p e rio d the se v e n tu re c a p ita l m an ag ers m ad e n e w a n d fo llo w - o n in v e s tm e n ts
to ta llin g $ 1 1 2 4 m illio n .
V e n tu re c a p ita l fu n d m a n a g e rs g e n e ra lly in v e s t a m o u n ts in th e o rd e r o f $ 5 0 0 0 0 0 to $2 0 m illio n f o r
p e rio d s o f 3 to 7 years. T hey lo o k f o r a bu sin ess w ith g o o d p ro sp e cts f o r g ro w th , m a n a g e d b y p e o p le w h o
are capable, h o n e s t a n d c o m m itte d to th e success o f th e bu sin ess. P riv a te e q u ity in v e s tm e n ts ty p ic a lly
have a h ig h e r le ve l o f r is k th a n m o s t o th e r in v e s tm e n ts . T h ere fore, fu n d m an ag ers seek a re la tiv e ly h ig h
ra te o f r e tu r n t h a t w ill v a ry w it h th e p e rce ive d ris k . F o r e xa m p le , p ro v is io n o f seed a n d s ta rt-u p c a p ita l
in vo lve s a h ig h le v e l o f r is k a n d in v e s to rs m a y seek a ra te o f r e tu r n o f a t le a st 30 to 4 0 p e r c e n t p e r a n n u m
o ve r th e life o f th e in v e s tm e n t. A t a la te r stage w h e n p r o d u c tio n has co m m e n ce d a n d p ro d u c t is b e in g
sold, p ro v is io n o f c a p ita l f o r e x p a n s io n in v o lv e s lo w e r r is k so t h a t th e m in im u m ra te o f r e tu r n s o u g h t
m a y be 20 to 30 p e r c e n t p e r a n n u m .
To o b ta in p riv a te e q u ity i t is e s s e n tia l to have a w e ll-d o c u m e n te d a n d b e lie v a b le b u sin ess p la n . The
p la n s h o u ld p ro v id e in fo r m a t io n on:
•
th e s tru c tu re , a c tiv itie s a n d fin a n c ia l h is to r y o f th e bu sin ess
•
analysis o f th e in v e s tm e n t o p p o r tu n ity
•
th e a m o u n t o f c a p ita l s o u g h t
•
h o w th e c a p ita l w ill be used
•
fin a n c ia l p ro je c tio n s
•
th e q u a lific a tio n s a n d e xp e rie n ce o f th e m a n a g e m e n t team .
As w e ll as b e c o m in g p a r t o w n e rs o f th e businesses th e y in v e s t in , fu n d m an ag ers ty p ic a lly re q u ire a
seat on th e c o m p a n y s B o a rd o f D ire c to rs . This does n o t m e a n t h a t th e y seek d a y -to -d a y c o n tro l. R a th er,
p riv a te e q u ity fu n d s g e n e ra lly ta k e a s ig n ific a n t m in o r it y share in th e c o m p a n y a n d a im to p ro v id e v a lu a b le
advice o n b o th te c h n ic a l a n d m a n a g e m e n t issues. A n e n tre p re n e u r m a y be able to o b ta in c a p ita l fr o m a
v a rie ty o f sources, b u t a fu n d m a n a g e r can also p ro v id e m a n a g e m e n t in p u t based o n th e e xp erience o f
h e lp in g o th e r com p an ies ove rco m e th e p ro b le m s ty p ic a lly e n c o u n te re d b y new , fa s t-g ro w in g businesses.
The in v e s tm e n t veh icle s d iffe r c o n s id e ra b ly in size, th e ty p e o f in d u s trie s th e y in v e s t in an d th e typ e s o f
m a n a g e m e n t s u p p o rt th e y can p ro v id e . T h e re fo re , i t is im p o r t a n t t h a t an e n tre p re n e u r se e kin g p riv a te
e q u ity s h o u ld be aw are o f the se d iffe re n ce s a n d a p p ro a ch th e fin a n c ie rs t h a t are b e s t e q u ip p e d to p ro v id e
th e c a p ita l a n d s u p p o rt t h a t th e b u sin e ss is lik e ly to need.
M o s t fu n d m an ag ers a im t o achieve th e m a jo r ity o f t h e ir r e tu r n in th e f o r m o f c a p ita l g a in ra th e r th a n
d iv id e n d s . A c c o rd in g ly , th e y u s u a lly p la n to d ispo se o f th e in v e s tm e n t, ty p ic a lly w it h in a p e rio d o f 3 to 7
years. D isp o sa l m a y ta k e place in one o f th re e ways:
a
an in it ia l p u b lic o ffe rin g a sso cia te d w it h s to c k exchange lis tin g
b
sale
C voluntary liquidation.
W h e re a sale occurs th e b u y e r m a y be a la rg e r co m p a n y (a ‘tra d e sale’) ，th e m a jo r ity o w n e r, th e
m a n a g e m e n t o r a n o th e r o u ts id e in v e s to r. W h ile d isp o sa l o f th e in v e s tm e n t can re s u lt in s p e c ta c u la r
gains, th e le ve l o f r is k is h ig h a n d i t is to be e xp ected t h a t a s ig n ific a n t p r o p o r tio n o f th e d isp o sa ls th a t
occur w ill in v o lv e a loss. In som e cases th e p ro je c t w ill fa il a n d th e in v e s tm e n t w i ll be liq u id a te d .
P riva te e q u ity in v e s tm e n t in A u s tra lia has g ro w n ra p id ly since th e e a rly 1 9 9 0 s. F actors t h a t have
c o n trib u te d to th is g ro w th in c lu d e :
•
g ro w th in th e v o lu m e o f fu n d s flo w in g in to s u p e ra n n u a tio n , to g e th e r w it h in cre a se d re c o g n itio n b y
•
g o v e rn m e n t p ro g ra m s to en cou rage in v e s tm e n t in n e w v e n tu re s , such as th e In n o v a tio n In v e s tm e n t
fu n d m anagers o f th e ro le o f p riv a te e q u ity in v e s tm e n ts as p a r t o f a d iv e rs ifie d p o r tf o lio
F u n d p ro g ra m a n d th e E a rly Stage V e n tu re C a p ita l L im ite d P a rtn e rs h ip s p ro g ra m (see w w w .
ausindustry.gov.au).
•
re g u la to ry changes t h a t a llo w b a n ks to m a ke e q u ity in v e s tm e n ts .
|www j
9.4
Information disclosure
C h a p te r 6 D o f th e
LEARNING
OBJECTIVE 4
Identify the information
Corporations Act
co n ta in s p ro v is io n s designed to ensure th a t in v e s to rs in p u b lic
com panies are p ro te c te d b y disclosu re o f in fo rm a tio n . There are p a rtic u la r disclosure re q u ire m e n ts th a t
a p p ly to o ffe rs o f secu ritie s so th a t in v e s to rs s h o u ld be able to m ake an in fo rm e d de cisio n on w h e th e r to
that must be disclosed
purchase th e securities. These re q u ire m e n ts are g e n e ra lly sa tisfie d b y p ro v id in g p o te n tia l in ve sto rs w ith a
when issuing securities
disclosure docum ent c o n ta in in g in fo rm a tio n a b o u t th e issu er a nd d e tails o f th e secu ritie s o ffe re d fo r sale.
H ow ever, th e re are v a rio u s e x e m p tio n s th a t m ean a disclosu re d o c u m e n t is n o t needed f o r som e o ffe rs o f
secu ritie s.
DISCLOSURE
DOCUMENT
prospectus, profile
statement o r offer
In cases w h e re d is c lo s u re is needed, th e d isclo su re re q u ire m e n ts v a ry d e p e n d in g o n w h e th e r th e
s e c u ritie s are a lre a d y lis te d o n th e s to c k exchange. W e n o w discuss th e d isclo su re re q u ire m e n ts f o r o ffe rs
o f s e c u ritie s t h a t do n o t fa ll in to a n y o f th e e x e m p t categories.
information statement
that must be supplied
9.4.1 | Offers of unlisted securities
to potential investors
to provide information
about an offer of
O ffe rs o f u n lis te d s e c u ritie s in c lu d e in it ia l p u b lic o ffe rin g s o f o r d in a r y shares a n d issues b y lis te d
securities
co m p a n ie s o f a n e w class o f se c u ritie s . In the se cases, th e s e c u ritie s do n o t have an o b se rva b le m a rk e t
p ric e a n d in th e case o f an in it ia l p u b lic o ffe rin g th e re m a y be lit t le , i f any, p u b lic ly a va ila b le in fo r m a tio n
a b o u t th e com p an y. T h ere fore, th e disclo su re re q u ire m e n ts t h a t a p p ly to o ffe rs o f u n lis te d se c u ritie s are
m o re s tr in g e n t th a n th o se f o r lis te d se cu ritie s.
The g e n e ra l ru le is t h a t an o ffe r o f s e c u ritie s to in v e s to rs c a n n o t p ro cee d u n t il a d isclo su re d o c u m e n t
has b e e n lo d g e d w it h th e A u s tra lia n S e cu ritie s a n d In v e s tm e n ts C o m m is s io n (A S IC ). D isclo su re
d o c u m e n ts m a y be g iv e n to p o te n tia l in v e s to rs as so o n as th e y have b e en lo d g e d w it h A S IC . F o r u n lis te d
s e c u ritie s , a w a itin g p e rio d o f a t le a st 7 days is im p o s e d b e fo re a p p lic a tio n s b y in v e s to rs can be accepted.
The w a itin g p e rio d a llo w s th e d isclo su re d o c u m e n t to be e x a m in e d b y A S IC a n d o th e r in te re s te d p a rtie s .
I f th e d o c u m e n t is fo u n d to be d e fic ie n t, th e issue o f s e c u ritie s can be delayed u n t il an acceptable
s u p p le m e n ta ry o r re p la c e m e n t d o c u m e n t is p ro v id e d .
The in fo r m a t io n t h a t m u s t be in c lu d e d va rie s w it h th e ty p e o f d is c lo s u re d o c u m e n t. The typ e s m o s t
c o m m o n ly used are:
•
a p ro s p e c tu s
•
a s h o r t- fo rm p ro sp e ctu s
•
an o ffe r in fo r m a t io n s ta te m e n t.12
Prospectuses
PROSPECTUS
a docum ent that,
A p ro sp ectu s is th e m o s t c o m p re h e n sive d o c u m e n t a n d g e n e ra lly c o n ta in s in fo r m a t io n o f fo u r m a in
types:
a m o ng other things,
provides details of
a
the co m p a n y and
fu n d s w ill be used, a n y u p p e r o r lo w e r lim it s o n th e a m o u n t t h a t each in d iv id u a l can in v e s t a n d any
the terms of the issue
of securities, w hich
must be pro vided to
in fo r m a t io n a b o u t th e s e c u rity issue— h o w m u c h c a p ita l is s o u g h t, th e s u b s c rip tio n p ric e , h o w th e
m in im u m s u b s c rip tio n le ve l th a t m u s t be ach ie ved
b
n o n -fin a n c ia l in fo r m a t io n a b o u t th e issu e r— a d e ta ile d d e s c rip tio n o f it s b u sin ess a n d re p o rts fro m
d ire c to rs o r e x p e rts in th e in d u s tr y
potential investors by
a co m p a n y seeking to
C
a d e ta ile d d is c u s s io n o f th e ris k s associated w ith th e bu sin ess
issue shares or other
d
fin a n c ia l in fo r m a tio n a b o u t th e is s u e r— th e m o s t re c e n t a u d ite d fin a n c ia l s ta te m e n ts an d, in m a n y
securities
cases, fin a n c ia l fo re ca sts in c lu d in g fo re ca sts o f p r o fits a n d d iv id e n d s .
The t e x t o f a ll p ro sp e ctu se s issu ed in A u s tra lia since 2 0 0 1 is a va ila ble a t w w w .s e a rc h .a s ic .g o v .a u /
o f f e r li s t / o f f e r l is t 一 is s u e r 一 n a m e .h tm l.
A p ro s p e c tu s is th e m o s t exp e n sive o f th e d o c u m e n ts to p re p a re , p r i n t a n d d is trib u te . The fa c to rs th a t
c o n trib u te to these costs in c lu d e th e size o f th e d o c u m e n t a n d th e fees payable to e x p e rts w h ose re p o rts
12 These disclosure documents apply in the case of security issues by companies. If funds are being raised for a managed
investment, such as a property trust, a different type of disclosure document known as a product disclosure statement (PDS)
is required.
C hapter n in e S ources
are in clu d e d . M o re o v e r, d e ficie n cie s in a d isclo su re d o c u m e n t can lead to p e op le w h o w ere in v o lv e d in its
p re p a ra tio n o r in th e is s u in g o f s e c u ritie s b e in g lia b le f o r c r im in a l p ro s e c u tio n . T hey m a y also be re q u ire d
to com pensate in v e s to rs f o r losses su ffe re d as a re s u lt o f a m is s ta te m e n t in , o r an o m is s io n fro m , th e
d o cu m e n t. H o w eve r, th e
Corporations Act p ro v id e s
a *due d ilig e n c e , defence in re la tio n to a p ro s p e c tu s and
o th e r d isclo su re d o cu m e n ts. T his is a defence a g a in s t a c la im o f m is s ta te m e n t o r o m is s io n i f th e p e rso n
m ade a ll reasonable e n q u irie s a n d b e lie ve d o n rea son able g ro u n d s t h a t th e s ta te m e n t w as n o t m is le a d in g
o r de ceptive, o r th a t th e re w as n o o m is s io n . The p re p a ra tio n o f a p ro s p e c tu s can in v o lv e e x te n s iv e an d
c o s tly in v e s tig a tio n s to e n su re t h a t th e in fo r m a tio n p ro v id e d is as accurate as p o ssib le a n d t h a t th e due
d ilig e n ce defence w ill be a va ila b le i f a n y d e fic ie n c y is fo u n d .
The p ro sp e ctu s d is tr ib u te d to p o te n tia l in v e s to rs can be in a s h o r t f o r m 1, w h ic h m ea ns t h a t i t re fe rs
to m a te ria l in d o c u m e n ts lo d g e d w ith A SIC in s te a d o f p ro v id in g t h a t m a te ria l in th e p ro sp e ctu s. A s h o rt
fo rm pro sp e ctu s m u s t in fo r m in v e s to rs t h a t th e y are e n title d to a fre e cop y o f th e a d d itio n a l m a te ria l o n
request.
O ffer information statements
A n o ffe r in fo r m a tio n s ta te m e n t (O IS ) m a y be used in s te a d o f a p ro s p e c tu s i f th e a m o u n t o f m o n e y to
be raised is re la tiv e ly sm a ll. S p e cifica lly, an O IS m a y be used o n ly i f th e a m o u n t o f m o n e y to be ra ise d
b y th e issuer, w h e n adde d to a ll a m o u n ts p re v io u s ly raised, is less th a n $ 1 0 m illio n . A n O IS is m u c h less
c o s tly to p re p a re th a n a p ro s p e c tu s because th e in fo r m a tio n to be disclose d is m in im a l a n d e x te n s iv e *due
d ilig e n c e ’ e n q u irie s are n o t needed.
9 .4 .2 1 Offers of listed securities
The d isclosu re re q u ire m e n ts are less o n e ro u s f o r o ffe rs o f s e c u ritie s t h a t are a lre a d y lis te d o n a s to c k
exchange. A n exa m ple is a rig h ts issue w h e re n e w shares are o ffe re d to e x is tin g sh a re h o ld e rs. As
discussed in S e ctio n 9.6 .1 , a p ro s p e c tu s is n o lo n g e r re q u ire d f o r a rig h ts issue, b u t th e re m a y be cases
w h ere such issues are a cco m p a n ie d b y a p ro sp e ctu s. A lis te d e n t it y is s u b je c t to c o n tin u o u s d isclo su re
re q u ire m e n ts u n d e r s to c k exchange lis tin g ru le s backed b y th e
Corporations Act.
A n y m a te ria l p ric e -
se n sitive in fo r m a tio n has to be d isclo se d to th e s to c k exchange o n a c o n tin u o u s basis. T h e re fo re , m u c h
o f th e in fo r m a tio n t h a t w o u ld n o rm a lly have to be in c lu d e d in a p ro s p e c tu s is a lre a d y p u b lic ly ava ila ble,
so, i f a rig h ts issue is m ad e u n d e r a p ro sp e ctu s, i t does n o t n e ed to be as d e ta ile d as a p ro s p e c tu s f o r an
issue o f u n lis te d se c u ritie s .
9 .4 .3 1 Offers that do not need disclosure
There are v a rio u s e x e m p tio n s t h a t m e a n a d isclo su re d o c u m e n t is n o t ne eded f o r som e o ffe rs o f
se c u ritie s .13 The m a in e x e m p tio n s are o u tlin e d in Table 9.2.
TABLE 9.2 Main types of offer that do not need disclosure
D e s c rip tio n
O ff e r ty p e
Small-scale offerin gs
Personal offers th a t re s u lt in issues to no m ore th a n 20 in vestors in a ro llin g
1 2 -m o n th p e rio d , w ith a m a x im u m o f $2 m illio n raised.
Rights issues
A p ro -ra ta o ffe r made o f a d d itio n a l shares to e x is tin g shareholders. The term s
o f the o ffe r to each shareholder m u s t be id e n tic a l and the new shares m u s t be
o f the same class as those already held.
S ophisticated investors:
The a m o u n t payable fo r securities m u s t be a t least:
• Large offers
$ 5 0 0 0 0 0 , OR
continued
13 The circumstances where a disclosure document is not required are set out in section 708 of the
C o rp o ratio n s A ct.
of f in a n c e : equity
B usiness finance
Table 9 .2
continued
O f f e r ty p e
D e s c rip tio n
• O ffers to w e a lth y
in vestors
th e in v e s to r had a gross incom e over each o f the previous tw o fin a n c ia l years
o f a t least $250 000 o r n e t assets o f a t least $2.5 m illio n , OR
• O ffers to experienced
in vestors
th e o ffe r is made th ro u g h a licensed securities dealer w h o is satisfied th a t the
in v e s to r has s u ffic ie n t previous experience in in v e s tin g in securities to assess
m a tte rs such as th e m e rits o f th e o ffe r and th e risks involved.
Executive officers and
O ffers to d irectors and o th e r persons in vo lve d in th e m anagem ent o f the
associates
issu ing e n tity and ce rta in o f th e ir relatives and associated e n titie s .
E x is tin g s e c u rity holders
O ffers o f fu lly pa id o rd in a ry shares u n d e r a d iv id e n d re in v e s tm e n t plan, bonus
share pla n o r share purchase plan. O ffers o f debentures to e x is tin g debenture
holders.
9.5
Floating a public com pany
W h e n a c o m p a n y f ir s t in v ite s th e p u b lic to su b scrib e f o r shares i t is u s u a l to re fe r to t h is as
L E A R N IN G
OBJECTIVE 5
Outline the process
floating th e
com pany. A n a lte rn a tiv e te r m is t h a t th e c o m p a n y m akes an in it ia l p u b lic o ffe rin g (IP O ). A co m p a n y
m a k in g it s f ir s t issue o f o rd in a ry shares to th e p u b lic w ill u s u a lly a p p ly f o r s to c k exchange lis tin g , w h ic h
of floating a public
m ea ns t h a t sh a re h o ld e rs in th e c o m p a n y can se ll t h e ir shares o n th e s to c k exchange.14 To o b ta in lis tin g ,
co m p a n y
th e d ire c to rs o f th e c o m p a n y m u s t e n sure t h a t it s p ro p o s e d s tru c tu re c o m p lie s w it h th e re q u ire m e n ts
o f th e exchange. F o r exa m ple, th e A S X has e xte n sive lis tin g ru le s t h a t are based o n seve ral p rin c ip le s
d e sig n e d to p ro te c t th e in te re s ts o f lis te d e n titie s , in v e s to rs a n d th e r e p u ta tio n o f th e m a rk e t.
L is te d e n titie s m u s t s a tis fy m in im u m s ta n d a rd s o f q u a lity a n d size, a n d c o m p ly w it h s trin g e n t
re q u ire m e n ts o n d isclo su re o f in fo r m a tio n . F o r exa m ple, to achieve lis tin g o n th e ASX, a c o m p a n y m u s t
u s u a lly have a t le a s t 3 0 0 sh a re h o ld e rs, each s u b s c rib in g f o r shares w it h a v a lu e o f a t le a s t $ 2 0 0 0 . E n titie s
to be lis te d m u s t also s a tis fy e ith e r a p r o f it te s t o r an assets te s t. The p r o f it te s t re q u ire s th e co m p a n y
to have g e n e ra te d a m in im u m aggregate p r o f it o f $1 m illio n o v e r th e p re v io u s th re e years a n d a t le ast
$ 4 0 0 0 0 0 in th e p re v io u s 12 m o n th s . The re q u ire m e n ts o f th e assets te s t in c lu d e n e t ta n g ib le assets o f
a t le a st $3 m illio n (a fte r d e d u c tin g th e costs o f fu n d ra is in g ) o r a m a rk e t c a p ita lis a tio n o f a t le a s t $10
m illio n . 15
The A S X sets the se c o n d itio n s in an e f f o r t to ensure t h a t th e re w ill be an a ctive m a rk e t in th e co m p a n y s
shares a fte r th e y are lis te d . C o m pa nie s t h a t are u n a b le to s a tis fy th e re q u ire m e n ts f o r lis tin g o n th e ASX
WWW
m a y o p t f o r lis tin g o n one o f th e m a rk e ts t h a t have d e ve lo p e d to m e e t th e needs o f s m a lle r com panies.
These in c lu d e th e A s ia Pacific S to ck Exchange (w w w .a p x .c o m .a u ) a n d th e N a tio n a l S to ck Exchange o f
A u s tra lia (w w w .n s x a .c o m .a u ), b o th o f w h ic h a im to p ro v id e a m a rk e t in th e shares o f s m a ll a n d m e d iu m ­
sized e n titie s w it h as fe w as 50 s e c u rity h o ld e rs.
9.5.1 I Public versus private ownership
A co m p a n y u n d e rta k in g a flo a t m a y be e ith e r a n e w c o m p a n y o r an e x is tin g p riv a te com pany. In th e
la tte r case, th e co m p a n y is said to be g o in g p u b lic 1. There are tw o m a in reasons w h y a p riv a te c o m p a n y
m a y go p u b lic . F irs t, lis te d p u b lic com p an ies u s u a lly have b e tte r access to th e c a p ita l m a rk e t th a n p riv a te
com p an ies. A s discussed in S e c tio n 9.3, p riv a te e q u ity in v e s to rs are v e ry se le ctive a n d th e te rm s t h a t th e y
re q u ire m a y n o t be a ttra c tiv e to th e o w n e rs o f a com p an y. G re a te r access to th e c a p ita l m a rk e t is m o s t
v a lu a b le to h ig h -g ro w th co m p a n ie s t h a t re q u ire fu n d s to im p le m e n t a ttra c tiv e n e w p ro je c ts . Second, a
14 While stock exchange listing normally follows a public issue, a company can list without raising any capital at the time of
listing provided it complies with the ASX Listing Rules. This approach is referred to as a compliance listing*. An alternative
way to become a listed public company is by a 'back-door listing*. This involves an unlisted company taking over a company
that is listed on the stock exchange.
15 These and other listing requirements apply to all companies. There are additional requirements that differ depending on
whether the company s main activities involve investment, mining exploration or scientific research. They are set out in
Chapter 1 of the ASX Listing Rules.
C hapter n in e S ources
p u b lic flo a t a llo w s th e o w n e rs o f a c o m p a n y to cash in o n th e success o f th e bu sin ess th e y have developed.
The cash th e y receive b y s e llin g p a r t o f t h e ir in te re s t in th e co m p a n y can be used to d iv e rs ify t h e ir
in v e s tm e n t p o rtfo lio .
G o in g p u b lic also has several costs t h a t m u s t be co n sid e re d . The m o s t s ig n ific a n t is u s u a lly th e loss
o f c o n tro l associated w it h s h a rin g o w n e rs h ip o f th e co m p a n y w it h m a n y o th e r in v e s to rs . The o rig in a l
owners* v o tin g p o w e r w ill be red uce d a t th e tim e o f a flo a t a n d t h e ir p ro p o r tio n a l o w n e rs h ip m a y d e clin e
ove r tim e as th e y sell som e o f t h e ir shares o r as th e co m p a n y raises c a p ita l b y is s u in g m o re shares to n e w
in ve sto rs.
A p u b lic lis tin g also in v o lv e s d ire c t costs such as s to c k exchange lis tin g fees a n d s h a re h o ld e r s e rv ic in g
costs. In a d d itio n , lis te d c o m p a n ie s in c u r costs associated w it h g re a te r in fo r m a tio n d isclo su re . These costs
in c lu d e p ro d u c in g th e re q u ire d in fo r m a tio n a n d th e tim e s p e n t b y m a n a g e m e n t o n in v e s to r re la tio n s . In
p a rtic u la r, m anagers m a y n e e d to discuss th e c o m p a n y s p la n s a n d p ro sp e cts w it h a n a lysts e m p lo y e d b y
b ro ke rs a n d in s titu t io n s because th e re c o m m e n d a tio n s p ro d u c e d b y a n a lysts can in flu e n c e a co m p a n y s
share p ric e a n d its a b ility to raise c a p ita l b y is s u in g m o re shares. F in a lly , th e in fo r m a tio n t h a t a lis te d
com p an y is re q u ire d to disclose m a y in c lu d e d e ta ils t h a t are v a lu a b le to c o m p e tito rs .
9 .5 .2 | Initial public offering of ordinary shares
As s h o w n in Table 9.3, th e n u m b e r o f IPO s a n d t h e ir v a lu e can v a ry c o n s id e ra b ly fr o m yea r to year.
