2015
BUSINESS FINANCE
DECISIONS
PRACTICE KIT
ICAP
Practice Kit
Business finance decisions
First edition published by
Emile Woolf Limited
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© Emile Woolf International, September 2015
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C
Contents
Page
Question and Answers Index
v
Section A
Questions
1
Section B
Answers
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Business finance decisions
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Business finance decisions
I
Index to questions and answers
Question
page
Answer
page
Chapter 1 – An introduction to business finance decisions
1.1
Company objectives
1
149
1.2
Possible conflicts
1
151
1.3
Ownership
1
152
Chapter 2 – Relevant cash flows
2.1
Shockolat
2
154
2.2
Topaz Limited
3
156
2.3
Tychy Limited
4
157
Chapter 3 – Decision making
3.1
Pakpattan Electronics Limited
5
159
3.2
Wazir Manufacturing Ltd
6
160
3.3
Khokhar Perfumers Limited
7
163
Chapter 4 – Linear programming
4.1
Proglin
9
166
4.2
Light engineering
10
167
Chapter 5 – Introduction to investment appraisal
There are no specific questions in this area. The topic is covered as
parts of other questions.
Chapter 6 – Discounted cash flow
6.1
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11
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Business finance decisions
Question
page
Answer
page
6.2
Hasan and Sons Limited
12
172
6.3
DCF and relevant costs
13
172
6.4
Sadeeq Energy Plc
14
173
6.5
Beta Limited
15
174
Chapter 7 – DCF: taxation and inflation
7.1
More investment appraisal and tax
16
176
7.2
Investment appraisal and tax
16
177
7.3
Alawada Limited
17
178
7.4
Kohat Limited
17
179
7.5
JAP Recreation Club
18
180
7.6
ARG Limited
19
182
7.7
Hafeez Ltd
22
185
Chapter 8 – DCF: risk and uncertainty
8.1
Risk in investment appraisal
23
187
8.2
Calm Plc
23
188
8.3
Outlook Plc
24
190
8.4
Zaheer Ltd
25
191
8.5
JKL Phone Limited
26
192
8.6
Khayyam Limited
26
193
Chapter 9 – DCF: specific applications
9.1
Lease or buy
28
194
9.2
Mohani Limited
28
196
9.3
DS Leasing Company Limited
29
197
9.4
HIN Textiles Mills Limited
30
199
9.5
Crank Plc
30
200
9.6
Asset replacement
31
202
9.7
Rotor Plc
31
204
9.8
UVW Rental Services
32
204
Chapter 10 – Evaluating financial performance
10.1
Equity ratios
33
206
10.2
Ayeland and Zedland
33
207
10.3
Khan Industries plc
34
209
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Index to questions and answers
Chapter 11 – Capital rationing
11.1
Capital rationing
36
211
11.2
Basril Company
36
212
11.3
CB Investment Limited
37
214
Chapter 12 – Sources of finance
12.1
Rights
38
216
12.2
Kamalia Carriers Plc
38
216
12.3
Rights issue
39
218
12.4
Stock exchange listing
39
219
12.5
Convertible bonds
39
220
12.6
Shoaib Investment Company
40
220
12.7
Sajawal Sugar Mills Limited
40
222
12.8
PSD Engineering Limited
41
224
Chapter 13 – Cost of capital
13.1
Cost of capital – short questions
43
228
13.2
WACC
44
229
13.3
Redskins
44
229
13.4
Chasanda Agates Plc.
45
230
13.5
Misteri Company
46
233
13.6
Faiz Limited
46
234
Chapter 14 – Portfolio theory and the capital asset pricing model
14.1
Two-asset portfolio
48
238
14.2
Coefficient of variation
49
237
14.3
Portfolio return
49
238
14.4
Dolphin Plc.
50
239
14.5
Risk and return
51
241
14.6
Obtaining a beta factor
51
241
14.7
Sodium Plc
52
242
14.8
Dr Jamal
53
244
14.9
Mr Faraz
53
247
14.10
Mushtaq Limited
54
249
14.11
Attock Index Tracker Fund
55
250
14.12
Iron Limited
56
252
14.13
FR Co-operative Housing Society
56
253
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Chapter 15 – Dividend policy
15.1
Dividends and retentions
58
254
15.2
Ackers Plc
58
254
15.3
Dividend policy
59
256
15.4
YB Pakistan Limited
59
258
15.5
Al-Ghazali Pakistan Limited
61
260
Chapter 16 – Financing of projects
16.1
Gearing
62
263
16.2
Financing schemes
63
264
16.3
MM, gearing and company valuation
64
265
16.4
Diversify
64
265
16.5
Financial and operating gearing
65
266
16.6
Optimal WACC
66
267
16.7
Geared beta
66
268
16.8
Adjusted Present Value
66
269
16.9
APV method
67
272
16.10
More APV
68
274
16.11
Jalib Limited
69
275
16.12
Javed Limited
69
277
16.13
GHI Limited
70
278
16.14
NS Technologies Limited
71
278
16.15
Copper Industries Limited
71
279
16.16
Mac Fertilizer Limited
72
282
Chapter 17 – Business valuation
17.1
Valuation model
74
285
17.2
Valuation
74
285
17.3
Valuation of bonds
74
285
17.4
Annuities and bond prices
75
286
17.5
Warrants and convertibles
75
287
17.6
Kencast Limited
76
288
17.7
A Plc’s and B Plc’s
78
290
17.8
MNO Chemicals Limited
79
292
17.9
Free cash flow
80
293
17.10
Financial plan
80
294
17.11
Takeover
82
296
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Index to questions and answers
17.12
MK Limited
83
299
17.13
Platinum Limited
84
302
17.14
EMH
85
303
17.15
X Plc. and Y Plc
86
304
Chapter 18 – Mergers and acquisitions
18.1
Acquisition
87
307
18.2
Adam Plc
87
308
18.3
D Limited
88
309
18.4
Clooney Plc and Pitt Plc
89
310
18.5
Nelson Plc
90
312
18.6
Hali Ltd
91
313
18.7
URD Pakistan Limited
92
316
18.8
FF International
93
319
95
324
Chapter 19 – Foreign exchange rates
19.1
Interest rate parity
Chapter 20 – International investment decisions
20.1
Cash flows from a foreign project
96
325
20.2
Lahore Pharma Plc
96
325
20.3
Foreign investment
97
327
20.4
Gold Limited
97
328
20.5
Ghazali Limited
99
331
Chapter 21 – Managing foreign exchange risk (I)
21.1
Foreign exchange
100
334
21.2
Money market hedge
100
334
21.3
Dunborgen
101
335
21.4
Currency swap
101
335
21.5
Momin Industries Limited
102
337
21.6
Qalat Industries Limited
103
340
21.7
Silver Limited
104
341
21.8
Khaldun Corporation
106
343
Chapter 22 – Managing foreign exchange risk (II): Currency
futures
22.1
Currency futures
107
344
22.2
More currency futures
107
344
22.3
Basis
108
345
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22.4
Imperfect hedge and basis
108
346
22.5
Currency hedge
108
347
Chapter 23 – Managing foreign exchange risk (III): Currency
options
23.1
Traded equity options
110
349
23.2
Currency options
110
350
23.3
DEF Securities Limited
111
351
23.4
Alpha Automobiles Limited
111
352
Chapter 24 – Managing interest rate risk
24.1
FRA
113
354
24.2
Swap
113
354
24.3
Credit arbitrage
113
355
24.4
Credit arbitrage
114
355
24.5
Hedging with STIRS
114
356
24.6
More hedging with STIRs
114
356
24.7
FRAs and futures
115
357
24.8
Interest rate hedge
116
359
24.9
Definitions
116
360
24.10
Imran Limited
117
362
Chapter 25 – Forecasting and budgeting
25.1
Gazelle
118
363
25.2
Functional budgets (I)
119
364
25.3
Functional budgets (II)
120
365
25.4
Flexed budget
120
366
25.5
Norton Care Home
121
367
25.6
Three services
122
369
25.7
Private medical practice
123
370
25.8
Headgear Limited
124
371
25.9
Daska Design Limited
126
374
Chapter 26 – Variance analysis
26.1
Good Harvest Limited
127
377
26.2
Moongazer
127
380
26.3
ABC Limited
128
383
27.4
Kasur Mf Limited
129
385
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Chapter 27 – Advanced variance analysis
27.1
Toxic Kems
130
389
27.2
BRK
130
391
27.3
Carat
131
394
Chapter 28 – Transfer pricing
28.1
Two divisions
133
399
28.2
Shadow price
133
400
28.3
Froom Plc
134
400
28.4
Training company
135
401
28.5
Bricks
135
403
Chapter 29 – Working capital management
29.1
Cash operating cycle
137
405
29.2
Working capital
137
406
29.3
Waseem Limited
139
408
Chapter 30 – Inventory management
30.1
Marx Limited
140
409
30.2
Engels Limited
140
410
30.3
Lenin Limited
140
411
Chapter 31 – Management of receivables and payables
31.1
Trade receivables management
142
413
31.2
Bahawalpur Buliders Ltd
142
414
31.3
Chishtian Construction Plc
143
415
31.4
Discount and factor
143
416
31.5
Vehari IT Solutions Limited
144
417
31.6
Ulnad Co
145
418
31.7
Brutus Company
145
420
Chapter 32 – Cash management
32.1
Baumol and Miller-Orr
146
422
32.2
Renpec Co
146
422
32.3
Baumol
147
424
32.4
Cassius Company
147
425
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SECTION
Certified finance and accounting professional
Business finance decisions
A
Questions
CHAPTER 1 – AN INTRODUCTION TO BUSINESS FINANCE DECSIONS
1.1
1.2
COMPANY OBJECTIVES
(a)
Justify and criticise the usual assumption made in financial management
literature that the objective of a company is to maximise the wealth of the
shareholders. (Do not consider how this wealth is to be measured.)
(b)
Outline other goals that companies claim to follow, and explain why these
might be adopted in preference to the maximisation of shareholder wealth.
POSSIBLE CONFLICTS
“The major objective of financial management is to maximise the value of the
firm.”
Analyse how the achievement of the above objective might be compromised by
the conflicts which may arise between the management and the other
stakeholders in an organisation.
1.3
OWNERSHIP
“Ascertaining exactly who owns a company’s shares and what, if any, are their
particular preferences and objectives” is a basic piece of information needed by
management, if it is to ensure that, as far as possible, it is acting in the shareholder’s
interest.
(a)
Explain why a publicly quoted company might seek to know the detailed
composition of its shareholders and their objectives in investing in the
company.
(b)
Explain any FIVE the major advantages which may accrue to the corporate
finance manager from obtaining this information.
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CHAPTER 2 – RELEVANT CASH FLOWS
2.1
SHOCKLAT CO
Shoklat Co manufactures and sells one type of chocolate, which is sold as a very wellknown branded item at a price of Rs. 14 per kilogram. This product is targeted mainly
at children.
The product is made in a single process which combines a chocolate casing (material
M1) with a filling (material M2). Material M1 costs Rs. 9 per kilogram and material M2
costs Rs. 7 per kilogram. They are combined in the ratio of 3 kilos of material M1 for
every 4 kilos of material M2 and there is no loss in process.
The product research team, using information obtained from market research, has
now developed two possible new products. By adding an extra ingredient M3 to the
existing product formula Shoklat Co would be able to make a new chocolate product
(CP1) that might appeal to men. Similarly by adding an extra ingredient M4 to the
existing product formula it would be possible to make another new product (CP2) that
might have a particular appeal to women. The market research also suggests that the
appeal of the new products to the target customers would so strong that they could
each be sold for a premium price. The market research cost Rs. 20,000.
Senior management of Shoklat Co are trying to decide whether to experiment with the
two new products for a period of two or three months. The proposal is that about 10%
of normal monthly production would be processed further and made into the two new
products CP1 and CP2.
Data relating to this proposal for each month of the trial period is as follows.
(1)
35,000 kilos of the basic product will be produced and used to make the
CP1 and CP2. Production of this quantity of the basic product will require
2,000 direct labour hours. Direct labour is paid Rs. 20 per hour.
(2)
800 kilos of ingredient M3 will be added to 6,000 kilos of the basic product
to make 6,800 kilos of product CP1. M3 costs Rs. 19 per kilo. Additional
processing will require 900 extra direct labour hours. CP1 is expected to
sell for Rs. 30 per kilo.
(3)
1,200 kilos of ingredient M4 will be added to 29,000 kilos of the basic
product to make 30,200 kilos of product CP2. M4 costs Rs. 80 per kilo.
Additional processing will require 1,250 extra direct labour hours. CP2 is
expected to sell for Rs. 20.50 per kilo.
(4)
Shoklat Co has sufficient machinery to carry out the further processing.
However direct labour is in short supply and the labour needed to making
CP1 and CP2 would have to be taken off making the basic product. It will
not be possible to hire additional labour within the next three months.
(5)
The production of CP1 and CP2 would be supervised by the most
experienced supervisor in the production department. His current annual
salary is Rs. 80,000 which is 10% more than other supervisors in the
department. It is expected that about 10% to 15% of this time would be
taken up with supervision of the new work. This time will be divided 25% to
CP1 and 75% to CP2.
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Questions
(6)
In the company’s costing system, fixed production overheads are absorbed
into product costs at the rate of Rs. 40 per direct labour hour. There are no
variable production overheads.
Required
2.2
(a)
Explain briefly the financial and other factors that Shoklat Co should
consider when deciding whether or not to make the CP1 and CP2 for a test
period of three months. No calculations are required for this part of your
answer.
(b)
Prepare calculations to assess whether Shoklat Co should decide to
experiment with making the two products CP1 and CP2 for a test period.
Make separate recommendations about producing CP1 and CP2.
(c)
Calculate a selling price per kilogram for CP2 that would achieve
breakeven for production and sales of the product during the test period.
TOPAZ LIMITED
Topaz Limited (TL) is the manufacturer of consumer durables. Pearl Limited, one
of the major customers, has invited TL to bid for a special order of 150,000 units of
product Beta.
Following information is available for the preparation of the bid.
(i)
Each unit of Beta requires 0.5 kilograms (kg) of material “C”. This
material is produced internally in batches of 25,000 kg each, at a variable
cost of Rs. 200 per kg. The setup cost per batch is Rs. 80,000. Material “C”
could be sold in the market at a price of Rs. 225 per kg. TL has the
capacity to produce 100,000 kg of material “C”; however, the current
demand for material “C” in the market is 75,000 kg.
(ii)
Every 100 units of product Beta requires 150 labour hours. Workers are
paid at the rate of Rs. 9,000 per month. Idle labour hours are paid at
60% of normal rate and TL currently has 20,000 idle labour hours. The
standard working hours per month are fixed at 200 hours.
(iii)
The variable overhead application rate is Rs. 25 per labour hour. Fixed
overheads are estimated at Rs. 22 million. It is estimated that the special
order would occupy 30% of the total capacity. The production capacity
of Beta can be increased up to 50% by incurring additional fixed
overheads. The fixed overhead rate applicable to enhanced capacity would
be 1.5 times the current rate. The utilized capacity at current level of
production is 80%.
(iv)
The normal loss is estimated to be 4% of the input quantity and is
determined at the time of inspection which is carried out when the unit
is 60% complete. Material is added to the process at the beginning while
labour and overheads are evenly distributed over the process.
(v)
TL has the policy to earn profit at the rate of 20% of the selling price.
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Business finance decisions
Required
Calculate the unit price that TL could bid for the special order to Pearl Limited.
2.3
TYCHY LIMITED
Tychy Limited (TL) is engaged in the manufacture of specialised motors. The
company has been asked to provide a quotation for building a motor for a large
textile industrial unit in Punjab. Following information has been obtained by TL’s
technical manager in a one-hour meeting with the potential customer. The
manager is paid an annual salary equivalent to Rs. 2,500 per eight-hour day.
(i)
The motor would require 120 ft. of wire-C which is regularly used by TL in
production. TL has 300 ft. of wire-C in inventory at the cost of Rs. 65 per ft.
The resale value of wire-C is Rs. 63 and its current replacement cost is Rs.
68 per ft.
(ii)
The motor would also require 50 kg of Wire-D and 30 other small
components. Wire-D would be purchased from a supplier at Rs. 10 per kg.
The supplier sells a minimum quantity of 60 kg per order. However, the
remaining quantity of wire-D will be of no use to TL after the completion of
the contract. The other small components will be purchased from the
market at Rs. 80 per component.
(iii)
The manufacturing process would require 250 hours of skilled labour and
30 machine hours.
The skilled workers are paid a guaranteed wage of Rs. 20 per hour and
the current spare capacity available with TL for such class of workers is
100 direct labour hours. However, additional labour hours may be obtained
by either:
‰
Paying overtime at Rs. 23 per hour; or
‰
Hiring temporary workers at Rs. 21 per hour. These workers would
require 5 hours of supervision by AL’s existing supervisor who would
be paid overtime of Rs. 20 per hour.
The machine on which the motor would be manufactured was leased by TL
last year at a monthly rent of Rs. 5,000 and it has a spare capacity of 110
hours per month. The variable running cost of the machine is Rs. 15 per
hour.
(iv)
Fixed overheads are absorbed at the rate of Rs. 25 per direct labour hour.
Required
Compute the relevant cost of producing textile motor. Give brief reasons for
the inclusion or exclusion of any cost from your computation.
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Questions
CHAPTER 3 – DECISION MAKING
3.1
PAKPATTAN ELECTRONICS LIMITED
Pakpattan Electronics Limited is contemplating outsourcing some of its production.
The company’s management accountant has asked for your advice on the relevant
costs for the contract. The following information is available:
Materials
The contract requires 3,000 kg of material K, which is a material used regularly by the
company in other production. The company has 2,000 kg of material K currently in
stock which had been purchased last month for a total cost of Rs. 19,600. Since then
the price per kilogram for material K has increased by 5%.
The contract also requires 200 kg of material L. There are 250 kg of material L in stock
which are not required for normal production. This material originally cost a total of Rs.
3,125. If not used on this contract, the stock of material L would be sold for Rs. 11 per
kg.
Labour
The contract requires 800 hours of skilled labour. Skilled labour is paid Rs. 9·50 per
hour. There is a shortage of skilled labour and all the available skilled labour is fully
employed in the company the manufacture of product P. The following information
relates to product P:
Rs. per unit
Selling price
Less
Skilled labour
Other variable costs
38
22
–––
Contribution per unit
Rs. per unit
100
(60)
–––
40
–––
Required
(a)
Prepare calculations showing the total relevant costs for making a decision
about the contract in respect of the following cost elements:
(i)
materials K and L; and
(ii)
skilled labour.
(ii)
the maximum price the company should pay the outsourcing
company
(b)
Explain how you would decide which overhead costs would be relevant in
the financial appraisal of the contract.
(c)
Prepare a report for senior management highlighting factors that should be
taken into account when considering an outsourcing decision.
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3.2
WAZIR MANUFACTURING LTD
The managers of Wazir Manufacturing Ltd are reviewing the operations of the
company with a view to making operational decisions for the next month. Details of
some of the products manufactured by the company are given below.
AR2
GL3
HT4
21.00
28.50
27.30
Material R2 (kg per unit
2.0
3.0
3.0
Material R3 (kg/unit)
2.0
2.2
1.6
3.0
Direct labour (hours/unit)
0.6
1.2
1.5
1.7
Variable production overheads (Rs./unit)
1.10
1.30
1.10
1.40
Fixed production overheads (Rs./unit)
1.50
1.60
1.70
1.40
Expected demand for next month (units)
950
1,000
900
Selling price (Rs./unit)
XY5
Products AR2, GL3 and HT4 are sold to customers of Wazir Manufacturing Ltd, while
Product XY5 is a component that is used in the manufacture of other products. The
company manufactures a wide range of products in addition to those detailed above.
Material R2, which is not used in any other of the company’s products, is expected to
be in short supply in the next month because of industrial action at a major producer of
the material. Wazir Manufacturing Ltd has just received a delivery of 5,500 kg of
Material R2 and this is expected to be the amount held in inventory at the start of the
next month.
The company does not expect to be able to obtain further supplies of Material R2
unless it pays a premium price. The normal market price is Rs. 2.50 per kg. Material
R3 is available at a price of Rs. 2.00 per kg and the company does not expect any
problems in securing supplies of this material. Direct labour is paid at a rate of Rs. 4.00
per hour.
Kenzi Chemicals Ltd Company has recently approached Wazir Manufacturing Ltd with
an offer to supply a substitute for Product XY5 at a price of Rs. 10.20 per unit. Wazir
Manufacturing Ltd would need to pay an annual fee of Rs. 50,000 for the right to use
this patented substitute.
Required
(a)
Determine the optimum production schedule for Products AR2, GL3 and
HT4 for the next month, on the assumption that additional supplies of
Material R2 are not purchased.
(b)
If Wazir Manufacturing Ltd decides to purchase further supplies of Material
R2 to meet demand for Products AR2, GL3 andHT4, what should be the
maximum price per kg that the company is prepared to pay?
(c)
Discuss whether Wazir Manufacturing Ltd should manufacture Product XY5
or buy the substitute offered by Kenzi Chemicals Ltd.
Your answer must be supported by appropriate calculations.
(d)
Discuss the limitations of marginal costing (variable costing) as a basis for
making short-term decisions.
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Questions
3.3
KHOKHAR PERFUMERS LIMITED
Khokhar Perfumers Limited manufactures and sells its standard perfume by blending a
secret formula of aromatic oils with diluted solvent. The oils are produced by another
company following a lengthy process and are very expensive. The standard perfume
is highly branded and successfully sold at a price of Rs. 39·98 per 100 millilitres (ml).
Khokhar Perfumers Limited is considering processing some of the perfume further by
adding a hormone to appeal to members of the opposite sex. The hormone to be
added will be different for the male and female perfumes. Adding hormones to
perfumes is not universally accepted as a good idea as some people have health
concerns. On the other hand, market research carried out suggests that a premium
could be charged for perfume that can ‘promise’ the attraction of a suitor. The market
research has cost Rs. 3,000.
Data has been prepared for the costs and revenues expected for the following month
(a test month) assuming that a part of the company’s output will be further processed
by adding the hormones.
The output selected for further processing is 1,000 litres, about a tenth of the
company’s normal monthly output. Of this, 99% is made up of diluted solvent which
costs Rs. 20 per litre. The rest is a blend of aromatic oils costing Rs. 18,000 per litre.
The labour required to produce 1,000 litres of the basic perfume before any further
processing is 2,000 hours at a cost of Rs. 15 per hour.
Of the output selected for further processing, 200 litres (20%) will be for male
customers and 2 litres of hormone costing Rs. 7,750 per litre will then be added. The
remaining 800 litres (80%) will be for female customers and 8 litres of hormone will be
added, costing Rs. 12,000 per litre. In both cases the adding of the hormone adds to
the overall volume of the product as there is no resulting processing loss.
Khokhar Perfumers Limited has sufficient existing machinery to carry out the test
processing.
The new processes will be supervised by one of the more experienced supervisors
currently employed by Khokhar Perfumers Limited. His current annual salary is Rs.
35,000 and it is expected that he will spend 10% of his time working on the hormone
adding process during the test month. This will be split evenly between the male and
female versions of the product.
Extra labour will be required to further process the perfume, with an extra 500 hours for
the male version and 700 extra hours for the female version of the hormone-added
product. Labour is currently fully employed, making the standard product. New labour
with the required skills will not be available at short notice.
Khokhar Perfumers Limited allocates fixed overhead at the rate of Rs. 25 per labour
hour to all products for the purposes of reporting profits.
The sales prices that could be achieved as a one-off monthly promotion are:
‰
Male version: Rs. 75·00 per 100 ml
‰
Female version: Rs. 59·50 per 100 ml
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Required
(a)
Outline the financial and other factors that Khokhar Perfumers Limited
should consider when making a further processing decision.
Note: no calculations are required.
(b)
Evaluate whether Khokhar Perfumers Limited should experiment with the
hormone adding process using the data provided. Provide a separate
assessment and conclusion for the male and the female versions of the
product.
(c)
Calculate the selling price per 100 ml for the female version of the product
that would ensure further processing would break even in the test month.
(d)
Khokhar Perfumers Limited is considering outsourcing the production of the
standard perfume. Outline the main factors it should consider before
making such a decision.
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Questions
CHAPTER 4 – LINEAR PROGRAMMING
4.1
PROGLIN
(a)
Proglin is a manufacturing company. It makes and sells two versions of a
product, Mark 1 and Mark 2. The two products are made from the same
direct materials and by the same direct labour employees.
The following budgeted data has been prepared for next year:
Direct materials per unit
Direct labour hours per unit
Maximum sales demand
Contribution per unit
Mark 1
Mark 2
Rs. 2
Rs. 4
3 hours
2 hours
5,000 units
unlimited
Rs. 10 per unit
Rs. 15 per unit
Direct materials and direct labour will be in restricted supply next year, as
follows:
Maximum available
Direct materials
Rs. 24,000
Direct labour hours
18,000 hours
There is no inventory of finished goods at the beginning of the year.
Required
Use the graphical method of linear programming to identify the quantities of
Mark 1 and Mark 2 that should be made and sold during the year in order to
maximise profit and contribution.
Calculate the amount of contribution that will be earned.
(b)
Suppose that the maximum available amount of direct materials next year
is Rs. 24,001, not Rs. 24,000.
Required
(i)
Identify the quantities of Mark 1 and Mark 2 that should be made and
sold during the year in order to maximise profit and contribution.
(ii) Calculate the amount of contribution that will be earned.
(iii) Compare the total contribution you have calculated in (b) with the total
contribution that you calculated in (a), to calculate the shadow price per
Rs. 1 of direct materials.
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Business finance decisions
4.2
LIGHT ENGINEERING
A light engineering company makes water tanks and water butts. Both products
involve the same staff and equipment. Each product passes through a cutting
and an assembly stage. One water tank makes a contribution of Rs. 50, and
takes six hours cutting time and four hours assembly time. One water butt makes
a contribution of Rs. 40, and takes three hours cutting time and eight hours
assembly time. There are a maximum of 36 cutting hours each week and 48
assembly hours.
The company has to produce at least two water tanks and three water butts.
Calculate the number of water butts and water tanks that should be produced
each week to maximise contribution.
Required
(a)
state the objective function and constraints algebraically
(b)
draw a graph of the problem, shading the feasible region
(c)
find the product mix that best suits company policy, and
(d)
calculate the shadow price of one more unit of cutting time and one more
unit of assembly time.
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Questions
CHAPTER 6 – DISCOUNTED CASH FLOW
6.1
BADGER PLC
Badger plc., a manufacturer of car accessories is considering a new product line. This
project would commence at the start of Badger plc.’s next financial year and run for
four years. Badger plc.’s next year end is 31st December 2016.
The following information relates to the project:
A feasibility study costing Rs. 8 million was completed earlier this year but will not be
paid for until March 2017. The study indicated that the project was technically viable.
Capital expenditure
If Badger plc. proceeds with the project it would need to buy new plant and machinery
costing Rs. 180 million to be paid for at the start of the project. It is estimated that the
new plant and machinery would be sold for Rs. 25 million at the end of the project.
If Badger plc. undertakes the project it will sell an existing machine for cash at the start
of the project for Rs. 2 million. This machine had been scheduled for disposal at the
end of 2020 for Rs. 1 million.
Market research
Industry consultants have supplied the following information:
Market size for the product is Rs. 1,100 million in 2016. The market is expected to
grow by 2% per annum.
Market share projections should Badger plc. proceed with the project are as follows:
2017
7%
2018
9%
2019
15%
2020
15%
2017
Rs. m
Purchases
40
Payables (at the year-end)
8
Payments to sub-contractors, 6
2018
Rs. m
50
10
9
2019
Rs. m
58
11
8
2020
Rs. m
62
nil
8
Fixed overheads (total for Badger plc)
With new line
133
Without new line
120
110
100
99
90
90
80
Market share
Cost data:
Labour costs
At the start of the project, employees currently working in another department would
be transferred to work on the new product line. These employees currently earn Rs.
3.6 million per annum. They will not be replaced if they work on the new project.
An employee currently earning Rs. 2 million per annum would be promoted to work on
the new line at a salary of Rs. 3 million per annum. A new employee would be
recruited to fill the vacated position.
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As a direct result of introducing the new product line, employees in another department
currently earning Rs. 4 million per annum would have to be made redundant at the end
of 2017 and paid redundancy pay of Rs. 6.2 million each at the end of 2018.
Material costs
The company holds a stock of Material X which cost Rs. 6.4 million last year. There is
no other use for this material. If it is not used the company would have to dispose of it
at a cost to the company of Rs. 2 million in 2017. This would occur early in 2017.
Material Z is also in stock and will be used on the new line. It cost the company Rs. 3.5
million some years ago. The company has no other use for it, but could sell it on the
open market for Rs. 3 million early in 2017.
Further information
The year-end payables are paid in the following year.
The company’s cost of capital is a constant 10% per annum.
It can be assumed that operating cash flows occur at the year end.
Time 0 is 1st January 2017 (t1 is 31st December 2017 etc.)
Required
Calculate the net present value of the proposed new product line (work to the nearest
million).
6.2
HASAN AND SONS LIMITED
Hasan and Sons Limited is considering the purchase of a locally manufactured
machine for Rs. 3 million. In view of the fact that the shares of the company are
not quoted, it finds it difficult to raise money through the issue of shares. The
purchase of this machine becomes absolutely necessary if the sales target given
to the sales manager is to be achieved. In order to ensure that the machine is
purchased, the domineering proprietor of the company and the accountant met
informally to decide on how to source for funds.
Many finance options were considered and they eventually agreed to negotiate
for a loan from Microfinance Bank Ltd. The bank agreed to give the company a
loan of Rs. 2.5 million, which means that the company will have to source for the
balance of Rs.0.5 million elsewhere. However, the company has no tangible
collateral with which to secure additional loan to cover the balance of the value of
the machine. In view of this difficulty, the finance officer offered to advance the
shortfall. The proprietor graciously accepted this offer.
The duration of the loan is 20 years with an interest rate of 12% per annum. The
annual interest charge is to be calculated on the balance outstanding at the
beginning of each year. Repayment is to be made in 20 equal annual
instalments. Each instalment will include both interest and capital. A working
capital of Rs. 250,000 will be required at the beginning of the year. The amount
will be sourced internally. The machine is expected to generate net cashflows of
Rs. 540,000 per annum for FIVE consecutive years from its predominantly local
sales.
Required
(a)
Calculate the amount to be paid in each year on the loan;
(b)
Calculate the NPV of the machine and advise on its viability; and
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Questions
6.3
DCF AND RELEVANT COSTS
Consolidated Oil wants to explore for oil near the coast of Ruritania. The Ruritanian
government is prepared to grant an exploration licence for a five-year period for a fee
of Rs. 300,000 per year. The option to buy the licence must be taken immediately;
otherwise another oil company will be granted the licence.
However if it does take the licence now, Consolidated Oil will not start its explorations
until the beginning of the second year.
To carry out the exploration work, the company will have to buy equipment now. This
would cost Rs. 10,400,000, with 50% payable immediately and the other 50% payable
one year later. The company hired a specialist firm to carry out a geological survey of
the area. The survey cost Rs. 250,000 and is now due for payment.
The company’s financial accountant has prepared the following projected statements
of profit or loss. The forecast covers years 2-5 when the oilfield would be operational.
Projected statements of profit or loss
Year
2
Rs.
‘000
Sales
Minus expenses:
Wages and salaries
Materials and
consumables
Licence fee
Overheads
Depreciation
Survey cost written off
Interest charges
Rs.
‘.000
4
Rs.
‘000
8,300
Rs.
‘000
5
Rs.
‘000
9,800
Rs.
‘000
550
340
580
360
620
410
520
370
600
220
2,100
250
650
300
220
2,100
650
300
220
2,100
650
300
220
2,100
650
–––––
Profit
3
Rs.
‘000
7,400
4,710
–––––
4,210
–––––
4,300
–––––
Rs.
‘000
5,800
4,160
–––––
–––––
–––––
–––––
2,690
4,090
5,500
1,640
–––––
–––––
–––––
–––––
Notes
(i)
The licence fee charge in Year 2 includes the payment that would be made
at the beginning of year 1 as well as the payment at the beginning of Year
2. The licence fee is paid to the Ruritanian government at the beginning of
each year.
(ii)
The overheads include an annual charge of Rs. 120,000 which represents
an apportionment of head office costs. The remainder of the overheads are
directly attributable to the project.
(iii)
The survey cost is for the survey that has been carried out by the firm of
specialists.
(iv)
The new equipment costing Rs. 10,400,000 will be sold at the end of Year
5 for Rs. 2,000,000.
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Business finance decisions
(v)
A specialised item of equipment will be needed for the project for a brief
period at the end of year 2. This equipment is currently used by the
company in another long-term project. The manager of the other project
has estimated that he will have to hire machinery at a cost of Rs. 150,000
for the period the cutting tool is on loan.
(vi)
The project will require an investment of Rs. 650,000 working capital from
the end of the first year to the end of the licence period.
The company has a cost of capital of 10%. Ignore taxation.
Required
Calculate the NPV of the project.
6.4
SADEEQ ENERGY PLC
Sadeeq Energy Plc is a fast growing profitable company. The company is based
in Lahore and has just won a new contract to supply gas to the State Electricity
Board. In this regard, the company planned to commission a 35-kilometre
pipeline at a cost of Rs. 260m to enable it execute the contract. The pipeline,
when installed, will carry the gas to an agreed location under the control of the
State Electricity Board.
The anticipated revenue from sales to the State Electricity Board is expected to
be Rs. 120m per annum.
Apart from this contract, the pipeline could also be used to transport Liquefied
Natural Gas (LNG) to other willing customers in the suburb. The sales from this
source are put at Rs. 80m per annum.
The management of Sadeeq Energy Plc considers the useful life of the pipeline
to be 20 years. The financial manager estimates a profit to sales ratio of 20% per
annum for the first 12 years and 17% per annum for the remaining life of the
project.
The project is not likely to have any salvage value.
Sadeeq Energy Plc will enjoy exemption from tax for this project as a result of a
recent government investment incentive.
The company’s cost of capital is 15%.
Required
(a)
Distinguish between mutually exclusive investment and independent
investment.
(b)
Why is the investment decision important to organizations and what
techniques can be used to ensure that optimal investments are undertaken
by firms?
(c)
Evaluate the project by estimating its payback period?
(e)
Compute the project’s NPV and IRR.
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Questions
6.5
BETA LIMITED
Beta Limited (BL) is engaged in the business of manufacturing and marketing of
high quality plastic products to the large departmental stores in Pakistan and United
Arab Emirates. BL is presently experiencing a decline in sales of its products. Market
research carried out by the Marketing Department suggests that sustained growth
in sales and profits can be achieved by offering a wide range of products rather
than a limited range of quality products. In this regard, BL is considering the following
two mutually exclusive options:
Option I : Introduce low quality products in the market
Following information has been worked out by the Chief Financial Officer of the
company:
Net present value using a nominal discount rate of 13%
Discounted payback period
Rs. 82 million
3.1 years
Internal rate of return
10.5%
Modified internal rate of return
13.2% approximately
Option II : Import variety of plastic products from China
BL would buy in bulk from Chinese suppliers and sell it to the existing customers.
The projected net cash flows at current prices after acceptance of this option are as
follows:
Against import from
China (US$ in million)
From operation in
UAE (US$ in million)
From operations in
Pakistan (Rs. in million)
Year 0
Year 1
Year 2
Year 3
Year 4
(25.00)
(20.00)
(21.33)
(22.33)
(20.67)
-
22.47
24.15
25.23
23.37
333
350
414
450
-
The following information is also available:
(i)
The current spot rate is Re. 1=US$ 0.0111.
(ii)
BL evaluates all its investment using nominal rupee cash flows and a
nominal discount rate.
(iii)
Inflation in Pakistan and USA is expected to be 10% and 3% per annum
respectively.
Tax may be ignored.
Required
Evaluate the two options using net present value, discounted payback period,
internal rate of return and modified internal rate of return. Give brief comments on
each of the above methods of evaluation and their relevance in the given situation.
For the purpose of evaluation, assume that BL has a four year time horizon for
investment appraisal.
© Emile Woolf International
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Business finance decisions
CHAPTER 7 – DCF: TAXATION AND INFLATION
7.1
MORE INVESTMENT APPRAISAL AND TAX
CVB is considering whether to invest in new equipment costing Rs. 600,000. The
equipment is expected to have an economic life of five years and will have no
disposal value at the end of Year 5 (and no disposal costs).
CVB’s after-tax cost of capital is 15%. Tax is charged at an annual rate of 35%
and is payable in the year following the year in which the taxable profits arise.
The following forecasts relate to the project under consideration:
Rs.000s
Year
Sales income
Direct materials
Direct labour
Total direct costs
Depreciation
1
250
50
25
75
120
2
250
55
25
75
120
3
300
58
30
88
120
4
350
64
30
94
120
5
400
70
35
105
120
There will be tax allowances on the cost of the equipment, calculated at 25%
each year on the reducing balance basis. The first depreciation tax allowance
(capital allowance) would be claimed in year 0 (or very early in year 1).
Assume that:
(1)
taxable profits are defined as income minus direct costs and capital
allowances
(2)
cash profits in each year = sales minus direct costs
Required
Calculate the net present value of the project and recommend whether or not the
project should be undertaken.
7.2
INVESTMENT APPRAISAL AND TAX
JKL is considering whether to invest in the purchase of a new machine costing
Rs. 250,000. The machine will have a four-year life and a net disposal value of
Rs. 100,000 at the end of Year 4.
In addition, Rs. 38,000 of working capital will be required from the start of the
project, increasing to Rs. 50,000 at the beginning of the second year. All the
working capital will be recovered at the end of Year 4.
The project is expected to generate extra annual revenues of Rs. 200,000 and
incur annual cash operating costs of Rs. 80,000 for each year of the project.
JKL’s cost of capital is 10% after tax.
Corporation tax is charged on profits at 35%. Tax is payable in the year following
the year in which the profits occur. There will be a 25% annual writing-down
allowance on capital expenditure, for tax purposes. The tax-allowable
depreciation is calculated by the reducing balance method.
© Emile Woolf International
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Questions
Required
Calculate the NPV of the project and state whether or not it should be
undertaken.
7.3
ALAWADA LIMITED
Alawada Limited is considering a five-year project whose initial cost would be Rs.
3million. The contribution consists of annual sales of Rs. 2.8million and variable
costs of Rs. 2million for 1,000,000 units of sales per annum. These are the
expected money values in year 1.
All sales would be made through a single distributor who has asked for a fixed
selling price of Rs. 2.80 per unit for three years after which prices could be
increased by 20% for year 4 and held constant at this new price for years 4 and
5. The variable cost is Rs. 2.00 per unit and it consists of material cost of
Rs.0.80 which is expected to increase by 5% per annum and the balance
represents labour cost which is expected to increase by 10% per annum for each
year. The company’s cost of capital is assumed to be 10%.
Required
7.4
(a)
Calculate the net present value of the project and advise on its viability.
(b)
State TWO features of capital budgeting decision.
(c)
Give FOUR reasons why capital budgeting decision is important.
KOHAT LIMITED
Kohat Limited (KL) is considering to set-up a plant for the production of a single
product IGM3. The initial capital investment required to set up the plant is Rs. 15
billion. The expected life of the plant is only 5 years with a residual value of 20% of
the initial capital investment. The plant will have an annual production capacity of 1.0
million tons.
A local group has offered to purchase all the production for Rs. 8,000 per ton in
year 1 and thereafter at a price to be increased 5% annually. Other relevant
information is as under:
(i)
In year 1, operating costs (other than wages and depreciation) per annum
would be Rs. 2,000 per ton. They are expected to increase in line with
Producer Price Index (PPI). Annual wages would be Rs. 1.0 billion and are
linked to Consumer Price Index (CPI).
(ii)
KL’s cost of capital for this project, in real terms is 6%. General inflation rate
is 11%.
(iii)
The tax rate applicable to the company is 30% and the tax is payable in
the same year. The company can claim normal tax depreciation at 20% per
annum under the reducing balance method.
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Business finance decisions
Price indices of the last six years are given below:
Year
2010
2011
2012
2013
2014
2015
PPI
107
119
130
142
160
175
CPI
112
125
139
155
173
195
The costs linked to the above indices are expected to grow at their historic
compound annual growth rate.
Required
Advise whether KL should invest in the project.
7.5
JAP RECREATION CLUB
The management of JAP Recreation Club is evaluating the option to launch a
restaurant that would serve complete meal to its members. Presently, it has a
snack bar shop which sells snacks and drinks only.
A management consultant firm was hired at a fee of Rs. 85,000 to prepare the
feasibility of the project. JAP’s Accountant has extracted the following information
from the consultant’s report:
(i)
The restaurant will be launched on the first day of the next year.
(ii)
The club membership has been increasing at the rate of 5% per annum.
As a result of this facility, it is expected that the rate would increase to 10%
per annum.
(iii)
The cost of equipment for the restaurant is estimated at Rs. 7,000,000.
It would have a residual value of Rs. 510,000 at the end of its estimated
useful life of four years.
(iv)
It is estimated that during the first year, an average of 100 customers
would visit the restaurant, per day. The number would increase in line with
the increase in membership. The average revenue from each customer is
estimated at Rs. 400 whereas variable costs per customer would be Rs.
260.
(v)
Four employees would be appointed in the first year at an average salary
of Rs. 200,000 per annum. A fifth employee would be hired from the third
year.
(vi)
The annual fixed overheads for the current year are estimated at Rs. 4.8
million. 15% of the fixed overheads are allocated to the snack bar. As a
result of the establishment of the restaurant the annual expenditure would
increase as follows:
Rupees
Electricity and gas
340,000
Advertising
170,000
Repair and maintenance
© Emile Woolf International
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Questions
After the establishment of restaurant, 20% of the overheads would be
allocated to the restaurant whereas allocation to snack bar would reduce to
10%.
(vii) The snack bar is presently serving an average of 250 customers per day
and the number is increasing in proportion to the number of members. If
the restaurant is launched, the number of customers would reduce by 40%
in the first year but would continue to increase in subsequent years in line
with the member base. The average contribution margin from snack bar is
Rs. 50 per customer.
(viii) The tax rate applicable to the company is 35% and it is required to pay
advance tax in four equal quarterly instalments. JAP can claim tax
depreciation at 25% under the reducing balance method. Any taxable
losses arising from this investment can be set off against profits of other
business activities.
(ix)
JAP’s post tax cost of capital is 17% per annum before adjustment for
inflation. The rate of inflation is 10%.
Required
Advise whether JAP should invest in the project. Assume that each year has 360
days.
7.6
ARG COMPANY
ARG Company is a leisure company that is recovering from a loss-making venture into
magazine publication three years ago. Recent financial statements of the company are
as follows.
Statement of profit or loss for the year ending 30 June 20X5
$000
140,400
Sales revenue
Cost of sales
112,840
–––––––
27,560
Gross profit
Administration costs
23,000
––––––
4,560
900
––––––
3,660
Profit before interest and tax
Interest
Profit before tax
Tax
1,098
––––––
2,562
––––––
400
Profit after tax
Dividends paid
Retained profit
© Emile Woolf International
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––––––
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Business finance decisions
Statement of financial position as at 30 June 20X5
$000
Non-current assets
$000
50,000
Current assets
Inventory
Receivables
2,400
20,000
Cash
1,500
––––––
23,900
––––––
73,900
––––––
Equity and liabilities
Ordinary shares, $1 par value
2,000
Capital reserves
27,000
Accumulated profits
1,900
––––––
30,900
9% Bonds (redeemable in 9 years)
Current liabilities
10,000
33,000
––––––
73,900
––––––
The company plans to launch two new products, Alpha and Beta, at the start of July
20X5, which it believes will each have a life-cycle of four years. Alpha is the deluxe
version of Beta. The sales mix is assumed to be constant.
Expected sales volumes for the two products are as follows.
Year
1
2
3
4
Alpha
60,000
110,000
100,000
30,000
Beta
75,000
137,500
125,000
37,500
The standard selling price and standard costs for each product in the first year will be
as follows.
Product
Direct material costs
Incremental fixed production costs
Standard mark-up
Selling price
© Emile Woolf International
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Alpha
Beta
$/unit
$/unit
12.00
8.64
––––––
20.64
10.36
––––––
31.00
––––––
9.00
6.42
––––––
15.42
7.58
––––––
23.00
––––––
The Institute of Chartered Accountants of Pakistan
Questions
ARG Company traditionally operates a cost-plus approach to product pricing.
Incremental fixed production costs are expected to be $1 million in the first year of
operation and are apportioned on the basis of sales value. Advertising costs will be
$500,000 in the first year of operation and then $200,000 per year for the following two
years. There are no incremental non-production fixed costs other than advertising
costs.
In order to produce the two products, investment of $1 million in premises, $1 million in
machinery and $1 million in working capital will be needed, payable at the start of July
20X5. The investment will be financed by the issue of $3 million of 9% debentures,
each $100 debenture being convertible into 20 ordinary shares of ARG Company after
8 years or redeemable at par after 12 years.
Selling price per unit, direct material cost per unit and incremental fixed production
costs are expected to increase after the first year of operation due to inflation:
Selling price inflation: 3% per year
Direct material cost inflation: 3% per year
Fixed production cost inflation: 5% per year
These inflation rates are applied to the standard selling price and standard cost data
provided above. Working capital will be recovered at the end of the fourth year of
operation, at which time production will cease and ARG Company expects to be able
to recover $1.2 million from the sale of premises and machinery. All staff involved in
the production and sale of Alpha and Beta will be redeployed elsewhere in the
company.
ARG Company pays tax in the year in which the taxable profit occurs at an annual rate
of 25%. Investment in machinery attracts a first-year capital allowance of 100%. ARG
Company has sufficient profits to take the full benefit of this allowance in the first year.
For the purpose of reporting accounting profit, ARG Company depreciates machinery
on a straight line basis over four years. ARG Company uses an after-tax discount rate
of 13% for investment appraisal.
Other information
Assume that it is now 30 June 20X5
The ordinary share price of ARG Company is currently $4.00
Average interest cover for ARG Company’s sector is 7.0 times.
Average gearing for ARG Company’s sector is 45% (long-term debt/equity using book
values)
Required
(a)
Calculate the net present value of the proposed investment in products
Alpha and Beta.
(b)
Identify and discuss any likely limitations in the evaluation of the proposed
investment in Alpha and Beta.
(c)
Evaluate and discuss the proposal to finance the investment with a $3
million 9% convertible debenture issue.
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7.7
HAFEEZ LTD
Hafeez Ltd is planning to bid for a contract to supply a machine under an operating
lease arrangement, for 5 years. The terms of proposed contract include a special
arrangement whereby the supplier / lessor will have to operate and maintain the
machine, during the term of lease. Hafeez Ltd is required to quote a consolidated
annual fee consisting of lease rentals and operating changes which shall be payable in
arrears. The following relevant information is available:
(i)
The cost of machine is Rs. 50 million and the expected useful life is 10
years. The residual value at the end of five years is estimated to be 25% of
the cost of machine.
(ii)
Operating cost for the first year is estimated at Rs. 6 million and is expected
to increase at the rate of 10% per annum.
(iii)
The tax rate applicable to the company is 35% and the tax is payable in the
same year. The company can claim initial and normal depreciation at 25%
and 10% respectively under the reducing balance method.
(iv)
The weighted average cost of capital of the company is 14%.
Required
(a)
Calculate the annual consolidated fee to be quoted for the contract if the
company’s target is to achieve a pre-tax net present value of 15% of total
capital outlay.
(b)
Using the fee quoted above, calculate the project’s internal rate of return
(IRR) to the nearest percent
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Questions
CHAPTER 8 – DCF: RISK AND UNCERTAINTY
8.1
RISK IN INVESTMENT APPRAISAL
East must purchase a new machine for making a new product. There is a choice
between two machines, Machine A and Machine B. Each machine has an
estimated life of three years with no expected scrap value.
Machine A costs Rs. 15,000 and Machine B costs Rs. 20,000.
The variable costs of manufacture would be Rs. 1 per unit of Machine A is used
and Rs.0.50 per unit if Machine B is used. The product will sell for Rs. 4 per unit.
The demand for the product is uncertain. Following some market research, the
following estimates of annual sales demand have been made:
Annual demand
Probability
Units
2,000
0.2
3,000
0.6
5,000
0.2
The sales demand in each year will be the same. For example, if the demand is
2,000 units in Year 1, it will be 2,000 units for every year of the project.
Taxation and fixed costs will be unaffected by any decision made.
East’s cost of capital is 6%.
Required
8.2
(a)
Calculate the NPV for each of investment options, Machine A and Machine
B, for each of the possible levels of sales demand.
(b)
Calculate the expected NPV for each of the investment options.
(c)
Assume now that the decision is taken to buy Machine A.
(i)
Calculate the probability that the NPV of the project will be negative
(ii)
Calculate the minimum annual sales required for the NPV of the
project to be positive.
CALM PLC
Calm Plc designs and manufactures Personal Stress-Monitoring Device (PSMD).
The device is designed for checking individuals’ stress levels. A typical device
has a commercial life of three years.
Recently, the company developed a new device known as “SIMPLE” and paid
Rs. 10 million as development cost.
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The following projections were made in respect of the product “SIMPLE”:
Sales Revenue
Probability
Year 1
Rs. m
Year 2
Rs. m
Year 3
Rs. m
If demand is above average
0.25
240
500
160
If demand is average
If demand is below average
0.60
0.15
140
50
340
180
80
50
Variable costs will amount to 30% of sales. Sales revenue and variable cost will
be received and paid respectively on the last day of the year in which they arise.
If “SIMPLE” is produced, a special machine will have to be purchased at the
beginning of Year 1 at a cost of Rs. 190 million, payable at the time of purchase.
The machine will have a scrap value of Rs. 10 million at the end of the product’s
life. The amount is receivable one year after the last year in which production
takes place. If purchased, the machine will be installed in an unused part of one
of Calm Plc.’s factories. The company has been trying to let this unused factory
space at a rent of Rs. 16 million per annum. Although, there seems to be no
chance of letting the space in year 1, there is a 60% chance of letting it for two
years at the beginning of year 2 and a 50% chance of letting it for one year at the
beginning of year 3 provided it has not been let at the beginning of year 2. All
rental income will be received annually in advance. Fixed costs, which include
depreciation of the special machine on a straight-line basis, are expected to
amount to Rs. 70 million per annum.
These costs which are all specific to the production of “SIMPLE” and will be paid
on the last day of the year in which they arise with the exception of depreciation,
Advertising expenses will be paid on the first day of each year and will amount to
Rs. 30 million at the start of year 1, Rs. 20 million at the start of year 2 and Rs. 10
million at the start of year 3. Calm Plc. has a cost of capital of 20%.
Required
Analyse and evaluate the production of “SIMPLE” based on expected present
value. (Show all relevant calculations).
8.3
OUTLOOK PLC
Outlook Plc is considering a new project for which the following information is
relevant:
‰
Initial investment of Rs. 350,000 with nil scrap value.
‰
Expected life span of 10 years
‰
Sales volume - 20,000 units per annum
‰
Selling price - Rs. 20 per unit
‰
Direct variable cost of Rs. 15 per unit
‰
Fixed cost excluding depreciation of Rs. 25,000 per annum.
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Questions
The project has IRR of 17%.
The company’s hurdle rate of 15%.
Required
(a)
(b)
8.4
Compute the sensitivity of the NPV to each of the underlisted variables:
(i)
Sales price
(ii)
Initial outlay
(iii)
Sales volume
(iv)
Variable cost
(v)
Fixed cost
State the TWO most sensitive variables
ZAHEER LTD
Zaheer Ltd is a manufacturer of auto parts and is currently operating at below capacity
due to slump in the demand for automobiles. The company has received a proposal
from a truck assembler for supply of 40,000 gear boxes per annum for five years at Rs.
1,900 per gear box.
The cost of each gear box is as follows:
Rupees
800
500
150
200
150
1,800
Material costs
Labour costs
Variable production overheads
Variable selling overheads
Fixed overheads (allocated)
Company has already incurred a cost of Rs. 5 million on the preparation of technical
feasibility. The additional cost for setting up the facility for this order would be Rs. 20
million. The company qualifies for tax allowable depreciation on the cost of setting up
the facility on a straight-line basis over the life of the project.
The company has a post-tax cost of capital of 15%. The rate of tax applicable to the
company is 30%.
Required
(a)
Evaluate whether the proposal is financially feasible for the company.
Assume that revenue and cost of gear box will remain the same during the
next five years.
(b)
Carry out a sensitivity analysis to determine which of the following variables
is most sensitive to the feasibility of the order:
‰
Material costs
‰
Labour costs
‰
Additional cost of setup
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8.5
JKL PHONE LIMITED
JKL Phone Limited is a cellular service provider. The Marketing Director has
recently proposed a marketing strategy which envisages the introduction of a new
package for pre- paid customers, to gain market share. He has carried out a
market research and suggests that the call rates forming part of the proposed
package should either be Re. 0.75 or Re. 1.00 or Rs. 1.25 per minute.
Based on market research, sales demand at different levels of economic growth is
estimated as follows:
Call Rates
Probability
Rs. 0.75
Re. 1
Rs. 1.25
Subscribers in million
Recession
0.30
0.70
0.50
0.30
Moderate
0.50
0.80
0.60
0.40
Boom
0.20
0.90
0.80
0.60
He foresees that the average airtime usage per subscriber would be 1800 minutes or
1600 minutes with a probability of 40% and 60% respectively. In order to cater to the
increased subscriber base, the company would need to commission new cell sites,
details of which are as follows:
No. of subscribers (in million)
Cost of new sites (Rs. in million)
Up to 0.5 million
180.00
Between 0.5 – 0.8 million
300.00
Between 0.8 – 1.0 million
540.00
It is assumed that the present customers of the company would continue to use the
existing packages.
Required
Evaluate the proposal submitted by the Marketing Director and advise the most
suitable call rates.
8.6
KHAYYAM LIMITED (KL)
The directors of Khayyam Limited (KL) are considering an investment proposal
which would need an immediate cash outflow of Rs. 500 million. The investment
proposal is expected to have two years economic life with salvage value of Rs. 50
million at the end of second year.
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Questions
KL’s Budget and Planning Department anticipates that Net Cash Inflows After Tax
(NCIAT) are dependent on exchange rate of the US $ and has made the following
projections:
Exchange Rate
Exchange Rate
Exchange Rate
Rs. 84-87
Rs. 88-91
Rs. 92-95
NCIAT
Probability
NCIAT
Probability
NCIAT
Probability
250
65%
320
35%
-
-:
If Year 1
exchange
rate is
Rs. 84-87
280
20%
330
65%
360
15%
If Year 1
exchange
rate is
Rs. 88-91
340
5%
380
50%
400
45%
Year 1
Year 2
−
−
All NCIATs are in millions of rupees
KL uses a 14% discount rate for investments having similar risk levels.
Required
(a)
Draw a decision tree to depict the above possibilities.
(b)
Determine whether it would be advisable for Khayyam Limited to undertake
this project.
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Business finance decisions
CHAPTER 9 – DCF: SPECIFIC APPLICATIONS
9.1
LEASE OR BUY
A company is considering whether to acquire a new machine. The machine has a
purchase cost of Rs. 30,000, an expected useful life of five years and a disposal
value of Rs. 6,000 at the end of year 5. The machine would generate additional
cash flows of Rs. 10,000 in each of its five years.
Two methods of financing are under consideration:
(i)
To buy the machine with money obtained from a bank loan, at an interest
rate of 8% after tax.
(ii)
To lease the machine. The lease payments to the lessor would be Rs.
7,000 at the end of each of the next five years.
The company's cost of capital is 10% after tax.
Corporation tax is 30%. If the machine is purchased, the company will be able to
claim capital allowances (tax depreciation allowances) of 25% each year on a
reducing balance basis. Tax is payable at the end of the year following the year
in which the profits are earned. The first capital allowance would be claimed
against profits earned during Year 1.
Required
9.2
(a)
Recommend whether the machine should be acquired.
(b)
If your recommendation is to acquire the machine, recommend whether it
should be purchased or leased.
MOHANI LIMITED
Mohani Limited (ML) has decided to acquire an additional machine to augment
its production. The cost of the machine is Rs. 3,200,000 and the expected useful life
of the machine is 5 years. The salvage value at the end of its useful life is
estimated at Rs. 400,000.
To finance the cost of machine, the company is considering the following options:
(A)
Enter into a leasing arrangement on the following terms:
Lease term
5 years
Security deposits
10% of the cost of machine
Insurance costs
payable by lessor
Installment
Rs. 860,000 payable annually at the
beginning of the year.
Purchase Bargain Option
At the end of lease term against
security deposit.