W h e n a c o m p a n y is to go p u b lic ,, its p ro m o te rs u s u a lly seek th e assistance o f a fin a n c ia l in s t it u t io n w ith
e xp e rtise in a rra n g in g share issues. T y p ic a lly , th is has b e en th e fu n c tio n o f th e la rg e r s to c k b ro k e rs an d
in v e s tm e n t b a n ks. B o th typ e s o f in s t it u t io n can advise o n th e p ric e o f th e issue, u n d e rw rite th e issue a n d
h a n d le th e sale o f th e shares.
TABLE 9.3 New listings on the ASX
Year en d e d June 3 0
2009
N u m be r o f new lis tin g s
45
In itia l cap ital raised
1.9
2010
93
11.5
2011
160
29.4
2012
99
10.2
2013
82
9.9
($ b illio n )
Source: ASX Limited, 2 0 1 3 Annual Report.
9 .5 .3 | Pricing a new issue
D e cid in g o n th e p ric e o f a n e w issue is a d iff ic u lt ta sk. The is s u e r faces p o te n tia l p ro b le m s i f th e o ffe r p ric e
is set to o h ig h o r to o lo w . I f th e p ric e is set to o h ig h , fe w in v e s to rs w ill w a n t to sub scrib e a n d th e issue m a y
fa il unless i t is u n d e rw ritte n , in w h ic h case th e u n d e r w r ite r w ill have to m e e t th e s h o rtfa ll. In t u r n , th is
o u tco m e w ill have a n e g a tive e ffe c t o n th e m a rk e t p ric e o f th e shares a fte r th e y are lis te d . I f th e p ric e is
set to o lo w , th e o w n e rs w ill s u ffe r an o p p o r tu n it y loss because th e y w o u ld have received a h ig h e r p a y m e n t
i f th e n e w issue h a d been m ad e a t a h ig h e r p rice . The a va ila b le evide nce suggests th a t, o n average, n e w
issues in it ia lly tra d e a t a p ric e above th e issue p rice . In t h is sense th e y are u n d e rp ric e d ,. The u n d e rp ric in g
o f in it ia l p u b lic o ffe rin g s is discussed in S e c tio n 9.5 .6 .
The ta s k o f s e ttin g th e issue p ric e is p a r tic u la r ly d iff ic u lt w h e n th e co m p a n y has ju s t b e e n fo rm e d ,
as th e re is n o re co rd o f fin a n c ia l p e rfo rm a n c e . W h e re th e co m p a n y has p re v io u s ly o p e ra te d as a p riv a te
com pany, th e ta s k is n o t as d iff ic u lt because p a s t p r o fits m a y be a g u id e to f u tu r e p ro fits . The m o s t
c o m m o n a p pro ach to p r ic in g used b y advisers is to use h is to ric a l p r o fits as th e basis f o r e s tim a tin g
fu tu re e a rn in g s p e r share. The a d vise r w ill also e x a m in e th e p ric e -e a rn in g s (P /E ) ra tio (th e m a rk e t price
o f a share, d iv id e d b y th e e a rn in g s p e r share) o f e x is tin g co m p a n ie s in th e sam e o r s im ila r in d u s trie s .
Forecasts o f fu tu re e a rn in g s p e r share a n d th e in fo r m a tio n o n p ric e -e a rn in g s ra tio s w ill th e n be used b y
th e a d vise r to suggest a p o ssib le range o f issue p rice s f o r th e co m p a n y s shares. F o r exa m ple, i f a c o m p a n y
is expected to e a rn 30 cen ts p e r share a n d th e p ric e -e a rn in g s ra tio s o f s im ila r co m p a n ie s are b e tw e e n 9
and 14, th is suggests an issue p ric e o f b e tw e e n $ 2 .7 0 a n d $ 4 .2 0 p e r share. I f in s titu t io n s are e n th u s ia s tic
a b o u t th e p ro p o se d issue, th e issue p ric e m a y be set close to $ 4 .2 0 . In c o n tra s t, i f th e re is li t t le in te re s t
of fin a n c e : equity
A
B usiness finance
in th e issue, th e issue p ric e m a y be set clo se r to th e lo w e r e n d o f th e range. As is e v id e n t fr o m th e above
d e s c rip tio n , use o f th is a p p ro a ch to set th e issue p ric e in v o lv e s co n sid e ra b le ju d g m e n t.
In th e case o f a fix e d -p ric e o ffe r, th e p ric e m u s t be se t b e fo re th e p ro s p e c tu s is p r in te d a n d th e o ffe r
is u s u a lly o p e n f o r a t le a s t 2 to 3 w eeks. C o n se q u e n tly, th e success o f th e o ffe r is s u b je c t to general
m o v e m e n ts in share p rice s d u rin g a p e rio d o f seve ral w eeks. F o r exa m ple, i f th e g e n e ra l le v e l o f share
prices increases s ig n ific a n tly d u rin g t h a t p e rio d , i t is lik e ly t h a t th e fix e d p ric e w ill be to o low . H o w eve r,
i f share p rice s decrease s ig n ific a n tly d u r in g t h a t p e rio d , in v e s to rs m a y re g a rd th e fix e d p ric e as b e in g to o
h ig h , a n d th e issue w ill close u n d e rs u b s c rib e d .
A n a lte rn a tiv e a p p ro a ch w h e n p r ic in g a n e w issue is to use
book-building— a
process t h a t in v o lv e s
c o m p e titiv e b id d in g b y m a rk e t p a rtic ip a n ts , p a r tic u la r ly in s titu t io n a l in v e s to rs . T his a p p ro a ch uses
e ith e r
open pricing o r constrained open pricing.
In b o th cases, p o te n tia l in v e s to rs place b id s f o r th e shares
w h e re th e y in d ic a te th e q u a n titie s th e y w is h to p u rcha se a t v a rio u s prices. The fin a l p ric e is d e te rm in e d
a t th e e n d o f th e b id d in g process. In th e case o f o p e n p ric in g , shares are u s u a lly a llo c a te d o n ly to b id d e rs
w h o o ffe re d p rice s e q u a l to o r h ig h e r th a n th e fin a l p rice . O p e n p r ic in g has b e en used in som e A u s tra lia n
flo a ts , b u t c o n s tra in e d o p e n p r ic in g is m o re c o m m o n . In c o n s tra in e d o p e n p ric in g , b o th u p p e r an d lo w e r
lim it s are placed o n th e p ric e a n d a ll b id s b e tw e e n th o s e lim it s are co n sid e re d . The p ro s p e c tu s w ill set o u t
th e c r ite r ia to be used in a llo c a tin g shares to b id d e rs . U su a lly, th e p ric e ran ge can be re v is e d d u rin g th e
b id d in g process i f d e m a n d f o r th e shares is fo u n d to be s u b s ta n tia lly g re a te r o r less th a n expected. O nce
th e fin a l p ric e has been d e te rm in e d , a ll successful b id d e rs p a y th e sam e p ric e b u t th o se w h o m ade h ig h e r
b id s have a h ig h e r p r o b a b ility o f re c e iv in g an a llo c a tio n o f shares.
O ffe rs to in s titu t io n s u n d e r a b o o k -b u ild in g process are o fte n a cco m p a n ie d b y an o ffe r to th e general
p u b lic (a 'r e ta il o ffe r*), w h e re a m a x im u m p ric e is sp e cifie d in advance a n d r e ta il in v e s to rs m a y also be
o ffe re d a p ric e d is c o u n t. F o r exa m ple, in th e flo a t o f Q R N a tio n a l L td in N o v e m b e r 2 0 1 0 , th e re was an
in s titu t io n a l b o o k -b u ild w it h an in d ic a tiv e p ric e ran ge o f $ 2 .5 0 to $3 a n d a re ta il o ffe r, w h ic h was su b je ct
to a m a x im u m p ric e o f $ 2 .8 0 p e r share. Successful a p p lic a n ts in th e re ta il o ffe r p a id th e lo w e r o f th e fin a l
p ric e p a id b y in s titu t io n s less a d is c o u n t o f 10 cen ts p e r share a n d th e m a x im u m r e ta il p ric e o f $2 .80.
B o o k -b u ild in g was f ir s t used in A u s tra lia b y th e N e w S o u th W ales G o v e rn m e n t w h e n i t so ld th e
G o v e rn m e n t In s u ra n c e O ffic e (G IO ) in 19 92 . Since th e G IO issue, i t has b e en use d in m a n y la rg e issues,
in c lu d in g th e W o o lw o rth s , Q an ta s, T e ls tra a n d N in e E n te rta in m e n t flo a ts , a n d in som e s m a lle r flo a ts
such as th o s e o f K a th m a n d u H o ld in g s ($ 3 4 0 m illio n in N o v e m b e r 2 0 0 9 ) a n d th e c re d it-c h e c k in g co m p a n y
Veda G ro u p ($ 3 4 1 m illio n in D e cem b er 2 0 1 3 ). The m a in a d va n ta g e o f b o o k -b u ild in g is t h a t i t a llo w s th e
is s u e r a n d its ad vise rs to o b ta in fee dba ck fr o m in fo rm e d in s titu t io n a l in v e s to rs o n t h e ir assessm ent o f
th e va lu e o f th e shares. The in fo r m a tio n g a th e re d fr o m th e se in v e s to rs can be used in s e ttin g th e issue
p rice . W h ile th is a p p ro a ch is e xp ected to re s u lt in a lo w e r le v e l o f u n d e rp ric in g , c o n d u c tin g a b o o k -b u ild is
a c o s tly process, so i t is u s u a lly w o r th w h ile o n ly f o r la rg e r flo a ts . H ence, th e m a jo r ity o f flo a ts in A u s tra lia
s t ill in v o lv e fix e d -p ric e o ffe rs.
W it h a fix e d -p ric e o ffe r, once th e te rm s h a ve b e e n se t, th e a d v is e r u s u a lly e n su re s t h a t th e p ro p o s e d
o ffe r s a tis fie s a ll re le v a n t le g a l re q u ire m e n ts a n d a s sists in p r e p a rin g th e o ffe r d o c u m e n t (u s u a lly
a p ro s p e c tu s ), e n su re s t h a t s to c k exch an ge lis t in g re q u ire m e n ts are m e t, lo d g e s th e p ro s p e c tu s
w it h A S IC a n d m a rk e ts th e shares to in s t it u t io n a l a n d p r iv a te in v e s to rs . The co sts o f p re p a rin g th e
p ro s p e c tu s in c lu d e le g a l fees, fees f o r th e p re p a ra tio n o f a n in v e s tig a tin g a c c o u n ta n t's r e p o r t a n d th e
co st o f p r in t in g . The t o t a l costs o f th e a d v is o ry se rv ic e s , in c lu d in g th e c o sts o f p re p a rin g a p ro s p e c tu s
a n d o b ta in in g s to c k exch a n g e lis tin g , can v a r y w id e ly a n d u s u a lly re p re s e n t b e tw e e n 2 a n d 5 p e r c e n t
o f th e a m o u n t ra is e d . A s discu sse d in S e c tio n 9 .5 .6 , th e costs can be less th a n 2 p e r c e n t o f th e a m o u n t
ra is e d f o r la rg e r flo a ts . C o n ve rse ly, f o r v e r y s m a ll flo a ts t h a t ra is e $ 1 0 m illio n o r less, th e co sts are
u s u a lly m u c h h ig h e r th a n 5 p e r c e n t. I f th e p ro m o te rs agree w i t h th e a d v is e rs re c o m m e n d a tio n s o n
th e te rm s o f th e flo a t, th e sam e a d v is e r w i ll u s u a lly be a p p o in te d to u n d e r w r ite a n d h a n d le th e sale
o f th e shares.
A s p re v io u s ly in d ic a te d , w ith a fix e d -p ric e o ffe r th e is s u e r is s u b je c t to th e vag aries o f th e m a rk e t fr o m
th e tim e w h e n th e p ric e is set u n t il th e issue closes. In m a n y cases th e issu e r w ill pass th is r is k o n to an
u n d e rw rite r, w h ic h is ty p ic a lly an in v e s tm e n t b a n k o r a m a jo r s to c k b ro k e r. I f th e b o o k -b u ild in g process is
used, o n e o r m o re in v e s tm e n t b a n ks o r b ro k e rs w ill be n e ed ed to receive a n d c o lla te th e in s titu t io n a l bids,
advise th e p ro m o te rs o n th e issue p ric e a n d m an ag e th e issue. In th is case, th e in s titu t io n s in v o lv e d are
C hapter n in e S ources
of fin a n c e : equity
ty p ic a lly re fe rre d to as 'lea d m anagers* o f th e issu e .16 N a tu ra lly , w h e n an u n d e r w r ite r acts as b o th a lead
m anager as w e ll as f u lf illin g th e m o re t r a d itio n a l u n d e r w r itin g ro le , separate fees are o fte n charged. F o r
exam ple, w h e n T en N e tw o rk H o ld in g s ra ise d $ 1 6 1 m illio n v ia th e in s titu t io n a l tra n c h e o f its e n title m e n t
o ffe r in Ju n e 20 1 2 , i t p a id its ad vise rs, C itig ro u p , 1.8 5 p e r c e n t o f th e gross pro cee ds as an u n d e r w r itin g
fee and a n o th e r 0.5 p e r ce n t as an o ffe r m a n a g e m e n t a n d a rra n g e m e n t fe e ,.
I f th e issue is u n d e rw ritte n , th e o b lig a tio n s o f th e co m p a n y a n d th e u n d e rw rite r are c o n ta in e d in an
u n d e rw ritin g ag ree m ent. The u n d e r w r ite r co n tra c ts to purchase a ll shares f o r w h ic h a p p lic a tio n s have n o t
been received b y th e c lo sin g date o f th e issue. In re tu rn , th e u n d e rw rite r charges a fee, u s u a lly based o n a fix e d
percentage o f th e a m o u n t to be raised b y th e issue. The fee is n e g o tia te d an d w ill re fle c t th e u n d e rw rite r s
p e rce p tio n o f th e d iffic u lty o f s e llin g th e issue a n d th is in t u r n w ill be d e te rm in e d b y fa c to rs such as th e
com pany s sta tu re in th e m a rk e t, th e p ric e o f th e issue an d general m a rk e t c o n d itio n s . The u n d e rw ritin g
agreem ent n o rm a lly in clu d e s escape clauses th a t sp e cify th e circum stances in w h ic h th e u n d e rw rite r w ill be
released fro m its o b lig a tio n s .17 In som e cases, th e ro le o f th e in s titu tio n s th a t m anage a flo a t m a y in clu d e
price s ta b ilis a tio n once th e shares are lis te d . Price s ta b ilis a tio n , also k n o w n as a greenshoe o p tio n (a fte r
th e com p an y th a t f ir s t used it ) , re q u ire s a special d is p e n s a tio n fro m ASIC. A d is p e n s a tio n o f th is ty p e was
o b ta in e d b y th e in v e s tm e n t b a n ks th a t m anaged th e N o ve m b e r 2 0 1 0 flo a t o f ra il o p e ra to r Q R N a tio n a l,
w h ic h was p re v io u s ly w h o lly o w n e d b y th e Q ue enslan d S tate G o v e rn m e n t (see F inance in A c tio n ).
PRICE STABILISATION IN FLOAT OF RAIL OPERATOR____________
T h e Q R N a t io n a l m e d ia re le a s e a n d A S X a n n o u n c e m e n t a b o u t th e p r ic in g a n d a llo c a t io n o f
s h a re s in its f lo a t c o n t a in e d th e f o llo w in g s ta te m e n t:
'F o llo w in g th e tr a n s f e r o f Q R N a t i o n a l S h a re s b y th e S ta te to s u c c e s s fu l a p p lic a n t s , th e S ta te
w ill in it ia lly r e ta in 8 2 1 4 3 6 7 3 5 Q R N a t i o n a l S h a re s . T h is a m o u n t m a y in c r e a s e b y u p to
1 4 6 4 0 0 0 0 0 Q R N a t io n a l S h a r e s d e p e n d in g o n w h e t h e r th e J o in t L e a d M a n a g e r s e x e r c is e
a n o p t io n to p u r c h a s e u p t o 6 p e r c e n t o f Q R N a t i o n a l S h a re s o n is s u e to c o v e r a n y o v e ra llo c a t io n s m a d e a s p a r t o f th e O ff e r , a s d e s c r ib e d in s e c tio n 2 . 4 . 3 o f th e O f f e r D o c u m e n t /
T h e m e a n in g o f th is s ta te m e n t w a s e x p la in e d a n d d is c u s s e d in a r tic le s b y f in a n c ia l jo u r n a lis ts .
E x c e rp ts fr o m o n e s u ch a r t ic le a p p e a r b e lo w .
R e a d th e Q R N a t io n a l m e d ia r e le a s e a b o u t t o d a y ’ s f lo a t c a r e f u lly a n d y o u r e a lis e th o s e c a n n y
in v e s tm e n t b a n k e r s s o ld 6 6 p e r c e n t o f th e s h a re s in th e c o m p a n y .
W h y s e ttle o n 6 6 p e r c e n t?
T h e a n s w e r ta k e s us to th e d a r k a r t o f th e f lo a t 's jo in t le a d m a n a g e r s e n t e r in g th e m a r k e t a n d
b u y in g s h a re s to s u p p o r t Q R 7s p r ic e . T h e p r ic e s u p p o r t t o o l k n o w n a s 'th e g r e e n s h o e ' is ( v e r y
o p a q u e ly ) d is c lo s e d in th e p r o s p e c tu s . .. T h e t a n g le d t e c h n ic a lit ie s o f th e g r e e n s h o e s p e c if y it is
a n o v e r - a llo c a tio n o p t io n .
T h e te c h n ic a lit ie s m e a n th e o v e r - a llo c a te d s to c k c a n b e b o u g h t b a c k o n th e m a r k e t b y th e
in v e s tm e n t b a n k s , p r o v id in g th e p r ic e s u p p o r t.
G u e s s w h a t ? T h e o v e r - a llo c a t io n o p t io n — a n d th e r e f o r e th e p r ic e s u p p o r t — o n ly k ic k s in a f t e r
th e Q u e e n s la n d g o v e r n m e n t s e lls 6 0 p e r c e n t o f th e s to c k . A n d th e o v e r - a llo c a tio n o p t io n is
lim it e d to 6 p e r c e n t o f th e to ta l s to c k o n is s u e .
N o w 6 0 p e r c e n t p lu s 6 p e r c e n t e x p la in s w h y th e o f f e r s o ld a m a g ic 6 6 p e r c e n t o f th e
c o m p a n y . N o t 6 1 p e r c e n t. N o t 6 4 p e r c e n t. R ig h t o n th e k n o c k e r o f 6 6 p e r c e n t.
A s in a n y f lo a t , it is h a r d to s e e w h e r e t o d a y 's p r ic e la n d s .
continued
16 It is possible for a share issue to be underwritten and priced using book-building. As discussed in Section 9.6.2, this
approach is often used for share placements where issuers desire certainty of funding and, given the short time involved, the
underwriting risk is low and its cost may be acceptable. In the case of IPOs, vendors are generally prepared to accept the risk
that the market clearing price1established in a book-build may be less than they expected. In such cases, the indicative price
range may be lowered or the proposed share issue may be withdrawn.
17 The escape clauses in an underwriting agreement relate to factors that would seriously affect demand for shares in general,
such as the outbreak of war, a significant reduction in a benchmark market index such as the S&P/ASX 200, as well as
company-specific events that could reduce the value of the shares.
F in a n c e
in
ACTION
N e w s <W
n 墨.
B usiness finance
continued
B e c e r t a in o f th is : if th e s h a r e p r ic e f a lls b e lo w th e o f f e r p r ic e , th e r e is p r ic e s u p p o r t
a v a ila b l e in th e fo r m o f f iv e in v e s tm e n t b a n k s w it h a b o u t 9 p e r c e n t o f th e to ta l t r a d e d s h a re s
a v a ila b l e to b u y .
If th e s h a r e p r ic e is h o v e r in g a b o v e a n d b e lo w th e o f f e r p r ic e , r e a d th e Q u e e n s la n d
g o v e r n m e n t 's v ic t o r io u s m e d ia r e le a s e s w it h a d e g r e e o f s c e p tic is m . T h e s h a r e p r ic e is m o r e
th a n lik e ly b e in g g a m e d .
Source: 'Greenshoe on cue may be used to keep QR National 0^001', Stuart Washington, Sydney Morning Herald,
22 November 2010.
The la rg e r s to c k b ro k e rs are m a jo r u n d e rw rite rs , p r im a r ily because th e y have an e s ta b lis h e d c lie n te le
p re p a re d to su b scrib e f o r th e issues th e y u n d e rw rite . A n u n d e r w r ite r w ill fre q u e n tly a tte m p t to li m it its
e xp osu re to th e r is k o f u n d e rs u b s c rip tio n b y in v it in g o th e r in s titu t io n s to a ct as s u b u n d e rw rite rs . These
in s titu t io n s m a y in c lu d e life a n d g e n e ra l in s u ra n c e co m p a n ie s, b a n k s a n d s u p e ra n n u a tio n fu n d s . The ro le
o f th e s u b u n d e rw rite r is to ta k e u p a p r o p o r tio n o f a n y u n d e rs u b s c rip tio n in r e tu r n f o r a fee, p a id b y th e
u n d e rw rite r, w h ic h is based o n a fix e d p r o p o r tio n o f th e issue p ric e .18
I f a s to c k b ro k e r is th e u n d e r w r ite r o r le a d m a n a g e r o f an issue o f shares i t w ill u s u a lly a ct as a s e llin g ag en t
f o r th e issue. By p r o m o tin g an issue, a s to c k b ro k e r p ro te c ts its in te re s ts as u n d e r w r ite r a n d also earns
b ro k e ra g e fees. D e p e n d in g o n th e size o f th e issue, one o r m o re o th e r b ro k in g fir m s m a y also be a p p o in te d
as m a n a g e rs o r co-m a na gers to assist in p u b lic is in g th e issue a n d d is tr ib u tin g th e shares to a w id e range
o f c lie n ts . The fees p a id to the se firm s w ill u s u a lly be s tru c tu re d so t h a t b ro k e rs w h o can d is tr ib u te shares
to c lie n ts have an in c e n tiv e to co m p e te a g a in s t in s titu t io n a l b id s in a b o o k -b u ild . To th is end, th e fees
f o r b ro k e rs m a y be d iv id e d in to a ‘f ir m a llo c a tio n fe e ’ a n d a ‘h a n d lin g fee’. The separate h a n d lin g fee
encourages b ro k e rs to place b id s f o r a d d itio n a l shares above t h e ir f ir m a llo c a tio n in th e e x p e c ta tio n th a t
th e a d d itio n a l shares can be so ld to t h e ir c lie n ts . G re a te r c o m p e titio n b e tw e e n in s t it u t io n a l in v e s to rs and
b ro k e rs ’ c lie n ts (re ta il in v e s to rs ) is, o f course, d e sira b le f o r th e is s u e r a n d th e lead m an ag er.
W h e re a fix e d -p ric e issue is n o t u n d e r w r itte n , a b ro k e r w ill s t ill be engaged to a ssist in d is tr ib u tin g
th e shares. B roke rag e fees are n e g o tia b le a n d d e p e n d o n fa c to rs such as th e size o f th e issue, th e s ta tu s o f
th e is s u in g co m p a n y a n d th e p e rio d f o r w h ic h th e issue is to re m a in open. B roke rag e fees are u s u a lly set
b e tw e e n 1 a n d 2 p e r c e n t o f th e issue p rice .
I t was n o te d in S e c tio n 9 .2 .5 t h a t ra is in g c a p ita l b y is s u in g shares can in v o lv e s ig n ific a n t costs. In th e case
o f c o m p a n y flo a ts th e costs fa ll in to th re e m a in categories:
a
Stock exchange listing fees and the costs ofpreparing and distributing a prospectus. These
costs in c lu d e
le ga l fees, fees f o r th e p re p a ra tio n o f an in v e s tig a tin g a c c o u n ta n ts r e p o rt, fees f o r e x p e rt re p o rts
a n d p r in t in g costs.
b
Fees paid to underwriters or lead managers and commissions paid to brokers for selling the shares. The
t o ta l o f these fees a n d costs can v a ry c o n s id e ra b ly b u t f o r m o s t flo a ts th e costs w o u ld fa ll in th e
ran ge fro m 1 to 5 p e r c e n t o f th e fu n d s raised.
C
Underpricing. The
t h ir d c a te g o ry o f costs re la te s to th e fa c t t h a t th e issue p ric e o f shares s o ld in an
IP O is u s u a lly less th a n th e m a rk e t v a lu e o f th e shares once th e y are lis te d .
The costs t h a t fa ll in to th e f ir s t tw o cate gories m a y be c o m b in e d to fo r m a t o t a l cost o f lis tin g .
U n d e rp ric in g o f IPO s can be s ig n ific a n t a n d is discussed a fte r we discuss th e costs o f lis tin g .
The fa c to rs t h a t in flu e n c e th e costs o f lis tin g f o r a flo a t in c lu d e its size, th e ris k in e s s o f th e co m p a n y
a n d th e c o m p le x ity o f th e u n d e rly in g bu sin ess. The t o ta l costs w ill g e n e ra lly increase w it h th e size o f th e
18 The subunderwriting fee is usually only slightly less than the underwriting fee. For example, if the underwriting fee was 3 per
cent of the issue price, the subunderwriting fee would usually be about 2.5 per cent of the issue price.