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Questions
(B)
Obtain a 5 year bank loan at an interest of 11% per annum. The loan
including interest would be repayable in 5 equal annual instalments to be
paid at the end of each year.
The company plans to depreciate the machine using straight-line method. The
insurance premium is Rs. 96,000 per annum. The corporate tax rate is 35%. For
the purpose of taxation, allowable initial and normal depreciation is 50% and 10%
respectively under the reducing balance method. The weighted average cost of capital
is 14%.
Required
Which of the two methods would you recommend to the management? Show all
relevant calculations.
9.3
DS LEASING COMPANY LIMITED
DS Leasing Company Limited has been approached by BP Industries Limited,
with a request to arrange a 4-year lease contract in respect of a state of the art
machine. The cost of machine is Rs. 20 million and the expected useful life is 4
years. The residual value at the end of lease term is estimated at 10% of cost.
DS would finance the purchase of machine by borrowing at 16% per annum. The
interest would be payable annually and the principal amount would have to be repaid
in four equal annual instalments commencing from the end of first year.
DS provides free-of-cost maintenance services for all its leased assets. These
services are provided by the company’s Maintenance Department whose costs are
mostly fixed. If BP acquires this service from any other vendor, it would have to pay
an annual fee of 3% of the cost of machine. Insurance cost will be borne by BP and
is estimated at 4% of the cost of machine.
The tax rate applicable to both companies is 35% and the tax is payable in the next
year. Allowable initial and normal deprecation on the machine is 25% and 10%
respectively. The weighted average cost of capital of DS and BP are 18% and 20%
respectively.
Both companies follow the same financial year. It may be assumed that the
purchase would be finalized on the last day of the financial year.
Required
(a)
Calculate the annual rental (payable in advance) which DS should charge
in order to break even on the lease contract.
(b)
Assume that BP has the following two options for financing the cost of
machine:
(i)
DS has offered to lease the machine at an annual rental of
Rs. 7 million, payable in advance.
(ii)
EFT Bank has offered to finance the machine at 18% per
annum. The loan including interest would be repayable in 4 equal
annual installments to be paid at the end of each year. Insurance
costs would be borne by BP.
Determine which course of action BP should follow.
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9.4
HIN TEXTILE MILLS LIMITED
In order to reduce the cost of electricity consumption, HIN Textile Mills Limited has
decided to install a gas generator and discontinue the power supply being obtained
from a utility company. The gas generator which would meet their requirements
would cost Rs. 80 million. The following two proposals are being considered by HIN:
Option 1: Offer from BAL Leasing Company Limited
BAL has offered a three year lease at a quarterly rent of Rs. 7.46 million payable
in arrears. In addition, HIN would be required to pay a security deposit of Rs. 10
million at the time of signing the lease agreement. Generator will be transferred to
HIN at the end of the lease term, against the security deposit.
The fair value of the generator, at the end of lease period is estimated at Rs. 20
million. Operating and maintenance costs of the generator are estimated as follows:
Costs
Staff salary
Lubricants and filters
Parts replacement
Overhaul
Frequency
Rs. in million
Monthly
Quarterly
Half yearly
At the end of 2nd year
0.50
1.00
3.00
15.00
Option 2 : Offer from PUS Rental Services
PUS has also offered to sign a three year contract according to which HIN would
pay quarterly rent of Rs. 11 million in arrears, with a 10% increase in each
subsequent year. The lease rental would include the cost of maintenance and
overhauling of the generator, which will be borne by PUS.
It may be assumed that HIN’s cost of capital is equal to the IRR offered by BAL.
Required
Evaluate which of the above proposals should be accepted by HIN. (Ignore taxation)
9.5
CRANK PLC
The Board of Directors of Crank Plc. is concerned about the optimal replacement
cycle of one of its equipment. The initial outlay required to purchase a new
equipment is Rs. 1.5million. The longer the asset is held, the higher the
operating and maintenance costs and the lower the residual value. Relevant
data on the various cost items relating to the equipment are given below:
Year
0
Initial outlay (Rs.’000)
Operating and Maintenance Cost (Rs.’000)
Residual value (Rs.’000)
Cost of Capital is 10%
1
2
3
600
750
750
600
1500
300
1,050
Required
Determine the optimal period of replacing the equipment using the annual
equivalent cost method.
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Questions
9.6
ASSET REPLACEMENT
A business entity is considering its policy for the replacement of machines. One
type of machine in regular use is machine X. This machine has a maximum
useful life of four years, but maintenance costs and other running costs rise with
use. An estimate of costs and disposal values is as follows:
Machine X: Purchase cost Rs. 40,000
Year
Maintenance costs and
other running costs in the year
Disposal value
at the end of the year
Rs.
8,000
12,000
20,000
25,000
1
2
3
4
Rs.
25,000
20,000
10,000
0
The cost of capital is 10%.
Required
Calculate the equivalent annual cost of a replacement policy for the machine of
replacement:
(a)
every one year
(b)
every two years
(c)
every three years
(d)
every four years.
Recommend a replacement policy for the machine.
9.7
ROTOR PLC
Rotor Plc is considering investment in a computer-controlled machine which can
be replaced by an identical one when it gets to the end of its economic life. The
machine has a maximum life of four years but, as its productivity declines with
age, it could be replaced after either one, two, three or four years. The financial
details of the machine are as given below:
Cost
Running cost:
Year
Scrap value after:
Year
© Emile Woolf International
Rs.’000
6,000,000
1
2
3
4
450,000
480,000
570,000
630,000
1
2
3
4
4,500,000
3,900,000
3,000,000
2,100,000
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The Institute of Chartered Accountants of Pakistan
Business finance decisions
The board of directors of Rotor Plc is concerned with deciding on its replacement
policy.
As the financial manager of the company, you are required to advise the board
on the optimal replacement policy of the machine assuming that the company’s
cost of capital is 10%.
9.8
UVW RENTAL SERVICES
UVW Rental Services, a partnership concern, is in the business of providing power
back- up solutions to its corporate clients. At present, it is the policy of the company
to replace the old power generators with the new ones after every three years.
During a recent management meeting, the operation manager informed that a
350KVA generator has reached its replacement period. He suggested that since the
replacement cost of this generator has significantly increased due to depreciation
of rupee, the company should not dispose of the generator at the end of its
replacement period and rather get it overhauled and continue.
Following information relating to the generator is available:
(i)
Cost
Written
Down Value
Estimated
Cost of
Overhauling
Current
Disposal
Value
Replacemen
t
Cost
945,000
5,250,000
Amount in Rupees
3,900,000
(ii)
1,750,000
2,200,000
It is expected that after overhauling:
‰
the generator can be used for another two years. However, running
cost of overhauled generator would be Rs. 440 per hour which is
10% higher in comparison with the running cost of the new
generator.
‰
the overhauled generator would be sold after two years at a value of
15% of current replacement cost while the new generator is expected
to fetch 25% of current replacement value, after three years.
(iii)
The company rents out the generator at Rs. 2,000 per hour and such
generators are hired for approximately 2,500 hours per annum, irrespective
of their age.
(iv)
The company’s cost of capital is 17% per annum before adjustment for
inflation. The rate of inflation is 8%.
(v)
The company receives all payments after deduction of tax at the rate of 6%
which is considered full and final settlement of it’s tax liability.
Required
(a)
Advise whether the management should replace the generator or
overhaul and continue to use the existing one.
(b)
Calculate the percentage change in estimated cost of overhauling at
which the management would be indifferent between the two options.
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Questions
CHAPTER 10 – EVALUATING FINANCIAL PERFORMANCE
10.1
EQUITY RATIOS
The following figures have been extracted from the annual accounts of Rainy:
Issued share capital: 1,000,000 ordinary shares of Rs. 1 each, fully paid.
Issued debt capital: Rs. 250,000 10% debentures.
Reserves
Capital (share premium reserve)
Accumulated profits
Rs. 200,000
Rs. 800,000
Profit and distributions
Profit for the year
Rs. 600,000 (before interest and tax)
Ordinary dividend payments
Rs.0.20 per share
The current market price of Rainy’s equity shares is Rs. 3.20 each. Its
debentures are priced at Rs. 90 per cent. The company’s rate of corporation tax
(income tax) is 30%.
Required
Calculate the ratios that are likely to be of interest to an investor or potential
investor in Rainy.
Comment on each.
10.2
AYELAND AND ZEDLAND
An important client has asked you to review the performance of two overseas
companies in which he is thinking of investing. Both companies are claiming to
have been successful during the last four years.
One company is located in the country of Ayeland, the other in Zedland.
Company 1 in
Ayeland
Revenue
Profit after tax
Share price (lire)
Lire (million)
20X0
20X1
20X2
20X3
432
55
567
76
693
102
810
126
1,058
1,330
1,620
2,001
Equity beta
Company 2 in
Zedland
Revenue
Profit after tax
Share price (francs)
1·55
Francs (000)
20X0
20X1
20X2
20X3
12,000
12,430
13,100
14,569
1,840
2,004
2,320
2,540
236
192
204
229
Equity beta
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Data for the two
countries:
Ayeland
20X0
Retail price
(inflation) index
Stock market index
Risk free rate
Zedland
Retail price
(inflation) index
Stock market index
20X1
450·3
610·2
20X2
20X3
773·1
924·2
5,005
6,002
7,450
20X0
20X1
20X2
9,470
19%
20X3
104·3
8,896
107·1
9,320
110·8
9,457
100
10,200
Risk free rate
4%
The equity betas and the risk free rate were estimated over the period 20X0–
20X3.
Required
10.3
(a)
Prepare a report for the client discussing the performance of the two
companies. Relevant calculations should be included in the report.
(b)
Discuss what other information would be useful to assess the performance
of the two companies.
KHAN INDUSTRIES PLC
The directors of two divisions of Khan Industries plc were each asked last year to
improve their division's performance.
Summarised financial data at that time for the two divisions is shown below.
Revenue
Division
A
Division
B
Rs.'000
Rs.'000
840
610
Operating profit
Interest
95
6
78
8
Taxable profit
89
70
Non-current assets
Current assets
Current liabilities
580
290
210
430
250
180
Medium and long term debt
Shareholders' equity
40
620
55
445
Capital employed
660
500
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Questions
The results for the current year have just been announced as:
Division
A
Division
B
Rs.'000
Rs.'000
1,000
650
Operating profit
Interest
122
18
94
8
Taxable profit
104
86
Non-current assets
Current assets
Current liabilities
680
350
260
440
240
170
Medium and long term debt
Shareholders' equity
140
630
55
455
Capital employed
770
510
Revenue
Required
Analyse the performance of the two divisions, and from the perspective of the
future strategic development of Khan Industries suggest what controls the
directors of Khan Industries might introduce to influence the future development
of the divisions.
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Business finance decisions
CHAPTER 11 – CAPITAL RATIONING
11.1
CAPITAL RATIONING
A company has identified five investment projects that it would like to undertake.
None of the investments can be delayed. If they are not undertaken now, the
opportunity to invest will be lost. Details of the five investments are as follows:
Capital investment
required in Year 0
NPV of the investment
Rs.
Rs.
A
60,000
12,000
B
C
80,000
50,000
21,600
8,500
D
45,000
10,800
E
55,000
9,900
Investment
Capital is in short supply, and only Rs. 150,000 is available for investment. The
company cannot therefore undertake all five investments.
Required
In order to maximise the total NPV of its investments, recommend which
investments to undertake:
11.2
(a)
assuming that all five investment projects are divisible.
(b)
assuming that none of the five investments is divisible, and the choice is
either 0% and 100% of each investment.
BASRIL COMPANY
Basril Company is reviewing investment proposals that have been submitted by
divisional managers. The investment funds of the company are limited to Rs.
800,000 in the current year. Details of three possible investments, none of which
can be delayed, are given below.
Project 1
An investment of Rs. 300,000 in work station assessments. Each assessment
would be on an individual employee basis and would lead to savings in labour
costs from increased efficiency and from reduced absenteeism due to workrelated illness. Savings in labour costs from these assessments in money terms
are expected to be as follows:
Year
1
2
3
4
5
Cash flows (Rs.000)
85
90
95
100
95
Project 2
An investment of Rs. 450,000 in individual workstations for staff that is expected
to reduce administration costs by Rs. 140,800 per annum in money terms for the
next five years.
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Questions
Project 3
An investment of Rs. 400,000 in new ticket machines. Net cash savings of Rs.
120,000 per annum are expected in current price terms and these are expected
to increase by 3.6% per annum due to inflation during the five-year life of the
machines.
Basril Company has a money cost of capital of 12% and taxation should be
ignored.
Required
(a)
11.3
Determine the best way for Basril Company to invest the available funds
and calculate the resultant NPV:
(i)
on the assumption that each of the three projects is divisible
(ii)
on the assumption that none of the projects are divisible.
(b)
Explain how the NPV investment appraisal method is applied in situations
where capital is rationed.
(c)
Discuss the reasons why capital rationing may arise.
CB INVESTMENT LIMITED
CB Investment Limited (CBIL) has identified various projects for investments.
Details of the projects are as follows:
Projects
A
B
C
D
E
F
(300)
(120)
(240)
(512)
(800)
(400)
Forecasted annual net cash
inflows (Rs. in million)
150
50
140
256
440
300
Discount rate (based on risk
involved in the project)
10%
11%
12%
11%
13%
14%
Project duration (years)
4
5
3
6
3
2
Year from which net cash
inflows would commence
1
2
1
3
1
1
Initial investment required
now (Rs. in million)
Other relevant information is as follows:
(i)
Project A and B are mutually dependent and are non-divisible.
(ii)
Project C can be scaled down but cannot be scaled up.
(iii) Project D, E and F are mutually exclusive. They cannot be scaled down but
can be scaled up.
Total financing available with the company is Rs. 1,000 million. It may be
assumed that all cash flows would arise at the beginning of the year.
Required
Determine the most beneficial investment mix.
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CHAPTER 12 – SOURCES OF FINANCE
12.1
RIGHTS
A company wishes to increase its production capacity by purchasing additional
plant and equipment. To finance the new investment, the company will make a 1
for 4 rights issue. The shares are currently quoted on the Stock Exchange at Rs.
5.50 per share and the new shares will be offered to shareholders at Rs. 4.50 per
share.
Ignore the transaction costs of the share issue.
Required
Calculate:
12.2
(a)
the theoretical ex-rights price per share.
(b)
the value of the rights on each existing share.
KAMALIA CARRIERS PLC
(a)
Explain the term “rights issue”.
(b)
Differentiate between “rights issue” and “public issue”.
(c)
(i)
(ii)
Kamalia Carriers Plc is about to make a one-for-three rights issue. Its
current capital structure is as follows:
‰
6 million Ordinary shares of Rs. 1 each (current market value is
Rs. 6.20 per share)
‰
15% Debentures (Redeemable at par in 10 years time) – Rs. 6
million.
The money raised from the rights issue may be used to execute the
following;
‰
Buy back all the 15% debentures at their current market value.
It is expected that this investment will be priced to offer
investors a yield of 9% which is the current market-yield on
debenture loan.
‰
Finance a new project costing Rs. 1.6 million.
Required
(i)
Determine the finance required to redeem the debentures and finance
the new project.
(ii)
Determine the issue price per share;
(iii)
Calculate the theoretical ex-rights price; and
(iv)
Calculate the theoretical nil paid value of a right per share
Note:
The total finance required for (i) and (ii) should be rounded up to the next Rs.
100,000 for the purpose of the rights issue.
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Questions
12.3
RIGHTS ISSUE
Smeaton Furniture wishes to increase its production capacity by purchasing
additional plant and equipment at a cost of Rs. 3.8 million. The abridged profit
and loss account for the year ended 30th November 20X6 is as follows:
Rs. m
Sales turnover
140.6
Profit before interest and taxation
8.4
Interest
6.8
Profit before tax
1.6
Tax
0.4
Profit after taxation
1.2
Earnings per share
15 cents
In order to finance the purchase of the new plant and equipment, the directors of
the company have decided to make a rights issue equal to the cost of the
equipment. The shares are currently quoted on the Stock Exchange at Rs. 2.70
per share and the new shares will be offered to shareholders at Rs. 1.90 per
share.
Required
(a)
(b)
12.4
12.5
Calculate:
(i)
the theoretical ex-rights price per share
(ii)
the value of the rights on each existing share
(iii)
assuming the increase in production capacity will lead to an increase
in profit after tax of Rs. 600,000 per annum and the P/E ratio of the
company will remain unchanged after the rights issue, calculate the
market value per share after the rights issue.
What are the options available to a shareholder who receives a rights offer
from a company?
STOCK EXCHANGE LISTING
(a)
Outline the advantages and disadvantages of obtaining a stock exchange
listing.
(b)
What are the types of issue costs that are associated with obtaining a stock
exchange listing?
CONVERTIBLE BONDS
A company has the following equity shares and bonds in issue:
2,000,000 equity shares of Rs.0.50 each.
Rs. 1,000,000 of 4% convertible bonds.
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The current earnings per share (EPS) is Rs.0.25.
The rate of tax is 30%.
The convertible bonds are convertible into equity shares at the rate of 40 shares
for every Rs. 100 of bonds.
Required
On the basis of this information, calculate the expected change in EPS if all the
bonds are converted into equity shares.
12.6
SHOAIB INVESTMENT COMPANY
Shoaib Investment Company Limited is a listed company having a share capital
of Rs. 1,000 million consisting of 100 million shares of Rs. 10 each.
The company’s net equity at book value, as of March 31, 2016 was Rs. 2,000
million.
The company maintains a debt equity ratio of 70:30 based on market value. Long
term debt constitutes 90% of total liabilities of the company.
It is the policy of the company to invest 60% of its total assets in listed
securities. The correlation between the market value of these listed securities
held by the company and KSE-100 Index is 1.1.
On March 31, 2016, the company’s shares were traded at price to book value
ratio (P/B ratio) of 1.4.
During the quarter April 1, 2016 to June 30, 2016, KSE-100 Index fell by 20%.
This fall in the index also affected the market price of the company’s shares and
as of June 30, 2016, they were being traded at P/B ratio of 0.9. There was no
significant change in the amount of liabilities and other assets of the company,
during the quarter.
Required
12.7
(a)
Compute the amount of fresh equity required to be injected as of June 30,
2016 in order to maintain the debt equity ratio.
(b)
The company has been approached by Mr. Alam, a large investor, who has
offered to provide the required capital as computed in (a) above at a
discount of 10% of market value. Compute the % holding of Mr. Alam in the
company, if his proposal is accepted.
SAJAWAL SUGAR MILLS LIMITED
Sajawal Sugar Mills Limited (SSML), a medium sized listed company, is planning
to expand its production capacity. The management has estimated that the
expansion would require an outlay of Rs. 300 million.
Following figures have been extracted from SSML’s financial statements for the
year ended June 30, 2016.
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Statement of financial position
Rs. in million
Paid up capital (Rs. 10 each)
400
Retained earnings
150
Non-current liabilities
600
Current liabilities
100
1,250
Fixed assets
1,100
Current assets
150
1,250
Statement of comprehensive income
Rs. in million
Net profit after tax
125
EPS
3.13
To finance the expansion, SSML is considering a right issue. However, the
management of SSML wants to maintain its existing debt equity ratio, return on total
assets ratio and dividend payout percentage. Moreover, they wish to keep the exright price to be the same as current market price.
SSML follows a policy of retaining 30% of its profits. The current market price of its
shares is Rs. 20 whereas its share price beta is 1.23. Presently, market return is
16% whereas yield on one year treasury bills is 12%. Market is assumed to be
strong form efficient.
Required
Under the circumstances referred to in the above situation, what should be:
12.8
(a)
The right ratio
(b)
The right offer price
(c)
Theoretical ex-right price
(d)
Value of each right
PSD ENGINEERING LIMITED
The Directors of PSD Engineering Limited, a listed company, are planning to raise
Rs. 100 million for a new project. They are considering two possible options of fund
raising. The first is to make a two-for-five right issue of ordinary shares priced at
Rs. 12.50 per share. The second option is to issue 9% Term Finance Certificates
(TFCs) at par, redeemable in 2026.
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The following information has been extracted from the financial statements of PSD
for the year ended March 31, 2016:
Rs. in million
Issued ordinary shares Rs. 10 each
200
Retained earnings
390
590
10% TFCs at par, repayable in 2018
350
940
The shares of the company are currently traded at Rs. 16 per share. The profit before
interest and taxation of PSD for the year ended March 31, 2016 is Rs. 95 million.
It is expected that the right issue will not affect PSD’s current price earnings ratio.
However, the issue of TFCs would result in fall in price earnings ratio by 30%.
The tax rate applicable to the company is 35%.
Required
(a)
Make appropriate calculations in each of the following independent
situations:
(i)
(b)
Assuming a right issue of shares is made, calculate:
‰
the theoretical ex-rights price of an ordinary share.
‰
the value of the right.
(ii)
Assuming the market is strong form efficient and it is expected that
new project would generate positive net present value of Rs. 96
million. Calculate the theoretical ex-right price in this case.
(iii)
Assuming that the new project would increase the company’s
profit before interest and tax for the next year by 10%. Calculate the
price of an ordinary share in one year’s time under each of the two
financing options.
Briefly discuss why issue of term finance certificates is expected to result in
fall in price earnings ratio.
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Questions
CHAPTER 13 – COST OF CAPITAL
13.1
COST OF CAPITAL – SHORT QUESTIONS
(a)
(b)
(c)
(d)
Compute the market price of the following equities.
(i)
W has 50,000 ordinary shares in issue, current dividends Rs. 10 each
expected to remain constant; cost of equity 10%.
(ii)
X has 10,000 ordinary shares in issue, total dividend Rs. 500,000, no
growth expected; cost of equity 15%.
(iii)
Y has 1 million ordinary shares, the dividend just paid was Rs. 10 per
share and it is expected to grow at 5% per annum; cost of equity
15%.
(iv)
Z has 10,000 shares in issue, dividends for the next five years are
expected to be constant at Rs. 10 per share and then grow at 5% per
annum to perpetuity; cost of equity 15%.
Given the following data about share price, compute the cost of equity in
each case.
(i)
Market price per share Rs. 150 ex-dividend. Dividend just paid Rs.
7.5, which is expected to remain constant.
(ii)
Market price per share Rs. 165 cum-dividend. Dividend about to be
paid Rs. 15, which is expected to remain constant.
(iii)
Market price per share Rs. 120 ex-dividend. Dividend just paid Rs.
24, with expected annual growth rate of 5%.
(iv)
Market capitalisation of equity Rs. 10 million. Dividends just paid Rs.
1.5 million, which are expected to remain constant.
Calculate the current pre-tax cost of the following loans.
(i)
A 10% coupon rate irredeemable debenture issued at par.
(ii)
A 10% irredeemable debenture trading at Rs. 85 per cent.
(iii)
A 10% redeemable debenture trading at Rs. 74 per cent with three
years to go to redemption at par.
(iv)
A 10% redeemable debenture trading at par, with three years to go to
redemption at par.
(v)
A 5% irredeemable Rs. 100 preference share trading at Rs. 65.
Calculate the current post-tax cost with a corporation tax rate of 30% of the
loans in (a) above.
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13.2
WACC
A company has just paid an annual dividend of Rs.0.18. Investors expect the
annual dividend to grow by 3% each year in perpetuity, The current share price is
Rs. 1.55 and the total market value of the company’s shares is Rs. 1,200,000.
The company has debt capital on which the yield is 7.8% before tax. The rate of
tax is 30%. The total value of the company’s debt is Rs. 350,000.
Calculate the weighted average cost of capital. Use the dividend growth model to
estimate the cost of equity.
13.3
REDSKINS PLC
Redskins plc has an authorised share capital of 10 million Rs. 25 ordinary shares, of
which 8 million have been issued. The current ex-dividend market price per ordinary
share is Rs. 110. A dividend of Rs. 10 per share has been paid recently. This is
expected to grow at 9% per annum for the foreseeable future.
Extracts from Redskin’s latest statement of financial position are given below.
Redskins
Rs. m
2,000
1,960
3,745
_____
Issued share capital
Share premium
Reserves
Shareholders’ funds
7,705
_____
3% irredeemable debentures
9% debentures
6% loan stock
Bank loans
1,400
1,500
2,000
1,540
_____
6,440
_____
All debt interest is payable annually and all the current year’s payments will be made
shortly.
The current cum-interest market prices for Rs. 100 nominal value stock are Rs. 31.60
and Rs. 103.26 for the 3% and 9% debentures respectively. Both the 9% debentures
and the 6% loan stock are redeemable at par in ten years’ time.
The 6% loan stock is not traded on the open market but the analyst estimates that its
actual pre-tax cost is 10% per annum.
The bank loans bear interest at 2% above base rate (which is currently 11%) and are
repayable in six years. The effective tax rate of Redskins plc is 30%.
Required
Calculate the effective after-tax weighted average cost of capital for Redskins.
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Questions
13.4
CHASANDA AGATES PLC.
Chasanda Agates Plc. is considering an investment which it intends to finance by
the issue of new ordinary shares and debentures in a mix which will hold its
gearing ratio approximately constant.
The company has an issued share capital of 1 million ordinary shares of Rs. 1
each and also issued Rs. 700,000 8% debentures. The market price of the
ordinary shares is Rs. 3.76 per share and the debentures are priced at Rs. 75.
Dividends and interest are payable annually. An ordinary dividend has just been
paid while the next instalment of interest is payable in the near future.
Debentures are redeemable at par in twenty years’ time.
A summary of the company’s statement of financial position as at 31 December
2017 is as follows:
Rs.’000
Rs.’000
Non-current assets
1,276
Current assets
4,066
Less: Current liabilities
1,925
2,141
3,417
Financed by:
Ordinary share capital
1,000
Reserves
1,553
Deferred taxation
164
Debentures
700
3,417
Dividends and earnings have been as follows:
Dividends
Earnings
(before tax)
Rs.’000
Rs.’000
Earnings
(after tax)
Rs.’000
2013
200
575
350
2014
230
723
452
2015
230
682
410
2016
260
853
536
2017
300
906
606
The new investment which has the same risk characteristics as the existing
projects, would require an immediate outlay of Rs. 1,500,000 and would generate
an annual net cash inflow of Rs. 500,000 indefinitely.
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Required
13.5
(a)
Calculate Chasanda Agates Plc’s weighted average cost of capital
(WACC).
(b)
Discuss briefly any difficulties and uncertainties in your estimation.
(c)
Prepare calculations showing whether or not acceptance of the new project
is worthwhile.
(d)
Appraise the dividend policy of the company.
MISTERI COMPANY
Misteri Company is considering whether to purchase a machine for the
manufacture of a new product, Product X. It has been estimated that Product X
would have a life of four years and at a selling price of Rs. 8 per unit, annual
sales demand would be 400,000 units in Year 1, 600,000 units in Year 2 and
800,000 in each of Years 3 and 4.
Variable production and selling costs would be Rs. 6per unit. Incremental annual
fixed cost expenditures (all cash cost items) would be Rs. 500,000 in Year 1,
rising by Rs. 20,000 each year.
The machine, which has an annual output capacity of 700,000 units of Product X,
would cost Rs. 1,200,000 and would have a resale value of Rs. 200,000 at the
end of Year 4. Capital allowances would be available on a 25% annual reducing
balance basis, with a balancing charge or allowance in the year of disposal. Tax
at 25% is payable one year in arrears of the profits to which it relates.
Misteri Company is financed 70% by equity capital and 30% by debt capital. The
equity has a cost of 10% and the debt has a cost of 8.9%.
Required
Calculate the net present value of the proposed project and recommend whether
the investment in the machine should be undertaken.
13.6
FAIZ LIMITED
The share capital and term finance certificates (TFCs) of Faiz Limited (FL) are listed
on the Karachi Stock Exchange. An extract from the company’s latest statement of
financial position as on December 31, 2016 is as follows:
Rs. in million
Ordinary share capital of Rs. 10 each
400
Revenue reserves
350
Other reserves
150
900
6% TFCs of Rs. 100 each
Short term loan – At KIBOR + 3%
Total debt and equity
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Questions
6 years TFCs were issued on January 1, 2016. The coupon rate is 6% payable
annually and the expected IRR is 10%. These TFCs were issued to fund a medium
term project. The prevailing commercial rate for similar risk bonds is KIBOR plus 2%.
The accounting policy of the company states that TFCs and other held to maturity
liabilities are carried at the amortised cost.
KIBOR is currently 9% which can be considered as risk free. FL has an equity beta
value of 1.6 with market equity premium of 6.25%. The rate of income tax is 35%.