C hapter n in e S ources
of f in a n c e : equity
flo a t, b u t because o f th e fix e d n a tu re o f som e c o m p o n e n ts o f th e costs, th e y w ill be la rg e r in p e rcen ta ge
te rm s w h e n th e a m o u n t o f fu n d s s o u g h t is sm a ll. F o r exa m ple, w h e n th e a m o u n t s o u g h t is less th a n
$ 1 0 m illio n , th e costs can be m o re th a n 15 p e r c e n t o f th e a m o u n t s o u g h t. F o r flo a ts t h a t raise m o re th a n
$ 1 0 0 m illio n , th e costs are u s u a lly fr o m 2 to 5 p e r c e n t o f th e a m o u n t s o u g h t a n d can be even lo w e r f o r
la rg e r flo a ts . H o w eve r, v e ry la rg e flo a ts m a y be h a rd e r to sell a n d re q u ire a g re a te r m a rk e tin g e ffo r t. F o r
exam ple, i f a flo a t is so la rge t h a t i t is necessary to a ttr a c t m a n y in te r n a tio n a l in v e s to rs , th e average cost
m a y be h ig h e r th a n f o r a s m a lle r flo a t t h a t is s o ld o n ly in th e A u s tra lia n m a rk e t. I f a co m p a n y has aboveaverage business ris k , i t w i ll g e n e ra lly be m o re d iff ic u lt to d e te rm in e an a p p ro p ria te p ric e f o r th e shares a n d
m o re d iffic u lt to se ll th e shares to in v e s to rs . T h ere fore, a m in in g e x p lo ra tio n co m p a n y w ill be m o re c o s tly
to flo a t th a n an e s ta b lis h e d in d u s tr ia l co m p a n y w it h sta b le cash flo w s. F in a lly , i f a co m p a n y s o p e ra tio n s
are c o m p le x o r d iff ic u lt to u n d e rs ta n d , i t w ill be m o re c o s tly to c a rry o u t ‘due d ilig e n c e ’ in v e s tig a tio n s o f
th e com pany, a n d to engage in research a n d m a rk e tin g . F o r exa m ple, a d d itio n a l in d e p e n d e n t experts*
re p o rts m a y be re q u ire d a n d a d d itio n a l costs m a y be in c u rre d in p r o m o tin g th e flo a t.
W h e re a flo a t is u n d e r w r itte n , th e u n d e r w r itin g fee g e n e ra lly ranges fr o m 1 to 5 p e r c e n t o f th e
fu n d s so u g h t. H is to ric a lly , th e m a jo r ity o f A u s tra lia n flo a ts have be en u n d e r w r itte n , b u t in re c e n t years
th e p o p u la rity o f u n d e r w r itin g has d e c lin e d as m o re flo a ts have be en p ric e d a n d so ld u s in g th e b o o k ­
b u ild in g process. W h e re b o o k -b u ild in g is used, in v e s tm e n t b a n ks a n d b ro k e rs are s t ill in v o lv e d in th e IPO.
H ow ever, in s te a d o f b e in g p a id to g u a ra n te e t h a t a c e rta in su m w ill be raised, th e y are p a id to p ro v id e
a range o f services, in c lu d in g p re p a ra tio n o f research re p o rts o n th e com pany, a rra n g in g s e m in a rs an d
a n a lyst b rie fin g s , a n d m a n a g in g th e b o o k -b u ild in g process. T h ere fore, b o o k -b u ild in g in v o lv e s s ig n ific a n t
costs a n d w ill n o t ne ce ssa rily be che ap er th a n h a v in g a flo a t u n d e r w r itte n . In s u m m a ry , th e costs o f
lis tin g are g e n e ra lly lo w e s t f o r la rge , lo w - r is k flo a ts w h e re th e u n d e rly in g b u sin ess is e a sily u n d e rs to o d b y
in v e s to rs . F o r exa m ple, in th e 2 0 1 0 flo a t o f Q R N a tio n a l, w h ic h ra ise d $ 4 .0 5 b illio n , issue costs as d e ta ile d
in se ctio n 1 0 .1 3 .4 o f th e c o m p a n y s O ffe r D o c u m e n t a m o u n te d to $ 7 5 .5 m illio n , w h ic h is less th a n 1.9
p e r ce n t o f th e fu n d s raised.
U n d e rp ric in g o f a n IP O re p re s e n ts a re a l co st to th e o rig in a l sh a re h o ld e rs, w h o are e ffe c tiv e ly s e llin g
assets to th e n e w sh a re h o ld e rs f o r less th a n t h e ir f a ir value. T his d iffe re n c e in v a lu e is o fte n re fe rre d to as
m o n e y le ft o n th e ta b le 1. M o re pre cise ly, m o n e y le f t o n th e ta b le is u s u a lly d e fin e d as th e r e tu r n o n th e
f ir s t day o f tra d in g , an d is ty p ic a lly m e a su re d b y th e n u m b e r o f shares sold, m u ltip lie d b y th e d iffe re n c e
b e tw e e n th e firs t-d a y c lo s in g m a rk e t p ric e a n d th e issue p rice . I t has b e e n w e ll d o c u m e n te d t h a t in IPO s
th e a m o u n t o f m o n e y le f t o n th e ta b le is ty p ic a lly large. F o r exa m ple, R itte r a n d W e lch fo u n d t h a t th e
average firs t-d a y r e tu r n f o r 6 2 4 9 IP O s in th e US b e tw e e n 1 9 8 0 a n d 2 0 0 1 was 1 8 .8 p e r c e n t.19 R itte r a n d
W elch also fo u n d t h a t th e average firs t-d a y r e tu r n v a rie d c o n s id e ra b ly o v e r tim e . In th e 19 80 s, th e average
firs t-d a y r e tu r n was 7 .4 p e r c e n t a n d i t in crea sed to a lm o s t 1 1 .2 p e r c e n t d u r in g 1 9 9 0 -9 4 a n d 1 8 .1 p e r
cent d u rin g 1 9 9 5 -9 8 b e fo re ju m p in g to 65 p e r c e n t d u rin g th e in t e r n e t b u b b le , p e rio d in 1 9 9 9 -2 0 0 0 and
th e n re v e rtin g to 14 p e r c e n t in 2 0 0 1 .20
In A u s tra lia , a s tu d y b y Lee, T a y lo r a n d W a lte r (1 9 9 6 ) o f 2 6 6 in d u s tr ia l IP O s b e tw e e n 1 9 7 6 a n d 1 9 8 9
fo u n d an average firs t-d a y a b n o rm a l r e tu r n o f 11 .9 p e r ce n t. D im o v s k i a n d B ro o ks (2 0 0 3 ) s tu d ie d 3 5 8
in d u s tria l a n d resource IP O s in A u s tra lia fr o m 1 9 9 4 to 1 9 9 9 a n d fo u n d t h a t th e average firs t-d a y r e tu r n
was 25 .6 p e r c e n t, w h ile th e m e d ia n firs t-d a y r e tu r n was 9.3 p e r ce n t. The IP O s th e y s tu d ie d ra ise d a to ta l
o f $ 2 4 ,4 3 9 b illio n in c a p ita l, th e t o ta l a m o u n t o f m o n e y le f t o n th e ta b le was $ 5 ,6 7 8 b illio n a n d t o t a l issue
costs w ere $ 5 9 2 m illio n . Da S ilva Rosa, V e la y u th e n a n d W a lte r (2 0 0 3 ) re p o rte d m e d ia n u n d e rp ric in g o f
12 p e r c e n t f o r t h e ir sam p le o f 3 3 3 A u s tra lia n in d u s tr ia l IP O s f r o m 1 9 9 1 to 19 9 9 . G on g a n d S h e kh a r
(2 0 0 1 ) s tu d ie d a ll 11 g o v e rn m e n t-s e c to r IPO s in A u s tra lia b e tw e e n 1 9 8 9 a n d 19 99 . T hey fo u n d an average
firs t-d a y a b n o rm a l r e tu r n f o r r e ta il in v e s to rs o f a p p ro x im a te ly 11 p e r c e n t a n d c o n c lu d e d t h a t th e re is
n o evidence th a t th e u n d e rp ric in g o f the se IPO s d iffe rs fr o m t h a t o f A u s tra lia n p riv a te -s e c to r IPO s o r o f
g o v e rn m e n t-s e c to r IP O s in o th e r O EC D c o u n trie s . The u n d e rp ric in g p h e n o m e n o n is n o t re s tric te d to
th e US a n d A u s tra lia . P ro fe s s o r Jay R itte r fr o m th e U n iv e rs ity o f F lo rid a is one o f th e w o r ld s fo re m o s t
e xp e rts in th e area o f IP O u n d e rp ric in g a n d has c o lle c te d th e e m p iric a l re s u lts fr o m m a n y stu d ie s
u n d e rta k e n in d iffe re n t c o u n trie s a ro u n d th e w o rld (see h t t p : / / b e a r . w a r r in g t o n . u f l. e d u / r it t e r / ip o d a t a .
h tm ) . F igu re 9.1 d e m o n s tra te s th e in it ia l re tu rn s en jo yed, o n average, b y IP O su b scrib e rs in te r n a tio n a lly
an d illu s tra te s ju s t h o w p e rv a s iv e IP O u n d e rp ric in g has been.
19 Ritter and Welch (2002). The equally-weighted average first-day return measured from the offer price to the first closing price
listed by CRSP is 18.8 per cent.
20 For an analysis of possible reasons for this variation, see Loughran and Ritter (2004).
|wwwj
B usiness finance
Source: Loughran, T., Ritter, J. and Rydqvist, K., Initial public offerings: International insights: 2014 update', 17 January
2014, http://bear.warrington.ufl.edu/ritter/lnt2014.pdif.
Reasons for underpricing
M a n y p o s s ib le e x p la n a tio n s f o r th e u n d e rp ric in g o f IPO s have b e en p ro p o s e d . O n e e x p la n a tio n is based
o n in fo r m a t io n a s y m m e try in t h a t som e in v e s to rs are m o re in fo rm e d th a n th e issu er, p e rh a p s a b o u t
LEARNING
OBJECTIVE 6
Discuss alternative
explanations for the
underpricing of initial
public offerings
th e g e n e ra l d e m a n d f o r shares in th e m a rk e t. I t is also based o n th e c o n ce p t t h a t som e in v e s to rs are
w e ll in fo rm e d a b o u t th e value o f th e shares b e in g o ffe re d w h ile o th e rs are u n in fo r m e d a n d th e re fo re
have d iff ic u lt y e s tim a tin g th e fu tu r e m a rk e t p ric e o f th e shares. T his a p p ro a ch pro po ses t h a t a degree
o f u n d e rp ric in g is necessary to a ttr a c t the se in v e s to rs . U n in fo rm e d in v e s to rs m a y a p p ly f o r a n y IP O
b u t in fo r m e d in v e s to rs w ill o n ly s u b scrib e w h e n an issue is u n d e rp ric e d . T h e re fo re , w h e n an issue is
o v e rp ric e d , a ll th e shares w ill be a llo c a te d to u n in fo rm e d in v e s to rs . C onversely, w h e n an issue is
u n d e rp ric e d , in fo r m e d in v e s to rs w ill c ro w d out* th e u n in fo rm e d , w h o w i ll be a llo c a te d o n ly a fra c tio n o f
th e shares.
T his e x p la n a tio n m a y be illu s tra te d w it h a s im p le exa m ple. C o n s id e r tw o IPO s, one o f w h ic h records
a firs t-d a y r e t u r n o f + 2 0 p e r ce n t, w h ile th e o th e r re co rd s a firs t-d a y r e t u r n o f - 1 0 p e r ce n t. Hence, th e
average firs t-d a y r e tu r n is 5 p e r ce n t. Because th is r e tu r n is p o s itiv e , th e re appears to be u n d e rp ric in g .
N o w c o n s id e r th e r e tu r n e a rn e d b y an u n in fo rm e d in v e s to r w h o a p p lie s f o r $ 1 0 0 0 0 w o r th o f shares in
each o f th e se IP O s a n d is a llo c a te d $ 5 0 0 0 w o r th o f shares in th e f ir s t IP O a n d th e f u ll $ 1 0 0 0 0 w o r th o f
shares in th e second. The u n in fo rm e d in v e s to r s r e t u r n is 0 p e r c e n t. T h e re fo re , fr o m th e v ie w p o in t o f th e
u n in fo r m e d in v e s to r, th e IPO s are o n average f a ir ly p ric e d . In s u m m a ry , w h ile IPO s in v o lv e la rg e average
in it ia l r e tu rn s , th is does n o t n e ce ssa rily m e a n t h a t e v e ry in v e s to r can e xp e ct to e a rn a b n o rm a l r e tu rn s b y
s u b s c rib in g f o r co m p a n y flo a ts .
W IN N E R ^ CURSE
problem that arises
in bidding because
the bidder who
’wins’ is likely to be
the one who most
overestimates the
value of the assets
offered for sale
U n in fo rm e d in v e s to rs , th e re fo re , face a
w inn er^ curse.
I f th e y g e t a ll o f th e shares th e y d e m an d,
i t is because th e in fo r m e d in v e s to rs d id n o t w a n t th e m . Faced w it h th is s itu a tio n , u n in fo r m e d in v e s to rs
w ill o n ly s u b scrib e to IPO s i f th e y are s u ffic ie n tly u n d e rp ric e d , o n average, to c o m p e n sa te f o r th e bias
in th e a llo c a tio n o f shares ( fo r m o re d e ta ils , see R o ck 1 9 8 6 ). In research re la te d to th e ‘w in n e r ’s curse’
e x p la n a tio n i t is c o m m o n to assum e t h a t la rg e r in v e s to rs are b e tte r in fo rm e d th a n s m a ll in v e s to rs .
Lee, T a y lo r a n d W a lte r (1 9 9 9 ) e xa m in e th is issue b y s tu d y in g IPO s o n th e S to ck E xchange o f S in ga pore
w h e re d e ta ile d d a ta o n a p p lic a tio n s f o r a n d a llo c a tio n s o f shares are ro u tin e ly p ro v id e d . T h e ir re s u lts are
c o n s is te n t w it h R o c k s (1 9 8 6 ) m o d e l: la rg e r in v e s to rs are m o re in fo rm e d in t h a t th e y a p p ly f o r re la tiv e ly
m o re shares in issues t h a t are u n d e rp ric e d . Thus, s m a ll in v e s to rs are c ro w d e d o u t o f th e m o s t u n d e rp ric e d
issues a n d receive la rg e r p r o p o r tio n s o f th e less a ttra c tiv e issues.
A seco nd e x p la n a tio n f o r th e u n d e rp ric in g o f IP O s is t h a t p o te n tia l in v e s to rs w i ll a tte m p t to ju dg e
th e in te re s t o f o th e r in v e s to rs a n d w ill o n ly s u b scrib e f o r IP O s t h a t th e y b e lie ve w i ll be p o p u la r. I f
an in v e s to r perceives t h a t a flo a t is n o t p o p u la r w it h o th e r in v e s to rs , th e n he o r she m a y decide n o t
to sub scrib e. I f th e is s u e r sets a p ric e t h a t is p e rce ive d as o n ly a l i t t le to o h ig h , th e re is a s ig n ific a n t
p r o b a b ility t h a t th e issue w ill be a fa ilu re , w it h in v e s to rs d e c id in g n o t to s u b scrib e because o th e rs have
also de cid e d n o t to sub scrib e. T h ere fore, issu ers m a y have an in c e n tiv e to u n d e rp ric e an issue in o rd e r
to in d u c e som e p o te n tia l in v e s to rs to buy. The a c tio n o f the se in v e s to rs m a y th e n se t o f f a cascade in
C hapter n in e S ources
w h ic h o th e r in v e s to rs are w illin g to sub scrib e. R itte r a n d W e lch (2 0 0 2 ) n o te t h a t th is e x p la n a tio n is
s u p p o rte d b y evidence t h a t IP O s te n d to be e ith e r u n d e rs u b s c rib e d o r h e a v ily o v e rsu b scrib e d , w it h fe w
b e in g m o d e ra te ly o v e rsu b scrib e d .
U s in g b o o k -b u ild in g to p ric e an IPO, w h ic h in c re a s in g ly has becom e s ta n d a rd p ra ctice , a llo w s issuers
to o b ta in in fo r m a tio n fro m in fo rm e d in v e s to rs . A f te r an in d ic a tiv e p ric e ran ge has been set, th e issu e r
a n d th e lead m a n a g e r u s u a lly go o n a ‘ro a d s h o w ’ to p ro m o te th e co m p a n y to p ro s p e c tiv e in v e s to rs . The
lead m a n a g e r can th e n gauge d e m a n d f o r th e shares as exp re ssio n s o f in te re s t are rece ive d fr o m p o te n tia l
in ve sto rs. I f d e m a n d is h ig h , th e o ffe r p ric e w ill be set a t th e to p o f th e in d ic a tiv e p ric e range o r i t m a y
be set above th a t le ve l i f d e m a n d is p a r tic u la r ly s tro n g . H o w e ve r, p o te n tia l in v e s to rs w ill be u n w illin g
to reveal t h e ir tru e in te re s t in th e IP O i f th e y k n o w t h a t s h o w in g s tro n g in te re s t is lik e ly to re s u lt in a
h ig h e r o ffe r p ric e — un le ss th e y are o ffe re d s o m e th in g in re tu rn . U n d e rp ric in g th e n becom es p a r t o f th e
in d u c e m e n t needed to g e t p o te n tia l in v e s to rs to t r u t h f u lly re ve a l t h a t th e y are w illin g to pu rcha se th e
shares a t a h ig h price. A n a ly s is o f d a ta o n IPO s p ric e d u s in g b o o k -b u ild in g in th e US is c o n s is te n t w ith
th is a rg u m e n t. F o r e xa m p le , R itte r a n d W e lch fo u n d t h a t o v e r th e 1 9 8 0 to 2 0 0 1 p e rio d , f o r IP O s th a t
were p ric e d w it h in th e in d ic a tiv e p ric e range, average u n d e rp ric in g was 12 p e r ce n t. H o w e ve r, w h e n th e
o ffe r p ric e was above th e in d ic a tiv e p ric e range, average u n d e rp ric in g was 53 p e r ce n t. The a d d itio n a l
u n d e rp ric in g is re g ard ed as c o m p e n s a tio n to in d u c e in v e s to rs to reve al t h e ir h ig h in d iv id u a l d e m a n d
f o r th e shares— b u t as R itte r a n d W e lch n o te , average u n d e rp ric in g o f 53 p e r c e n t seems to be excessive
c o m p e n s a tio n f o r re v e a lin g in fo r m a tio n .
Several stu d ie s have fo u n d t h a t g re a te r u n d e rp ric in g is a sso cia te d w it h h ig h e r tra d in g v o lu m e once
th e shares becom e lis te d . A c c o rd in g ly , a t h ir d e x p la n a tio n f o r u n d e rp ric in g is t h a t i t p ro v id e s b e n e fits
th ro u g h g re a te r liq u id ity . F o r exa m ple, a b ro k e r w h o u n d e rw rite s an IP O can e a rn h ig h e r b ro ke ra g e
fees fo r h a n d lin g tra d e s in th e p o s t-lis tin g m a rk e t i f th e issue is u n d e rp ric e d . L iq u id ity can also b e n e fit
issuers, p a rtic u la rly i f th e y have re ta in e d a h ig h p r o p o r tio n o f th e c o m p a n y s shares. P ham , K a le v an d
Steen (2 0 0 3 ) argue t h a t g re a te r u n d e rp ric in g encourages s m a ll in v e s to rs to su b scrib e f o r an IPO, w h ic h
re su lts in a b ro a d e r an d m o re d iffu s e o w n e rs h ip base. U s in g a sam ple o f A u s tra lia n IPO s th e y s h o w t h a t
these fa c to rs are s ig n ific a n tly a n d p o s itiv e ly a sso cia te d w it h th e liq u id it y o f th e shares once th e y are
lis te d . C onversely, th e y argue t h a t lo w e r u n d e rp ric in g w ill g ive ris e to a m o re c o n c e n tra te d o w n e rs h ip
s tru c tu re , w h ic h m a y be p re fe rre d i f la rge sh a re h o ld e rs o b ta in b e n e fits fr o m c o n tro l o r can p ro v id e
va lua ble m o n ito r in g o f th e c o m p a n y s m a n a g e m e n t.
A f o u r t h e x p la n a tio n is t h a t u n d e rp ric in g o f IPO s is in th e in te re s ts o f th e is s u in g com p an y. O ne
aspect o f th is e x p la n a tio n is t h a t u n d e rp ric e d IP O s *leave a g o o d taste* w it h in v e s to rs , ra is in g th e p ric e
a t w h ic h sub se q u e n t share issues b y th e c o m p a n y can be s o ld .21 A re la te d a rg u m e n t is t h a t u n d e rp ric in g
re fle cts, a t le ast in p a rt, th e co st to th e is s u in g co m p a n y o f p u rc h a s in g research coverage b y a n a lysts.
C liff a n d D e nis (2 0 0 4 ) n o te t h a t in a d d itio n to p re -IP O a c tiv itie s re la te d to th e p r ic in g a n d m a rk e tin g o f
a share issue, in v e s tm e n t b a n k s p ro v id e a ran ge o f p o s t-is s u e services such as m a rk e t-m a k in g a n d a n a ly s t
research coverage. T hey also n o te t h a t is s u in g co m p a n ie s a p p e a r to place a v a lu e o n s e c u rin g research
coverage fr o m a n a lysts, p a r tic u la r ly th o s e w it h s tro n g re p u ta tio n s . A c c o rd in g ly , issu ers p la n n in g an IPO
m a y seek o u t u n d e rw rite rs w h o th e y e xp e ct w ill p ro v id e research coverage b y a h ig h ly ra te d a n a ly s t a n d
issuers w ill be p re p a re d to p a y f o r t h a t a n a ly s t coverage— p e rh a p s d ire c tly b y w a y o f h ig h e r u n d e r w r itin g
fees. H o w eve r, C lif f a n d D e n is fo u n d t h a t u n d e r w r itin g fees are la rg e ly u n ifo r m a n d p ro p o se in s te a d t h a t
gre a te r u n d e rp ric in g serves to in d ir e c tly com p e n sa te u n d e rw rite rs f o r p ro v id in g a n a ly s t coverage. F o r
exam ple, u n d e rw rite rs can b e n e fit fr o m u n d e rp ric in g b y a llo c a tin g shares to fa v o u re d c lie n ts w h o are
expected to p ro v id e th e u n d e r w r ite r w it h in v e s tm e n t b a n k in g o r b ro k in g b u sin e ss in th e fu tu re .
A f if t h e x p la n a tio n is t h a t issu e rs u n d e rp ric e IP O s to reduce th e r is k o f b e in g sued b y in v e s to rs . W h ile
th e p o te n tia l le ga l lia b ilit y o f issu e rs m a y be a fa c to r in som e IPO s, p a r tic u la r ly in th e US, o th e r c o u n trie s ,
w h ere litig a t io n is m u c h less c o m m o n , e xp erience s im ila r levels o f u n d e rp ric in g . T h e re fo re , i t seems
u n lik e ly th a t le ga l lia b ilit y is th e m a in fa c to r t h a t d e te rm in e s th e u n d e rp ric in g o f IPO s.
F in a lly , L o u g h ra n a n d R itte r (2 0 0 2 ) n o te t h a t issuers ra re ly ap p e a r to be u p s e t a b o u t le a v in g
s u b s ta n tia l a m o u n ts o f m o n e y o n th e ta b le in IPO s. T hey p ro p o se a b e h a v io u ra l e x p la n a tio n f o r th is
p u z z lin g p h e n o m e n o n . T h e ir e x p la n a tio n can be illu s tra te d u s in g a h y p o th e tic a l e xa m p le . Suppose th a t
M arcus T h o m p s o n o w n s a la rg e successful b u sin ess an d, a fte r d is c u s s io n w ith an in v e s tm e n t b a n k , he
plan s to sell 60 p e r c e n t o f th e co m p a n y in an IPO , w h ic h w ill be p ric e d u s in g a b o o k -b u ild . The in d ic a tiv e *1
4
9
21 For an analysis of this explanation, see Welch (1989). The explanations for underpricing of IPOs outlined above are only some
of the possible explanations that have been proposed. Further explanations are discussed by Ibbotson, Sindelar and Ritter
(1994) and Brau and Fawcett (2006).
of f in a n c e : equity
B usiness finance
p ric e ran ge f o r th e b o o k -b u ild is set a t $ 4 .5 0 to $5 p e r share, b u t, a fte r a successful ro a d s h o w , w h e re th e
in v e s tm e n t b a n k reco rds s tro n g in te re s t fr o m in s titu tio n s , i t advises M a rcu s t h a t th e issue p ric e s h o u ld
be in cre a se d to $6 p e r share. G iv e n th e g o o d ne w s t h a t h is c o m p a n y is w o r th a t le a st 2 0 p e r c e n t m o re
th a n he p re v io u s ly th o u g h t, M a rcu s accepts th e advice a n d does n o t b a rg a in f o r a h ig h e r issue price.
W h e n th e shares are lis te d o n th e ASX, th e firs t-d a y c lo s in g m a rk e t p ric e is $1 0. M a rc u s has le f t a large
a m o u n t o f m o n e y o n th e ta b le b u t he has also d isco ve re d t h a t th e in te re s t he re ta in e d — 4 0 p e r c e n t o f th e
shares— is w o r th tw ic e as m u c h as he expected. G ive n th e p le a s a n t s u rp ris e a b o u t h is n e w -fo u n d w e a lth ,
M a rcu s m a y fe e l happy, d e sp ite th e o p p o r tu n it y loss o n th e shares t h a t he so ld to o th e r in v e s to rs .