The dividend paid in the year 2016 was 12.5% and current year’s dividend will be
paid shortly. The dividend is expected to grow at a constant rate of 10%.
Required
Compute the following as on December 31, 2016:
(a)
Market price of Faiz Limited’s equity shares and TFCs; and
(b)
Weighted average cost of capital.
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CHAPTER 14 – PORTFOLIO THEORY AND THE CAPITAL ASSET PRICING
MODEL
14.1
TWO-ASSET PORTFOLIO
An investor is planning to invest in two securities, Security X and Security Y. The
expected return from each security will depend on the state of the economy, as
follows:
State of the
economy
Probability
Return from
Security X
Return from
Security Y
%
%
Strong
0.25
15
20
Fair
0.60
10
8
Weak
0.15
2
(6)
Required
(a)
Calculate the mean and standard deviation of the expected return from
Security X.
(b)
Calculate the mean and standard deviation of the expected return from
Security Y.
(c)
Calculate the covariance of the returns from Security X and Security Y. The
formula for a covariance is:
Cov x,y 6r x x y y
(d)
Calculate the correlation coefficient for returns from Security X and Security
Y, for a portfolio consisting of 50% of the funds invested in Security X and
50% of the funds invested in Security Y. The formula for correlation
coefficient is:
U x,y Cov x,y
Vx x Vy
where:
V x = the standard deviation of returns from Security X
Vy
= the standard deviation of returns from Security Y
Comment on the correlation coefficient.
(e)
Calculate expected return, the variance and standard deviation of a
portfolio consisting of 50% of the funds invested in Security X and 50% of
the funds invested in Security Y. The formula for correlation coefficient is:
a2(Variance X)2 + (1 – a)2(Variance Y)2 + 2a(1 – a) Covx,y
where:
a = the proportion of the portfolio invested in Security X
(1 – a) = the proportion of the portfolio invested in Security Y
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Variance X = the variance of the returns from Security X
Variance Y = the variance of the returns from Security Y
(f)
14.2
Calculate expected return, the variance and standard deviation of a
portfolio consisting of 80% of the funds invested in Security X and 20% of
the funds invested in Security Y.
COEFFICIENT OF VARIATION
A multinational company is planning to invest in two developing countries, and it will
invest equal amounts of capital in each country. It is looking at returns and risk in each
of three possible countries that might be selected for investment.
The company is particularly concerned about the political risk in each country, and the
threat of political risk to its expected returns. A firm of management consultants has
produced the following statistical estimates of expected returns ad political risk in each
of the countries.
Expected investment
return (%)
Political
risk (%)
Country A
16
25
Country B
22
36
Country C
30
45
Country
The expected return from investing in any of the three countries is independent of the
returns that would be obtained from the other countries.
Required
(a)
(b)
14.3
Calculate the risk, return and coefficient of variation of the following three
investment portfolios:
(i)
50% in Country A, 50% in Country B
(ii)
50% in Country A, 50% in Country C
(iii)
50% in Country B, 50% in Country C
Comment on the results.
PORTFOLIO RETURN
A client has asked for advice on his investment portfolio. Details of his securities
in the stock market (which is regarded as efficient) with the associated risk
characteristics are given below:
SECURITIES
X
Y
Z
Standard deviation (%)
5
15
14
Correlation coefficient (%)
80
40
60
Proportion of amount invested (%)
30
30
40
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The expected return on shares in general and on the basis of past return and
inflationary expectation was estimated to be 20%. It is expected that the risk
premium will be about 5%. The risk of the market as measured by its standard
deviation is 8%. All the three securities lie on the Securities Market Line (SML).
Required
Prepare the following computations for a discussion with your client, as a
prelude to your advice:
14.4
(i)
The expected portfolio return
(ii)
The risk of the portfolio
DOLPHIN PLC.
Dolphin Plc. is all equity financed.
The directors are considering investment in one of two projects which are
mutually exclusive. The cash flows of the two projects are as follows:
Project A
Project B
(Hire Purchase Finance)
(Mortgage Finance)
Initial Outlay
Rs. 10 million
Rs. 24 million
Years 1 – 3
Rs. 4.8million p.a.
Rs. 7.8million p.a.
Years 4 and 5
Rs. 5.6million p.a.
Rs. 8.9million p.a.
Rs. 1million
Rs. 1 million
Cash flow:
Residual Value
Other additional information is given as follows:
Current market price/share
=
Rs. 150
Current annual gross dividend/share
=
Rs. 15
Expected dividend growth rate p.a.
=
10%
Beta co-efficient for company’s shares
=
0.7
Expected rate of return on risk free securities
=
9%
Expected rate of return on market portfolio
=
17%
Required
(a)
Evaluate the viability of each project using the Capital Asset Pricing Model
(CAPM) and Dividend Growth Model (DGM).
(b)
Identify which project to accept giving your reasons.
(c)
Explain the THREE factors that must be estimated for any valuation model.
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Questions
14.5
RISK AND RETURN
A divisional manager’s attitude to investing in new projects is affected by his attitude to
risk. He is prepared to invest in a project that is more risky, provided that it offers a
higher expected return.
He is currently considering four mutually exclusive projects, for which the estimated
returns and risk are as follows:
Project
Estimated project NPV
Risk (σ)
Project 1
80% chance of + Rs. 4 million, 20% chance of +
Rs. 2 million
0.80
Project 2
70% chance of + Rs. 5 million, 30% chance of +
Rs. 1.5 million
1.60
Project 3
60% chance of + Rs. 6 million, 40% chance of +
Rs. 1 million
Not yet
calculated
Project 4
50% chance of + Rs. 8 million, 50% chance of –
Rs. 1 million
Not yet
calculated
Required
14.6
(a)
Calculate the risk with Project 3 and Project 4.
(b)
Suggest which of the four projects the divisional manager will select.
OBTAINING A BETA FACTOR
A beta factor will be estimated for Security Y from the following data.
Returns from the
market portfolio
Returns from Security
Y
%
%
1
+2
+3
2
–1
–2
3
–2
–2
4
+3
+5
+ 0.5
+ 1.0
Month
EV of monthly return
Required
(a)
Use this data to calculate:
(i)
the standard deviation of the monthly return from the market portfolio
and
(ii)
the standard deviation of the monthly return from Security Y.
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(b)
Calculate the correlation coefficient for the market returns and the returns
from Security Y. This is calculated as:
Um, y Cov m, y
Vm x Vy
where:
Vm = the standard deviation of returns from the market portfolio
Vy
= the standard deviation of returns from Security Y
The formula for the covariance is:
Cov x,y 6 x x y y
(c)
Use this data to calculate the beta factor for Security Y. You can use either
of the following formulas.
E
Cov m, y
Var m
Alternatively
E
14.7
Um, y x V y
Vm
SODIUM PLC
Sodium Plc is a highly diversified company operating in a number of different
industries. Its shares are widely traded on the Stock Exchange and have a
current market price of Rs. 3.20.
Its dividend payments over the last five years are:
Year
DPS
2016
0.25
2015
0.23
2014
0.20
2013
0.19
2012
0.18
Sodium Plc is considering two investment opportunities: one is the Hotel and
Tourism (H&T) sector and the other is the Food and Beverages (F&B) sector.
Both projects have relatively short lives and their cash flows are as follows:
H&T
F&B
Year
Rs.’m
Rs.’m
1
85
190
2
170
180
3
150
200
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Questions
The investment in Hotel and Tourism would cost Rs. 300 million while that in
Food and Beverages would cost Rs. 400 million.
The directors have discovered that industry beta for Hotel & Tourism and Food
and Beverages sectors are 1.2 and 2.2 respectively. They believe the
investments being considered are typical of projects in the relevant industries.
Sodium Plc industries beta is 1.6, treasury bill rate is 9% and the average return
on companies quoted on the stock exchange is 14%.
Required
(a)
(b)
14.8
(i)
Compute the net present values of both projects using the company’s
weighted average cost of capital as a discount rate.
(ii)
Compute the NPVs using a discount rate which takes account of the
risk associated with the individual projects.
(iii)
Advise the directors regarding the project to accept.
Enumerate the uses and limitations of the Capital Asset Pricing Model
(CAPM)
DR JAMAL
Dr Jamal has the following portfolio of shares in five listed companies:
Companies
Black
Blue
Yellow
Purple
White
Shares held (units)
15,000
18,000
10,000
12,000
20,000
Price per unit
Rs.0.50
Rs.0.60
Rs.0.40
Rs.0.25
Rs.0.35
The following data are given in relation to the shares:
Companies
Black
Blue
Yellow
Purple
White
Market value per share
Rs. 2.50
Rs. 2.20
Rs. 1.90
Rs. 1.50
Rs.0.60
Current dividend yield
2.2%
4.0%
5.2%
2.6%
1.8%
Beta factor
1.32
1.20
0.80
1.05
0.80
At present the risk-free rate of return is 8% while the market return is 14%.
Required
(a)
(b)
14.9
Calculate
(i)
the beta factor
(ii)
the required return on the portfolio.
Explain the relevance of portfolio theory to Dr Jamal
MR. FARAZ
Mr. Faraz, a large investor, wants to invest Rs. 100 million in the stock market by
developing a portfolio consisting of those shares which have a track record of good
performance.
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He contacted a Stock Analyst to identify such stocks. After a detailed study, the
Stock Analyst recommended investments in shares of five different companies.
Based on his recommendation, Mr. Faraz invested the amount on January 1, 2016.
The relevant details are as follows:
Investment
(Rs.)
Company
Price per
Share on
Jan 1, 2016
(Rs.)
Expected
Dividend
Yield
Standard
Deviation
Covariance
with
KSE 100
A
15,000,000
60
3.50%
24%
2.10%
B
18,000,000
245
3.00%
22%
3.00%
C
22,000,000
225
2.50%
18%
2.60%
D
25,000,000
130
8.00%
15%
1.90%
E
20,000,000
210
5.00%
20%
2.80%
The stock analyst also informed him that the standard deviation and market return of
the KSE-100 Index is 15% and 20% respectively. The risk free rate of return is 8%.
Required
14.10
(a)
Assuming that Mr. Faraz estimates his cost of equity by using the
Capital Asset Pricing Model, compute the required rate of return on each
security.
(b)
As at December 31, 2016, compute the following:
‰
Estimated value of portfolio.
‰
Portfolio beta.
‰
Estimated total return on portfolio.
MUSHTAQ LIMITED
Mushtaq Limited is considering two possible investment projects. Both the projects
have a life of one year only. The returns from new projects are uncertain and depend
upon the growth rate of the economy. Estimated returns at different levels of economic
growth are shown below:
Economic
Probability of
Returns (%)
Growth
Occurrence
Project 1
Project 2
Market
1%
0.25
20
22
30
3%
0.50
30
28
25
5%
0.25
40
40
40
(Annual Avg.)
Risk free rate of return is 10%.
Required
Evaluate the above projects using the Capital Assets Pricing Model.
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Questions
14.11
ATTOCK INDEX TRACKER FUND
Attock Index Tracker Fund (AITF) is an open-end mutual fund and was
incorporated in 2011. However, since inception, its performance has remained
unimpressive and it has generally been outperformed by KSE-100 index.
You have recently joined AITF as its Fund Manager and have been asked by the
management to review the current composition of the portfolio. Details relating to the
shares currently held in the portfolio are as follows:
Price
Market
forecast Dividend
No of
after per share
Name of price per shares Standard
Covariance
next year
one
company share
deviation
year
Rupees
in 000
Rupees
Rupees
A
25
150
0.15
0.024
27
2.00
B
15
230
0.24
0.039
17
1.00
C
46
190
0.16
0.044
52
2.50
D
106
50
0.32
0.033
111
4.00
E
75
100
0.19
0.018
85
2.00
F
114
120
0.22
0.041
125
3.00
G
239
60
0.19
0.032
220
5.50
H
156
80
0.21
0.04
168
3.00
I
145
35
0.18
0.034
170
2.50
J
67
45
0.22
0.033
75
1.00
Following information is also available:
(i)
The average market return of the KSE-100 Index companies is 12% and
the standard deviation is 18%.
(ii)
The risk free rate of return is 8%.
(iii)
The correlation between the market value of securities held by AITF and
KSE-100 Index is 0.737.
(iv)
The average return on AITF’s shares is 11% with standard deviation of
22%.
Required
(a)
Compute the AITF's systematic risk and assess the extent to which AITF
has matched the performance of KSE-100 Index.
(b)
Determine whether AITF achieves the return according to its risk profile.
(c)
Identify those shares in AITF’s portfolio which are expected to
underperform and should be removed.
(d)
Compute the revised beta of AITF i.e. after excluding the
underperforming shares. Assume that cash generated from disposal of
underperforming shares will be used to buy the remaining shares in
proportion to their current holdings.
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14.12
IRON LIMITED
Iron Limited (IL) is considering four projects for investing the excess liquidity
available with the company. Each project will last for three years. The details are as
follows:
Projects
A
B
C
D
85
87
90
95
Expected return
16%
14%
17%
15%
Standard deviation of returns
20%
18%
27%
30%
Estimated correlation of returns with market
returns
0.82
0.85
0.91
0.78
Net annual cash flows (Rs. in millions)
The current market returns are 14% with a standard deviation of 16%. Risk free rate of
return is 10%.
Required
14.13
(a)
Evaluate which of the above projects may be selected for investment by
Iron Limited. Rank the selected projects in order of preference.
(b)
Determine the overall systematic risk that would be associated with the
above investments if IL decides to invest in all the projects selected in (a)
above.
FR CO-OPERATIVE HOUSING SOCIETY
The Trustees of FR Co-operative Housing Society are planning to invest its
surplus funds in different open end mutual funds. Details of proposed investments
along with market information gathered from a stock analyst are as follows:
Mutual Funds
B
A
Information on proposed
investment
Date of investment
01-Jul-16
Amount of investment
Estimated net asset value on
acquisition
Estimated net asset value as
on December 31, 2016
Expected dividends
(during the investment
holding period)
Cash dividend to be received
Bonus to be received
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C
Rs. 500,000
01-Aug-16
Rs.
1,000,000
01-Sep-16
Rs. 500,000
Rs. 10.50
Rs. 10.00
Rs. 9.70
Rs. 10.40
Rs. 10.00
Rs. 9.90
Rs. 9,500
10%
Rs. 15,000
5%
5%
The Institute of Chartered Accountants of Pakistan
Questions
Mutual Funds
B
A
Funds characteristics
Front end load (Buying load)
Back end load (Selling load)
Sharpe ratio
Correlation with benchmark
indices
Expected performance of
benchmark indices
Benchmark index
Total annual return %
Standard deviation of annual
returns
C
3.00%
1.00%
0.71
2.00%
0.00%
0.31
1.50%
2.00%
0.16
0.75
0.9
0.83
KSE 100
16
KSE 30
17
KMI 30
12
0.1
0.18
0.13
The yield on 1-year treasury bills is 9%.
Required
(a)
Estimate the effective annual yield which FR would earn, from the date of
investment up to December 31, 2016.
(b)
In respect of each fund, evaluate whether it would achieve the return in
accordance with its risk profile.
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CHAPTER 15 – DIVIDEND POLICY
15.1
DIVIDENDS AND RETENTIONS
The directors of an all-equity company are considering the company’s policy on
dividends and retentions. The cost of capital is 9% and the company is able to invest in
new capital projects that will earn this return. The company’s shares are quoted and
traded on a major stock market.
In the year just ended, the earnings per share were Rs. 2.00 per share. The company
pays a dividend annually, and is about to pay a dividend for the year just ended on the
basis of its selected dividend and retentions policy.
Required
Suggest what the company’s share price might be if the directors select a policy of
paying annual dividends that are equal to:
15.2
(a)
25% of earnings
(b)
50% of earnings
(c)
70% of earnings
ACKERS PLC
Ackers Plc. has been experiencing difficult trading conditions over the past few
years. In the current year, net earnings are likely to be Rs. 20 million, which will
just be sufficient to pay a dividend of Rs. 1 per share. The earnings and
dividends for the company over the past five years are shown below:
Year
Net earnings
per share
Net dividend
per share
Rs.
Rs.
2012
1.40
0.84
2013
1.35
0.88
2014
1.35
0.90
2015
1.30
0.95
2016
1.25
1.00
There are 20,000,000 ordinary shares in issue, majority of which, are owned by
private investors. There is no debt in the capital structure. Members of the Board
of Directors are considering a number of strategies for the company, some of
which, will have an impact on the company’s future dividend policy. The
company’s shareholders require a return of 15% on their investment.
The following four dividend payment options are being considered:
(i)
Pay out all earnings as dividend
(ii)
Pay a dividend of 50% out of earnings and retain the remaining 50% for
future investment
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(iii)
Pay a dividend of 25% out of earnings and retain the remaining 75% for
future investment.
(iv)
Retain all earnings for an aggressive expansion programme and pay no
dividend at all.
The directors have not been able to agree on any of the four options.
Some of them prefer option (i) because they believe that doing anything else
would have an adverse impact on the share price.
Others favour either option (ii) or option (iii) because the company has identified
some good investment opportunities and they believe one of these options would
be in the best long-term interest of the shareholders.
An adventurous minority favours option (iv) and thinks that the option will allow
the company to take over a relatively small but vibrant competitor.
Required
(a)
Discuss the company’s dividend policy between 2012 and 2016 and its
possible consequences on earnings.
(b)
Advise the directors of Ackers Plc. on the share price which might be
expected immediately following the announcement of their decision if they
pursue each of the four options, using an appropriate valuation model
Note: (Make necessary assumptions).
15.3
DIVIDEND POLICY
The objective of dividend policy should be to maximise the shareholders’ return
so that the value of their investment is maximised.
(a)
State and explain any SIX factors which determine the dividend policy of a
large public company whose shares are quoted on the stock exchange.
(b)
State why a stable dividend policy might be expected to lead to a higher
market valuation of a company’s share.
(c)
Mainland Plc. has just made earnings of Rs. 2,250,000. Its Directors are
trying to decide on a dividend policy. If they retain 20% of earnings, they
believe they can achieve an annual growth rate of 5% in earnings and
dividend. If they retain only 10% of earnings, the growth rate would be 2%
and shareholders would expect a return of 14%.
Which retention policy would maximise the value of the company’s shares.?
15.4
YB PAKISTAN LIMITED
YB Pakistan Limited is engaged in the manufacture of pharmaceutical products. On
April 1, 2016 the Board of Directors approved a plan which envisages an investment of
Rs. 300 million on account of capital expenditures over the next five years. Following
information has been extracted from the management accounts of the company
which have been prepared in respect of the year ended March 31, 2016:
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Rs. in millions
Sales revenue
190.00
Cost of goods sold
110.00
Operating expense
30.00
Interest expense
15.00
Property plant and equipment
100.80
Shareholders’ equity
135.00
The following information is also available:
(i)
Annual outlay of investment in next five years is estimated to be 13%,
16%, 22%, 22% and 27% respectively of the total amount.
(ii)
The company expects that the operating profit (excluding depreciation)
generated by the existing assets will grow at the rate of 12% per annum. In
addition, the new investments would yield pre-tax cash flows of 15% per
annum.
(iii)
The company follows a policy of maintaining a debt equity ratio of 40:60.
(iv)
Interest rates on existing and future long term debts are expected to be
the same and are not expected to change during the next five years. The
current debt is repayable at the end of five years. All future debts would be
repayable on or after six years.
(v)
The company has a short term financing facility of Rs. 50 million. The
outstanding balance as of March 31, 2016 was Rs. 20 million. Assume
that interest @ 16% is payable at the end of each year on the closing
balances.
(vi)
The company invests its surplus funds into highly secured investments
which yield 8% per annum.
(vii) The additional working capital requirements are estimated at 10% of
additional capital expenditures.
(viii) Accounting depreciation is calculated at the rate of 15% of written down
value. It is equal to tax depreciation and therefore is allowable for tax
purposes. The current corporate tax rate is 40%. To promote corporate
business, the Government has announced an annual reduction of 2% in tax
rate till it is reduced to 34%.
(ix)
The company follows the residual dividend policy for payment of dividends.
You may assume that all cash flows are incurred at year end.
Required
(a)
Calculate the expected dividend for the next five years in accordance with
the existing payout policy of the company.
(b)
Ascertain whether the company would be able to pay off its existing loan at
the expiry of five years.
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Questions
15.5
AL-GHAZALI PAKISTAN LIMITED
(a)
Briefly discuss the Dividend Irrelevance Theory developed by Miller and
Modigliani (MM). State three arguments against the validity of this theory.
(b)
Al-Ghazali Pakistan Limited (AGPL) is a listed company whose shares are
currently traded at Rs. 80 per share. AGPL’s Board has approved a
proposal to invest Rs. 600 million in a project which is expected to
commence on 31 December 2016. There are no internal funds available
for this investment and the company would have to finance the project
from the profit for the year ending 31 December 2016 and through right
issue.
AGPL has a share capital consisting of 20 million shares of Rs. 10 each
and its profit for the year ending 31 December 2016 is projected at Rs. 250
million.
The annual return on 1-year treasury bills, the standard deviation of returns
on AGPL’s shares and the estimated correlation of returns with market
returns are 7.5%, 8% and 0.8 respectively. The current market return is
12.9% with a standard deviation of 5%.
Required
Using MM Theory of Dividend Irrelevance, estimate the price of AGPL’s
shares as at 31 December 2016, if the company declares:
(c)
(i)
20% dividend
(ii)
Nil dividend
Justify the MM Theory of Dividend Irrelevance, based on your computation
in (b) above.
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CHAPTER 16 – FINANCING OF PROJECTS
16.1
GEARING
The following information is available about Company A and Company B:
Capital structure
Equity shares of Rs. 1
Reserves
10% debt capital
Annual profit
Sales
Variable costs
Contribution
Fixed operating costs
Profit before interest and tax
Interest costs
Profit
Tax (20%)
Profit after tax (= earnings after interest and tax)
Company A
Rs.
10,000
20,000
Company B
Rs.
10,000
90,000
––––––––
––––––––
30,000
70,000
100,000
0
––––––––
––––––––
100,000
100,000
––––––––
––––––––
Rs.
80,000
10,000
Rs.
80,000
60,000
––––––––
––––––––
70,000
60,000
20,000
10,000
––––––––
––––––––
10,000
7,000
10,000
0
––––––––
––––––––
3,000
600
10,000
2,000
––––––––
––––––––
2,400
8,000
––––––––
––––––––
Assume that annual sales now increase for both companies by 25% to Rs.
100,000.
Required
(a)
Calculate the increase in earnings for each company as a result of the
increase in sales. Assume that there is no change in the variable costs as a
percentage of sales or in total annual fixed costs.
(b)
For each company, calculate:
(i)
the operational gearing ratio (the percentage change in earnings
before interest and tax as a ratio of the percentage increase in sales)
(ii)
the financial gearing ratio (the percentage change in earnings after
tax as a ratio of the percentage increase in earnings before interest
and tax)
(iii)
the combined gearing effect.
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Questions
16.2
FINANCING SCHEMES
The statement of financial position of Brunel as at 31st November Year 6 is as
follows:
Statement of financial position as at 30th November Year 6
Rs. m
Non-current assets
Current assets
Inventory
Trade receivables
Bank
Rs. m
24.8
18.5
21.4
1.9
––––––––
41.8
––––––––
Total assets
66.6
––––––––
Equity and liabilities
Rs.0.50 ordinary shares
Accumulated profits
10.0
22.4
––––––––
Total equity
10% Debentures
Current liabilities
Trade payables
Taxation
32.4
15.0
15.1
4.1
––––––––
19.2
––––––––
Total equity and liabilities
66.6
––––––––
An statement of profit or loss for the year to 30th November Year 6 is as follows:
Rs. m
Sales
Profit before interest and taxation
Interest payable
Profit before taxation
Tax (25%)
Profit after taxation
115.4
17.9
1.5
16.4
4.1
12.3
The company wishes to expand its production facilities to meet an increase in
sales demand for its products. It will need Rs. 18 million of new capital to invest
in equipment. It is expected that annual profit before interest and taxation will
increase by Rs. 5 million.
Brunel is considering the following three possible methods of financing the
expansion programme:
(i)
Issuing 9 million Rs.0.50 equity shares at a premium of Rs. 1.50 per share.
(ii)
Issuing 12 million 12% Rs. 1 preference shares at par and Rs. 6 million
10% debentures at par.
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(iii)
Issuing 6 million equity shares at a premium of Rs. 1.50 per share and Rs.
6 million 10% debentures at par.
Assume that the rate of tax on profits is 25%.
Required
(a)
(b)
16.3
For each of the financing schemes under consideration:
(i)
prepare a projected statement of profit or loss for the year ended 30th
November Year 7.
(ii)
calculate the expected earnings per share for the year ended 30th
November Year 7.
(iii)
calculate the expected level of financial gearing as at 30th November
Year 7, assuming that dividend payments during the year are Rs.0.30
per share.
Assess each of the three financing schemes under consideration from the
viewpoint of an existing equity shareholder in Brunel.
MM, GEARING AND COMPANY VALUATION
A company has 4,000,000 equity shares in issue. The shares have a current
market value of Rs. 10 each. The company is considering whether to issue Rs.
15,000,000 of debt finance and use the cash to buy back and cancel some equity
shares. The tax rate is 30%.
According to Modigliani and Miller, if the company decided to issue the debt
capital and repurchase shares, what would be:
16.4
(a)
the total value of the geared company, and
(b)
the value of equity in the company?
DIVERSIFY
Bustra Company is engaged in plastics manufacture. It is now considering a new
investment that would involve diversification into chemicals manufacture, where
the business risk is very different from the plastics manufacturing industry.
Research has produced the following information about three companies
currently engaged in chemicals manufacturing, in the same part of the industry
that Bustra is planning to invest.
Company
Equity beta
Financed by:
A
2.66
40% equity capital, 60% debt capital
B
1.56
75% equity capital, 25% debt capital
C
1.45
80% equity capital, 20% debt capital
Bustra is financed by 60% equity capital and 40% debt capital, and would intend
to maintain this same capital structure if the new capital investment is
undertaken.
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Questions
The risk-free rate of return is 5% and the return on the market portfolio is 9%. Tax
is at the rate of 25%. You should assume that the debt capital of Bustra and
Companies A, B and C is risk-free.
Required
16.5
(a)
Calculate a suitable cost of equity for the proposed investment by Bustra in
chemicals manufacturing.
(b)
Suggest a weighted average cost of capital that should be used to carry out
an investment appraisal (NPV calculation) of the proposed project.
FINANCIAL AND OPERATING GEARING
SETH produces and sells a single product. The company has issued share
capital of 800,000 equity shares of Rs. 1 each. For the year ended 31st March
Year 4, the company sold 60,000 units of the product at a price of Rs. 30 each.
The statement of profit or loss for the year to 31st March Year 4 is as follows:
Rs.000
Sales
Variable costs
Fixed costs
Rs.000
1,800
720
360
––––––––
1,080
––––––––
Net profit before interest and tax
Minus interest payable
720
190
––––––––
Net profit before tax
Tax at 35%
530
186
––––––––
Net profit after tax
344
––––––––
The company has decided to introduce a new automated production process, in
order to improve efficiency. The new process will increase annual fixed costs by
Rs. 120,000 (including depreciation) but will reduce variable costs by Rs. 7 per
unit. There will be no increase in annual sales volume.
The new production process will be financed by the issue of Rs. 2,000,000 12.5%
debentures.
Required
(a)
Calculate the change in earnings per share if the company introduces the
new production process.
(b)
Assume that the company introduces the new production process
immediately on 1st April Year 5. Calculate for the year to 31st March Year 5:
(i)
the degree of operating gearing
(ii)
the degree of financial gearing
(iii)
the combined gearing effect.
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16.6
OPTIMAL WACC
A company has estimated that its cost of debt capital varies according to the level
of gearing, as follows:
Gearing
Cost of debt
%
20
5.0
30
5.4
40
5.8
50
6.5
60
7.2
Gearing is measured as the market value of the company’s debt as a proportion
of the total market value of its equity plus debt.
The rate of tax is 30%. The ungeared equity beta factor for the company is 0.90.
The risk-free rate of return is 4% and the return on the market portfolio is 9%
Required
Identify the optimal gearing level and WACC.
16.7
GEARED BETA
A company has Rs. 1,500,000 in equity capital and Rs. 500,000 in debt capital
(at market values). The beta value of the equity is 1.126 and the beta of the debt
capital is 0.
The risk-free cost of capital is 5% and the market portfolio return is 11%. The tax
rate is 30%.
Required
16.8
(a)
Calculate the current weighted average cost of capital (WACC).
(b)
Calculate the asset beta for the company and explain what this means.
(c)
Calculate what the equity beta, the cost of equity and the WACC would be
if the company consisted of 60% equity and 40% debt.
ADJUSTED PRESENT VALUE
Harvey is an aluminium engineering company. It now wishes to diversify its operations
into the plastics business. The proposed investment project will require the purchase of
a machine costing Rs. 450,000. This will produce cash flows of Rs. 220,000 for each
of the three years of its life, and it will have no residual value at the end of that time.
It is proposed to finance the purchase of the machine with a mixture of debt and equity
capital. 40% of the cost will be financed by a three-year loan that will be repaid in three
equal instalments. The remaining 60% of the cost will be financed by a placing of new
equity.
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Issue costs, which are tax-allowable, will be 5% for the equity and 2% for the debt,
measured as a percentage of the net finance raised.
The plastics industry has an average equity beta of 1.356 and an average debt: equity
ratio of 1:5, at market values. Harvey’s current equity beta is 1.8 and 20% of its capital
(at market value) consists of long-term debt which is regarded as risk-free.
The risk-free rate is 10% per annum and the expected return on an average market
portfolio is 15%. Corporation tax is at 35%, payable one year in arrears. The machine
will attract a 70% capital allowance in the first year, and the balance will be allowable
against tax over the next three years, at an equal amount in each year.
Required
Carry out an appraisal of the investment using each of the three following methods:
16.9
(a)
PV of the project, using the company’s current weighted average cost of
capital (WACC)
(b)
NPV of the project, using a WACC adjusted for business risk and financial
risk
(c)
the adjusted present value (APV) of the project
APV METHOD
A company in the engineering industry is considering making an investment in a
telecommunications project. The investment will cost Rs. 2,000,000, and will be
financed by a new issue of Rs. 1,000,000 in equity and a new issue of Rs. 1,000,000
debt capital.
The company’s current gearing level is 30% debt and 70% equity.
The telecommunications industry has an average industry equity beta of 1.30625. The
average gearing ratio in the industry is 20% debt and 80% equity.
The rate of taxation is 25%.
The risk-free rate of return is 4% and the average market return is 9%. The company’s
debt is risk-free.
The cash flows from the project before taxation are expected to be:
Year
Cash flow
Rs.
1
100,000
2
140,000
3
120,000
Tax is payable one year in arrears.
You should ignore tax depreciation (capital allowances) on the initial investment.
The costs of raising the equity capital will be 4% of the amount raised. The costs of
raising the debt capital will be 3% of the amount raised. The debt will be in the form of
a three-year loan, and the principal will be repaid in full at the end of Year 3.
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Required
Calculate:
16.10
(a)
the NPV of the project, using the Modigliani and Miller formulas to derive a
cost of capital for the project
(b)
calculate the adjusted present value (APV) of the project.
MORE APV
Pobol Company specialises in business consultancy, but its directors are considering
an investment in software development, which would represent a major diversification
of the company’s business activities. The following draft financial proposal has been
prepared:
Year
0
1
2
3
4
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
Revenue
6,800
7,800
8,800
9,200
Cash operating costs
Allocated head office costs
Royalty payments
Market research costs
600
120
5,500
100
500
-
6,600
150
400
-
7,100
150
300
-
7,500
200
200
-
720
6,100
7,150
7,550
7,900
Expenditure on equipment
Working capital
3,000
400
The following information is also available:
(1)
The project will have a six-year life.
(2)
All prices are calculated in money terms, allowing for inflation. After Year 4,
it is expected that revenues and cash operating costs will remain
unchanged in real terms, but will increase at the rate of inflation which is
expected to be 3% per year. Royalty payments are expected to be Rs.
200,000 per year in Years 5 and 6.
(3)
Head office cash flows will increase as a consequence of the investment by
Rs. 50,000 per year in Years 1 – 3 and by Rs. 60,000 per year in Years 4 –
6.
(4)
The market research costs in Year 0 have already been incurred.
(5)
Highly-skilled consultancy staff will have to be switched to managing the
project, resulting in lost contribution of Rs. 100,000 per year in Years 1 and
2.
(6)
The working capital investment will remain unchanged. The investment in
equipment and working capital will be financed by a new six-year loan at
6% interest. Issue costs for the loan will be 2% and are not tax-allowable.
(7)
The cash for the royalty payments and market research in Year 0 come
from internally-generated cash flows.
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(8)
Tax is payable at the rate of 25%, and is payable in the same year that the
tax liability arises.
(9)
Tax-allowable depreciation will be 20% in Year 1 and will then be a
constant amount for the next five years.
(10) The average equity beta of companies in the software sector that Pobol
Company is considering is 1.39. The market return is 10% and the risk-free
interest rate is 6%.
(11) The average gearing of companies in the software sector that Pobol
Company is considering is 80% equity and 20% debt.
Required
Calculate the adjusted present value (APV) of this project.
16.11
JALIB LIMITED
Jalib Limited (JL) is planning to invest in a project which would require an
initial investment of Rs. 399 million. The project would have a positive net present
value of Rs. 60 million if funded only from equity. There are no internal funds
available for this investment and the company wants to finance the project through
debt. However, JL’s existing TFCs contain a covenant that at any point in time, the
debt to equity ratio in terms of Market Values should not exceed 1:1.
Currently, the market values of JL’s equity (40 million shares are outstanding) and
debt are Rs. 672 million and Rs. 599 million respectively. Markets can be
assumed to be strong form efficient.
Required
(a)
Using Modigliani & Miller theory relating to capital structure, calculate the
minimum amount of equity that the company will have to issue to comply
with the TFCs’ covenant.
(b)
Advise the Board of Directors as regards the following:
‰
the right share ratio and the price at which right shares may be issued
to raise the amount of equity as determined in (a) above, without
affecting the market price of shares.
‰
What would be the impact on the market price of the company’s
shares if the required amount of equity is arranged by issue of shares
at Rs. 14 per share?
(Round off all the amounts to nearest millions and price computations to two decimal
places)
16.12
JAVED LIMITED
Javed Limited is a listed company and is engaged in the business of manufacture and
export of garments. 100% of the company’s revenue comes from exports which are
taxable @ 1% under final tax regime.
An extract of the company’s latest statement of financial position as on June 30,
2016 is as follows:
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Rs. in million
100
40
85
225
150
375
Ordinary Share capital (Rs. 10 each)
Capital Reserves
Retained Earnings
Term Finance Certificates (Rs. 100 each)
Term Finance Certificates (TFCs) are due to be redeemed at par on June 30,
2010. TFCs carry floating mark up i.e. 6 months KIBOR plus 2% which is payable
at half yearly intervals. Currently, TFCs with similar credit rating are available at
six months KIBOR plus 1%.
During the year ending June 30, 2017, the company expects to post a net profit
of Rs. 15 million. Cost of equity of a similar ungeared company is 19%. The
shares of other companies in this sector are being traded at P/E ratio of 8. On
June 30, 2016 the six monthly KIBOR was 14%.
Required
Compute the weighted average cost of capital of the company as at July 1, 2016.
16.13
GHI LIMITED
GHI Limited is an all equity financed company with a cost of capital of 14%. For
last several years, the company has been distributing 70% of its profits to the
ordinary shareholders and is expected to continue to do as in future. The company
plans to enter into a new line of business. Taking it as an opportunity to reduce the
cost of capital, it is considering to issue debt to finance the expansion. The Corporate
Consultant of GHI has provided the following industry data relating to different levels
of leverage:
Debt/Assets
0%
10%
40%
50%
Cost of Debt
-
8%
10%
12%
Equity Beta
1.20
1.30
1.50
1.70
The following information is also available:
(i)
The estimated value of assets after the investment in new line of business
would be Rs. 250 million.
(ii)
The forecasted revenue for the next year is Rs. 200 million.
(iii)
Fixed costs for the next year are estimated at Rs. 40 million whereas
variable costs will be 60% of the revenue.
(iv)
The par value of GHI’s ordinary share is Rs. 10.
(v)
The tax rate applicable to the company is 35%.
The rate of return on 1-year Treasury Bills is 6% and the market return is 10%.
Required
Advise the optimal capital structure which GHI Limited should formulate. Show all
relevant workings.
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16.14
NS TECHNOLOGIES LIMITED
(a)
Briefly explain the Adjusted Present Value (APV) method and identify its
advantages over the Weighted Average Cost of Capital method.
(b)
NS Technologies Limited is in the business of developing financial
software. The directors of the company believe that the scope of future
growth in the software sector is limited and are considering to diversify into
other activities. An option available with the company is to sign an eight
year distribution contract with a leading manufacturer of telecommunication
equipment.
Some of the important information related to the above proposal is as follows:
(i)
Total investment is estimated at Rs. 600 million. It includes developing
the necessary infrastructure, purchase of equipment and working capital
requirements.
(ii)
The investment is expected to generate pre-tax net cash flows of Rs. 180
million per year.
(iii)
Presently NS is paying interest @ 9% on its long term debt.
(iv)
NS maintains a debt equity ratio of 55:45 whereas its equity beta is 0.9.
(v)
Average debt ratio, overall beta and debt beta of telecommunication
equipment distribution segment is 40%, 1.5 and 1.3 respectively.
(vi)
The market rate of return is 14% whereas yield on one year treasury bills is
6%.
(vii) Costs associated with the issuance of debt and equity instruments are
estimated at 1% and 3% respectively.
(viii) Tax rate applicable to the company is 35%. Tax is paid in the same year
as the income to which it relates.
(ix)
In case the contract is not renewed upon expiry, after tax cash flows of
Rs. 90 million would be generated from disposal of allied resources.
Required
Evaluate the above proposal using the APV method.
16.15
COPPER INDUSTRIES LIMITED
The management of Copper Industries Limited (CIL) intends to raise financing for
the company’s expansion project but is concerned about the impact of proposed
additional financing on the company’s existing capital structure and values.
The management is aware that there is an inverse relationship between interest
cover and cost of long term debt and the following relationship exist between interest
cover and cost of debt:
Interest cover (times)
>8
6 to 8
4 to 6
2 to 4
Cost of long term debt
8%
9%
11%
13%
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The management has found that the following two debt equity ratios are usually
prevalent in the industry and are also acceptable to the company’s banker.
(i)
70% equity, 30% debt by market values
(ii)
50% equity, 50% debt by market values
The latest audited financial statements depict the following position:
Rs. in million
Net profit before tax
272
Depreciation
50
Interest @ 9%
55
Capital expenditure
150
Market value of existing equity and debt is Rs. 825 million and Rs. 550 million
respectively. CIL’s equity beta is 1.25 and its debt beta may be assumed to be
zero. The risk-free rate of return and market return are 7% and 15% respectively.
Applicable tax rate is 35%.
Assume that:
‰
CIL’s cash flow growth rate would remain constant and would not be
affected by any change in capital structure.
‰
Market value of the company at the existing weighted average cost of
capital, after the proposed expansion, would remain the same.
Required
(a)
(b)
16.16
Calculate the following under the current as well as each of the above debt
equity ratios being considered by the company:
(i)
Weighted average cost of capital
(ii)
Value of the company
Compare the three options and give recommendations in respect thereof to
the company.
MAC FERTILIZER LIMITED
Mac Fertilizer Limited (MFL) is a listed company and is engaged in the business of
manufacturing of phosphate fertilisers. MFL intends to diversify its operations by
manufacturing and distributing steel products. This diversification would require an
investment of Rs. 3,600 million for establishing the plant and meeting the working
capital requirement. MFL plans to finance the investment as follows:
‰
55% of the investment would be financed by issuing Term Finance
Certificate (TFCs) carrying interest at 12% per annum and repayable in
2022.
‰
The balance amount would be generated by issuing right shares at Rs. 65
per share.
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An extract of MFL’s statement of financial position as at 31 December 2015 is given
below:
Equity and liabilities
Share capital (Rs. 10 each)
Rs. in
million
7,000
Retained earnings
23,000
TFCs (Rs. 100 each)
28,000
Current liabilities
32,000
Assets
Rs. in
million
Non-current assets
50,000
Current assets
40,000
90,000
90,000
The existing TFCs carry mark-up @ 11.5% per annum and are due for redemption at
par in 2020.
Currently, MFL’s shares and TFCs are traded at Rs. 80 and Rs. 102.50
respectively. Equity beta of the company is 1.3.
The proposed investment has been evaluated at a discount rate of 17% which is
based on existing cost of equity plus a premium that takes cognisance of the risks
inherent in the steel industry. However, there are divergent views among the
directors regarding the discount rate that has been used.
‰
Director A is of the view that the premium charged to reflect the risk in the
steel industry is too low. He is of the opinion that the company’s existing
weighted average cost of capital is more appropriate discount rate for
evaluation of this investment.
‰
Director B suggests that the discount rate should be representative of the
steel industry. He has provided the following data pertaining to a listed
company, Pepper Steel Limited (PSL).
x
900 million shares of Rs. 10 each are outstanding which are currently
being traded at Rs. 35.
x
Long term loan amounted to Rs. 8,000 million obtained from local
banks at the average rate of 13%.
x
Equity beta of the company is 1.5.
You have been appointed as the Lead Advisor by an Investment Bank working on
this transaction. You have obtained the following information:
Interest rate for 6-months treasury bills
8%
Market return
13%
Applicable tax rate for all companies
30%
Debt beta of MFL and PSL is assumed to be zero.
Required
Compute the discount rate based on suggestions given by Directors A and B
and discuss which suggestion is more appropriate.
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CHAPTER 17 – BUSINESS VALUATION
17.1
VALUATION MODEL
The shareholders in a company expect a return of 8% per year on their
investment. In the year just ended, the company paid dividends of Rs.0.24 per
share.
Required
(a)
Assume that the company pays out all of its annual profits as dividends,
and the annual dividend per share is expected to be Rs. 24 in perpetuity.
Using the dividend valuation model, suggest what the expected share price
of the company should be.
(b)
Assume that the expected annual rate of growth in dividends is expected to
be 3%.
Using the dividend growth valuation model, suggest what the expected
share price of the company should be.
(c)
Assume that the company is expected to retain 60% of its profits and
reinvest the money to earn an annual return of 9%.
Using the dividend growth valuation model (the Gordon growth model),
suggest what the expected share price of the company should be.
17.2
VALUATION
A company has just paid an annual dividend of Rs. 38. The board of directors
has a target of increasing the share price to Rs. 800, and is considering policies
for investment and growth.
Shareholders expect a return on their investment of 10% per year.
Required
Calculate the annual expected growth rate in dividends that would be required to
raise the share price to Rs. 800. Use the dividend growth model to make your
estimate.
17.3
VALUATION OF BONDS
Assume that bond investors require a return of 9% per year on their investments.
Required
Estimate the market value of the following bonds:
(a)
Irredeemable 7.5% bonds that pay interest annually.
(b)
Bonds paying coupon interest of 6% per year annually, that are redeemable
at par in four years’ time.
(c)
Bonds paying coupon interest of 10%, redeemable at par after three years,
where interest is payable every six months.
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Notes:
An annual cost of capital of 9% is equal to a six-monthly cost of capital of
4.4%.
DCF factor at 4.4%, periods 1 – 7 = 5.914
DCF factor at 4.4%, periods 1 – 8 = 6.623
(d)
17.4
A convertible bond with a coupon of 5% and interest payable annually:
these bonds are convertible after three years into equity shares at the rate
of 20 shares for every Rs. 100 nominal value of bonds. The expected share
price in three years’ time is Rs. 7.
ANNUITIES AND BOND PRICES
(a)
Calculate the value of the following bonds:
(i)
a zero coupon bond redeemable at par in ten years’ time
(ii)
a bond with an 8% coupon, with interest payable half-yearly, and
redeemable at par after ten years.
Assume that the yield required by investors is 5%, and that this is 2.5%
each half year for the purpose of valuing the 8% coupon bond.
(b)
17.5
Calculate the value of both bonds in part (a) of the question if the yield
required by investors goes up by 1%, to 6% for the zero coupon bond and
3% each half year for the 8% coupon bond.
WARRANTS AND CONVERTIBLES
Conver and Warren each have in issue 2,000,000 ordinary shares of Rs. 1
nominal value.
Conver also has Rs. 2,500,000 of 12% convertible debentures in issue. Each Rs.
100 of bonds is convertible into 20 ordinary shares at any time until the date of
expiry of the bonds. If the bonds have not been converted by the expiry date,
they will be redeemed at 105.
Warren has 500,000 equity warrants in issue. Each warrant gives its holder an
option to subscribe for 1 ordinary share at a price of Rs. 5.00 per share. The
warrants can be exercised at any time until the date of their expiry.
The shares of both companies, the convertible debentures and the warrants are
all actively traded in the stock market.
Required
(a)
Calculate the value of each Rs. 100 unit of convertible debentures of
Conver and the value of each warrant of Warren on the day of expiry, if the
share price for each company at that date is:
(i)
Rs. 4.40
(ii)
Rs. 5.20
(iii)
Rs. 6.00
(iv)
Rs. 6.80
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In each of the four cases (i)–(iv), advise the holders of the convertibles and
warrants whether they should exercise their conversion and option rights.
Ignore taxation.
(b)
Calculate the earnings per share for each company.
(i)
In a year when all the convertibles and warrants remained
outstanding for the whole period.
(ii)
For the first full year following conversion of all the convertibles in
Conver and the exercise of all the warrants in Warren.
Profits for each company are currently Rs. 1.2 million each year
before interest and taxation. The corporation tax rate is 50%.
Assume that any new cash raised by the company will be invested to
earn 10% each year before taxation.
17.6
KENCAST LIMITED
The entire share capital of Kencast Limited, an unlisted company, is held by the
three directors of the company – Parvez, Qadir and Rizwan. They have decided
to sell their shares in order to complete a divestment proposal agreed with
management and, as such, wish to know the likely value of the shares before
approaching prospective buyers. Should they fail to get buyers for the shares,
the company will go into liquidation.
The following information is provided in respect of the company:
(a)
Statement of financial position of Kencast Limited as at 31 December,
2017.
Non-current assets:
Rs.’000
Freehold properties at cost
Rs.’000
6,500
Equipment at cost less depreciation
Current assets:
15,600
Inventories
6,975
Accounts receivables
4,825
Cash equivalent – bank
650
12,450
Less: Current liabilities
4,150
8,300
30,400
(b)
Extracts from the published statement of profit or loss and other
comprehensive income for the last three years are
2015
2016
2017
Rs.’000 Rs.’000
Rs.’000
Depreciation
2,250
2,250
2,250
Directors remuneration
2,500
2,900
3,000
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2015
2016
2017
Rs.’000 Rs.’000
Rs.’000
Profit for the year
3,250
3,600
4,175
Dividends
2,250
2,250
2,250
It was discovered that inventories were over-valued at the end of 2016 by
Rs. 600,000. The directors have increased their remuneration in order to
reduce the company’s tax liability. A realistic charge for services rendered
would be Rs. 1,875,000. The equipment is old and it is in need of
replacement. The annual depreciation, based on current replacement cost,
is in the region of Rs. 3,000,000.
(c)
Each of the directors expressed different opinions on the valuation method
to be adopted.
Parvez believes that the shares should be valued using a price/earnings
ratio. For this purpose, he argues that earnings should be defined as the
average reported profits for the last three years, after making proper
charges for depreciation and directors’ remuneration and correcting the
error made on inventories in 2008.
Qadir recommends break-up basis using liquidation values as provided by
experts.
Rizwan, on the other hand, believes that dividend yield basis should be
used, with available data obtained from two similar but listed companies
where he is a shareholder.
(d)
(e)
The relevant data of the two listed companies engaged in similar line of
business as Kencast Limited are as follows:
Dividend yield
Price earnings
Company 1
9%
5.4
Company 2
11%
6.6
Figures obtained from experts for items appearing in the Statement of
Financial Position of Kencast Limited as at 31 December 2017 are as
stated below:
Replacement
Liquidation
values
values
Rs.’000
Rs.’000
Freehold properties
15,000
15,000
Equipment
8,650
5,400
Inventories
4,350
8,000
Required
(a)
Compute the value for the entire share capital of Kencast Limited using
(i)
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(ii)
Liquidation (break-up) basis and
(iii)
Dividend yield basis
Note: Assume you are making the valuation as at 31 December, 2017.
Ignore taxation and liquidation costs. (Show all workings).
(b)
17.7
Identify any TWO limitations associated with each of the methods above.
A PLC’S AND B PLC
A Plc is proposing to take over B Plc by means of an issue of its own shares in
exchange for those of Bayela and has to decide on the terms of its offer.
Extracts from A Plc’s and B Plc’s statement of financial position are set out
below.
Ordinary shares of Rs. 1 each
A Plc
B Plc
Rs.’000
Rs.’000
1,000,000
500,000
Preference share capital
200,000
-
Share premium account
-
20,000
380,000
40,000
150,000
50,000
1,730,000
610,000
Profit and loss account
10% Debentures
Other pieces of information concerning the two companies are as follows:
Maintainable annual profits after tax
attributable to equity
A Plc
B Plc
Rs.
Rs.
240,000,000
150,000,000
Current market value of ordinary shares
2.40
2.70
Current EPS
0.24
0.30
10
9
125%
125%
P/E ratio
Current market price of debts
The company’s income tax rate is 30%.
Required
Determine the offer which the directors of A Plc would make to the shareholders
of B Plc on each of the following bases:
(a)
Net Asset
(b)
Earnings
(c)
Market value
(d)
Financial analysis
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17.8
MNO CHEMICALS LIMITED
MNO Chemicals Limited is a fertilizer company. The company is planning to
diversify into the food business and has identified two companies, PQ (Pvt.)
Limited and RS Limited (a listed company), as potential target for acquisition. MNO
Chemicals Limited intends to buy one of these companies in a share exchange
arrangement.
Extracts from the latest financial statements of the three companies are given below:
Statement of financial position
MNO
Chemicals
PQ (Pvt.)
Limited
RS Limited
Rupees in millions
Share capital (Rs 10 each)
Retained earnings
TFCs
Current liabilities
Non-current assets
Investment held for trading
Current assets
1,500
800
1,200
700
300
350
1,000
400
500
300
100
200
3,500
1,600
2,250
3,000
1,400
1,800
-
-
300
500
200
150
3,500
1,600
2,250
Statement of comprehensive income
MNO
Chemicals
PQ (Pvt.)
Limited
RS
Limited
Rupees in millions
Sales
2,500.00
800.00
1,200.00
Operating profit before interest,
depreciation and income tax
1,250.00
400.00
540.00
Interest
(100.00)
(48.00)
(55.00)
Depreciation
(450.00)
(180.00)
(270.00)
Other income
200.00
20.00
45.00
Net profit before tax
900.00
192.00
260.00
(315.00)
(67.20)
(91.00)
Net profit
585.00
124.80
169.00
Dividend payout (50%:70%:50%)
292.50
87.36
84.50
Tax @ 35%
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Additional information:
(i)
All companies maintain a stable dividend payout policy.
(ii)
It is estimated that earnings of PQ and RS will grow by 4% and 5%
respectively.
(iii)
The risk free rate of return is 8% per annum and the market return is
13% per annum. The market applies a premium of 300 basis point on the
required returns of unlisted companies.
(iv)
RS Limited’s equity beta is estimated to be 1.20.
(v)
Synergies in administrative functions arising from merger would increase
after tax profits by 5% in the case of PQ and 6% in the case of RS.
Required
Which of the two companies should be acquired by MNO Chemicals Limited?
Show necessary computations to support your answer.
17.9
FREE CASH FLOW
A company expects to make profits before interest and tax next year of Rs. 3
million.
Other budgeted information is as follows:
Rs.
Interest charges
Taxation
400,000
600,000
Dividend payments
Depreciation charges
1,200,000
550,000
Increase in working capital
Capital expenditure:
Asset replacement expenditure
150,000
1,000,000
Discretionary expenditure
700,000
Required
Calculate the expected amount of free cash flow next year.
17.10
FINANCIAL PLAN
The board of directors of NNW have asked for a four-year financial plan to be prepared
for Year 5 to Year 8. They have approved the following assumptions for the plan:
(1)
Sales growth will be at the rate of 8% each year into the foreseeable future.
(2)
Cash operating costs will be 70% of sales.
(3)
Investment in new plant and equipment is expected to grow in line with the
growth in sales, and the net book value of plant and equipment will grow at
the same rate.
(4)
Tax-allowable depreciation will grow in line with the growth in sales.
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(5)
Inventory, receivables, cash and trade payables will also increase at the
same rate as the growth in sales.
(6)
There will be no change in long-term borrowing. Interest on the bank
overdraft will be payable at 7%. The interest charge for bank overdraft in
the statement of profit or loss each year should be calculated on the
opening bank overdraft at the beginning of the year.
(7)
Tax on company profits will be 30%.
(8)
The company policy is to pay dividends as a constant percentage amount
of earnings. This policy will not change.
(9)
The cost of equity capital has been estimated as 12%.
The statement of profit or loss of NNW for the year to 31st December Year 4 is as
follows:
Rs. million
Sales
1,800
Cash operating costs
(1,260)
EBITDA
Tax allowable depreciation
540
(160)
Earnings before interest
Interest
380
(78)
Profit before tax
Tax at 30%
302
(91)
Profit after tax
211
Dividends
(135)
Retained profit
76
The statement of financial position of NNW as at the end of Year 4 is as follows:
Rs. m
Plant and equipment
Current assets
Inventory
Receivables
Cash
520
640
30
1,190
3,210
Total assets
Share capital (shares of Rs.0.05 each)
Reserves
Long term loan at 8%
Trade payables
Bank overdraft
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Rs. m
2,020
81
450
1,200
1,650
800
450
310
3,210
The Institute of Chartered Accountants of Pakistan
Business finance decisions
Required
17.11
(a)
Prepare a financial plan for Years 5 to 8, showing the profit after tax,
dividends, retained profits for each year and a summary statement of
financial position as at the end of each year.
(b)
Calculate the expected free cash flow in each year of the financial plan.
(c)
Comment briefly on the financial plan.
(d)
Use the dividend growth model to estimate a market value per share as at
the end of Year 8 (the end of the financial planning period). State any
assumptions that you make in your estimate.
TAKEOVER
Flat Company intends to make a takeover bid for Slope Company, a company in the
same industry. The initial offer will be to exchange every 3 shares in Slope for 2 new
shares in Flat.
The most recent annual data for the two companies is shown below.
Sales revenue
Operating costs
Tax allowable depreciation
Earnings before interest and taxation
Interest
Profit before tax
Tax at 30%
Dividends
Retained earnings
Flat
Rs.000
7,619
4,962
830
1,827
410
1,417
425
992
500
492
Slope
Rs.000
6,000
3,480
700
1,820
860
960
288
673
410
263
920
790
Annual replacement capital expenditure
Other information
Expected annual growth in sales, operating costs
including depreciation, replacement capital expenditure
and dividends for the next 4 years
Expected annual growth in these items from year 5
onwards
Gearing, measured as the ratio of debt to debt plus
equity, (both debt and equity measured at market value)
Market price per share (cents)
Number of shares in issue (millions)
Market cost of fixed interest debt
Equity beta
Flat
Slope
5%
4%
3%
2%
25%
320
6
7%
1.20
40%
154
9
8%
1.35
The risk-free rate of return is 5% and the market return is 11%.
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The takeover will result in some cost savings in operations so that the earnings before
interest and taxation of the combined group would be Rs. 4,100,000 in Year 1 after the
takeover, and growth in sales, costs, depreciation and replacement capital expenditure
would by 5% per year for the following three years and then 4% per year from Year 5
onwards.
The senior financial manager of Flat Company has been assessing the value of the
takeover bid for the shareholders of both companies, and has decided to use free cash
flow analysis as a basis for valuing the companies before and after the takeover. He
believes that the total equity value of the group after the takeover will be significantly
higher than the sum of the current equity values of the two separate companies.
The weighted average cost of the combined company should be calculated as the
weighted average of the current cost of capital of the individual companies, weighted
by the current market value of their debt and equity.
Required
(a)
17.12
Using free cash flow analysis, and making any assumptions you consider
necessary, calculate a value for:
(i)
the current equity in Flat Company
(ii)
the current equity in Slope Company
(iii)
the equity in Flat Company after the takeover.
(b)
Explain the limitations of your estimates in (a).
(c)
Give your views as to whether the takeover bid is likely to have the support
of the shareholders in (1) Flat Company and (2) Slope Company.