I f th e la rge in it ia l re tu rn s o n IPO s re fle c t ra tio n a l b e h a v io u r b y issuers a n d in v e s to rs , th e n these
re tu rn s s h o u ld be re la te d to fa c to rs such as th e a m o u n t o f in fo r m a tio n a va ila ble to in v e s to rs a n d th e
b e n e fits t h a t issu ers m a y d e riv e f r o m u n d e rp ric in g . E m p iric a l evide nce s u p p o rts th is e x p e c ta tio n . F or
exa m ple, Lee, T a y lo r a n d W a lte r (1 9 9 6 ) fo u n d a s tro n g in v e rs e re la tio n s h ip b e tw e e n th e le n g th o f th e
de la y b e tw e e n p ro sp e ctu s re g is tra tio n a n d exchange lis tin g a n d th e le v e l o f u n d e rp ric in g . In o th e r w o rd s,
IPO s w it h s h o rte r delays in lis tin g are s ig n ific a n tly m o re u n d e rp ric e d . T his fin d in g is c o n s is te n t w it h th e
^w in n e rs curse* e x p la n a tio n in w h ic h in fo rm e d in v e s to rs w ill q u ic k ly s u b scrib e f o r u n d e rp ric e d issues
th e re b y e n s u rin g t h a t th e issue w ill be fille d in a s h o rt p e rio d . H o w , Iz a n a n d M o n ro e (1 9 9 5 ) also fo u n d
a s tro n g re la tio n s h ip b e tw e e n de la y in lis tin g a n d th e le ve l o f u n d e rp ric in g . F u rth e r, th e y fo u n d th a t
u n d e rp ric in g is re la te d to m easures o f b o th th e q u a lity a n d q u a n tity o f in fo r m a t io n a va ila b le a b o u t th e
com pany. S pe cifica lly, u n d e rp ric in g was lo w e r w h e n th e u n d e r w r ite r h a d a g o o d re p u ta tio n a n d i t was
also lo w e r f o r co m p a n ie s w it h m o re in fo r m a t io n a va ila b le .22
C am p, C o m e r a n d H o w (2 0 0 6 ) s tu d ie d 4 9 N e w Z e a la n d IPO s t h a t lis te d b e tw e e n 1 9 8 9 a n d 2 0 0 2 . They
fo u n d t h a t u n d e rp ric in g was s ig n ific a n tly lo w e r f o r issues t h a t used b o o k -b u ild in g ra th e r th a n a fix e d p ric e o ffe r. T his re s u lt is c o n s is te n t w it h th e a rg u m e n t t h a t b o o k -b u ild in g p ro v id e s issuers w ith feedback
fr o m in fo rm e d in v e s to rs , w h ic h a llo w s m o re accurate p r ic in g o f th e IPO. T hey also fo u n d t h a t g re a te r
u n d e rp ric in g is associated w it h h ig h e r tra d in g v o lu m e in th e p o s t-lis tin g m a rk e t, su g g e s tin g a tra d e -o ff
b e tw e e n th e cost (u n d e rp ric in g ) o f g o in g p u b lic a n d th e b e n e fit (g re a te r liq u id ity ) o f d o in g so. C am p e t
al. also fo u n d t h a t u n d e rp ric in g is p o s itiv e ly re la te d to th e p r o p o r tio n o f shares re ta in e d b y th e p re -IP O
sh a re h o ld e rs. C o n s is te n t w it h L o u g h ra n a n d R itt e r s e x p la n a tio n , issu ers w h o re ta in m o re shares in th e
c o m p a n y a p pe ar to be less co n ce rn e d a b o u t u n d e rp ric in g because a n y loss o f w e a lth o n th e shares sold in
th e IP O w i ll be o ffs e t b y a g a in o n th e shares th e y re ta in .
U n d e rp ric in g o f IPO s is a p e rs is te n t p h e n o m e n o n t h a t is y e t to be f u lly e x p la in e d . In e v a lu a tin g th e
p ro p o s e d e x p la n a tio n s o u tlin e d p re v io u s ly , th e q u e s tio n s h o u ld n o t be: ‘W h ic h m o d e l is co rre c t? ’ R a th er,
w e s h o u ld ask q u e s tio n s such as: ‘W h ic h m o d e l is m o re u s e fu l in th is case?’ A lso , w e s h o u ld re m e m b e r
t h a t th e reasons f o r u n d e rp ric in g can change o v e r tim e . F o r exa m ple, th e re is evidence t h a t u n d e rp ric in g
is g e n e ra lly lo w e r f o r com p an ies t h a t engage h ig h e r-q u a lity u n d e rw rite rs a n d h ig h e r-q u a lity a u d ito rs .
These p a rtie s have been v ie w e d as p ro v id in g a c e rtific a tio n role; in v e s to rs are c o n fid e n t t h a t a h ig h q u a lity u n d e r w r ite r w ill n o t o v e rp ric e an IP O because d o in g so w o u ld h a rm its r e p u ta tio n w it h in v e s to rs .
H o w e ve r, th e u s u a l re la tio n s h ip b e tw e e n u n d e rp ric in g a n d u n d e r w r ite r q u a lity re ve rse d d u rin g th e
1 9 9 9 -2 0 0 0 in t e r n e t b u b b le \ A s discussed p re v io u s ly , one e x p la n a tio n f o r th is re v e rs a l is t h a t th e
o b je c tiv e s o f issu ers cha ng ed in t h a t th e y becam e less co n ce rn e d a b o u t u n d e rp ric in g a n d w e re p re p a re d
to p a y f o r research coverage b y le a d in g an alysts.
The c o n s is te n t fin d in g t h a t IPO s are o n average u n d e rp ric e d does n o t ne ce ssa rily m e a n t h a t issue prices
are ‘to o lo w ’ 一 i t is also p o ssib le t h a t firs t-d a y m a rk e t p rice s are 'to o h ig h ,. T his p o s s ib ility is c o n s is te n t
LEARNING
OBJECTIVE 7
Outline evidence
on the long-term
performance of
companies that are
floated
w it h evide nce t h a t th e p o s itiv e firs t-d a y re tu rn s o n IP O s are o fte n reve rsed o v e r tim e — t h a t is, several
stu d ie s have fo u n d t h a t th e shares o f n e w ly lis te d co m p a n ie s te n d to u n d e rp e rfo rm d u r in g th e f ir s t fe w
years a fte r lis tin g . U n fo rtu n a te ly , i t is v e ry d iff ic u lt to a c c u ra te ly assess th e lo n g -ru n p e rfo rm a n c e o f
c o m p a n ie s t h a t go p u b lic . O n e rea son is t h a t th e m a rk e t m o d e l, w h ic h was in tro d u c e d in S e ctio n 7.6.3,
c a n n o t be used to e s tim a te th e be tas o f th e s e c u ritie s because p re -lis tin g r e tu r n d a ta does n o t e x is t
f o r IPO s. T h ere fore, researchers have used a v a r ie ty o f o th e r approaches to assess w h e th e r p o s t-lis tin g
re tu rn s are a b n o rm a l. O ne a p p ro a ch is to com p are p o s t-lis tin g r e tu rn s o n IP O co m p a n ie s to one o r m o re
22 The underwriting fee as a percentage of the issue proceeds was used as a measure of the underwriters reputation and the size
of the company was used as a measure of the quantity of information.
C hapter n in e S ources
of fin a n c e : equity
m a rk e t in d ice s, w ith o u t a n y a d ju s tm e n t f o r ris k . A n o th e r a p p ro a ch is to co m p a re th e re tu rn s o n th e
IPO com panies w ith a c o n tro l sam ple o f o th e r lis te d co m p a n ie s m a tc h e d o n th e basis o f one o r m o re
ch a ra cte ristics such as size (m a rk e t c a p ita lis a tio n ) a n d in d u s try .
R itte r (1 9 9 1 ) s tu d ie d co m p a n ie s t h a t w e n t p u b lic in th e US in th e p e rio d 1 9 7 5 to 1 9 8 4 .23 H e fo u n d
t h a t an in v e s to r w h o p u rc h a s e d shares in IP O co m p a n ie s a t th e c lo s in g p ric e o n th e f ir s t d a y o f p u b lic
tra d in g an d th e n h e ld th e shares f o r 3 years w o u ld have e a rn e d an average t o ta l r e tu r n o f 3 4 .4 7 p e r cen t.
F o r a c o n tro l sam ple o f n o n -IP O com p an ies m a tc h e d b y size a n d in d u s try , th e average t o ta l r e tu r n o ve r
th e same p e rio d was 6 1 .8 6 p e r cen t. The u n d e rp e rfo rm a n c e b y IP O co m p a n ie s v a rie d s ig n ific a n tly fr o m
yea r to yea r a n d across in d u s trie s b u t i t was c o n c e n tra te d a m o n g re la tiv e ly y o u n g , g ro w th com p an ies,
p a rtic u la rly th o s e t h a t w e n t p u b lic in years w h e n th e re was a h ig h v o lu m e o f IPO s.
L o u g h ra n a n d R itte r (1 9 9 5 ) fo u n d t h a t th e p o o r lo n g -te rm p e rfo rm a n c e o f IP O s c o n tin u e d b e y o n d
3 years a n d was sha red b y com p an ies m a k in g su b s e q u e n t e q u ity issues— k n o w n as s e a s o n e d e q u i t y
SEASONED EQUITY
o f f e r in g s (SEOs) in th e US. U s in g la rge sam ples o f co m p a n ie s t h a t issu ed e q u ity in th e p e rio d 1 9 7 0 to
OFFERING
19 9 0 , th e y re p o rte d average a n n u a l re tu rn s o v e r th e 5 years a fte r th e is s u in g o f o n ly 5 p e r c e n t f o r IPO s
a n d 7 p e r c e n t f o r com p an ies m a k in g SEOs. In c o n tra s t, in v e s tin g in n o n -is s u in g com p an ies o f th e same
size an d h o ld in g th e in v e s tm e n t f o r th e sam e p e rio d w o u ld have p ro d u c e d an average a n n u a l re tu r n
o f 12 p e r ce n t f o r IPO s a n d 15 p e r c e n t f o r SEOs. L o u g h ra n a n d R itte r p ro p o se t h a t t h e ir evide nce is
c o n s is te n t w ith a m a rk e t w h e re shares are p e rio d ic a lly o v e rv a lu e d a n d t h a t com p an ies ta ke ad van ta ge o f
these E n d o w s o f o p p o r tu n it y 1 b y is s u in g e q u ity a t th o s e tim e s . T h a t idea, a n d th e re la te d p ro p o s itio n
th a t in v e s to rs w ill re s p o n d b y c u ttin g share p rice s w h e n an issue is a n n o u n ce d , are n o t new . F o r e xa m ple,
S m ith (1 9 8 6 ) re p o rte d t h a t w h e n a US co m p a n y a n n o u n ce s an SEO, its share p ric e fa lls b y a b o u t 3 p e r
cen t o n average. L o u g h ra n a n d R itte r p o in t o u t t h a t i f in v e s to rs are to receive th e sam e lo n g -te rm re tu rn s
on issuers as o n n o n -is s u e rs o f th e sam e size, th e fa ll in p ric e w h e n an issue is a n n o u n c e d s h o u ld be m u c h
larger. T h e ir n u m b e rs *im p ly t h a t i f th e m a rk e t re a cte d f u lly to th e in fo r m a tio n im p lie d b y a n e q u ity issue
a n n o u n c e m e n t, th e average a n n o u n c e m e n t e ffe c t w o u ld be - 3 3 p e r c e n t, n o t - 3 p e r cent* (L o u g h ra n an d
R itte r 19 9 5 , p. 4 8 ). L o u g h ra n a n d R itte r r e fe r to th e u n e x p la in e d lo w lo n g -te rm re tu rn s fo llo w in g e q u ity
issues as ‘th e n e w issues p u z z le ’.
The sig n ifica n ce o f th e n e w issues p u z z le is c o n tro v e rs ia l. B rav a n d G o m p e rs (1 9 9 7 ) s h o w t h a t lo w
p o s t-lis tin g re tu rn s te n d to be c o n c e n tra te d a m o n g s m a ll com p an ies, w h ic h m ea ns t h a t m ea sure d
u n d e rp e rfo rm a n c e is m u c h s m a lle r w h e n re tu rn s are v a lu e w e ig h te d ra th e r th a n e q u a lly w e ig h te d . They
also fin d t h a t u n d e rp e rfo rm a n c e is a c h a ra c te ris tic o f s m a ll com p an ies w it h lo w b o o k -to -m a rk e t ra tio s
regardless o f w h e th e r th e y are n e w ly lis te d o r n o t. I n o th e r w o rd s , B ra v a n d G o m p e rs f in d t h a t c om p an ies
th a t go p u b lic do n o t e x h ib it lo n g -te rm u n d e rp e rfo rm a n c e w h e n r e tu rn s are m e a su re d re la tiv e to c o n tro l
com panies m a tc h e d o n b o th size a n d b o o k -to -m a rk e t ra tio .
Eckbo, M a s u lis a n d N o r li (2 0 0 0 ) arg ue t h a t th e *new issues puzzle* id e n tifie d b y L o u g h ra n a n d R itte r
can be reso lve d w ith o u t re s o rtin g to e x p la n a tio n s based o n m a rk e t u n d e rre a c tio n to th e in fo r m a tio n
in a n n o u n c e m e n ts o f s e c u rity issues. E ckbo e t al. analyse re tu rn s fo llo w in g a la rg e sam p le o f seasoned
issues o f b o th e q u ity a n d d e b t fr o m 1 9 6 4 to 1 9 9 5 . T hey argue t h a t th e m a tc h e d -firm te c h n iq u e does n o t
p ro v id e a p ro p e r c o n tro l f o r r is k f o r tw o reasons. F irs t, an e q u ity issue lo w e rs th e fin a n c ia l leverage o f
th e is s u in g c o m p a n y so issu ers also lo w e r t h e ir ris k , a n d th e re fo re t h e ir e xp e cte d r e tu rn , re la tiv e to th e
m a tch e d firm s . Second, th e y f in d t h a t share t u r n o v e r increases s ig n ific a n tly a fte r SEOs, b u t tu r n o v e r does
n o t change f o r th e m a tc h e d firm s . In o th e r w o rd s , liq u id it y increases a fte r SEOs so th e shares o f is s u in g
com panies c o u ld re q u ire lo w e r liq u id it y p re m iu m s a fte r an issue. In sum , th e y con clu de t h a t evidence
o f lo n g -ru n u n d e rp e rfo rm a n c e p ro d u c e d b y th e m a tc h e d -firm te c h n iq u e is an a r tifa c t o f th e te c h n iq u e
its e lf* (Eckbo, M a s u lis & N o r li 2 0 0 0 , p. 2 5 3 ).
G om pe rs a n d L e rn e r (2 0 0 3 ) p o in t o u t t h a t m o s t stu d ie s th a t re p o rt u n d e rp e rfo rm a n c e b y IP O s have
e xa m in e d d a ta fr o m th e tim e p e rio d a fte r fo r m a tio n o f th e N asdaq syste m w h e re m o s t US IPO s are
tra d e d . The N asdaq is th e la rg e s t e le c tro n ic e q u ity s e c u ritie s tra d in g m a rk e t in th e US. W h e n e sta b lish e d
in th e e a rly 19 70 s b y th e N a tio n a l A s s o c ia tio n o f S e cu ritie s D ealers, i t was th e w o r ld s f ir s t e le c tro n ic
sto c k m a rk e t. To te s t w h e th e r th e re is a ‘N a sda q e ffe c t’，G o m p e rs a n d L e rn e r c o n d u c te d an o u t-o f-s a m p le
in v e s tig a tio n u s in g d a ta o n 3 6 6 1 IPO s fr o m 1 9 3 5 to 1 9 7 2 — a p e rio d p r io r to th e c re a tio n o f N asdaq. They
fo u n d t h a t th e re la tiv e p e rfo rm a n c e o f a n IP O sam p le depends c r itic a lly o n th e m e th o d used to assess
p e rfo rm a n c e . O ne m e th o d re ve aled som e u n d e rp e rfo rm a n c e , b u t th is m e a su re d u n d e rp e rfo rm a n c e
23 Updated evidence on the long-term performance of US IPOs from 1970 to 2013 is available at http://bear.w arrington.ufl.
edu/ritter/ipodata.htm.
offer to sell equity
securities of a class
that is already traded
B usiness finance
d isa p p e a re d w h e n th e sam e sam p le was s tu d ie d u s in g o th e r m e th o d s , in c lu d in g re g re ssio n s based o n th e
C A P M (see S e c tio n 7 .6 .2 ) a n d th e Fam a a n d F re n c h th re e -fa c to r m o d e l (see S e ctio n 7 .7 ). G om pe rs and
L e rn e r co n clu d e t h a t th e evide nce f o r u n d e rp e rfo rm a n c e b y IP O s is w eak.
M ix e d evide nce o n th e lo n g -te rm p e rfo rm a n c e o f c o m p a n ie s t h a t go p u b lic is n o t c o n fin e d to th e US.
F o r A u s tra lia n IPO s, lo n g -te rm u n d e rp e rfo rm a n c e , re la tiv e to th e m a rk e t in d e x , has b e en re p o rte d by
Lee, T a y lo r a n d W a lte r (1 9 9 6 ) o v e r 3 years, a n d D im o v s k i a n d B ro o ks (2 0 0 3 ) o v e r 1 year, a fte r lis tin g .
F o r t h e ir sam p le o f 2 6 6 IPO s, Lee e t al. re p o rte d a m a rk e t-a d ju s te d r e t u r n o f - 5 1 p e r c e n t o v e r 3 years.
D im o v s k i a n d B ro o ks re p o rte d a n average m a rk e t-a d ju s te d r e tu r n o f - 4 . 0 p e r ce n t o v e r 1 ye a r f o r a
sam p le o f 2 5 1 IP O s fr o m 1 9 9 4 to 19 9 8 . H o w e ve r, th e re s u lts w e re n o t u n if o r m ly n e g a tiv e w h e n th e
sam p le w as d iv id e d in to su b g ro u p s. F o r exa m ple, th e average m a rk e t-a d ju s te d r e tu r n f o r 7 8 n o lia b ilit y
co m p a n ie s w as - 3 0 p e r c e n t a fte r 1 ye a r b u t f o r th e 1 7 3 lim it e d lia b ilit y co m p a n ie s th e c o rre s p o n d in g
average r e t u r n w as +7.7 p e r ce n t. The m e d ia n m a rk e t-a d ju s te d r e t u r n a fte r 1 y e a r w as n e g a tiv e f o r th e
sam p le as a w h o le a n d f o r e ve ry su b g ro u p . In c o n tra s t, da S ilva Rosa, V e la y u th e n a n d W a lte r (2 0 0 3 ) used
several b e n c h m a rk s a n d co n clu d e d t h a t th e sam p le th e y s tu d ie d d id n o t u n d e rp e rfo rm in th e 2 years
fo llo w in g lis tin g .
In s u m m a ry , th e evidence o n lo n g -ru n p e rfo rm a n c e fo llo w in g IP O s re m a in s c o n tro v e rs ia l. M a n y
stu d ie s have re p o rte d u n d e rp e rfo rm a n c e b y IP O co m p a n ie s o v e r p e rio d s o f 1 to 5 years a fte r lis tin g .
There is evide nce t h a t co m p a n ie s t h a t issue e q u ity , w h e th e r th r o u g h an IP O o r a seasoned o ffe rin g , te n d
to be p o o r lo n g -te rm in v e s tm e n ts . H o w e ve r, several a u th o rs have q u e s tio n e d w h e th e r th e *new issues
puzzle* is re a l a n d p ro v id e evide nce t h a t suggests t h a t i t m a y be n o m o re th a n a n illu s io n .
9.6
LEARNING
OBJECTIVE 8
Explain how
companies raise
capital through rights
issues, placements,
share purchase plans
and share options
Subsequent issues of o rd in a ry shares
A f te r a c o m p a n y has been flo a te d , a d d itio n a l e x te rn a l fin a n c e w i ll u s u a lly be re q u ire d a t som e tim e to fin a n c e
e x p a n s io n . M a n a g e m e n t has th e choice o f is s u in g m o re shares a n d /o r b o rro w in g . I f i t is de cid e d to issue
m o re shares, th e re are several choices ava ila ble. I f th e fu n d s are to be ra is e d f r o m e x is tin g sh a re h o ld e rs,
th e c o m p a n y can m ake a p ro -ra ta share issue (e n title m e n t o ffe r) o r set u p a share p u rch a se p la n (SPP). A
p ro -ra ta sha re issue m a y in t u r n be e ith e r a tr a d itio n a l r ig h ts issue o r a n a ccelerated e n title m e n t o ffe r an d
in e ith e r case th e o ffe r m a y be re n o u n ce a b le o r n o n -re n o u n c e a b le . I f m a n a g e m e n t decides to raise fu n d s
fr o m selected in v e s to rs , w h o m a y o r m a y n o t be e x is tin g s h a re h o ld e rs in th e co m p a n y, i t m u s t choose a
p la c e m e n t. Share issues o f the se typ e s m a y be c a rrie d o u t in d iv id u a lly o r in c o m b in a tio n . F o r exa m ple,
a co m p a n y m a y raise c a p ita l th ro u g h a p la c e m e n t a n d an SPP t h a t are a n n o u n c e d s im u lta n e o u s ly . The
re g u la to ry re g im e t h a t g o ve rn s c a p ita l ra is in g s b y lis te d co m p a n ie s is o u tlin e d in Table 9.4.
TABLE 9.4 The Australian capital-raising regime for listed companies
R e g u la to ry re q u ire m e n ts
M a in c h a ra c te ris tic s
T yp e o f c a p ita l ra is in g
Renounceable
P a rtic ip a tio n is based on each
The tim e ta b le fo r e n title m e n t offers is
e n title m e n t o ffe r
shareholder s e x is tin g in te re s t in the
specified in th e ASX L is tin g Rules. The
company. A prospectus m ay be needed.
disclosure req uire m en ts are set o u t in
Shareholders are able to sell th e ir rig h t
th e
Corporations Act.
to p a rtic ip a te in th e e n title m e n t offer.
N on-renounceable
P a rtic ip a tio n is based o n each
The tim e ta b le fo r e n title m e n t offers
e n title m e n t o ffe r
shareh old er’s e x is tin g in te re s t in the
is specified in th e ASX L is tin g Rules.
company. A prospectus m ay be needed.
The L is tin g Rules lim it th e size o f the
Shareholders are n o t able to sell th e ir
rig h t to p a rtic ip a te in th e offer. A n y
o ffe r to a m a x im u m o f one new share
fo r each e x is tin g share. The disclosure
rig h ts n o t take n up m ay be placed a t the
re q u ire m e n ts are set o u t in the
d iscre tio n o f th e com pany s Board o f
Corporations Act.
D irectors.
C hapter n in e S ources
of fin a n c e : equity
Table 9 .4 continued
—
T ype o f c a p ita l ra is in g
R e g u la to ry re q u ire m e n ts
M a in c h a ra c te ris tic s
Placement
P a rtic ip a tio n b y in vestors is at the
ASX L is tin g Rules re s tric t placem ents
d is c re tio n o f th e com pany’s Board o f
to no m ore th a n 15 p e r cent o f issued
D ire cto rs and m anagem ent. O pen
cap ital over a 1 2 -m o n th p e rio d w ith o u t
to ‘s o p h istica te d ’ o r ‘p ro fe ssio nal’
appro val by shareholders. U n de r certain
investors. A prospectus is n o t required.
circum stances, th is lim it increases to
25 p e r cent o f issued cap ital fo r sm aller
firm s w ith m a rk e t cap ita lisa tio n s o f less
th a n $300 m illio n . The
Corporations Act
p e rm its placem ents w ith o u t a disclosure
d o cu m e n t p ro vid e d a cleansing notice*
is issued.
The SPP m echanism is stip u la te d in the
Share purchase plan
P a rtic ip a tio n is open to e x is tin g
(SPP)
shareholders. There is no re q u ire m e n t
L is tin g Rules. The disclosure regim e has
fo r a prospectus p ro v id e d a cleansing
been p ro vid e d by ASIC in a series o f
n o tice is issued, offers are lim ite d
R e gu latory Guides and Class Orders.
to $15 000 p e r shareholder over a
1 2 -m o n th p e rio d , and th e shares are
fu lly p a id a nd issued a t a d isco u n t to
th e m a rk e t price d u rin g the 30 days o f
tra d in g p rio r to e ith e r th e o ffe r date o r
th e issue date.
9 .6 .1 1 Rights issues
A rig h ts issue— also k n o w n as an e n title m e n t o ffe r— is a n issue o f n e w shares to e x is tin g sh a re h o ld e rs.
U n d e r th e te rm s o f a rig h ts issue, sh a re h o ld e rs receive th e r ig h t to s u b scrib e f o r a d d itio n a l shares in a
fix e d ra tio to th e n u m b e r o f shares a lre a d y h e ld . P ro v id e d each s h a re h o ld e r accepts th e o ffe r, th e re is no
d ilu tio n o f a n y s h a re h o ld e rs pe rce n ta g e o w n e rs h ip in th e com pany.
To illu s tra te th e e le m e n ts o f a r ig h ts issue: assum e t h a t an in v e s to r h o ld s 1 0 0 0 shares, w h ic h re p re s e n t
1 p e r ce n t o f a c o m p a n y s issu e d c a p ita l o f 1 0 0 0 0 0 shares. I f th e c o m p a n y m akes a rig h ts issue th a t
e n title s each s h a re h o ld e r to p u rch a se one a d d itio n a l share f o r e v e ry fo u r shares h e ld , th e s h a re h o ld e r is
SUBSCRIPTION PRICE
e n title d to b u y an e x tra 2 5 0 shares, th u s in c re a s in g th e s h a re h o ld in g to 1 2 5 0 . In to ta l, th e c o m p a n y w ill
the price that must be
paid to obtain a new
share
issue 25 0 0 0 n e w shares. T h e re fo re , th e p e rcen ta ge o w n e rs h ip o f th e s h a re h o ld e r in th e c o m p a n y re m a in s
un cha ng ed a t 1 p e r ce n t because 1 2 5 0 /1 2 5 0 0 0 = 1 p e r ce n t.
W ith a rig h ts issue, s h a re h o ld e rs b u y a d d itio n a l shares. The com p an y, th e re fo re , has to se t a
subscription price.
U su a lly, th e s u b s c rip tio n p ric e is less th a n th e c u rre n t m a rk e t p ric e o f th e shares,
because o th e rw is e n o -o n e w o u ld w a n t to s u b scrib e f o r th e n e w shares. G ive n t h a t th e s u b s c rip tio n p ric e
is b e lo w th e c u rre n t m a rk e t p ric e , th e r ig h t to b u y a n e w share has a value . I f th e rig h ts are re n o u n ce a b le ,
a s h a re h o ld e r is able to se ll th e rig h ts to a n o th e r in v e s to r i f th e y w is h to .
A fo rm u la k n o w n as th e
theoretical rights price can
be used to e s tim a te th e v a lu e o f a r ig h t. To de ve lo p
th is fo rm u la suppose t h a t a c o m p a n y m akes a 1 - fo r - N re n o u n ce a b le rig h ts issue a t a s u b s c rip tio n p ric e
of
S d o lla rs
p e r sha re— t h a t is, each s h a re h o ld e r o b ta in s th e r ig h t to pu rcha se o n e n e w share f o r e v e ry
shares th a t th e y c u rre n tly h o ld an d w ill p a y
S d o lla rs
N
f o r each n e w share. A ll re n o u n ce a b le rig h ts issues
ex-rights date. I f an in v e s to r pu rcha ses shares in th e c o m p a n y b e fo re th e
pu rcha se is said to be cum righ ts a n d th e in v e s to r w ill receive rig h ts to purcha se n e w
sp e cify a date, called th e
e x -rig h ts date, th e
shares. The rig h ts th e m s e lv e s m a y be tra d e d s e p a ra te ly f r o m th e shares o n o r a fte r th e e x -rig h ts date.
I f an in v e s to r purchases shares o n o r a fte r th e e x -rig h ts da te th e p u rcha se is sa id to be
in v e s to r
will not receive
a n y rig h ts .
ex-rights a n d
th e
EX-RIGHTS DATE
date on which a
share begins trading
ex-rights. After fhis
date a share does not
have attached to it the
right to purchase any
additional share(s) on
the subscription date
CUM RIGHTS
when shares are
traded cum rights
the buyer is entitled
to participate in the
forthcoming rights
issue
A ssu m e t h a t a n in v e s to r purchases
is
NM w h e re M is
N shares
ju s t b e fo re th e e x -rig h ts date. The co st o f th is purchase
th e m a rk e t p ric e o f a share cu m rig h ts . T his in v e s to r is e n title d to th e r ig h t to purchase
one n e w share. E x a c tly th e sam e in v e s tm e n t can be a ch ie ved b y e n te rin g th e m a rk e t ju s t a fte r th e shares
b e g in tra d in g e x -rig h ts a n d p u rc h a s in g
T his w ill c o st
NX + R} w h e re X is
N shares e x -rig h ts
a n d also p u rc h a s in g th e r ig h t to one n e w share.
th e m a rk e t p ric e o f a share e x -rig h ts a n d
R is
th e m a rk e t p ric e o f th e r ig h t
to p u rcha se one n e w share. In th e absence o f a n y n e w in fo r m a tio n t h a t causes p ric e s to change, b o th
in v e s tm e n t stra te g ie s s h o u ld co st th e same. T h a t is:
9.1
N M =N X +R
I f th e s u b s c rip tio n p ric e is pa yab le im m e d ia te ly , th e n th e r ig h t to one n e w share can be im m e d ia te ly
c o n v e rte d to a n e w share b y p a y m e n t o f th e s u b s c rip tio n p ric e . T h e re fo re , w h e n th e shares b e g in tra d in g
R and
X. To p re v e n t a rb itra g e ,
e x -rig h ts , an in v e s to r c o u ld o b ta in a share e ith e r b y b u y in g th e r ig h t to one n e w share a t a cost o f
th e n p a y in g th e s u b s c rip tio n p ric e o f
S, o r b y b u y in g
a share d ir e c tly a t a p ric e o f
b o th in v e s tm e n t s tra te g ie s m u s t co st th e same. T h a t is:
_______
R+ S= X
THEORETICAL RIGHTS
S u b s titu tin g E q u a tio n 9.2 in to E q u a tio n 9.1, a n d re a rra n g in g , gives:
PRICE
N+
1
S u b s titu tin g E q u a tio n 9.3 in to E q u a tio n 9.2, a n d re a rra n g in g , gives:
NM+S
X
THEORETICAL
EX-RIGHTS SHARE
PRICE
the expected price
of one share when
shares begin to be
traded ex-rights
N(M -S)
R.
the expected price of
one right calculated
on the basis of the
cum-rights share price
The p ric e s t h a t r e s u lt fr o m u s in g E q u a tio n s 9.3 a n d 9 .4 are o fte n re fe rre d to as th e
price
a n d th e
theoretical ex-righ ts sh are price,
theoretical righ ts
resp ective ly.
W h a t is th e e ffe c t o f a rig h ts issue o n th e va lu e o f an in v e s tm e n t in shares? To a n s w e r th is q u e s tio n ,
c o n s id e r E xam p le 9.1.
E x a m p l e 9 .1
A th o l o w n s 1 0 0 0 s h a re s in R a ven E n te rp ris e s Ltd (REL), w h o s e c u rre n t s h a re p r ic e (cu m rig h ts ) is $ 2
p e r s h a re . REL m a k e s a l- f o r - 4 rig h ts issu e w ith a s u b s c rip tio n p r ic e o f $ 1 . 4 0 p e r s h a re . A th o l w is h e s
to c a lc u la te :
a)
th e v a lu e , R, o f th e r ig h t to b u y 1 n e w s h a re
b)
th e e x -rig h ts s h a re p r ic e , X
c)
th e v a lu e o f h is in v e s tm e n t c u m rig h ts a n d e x -rig h ts .
In th is c a s e , N = 4 , M = $ 2 . 0 0 a n d S = $ 1 . 4 0 .
SOLUTION
a)
U s in g E q u a tio n 9 . 3 , th e v a lu e o f th e r ig h t to b u y 1 n e w s h a re is:
R _ N IM - S )
N+ 1
4($2.00-$1.40)
471
—
= 4 8 cents
b)
U s in g E q u a tio n 9 . 4 , th e e x -rig h ts s h a re p r ic e is:
v
NM + S
A =
-----------------
N+ 1
4($2.00)-$1.40
—
= $
4^1
1.88
C hapter n in e S ources
c)
of f in a n c e : equity
C u m rig h ts , th e in v e s tm e n t is w o r th :
( 1000)($2)
=$2000
E x -rig h ts , th e in v e s tm e n t is w o r th :
(1 0 0 0 )($ 1 .8 8 ) + (2 5 0 )($ 0 .4 8 )
=$2000
A c c o r d in g to th is a n a ly s is th e to ta l v a lu e o f th e in v e s tm e n t is u n a ffe c te d . B e fo re th e issu e A th o l o w n e d
1 0 0 0 s h a re s w o r th $ 2 e a c h — a to ta l o f $ 2 0 0 0 . A fte r th e issu e h e o w n s 1 0 0 0 s h a re s w o r th $ 1 . 8 8
e a c h ( $ 1 8 8 0 ) p lu s 2 5 0 rig h ts w o r th 4 8 c e n ts e a c h ( $ 1 2 0 ) , w h ic h in to ta l is a ls o w o r th $ 2 0 0 0 .
C le a rly , th e v a lu e o f th e rig h ts ju st o ffs e ts th e d e c lin e in th e v a lu e o f th e s h a re s . If A th o l d e c id e s to sell
his rig h ts he c a n e x p e c t to r e c e iv e $ 1 2 0 , w h ic h s h o u ld b e r e g a r d e d a s a p a r tia l re tu rn o f c a p it a l as
d is tin c t fro m a p r o fit o r re tu rn on c a p it a l. F in a lly , s u p p o s e th a t in s te a d o f a l- f o r - 4 rig h ts issu e w ith a
s u b s c rip tio n p r ic e o f $ 1 . 4 0 p e r s h a re , REL m a k e s a l- f o r - 2 issu e w ith a s u b s c rip tio n p r ic e o f 7 0 ce n ts
p e r s h a re . C le a rly , b o th issues w o u ld ra is e e x a c tly th e s a m e fu n d s f o r REL a n d r e w o r k in g th e a b o v e
c a lc u la tio n s w o u ld s h o w th a t th e e x -rig h ts v a lu e o f A t h o l’s in v e s tm e n t w o u ld a g a in b e $ 2 0 0 0 .
This a n alysis relates to th e v a lu e o f a n in v e s tm e n t m ad e a t th e tim e o f th e e x -rig h ts da te a n d i t
suggests th re e im p o r t a n t c o n c lu s io n s . F irs t, sha reh old ers* w e a lth is n o t a ffe c te d b y th e m e re fa c t o f
a share b e g in n in g to tra d e o n an e x -rig h ts basis. In t u r n , th is suggests th e second c o n c lu s io n th a t, o f
its e lf, a rig h ts issue has n o v a lu e to sh a re h o ld e rs. T his c o n c lu s io n s h o u ld n o t be a s u rp ris e . I f a rig h ts
issue increased (decreased) sha reh old ers* w e a lth w e w o u ld e xp e ct rig h ts issues to o c c u r m u c h m o re (less)
fre q u e n tly th a n th e y do. T h ird , i t suggests t h a t in th e case o f a rig h ts issue th e le v e l o f th e s u b s c rip tio n
price has n o e ffe c t o n sha reh old ers* w e a lth . I f a ll s h a re h o ld e rs su b scrib e f o r a rig h ts issue, th e n w h e th e r
a co m p a n y raises, say, $2 m illio n b y is s u in g 1 m illio n shares a t $2 each, o r 2 m illio n shares a t $1 each,
s h o u ld n o t m a tte r to its sh a re h o ld e rs.
H o w eve r, th e above a n a lysis ig n o re s som e fa c to rs t h a t can be im p o r ta n t. F irs t, th e
announcement o f a
rig h ts issue m a y a ffe c t sha reh old ers* w e a lth because th e a n n o u n c e m e n t can have in fo r m a tio n c o n te n t. F o r
exam ple, US a n d A u s tra lia n evide nce suggests th a t, o n average, th e m a rk e t in te rp re ts th e a n n o u n c e m e n t
o f e q u ity c a p ita l issues, in c lu d in g rig h ts issues, as 'bad* n e w s .24 S m ith (1 9 8 6 ) p ro v id e d an e x p la n a tio n o f
th e n e g a tive a n n o u n c e m e n t e ffe c t: m an ag ers w ill t r y to issue e q u ity w h e n th e y be lie ve i t is o ve rva lu e d .
In v e s to rs are aw are o f m anagers* in fo r m a tio n ad van ta ge a n d w ill re s p o n d b y re d u c in g t h e ir e s tim a te o f
th e co m p a n y s va lu e w h e n an issue is a n n o u n ce d . The im p lic a tio n s f o r fin a n c in g d e cisio n s are discussed
in S ectio n 12 .9.4.
Second, th e te rm s o f a rig h ts issue such as th e s u b s c rip tio n p ric e m a y a ffe c t th e m a rk e t re a c tio n to
an issue w h e n i t is a n n o u n ce d . I f th e s u b s c rip tio n p ric e is se t o n ly s lig h tly b e lo w th e m a rk e t p ric e o f th e
shares, a m in o r fa ll in th e co m p a n y s share p ric e c o u ld cause th e issue to fa il— n o ra tio n a l s h a re h o ld e r w ill
sub scrib e f o r th e rig h ts issue i f th e shares can be p u rch a se d m o re ch e a p ly o n th e s to c k m a rk e t. C learly,
th is ris k can be red uce d b y s e ttin g a lo w e r s u b s c rip tio n p rice , b u t d o in g so m a y w a rn in v e s to rs t h a t
m a n a g e m e n t is fe a rfu l o f a p o ssib le fa ll in th e co m p a n y s share p rice . Hence, s e ttin g a lo w e r s u b s c rip tio n
p rice m a y re s u lt in a la rg e r fa ll in share p ric e w h e n th e issue is a n n o u n ce d .
T h ird , th e a n a lysis assum es t h a t th e s u b s c rip tio n p ric e is payable o n th e e x -rig h ts da te, w h ere as, in
fact, i t is u s u a lly n o t pa yab le u n t il several w eeks la te r. T his gives ris e to th e f u r t h e r p o in t t h a t th e h o ld e r
o f a r ig h t is p e r m itte d to p u rch a se shares a t th e s u b s c rip tio n p ric e , b u t is n o t o b lig e d to do so. I f th e share
p rice o n th e s u b s c rip tio n d a te is less th a n th e s u b s c rip tio n p ric e , th e h o ld e r o f th e r ig h t does n o t have to
purchase th e shares. T his ty p e o f a g re e m e n t is k n o w n as an o p t io n , b u t th e th e o re tic a l m o d e l ig n o re s th e
o p tio n -lik e fe a tu re s o f a r ig h t a n d is th e re fo re lik e ly to u n d e rs ta te th e v a lu e o f a r ig h t.
24 There is evidence that the market response to the announcement of equity issues differs between countries but is consistently
negative on average. Thus, in the US, Smith reports an average decline of about 3 per cent for rights issues by industrial
companies (see Smith 1986), while in the UK, Marsh found a much smaller decline for such issues (see Marsh 1979). In
Australia, a study of 636 rights issues by Balachandran, Faff and Theobald (2008) found an average fall in share price of
1.74 per cent when the issues were announced.
OPTION
the right but not the
obligation to buy or
sell underlying assets
at a fixed price for a
specified period
B usiness finance
The option component o f a rig h ts value is usually small in dollar terms b u t can be a significant
p ro po rtio n o f the value o f a rig ht, particularly i f the share price is close to the subscription price. For
example, the subscription price fo r the rights issue by Colonial Group in 1998 was $4.50, payable no later
than 13 July, and the rights were traded on the ASX from 4 June to 2 July. On 11 June, the closing price
o f Colonial shares was $4.53 while the rights closed at 14.5 cents. I f holders o f the rights were obliged
to pay the subscription price and had to pay it immediately, the rights would have been w orth only
$4.53 - $4.50 = 3 cents. In this case, the option component o f the rig hts’ value was 11.5 cents.
Disclosure and regulation of rights issues
Historically, a company m aking a rights issue was required to supply shareholders w ith a disclosure
document, usually a prospectus. The cost o f preparing a disclosure document was an im p o rta n t factor that
influenced issuers to prefer placements rather than rights issues. The requirements fo r rights issues have
been aligned w ith those fo r placements by changes to the Corporations Act contained in the Corporations
Legislation Amendment (Simpler Regulatory System) Act 2007. From 2007, issuers can proceed w ith a rights
issue w ith o u t a prospectus provided they:
•
•
lodge w ith the ASX a notice known as a ‘rights issue cleansing notice ’
；and
send to shareholders a short document th a t describes the reasons fo r the rights issue and sets out
the term s and tim in g o f the issue.
In addition to stating th a t the issuer complies w ith certain provisions o f the Corporations Act, a rights
issue cleansing notice m ust deal w ith two issues. First, it m ust contain any excluded* in fo rm a tio n — that
is, in fo rm a tio n that:
•
•
has previously been w ithheld from investors based on one o f the exceptions to disclosure contained
in the listing rules25
investors would reasonably require and expect to be included in a disclosure document fo r the
purpose o f assessing the financial position, performance and prospects o f the issuer.
Second, the notice m ust provide inform a tion about any effects th a t the issue could have on the control
o f the listed entity.
I f a company has disclosed all price-sensitive info rm a tio n related to its operations and makes a rights
issue fo r a general purpose such as raising w orking capital or repaying debt, a rights issue cleansing notice
would be the obvious choice. In other cases a prospectus may be preferred. For example, suppose th a t a
company makes a rights issue to raise funds fo r a new project th a t has been under development fo r some
tim e b u t whose existence has n o t been disclosed to the shareholders. In th a t case, a rights issue cleansing
notice should contain extensive details o f the new project. However, it may instead be preferable to issue
a prospectus containing the same inform ation. One factor favouring the use o f a prospectus is th a t a
cleansing notice is n o t defined as a disclosure document. Therefore, i f a cleansing notice is found to
contain errors or omissions, the ‘due diligence’ defence outlined in Section 9.4.1 is n o t available.
As discussed in Section 9.4.2, the prospectus fo r a rights issue can be much less detailed than the
prospectus fo r an issue o f unlisted securities. Provided the company s shares have been listed fo r at least
12 m onths p rio r to the issue, the prospectus does n o t have to contain extensive inform a tion on the
assets, liabilities, performance and prospects o f the issuing company. Rather, the prospectus can focus on
details o f the new securities and on the expected effects o f the new issue on the company.
The significance of rights issues
The frequency o f rights issues fluctuates over tim e but they continue to be an im p o rta n t way o f raising
equity fo r Australian companies. In the 2012-13 financial year, ASX-listed companies raised $4 b illio n
through rights issues. In comparison, in the 2008-09 financial year, $28.5 b illio n was raised through
rights issues. Details o f selected rights issues by listed companies are shown in Table 9.5.
25
R u le 3 .1 o f th e A u st r a lia n S e c u r it ie s E x c h a n g e L is t in g R u le s r e q u ir e s im m e d ia t e d is c lo s u r e o f m a t e r ia l in fo r m a t io n b y lis t e d
e n t it ie s b u t R u le 3 .1 A p r o v id e s s o m e e x c e p tio n s t o th e c o n tin u o u s d is c lo s u r e r e q u ir e m e n t s .
C hapter n in e S ources
TABLE 9.5 Details of selected rights issues by listed companies
Am ount
Issue
ra is e d ( $ m )：
p r ic e ($ )
P re-issue s h a re
p r ic e ($ )
1U n d e r w r itin g
fe e (%)
Com pany
D a te a n n o u n c e d
Wesfarmers Ltd
22/01/2009
3:7
3700
13.50
15.78
2.1
TEN Network
Holdings
15/06/2012
3:8
200
0.51
0.64
2.35
Billabong
21/06/2012
International Ltd
6:7
221
1.02
1.83
2.9
Bionomics Ltd
1:8
0.36
0.41
3.0
S o u rc e :
5/03/2013
Issue r a tio
16.4
Announ cem ents to the A S X a n d c o m p a n y prospectuses.
Designing a successful rights issue
A rights issue that failed to raise all or most o f the planned funds could be very costly fo r the issuing
company. The costs o f planning the issue and preparing a prospectus or other documentation have to be
paid regardless o f the outcome, and failure is likely to harm a company s reputation because it may be
thought th a t existing shareholders lack confidence in the company s prospects and/or the performance
o f its managers. Therefore, managers w ill employ various measures to maximise the probability th a t a
rights issue w ill be successful. An obvious measure o f this type is to have the issue underw ritten. Another
approach m ight be to make the issue renounceable and to set the subscription price substantially below
the current m arket price o f the shares so there is a high probability th a t shareholders w ill either exercise
their entitlem ent, or sell th e ir rights to others who w ill subscribe fo r the shares. In this case, i t m ig ht seem
that there should be no need fo r the company to have the issue underw ritten, b u t in fact the m ajority
o f rights issues in Australia are underw ritten. There appear to be fo ur m ain reasons fo r this practice.
First, while the subscription price may be well below the share price at the tim e an issue is announced, a
substantial unexpected fall in share price is always possible and could spell failure fo r a non-underw ritten
issue. Second, as discussed above, setting a low subscription price may result in a larger fall in the share
price when a rights issue is announced. Therefore, managers may tr y to m inim ise the adverse effect on
shareholders’ wealth by setting a higher subscription price and having the issue underw ritten. Third,
there w ill always be some shareholders who, fo r one reason or another, either do n o t receive n otification
o f an issue, or do n ot respond in tim e to subscribe fo r the new shares. Finally, because o f the high costs
o f complying w ith securities laws in countries such as the US, Australian companies usually specify
that a rights issue w ill be made only to shareholders whose registered address is in Australia or New
Zealand. ASX Listing Rule 7.7 requires th a t where foreign shareholders are n o t eligible to participate
in a renounceable rights issue, they m ust s till be advised o f the issue and th a t the value, i f any, o f th e ir
entitlements should be paid to them. Therefore, one role o f the und erw rite r is to sell any new shares
that represent the entitlem ents o f ineligible foreign shareholders. Orica Lim ited is an Australian-based
manufacturer o f chemicals and explosives w ith operations in about 50 countries and its shareholders
include both Australian and overseas investors. In November 2005, Orica announced a fu lly underw ritten
l-fo r-8 renounceable rights issue at $15 per share, substantially less than the m arket price o f $20.55.
The issue was made to all ordinary shareholders w ith a registered address in Australia or New Zealand
and to in s titu tio n a l ordinary shareholders in Hong Kong, Singapore and the UK. On 19 December 2005,
Orica announced a shortfall, including the entitlem ents o f ineligible foreign shareholders, o f 2.4 m illion
shares, or approximately 7 per cent o f the total. In this case, the sh ortfa ll shares were sold to in s titu tio n a l
investors w ith the issue price determ ined by an overnight book-build conducted by the underwriters. The
issue price fo r these shares was $20.30, which m eant th a t Orica received $15 per share and the balance o f
$5.30 per share was paid to the non-subscribing shareholders and ineligible foreign shareholders.
In summary, u nd erw riting is one way o f ensuring that the issuing company w ill receive all the planned
funds regardless o f the level o f subscriptions by shareholders and may be less costly than attem pting to
increase shareholder take-up by lowering the subscription price. The closer the subscription price on the
rights issue is set to the m arket price o f shares, the greater is the need to have the issue underw ritten,
of f in a n c e : equity
B usiness finance
SHORTFALL FACILITY
a m echanism under
w hich a co m p a n y
m ay issue shortfall
shares to eligible
shareholders or other
investors
SHORTFALL SHARES
new shares not
subscribed for b y
eligible shareholders
a c c o rd in g to their
entitlements under a
rights issue
.
and the higher the u nd erw riting fee. The u nd erw riting fee is usually between 1 and 3 per cent o f the
subscription price.
W hile u nd erw riting ensures th a t all the planned funds w ill be raised, there are other measures that
can be used to increase the likelihood th a t a rights issue w ill be successful. The m ain such measures
are issuing the rights w ith bonus share options as a sweetener* and providing a sh o rtfall facility.
As discussed in Section 9.6.5, bonus share options are issued ‘free’ in a fixed pro po rtio n to the new
shares taken up by existing shareholders. Balachandran, Faff and Theobald (2008) studied rights issues
announced by Australian companies from 1995 to 2005 and found th a t almost one-third o f the issues in
th e ir final sample provided bonus share options. A nother measure to increase the take-up o f new shares
by existing shareholders is the inclusion o f a shortfall facility. In its simplest form , a shortfall fa cility
allows existing shareholders to apply fo r extra shares in addition to th e ir pro-rata entitlem ent. In this
case, any shares n o t subscribed fo r by some shareholders (s h o rtfa ll shares*) w ill be issued to those who
applied fo r additional shares. A shortfall fa cility can also allow the company to issue sh o rtfall sh ares to
other investors, including underw riters, and the company may have the rig h t to accept oversubscriptions.
For example, in February 2007 Argo Investments made a rights issue th a t was n o t u nd erw ritte n and was
expected to raise $441 m illion , b ut shareholders taking up th e ir entitlem ents were invite d to apply for
additional shares and the company reserved the rig h t to accept oversubscriptions. The end result was that
the issue raised approximately $446 m illion.
As shown in Table 9.4, there is no upper lim it on the size o f a renounceable rights issue so an issue o f
this type can be used to raise a large amount, provided investors are prepared to subscribe fo r the new
shares. Further, provided shareholders take up th e ir entitlem ent, a rights issue w ill have no effect on the
control o f the company as there is no change in shareholders1relative vo ting strengths. For these reasons
a rights issue may appeal to a company s board as a means o f raising finance.
W hile many companies m aking rights issues specify th a t the issue is renounceable, sometimes a
rights issue w ill be non-renounceable. I f a company makes a non-renounceable issue, shareholders
cannot sell th e ir entitlem ent to take up new shares. The only choices available to them are to exercise
th eir entitlem ent, either fu lly or partly, or to p e rm it it to lapse.26 I f investors take the la tte r choices the
issue w ill be undersubscribed. For this reason non-renounceable issues are frequently underw ritten.
As noted earlier, the m arket often interprets the announcement o f equity capital issues, including
rights issues, as ‘bad’ news. Balachandran, Faff and Theobald (2008) found an average abnormal return
o f -1 .7 4 per cent over a 3-day announcement period fo r a sample o f 636 rights issues by Australian
companies from 1995 to 2005. I f the term s o f an issue such as whether the issue is renounceable or
und erw ritte n also convey info rm a tio n to investors, then the price response to issue announcements may
differ between rights issues w ith different terms. Balachandran, Faff and Theobald found th a t there is no
difference between the average m arket reaction to renounceable and non-renounceable issues b ut the
reaction to rights issue announcements is related to the u nd erw riting status o f the issue. Alm ost 60 per
cent o f the issues in th e ir sample were fu lly und erw ritte n and the average abnormal retu rn associated
w ith announcement o f these issues was -1.0 4 per cent, b ut fo r non-underw ritten issues the average
abnormal retu rn was -2.23 per cent.
As discussed in Section 9.5.6, underw riters are seen as certifying the value or quality* o f the securities
being offered. When deciding whether to have an issue underw ritten, issuers w ill consider the benefits
th a t u nd e rw ritin g provides relative to the cost o f the u nd erw rite rs fee. The fee w ill be related to the
risk o f undersubscription and w ill reflect any costs th a t the underw riter incurs in assessing th a t risk.
This is likely to include the costs o f investigating the current financial position and the prospects o f
the issuer. Thus, a decision to fu lly underw rite an issue w ill typically be associated w ith low risk and/or
low investigation costs and is associated w ith a smaller negative m arket reaction. Where the risk and/
or investigation costs are higher, issuers may choose to accept the risk o f undersubscription rather than
pay an underw riting fee. N ot surprisingly, w ith o u t an u n d erw rite rs certification, the m arket reaction is
more negative.