MK LIMITED
MK Limited is presently considering a proposal to acquire 100 % shareholdings
of ZA Limited which is engaged in the same business. The financial data extracted
from the latest audited financial statements and other records of the two companies
is presented below:
Sales revenue
Operating expense excluding depreciation
Depreciation
Profit before interest and tax
Interest
Profit after interest
Taxation (35%)
Profit after taxation
Dividend payout
Capital expenditure during the year (Rs. in million)
Debt ratio
Market rate of interest on debentures
Number of shares issued (in million)
Market price of share (Rs.)
Equity beta
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MK
ZA
Rs. in million
12,000
8,460
(7,695)
(4,905)
(1,305)
(990)
3,000
2,565
(644)
(1,494)
2,356
1,071
(825)
(375)
1,531
696
50%
55%
700
650
40%
55%
6.5%
7.5%
100
90
20
12
1.1
1.3
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The following further information is available:
(i)
Both the companies follow the policy of maintaining stable dividend
payouts and debt ratios.
(ii)
Annual growth in sales, operating expenses, depreciation and capital
expenditures are estimated as under:
Year 1 – 2
Year 3 onward
MK
4.0%
5.0%
ZA
5.5%
5.0%
(iii)
Accounting depreciation is the same as tax depreciation.
(iv)
The prevailing risk-free rate of return is 8% whereas the market return is
13%. The key aspects of the feasibility study carried out by MK are as
follows:
‰
MK would issue 7 shares in exchange for 9 shares of ZA.
‰
A rationalization of administrative and operational functions after
takeover would reduce operating expenses including depreciation,
from 75% to 70% of total sales.
‰
The annual growth in sales, operating costs, depreciation and
capital expenditures in the merged company would be as follows:
Year 1 – 2
5.0%
Year 3 onward
5.5%
Required
17.13
(a)
Based on an analysis of Free Cash Flows, calculate the value of MK
Limited, ZA Limited and the company which would be formed after the
merger.
(b)
Estimate the synergy effect which is expected to accrue to MK Limited on
account of acquisition of ZA Limited.
PLATINUM LIMITED
(a)
Briefly discuss the possible synergistic effects which are the primary
motivation for most mergers and takeovers.
(b)
The board of directors of Platinum Limited (PL), a leading manufacturer of
electrical goods, is considering to takeover Diamond Limited (DL), a
competitor of an important product line, by offering seven ordinary shares
for every six ordinary shares of DL.
The summarized statement of financial position and summarized statement
of profit or loss of the two companies for the latest financial year are given
below:
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Summarised Statement of Financial Position
PL
DL
Rupees in
million
4,535
959
Total assets
Shareholders equity
Ordinary shares (Rs. 10 each)
Reserves
900
1,089
1,989
2,546
4,535
Total liabilities
Total equity and liabilities
192
121
313
646
959
Summarised Statement of profit or loss
PL
DL
Rupees in
million
3,638
901
312
86
81
28
231
58
Turnover
Profit before tax
Tax
Profit after tax
The current price earnings ratios of PL and DL are 15 and 19 respectively.
In case of successful bidding, the directors envisage that:
‰
after tax savings in administrative costs would be Rs. 24 million per
annum.
‰
the price earnings ratio of the merged company would be 18.
‰
the dividend payout ratio of PL would not be affected.
Required
17.14
(i)
Total value of the proposed bid based on PL’s current share price.
(ii)
Expected earnings per share and share price of PL following the
successful acquisition of DL.
(iii)
The board of directors is also considering the alternative to offer
three zero coupon debentures (redeemable in 8 years at Rs. 100)
for every 2 DL shares. PL can currently issue new 8 year loan at an
interest rate of 11% per annum. Discuss whether this proposal is
likely to be viewed favourably by DL’s shareholders.
EMH
Several studies show that the annual reports and financial statements are
regarded as important sources of information for making decisions on equity
investment. Other types of studies indicate that the market price of the shares in
a company does not react in the short term to the publication of its annual reports
and financial statements.
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Required
(a)
Explain briefly the concept of the Efficient Market Hypothesis (EMH) and
each of its forms and the degree to which existing empirical evidence
supports them.
A company’s board of directors makes a decision on 1st May to invest in a new
project that will have an NPV of + Rs. 4,000,000. The decision is announced to
the stock market on 12th May.
(b)
The company has 50 million shares in issue and at close of trading on 30th
April these had a market value of Rs. 4 each.
Required
State what would happen to the share price of the company if the stock
market:
17.15
(i)
has weak form efficiency
(ii)
has semi-strong form efficiency
(iii)
has strong-form efficiency.
X PLC AND Y PLC
The following information relate to X Plc. and Y Plc. each having 30,000,000 and
80,000,000 ordinary shares in issue respectively:
Day 1: The price per share is Rs. 3 for X Plc and Rs. 6 for Y Plc.
Day 2: The management of Y Plc., at a private meeting, decided to make a
takeover bid for X Plc at a price of Rs. 5 per share with settlement on day 20.
The takeover will produce operating savings with a present value of Rs.
80,000,000.
Day 5: Y Plc. publicly announces an unconditional offer to purchase all shares of
X Plc. at a price of Rs. 5 per share with settlement on day 20. Y Plc. does not
announce nor make public, the operating savings of the takeover.
Day 10: Y Plc. announces details of the savings derivable from the takeover.
Required
Assuming that the details given are the only factors having effect on the share
price of both companies, determine the day 2, day 5 and day 10 share price of X
Plc and Y Plc if the capital market is
(a)
Semi-strong form efficient,
(b)
Strong form efficient;
given that:
(i)
The purchase consideration is cash as stated above.
(ii)
The purchase consideration, decided on day 2 and publicly announced on
day 5, is five new shares of Y Plc. for six shares of X Plc.
Note: Ignore tax and time value of money.
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Questions
CHAPTER 18 – MERGERS AND ACQUISITIONS
18.1
ACQUISITION
Big Entity is considering a takeover bid for Little Entity, another company in the
same industry. Little is expected to have earnings next year of Rs. 86,000.
If Big acquires Little, the expected results from Little will be as follows:
Year after the acquisition
Year 1
Year 2
Year 3
Sales
Cash costs/expenses
Capital allowances
Interest charges
Cash flows to replace assets and finance growth
Rs.
200,000
120,000
20,000
10,000
25,000
Rs.
280,000
160,000
30,000
10,000
30,000
Rs.
320,000
180,000
40,000
10,000
35,000
From Year 4 onwards, it is expected that the annual cash flows from Little will
increase by 4% each year in perpetuity.
Tax is payable at the rate of 30%, and the tax is paid in the same year as the
profits to which the tax relates.
If Big acquires Little, it estimates that its gearing after the acquisition will be 35%
(measured as the value of its debt capital as a proportion of its total equity plus
debt). Its cost of debt is 7.4% before tax. Big has an equity beta of 1.60.
The risk-free rate of return is 6% and the return on the market portfolio is 11%.
Required
18.2
(a)
Suggest what the offer price for Little should be if Big chooses to value
Little on a forward P/E multiple of 8.0 times.
(b)
Calculate a cost of capital for Big.
(c)
Suggest what the offer price for Little might be using a DCF-based
valuation.
ADAM PLC
Adam Plc is considering acquiring Eve Plc. The summary of their most recent
accounts is presented below:
Statement of financial position
Adam Plc
Eve Plc
Rs.’m
Rs.’m
Net assets
3,150
946
Ordinary shares
1,000
500
Reserves
2,150
446
3,150
946
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Statement of profit or loss
Rs.’m
Profit after tax
Dividend
Retained earnings
Rs.’m
400
150
(300)
(50)
100
100
Both companies retain the same proportion of profits each year and are expected
to do so in the future. Adam Plc’s return on investment is 16%, while that of Eve
Plc is 21%. After the acquisition in one year’s time, Adam Plc will retain 60% of
its earnings and expects to earn a return of 20% on new investment.
The dividends of both companies have been paid. The required rate of return of
ordinary shareholders of Adam Plc is 12% and Eve Plc 18%. After the
acquisition, this will become 16%.
Required
(a)
(b)
18.3
If the acquisition is to proceed immediately, calculate the:
(i)
pre-acquisition market values of the two companies.
(ii)
maximum price Adam Plc will pay for Eve Plc.
Briefly explain the following actions a target company might take to prevent
a hostile takeover bid:
(i)
White knight
(ii)
Shark repellants
(iii)
Pac-man defence
(iv)
Poison pill
(v)
Golden parachute
D LIMITED
D Limited is a private company established about a decade ago to produce
plastic bottles. The first six years of the company witnessed strong growth,
generally facilitated by successful business operations and reduced competition.
As a result of the global economic meltdown and losses sustained in recent
years, the directors and the entire management of the company became worried
and were contemplating closing down the company for six months in the first
instance. The concomitant effect of the proposed closure would be further loss of
sales and profits. For how long will this continue? This was the question being
asked by the chairman and chief executive of the company.
In an attempt to avert the problem, the management held an emergency meeting
where various suggestions were put forward but none of them seems to proffer
solutions to the problem. The chairman and chief executive thought of outright
sale of the company to a willing competitor, F Limited, but this idea was not
acceptable to the board of directors as this could lead to the extinction of the
company.
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Following deliberations and resolutions as to ways of taking the company out of
the current predicament, negotiations between the two boards of directors began.
The most recent information relating to each of the two businesses is set out
below:
Current earnings
Number of shares in issue
Earnings per share
D Limited Ltd
F Limited Ltd
Rs. 20,000,000
4,000,000
Rs. 5
Rs. 9,000,000
3,000,000
Rs. 3
Rs. 80
16 Times
Rs. 30
10 Times
Price per share
Price earnings ratio
If negotiations are successful, F Limited would be willing to accept an offer of Rs.
40.00 per share in exchange for a share of D Limited.
Required
18.4
(a)
From the strategic financial management perspective, what options would
you advise management of D Limited to explore in order to prevent a shutdown or outright discontinuation of business?
(b)
If merger option is adopted, what are the likely financial effects on the
shareholders of the two companies?
CLOONEY PLC AND PITT PLC
Clooney Plc made an offer of 1 of its ordinary shares for every 2 shares in Pitt Plc
on 5 June 2016. If the offer was successful Clooney Plc will use Pitt Plc’s
distribution facilities to expand its sales of fertilizers to farmers and this would
result in an increased cash flow of Rs. 4.5million per year after tax. Clooney Plc’s
financial analyst estimate that the capitalized value of the cash flow is Rs. 45
million.
Extract from the accounts of the two companies are given below.
STATEMENT OF FINANCIAL POSITION AS AT 31 DECEMBER 2015
Non-current assets
Current assets
Less current liabilities
Total assets less current liabilities
Less long term loans
Issued share capital and reserves:
Share capital
Rs. 1 each
0.5 rupees each
Reserves
Note: Current assets include stock of
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Clooney Plc
Rs.’m
750
900
(600)
1,050
(300)
750
Pitt Plc
Rs.’m
360
210
(210)
360
(180)
180
300
450
750
300
150
30
180
150
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Business finance decisions
Clooney Plc
Rs.’m
Pitt Plc
Rs.’m
Rs.’m
Rs.’m
Statement of profit or loss for the year
ended 31/12/2015
Profit after taxation
Dividends
Retained profit
150
60
90
30
21
9
Price per share of Clooney Plc is Rs. 5 while that of Pitt Plc is Rs. 2.
Required
18.5
(a)
Calculate the price earnings ratios of Clooney Plc and Pitt Plc before the
merger.
(b)
Determine what the price earnings ratio of the group will be if the value of
Clooney Plc’s shares increases by Rs.0.5 after the merger.
(c)
Calculate the market capitalization of Clooney Plc after the merger
assuming that the stock market is rational and that there are no events
other than those which would influence the share price. Ignore the Rs.0.5
increase in Clooney Plc’s share price mentioned in (b) above.
(d)
Calculate the net dividend income the holder of 1 share in Pitt Plc would
receive before and after the merger assuming that Clooney Plc maintains
the same dividend per share as before the merger.
NELSON PLC
Nelson Plc is considering making an offer for Drake Plc. The offer is in the form
of merger where the shares in both companies will be swapped for shares in
Nelson Plc. Extract of the latest accounts of the two companies are as follows:
Statements of financial position:
Net Assets
Ordinary shares
Reserves
Statements of profit or loss
Nelson Plc
Drake Plc
Rs.
Rs.
1,419,000
4,725,000
750.000
1,500,000
669,000
3,225,000
1,419,000
4,725,000
Rs.
Rs.
Profit after tax
Dividend
225,000
(75,000)
600,000
(450,000)
Retained Profit
150,000
150,000
The two companies retain the same proportion of profits each year and this is
expected to continue indefinitely. Nelson Plc earns a return of 21% on new
investments while Drake Plc earns 16%. After the merger, Nelson Plc is
expected to retain 60% of its earnings and earn a return of 20% on investment.
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The dividends of both companies have been paid. Ordinary shareholders of
Nelson Plc require 18% rate of return and those of Drake Plc expect 12%. This
will rise to 16% after the merger.
Required
Determine the
18.6
(a)
Market value of each of the TWO companies before the merger.
(b)
Maximum price Nelson Plc should pay for Drake Plc
HALI LTD
Hali Ltd. (HL) is listed on the stock exchange of Country X and has its operations
in Country X and Country Y. The functional currency of both the countries is Rupee
(Rs.). In the latest statement of financial position of the company, net assets were
represented by the following:
Rupees in
50
170
220
30
40
290
Ordinary share capital of Rs. 10 each
Retained earnings
10% Debentures
10% Long term loans
The current market price of ordinary shares and debentures are Rs. 90 per share
and Rs. 130 per certificate respectively. In view of various legal and taxation issues,
HL is considering a demerger scheme whereby two different companies, HX and HY
will be formed. Each company would handle the operations of the respective country.
Mr. Bader, a director of HL, has proposed the following demerger scheme:
(i)
The existing equity would be split equally between HX and HY. New
ordinary shares would be issued to replace the existing shares.
(ii)
The debentures which are redeemable at par value of Rs. 100 in 2012,
would be transferred to HX as these were issued in Country X.
(iii)
The long term loan was obtained in Country Y and will be taken over by HY.
Demerger would require a one time cost of Rs. 17 million in year one, which would
be split between the two companies equally. The finance director has submitted the
following projections in respect of the demerged companies:
HX
Year 1 Year 2
HY
Year 3 Year 1 Year 2 Year 3
Rupees in million
Profit before tax and
depreciation
39
42
44
26
34
36
Depreciation
12
11
13
9
10
11
The projections for year 3 are expected to continue till perpetuity.
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Accounting depreciation is equivalent to tax depreciation and therefore it is allowable
for tax purposes. HX and HY will be subject to corporate tax at the rate of 30% and
25% respectively. Over the next few years, the rate of inflation in Country X and
Country Y is expected to be 5% and 7% respectively.
Required
Assuming your name is XYZ and HL’s weighted average cost of capital is 18%,
prepare a brief report for the Board of Directors discussing:
18.7
(a)
the feasibility of the demerger scheme for the equity shareholders of Hali
Limited, based on discounted cash flow technique. Your answer should be
supported by all necessary workings.
(b)
the additional information and analysis which could assist the Board of
Directors in the process of decision making.
URD PAKISTAN LIMITED
URD Pakistan Limited, a listed company, is presently considering to acquire 100%
shareholdings of CHI Limited, an unlisted company, which is engaged in the same
business.
The following information has been extracted from the latest audited financial
statements of the two companies:
Non-current liabilities – Term Finance Certificates
Share capital (Rs. 10 each)
Retained earnings
Net profit after tax
URD
CHI
Rs. in million
1,500
400
200
100
100
300
250
Tax rate applicable to both the companies is 35%.
The directors of URD believe that a cash offer for the shares of CHI would have the
best chance of success. They are considering various options to finance this
acquisition. The initial negotiations suggest that interest rate on debt financing
would depend upon the debt equity ratio of the company as shown below:
Debt equity ratio (up to)
40:60
50:50
60:40
70:30
Interest rate
16%
17%
18%
20%
The shares of URD are currently traded at Rs. 52.50. According to the prevailing
practice in the market, price earning ratios of unlisted companies are 10% less than
those of listed companies.
Required
Write a report to the Board of Directors, on behalf of Mr. Shah Rukh, the Chief
Financial Officer of the company, discussing the following:
(a)
Which of the following financing option should the company adopt?
(i)
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(ii)
(b)
18.8
The acquisition is financed by issue of debt and equity in the ratio of
60:40. The equity is to be generated by the issue of right shares at
Rs. 45 per share.
What other matters should be considered and what impact these may
have on the decision arrived in (a) above?
FF INTERNATIONAL
FF International (FFI) is considering the opportunity to acquire CS Limited (CSL).
You have been appointed as a consultant to advise the FFI’s management on the
financial aspects of the bid.
The latest summarized annual financial statements of CSL are given below:
Summarised Statement of Financial Position
Rs. in
million
5,000
Total assets
Share capital
Accumulated profit
Long term loan
Short term loan
Other current liabilities
2,000
150
700
1,300
850
5,000
Summarised Statement of profit or loss
Sales
Less: Cost of sales
Gross profit
Selling and administration expenses
Financial charges
Profit before taxation
Taxation
Profit after taxation
Rs. in
million
1,000
(430)
570
(250)
(280)
40
(14)
26
You have also gathered the following information:
(i)
CSL produces a single product X-201 and has a market share of 30%.
A market survey conducted to identify the impact of increase or decrease in
price has revealed the following relationship between price of X-201 and
market share:
Increase / (decrease) in price
(10%)
5%
10%
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Market share
45%
23%
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(ii)
In order to increase production, CSL would have to invest Rs. 150
million in plant and machinery which would be financed through long term
loan on terms and conditions similar to those of the existing long term loan,
as specified in point (v) below.
(iii)
Fixed production costs amount to Rs. 100 million which include depreciation
of Rs. 75 million.
(iv)
80% of selling and administration expenses are fixed. Fixed costs include
depreciation of Rs. 25 million and salaries of Rs. 160 million. After
acquisition, FFI expects to reduce the staff in sales and administration by
making one-time payment of Rs. 100 million. It would reduce the
department’s salaries by 25% and the remaining fixed costs by 30%.
(v)
Long term loan carries mark- up @ 15% per annum. The balance
amount of principal is repayable in five equal annual instalments payable
in arrears.
(vi)
Mark up on short term loan is 14% per annum. CSL has failed to meet
certain debt covenants and therefore its bankers have advised CSL to
reduce the short term loan to Rs. 1,000 million.
(vii) It is the policy of the company to depreciate plant and machinery at
20% per annum using straight line method. Accounting depreciation may
be assumed to be equal to tax depreciation. (viii) Working capital would
vary at the rate of 40% of increase / decrease in sales.
(ix)
Tax rate applicable to both companies is 30% and tax is payable in the
same year. CSL has unutilized carry forward tax losses of Rs. 80 million.
(x)
All costs as well as sales are expected to increase by 10% per annum.
(xi)
Free cash flows of CSL are expected to grow at 5% per annum after Year
5.
(xii) Based on the risk analysis of this investment, the discounting rate is
estimated at 18%.
Required
(a)
Discuss any two advantages and disadvantages of growth through
acquisition.
(b)
Determine the following:
(c)
‰
Optimal sales level at which CSL’s profit would be maximised.
‰
Amount of cash flow gap at optimal level of sales during the first five
years of acquisition.
Calculate the bid price that FFI may offer for the acquisition of CSL
assuming that cash flow gap identified in (b) above would have to be filled
by FFI by way of an interest free loan.
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CHAPTER 19 – FOREIGN EXCHANGE RATES
19.1
INTEREST RATE PARITY
The following are spot exchange rates.
US$/£1: 1.8000 (i.e. $1.8 will buy £1)
€/£1: 1.5000 (i.e. €1.5 will buy £1)
US$/ €1: 1.2000 (i.e. $1.2 will buy €1)
The rates of interest for the next three years are 2.5% on the euro, 3.5% on the
US dollar and 5% on sterling.
Required
If the interest rate parity theory applies, what will the spot exchange rates be:
(a)
after one year
(b)
after three years?
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CHAPTER 20 – INTERNATIONAL INVESTMENT DECISIONS
20.1
CASH FLOWS FROM A FOREIGN PROJECT
A UK company intends to invest in a foreign country, Frankland. The cost of the
investment will be 45 million francs, which is £9 million in sterling at the current
exchange rate. The entire cost of the investment will be paid at the beginning of the
project.
A DCF analysis has been carried out on the project’s expected cash flows in
Frankland, and the NPV is positive.
The project is expected to generate the following dividend payments to the company in
the UK:
Year
Francs
1
10 million
2
20 million
3
25 million
4
10 million
The current exchange rate is £1 = 5 francs. The expected annual rate of inflation in the
UK for the next four years is 3% and in Frankland it is 5%.
Tax in the UK is 30%, and will be payable one year in arrears of dividend receipts. The
company’s weighted average cost of capital is 9%.
Required
Calculate the NPV of the company’s expected sterling cash flows, to decide whether
the project should be undertaken.
20.2
LAHORE PHARMA PLC
Lahore Pharma Plc is planning an investment project in Malaysia where the
currency is the ringgit. The expected cash flows from the project are as follows:
Year
Ringgit
(Million)
0
160
1
80
2
3
96
64
The ringgit/rupee spot rate is Rs. 22 = 1 ringgit. The ringgit is expected to
appreciate by 2% per annum. A similar project based in Pakistan would be
expected to earn a minimum required rate of return of 10 percent.
Required
(a)
Appraise the viability of the project, discounting the foreign cash flows at
the foreign cost of capital
(b)
State FIVE reasons why business organisations engage in cross-border
investments
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20.3
FOREIGN INVESTMENT
Green Limited is a company whose domestic currency is dollars. It is considering an
investment in a country, Francia, where the domestic currency is Francs (FR).
The investment will involve buying equipment in the foreign country at a cost of
1,000,000 Francs. The currency to make the purchase will be bought spot in the FX
market.
The equipment and the project will have a four-year life. At the end of this time, the
equipment will have no residual value. The equipment will attract an allowance for tax
purposes of 25% of its cost each year. The first capital allowance will be claimed
against profits in Year 1.
The cash profits from the project will be 500,000 Francs in each of the four years. Tax
is payable at 40% and is paid one year in arrears of the profits to which they relate.
There are foreign exchange restrictions in the country, and only 50% of the profits after
tax each year can be paid to any shareholder in another country. The balance of the
profits from the project can be paid out as a dividend to Green Limited at the end of
Year 5.
Green Limited has a cost of capital of 10%, but a cost of capital of 16% is considered
appropriate for evaluating the investment cash flows.
The current exchange rate is $1 = FR3.00. However, the rate of inflation is expected to
be 10% in each year in the Francia and 4% each year in Green Limited’s country.
Required
20.4
(a)
Calculate the NPV of the project in the currency of the investment, using a
discount rate appropriate to the investment.
(b)
Calculate the expected annual dividend payments, in Francs.
(c)
Calculate the dollar value of the expected annual dividend payments.
(d)
Evaluate the NPV of the investment in dollars, using an appropriate
discount rate.
GOLD LIMITED
Gold Limited (GL) manufactures textile machinery. The management has explored
opportunities in various South Asian countries and is optimistic that there is
considerable demand for GL’s machines in the region. However, exports from
Pakistan are not financially viable on account of higher input costs. Therefore, GL
intends to establish a subsidiary either in Bangladesh or in Sri Lanka. Based on
initial studies, the management projections, at current prices, are as follows:
Alternative 1: Subsidiary in Bangladesh (SIB)
(i)
SIB would require immediate outlay of BDT 110 million for the construction
of a new factory, i.e. BDT 80 million for acquisition of land and BDT 30
million as advance payment for construction of factory. Balance payment of
BDT 75 million would be made in year 1.
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(ii)
The installation and commissioning of plant and machinery would be
completed in year 1 at a cost of BDT 115 million.
(iii)
The estimated working capital requirement in year 1 and year 2 is BDT 20
million and BDT 110 million respectively.
(iv)
Production and sales in year 2 are estimated at 3,000 units and in years 35 at 4,000 units per annum. The average price in year 2 is estimated at
BDT 300,000 per unit.
(v)
Total variable costs in year 2 are expected to be BDT 165,000 per unit.
(vi)
Fixed overhead costs excluding depreciation, in year 2 are estimated at
BDT 350 million.
(vii) Allowable tax depreciation on all fixed assets except land is 20% per
annum on a reducing balance method.
(viii) Applicable tax rate on SIB is 35%.
Alternative 2: Subsidiary in Sri Lanka (SISL)
(i)
The investment would involve the purchase of an existing factory via a
takeover bid. The estimated cost of acquisition is LKR 90 million.
(ii)
Additional investment of LKR 18 million in new plant and machinery and
LKR 36 million in working capital would be required immediately after the
acquisition.
(iii)
Pre-tax net cash flows (including tax savings from depreciation) are
estimated at LKR 27 million in year 1 and LKR 35 million in year 2.
(iv)
Applicable tax rate on SISL is 25%.
All the above projections are based on current prices and are expected to increase
annually at the current rate of inflation. Inflation rates for each of the next five years
in Pakistan, Bangladesh and Sri Lanka are expected to be 12%, 10% and 8%
respectively.
The after-tax realizable value of the investment at the prices prevailing in year 5,
is estimated at BDT 145 million and LKR 115 million in case of Bangladesh and Sri
Lanka respectively.
Current exchange rates are as follows:
BDT /PKR
Rs. 0.83 – Rs. 0.85
LKR/PKR
Rs. 1.31 – Rs. 1.34
GL’s cost of equity is 18%. It would finance the investment by borrowing at 12%
per annum in
Pakistan after which its debt equity ratio would be approximately 30:70.
The tax rate applicable to GL in Pakistan is 30%. Pakistan has double taxation
treaty agreements with both the countries.
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Required
Evaluate which of the two subsidiaries (if any) should be established by GL.
(Assume that tax in all countries is payable in the same year and that all cash
flows arise at the end of the year)
20.5
GHAZALI LIMITED
Ghazali Limited (GL) operates a chain of large retail stores in country X where the
functional currency is CX. The company is considering expanding its business by
establishing similar retail stores in country Y where functional currency is CY. As
a policy, GL evaluates all investments using nominal cash flows and a nominal
discount rate.
The required investments and the estimated cash flows are as follows:
(i)
Investment in country X
CX 7 million would be required to establish warehouse facilities which
would stock inventories for supply to the retail stores in country Y at cost. At
current prices, the annual expenditure on these facilities would amount to
CX 0.5 million in Year 1 and would grow @ 5% per annum in perpetuity.
Investment in country Y
Investment of CY 800 million would be made for establishing retail stores
in country Y. At current prices, the net cash inflows for the first three
years would be CY 170 million, 250 million and 290 million respectively.
After Year 3, the net cash inflows would grow at the rate of 5% per annum,
in perpetuity.
(ii)
Inflation in country X and Y is 7% and 20% per annum respectively and are
likely to remain the same, in the foreseeable future. Presently, country Y is
experiencing economic difficulties and consequently GL may face problems
like increase in local taxes and imposition of exchange controls.
(iii)
The current exchange rate is CX 1 = CY 45.
(iv)
GL’s shareholders expect a return of 22% on their investments. GL uses
this rate to evaluate all its investment decisions.
Required
Prepare a report to the Board of Directors evaluating the feasibility of the
proposed investment. Your report should include the following:
(a)
Computation of net present value of the project and a recommendation
about the viability of the project.
(b)
Identification of the risk and uncertainties involved.
(c)
Brief discussions on management strategies which may be adopted to
counter the risks of increase in local taxes and imposition of exchange
controls.
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CHAPTER 21 – MANAGING FOREIGN EXCHANGE RISK (I)
21.1
FOREIGN EXCHANGE
(a)
A UK company expects to pay $750,000 to a supplier in three months’ time.
The following exchange rates are available for the dollar against sterling
(GBP/USD):
Spot
1.8570
–
1.8580
3 months forward
1.8535
–
1.8543
The company is concerned about a possible increase in the value of the
dollar during the next three months, and would like to hedge its FX risk.
Required
Explain how the exposure to currency risk might be hedged, and the
amount that the UK company will have to pay in sterling in three months’
time to settle its liability.
(b)
A German company expects to receive US$450,000 from a customer in two
months’ time. It is concerned about the risk of a fall in the value of the dollar
in the next two months, and would like to hedge the currency risk using a
forward contract.
The following rates are available for the dollar against the euro (EUR/USD):
Spot
1.3015
–
1.3025
25c
–
18c
2 months forward
Premium
Calculate the company’s income in euros from settlement of the forward
contract in two months’ time.