That is n ot to suggest th a t certification by a reputable underw riter guarantees the success o f a capital
raising. To illustrate this point, consider the announcement o f a proposed $225 m illio n 6:7 entitlem ent
offer by Billabong International Ltd in June 2012. The issue was jo in tly u nd erw ritte n by Goldman Sachs
and Deutsche Bank, and was priced at a significant 44 per cent discount to the pre-announcement share
26
I g n o r in g tr a n s a c t io n c o s t s , th e c h o ic e s a v a ila b le to s h a r e h o ld e r s a r e n o t r e d u c e d b y a r ig h t s is s u e b e in g n o n - r e n o u n c e a b le
r a t h e r t h a n re n o u n c e a b le . I f a n is s u e is n o n - r e n o u n c e a b le , s h a r e h o ld e r s c a n t a k e u p th e r ig h t s a n d th e n r e a lis e t h e ir v a lu e b y
s e llin g t h e s h a r e s o b ta in e d .
C hapter n in e S ources
price. The m arket responded very negatively to the announcement, w ith Billabong shares closing down
48 per cent when the m arket reopened. A lthough the share price subsequently recovered slightly, to be
above the proposed subscription price, approximately 49 per cent o f retail investors s till chose n ot to
participate in the issue, leaving the underw riters to purchase the rem aining 33.2 m illio n shares. In an
amazing example o f managerial o ptim ism the CEO o f Billabong, Launa Inman, issued a statement on the
company s behalf stating that <rThe company is pleased by the support shown by our retail shareholders fo r
the Entitlem ent Offer. The Retail E ntitlem ent O ffer completes an im p o rta n t capital raising fo r Billabong,
allowing the Company to focus on the next phase o f its strategy’.27 As at February 2014, Billabong shares
were trading at about a 30 per cent discount to the subscription price o f the retail offer.
Traditional and accelerated rights issues
One disadvantage o f a trad ition al renounceable rights issue is th a t it is a relatively slow way o f raising
funds. W hile the ASX has revised its timetables to shorten the offer period, a trad ition al renounceable
rights issue cannot be completed in fewer than 23 business days. A non-renounceable issue is potentially
quicker since no rights trading period is required, b u t i t is s till slower than a share placement.
The traditional rights issue structure has been adapted to allow companies to raise funds more
quickly. The ASX commonly grants waivers o f its listin g rules to allow companies to make non-traditional
or Accelerated* rights issues. These issues involve tw o stages: an in itia l accelerated offer o f shares to
institutio ns and a second offer to retail shareholders.28 The structures used fo r these issues include:
•
•
•
Accelerated Non-Renounceable E ntitlem ent O ffer (or 'JumboO structure. A non-renounceable pro­
rata offer is made to in s titu tio n a l shareholders over a period o f 1 or 2 business days. The issue price
may be determined by an in s titu tio n a l book-build or i t may be fixed p rio r to the announcement of
the issue. In the second stage, a non-renounceable pro-rata offer is made to retail shareholders at the
same price as the first-stage pro-rata offer.
Accelerated Renounceable E ntitlem ent O ffer (AREO), which differs fro m the Uumbo* structure in
two ways: the offer is renounceable and the procedure involves two book-builds. In the firs t stage,
eligible in stitu tio n a l shareholders may subscribe fo r th e ir pro-rata e ntitlem ent to new shares at a
fixed offer price. Any shares n o t taken up by in s titu tio n a l shareholders are then offered to other
in stitu tio n a l investors through a book-build— so there is no trading o f rights on the exchange and
any entitlem ents th a t are renounced are sold off-m arket1. The second stage is a pro-rata entitlem ent
offer to retail shareholders at the same fixed offer price as the in s titu tio n a l entitlem ent offer. Retail
shareholders w ill be provided w ith details o f the offer in a prospectus or offer booklet and w ill
usually have about 2 weeks to decide whether to take up th e ir entitlem ents. Finally, a second bookbuild is undertaken where any shares not taken up by retail shareholders are offered to in s titu tio n a l
investors. I f the prices established in either o f the book-builds exceed the fixed offer price, the excess
is paid to the shareholders who did n ot take up th e ir entitlem ents.
Simultaneous Accelerated Renounceable E ntitlem ent O ffer (SAREO), which is essentially the same
as the AREO structure except th a t any renounced entitlem ents are sold through a single bookbuild. This book-build is open only to in s titu tio n a l investors and is carried out after b oth o f the
entitlem ent offers have been completed, so it ensures th a t each group o f investors receives the same
price for any entitlem ents they renounce.
While accelerated rights issues can differ in significant details, all such issues have one im p orta nt
feature: the proceeds o f the in s titu tio n a l component w ill be received very soon after the issue is launched.
For a company w ith large in s titu tio n a l shareholdings, the proceeds o f the in s titu tio n a l offer w ill make up
the m ajority o f the issue proceeds, so the outcome is, to a large extent, sim ilar to m aking a placement.
Because the tim e period involved is short, the risk o f a significant sh ortfa ll is lower than fo r a trad ition al
rights issue, so the cost o f u n d e rw ritin g should also be lower. Im portantly, the accelerated structures
allow funds to be raised quickly w hile retail shareholders can s till participate in the capital raising.
Also, renounceable rights issues are regarded as the m ost equitable because shareholders who choose
not to participate can realise some value by selling th e ir rights. However, the accelerated structures do
27
A S X A n n o u n c e m e n t, 'B illa b o n g c o m p le t e s $ 2 2 5 m illio n c a p it a l r a isin g *, 2 0 J u l y 2 0 1 2 .
28
A m e n d m e n ts to th e C o rp o ratio n s A c t in 2 0 0 7 in t r o d u c e d a n e w d e fin itio n o f l i g h t s 1 is s u e , w h ich r e q u ir e s t h a t th e t e r m s o f
su c h a n is s u e m u s t b e th e s a m e f o r a ll s h a r e h o ld e r s . S in c e a c c e le r a te d is s u e s in v o lv e d iffe r e n t t e r m s fo r in s t it u t io n a l a n d
r e ta il s h a r e h o ld e r s th e y d o n o t c o n fo r m t o t h is d e f in it io n a n d a r e m o r e c o r r e c tly d e s c r ib e d a s e n t it le m e n t o ff e r s . F o r e a s e o f
e x p o s it io n w e u s e th e t e r m r ig h t s is s u e to e n c o m p a s s b o t h t r a d it io n a l r ig h t s is s u e s a n d a c c e le r a te d is s u e s .
of f in a n c e : equity
not necessarily ensure th a t all shareholders are treated fairly. First, the tim e allowed fo r completion of
the in s titu tio n a l component can disadvantage shareholders who do n o t have sufficient funds available
to take up th e ir fu ll entitlem ents at short notice. Second, the AREO structure w ith tw o separate bookbuilds means th a t any prem ium d istributed to shareholders who renounce th e ir entitlem ents can
differ depending on whether the shareholder is an in s titu tio n a l or retail investor. The SAREO structure
addresses the la tte r concern b u t may n o t provide a perfect solution because it means th a t in stitu tio n a l
shareholders who sell1th e ir rights have to w ait fo r some weeks to find out w hat price they w ill receive.
F in a n c e
in
ACTION
UNDERWRITER BUYS SHARES TO PROVIDE IMMEDIATE
FUNDING_____________________________________________________
New sC ^^
In s o m e c a s e s it is im p o r t a n t f o r th e is s u e r t o re c e iv e a ll o f th e fu n d s b y a c e r t a in d a t e a n d th is
c a n b e a c h ie v e d b y e x te n d in g th e r o le o f th e u n d e r w r it e r to in c lu d e th e p r o v is io n o f s h o rt-te rm
f u n d in g . F o r e x a m p le , o n 9 M a r c h 2 0 0 7 , S u n c o r p - M e t w a y Ltd a n n o u n c e d a 2 - f o r - 1 5 e n title m e n t
=
1
o f f e r to ra is e a p p r o x im a t e ly $ 1 . 1 7 b illio n f r o m s h a r e h o ld e r s . T h e p u r p o s e o f th e is s u e w a s to
p a r t ia lly fu n d th e c a s h c o m p o n e n t o f th e c o n s id e r a t io n p a y a b le b y S u n c o r p - M e t w a y in c o n n e c tio n
w ith its th e n p r o p o s e d m e r g e r w ith P r o m in a Ltd. T h e S u n c o r p - M e t w a y issu e w a s d iv id e d in to
in s titu tio n a l a n d r e ta il o ffe r s , e a c h f o llo w e d b y a n in s titu tio n a l b o o k - b u ild . T h e m e r g e r in v o lv e d a
S c h e m e o f A r r a n g e m e n t t h a t w a s s u b je c t to c o u r t a p p r o v a l a t a h e a r in g s c h e d u le d to ta k e p la c e
o n 1 2 M a r c h 2 0 0 7 . O n c e th e c o u r t a p p r o v e d th e s c h e m e , S u n c o r p - M e t w a y h a d a n o b lig a t io n to
m a k e p a y m e n ts to P r o m in a s h a r e h o ld e r s , so it n e e d e d a c c e s s to th e issu e p r o c e e d s s h o r tly a ft e r
th e c o u r t h e a r in g . T h is w a s a c h ie v e d b y n e g o tia t in g a n u n d e r w r it in g a g r e e m e n t w h e r e b y th e
u n d e r w r it e r , C it ig r o u p G lo b a l M a r k e ts A u s t r a lia , s u b s c r ib e d f o r a ll o f th e n e w s h a re s t h a t w e r e
o f f e r e d f o r s a le . T h e n e w s h a re s w e r e th e n t r a n s fe r r e d b y C it ig r o u p to s h a r e h o ld e r s w h o c h o s e
t o t a k e u p t h e ir e n title m e n ts a n d to in v e s to rs w h o a c q u ir e d s h a re s t h r o u g h th e t w o b o o k - b u ild s .
T h e c a p it a l r a is in g w a s c o m p le te d w ith th e s e c o n d b o o k - b u ild o n 1 3 A p r i l 2 0 0 7 b u t S u n c o r p M e t w a y h a d re c e iv e d th e fu ll p r o c e e d s f r o m C it ig r o u p o n 1 2 M a r c h . O f c o u r s e , th e u n d e r w r it in g
a g r e e m e n t r e q u ir e d S u n c o r p - M e t w a y to p a y a d a ily f u n d in g fe e r e p r e s e n tin g in te re s t o n th e fu n d s
t h a t it e ffe c tiv e ly b o r r o w e d fr o m th e u n d e r w r ite r .
9 .6 .2 1 Placements (private issues)
PLACEMENT
an issue of securities
direct to chosen
investors rather than
the ge neral public
A placem ent o f ordinary shares is a new issue o f shares made to a lim ite d number o f investors. These
issues are typically made to larger in s titu tio n s such as life insurance companies and investm ent funds.
Such organisations are m ajor holders o f Australian shares and have become the prim e targets for
placements because they have large sums to invest. Hence, a significant am ount o f capital can be raised
quickly by making a placement to a small num ber o f in s titu tio n s o r to a single in s titu tio n . Details o f some
recent placements are shown in Table 9.6.
TABLE 9.6 Details of selected placements 2013-14
Am ount
C om pany
D a te a n n o u n c e d i ra is e d ($ m )
Issue p r ic e as % o f
P ric in g a n d
p re -a n n o u n c e m e n t m a rk e t p ric e
issue m e th o d
The Reject Shop
A pril 2013
30
96.9
Underwritten
ERM Power
November 2013
75
93.4
Underwritten
Insurance
Australia Group
December 2013
1200
96.2
Underwritten
Alumina
February 2014
452
103.0
S o u rce :
C o m p ile d from c o m p a n y announcem ents.
Issue to a single
investor
C hapter n in e S ources
In some cases the shares are purchased by another company rather than by financial institutio ns,
often as part o f the form ation o f a strategic alliance between tw o companies whose businesses are related.
For example, in December 2006, Queensland Gas Company (QGC) entered in to an agreement w ith AGL
Energy under which AGL Energy purchased a 27.5 per cent ownership interest in QGC fo r $327 m illion.
The two companies also entered in to a 20-year gas supply agreement and AGL Energy was entitled to
appoint three directors on the QGC board.
A company m aking a placement w ill usually n o t be required to issue a disclosure document.
Placements usually involve offers o f securities to sophisticated and in s titu tio n a l investors. As discussed
in Section 9.4.3, these offers o f securities do n o t require a disclosure document.
Many placements are underw ritten, p articularly where the issue is large and /or the new shares
are distributed to many investors. Where an issue is n o t underw ritten, the company m aking the issue
generally uses the services o f a broker or investm ent bank to assist in placing the shares w ith investors.
The broker is n ot obliged to dispose o f all the shares: the brokers task is best described as undertaking the
placement o f the shares on a ‘best-efforts’ basis. U nd erw ritin g fees fo r share placements are influenced
by several factors, including the absolute size o f the placement, the size, liq u id ity and perceived m arket
risk o f the issuing company and the reason fo r raising the equity. For example, a placement to fund a
profitable acquisition w ill involve lower m arket risk, and lower fees, than one th a t is needed to recapitalise
a company whose financial leverage has become excessive. The fees fo r arranging and/or u nd erw riting a
placement are usually n o t disclosed. Macquarie Capital Advisers Lim ited has indicated th a t fo r placements
by ASX-listed companies, u nd e rw ritin g fees can range from around 1 per cent to 5 per cent o f the gross
offer proceeds.
It has become common fo r larger placements to in s titu tio n s to be priced using the book-building
process and in some cases the managers o f the book-build may also underw rite the issue. For example,
in November 2006, O rigin Energy raised $400 m illio n by a placement th a t was priced using a book-build
and also underw ritten by the two investm ent banks th a t conducted the book-build. U nderw ritin g may
be preferred when a company has entered in to a com m itm ent th a t creates a specific need fo r additional
funds. In the case o f the O rigin Energy placement, the proceeds were used to p a rtly fund the acquisition
o f a gas retailing business th a t O rigin had agreed to purchase from the Queensland Government.
There has been considerable opposition from shareholders to companies m aking placements o f
shares. Some shareholders may oppose placements because they reduce the percentage o f ownership and
voting power o f existing shareholders. Also, some shareholders may believe th a t they are being deprived
o f a possible p ro fit from the sale o f the rights. However, we have already shown th a t the retu rn that
shareholders receive from the sale o f rights represents, in effect, a retu rn o f a p o rtio n o f th e ir investm ent
in the company. More im p orta ntly, i f the placement is made to new shareholders at a price below the
current m arket price, there is a reduction in the value o f the existing shareholders’ investment.
The ASX has placed a general lim it o f 15 per cent on the am ount o f capital th a t a company can issue
privately in any 1 year w ith o u t the p rio r approval o f its shareholders.29 However, it is n o t d ifficu lt to
exceed this lim it w ith o u t viola ting the ASX rules. A fte r m aking a placement th a t falls w ith in the 15 per
cent lim it, a company w ill often have the placement ratified by shareholders. Ratification o f a placement
‘refreshes’ the company’s capacity to raise capital because it means th a t the placement w ill n o t be included
when assessing the company s a b ility to make a future placement. In other words, a company may make
two or more placements in a 12-m onth period, provided each placement increases its issued capital by
less than 15 per cent and each placement is ratified by shareholders before the next placement occurs.
Also, the ASX has allowed larger placements in cases where i t is confident th a t a company s issued capital
is about to be increased by another share issue. In such cases, the ASX is w illin g to apply the 15 per cent
lim it to the expanded capital base rather than to the existing issued capital. For example, a company that
is comm itted to m aking a fu lly und erw ritte n 1 -fo r-l e ntitlem ent offer could obtain a waiver o f the '15 per
cent rule, th a t allows i t to make a placement o f 30 per cent o f its issued capital p rio r to the entitlem ent
offer (ISS Governance Services, 2010, p. 13).
29
S e e R u le s 7 .1 a n d 7 .2 o f th e A u s t r a lia n S e c u r it ie s E x c h a n g e L is t in g R u le s, w h ich p r o v id e t h a t , in g e n e r a l, o n ly 1 5 p e r c e n t o f
a c o m p a n y s is s u e d s h a r e c a p it a l m a y b e is s u e d t o n o n - s h a r e h o ld e r s w ith o u t th e p r io r a p p r o v a l o f s h a r e h o ld e r s a t a g e n e r a l
m e e tin g . T h ere a re e x c e p tio n s to t h is r u le t h a t r e la te sp e c ific a lly t o s m a ll a n d m id - siz e c o m p a n ie s w ith m a r k e t c a p it a lis a t io n s
le s s t h a n $ 3 0 0 m illio n .
of fin a n c e : equity
B usiness finance
CONTRIBUTING SHARES
shares on w hich only
part of the issue price
has been paid. A lso
known as p a 厂
f/y pa/c/
shares
INSTALMENT RECEIPT
marketable security
for w hich on ly part
of the issue price
has been paid. The
balance is p a y a b le in
a final instalment on
As discussed in Section 9.2, con tributing sh ares, also known as p a rtly paid shares, are shares on which
only p a rt o f the issue price has been paid. The issuing company can call up the unpaid part o f the issue
price in one or more instalments (known as calls*) and, in the case o f a lim ite d lia b ility company, the
holder has a legal obligation to pay these calls. C ontributing shares are quite common in Australia and can
be used to provide a company w ith a reliable source o f funds. The unpaid am ount is referred to as Reserve
capital1and the shares can be created by a rights issue where the issue price is to be contributed in stages
at specified times. Many co ntribu ting shares are issued by m ining and oil exploration companies, which
make calls when additional funds are required. C ontributing shares can be im p o rta n t in raising capital
b ut the amounts involved are typically small in comparison to other sources o f equity.30
Typically, in stalm en t receipts are issued when existing fu lly paid shares are offered to the public,
w ith the sale price to be paid in two instalments. A ll three sales by the Australian Government o f shares
in Telstra Ltd involved instalm ent receipts. For example, in the case o f the th ird Telstra share offer in
November 2006, retail investors paid a firs t instalm ent o f $2 w ith a second instalm ent o f $1.60 payable
by 29 May 2008. Partly paid shares and instalm ent receipts are very sim ilar b ut there are some im p orta nt
differences between them. These differences include:
or before a specified
date
•
•
•
fo r instalm ent receipts, the amount and tim in g o f all instalm ents are specified at the tim e o f the
original sale rather than being at the discretion o f directors
instalm ents are payable to the vendor o f the shares rather than to the issuing company
holders o f instalm ent receipts are usually e ntitled to the same dividends as holders o f fu lly paid
shares, whereas holders o f p artly paid shares usually receive a p artial dividend based on the
p roportion o f the issue price th a t has been paid.
Companies listed on the ASX are p erm itted to raise lim ite d amounts o f funds from existing shareholders
through share purchase plans (SPPs). These issues do n o t require a prospectus provided they comply
w ith ASIC Regulatory Guide 125, which requires th a t SPPs are accompanied by a cleansing notice. ASIC
recognises th a t the costs o f preparing and d istrib u tin g a prospectus could be very high relative to the
benefits when the risk to investors is lim ite d because the am ount th a t can be invested is restricted.
Accordingly, the am ount th a t a listed company can raise in this way is restricted to $15 000 per annum from
each shareholder. Share purchase plans may be attractive to shareholders because the subscription price
m ust be less than the m arket price p rio r to the announcement o f the issue and there is no brokerage. As
discussed in Section 9.6.6’ share purchase plans are sometimes used in conjunction w ith an in s titu tio n a l
placement, giving all existing shareholders the o p p o rtu n ity to purchase additional shares at the price paid
by the in stitu tio n s th a t took up the placement.
An o ption to purchase the shares o f a company gives the holder o f that option the rig h t to take up shares
in the company by a specified date on predeterm ined term s.31 For example, a company may issue, at
no cost, 10000 options th a t may be exercised by the payment o f $1 per option during the next 5 years.
Consequently, option holders can purchase a m axim um o f 10 000 shares fo r $1 each at any tim e during the
next 5 years, regardless o f th e ir m arket price at the tim e. The option holder therefore has the o pp ortu nity
to benefit from an increase in the m arket price o f the company s shares. I f the company s share price
30
C o n t r ib u t in g s h a r e s c a n a ls o b e is s u e d t o d ir e c t o r s a n d o t h e r s a s p a r t o f a c o m p e n s a t io n p a c k a g e . T h is u s e o f c o n tr ib u t in g
31
A n im p o r t a n t d iffe re n c e b e tw e e n th e o p t io n s d is c u s s e d h e r e a n d th e e x c h a n g e - t r a d e d o p t io n s d is c u s s e d in C h a p t e r 1 8 is th a t
s h a r e s is a n a ly s e d b y B ro w n a n d H a th a w a y ( 1 9 9 1 ).
t h is s e c t io n d is c u s s e s o p t io n s is s u e d b y th e c o m p a n ie s t h e m s e lv e s . In c o n t r a s t , a n e x c h a n g e - t r a d e d o p t io n is c r e a te d b y a
c o n tr a c t b e tw e e n tw o in v e s t o r s a n d d o e s n o t in v o lv e th e c o m p a n y w h o se s h a r e s u n d e r lie t h e o p t io n . T h a t is , u p o n e x e r c ise o f
a c o m p a n y - is s u e d o p t io n , th e c o m p a n y c r e a t e s a n d i s s u e s n e w s h a r e s , w h e r e a s w h e n a n e x c h a n g e - t r a d e d o p t io n is e x e r c ise d ,
o n ly e x is t in g s h a r e s c h a n g e o w n e r s h ip a n d n o n e w s h a r e s a r e c r e a te d .
C hapter n in e S ources
increases to $1.20, then option holders can purchase 10000 shares fo r $10000, which is $2000 below
their current m arket value.
There are three m ajor provisions included in an option agreement:
•
•
•
the exercise price o f the option
the period during which the options may be exercised
the rights o f option holders in the event o f new issues o f shares by the company.
In general, it is usual fo r the exercise price o f an option to be set near the share price at the tim e the
option is issued. The term o f an option may extend fo r several years and, other things being equal, a
long-term option is more valuable than a short-term option. In the case o f company-issued options, the
option holder is often prevented from exercising the option fo r a certain period after it has been granted.
I f a company makes an issue o f shares during the o ptio ns life, it is possible fo r the value o f the option
to be reduced to almost zero. For example, i f a company splits each o f its shares in to two, other things
being equal, the price per share w ill be halved. In tu rn , this w ill result in a corresponding reduction in the
benefit that the option holder w ill receive from any subsequent increase in the share price. As a result,
option agreements usually provide holders w ith the rig h t to participate in share issues by the company
during the life o f the option.
Options may be issued as follows:
To employees. The objective when m aking o ption issues is to reward employees in a way th a t is likely
to encourage them to w ork towards im proving the company s profitability. Such issues are typically
made w ith an exercise price equal to the current share price, which does n ot expose the employee
to any immediate tax obligation. I f the company becomes more profitable, it is likely to command a
higher share price, which, in tu rn , w ill increase the value o f the option,
b As a sweetener to an equity issue. Many exploration and m in ing companies issue both ordinary
shares and options to subscribe fo r additional shares. For example, an investor purchasing 1000
shares in a new issue may also receive 1000 options, each o f which entitles the investor to buy one
additional share at a fixed price before a specified date. Frequently these options are listed separately
on the stock exchange. Therefore, an investor obtains the o p p o rtu n ity to make an additional gain
from an increase in the company s share price. A company th a t issues shares accompanied by
options hopes to encourage investors to participate in the issue, thereby reducing the possibility o f
undersubscription.
c As a sweetener to a private debt issue. On occasions, a company seeking debt finance w ill offer share
options to the lender. The company benefits either by obtaining debt finance th a t i t would not
otherwise have received o r by obtaining the funds on better term s— fo r example, at a lower interest
rate. However, neither p arty to an agreement o f this type w ill make the options conditional on the
granting o f the loan because this may jeopardise the tax d eductibility o f interest on the debt.
a
In the cases outlined above, i t is evident th a t options are n ot issued p rim a rily as a means o f raising
finance, although they are often issued as p art o f a finance package. Nevertheless, significant sums can be
raised when company-issued options are exercised.
9.6.6 | Choosing between equity-raising methods
The previous sections have outlined several external methods to raise equity funds, including rights
issues, placements, share purchase plans, calls on p a rtly paid shares and the exercise o f company-issued
options. M ost o f these methods involve long-term arrangements and i f a significant ‘one-off’ equity
raising is needed, it w ill involve a rights issue a nd/or a placement o f shares.
W hat factors influence the choice between these methods? Chan and Brown (2004) studied this
question using Australian data from July 1996 to March 2001, a period in which the ASX increased
the annual ceiling fo r placements w ith o u t shareholder agreement* from 10 per cent to 15 per cent o f
ordinary share capital. They found th a t the ceiling imposed by the lis tin g rules has a strong effect on
company behaviour, w ith a significant tendency fo r the issue size to be chosen so th a t i t falls just under
the prescribed ceiling. As expected, placements w ith o u t shareholder agreement* became more common
after the ceiling was increased to 15 per cent and it was rare fo r companies to make rights issues where
of f in a n c e : equity
B usiness finance
the am ount o f funds raised was less than the ceiling fo r placements. Where the am ount o f funds sought
exceeded the prescribed ceiling, it was more common fo r companies to make a placement w ith shareholder
agreement than to make a rights issue. In summary, th e ir m ain conclusion was th a t companies generally
prefer placements to rights issues.
A part from the influence o f any ceiling imposed by stock exchange lis tin g rules, the m ain advantages
o f placements are speed (funds can be raised in a few days rather than weeks), certainty (a placement
may be u nd erw ritte n and, given th a t the risk o f a shortfall exists fo r only a short period, i t should n ot be
d ifficu lt to obtain the support o f an underw riter), lower transaction costs and the shares may be placed
w ith investors considered to be frien dly* to the existing management. Rights issues have the advantage
that shareholders can preserve th e ir ownership proportions and voting power. Thus, rights issues are seen
as being more equitable to existing shareholders. A rights issue may require a prospectus and is slower
than a placement, but, as noted in Section 9.6.1, fo r companies w ith m ostly in s titu tio n a l shareholders,
the m a jo rity o f the funds raised by a rights issue can be received quickly i f one o f the accelerated offer
structures is used.
C om bination issues
As noted above, where the am ount o f funds sought is below the ceiling fo r a placement w ith o u t
shareholder agreement,, companies almost invariably opt fo r a placement rather than a rights issue. Where
the am ount o f funds sought is above the ceiling, a rights issue may be chosen b ut the choice involved is
n ot sim ply lig h ts issue versus placement w ith shareholder agreement'. Rather, the company may make a
placement in combination w ith another m ethod o f equity raising, such as a share purchase plan or a nonrenounceable rights issue. Where these com bination issues are used, the placement component is almost
invariably just under the 15 per cent ceiling so th a t shareholder agreement is n ot required.
Another feature o f combination issues is th a t the placement is often priced using an in s titu tio n a l
book-build. The issue price established by the book-build is then used to determine the price o f the shares
fo r the second component o f the issue. Since retail shareholders have the o pp o rtu n ity to participate in
the capital raising at the same price as institutio ns, this approach addresses the concern th a t a placement
alone discriminates against those shareholders who are n o t invited to participate. Com bination issues
involving a placement and an SPP in close p ro xim ity have become common.
W hile the placement/SPP combination may be appealing as a way o f accommodating small
shareholders, it has been criticised as being far less equitable to small shareholders than a rights issue. The
critics make two main points. First, the lim it o f $15 000 per shareholder fo r share purchase plans means
th a t the b ulk o f new shares is issued to institutio ns. Second, i f the SPP price is set at a large discount to
the m arket price, demand w ill be high and retail investors can end up w ith much less than th e ir $15 000
entitlement*. This problem arose w ith the issues by O rigin Energy, which started w ith a $400 m illion
placement to in stitu tio n s in November 2006. The issue price was $7.10 per share, which represented a
discount o f about 2.5 per cent to the m arket price at the tim e. A t the same tim e, O rigin announced th a t
it would raise additional funds on sim ilar term s through an SPP early in 2007. The details announced in
January 2007 included a target o f $75 m illio n fo r the SPP. By the closing date fo r applications, the m arket
price o f O rigin shares had increased to about $9. N ot surprisingly, many shareholders applied to purchase
shares, w ith the result th a t allocations were scaled back to a m axim um o f 200 shares per shareholder.
A nother type o f com bination involves three offers o f shares: a placement, an in s titu tio n a l entitlem ent
offer and a retail entitlem ent offer. For example, Alesco Corporation used this approach to raise a total
o f $193 m illio n in July and August 2007. The closing price o f Alesco shares on 23 July was $13.96, after
which the company announced the acquisition o f another business and details o f an associated capital
raising, including an in s titu tio n a l placement w ith the issue price to be determ ined by a book-build w ith
an indicative price range o f $12.10 to $12.80 per share. The capital raising also included an in stitu tio n a l
e ntitle m e nt offer and a non-renounceable und erw ritte n l-fo r-9 rights issue (retail entitlem ent offer).
It was announced th a t the issue price fo r both o f these offers would be set equal to the price set fo r the
in s titu tio n a l placement. On 26 July, the company announced th a t the issue price had been set at the
top o f the book-build price range at $12.80 per share and th a t the in s titu tio n a l offers were *strongly
oversubscribed’. On 23 August, Alesco announced th a t its retail e ntitlem ent offer had raised approximately
$61 m illio n in addition to the am ount o f approximately $132 m illio n raised from in s titu tio n s in late July.
The company stated th a t the retail offer had been ^strongly supported by existing shareholders w ith over
C hapter n in e S ources
of fin a n c e : equity
60 per cent o f the rights being taken up by eligible shareholders1. The approach used by Alesco has been
used by several other companies, including Asciano Group, which raised $2.35 b illio n in June 2009, and
Graincorp, which raised about $600 m illio n in October 2009.
W hile it is n ot very common, i t is also possible to combine an issue to existing shareholders w ith a
public offer o f shares. This approach may be favoured i f the company wishes to attract a wider spread o f
shareholders, or i f the am ount o f funds sought is large relative to the size o f the company. For example,
in October 2007, Essential Petroleum Resources Ltd (EPR) (see Finance in Action), a small explorer w ith a
market capitalisation o f less than $20 m illion , made a l-fo r-2 non-renounceable rights issue and a public
offer to raise a total o f $10 m illio n .32
ESSENTIAL PETROLEUM MAKES RIGHTS ISSUE A N D PUBLIC
OFFER
E s s e n tia l P e tro le u m h a s n 't e x a c t ly s e t th e w o r ld o n f ir e s in c e its F e b r u a r y 2 0 0 1
Finance
in ACTION
lis tin g . F r id a y ’s
c lo s in g p r ic e o f 5 . 5 c e n ts a s h a r e te lls a s m u c h . B u t p a t ie n c e w it h th e O t w a y B a s in o il a n d g a s
e x p lo r e r , lik e t h a t s h o w n b y th e g r o u p ’ s b ig g e s t s h a r e h o ld e r , f o r m e r JB W e r e re s o u rc e s g u r u
P e te r W o o d f o r d , m ig h t ju s t d e liv e r s o m e b ig r e w a r d s in 2 0 0 8 . M a n a g in g d ir e c t o r J o h n R e m fry
h a s w o r k e d th e g r o u p in to a p o s it io n w h e r e it w i ll b e a s to c k t o w a t c h n e x t y e a r a s it sets
a b o u t d r illin g n e a r-te rm d e v e lo p m e n t o p p o r t u n it ie s in th e o n s h o r e O t w a y w h ile a ls o c h a s in g
u p th e b ig - t im e p o t e n t ia l o f its o f f s h o r e p e r m its , f la n k in g w h a t E s s e n tia l r e c k o n s c o u ld b e th e
n e x t m a jo r h y d r o c a r b o n p r o v in c e — th e D is c o v e r y B a y ' H i g h 7 o f f s h o r e fr o m P o r tla n d in w e s te r n
V ic t o r ia .
A n o t h e r g e o lo g ic a l f e a tu r e , th e P e c te n 'H i g h 7 o f f s h o r e fr o m P o rt C a m p b e ll h a s a l r e a d y b e e n
p r o v e n a s a h y d r o c a r b o n f a ir w a y . E s s e n tia l re c k o n s t h a t b a c k a t th e b i g g e r D is c o v e r y B a y
H ig h , th e p o t e n t ia l in its p e r m its is f o r m o r e th a n 5 t r illio n c u b ic f e e t o f r e c o v e r a b le g a s a n d
m o re th a n 2 b illio n b a r r e ls o f r e c o v e r a b le o il. T h a t ’s b ig t a lk f r o m a c o m p a n y o f E s s e n tia T s
s iz e , b u t w e l l s o o n k n o w i f it 7s h o t a i r o r n o t.
T h a t's b e c a u s e E s s e n tia l is p u llin g in $ 1 0 m illio n fr o m a $ 6 m illio n r ig h ts is s u e ( u n d e r w r it t e n
b y B e ll P o tte r a n d C o m s e c ) a n d $ 4 m illio n fr o m a p u b lic o f f e r a t 4 c e n ts a s h a r e . A t th e is s u e
p r ic e , th e g r o u p 's m a r k e t c a p it a lis a t io n w i ll b e a ll o f $ 2 2 m illio n .
S o u rc e :
2 9
'After a few quiet years, Essential m a y prove it h a s all the ingredie nts,/ B a rry Fitzgerald,
The A g e ,
O c to b e r 2 0 0 7 .
Table 9.1 shows th a t listed companies have raised significant funds through employee share plans,
although the prim ary purpose o f such plans is to m otivate senior managers and other employees by
giving them an ownership interest in th e ir employer. There are several types o f employee share plans that
have been used in Australia, including:3
33
2
•
•
32
Fully paid share plans. Employees are able to purchase new or existing shares, usually at a discount
from m arket value. The purchases are usually funded by loans from the company th a t are interestfree or at a low interest rate and dividends on the shares may be used to repay the loans. Sometimes
there is a provision to w rite o ff the loans i f the company fails.
Partly paid share plans. The shares issued to employees are in itia lly p a rtly paid and converted to
fu lly paid shares by a series o f calls. In this case employees can be liable fo r calls i f the company fails
before the shares are fu lly paid.
In th e y e a r t o 3 0 J u n e 2 0 0 8 , E P R r e c o r d e d a n e t lo s s o f $ 1 0 .9 m illio n a n d in th e fo llo w in g y e a r a fu r t h e r lo s s o f a lm o s t $ 2 4 .8
m illio n . In F e b r u a r y 2 0 1 0 , it s s h a r e h o ld e r s a p p r o v e d a c a p it a l r e s t r u c t u r e w h e r e b y d e b t o b lig a t io n s o f $ 2 3 m illio n w ere
c o n v e r te d in t o e q u it y o r fo r g iv e n . F o llo w in g th e r e s t r u c t u r e , 5 1 .9 p e r c e n t o f th e c o m p a n y s v o t in g s h a r e s w e re h e ld b y B e a c h
E n e r g y L t d ， a n e w b o a r d w a s a p p o in t e d a n d t h e c o m p a n y ’s n a m e c h a n g e d t o S o m e r t o n E n e r g y L td .
33
C h a r a c te r istic s o f th e v a r io u s t y p e s o f e m p lo y e e s h a r e p la n s a re d is c u s s e d in d e t a il b y S tr a d w ic k ( 1 9 9 6 ) .
LEARNING
OBJECTIVE 9
O utline the different
types of em ployee
share plans
B usiness finance
•
•
•
Option plans. Under these plans employees in itia lly purchase (or are granted) an option to buy shares
at some future tim e at a specified price. O ption plans involve a small in itia l outlay w ith potential for
large capital gains i f the company is successful.
Employee share trusts. Employees have an interest in a tru s t th a t holds shares in the employer
company. The tru s t is norm ally funded by the employer. Employees who hold units in the tru s t can
dispose o f the u nits only to other members o f the trust.
Replicator plans. Replicator plans do n ot involve shares in the employer company. Instead, payments
are made to employees based on the achievement o f certain performance criteria. For example, such
a plan may involve phantom shares* w ith a price th a t is linked to the p ro fita b ility o f the company or
to the performance o f a division.
The popularity o f the various plans varies among different types o f employers. For example, in Australia
the m a jo rity o f employee share plans are option plans and this type o f plan is p articularly popular as a way
o f rewarding the senior executives o f large listed companies. Recent changes in the taxation treatm ent of
employee share plans may encourage more widespread use o f plans o f other types fo r general staff. The
use o f a tru s t structure can be attractive fo r private companies where there are restrictions on ownership
o f shares in the company itself. Replicator plans are popular w ith unlisted companies, where i t is d ifficult
to establish a m arket price fo r the shares, and can also be useful fo r relatively new businesses, where
issuing shares would dilute the ownership and control o f the founders.
Over the years the Commonwealth Government has sought to encourage employee share ownership
by providing tax concessions in cases where shares or rights to shares are given to employees or issued to
them at a discount. The tax status o f employee share plans has been subject to frequent change and some
degree o f uncertainty.
The provisions th a t apply to employee shares mean that, in general, any benefit to an employee under
an employee share plan is taxable in the year in which the share or rig h t is acquired. Consequently, the
difference between the m arket value o f a share and the consideration paid to acquire i t is assessable in the
year o f acquisition. However, where the employee share scheme meets the conditions fo r classification as
a ‘tax-deferred’ scheme, tax may be deferred to a later date. The m ain conditions fo r ‘tax-deferred’ status
would generally be satisfied i f the shares have been purchased via a salary-sacrifice scheme or alternatively
where the employee faces a *real risk o f forfeiture* o f the shares due to em ploym ent circumstances such as
failing to meet performance hurdles or serving a m inim um term o f em ploym ent.34
Under the ASX Listing Rules a company m ust have a proposed employee share plan approved by
shareholders and employees may even have to be provided w ith a prospectus i f the prim ary m otivation
fo r the plan is fundraising as opposed to providing employees w ith the o pp o rtu n ity to participate in
ownership o f the company. Given the complexity o f the taxation provisions and other regulatory
requirements, the financial manager o f a company th a t introduces an employee share plan is likely to
need specialised advice.
9.8
LEARNING
OBJECTIVE 10
O u tline the
a d va ntage s of internal
funds a s a source of
finance
Internal funds
So far we have discussed external sources o f equity finance. However, a company th a t is operating profitably
w ill also generate funds internally. The relative importance o f interna l and external sources o f funds
may be assessed using different measures o f in te rn a l funds*. One approach is to define internal equity
finance as retained profits plus depreciation charges, where retained p ro fit is equal to accounting p ro fit
after company tax, less dividends paid to shareholders. A problem w ith this approach is th a t a company
cannot spend its accounting p ro fit— suppliers and employees m ust be paid w ith cash. In other words, the
prim ary source o f interna l funding is cash p ro fit, which can differ significantly from accounting profit,
which is prepared on an accrual basis. Cash p ro fit is reported by companies in th e ir cash flow statements.
The cash flow statement is a funds statement th a t shows the sources and uses o f funds, where funds are
defined as cash. A 2009 Reserve Bank o f Australia (RBA) analysis o f corporate sources and uses o f funds
relied on data from these statements.35 The approach adopted by the RBA divides sources o f funds into
two basic categories: interna l funding and external funding. Internal funding is equal to cash p ro fit— that
34
F o r fu r t h e r in fo r m a t io n o n th e t a x t r e a t m e n t o f e m p lo y e e s h a r e s c h e m e s s e e w w w .a t o .g o v .a u / G e n e r a l/ E m p lo y e e - s h a r e sc h e m e s/.
35
S e e R B A ( 2 0 0 9 ).
C hapter n in e S ources
is, cash received from customers and non-interest-bearing investments (e.g. dividends) less payments to
suppliers, wages and salaries paid to employees and tax payments. Thus, cash p ro fit is measured before
payment o f interest expense and any other financing charges and is n o t affected by depreciation. External
funding comprises tw o sources: net debt and net equity, where net debt is equal to funds borrowed from
intermediated (e.g. bank loans) and non-interm ediated (e.g. issuing corporate bonds) sources. Finally, net
equity is equal to funds raised by issuing new shares, less cash paid o ut to repurchase shares. Funds may
be used in three ways: investm ent in assets, payment o f dividends and payment o f interest.
The use o f internal funds as a source o f finance has im p o rta n t advantages. Using interna l funds does
not affect the control o f the company as it does n o t involve the company in issuing any additional shares.
Therefore, using internal funds does n o t com m it the company to increased dividend payments in the
future, w ith the result that no additional strain is placed on the company s cash resources. A fu rth e r
advantage is that, unlike a new issue o f shares, internal funding involves no issue costs such as brokerage,
fees paid to underw riters and other advisers or costs incurred in preparing a prospectus.
Internal funds are a convenient source o f finance th a t does n ot involve any explicit costs such as
transaction costs, but they are n ot a free source o f finance fo r a company. Internal funds generated by
a company are invested by the company on its shareholders’ behalf. I t follows th a t internal funds have
an o pportunity cost— th a t is, the funds could have been invested elsewhere by shareholders. Therefore,
when a company uses internal funds, shareholders w ill n ot benefit unless the company is able to invest
the funds profitably. This analysis is discussed in more detail in Chapter 14.
The relative importance o f interna l funds in providing a company s to ta l financial requirements is
related to the nature o f a company s business and can also vary considerably over tim e. Between 2003
and 2012, around 86 per cent o f funding fo r resource companies has been sourced internally, whereas
only about 68 per cent o f funding fo r non-resource based companies comes from internal sources.
Furthermore, both o f these percentages rose dramatically during the global financial crisis beginning
in 2007 when external finance was increasingly hard to obtain. (Reserve Bank o f Australia, March
2013, p. 53).
A dividend reinvestment plan (DRP) allows shareholders the choice o f using th e ir dividends to purchase
additional shares instead o f receiving cash.36 The firs t DRPs were introduced by Australian companies
in the early 1980s. W ith in 10 years, m ost o f Australia’s largest companies were offering such plans and
reinvestment o f dividends has become a significant source o f equity fo r listed companies, particularly
larger companies. The main reason fo r the popularity o f DRPs is related to the intro du ction o f the
dividend im putation tax system, which caused investors to demand high dividend payouts. A dividend
reinvestment plan allows a company to meet the demand fo r a high dividend payout w ith o u t straining
its cash resources. Technically, investors who participate in a DRP receive the dividends and therefore
obtain the tax benefits o f im putation, and then reinvest the cash in additional shares. This means that,
for tax purposes, dividends can be considered as being paid* to investors w ith o u t any cash payment by
the company. Provided the shares issued under a DRP are fu lly paid, there is no need fo r a prospectus and
shares issued under a DRP are exempt from the *15 per cent in 12 m onths1capital raising lim it contained
in the Listing Rules. DRPs are inflexible in th a t the tim in g o f any capital raising is tied to the tim in g o f
dividend payments and may n o t provide a reliable source o f funds because participation by shareholders
is voluntary. The la tte r problem can be overcome, at a cost, by having a company s DRP underw ritten.
The main advantage o f DRPs centres on transaction costs: fo r many companies, the costs o f operating
a DRP are lower than the costs involved in m aking rights issues and share placements to replace cash
paid out as dividends. D uring the 2012-13 financial year, A ustralian-listed companies used DRPs to raise
$6.9 b illion (Australian Financial Markets Association, 2013, p. 55).
36
A S X s t a t is t ic s in c lu d e d iv id e n d r e i n v e s t m e n t a s p a r t o f e q u it y r a is e d e x te rn a lly . H o w e v e r, w e d is c u s s D R P s in th e c o n te x t
o f in t e r n a l fu n d s b e c a u s e d iv id e n d r e in v e s t m e n t la r g e ly in v o lv e s fu n d s t h a t c o m p a n ie s w o u ld h a v e r e ta in e d , b u t fo r th e
h ig h e r d iv id e n d p a y o u t s n e e d e d t o t r a n s f e r f r a n k in g c r e d it s t o s h a r e h o ld e r s . In o t h e r w o r d s, e q u it y 'ra ise d * th r o u g h d iv id e n d
r e in v e st m e n t is, in e ffe c t, in t e r n a l fu n d s t h a t h a v e b e e n <r e la b e lle d , a s e x t e r n a lly p r o v id e d . D iv id e n d r e in v e s t m e n t p la n s a re
d is c u s s e d in m o re d e t a il in C h a p t e r 1 1 .
of fin a n c e : equity
9.9
M a n a g in g a com pany’s equity
structure
In this chapter we have discussed the various sources o f equity individually. In practice, the financial
manager w ill usually have a long-term plan fo r the management o f a company s capital structure,
including its equity structure. The m ost im p o rta n t aspect o f such a plan involves the tim in g and amounts
o f future capital raisings based on forecasts o f the company s cash flows, capital expenditures and loan
repayments. As part o f this process, companies, equity structures are sometimes rearranged through
procedures th a t change the number o f shares on issue w ith o u t either raising capital or returning capital
to shareholders. These procedures— which include bonus issues, share splits and consolidations— are
now considered.
9.9.1 | Bonus issues and share splits
L E A R N IN G
O B JEC TIVE 11
Outline the effects of
bonus issues, share
splits a n d share
consolidation s
A bonus issue is a ‘free’ issue o f shares made to existing shareholders in p ro p o rtio n to th e ir current
investm ent. Bonus issues used to be common in Australia and were used as a way o f increasing the
dividends paid to shareholders. A bonus issue is equivalent to a rights issue w ith a zero subscription
price. In accounting terms, a company could make a bonus issue by using the balances o f reserves, such
as a share premium reserve, and /or retained earnings— th a t is, p art o f a reserve is converted to issued
capital b u t the to ta l o f shareholders’ funds remains unchanged.
Regulatory changes, including the intro du ction o f the dividend im p utatio n tax system and the
abolition o f par value fo r shares, removed any tax advantage associated w ith bonus issues. Accordingly,
companies th a t have the capacity to pay higher dividends usually increase the rate o f dividend per existing
share rather than making a bonus issue and m aintaining the same dividend rate.
W hile bonus issues have virtu a lly disappeared from the Australian market, companies can achieve a
sim ilar result by sp littin g th e ir shares. For example, a share s p lit th a t doubles the num ber o f a company s
issued shares has the same effect fo r shareholders as a 1 -fo r-l bonus issue. Australian companies that
have made share splits since 2002 include Toll Holdings, W H K Group, CSL Lim ited, Incitec Pivot and
Fortescue Metals Group.
A bonus issue or share sp lit involves no cash flow — apart from the adm inistration costs involved—
and should n o t have any effect on shareholders’ wealth. Therefore, i f a company makes, say, a 1 -fo r-l
bonus issue, the num ber o f shares on issue w ill double and the m arket price o f each share should decrease
by half, leaving unchanged the to ta l m arket value o f the shares held by each investor. The Australian
evidence is consistent w ith this expectation— th a t is, bonus issues do n o t affect shareholders1wealth.37
A lthough a bonus issue— by its e lf— would n o t be expected to have an im pact upon shareholder wealth,
the in fo rm a tio n contained w ith in the announcement o f a bonus issue may result in a significant change
in wealth. Bonus issues and share splits are typically made by companies th a t have been perform ing well
and th a t have recently experienced significant increases in share price. Investors are aware that, follow ing
a bonus o r split, companies usually do n o t reduce dividends per share to the extent necessary to m aintain
the same to ta l dividend payout. For example, after a 1 -fo r-l bonus issue, a company currently paying
a dividend o f 10 cents per share would need to pay a dividend o f only 5 cents per share to m aintain its
dividend payout. However, companies w ill often n ot reduce th e ir dividend per share to th a t extent. For
example, the company may end up paying a dividend of, say, 7.5 cents per share after the bonus issue has
been made. I f the behaviour o f m ost companies after a bonus issue follows this pattern, the m arket w ill
be confident th a t a company m aking a bonus issue w ill probably increase its to ta l dividend payout (Ball,
Brown & Finn 1977). This, in tu rn , indicates the confidence o f management in the company s future.
Consequently, the share price may increase in response to this new inform ation. Therefore, bonus issues
may result in an increase in shareholder wealth— n o t sim ply because o f the new shares issued— but
instead because the announcement o f the issue provides an o pp o rtu n ity fo r management to signal to the
m arket positive info rm a tio n th a t was n o t already incorporated into the company s share price.
37
S e e S lo a n ( 1 9 8 7 ) . T h is e v id e n c e c o n t r a s t s w ith th e U S e v id e n c e , w h ich h a s fo u n d p o s it iv e a b n o r m a l r e t u r n s o n th e e x -b o n u s
d a y fo r U S s t o c k d iv id e n d s a n d s h a r e s p lit s ; s e e L a k o n is h o k a n d V e r m a e le n ( 1 9 8 6 ) a n d G r in b la t t , M a s u lis a n d T it m a n ( 1 9 8 4 ).
C hapter n in e S ources
The dividend-based explanation fo r the m arket reaction to bonus and sp lit announcements, which
was firs t proposed by Fama et al. (1969), does n o t appear to explain fu lly the m arket reaction to such
announcements. Asquith, Healy and Palepu (1989) studied share splits by companies th a t did n o t pay
cash dividends. They found th a t these companies had large earnings increases before the split, b u t no
unusual changes in earnings or in itia tio n o f dividends after the split. An im p o rta n t conclusion o f th eir
study was th a t the announcement o f a sp lit leads investors to expect th a t past earnings increases are
permanent.
A share split may be made by a company w ith a *thin, market fo r its shares. Management may believe
that reducing the m arket price per share w ill increase the demand fo r the company s shares. In September
2008, fe rtiliser and explosives m anufacturer Incitec Pivot, which had a share price around $140, made
a 2 0 -fo r-l share split. The stated purpose was to benefit shareholders by m aking the company s shares
more affordable to retail investors. W hile there is evidence th a t both announcement and execution
o f share splits are associated w ith significant positive returns, empirical evidence that splits lead to
improved liq u id ity and m arketability is mixed. On the one hand, there is evidence th a t both the number
o f shareholders and the num ber o f share transactions increase after splits, b ut little evidence th a t the
dollar value o f trading increases. On the other hand, there is evidence th a t splits increase bid-ask spreads
and return volatility, both o f which suggest a decrease in liq u id ity .38
A share consolidation— also know n as a reverse sp lit— decreases the number o f shares on issue and
increases the price per share. For example, i f a company w ith 100 m illio n issued shares makes a l-fo r-1 0
consolidation, i t w ill end up w ith 10 m illio n issued shares. A fte r the consolidation, the m arket price per
share should increase by a factor o f 10. Consolidations are unusual in Australia b ut have become more
common follow ing the global financial crisis. For example, in September 2010, gold m iner St Barbara
Ltd announced th a t it planned a share consolidation o f six existing shares fo r one new share. Directors
noted th a t the company s share price o f around 40 cents meant th a t some international in s titu tio n s that
were potential investors in the company were precluded from investing in companies w ith share prices
less than US$1. Sim ilar reasons usually given fo r consolidations include raising the share price into a
popular trading range, overcoming perceptions th a t a company is n o t respectable because o f its low share
price, and reducing shareholder servicing costs. O ther companies th a t have recently consolidated th e ir
securities include Australand, Boart Longyear and GPT Group.
I f these suggested reasons are correct and consolidations provide benefits fo r shareholders, the
market response to these events should be positive. This does n o t appear to be the case: several US studies
report th a t consolidations are associated w ith negative share returns. For example, Desai and Jain (1997)
report an average abnormal retu rn o f -4.5 9 per cent in the m onth th a t consolidations are announced.