(c)
A US company must pay £750,000 to a UK supplier in four months’ time. It
is concerned about the risk of a fall in the value of the dollar in the next two
months, and would like to hedge the currency risk using a forward contract.
The following rates are available for the dollar against sterling ($ per £1):
Spot
1.9820
r
0.002
4 months forward
1.9760
r
0.003
Calculate the cost to the US company of hedging its currency exposure
with a forward contract.
21.2
MONEY MARKET HEDGE
A UK company expects to receive $600,000 in six months’ time from a customer.
It intends to convert these dollars into sterling.
The current spot rate for the dollar against sterling (GBP/USD) is 1.8800. The sixmonth interest rates are 5% per year for sterling and 3.5% per year for the US
dollar.
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Required
21.3
(a)
Show how the company can create a money market hedge for its exposure
to a fall in the value of the dollar.
(b)
Estimate what the exchange rate should be for a six-month forward
contract, GBP/USD.
DUNBORGEN
The treasurer of Dunborgen Company wants to hedge an exposure to currency
risk. Dunborgen is a company whose domestic currency is the euro, and the
company must make a payment of US$500,000 to a US supplier in six months’
time.
The following market rates are available:
Exchange rates: $ per €1
Spot
1.604 r 0.002
6 months forward
1.570 r 0.004
Six month interest rates
Borrowing
Deposits
Euro
4.8%
4.4%
US dollar
2.5%
2.0%
(These interest rates are expressed as an annual rate of interest.)
Required
Compare the cost of hedging the currency risk exposure with:
(a)
a forward exchange contract
(b)
a money market hedge.
Recommend which method of hedging would be preferable in this situation.
21.4
CURRENCY SWAP
Small Company, a UK company, has an opportunity to invest in Zantland for
three years, by setting up and operating an operations centre on behalf of the
Zantland government. The cost of establishing the centre will be 3 million zants.
At the end of the three years, the Zantland government will pay 6 million zants to
purchase the centre from Small Company and take over the operations. During
the three years that Small Company will operate the centre, the Zantland
government will pay an annual fee of 200,000 zants. The entire operation will be
free from tax.
The current exchange rate is £1 = 9.00 zants spot. There is no forward market in
zants. Economic conditions in Zantland are unstable, and the expected inflation
rate in the country over the next three years could be anywhere between 10%
and 50%. Inflation is expected to be negligible in the UK.
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A bank in Zantland has identified a Zantland company that would be interested in
entering a currency swap with Small Company. The swap would involve the
exchange of 3 million zants at the current spot rate, at the beginning and the end
of the swap. An opportunity for credit arbitrage exists, because the rates at which
Small company and the Zantland swap counterparty can borrow directly for three
years are as follows.
Sterling
Zants
Small Company
6.5%
ZIBOR + 2%
Zantland counterparty
8.5%
ZIBOR + 1.5%
ZIBOR is the Zantland inter-bank offered rate, which is usually set very close to
the inflation rate in Zantland.
The bank would take an annual fee of 0.5% in sterling for arranging the swap, and
Small Company would receive 75% of the net arbitrage benefit from the swap.
Required
(a)
(b)
21.5
Suggest how a currency swap might be arranged between the
counterparties, and indicate whether Small Company would arrange the
swap if it decides to invest in the project.
Making whatever assumptions you consider necessary and using a
discount rate of 15%, recommend whether Small Company should
undertake the project.
MOMIN INDUSTRIES LIMITED
Momin Industries Limited (MIL) is engaged in the business of export of superior
quality basmati rice to USA and EU countries. On May 15, 2016, MIL negotiated an
order from TLI Inc. (TLI), a USA based company, for the supply of 10,000 tons of rice
at the rate of US$ 2,000 per ton. Immediately after acceptance of the order by MIL,
the Government imposed a ban on the export of rice. In view of the long standing
relationship, MIL has offered to supply rice through Thailand which has been
accepted by TLI. After due consultation with the Thai Company, MIL and TLI agreed
to the following terms and conditions on May 31, 2016:
‰
The quantity and price per ton will remain unchanged.
‰
First consignment of 4,000 tons will be shipped in the last week of June
2016 and the balance will be shipped during the last week of July 2016.
‰
Shipment will be made directly to TLI.
‰
TLI will make payment to MIL after one month of shipment.
It was agreed with the Thai Company that MIL shall make the payment on shipment,
at the rate of Thai Bhat 50,000 per ton.
MIL has a policy to hedge all foreign currency transactions in excess of Rs. 25
million by obtaining forward cover. MIL’s bank has arranged the forward cover and
advised the following exchange rates on May 31, 2016:
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Thai Bhat
Buy
Sell
US $
Buy
Sell
Spot
Rs. 2.33
Rs. 2.36
Rs. 65.12 Rs. 65.24
1 month forward
Rs. 2.30
Rs. 2.33
Rs. 65.45 Rs. 65.57
2 months forward Rs. 2.28
Rs. 2.31
Rs. 65.77 Rs. 65.89
3 months forward Rs. 2.26
Rs. 2.29
Rs. 66.10 Rs. 66.22
The bank charges a commission of 0.01% on each transaction.
Required
Calculate the profit or loss on the above transaction under each of the following
options:
(a)
the shipments are made according to the agreed schedule;
(b)
on July 31, 2016, the parties agree to delay the second shipment for a
period of two months. The rates expected to prevail on July 31, 2016 are as
follows:
Thai Bhat
(c)
21.6
US$
Spot – July 31, 2016
Rs. 2.29
Rs. 2.32
Rs. 65.61 Rs. 65.73
1 months forward
Rs. 2.27
Rs. 2.30
Rs. 65.84 Rs. 65.96
2 months forward
Rs. 2.25
Rs. 2.28
Rs. 66.16 Rs. 66.28
3 months forward
Rs. 2.23
Rs. 2.26
Rs. 66.38 Rs. 66.50
the second shipment is cancelled on July 31, 2016. The exchange rates are
expected to be the same as in (b) above.
QALAT INDUSTRIES LIMITED
Qalat Industries Limited (QIL) is a medium sized company which carries out
extensive trading (imports as well as exports) with various German companies. The
management of QIL is concerned about the recent fluctuations in the exchange
rate parity between Pak Rupee (Rs.) and Euro (€) and is considering to hedge the
following transactions which it expects to undertake, on December 15, 2016:
Nature of transaction
(i)
Amount
Import of IT equipment
Due date of
payment/receipt
€ 223,500
Jun. 15, 2017
(ii) Export of sports goods
€ 98,500
Mar.15, 2017
(iii) Export of medical instruments
€ 77,000
Jun. 15, 2017
(iv) Import of machinery
Rs. 22,500,000
Mar.15, 2017
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Other relevant information is as follows:
(i)
According to QIL’s bank the following exchange rates are expected to
prevail on December 15, 2016:
€1
Buy
(ii)
Sell
Spot
Rs. 124.22
Rs. 124.52
3 months forward
Rs. 123.62
Rs. 123.96
6 months forward
Rs. 123.21
Rs. 123.54
Interest rate on borrowing and lending in respective currencies are as
follows:
Rs.
€
3-months / 6 months borrowing
11%
5%
3-months / 6 months lending
6.5%
3%
Required
(a)
(b)
Calculate the net rupee receipts/payments that QIL should expect from
the above transactions under each of the following alternatives:
(i)
Hedging through forward cover
(ii)
Hedging through money market
Determine which would be the better alternative for QIL.
(Ignore transaction costs)
21.7
SILVER LIMITED
Silver Limited (SL) is a large manufacturing concern in Malaysia. It deals in four
major product lines. As the financial controller of the company, you are faced with the
following situations:
(I)
SL has made arrangements to export leather shoes to a major customer
in USA. It has been agreed that one consignment would be shipped in
each quarter and payment thereof would be made at the end of the
quarter. SL’s sole supplier of leather is in Pakistan and it has also agreed to
supply on 3 months credit. The estimated sales and purchases for the
first two quarters of 2016 are as follows:
Sales to US
Customer
Purchases from
Pakistani Supplier
First quarter ending
March 31, 2016
USD 1,020,000
USD 775,000
Second quarter ending
June 30, 2016
USD 1,224,000
USD 1,347,000
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The management is considering to hedge the foreign currency transactions. In
this regard SL’s bank has provided the following information:
USD 1
Exchange Rates
(II)
Buy
Sell
Spot rate
MYR 3.030
MYR 3.110
3 months forward rates premium
MYR 0.071
MYR 0.073
6 months forward rates premium
MYR 0.160
MYR 0.164
Interest Rates
Lending
Borrowing
MYR
6.6% p.a.
7.9% p.a.
USD
5.8% p.a.
7.2% p.a.
SL has sold one of its product lines for MYR 15 million. The proceeds
are expected to be received at the end of February, 2016. SL plans to
use these funds in September, 2016 for one of its major expansion project.
Consequently, the management wants to invest this amount in a fixed
deposit account for a period of six months at 6% per annum.
The management is considering to hedge the interest rate risk by using
interest rate futures. The current price of March six months’ futures is 95.50
whereas the standard contract size is MYR 3 million.
Required
(a)
(b)
Determine which of the following options would be more beneficial to the
company:
(i)
Hedging through forward cover
(ii)
Hedging through money market
Determine how beneficial would it be for SL to use interest rate futures to
hedge the interest rate risk if at the end of February, 2016 interest rates:
(i)
fall by 0.75% and future price moves by 1%; or
(ii)
rise by 1% and future price moves by 1%.
Ignore transaction costs.
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21.8
KHALDUN CORPORATION
Khaldun Corporation (KC) is a Pakistan based multinational company and has
number of inter- group transactions with its two foreign subsidiaries KA and KB,
which are located in USA and UK respectively. Details of receipts and payments
which are due after approximately three months are as follows.
Receiving Company
Paying Company
KC (Pak)
KA (USA)
KB (UK)
in million
KC (Pak)
-
KA (USA)
US $ 1.50
KB (UK)
Rs. 131
-
£ 4.00
£ 5.10
US $ 4.50
£ 1.80
-
The current exchange rates and interest rates are as follows:
Exchange Rates
US $ 1
UK £ 1
Buy
Sell
Buy
Sell
Spot
Rs. 86.56
Rs. 86.80
Rs. 134.79 Rs. 135.13
3 months forward
Rs. 87.00
Rs. 87.20
Rs. 135.87 Rs. 136.18
Interest Rates
Borrowing
Lending
KC (Pak)
10.50%
8.50%
KA (USA)
5.20%
4.40%
KB (UK)
5.90%
5.00%
Required
(a)
(b)
Calculate the net rupee receipts/payment that KC (Pak) should expect from
the above transactions under each of the following alternatives:
‰
Hedging through forward contract
‰
Hedging through money market
Demonstrate how multilateral netting might be of benefit to Khaldun Corporation.
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CHAPTER 22 – MANAGING FOREIGN EXCHANGE RISK (II): CURRENCY
FUTURES
22.1
CURRENCY FUTURES
The euro/US dollar currency future is a contract for €125,000. It is priced in US
dollars, and the tick size is $0.0001.
Currency futures are not normally used by companies to hedge currency risks.
However, assume that a French company intends to use currency futures to
hedge the following currency exposure.
It is now February. The French company has to make a payment of US$640,000
in May to a supplier.
The price of June euro/US dollar futures is currently 1.2800.
The company is concerned that the value of the dollar will increase in the next
few months, and it therefore decides to use futures to hedge the exposure to
currency risk.
Required
(a)
How should the company hedge its currency risk with futures?
(b)
Suppose that in May when the company must make the payment in dollars,
the June futures price is 1.2690 and the spot rate (US$/€1) is 1.2710.
Show what will happen when the futures position is closed, and calculate
the effective exchange rate that the company has obtained for the
US$640,000.
22.2
MORE CURRENCY FUTURES
The sterling/US dollar currency future is a contract for £62,500. It is priced in US
dollars, and the tick size is $0.0001.
Currency futures are not normally used by companies to hedge currency risks.
However, assume that a US company intends to use currency futures to hedge the
following currency exposure.
It is now October. The US company expects to receive £400,000 in January from a
customer.
The price of March sterling/US dollar futures is currently 1.8600.
The company is concerned that the value of sterling will fall in the next few months,
and it therefore decides to use futures to hedge the exposure to currency risk.
Required
(a)
How should the company hedge its currency risk with futures?
(b)
Suppose that in January when the company receives the sterling payment,
the March futures price is 1.8420 and the spot rate (US$/£1) is 1.8450.
Show what will happen when the futures position is closed, and calculate
the effective exchange rate that the company has obtained for the
£400,000.
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22.3
BASIS
It is 1st March. The current spot exchange rate for dollars against sterling (US$/£1) is
1.8540. The exchange rate is volatile, and the June futures price for sterling/US dollar
futures is 1.8760.
Assume that the settlement date for the June futures contract is 30th June.
A company has used sterling/US dollar futures to hedge two currency exposures, one
relating to a cash payment on 1st May and the other relating to a cash payment in midJune.
Required
Calculate the expected futures price for June futures:
22.4
(a)
at the end of the day’s trading on 30th April, if the spot sterling/dollar rate is
1.8610
(b)
at the end of the day’s trading on 15th June, if the spot sterling/dollar rate is
1.8690.
IMPERFECT HEDGE AND BASIS
It is 20th April. A US company expects to receive £625,000 in three months’ time, in
July and it wants to hedge its exposure to the risk of a fall in the value of the dollar by
hedging with US dollar/sterling futures.
A dollar/sterling futures contract is for £62,500 and the value of a tick is £6.25.
On 20th April, the spot exchange rate is $1.8050/£1. The company deals in the
September futures contracts at a price of 1.7800. Settlement date for the September
futures is in five months’ time exactly.
The US company receives the £625,000 on 20th July and immediately closes its
futures position. The spot rate on 20th July is 1.7700 and the futures price is 1.7600.
Required
22.5
(a)
To what extent does the futures position provide a hedge for the company
against currency risk, between 20th April and 20th July? To do this,
compare the gain or loss on the underlying currency exposure with the gain
or loss on the futures position.
(b)
Explain why the hedge is imperfect.
CURRENCY HEDGE
It is now the end of July. A UK company expects the following receipts and payments
in euros at the end of the month in three months’ time (at the end of October):
Receipts
Payments
€540,000
€2,650,000
The company is concerned about the exposure to a risk of a movement in the
sterling/euro exchange rate, and it has decided to hedge the exposure.
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It is considering three methods of hedging the exposure:
(a)
with a forward exchange contract
(b)
using a money market hedge
(c)
using currency futures.
Relevant data is as follows:
FX rates, €/£1
Spot
1.4537
–
1.4542
3 months forward
1.4443
–
1.4448
3-month interest rates
Borrow
Invest
Sterling (UK)
6.2%
5.6%
Euro
3.8%
3.4%
Currency futures
Currency futures for sterling/euro are each for €100,000 and are priced in sterling.
Assume that the futures contracts mature at the end of the month.
Assume for the purpose of this question that when the futures position is closed at the
end of October, the basis is 0.
Futures prices as at end of July
September futures
0.6890
December futures
0.6929
Required
Calculate the net cost in sterling of hedging the currency risk:
(a)
with a forward exchange contract
(b)
using a money market hedge
(c)
using currency futures.
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CHAPTER 23 – MANAGING FOREIGN EXCHANGE RISK (III): OPTIONS
23.1
TRADED EQUITY OPTIONS
It is mid-February. A UK investor believes that in the next few weeks, the share price of
company TBA will fall by a substantial amount. The share price is currently 982.
The investor has decided to speculate on a fall in the share price using equity options,
and is prepared to invest up to £12,000 in an options transaction.
On the LIFFE exchange, traded options are for 2,000 shares in a company, and the
following option prices (in pence) are currently available for TBA shares:
Strike price
pence
950
1,000
March
Calls
40
10
Puts
15
50
Required
23.2
(a)
Explain how this investor might use options to speculate on a fall in the
TBA.
(b)
Assuming that the investor purchased options with the lowest strike price
show what would happen when the options expire if the TBA share price is
910.
CURRENCY OPTIONS
A UK company will receive US$2 million in six months’ time. It is now 20th March. The
company is not sure whether the US dollar will rise or fall in value against sterling over
the next few months, and it has decided to hedge its exposure to currency risk using
traded currency options.
On the Philadelphia Stock Exchange, traded currency options are available in a
contract size of £31,250. Options are priced in cents per £1. Assume that option
contracts expire on 20th of each month.
The following option prices are currently available:
Exercise price
1.8500
Calls
June
1.4
Puts
September
1.9
June
4.0
September
5.1
The current spot exchange rate (US$/£1) is 1.8325 – 1.8375.
Required
(a)
Explain how the company’s currency exposure could be hedged using
traded currency options.
(b)
Show what would happen if the options are still held by the company at
expiry and the spot exchange rate is $1.9150 – 1.9200.
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23.3
DEF SECURITIES LIMITED
DEF Securities Limited (DEF) is a medium size investment company. During the
month of February 2016, the Research Department of DEF forecasted an increase in
oil prices by June 2016 which would have a positive impact on the share prices of oil
marketing companies and negative impact on the share prices of power generation
companies. Based on this research, the company entered into the following
transactions on April 1, 2016:
(I)
Purchased a three month American call option of 100,000 shares of Silver
Petroleum Limited (SPL), an oil marketing company, at Rs. 3 per share.
The exercise price is Rs. 155 per share.
(II)
Purchased a three month European put option of 5,000,000 shares of
Diamond Electric Supply Corporation Limited (DESC), a power
generation company, at Re. 0.50 per share. The exercise price is Rs. 3.50
per share.
However, when the price of oil actually increased on May 21, 2016, DESC
revised its power tariff upward while due to tough competition SPL’s margins are
expected to decline. As a result, the company feels that it is now advisable to
reconsider the situation. While evaluating various options, the management has
gathered the following information:
(i)
As of June 1, 2016, the ready market price per share and one month future
price per share were as follows:
Ready market
prices
1-month future
prices
SPL
Rs. 170 per share
Rs. 173 per share
DESC
Rs. 4.25 per share Rs. 4.35 per share
(ii)
DEF can obtain finances at the rate of KIBOR plus 2%. Presently, the
rate of KIBOR is 12.5%.
(iii)
Transaction costs are immaterial.
Required
Based on the available information, recommend the best strategy to the management.
23.4
ALPHA AUTOMOBILES LIMITED
Assume that the date today is 1 July 2016. Alpha Automobiles Limited (AAL) has
imported CNG kits from Japan and has to repay an amount of JPY 175 million in
three months’ time.
AAL intends to hedge the contract against adverse movements in foreign
exchange rates and its foreign exchange exposures. The following data are
available:
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Exchange rates quoted on 1 July 2016
JPY 1
Buy
Sell
Spot rate
Rs. 1.9223
Rs. 1.9339
One month forward rate
Rs. 1.9335
Rs. 1.9451
Three month forward rate
Rs. 1.9410
Rs. 1.9493
Interest rates available to AAL
Borrowing
Investing
Japan
5%
3%
Pakistan
8%
5%
JPY currency futures
Futures have a contract size of JPY 100,000 and the margin required is Rs.
1,000 per contract.
Contract prices (Rupee per JPY) are as follows:
JPY 1
July 2016
Rs. 1.9365
October 2016
Rs. 1.9421
January 2017
Rs. 1.9490
The contracts can mature at the end of the above months only.
Currency options
Options have a contract size of JPY 250,000. The premiums (paisa per Rupee)
payable on various options and the corresponding strike prices are shown below:
Calls
Puts
Strike
31 July
31 October
31 July
31 October
price
2016
2016
2016
2016
Rs.
Paisas
1.90
2.88
3.55
0.15
0.28
1.91
1.59
2.32
1.00
1.85
1.92
0.96
1.15
2.05
2.95
Options are exercisable at the end of relevant month only.
Required
Illustrate four methods by which Alpha Automobiles Limited might hedge its
currency exposure. Recommend which method should be selected.
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CHAPTER 24 – MANAGING INTEREST RATE RISK
24.1
FRA
A company will need to borrow $5 million for six months in three months’ time. It can
borrow at LIBOR + 0.50%. It expects interest rates to rise before it borrows the money,
and so has decided to use an FRA to hedge the risk.
The following FRA rates are available:
2v5
3v6
3v9
6v9
3.82
3.85
3.97
3.92
–
–
–
–
3.77
3.80
3.91
3.87
Required
24.2
(a)
How would the company use an FRA to hedge its interest rate risk, and
what effective interest rate would be obtained by the hedge.
(b)
What is the difference between an FRA and an interest rate coupon swap?
SWAP
A company has a bank loan of $8,000,000 on which it pays a floating rate of US
LIBOR plus 1.25%. The company believes that interest rates will soon increase
and remain high for the foreseeable future, and it would therefore like to switch its
debt liabilities from floating rate to fixed rate.
The loan has four years remaining to maturity. A bank has quoted the following
rates for four-year interest rate swaps in dollars:
5.20% - 5.25%
Required
Show how an interest rate swap can be used to switch from floating rate to fixed
rate liabilities, and calculate what the effective fixed rate would be.
24.3
CREDIT ARBITRAGE
Entity A has an AA credit rating and Entity B has a BBB- credit rating. Both
companies want to raise the same amount of long-term debt capital. Entity A
wants to borrow at a floating rate of interest and Entity B wants to borrow at a
fixed rate.
They are able to borrow at the following rates:
Fixed rate
Floating rate
Entity A
6.35%
LIBOR + 0.75%
Entity B
7.25%
LIBOR + 1.25%
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A bank has identified an opportunity to arrange interest rate swaps with the
companies. It would expect to receive a profit margin on the arrangement of
0.10% of the notional principal amount in the swap. The remaining benefits of the
credit arbitrage should be shared equally between the two entities.
Required
Explain how the interest rate swaps might be arranged, and show the effective
interest rate that will be paid by each entity as a result of the swap.
24.4
CREDIT ARBITRAGE
Company X can borrow for six years at a fixed rate of 7.25% or a variable rate of
LIBOR plus 1.25%. Company Y can borrow for six years at a fixed rate of 8.00% or a
variable rate of LIBOR plus 1.50%.
Company X wants to borrow at a floating rate and company Y wants to borrow at a
fixed rate.
The rates available on six-year swaps are 6.27 – 6.30.
Required
Show how an interest rate swap can be used by both companies to reduce their
borrowing costs.
24.5
HEDGING WITH STIRS
It is now December.
A UK company wants to borrow £4.5 million in two months for a period of five months.
The loan period will be from a date in February to a date in July.
It wants to use short-term interest rate futures to create a hedge against a rise in shortterm interest rates within the next two months.
Short sterling futures are for notional three-month deposits of £500,000.
Required
State how futures should be used as a hedge for the exposure to interest rate risk.
24.6
MORE HEDGING WITH STIRS
It is now 31st October.
A company must borrow US$12 million in three months’ time, on the first day of
February, for a period of four months. It can borrow at US dollar LIBOR + 1%.
The company is concerned about the risk of an increase in short-term interest rates
before February, and has decided to hedge the risk with short-term interest rate
futures.
Eurodollar futures are for three-month notional deposits of $1,000,000.
The current three-month LIBOR rate at the end of October is 5.5%.
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The following futures prices are available at the end of October:
Futures prices as at end of July
December futures
94.20
March futures
93.70
Assume that the settlement date for futures is the last day of the relevant month.
Required
(a)
State how a hedge would be created using eurodollar futures.
(b)
Suppose that at the beginning of February, three-month interest rates for
the dollar (spot) have risen by 2% to 7.5%.
Allowing for basis risk, state what the effective interest rate for borrowing
should be when the futures position is closed.
24.7
FRAS AND FUTURES
It is now 1st April. Your company will receive £8.2 million from a customer in four
months’ time, and it will invest this money for five months until the end of December,
when it will be needed for spending on a planned capital project. The company
treasurer intends to put the money on deposit for five months when it is received, and
expects to be able to invest short term to earn LIBOR plus 0.40%.
The treasurer is worried about the risk of a fall in interest rates and wants to secure an
effective interest rate for the investment of the £8.2 million for the five-month period.
The following information is available:
LIFFE £500,000 3 month sterling futures
Tick size (0.0001) £12.50
September: 95.35
December: 95.70
Futures contracts mature at the end of the relevant month.
The current three-month LIBOR rate is 5%.
FRA prices
4v5: 4.75 – 4.70
4v9: 4.57 – 4.52
5v9: 4.49 – 4.44
Required
(a)
Explain how you would lock in an effective interest rate for the income from
investing the £8.2 million, using:
(1)
FRAs
(2)
Interest rate futures
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(b)
24.8
Show what will happen at the end of July if the three-month LIBOR rate is
4.25% and the interest rate exposure had been hedged as indicated in part
(a) of the answer, using:
(1)
FRAs
(2)
Interest rate futures
INTEREST RATE HEDGE
A UK company will need to borrow £21 million for two months, starting in three months’
time. It is now mid-March. The current LIBOR rate is 5% and the company can borrow
at LIBOR + 0.75%.
The company is concerned about the possibility of an increase in short-term interest
rates during the next two months, and it is looking at methods of hedging its exposure
to the risk. The three methods it is considering are interest rate futures, options on
interest rate futures and an FRA.
Current prices for futures, options and FRAs are as follows. (Note: Assume that all
exchange-traded derivatives reach settlement on the last day of the relevant month).
Interest rate futures
Notional three-month deposit £500,000
Value of 1 tick = £12.50
March
94.740
June
94.610
September
94.500
Options on interest rate futures
Premium cost expressed as an annual interest rate %
Strike
price
24.9
Calls
Puts
March
June
September
March
June
September
94750
0.140
0.200
0.280
0.320
0.390
0.500
95000
0.124
0.080
0.120
0.470
0.560
0.850
DEFINITIONS
Briefly describe each of the following financial instruments:
(a)
Interest rate swaps
(b)
Forwards
(c)
Futures
(d)
Options
(e)
Caps, collars and floors
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24.10
IMRAN LIMITED
Imran Limited wants to borrow Rs. 70 million for two years with interest payable at six
monthly intervals. Due to recent hike in inflation, the company expects that the rate of
interest is likely to rise over the next 2 years. The company can borrow this amount
from a local bank at a floating rate of KIBOR plus 2% but wants to explore the use of
swap to protect it from any interest rate increase, during the next two years.
Another bank has offered the company that it will be willing to receive a fixed rate of
11% in exchange for payments of six month KIBOR.
Required
(a)
Calculate the six monthly interest payments if the swap arrangement is in
place.
(b)
Calculate the net amount receivable/payable by each party to the swap at
the end of the first 6 months if:
‰
KIBOR is 13.5%.
‰
KIBOR is 9%.
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CHAPTER 25 – FORECASTING AND BUDGETING
25.1
GAZELLE LIMITED
Gazelle Limited uses a budgeting system to control the costs of its only product
called KZX. The cost accountant for Gazelle Limited has asked for your
assistance in producing the budget for the year ending December 2017. He has
provided you with the following information:
(i)
The standard cost card for KZX for the immediately preceding year ended
31 December 2016 is as follows:
Rs.
(ii)
Selling price
250
Direct material (4kg at Rs. 8.00/kg)
(32)
Direct labour (6 hours at Rs. 15/hr)
(90)
Contribution
128
Gazelle Limited uses an additive time series analysis to forecast sales
volume. The trend in sales for 2016 and forecast seasonal variations for
2016 are as stated below:
Quarter
Trend (sales units)
1
2
3
4
1,200
1,300
1,400
1,500
-150
200
300
-350
Seasonal variation
(sales units)
(iii)
The sales trend figures for the first two quarters of 2017 are estimated at
1,600 and 1,700 units respectively. Quarterly seasonal variations are
expected to be as for 2016.
(iv)
It is the policy of Gazelle Limited to always carry sufficient inventory of
finished goods to meet 50% of the next quarter’s forecast sales, and
sufficient raw materials to meet 80% of the next quarter’s production.
Required
Prepare the following budgets for each of the four quarters of the year ending 31
December 2017.
(a)
Sales budget, showing units and sales value.
(b)
Production budget in units showing opening inventory, production and
closing inventory.
(c)
Labour budget in hours and cost.
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25.2
FUNTIONAL BUDGET (I)
A company makes and sells two products, Product A and Product B. The sales
price and expected sales volume for each product next year are as follows:
Sales price per unit
Budgeted sales volume
Product A
Product B
Rs. 2.50
Rs. 4.00
50,000
80,000
Required
Prepare the sales budget for the company for next year.
Production budget
A company produces Product L. Budgeted sales for Product L are 20,000 units
for next year. Opening inventory is 2,500 units and planned closing inventory is
2,000 units.