They also found th a t negative returns in the announcement period were followed by a d rift th a t averaged
10.76 per cent in 1 year and 33.90 per cent in 3 years. One interpretation is th a t consolidations convey
a signal th a t management lacks confidence th a t there w ill be future share price increases resulting from
improvements in earnings. There is evidence th a t consolidations are followed by higher trading volume
and a decrease in bid-ask spread. This finding suggests th a t consolidations enhance the liq u id ity o f a
stock, which should be beneficial fo r investors. Taken together, the evidence suggests th a t consolidations
*may be better characterised as a device th a t management, given its assessment o f future earnings, can
use to improve the liq u id ity o f the stock’ （
Han 1995, p. 169).
38
S tu d ie s t h a t r e p o r t e v id e n c e o n t h e e ffe c t s o f s h a r e s p l i t s o n liq u id ity in c lu d e Ik e n b e r ry , R a n k in e a n d S tic e ( 1 9 9 6 ) a n d
M u sc a r e lla a n d V e ts u y p e n s ( 1 9 9 6 ) .
〇
f fin a n c e : equity
B usiness finance
SUMMARY
•
•
In th is c h a p te r w e c o n s id e r e d th e w a y s in w h ic h
r a t io to th e n u m b e r o f s h a re s a lr e a d y h e ld . A
•
t r a d itio n a l
Those
who
in v e s t in
new
v e n tu re s
w h e re
an
issu e
is
s lo w
in v o lv e s
o f a n in v e n tio n o r id e a in c lu d e w e a lt h y in d iv id u a ls
ra is e la r g e a m o u n ts o f fu n d s . R ig h ts issues m a y
a n d p r iv a te e q u ity fu n d s .
b e r e n o u n c e a b le o r n o n -re n o u n c e a b le a n d c a n
W h e re
c a p it a l
a
is ra is e d
in v e s to rs
by
is s u in g
m u st g e n e r a lly
d is c lo s u re
d o c u m e n t.
b e m a d e w ith o u t a p ro s p e c tu s . T h e fu n d s c a n b e
s e c u ritie s ,
re c e iv e d s o o n e r th a n u s u a l b y a d o p tin g o n e o f
b e s u p p lie d
T h is
th e a c c e le r a te d o ffe r s tru ctu re s.
d o c u m e n t,
often a p ro s p e c tu s , sets o u t in fo r m a tio n to e n a b le
in v e s to rs to
assess th e
risks in v o lv e d
and
•
•
A
p la c e m e n t is a n issu e o f s h a re s to b r o k e r s 7
c lie n ts
th e
a n d /o r
in s titu tio n a l
in v e s to rs
s u ch
as
life in s u r a n c e c o m p a n ie s a n d in v e s tm e n t fu n d s .
v a lu e o f th e s e c u ritie s .
O r d in a r y s h a re h o ld e rs fa c e h ig h e r ris k th a n o th e r
Issue c o sts a r e
in v e s to rs,
rig h ts issu e s, b u t f o r a lis te d c o m p a n y a lim it
b u t a re
p ro te c te d
to so m e e x te n t b y
lim ite d lia b ility . A s p a rt-o w n e rs o f th e c o m p a n y ,
of
c a p it a l th a t it c a n ra is e b y p la c e m e n ts in a n y
v irtu e o f th e ir r ig h t to e le c t m e m b e rs o f th e B o a rd o f
y e a r w ith o u t th e p r io r a p p r o v a l o f s h a r e h o ld e r s .
D ire c to rs . S h a re h o ld e rs in a liste d p u b lic c o m p a n y
W h e re
m a y sell th e ir sh a re s o n a s to ck e x c h a n g e .
th e
E q u ity
has
im p o r ta n t a d v a n ta g e s
as a
s o u rc e
15
lo w e r f o r p la c e m e n ts th a n fo r
o r d in a r y s h a re h o ld e rs e x e rt a d e g r e e o f c o n tro l b y
p e r c e n t is
th e
15
A lte r n a tiv e ly ,
o r to re d e e m (re p a y ) o r d in a r y s h a re s. R a isin g n e w
w ith
e q u ity c a p ita l lo w e rs fin a n c ia l ris k a n d
issu e.
lo w e rs th e
•
a
cent
c e ilin g ,
th e
am ount of
sought exceeds
c o m p a n ie s
o fte n
p la c e m e n t c a n
p u rc h a s e
p la n
be
c o m b in e d
a n d /o r
a
rig h ts
E q u ity c a n a ls o b e ra is e d b y is s u in g c o n trib u tin g
o p tio n s
e m p lo y e e s .
(IPO ) o f o r d in a r y
a
s h a re
s h a re s ,
it b o rro w s .
on
s h a re s
E m p lo y e e s h a re
and
sh a re s
to
p la n s c a n q u a lif y
fo r ta x c o n c e s s io n s .
s h a re s is re fe r r e d to as f lo a t in g a c o m p a n y a n d is
u s u a lly a c c o m p a n ie d b y th e lis tin g o f th e s h a re s o n
on
a m o u n t o f fu n d s
per
fin a n c e . C o m p a n ie s a r e n o t re q u ire d to p a y d iv id e n d s
M a k in g a n in it ia l p u b lic o ffe r in g
p la c e d
m a k e a p la c e m e n t w ith s h a r e h o ld e r a p p r o v a l.
of
in te re s t ra te th a t th e c o m p a n y w ill h a v e to p a y w h e n
•
A m a jo r s o u rc e o f e q u ity fin a n c e is in te rn a l in th e
a s to c k e x c h a n g e . D e te r m in in g th e issu e p r ic e f o r a n
se n se th a t it re su lts fro m th e p o s itiv e n e t c a s h flo w s
IP O c a n b e d iff ic u lt a n d in la r g e flo a ts it h a s b e c o m e
th a t
c o m m o n to use c o m p e titiv e b id d in g
g e n e r a te d
b y in s titu tio n s
to set th e p ric e . D e ta ils o f th e issu e a n d th e is s u in g
a
s u c ce ssfu l
fu n d s
com pany
have
g e n e ra te s .
s e v e ra l
In te rn a lly
a d v a n ta g e s
over
e q u ity fu n d s ra is e d e x te rn a lly . In c o n ju n c tio n w ith
c o m p a n y m u st b e p r o v id e d in a p ro s p e c tu s . F lo a tin g
h ig h e r d iv id e n d p a y m e n ts u n d e r th e im p u ta tio n ta x
a
th e
syste m , m a n y A u s tr a lia n c o m p a n ie s h a v e in tro d u c e d
la rg e s t c o s t is a s s o c ia te d w ith th e u n d e r p r ic in g o f
d iv id e n d re in v e s tm e n t p la n s th a t a llo w in v e s to rs to
com pany
in v o lv e s
s ig n if ic a n t co sts.
O fte n ,
th e s h a re s — th e issu e p r ic e f o r a n IP O is u s u a lly less
use
th a n th e m a rk e t p r ic e w h e n t r a d in g c o m m e n c e s .
s h a re s . T h is a llo w s d iv id e n d s to b e p a id a n d f r a n k in g
A fte r a c o m p a n y h a s b e e n flo a te d , a d d itio n a l e q u ity
c re d its to b e d is tr ib u te d to in v e s to rs w h ile re ta in in g
can
c a s h w ith in th e c o m p a n y .
be
ra is e d
in
s e v e ra l
w ays,
in c lu d in g
rig h ts
th e ir
cash
d iv id e n d s
to
p u rc h a s e
issu es, p la c e m e n ts a n d s h a re p u rc h a s e p la n s .
KEY TERMS
c a ll
234
c o n trib u tin g sh a re s
c u m rig h ts
262
e x -rig h ts d a te
240
253
in fo rm a tio n a s y m m e try
in itia l p u b lic o ffe r in g
in s ta lm e n t re c e ip t
lim ite d lia b ilit y
o p tio n
237
237
262
234
260
p ro s p e c tu s
240
234
se a s o n e d e q u ity o ffe r in g
s h o rtfa ll f a c ility
258
s h o rtfa ll sh a re s
258
s ta p le d se c u ritie s
234
25 1
233
s u b s c rip tio n p ric e
253
th e o re tic a l e x -rig h ts s h a re p ric e
th e o re tic a l rig h ts p ric e
255
o r d in a r y sh a re s
p la c e m e n t
re s id u a l c la im
253
d is c lo s u re d o c u m e n t
270
and
h ig h e r co sts th a n a p la c e m e n t b u t c a n b e u se d to
w ith
•
rig h ts
e n tre p re n e u r n e e d s f in a n c e fo r th e d e v e lo p m e n t
p o te n tia l
•
rig h ts issu e (e n title m e n t o ffe r) is a n o ffe r to
s h a re s . E v e ry c o m p a n y m u st issu e o r d in a r y s h a re s.
•
•
A
e x is tin g s h a re h o ld e rs o f n e w s h a re s in a fix e d
a c o m p a n y m a y ra is e e q u ity b y is s u in g o r d in a r y
w in n e r ’s cu rs e
248
254
254
a d d itio n a l
C hapter n in e S ources
of f in a n c e : equity
1
[L0 1] The interest held by ordinary shareholders is a residual claim. E x p la in th e m e a n in g a n d s ig n ific a n c e
o f th is s ta te m e n t.
2
3
[L O 1] W h a t a re th e m o s t im p o r t a n t rig h ts o f s h a re h o ld e rs in a c o m p a n y ?
[ L O l ] W h a t a r e th e m a in s im ila ritie s b e tw e e n c o n tr ib u tin g s h a re s a n d in s ta lm e n t re c e ip ts ? H o w d o th e y
d iffe r?
4
5
[LO 2 ] W h a t a r e th e m a in a d v a n ta g e s o f r a is in g e q u ity ra th e r th a n b o r r o w in g ?
[LO 2: D is tin g u is h b e tw e e n lim ite d lia b ilit y a n d n o lia b ilit y c o m p a n ie s . W h y a r e n o lia b ilit y c o m p a n ie s
c o n fin e d to e x p lo r a t io n a n d m in in g c o m p a n ie s ?
6
[LO 3 ] D e fin e p r iv a te e q u ity . W h a t a r e th e m a in fe a tu re s th a t d is tin g u is h p r iv a te e q u ity fro m o th e r fo rm s o f
e q u ity fin a n c e ?
7
[LO 31 P riv a te e q u ity fu n d in g fo r n e w v e n tu re s is t y p ic a lly p r o v id e d in s ta g e s . W h a t a r e th e m a in re a s o n s fo r
th is a p p r o a c h ?
8
[LO 4 ] W h a t ty p e o f in fo r m a tio n is g e n e r a lly r e q u ire d in th e o f fe r d o c u m e n ts is s u e d p r io r to c a p it a l r a is in g ?
W h y d o y o u th in k r e g u la to rs m ig h t h a v e a v o id e d p r o v id in g a s im p le 'c h e c k lis t7 o f ite m s f o r in c lu s io n a n d
C H A P T E R Isfl^E R E V I E W
QUESTIONS
in s te a d ta k e n a b r o a d e r a p p r o a c h to r e g u la tio n ?
9
[L O 5 ] Listed p u b lic c o m p a n ie s h a v e th e a d v a n ta g e o f g r e a te r a c c e s s to th e c a p it a l m a rk e t th a n p r iv a te o r
u n lis te d c o m p a n ie s . H o w e v e r, th is a d v a n ta g e a ls o in v o lv e s s ig n ific a n t costs. W h a t a r e th e m a in co sts?
10
[L O 5 ] A com pany is floated by m aking a public issue of ordinary shores. O u t lin e th e p ro c e d u re s in v o lv e d
11
[L O 5 ]
12
[L O 5 ] O u tlin e th e m a in a d v a n ta g e s o f u s in g b o o k - b u ild in g fo r a n in it ia l p u b lic o ffe r in g o f s h a re s ra th e r th a n
13
[ L 0 5 ] W h a t a r e th e a d v a n ta g e s a n d d is a d v a n ta g e s o f h a v in g a s h a re issu e u n d e r w r itte n ?
14
[L O 5 ] W h y a r e u n d e r w r it in g fe e s h ig h e r f o r c o m p a n y flo a ts th a n f o r rig h ts issues?
15
[L O 6
in f lo a tin g a c o m p a n y .
A company usually seeks the assistance o f a financial institution before undertaking any large capital
raising. E x p la in w h y th is is so . D e s c rib e fu lly th e re le v a n t s e rv ic e s th a t a f in a n c ia l in s titu tio n p ro v id e s .
m a k in g a fix e d - p r ic e o ffe r. W h a t a r e th e d is a d v a n ta g e s o f b o o k - b u ild in g ?
In itia l p u b lic o ffe r in g s o f s h a re s a re t y p ic a lly u n d e r p r ic e d b u t v e n d o rs a r e r a r e ly u p s e t a b o u t le a v in g
la r g e a m o u n ts o f m o n e y o n th e ta b le . H o w is 'm o n e y le ft o n th e t a b le 7 u s u a lly m e a s u re d ? H o w c a n th e
p u z z lin g a ttitu d e o f v e n d o rs b e e x p la in e d ?
16
[ L 0 6 ] In d is c u s s in g th e ir re s e a rc h o n IP O s, C a m p e t a l. ( 2 0 0 6 ) c o n c lu d e th a t 'th e c h o ic e s issu ers m a k e a t
th e o ffe r in g re fle c t th e tr a d e - o ff b e tw e e n th e co sts a n d b e n e fits o f th e IP O 7. F o r issu e rs, th e m a in c o s t o f a n
IP O is re p re s e n te d b y u n d e r p r ic in g . W h a t a r e th e m a in b e n e fits ?
17
[L O 7 ] O u tlin e th e 'n e w issues p u z z le 7. W h y is th e e v id e n c e f o r its e x is te n c e c o n tro v e rs ia l?
18
[L O 8 ] A lth o u g h m o st c o m p a n ie s p e r m it rig h ts to b e tr a d e d o n th e s to c k e x c h a n g e , a n u m b e r o f c o m p a n ie s
h a v e m a d e n o n -re n o u n c e a b le rig h ts issu es. W h y w o u ld c o m p a n ie s w is h to m a k e th e ir rig h ts issues
n o n -re n o u n c e a b le ?
19
[ L 0 8 ] T h e re h a s b e e n re s is ta n c e to c o m p a n ie s r a is in g fu n d s b y a p r iv a te p la c e m e n t o f s h a re s . D e s c rib e th e
20
[ L 0 8 ] M W B Ltd is a p r o fita b le c o m p a n y w h o s e o r d in a r y s h a re s a r e lis te d o n th e A S X . T h e c o m p a n y ha s
a d v a n ta g e s a n d d is a d v a n ta g e s to e x is tin g s h a re h o ld e rs o f a p r iv a te p la c e m e n t.
p a id r e g u la r d iv id e n d s to s h a re h o ld e rs a n d h a s g e n e r a lly fin a n c e d its g r o w th b y r e ta in in g a b o u t 5 0 p e r c e n t
o f p ro fits . Its c u rre n t 5 - y e a r p la n in c lu d e s in v e s tm e n t in f ix e d a sse ts o n a s c a le th a t w ill re q u ire th e r a is in g o f
e x te rn a l e q u ity fin a n c e d u r in g th e p la n n in g p e r io d . A d v is e th e d ir e c to r s o n th e m a in fa c to rs th a t th e y s h o u ld
c o n s id e r in d e c id in g h o w to ra is e e q u ity . T he d ir e c to r s a r e c o n s id e r in g :
21
a)
a rig h ts issue
b)
a se rie s o f s h a re p la c e m e n ts
c)
e s ta b lis h in g a d iv id e n d re in v e s tm e n t p la n .
Combining a shore purchase plan with a placement to institutions should satisfy shareholders who
argue that as far as possible, companies should raise equity through rights issues. D o y o u a g r e e w ith th is
[L O 8 ]
s ta te m e n t? E x p la in y o u r a n s w e r.
271
B usiness finance
22
[ L 0 8 ] N o w that rights issues con be made without a prospectus, they w ill become much more popular and
placements may become rare. D o y o u a g r e e w ith th is s ta te m e n t? E x p la in y o u r a n s w e r.
23
[L O 8 ] O u tlin e th e m a in fe a tu re s o f a n a c c e le r a te d r e n o u n c e a b le e n title m e n t o ffe r. W h a t a r e th e m a in
d iffe re n c e s b e tw e e n su ch a n o ffe r a n d a t r a d itio n a l r e n o u n c e a b le rig h ts issue?
24
[L O 8 ] A lis te d c o m p a n y m a y m a k e a p u b lic o f fe r o f s h a re s , p o s s ib ly in c o n ju n c tio n w ith a rig h ts issue.
Id e n tify fa c to rs th a t m a y f a v o u r th e use o f a fu rth e r p u b lic o ff e r o f s h a re s ra th e r th a n a p la c e m e n t o r a rig h ts
issue a lo n e .
25
[L O 8 ]
Options are often used as on incentive to various groups or individuals. D e s c rib e h o w o p tio n s c a n b e
u se d to th e a d v a n ta g e o f a c o m p a n y a n d its s h a re h o ld e rs .
26
[ L 0 9 ] W h a t is th e in c e n tiv e fo r a c o m p a n y to p r o v id e c o m p e n s a tio n f o r m a n a g e rs in th e fo rm o f sh a re s
ra th e r th a n s a la r y ? W h a t is th e a d v a n ta g e o f s h a re c o m p e n s a tio n o v e r a n d a b o v e c o m p e n s a tio n u s in g
s h a re o p tio n s ?
27
[L O 1 0 ] W h a t a r e in te rn a l fu n d s ? W h a t a r e th e ir a d v a n ta g e s a s a s o u rc e o f e q u ity ?
28
[L O 1 0 ] O u t lin e th e im p a c t o f th e g lo b a l f in a n c ia l c ris is o n A u s tr a lia n c o m p a n ie s in te rm s o f th e ir m ix o f
in te rn a l ve rsu s e x te rn a l fu n d in g o v e r th e 2 -y e a r p e r io d fro m m id - 2 0 0 7 .
29
[L O ll]
W h a t is a s h a re s p lit? W h y m ig h t th e d ir e c to r s o f a c o m p a n y w is h to s p lit its s h a re s ?
30
[L O ll]
W h a t is a s h a re c o n s o lid a tio n ? E v a lu a te th e re a s o n s th a t m a y b e g iv e n to ju s tify a s h a re
c o n s o lid a tio n .
31
[L O 1 1 ] E x p la in b r ie f ly w h y th e s h a re p r ic e o f a c o m p a n y m a y in c re a s e w h e n th e c o m p a n y a n n o u n c e s a
b o n u s issu e o r s h a re s p lit.
PROBLEMS
1
E co n o m ic fa c to rs a n d f in a n c in g p o lic y [L O 2 】
C h o o s e a c o m p a n y a n d tra c e th e m a jo r c h a n g e s in its c a p ita l stru ctu re d u rin g th e p a s t 1 0 y e a rs . O u tlin e th e
e c o n o m ic fa c to rs th a t y o u c o n s id e r h a v e c o n trib u te d to th e m a jo r c h a n g e s in its fin a n c in g p o lic y d u r in g this
p e rio d .
2
P u b lic s h a re issu e [L O 5 ]
K a tz Pty Ltd is a w e ll-e s ta b lis h e d c o m p a n y w h o s e d ire c to rs h a v e d e c id e d to c o n v e rt to p u b lic c o m p a n y status,
m a k e a p u b lic s h a re issue a n d list o n th e s to ck e x c h a n g e . T he c o m p a n y n e e d s to ra is e $ 7 9 2 0 0 0 0 to e x p a n d
its o p e ra tio n s . Its p ro s p e c tu s fo re c a s ts a d iv id e n d o f 2 0 cen ts p e r sh a re in its firs t y e a r a s a p u b lic c o m p a n y
a n d d iv id e n d s a r e e x p e c te d to g r o w a t 6 p e r c e n t p e r a n n u m in d e fin ite ly . S h a re h o ld e rs re q u ire a re tu rn o f
1 4 p e r c e n t p e r a n n u m a n d th e c o s t o f lis tin g a m o u n ts to 1 2 p e r c e n t o f th e g ro s s p ro c e e d s fro m th e issue.
H o w m a n y s h a re s m ust K a tz issue?
3
R ig h ts issu e [L O 8 ]
C o m p a n y A h a s 4 m illio n sh a re s o n issue a n d w is h e s to ra is e $ 4 m illio n b y a l- f o r - 4 rig h ts issue.
4
a)
W h a t is th e th e o re tic a l v a lu e o f 1 r ig h t if th e m a rk e t p r ic e o f 1 s h a re (cum rig h ts) is $ 5 ?
b)
W h a t is th e th e o re tic a l s h a re p r ic e (ex-rights)?
c)
D o e s a n in v e s to r g a in th ro u g h a rig h ts issue?
R ig h ts issu e [L O 8 ]
C r o s lin g Ltd sh a re s a re tr a d in g a t $ 1 2 e a c h . Its d ire c to rs h a v e a n n o u n c e d a l- fo r - 6 rig h ts issue w ith a
s u b s c rip tio n p r ic e o f $ 1 0 . 6 0 p e r sh a re . W h a t is:
5
a)
th e th e o re tic a l v a lu e o f a r ig h t to o n e n e w s h a re
b)
th e th e o re tic a l e x -rig h ts s h a re p ric e ?
R ig h ts issu e [L O 8 ]
M a x w e ll Ltd is a liste d b io te c h n o lo g y c o m p a n y . O n 5 M a y 2 0 1 4 it a n n o u n c e d a l- fo r - 3 re n o u n c e a b le
rig h ts issue a t a s u b s c rip tio n p r ic e o f $ 6 . 2 0 p e r sh a re w ith a n e x -rig h ts d a te o f 2 5 M a y . T he c o m p a n y a ls o
a n n o u n c e d th a t fu n d s ra is e d b y th e issue w o u ld b e use d to e s ta b lis h p r o d u c tio n fa c ilitie s fo r its n e w a n tim a la r ia d ru g th a t re c e n tly p a s s e d its fin a l c lin ic a l tria ls . T he s h a re p r ic e ro s e fro m $ 6 . 9 0 to $ 7 . 0 5 a fte r th o se
a n n o u n c e m e n ts . T he c lo s in g p ric e o f M a x w e ll sh a re s o n 2 4 M a y w a s $ 7 p e r sh a re .
272
C hapter n in e S ources
W h a t is a r e n o u n c e a b le rig h ts issue?
b) W h a t is th e m o st lik e ly e x p la n a tio n fo r th e s h a re p ric e ris e o n 5 M a y a fte r th e c o m p a n y 's a n n o u n c e m e n ts ?
c)
W h a t d o y o u e x p e c t th e p r ic e o f th e sh a re s to b e o n 2 5 M a y ? S h o w a ll c a lc u la tio n s .
d)
W h a t is th e th e o re tic a l v a lu e o f a rig h t? S h o w a ll c a lc u la tio n s .
e)
E x p la in w h y th e sh a re p ric e c h a n g e fro m 2 4 M a y to 2 5 M a y d o e s n o t re fle c t a n y c h a n g e in s h a re h o ld e rs 7
w e a lth .
6
Alternative w ays of raising equity [LO 8 】
G e o rg e B a n ks In te rn a tio n a l (G B I) Ltd h a s 1 0 0 m illio n fu lly p a id o r d in a r y sh a re s o n issue a n d its sh a re s a r e
liste d o n th e A S X . A b o u t 6 0 p e r c e n t o f th e sh a re s a r e h e ld b y A u s tra lia n fin a n c ia l in s titu tio n s a n d th e c lo s in g
p ric e o f th e s h a re s o n 1 5 O c to b e r 2 0 1 4 w a s $ 4 . The c o m p a n y h a s a fu lly d r a w n $ 5 0 0 m illio n b a n k lo a n
fa c ility , w h ic h is d u e to b e r o lle d o v e r o r r e p a id o n 3 0 N o v e m b e r 2 0 1 4 . G B I Ltd is c lo s e to b re a c h in g a n
im p o rta n t c o v e n a n t a n d its d ire c to rs h a v e re s o lv e d to ra is e e q u ity to r e p a y th e lo a n o n o r b e fo re th e d u e d a te .
The c o m p a n y 's la s t sh a re issue o c c u rre d in 2 0 1 1.
a) A s s u m in g a n issue p r ic e o f $ 3 . 8 0 p e r s h a re , w h a t is th e m a x im u m a m o u n t th a t G B I Ltd c a n ra is e b y
m a k in g a s h a re p la c e m e n t w ith o u t s h a re h o ld e r a p p r o v a l?
b) A d v is e th e d ire c to rs o n th e fe a s ib ility o f ra is in g th e re q u ire d fu n d s b y a tr a d itio n a l re n o u n c e a b le o r
n o n -re n o u n c e a b le rig h ts issue.
c)
C H A P T E R NINE R E V I E W
a)
of f in a n c e : equity
A fte r r e c e iv in g y o u r a d v ic e , th e d ire c to rs a re c o n s id e rin g th e c o m b in a tio n o f a n in s titu tio n a l p la c e m e n t
fo llo w e d im m e d ia te ly b y a n a c c e le ra te d e n title m e n t o ffe r.
i) D o e s th e m a x im u m a m o u n t th a t c a n b e ra is e d b y th e p la c e m e n t re m a in th e s a m e a s in (a)? W h y , o r
w h y not?
ii) R e v ie w y o u r a n s w e r to (b). H o w w ill y o u r a d v ic e c h a n g e , g iv e n th a t a n a c c e le ra te d o ffe r s tru c tu re is to
b e used?
d)
A s s u m e th a t th e c o m p a n y p ro c e e d s w ith a n a c c e le ra te d e n title m e n t o ffe r. F rom th e v ie w p o in t o f G B I's
s h a re h o ld e rs , w h a t is th e m a in e ffe c t o f m a k in g th e o ffe r re n o u n c e a b le ra th e r th a n n o n -re n o u n c e a b le ? W ill
a re n o u n c e a b le o ffe r n e c e s s a rily e n s u re th a t a ll s h a re h o ld e rs a re tre a te d e q u a lly ? W h y , o r w h y not?
Lj
REFERENCES
Abernethy, M.