Required
Prepare the production budget for Production L for next year.
Labour budget
A company makes Product DOY which requires two grades of labour, Grade I
and Grade II.
Product DOY requires 4 hours of Grade I labour and (at Rs. 12 per hour) and 7
hours of Grade II labour (at Rs. 15 per hour).
Budgeted production of Product DOY is 25,000 units for the forthcoming year.
Required
Prepare the labour budget for Product DOY for the forthcoming year.
Materials budget
A company manufactures a single product. A single direct material, material X, is
used in its manufacture. A budget is being prepared for next year. Opening
inventory is expected to be 2,000 units of finished goods and 30,000 kilos of
direct material X. Each unit of the product requires 5 kilos of material X.
Budgeted sales next year are 25,000 units of the product. It is also planned to
increase finished goods inventory to 4,000 units before the end of the year and to
reduce inventories of direct material X by 50%.
Required
Prepare a materials usage budget and a material purchase budget for material X.
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25.3
FUNCTIONAL BUDGET (II)
R Limited manufactures three products: Gamma (G) , Beta (B) and Delta (D).
Data for preparation of the June budgets is as follows:
Product
Quantity
Price each
Sales
£
G
1000
110
B
2000
115
D
1500
120
Materials used in the company’s products are:
Material
X1
X2
X3
Unit cost
£5
£8
£7
Budgeted quantities of material use per product is:
Product
X1
X2
X3
G
3
3
1
B
2
3
2
D
4
-
2
Finished goods stock:
G
B
D
1st June
1100
1050
520
30th June
1200
1450
480
X1
X2
X3
1st June
22000
18000
14000
30th June
33400
26000
16000
Raw material stock:
Required
25.4
(a)
Explain the term ‘principal budget factor’
(b)
Prepare budgets for the month of June for:
(i)
sales in quantity and value, including total value;
(ii)
production quantities;
(iii)
material usage in quantities;
(iv)
material purchases in quantity and value, including total value.
FLEXED BUDGET
LAW operates a system of flexible budgets and the flexed budgets for
expenditure for the first two quarters of Year 3 were as follows:
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Flexed budgets - quarters 1 and 2
Activity
Quarter 1
Quarter 2
9,000
14,000
10,000
13,000
Rs.
Rs.
130,000
169,000
Production labour
74,000
81,500
Production overhead
88,000
109,000
Administration overhead
26,000
26,000
Selling and distribution overhead
29,700
36,200
347,700
421,700
Sales units
Production units
Budget cost allowances
Direct materials
Total budgeted cost
The cost structures in quarters 1 and 2 are expected to continue during quarter 3
as follows:
(a)
The variable cost elements behave in a linear fashion in direct proportion to
volume. However, for production output in excess of 14,000 units, the
variable cost per unit for production labour increases by 50%. This is due to
a requirement for overtime working. The extra amount is payable only on
the production above 14,000 units.
(b)
Fixed costs are not affected by changes in activity levels.
(c)
The variable elements of production costs are directly related to production
volume.
(d)
The variable element of selling and distribution overhead is directly related
to sales volume.
Required
Prepare a statement of the budgeted cost allowance for quarter 3. The activity
levels during quarter 3 were:
Units
25.5
Sales
14,500
Production
15,000
NORTON CARE HOME
Norton Care Home, which is linked to a large hospital, has been examining its
budgetary control procedures with particular reference to overhead costs.
The level of activity in the facility is measured by the number of patients treated in
the budget period. For the current year, the budget stands at 10,000 patients
and this is expected to be met.
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From January to June 2016, 5,600 patients were treated. The actual variable
overhead costs incurred during this six-month period are as follows:
Expenses
Rs.
Salaries & wages
79,500
Maintenance
35,000
Printing & Stationery
65,000
Miscellaneous
10,000
Total
189,500
The hospital accountant believes that the variable overhead costs will be incurred
at the same rate during the second half year (July – December 2016).
Fixed overheads budgeted for the whole year are as follows:
Expenses
Rs.
Supervision
300,000
Depreciation
197,500
Miscellaneous
150,000
647,500
You are required to
25.6
(a)
Present an overhead budget for the period of July – December 2016. You
are to show each expense, but should not separate individual months.
What is the total overheads cost for each patient that would be incorporated
into any statistics?
(b)
Examine how well the Organisation exercises control over its overheads,
given that the Organisation actually treated 6,400 patients during the July –
December 2016 period. The actual variable overheads were Rs. 206,000
and the fixed overheads were Rs. 380,000.
THREE SERVICES
A company provides three types of delivery service to customers: service A,
service B and service C. Customers are a mix of firms with a contract for service
with the company, and non-contract customers.
The following information relates to performance in the year to 31st December
Year 1:
Number of deliveries made
% of deliveries to contract customers
Service A
Service B
Service C
350,000
250,000
20,000
60%
60%
80%
Rs. 9
+ 30%
Rs. 15
+ 50%
Rs. 300
+ 20%
Price charged per delivery:
Contract customers
Premium for non-contract customers
The premium for non-contract customers is in addition to the rate charged to
contract customers.
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All employees in the company were paid Rs. 45,000 per year and sundry
operating costs, excluding salaries and fuel costs, were Rs. 4,000,000 for the
year.
The following operational data for the year relates to deliveries:
Services A and B
Service C
Average kilometres per vehicle/day
400
600
Number of vehicles
50
18
Operating days in the year
300
300
For Year 2, the company has agreed a fixed price contract for fuel. As a result of
this contract, fuel prices will be:
(a)
Rs.0.40 per kilometre for Services A and B
(b)
Rs.0.80 per kilometre for Service C.
Sales prices will be 3% higher in Year 2 than in Year 1, and salaries and
operational expenses will be 5% higher. Sales volume will be exactly the same
as in Year 1.
The number of employees will also be the same as in Year 1: 60 employees
working full-time on Services A and B and 25 employees working full-time on
Service C.
Required
25.7
(a)
Prepare a budgeted statement of profit or loss for the year to 31st
December Year 2.
(b)
Comment on vehicle utilisation.
PRIVATE MEDICAL PRACTICE
A private medical practice has five full-time doctors, five full-time assistants and
two administrators.
Each doctor treats 18 patients each day on average. The medical centre is open
for five days each week, 46 weeks each year.
Charges for patients vary according to the age of the patient and the nature of
the treatment provided.
Charges
Adults below
65 year of age
Children and
individuals aged 65
years old and over
Rs.
Rs.
No treatment: consultation only
50
30
Minor treatment
200
120
Major treatment
600
280
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The patient mix and the treatment mix are as follows:
Patients:
Treatment
Adults
45%
No treatment
20%
Children
25%
Minor treatment
70%
Over 65 years old
30%
Major treatment
10%
The salary of each doctor is Rs. 240,000, assistants earn Rs. 100,000 and
administrators earn Rs. 80,000. In addition, everyone receives a 5% bonus at the
end of the year.
The medical practice expects to pay Rs. 414,300 for materials next year and
other (fixed) costs will be Rs. 733,600.
Required
Using the information provided, present a statement of profit or loss for the
medical practice for next year. (Ignore the effects of inflation.)
25.8
HEADGEAR LIMITED
Headgear Limited manufactures and sells fur hats for men. The company is wellestablished and has a well-developed system of budgeting and budgetary control with
variance analysis. Departmental managers are responsible for the preparation and
control of their departmental budgets. Unusually, the company allows departmental
managers to ask for permission to revise their budgets during the year when planning
errors become apparent. When budgets are revised, variances are subsequently
reported as a combination of planning and operational variances.
A newly-appointed managing director has reported to the board that in the past year or
so the number of budget revisions by departmental managers has increased
significantly. As a consequence, most operational variances have been favourable but
there have been larger adverse planning variances. The managing director has
suggested to his colleagues on the board of directors that this is reducing the value of
the budgetary control information. He believes that revisions to the budget by
departmental managers are permitted far too often.
Required
(a)
Explain the circumstances in which budget revisions should be permitted
and when they should be disallowed.
Two situations in which budget revisions were requested by departmental managers
are as follows.
(1)
Labour. Early in the current budget year the company experienced
problems in its marketing and sales department. There were large numbers
of customer complaints and several lost sales orders due to poor service to
customers. A number of mistakes were also made in advertising and sales
promotion. The manager of the sales and marketing department submitted
a report to the board of directors, suggesting that the operational problems
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in the department were due largely to the use of largely poorly-qualified and
poorly-motivated staff. He asked for board permission to begin a
programme of recruitment of better-qualified but more highly paid staff into
the department, to replace the existing staff over a period of about two
years.
The board agreed to this request, and a programme of recruitment of
experienced marketing managers and university graduates was started. A
consequence in the current year staff costs in the department are much
higher than budgeted, and the manager asked for permission to revise the
departmental labour budget.
(2)
Materials. During the year a major supplier of cloth to Headgear Limited
became insolvent and went out of business. The buyer responsible for
purchasing cloth had the task of finding a substitute supplier at short notice.
After a hurried search, the buyer found an alternative supplier about 300
miles away and a contract to buy a quantity of cloth was agreed. There was
very little negotiation on price and the purchase cost of the cloth was much
higher than from the previous supplier. In addition the new supplier charged
delivery costs, which the previous supplier had not done.
Three months later, after more searching for a cloth supplier, the buying
department found a local supplier who agreed to sell cloth at a lower price
and without delivery charges. The buying department therefore switched to
the new supplier.
The head of the buying department asked for permission to revise the
materials purchasing budget for the three months during which the higherpriced supplier had been used.
Required
(b)
In each of the two cases described above, discuss the request for a budget
revision and give your reasoned views as to whether a budget revision
should be allowed.
The market for men’s hats has been in decline as fashions have changed. Headgear
Limited has produced the following data relating to the sale of fur hats for the year to
date.
Budget
Sales volume
11,200 units
Sales price per unit
Rs. 225
Standard contribution per unit
Rs. 100
Actual results for the same period
Sales volume
10,900 units
Average sales price per unit
Rs. 200
The total market for the style of men’s hats sold by Headgear Limited was estimated in
the budget to be 112,000 units. The actual total market for the same period declined to
just 100,000 units.
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Required
25.9
(c)
Calculate the sales price variance and sales volume (contribution) variance.
(d)
Analyse the total sales volume variance into a market size variance and a
market share variance.
(e)
Comment on the sales performance of Headgear Limited during this period.
DASKA DESIGN LIMITED
It is mid-June and the new managing director of Daska Design Limited is reviewing
sales forecasts for Quarter 3 of Year 7, which begins on 1 July, and for Quarter 4. The
company manufactures garden furniture and experiences seasonal variations in sales,
which has made forecasting difficult in the past. Sales for the last two calendar years
were as follows:
Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Year 5
Rs. 2,700,000
Rs. 3,500,000
Rs. 3,400,000
Rs. 3,000,000
Year 6
Rs. 3,100,000
Rs. 3,900,000
Rs. 3,600,000
Rs. 3,400,000
Sales in Quarter 1 of Year 7 were Rs. 3,600,000. There is two weeks to go until the
end of Quarter 2 and the managing director of Daska Design Limited is confident that it
will achieve sales of Rs. 4,400,000 in this quarter.
The existing sales forecasts for the two remaining quarters of the year were made by
the sales director (who has been with the company for several years) during last year’s
budget-setting process. These forecasts are Rs. 3,800,000 for Quarter 3 and Rs.
3,600,000 for Quarter 4.
Budgets within Daska Design Limited have traditionally been prepared and agreed by
the directors of the company before being implemented by junior managers. As a
basis for revising the sales forecasts for the two remaining quarters of Year 7, the
management accountant of Daska Design Limited has begun to apply time series
analysis in order to identify the seasonal variations in sales. He has so far calculated
the following centred moving averages, using a base period of four quarters.
Year
Quarter 1
Quarter 2
Year 5
Year 6
Rs. 3,375,000
Rs. 3,450,000
Quarter 3
Quarter 4
Rs. 3,200,000
Rs. 3,300,000
Rs. 3,562,500
Rs. 3,687,500
Required
(a)
Using the sales information and centred moving averages provided, and
assuming an additive model, forecast the sales of Daska Design Limited for
Quarter 3 and Quarter 4 of Year 7, and comment on the sales forecasts
made by the sales director.
(Note that you are NOT required to use regression analysis)
(b)
Discuss the limitations of the sales forecasting method used in part (a).
(c)
Discuss the relative merits of top-down and bottom-up approaches to
budget setting.
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CHAPTER 26 – VARIANCE ANALYSIS
26.1
GOOD HARVEST LIMITED
Good Harvest Limited makes a product – the vegetable guard. It is the organic
alternative to slug pellets and chemical sprays.
For the forthcoming period budgeted fixed costs were Rs. 6,000 and budgeted
production and sales were 1,300 units.
The vegetable guard has the following standard cost:
Rs.
Selling price
50
Materials 5kg u Rs. 4/kg
20
Labour 3hrs u Rs. 4/hr
12
Variable overheads 3hrs u Rs. 3/hr
9
Actual results for the period were as follows:
1,100 units were made and sold, earning revenue of Rs. 57,200.
6,600kg of materials were bought at a cost of Rs. 29,700 but only 6,300 kg were used
3,600 hours of labour were paid for at a cost of Rs. 14,220. The total cost for variable
overheads was Rs. 11,700 and fixed costs were Rs. 4,000.
The company uses marginal costing and values all inventory at standard cost.
26.2
(a)
Produce a statement reconciling actual and budgeted profit using
appropriate variances.
(b)
Assuming now that the company uses absorption costing, recalculate the
fixed production overhead variances
(c)
Discuss possible causes for the labour variances you have calculated.
MOONGAZER
MoonGazer produces a product – the telescope. Actual results for the period were:
‰
430 units made and sold, earning revenue of Rs. 47,300.
‰
Materials: 1,075 kg were used.
‰
1,200 kg of materials were purchased at a cost of Rs. 17,700
‰
Direct labour: 1,700 hours were worked at a cost of Rs. 14,637
‰
Fixed production overheads expenditure: Rs. 2,400.
‰
Variable production overheads expenditure: Rs. 3,870.
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The standard cost card for the product is as follows:
Rs.
Direct material
2 kg u Rs. 15
30
Direct labour
4hrs u Rs. 8.50
34
Variable overhead
4hrs u Rs. 2.00
8
Fixed production overhead per unit
5
77
The standard unit selling price is Rs. 100. The cost card is based on production and
sales of 450 units in each period.
The company values its inventories at standard cost.
Required
Produce an operating statement to reconcile budgeted and actual gross profit.
26.3
ABC LIMITED
ABC Limited produces and markets a single product. The company operates a
standard costing system. The standard cost card for the product is as under:
Sale price
Rs. 600 per unit
Direct material
2.5 kg per unit at Rs. 50 per kg
Direct labour
2.0 hours per unit at Rs. 100 per hour
Variable overheads
Rs. 25 per direct labour hour
Fixed overheads
Rs. 10 per unit
Budgeted production
500,000 units per month
The company maintains finished goods inventory at 25,000 units throughout the year.
Actual results for the month of August 20X3 were as under:
Rupees in ‘000
Sales
480,000 units
295,000
Direct material
950,000 kgs
55,000
Direct labour
990,000 hours
Variable overheads
105,000
26,000
Fixed overheads
5,100
Required
Reconcile budgeted profit with actual profit using relevant variances.
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26.4
KASUR MF LIMITED
Kasur Mf Limited is comparing budget and actual data for the last three months.
Budget
Rs.
Rs.
950,000
Sales
Cost of sales
Raw materials
Direct labour
Variable production overheads
Fixed production overheads
133,000
152,000
100,700
125,400
Actual
Rs.
Rs.
922,500
130,500
153,000
96,300
115,300
512,100
495,100
438,900
427,400
The budget was prepared on the basis of 95,000 units of production and sales, but
actual production and sales for the three-month period were 90,000 units.
Kasur Mf Limited uses standard costing and absorbs fixed production overheads on a
machine hour basis. A total of 28,500 standard machine hours were budgeted. A total
of 27,200 machine hours were actually used in the three-month period.
Required
(a)
Prepare a revised budget at the new level of activity using a flexible
budgeting approach.
(b)
Calculate the following:
(c)
(d)
(i)
raw material total cost variance
(ii)
direct labour total cost variance
(iii)
fixed overhead efficiency variance
(iv)
fixed overhead capacity variance
(v)
fixed overhead expenditure variance.
Suggest possible explanations for the following variances:
(i)
raw materials total cost variance
(ii)
fixed overhead efficiency variance
(iii)
fixed overhead expenditure variance.
Explain three key purposes of a budgeting system.
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CHAPTER 27 – ADVANCED VARIANCE ANALYSIS
27.1
TOXIC KEMS
A company make a product that involves three chemicals. The standard input per
batch is:
Material
Tonnes
A
B
C
460
345
345
–––––
1,150
–––––
Cost per tonne
Rs.
200
350
450
This produces 1,000 tonnes of output.
Actual results for a period were:
Material
Usage
Cost
A
9,000 tonnes
Rs. 1,935,000
B
4,000 tonnes
Rs. 1,368,000
C
7,000 tonnes
Rs. 3,164,000
It is now recognised that the material prices used in the standard cost card were 10%
too low.
Output from the process was 17,000 tonnes.
27.2
(a)
Calculate the operational and planning variances for material prices.
(b)
Using the updated prices calculate a materials mix variance for each
material and an overall yield variance.
(c)
Briefly discuss the behavioural consequences of different types of standard
cost.
BRK
BRK operates an absorption costing system and sells three products, B, R and K
which are substitutes for each other. The following standard selling price and cost data
relate to these three products:
Product
Selling
price per
unit
Direct material per unit
Direct labour per unit
B
Rs. 14·00
3·00 kg at Rs. 1·80 per kg
0·5 hrs at Rs. 6·50 per hour
R
Rs. 15·00
1·25 kg at Rs. 3·28 per kg
0·8 hrs at Rs. 6·50 per hour
K
Rs. 18·00
1·94 kg at Rs. 2·50 per kg
0·7 hrs at Rs. 6·50 per hour
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Budgeted fixed production overhead for the last period was Rs. 81,000. This was
absorbed on a machine hour basis. The standard machine hours for each product and
the budgeted levels of production and sales for each product for the last period are as
follows:
Product
B
R
K
Standard machine hours per unit
0·3 hrs
0·6 hrs
0·8 hrs
Budgeted production and sales (units)
10,000
13,000
9,000
Actual volumes and selling prices for the three products in the last period were as
follows:
Product
Actual selling price per unit
Actual production and sales (units)
B
R
K
Rs. 14·50
Rs. 15·50
Rs. 19·00
9,500
13,500
8,500
Required
Calculate the following variances for overall sales for the last period:
(i)
sales price variance;
(ii)
sales volume profit variance;
(iii)
sales mix profit variance
(iv)
sales quantity profit variance
and reconcile budgeted profit for the period to actual sales less standard cost.
27.3
CARAT
Carat plc, a premium food manufacturer, is reviewing operations for a three-month
period. The company operates a standard marginal costing system and manufactures
one product, ZP, for which the following standard revenue and cost data per unit of
product is available:
Selling price
Rs. 12.00
Direct material
A 2.5 kg at Rs. 1.70 per kg
Direct material
B 1.5 kg at Rs. 1.20 per kg
Direct labour
0.45 hrs at Rs. 6.00 per hour
Fixed production overheads for the three-month period were expected to be Rs.
62,500.
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Actual data for the three-month period was as follows:
Sales and production
48,000 units of ZP were produced and sold for Rs.
580,800
Direct material A
121,951 kg were used at a cost of Rs. 200,000
Direct material B
67,200 kg were used at a cost of Rs. 84,000
Direct labour
Employees worked for 18,900 hours, but 19,200 hours
were paid at a cost of Rs. 117,120
Fixed production
overheads
Rs. 64,000
Budgeted sales for the three-month period were 50,000 units of Product ZP.
Required
(a)
Calculate the following variances:
(i)
sales volume contribution and sales price variances;
(ii) price, mix and yield variances for each material;
(iii) labour rate, labour efficiency and idle time variances.
(b)
Prepare an operating statement that reconciles budgeted gross profit to
actual gross profit with each variance clearly shown.
(c)
Suggest possible explanations for the following variances:
(i)
material price, mix and yield variances for material A;
(ii) labour rate, labour efficiency and idle time variances.
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CHAPTER 28 – TRANSFER PRICING
28.1
TWO DIVISIONS
A company has two operating divisions, X and Y each of which is treated as a
profit centre for the purpose of performance reporting.
Division X makes two products, Product A and Product B. Product A is sold to
external customers for Rs. 62 per unit. Product B is a part-finished item that is
sold only to Division Y.
Division Y can obtain the part-finished item from either Division X or from an
external supplier. The external supplier charges a price of Rs. 55 per unit.
The production capacity of Division X is measured in total units of output,
Products A and B. Each unit requires the same direct labour time. The costs of
production in Division X are as follows:
Product A
Product B
Rs.
Rs.
Variable cost
46
48
Fixed cost
19
19
Full cost
65
67
Required
You have been asked to recommend the optimal transfer price, or range of
transfer prices, for Product B.
28.2
(a)
What is an optimal transfer price?
(b)
What would be the optimal transfer price for Product B if there is spare
production capacity in Division X?
(c)
What would be the optimal transfer price for Product B if Division X is
operating at full capacity due to a limited availability of direct labour, and
there is unsatisfied external demand for Product A?
SHADOW PRICE
Division A supplies a special chemical to Division B, another profit centre in the
same group. The output capacity for making the special chemical in Division A is
limited.
The variable cost of making the chemical is Rs. 500 per kilo.
There is no external intermediate market for the chemical.
Division B uses the chemical to manufacture a tablet. Each tablet uses ten grams
of the chemical.
Sales demand for the tablet exceeds the production capacity of Divisions A and
B.
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The selling price for each tablet is Rs. 10. Further variable processing costs in
Division B to make the tablet from the special chemical are Rs. 2 per tablet.
Required
28.3
(a)
Calculate the shadow price of each kilo of the special chemical. (The
shadow price of the special chemical is the amount by which total
contribution would be reduced (or increased) if one unit less (or more) of
the chemical were available.)
(b)
Identify the ideal transfer price.
(c)
Suggest whether this transfer price will provide a suitable basis for
performance evaluation of the two divisions.
FROOM PLC
(a)
Discuss the THREE key objectives of transfer pricing.
(b)
Froom Plc. has two divisions: A and B. The company is into the production
of bicycles. Division A produces the bicycle frame and Division B
assembles the bicycles’ components onto the frame. There is a market for
both the
sub-assembly and the final product. Each division has been
designed as a profit centre. The transfer price for the sub-assembly has
been set at the long-run average market price. The following data are
available for each division:
Rs.
Estimated selling price for final product
30,000
Long-run average selling price for intermediate product
20,000
Incremental costs for completion in Division B
15,000
Incremental costs in Division A
12,000
The Manager of Division B has made the following calculations:
Rs.
Selling price for final product
30,000
Transferred – in cost (market)
20,000
Incremental costs for completion
15,000
Contribution
Rs.
35,000
(5,000)
Required
(i)
Transfers should be made to Division B, assuming there is no excess
capacity in Division A. Is the market price the correct transfer price?
(ii)
Division A’s maximum capacity for this product is 1,000 units per
month and sales to the intermediate market are now 800 units and
assuming that for various reasons, A will maintain the Rs. 20,000
selling price indefinitely; (that is, A is not considering lowering the
price to outsiders even if idle capacity exists); should 200 units be
transferred to Division B and at what transfer price?
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28.4
TRAINING COMPANY
A Pakistan training company has two training centres, one in Karachi and one in
Lahore, each treated as a profit centre for the purpose of transfer pricing.
Each training centre hires its training staff to client organisations, and charges a
fixed rate for each ‘trainer day’. Trainers are either full-time staff of the company,
or are hired externally. Externally-hired trainers are all vetted for quality, and are
used when client demand for training exceeds the ability of the division to meet
from its full-time staff.
The Karachi centre is very busy and charges its client Rs. 2,000 per trainer day.
It pays Rs. 1,200 per day to external trainers. The variable cost of using its own
full-time trainers is Rs. 200 per day.
The other training centre is in Lahore. The manager of the Lahore centre is
meeting with the manager of the Karachi centre to discuss the possibility of the
Karachi centre using trainers from the Lahore centre instead of external trainers.
They have agreed this arrangement in principle, but need to agree a daily fee
that the Karachi centre should pay the Lahore centre for these of its trainers.
It has been estimated that if trainers from the Lahore centre are used in Karachi,
the variable costs incurred will be Rs. 200 per day, plus Rs. 250 per day for travel
and accommodation costs. These costs will be paid by the Lahore centre.
Required
Identify the optimal charge per day for the use of Lahore trainers by the Karachi
training centre, in each of the following circumstances:
28.5
(a)
assuming that the Lahore centre has spare consulting capacity
(b)
assuming that the Lahore training centre is fully occupied charging clients
Rs. 750 per trainer day
(c)
assuming that the Lahore training centre is fully occupied charging clients
Rs. 1,100 per trainer day.
BRICKS
ABC Company is organised into two trading groups. Group X makes materials
that are used to manufacture special bricks. It transfers some of these materials
to Group Y and sells some of the materials externally to other brick
manufacturers. Group Y makes special bricks from the materials and sells them
to traders in building materials.
The production capacity of Group X is 2,000 tonnes per month. At present, sales
are limited to 1,000 tonnes to external customers and 600 tonnes to Group Y.
The transfer price was agreed at Rs. 200 per tonne in line with the external sales
trade price at 1st July which was the beginning of the budget year. From 1st
December, however, strong competition in the market has reduced the market
price for the materials to Rs. 180 per tonne.
The manager of Group Y is now saying that the transfer price for the materials
from Group X should be the same as for external customers. The manager of
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Group X rejects this argument on the basis that the original budget established
the transfer price for the entire financial year.
From each tonne of materials, Group Y produces 1,000 bricks, which it sells at
Rs.0.40 per brick. It would sell a further 400,000 bricks if the price were reduced
to Rs.0.32 per brick.
Other data relevant are given below.
Group X
Group Y
Rs.
Rs.
Variable cost per tonne
Fixed cost per month
70
60
100,000
40,000
The variable costs of Group Y exclude the transfer price of materials from Group
X.
Required
(a)
Prepare estimated profit statements for the month of December for each
group and for ABC Company as a whole, based on transfer prices of Rs.
200 per tonne and of Rs. 180 per tonne, when producing at
(i)
80% capacity
(ii)
100% capacity, on the assumption that Group Y reduces the selling
price to Rs.0.32 per brick.
(b)
Comment on the effect that might result from a change in the transfer price
from Rs. 200 to Rs. 180.
(c)
Suggest an alternative transfer price that would provide an incentive for
Division Y to reduce the selling price and increase sales by 40,000 bricks a
month.
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CHAPTER 29 – WORKING CAPITAL MANAGEMENT
29.1
CASH OPERATING CYCLE
The working capital (or cash operating) cycle of a business is the length of time
between the payment for purchased materials and the receipt of payment from
selling the goods made with the materials.
The table below gives information extracted from the annual accounts of Entity M
for the past three years.
Entity M - Extracts from annual account
Year 1
Year 2
Year 3
Rs.
Rs.
Rs.
Inventory:
Raw materials
108,000
145,800
180,000
Work in progress
75,600
97,200
93,360
Finished goods
86,400
129,600
142,875
Purchases
518,400
702,000
720,000
Cost of goods sold
756,000
972,000
1,098,360
Sales
864,000
1,080,000
1,188,000
Trade receivables
172,800
259,200
297,000
86,400
105,300
126,000
Trade payables
Required
29.2
(a)
calculate the length of the working capital cycle (assuming 365 days in the
year); and
(b)
list the actions that the management of Entity M might take to reduce the
length of the cycle.
WORKING CAPITAL
DON is a small manufacturing company. Its summarised accounts for the last two
years are presented below:
Statements of financial position as at 31st March
Year 5
Rs.000
Fixed assets
Year 6
Rs.000
Rs.000
820
Rs.000
1,000
Current assets
Inventory
340
420
Trade receivables
360
570
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Year 5
Rs.000
Cash
Year 6
Rs.000
Rs.000
10
––––––––
Rs.000
0
710
––––––––
990
––––––––
––––––––
1,530
1,990
––––––––
––––––––
Equity shares of Rs.0.25
400
400
Accumulated profits
450
530
––––––––
––––––––
Total equity
850
930
Medium-term bank loan
200
200
Total assets
Equity and liabilities
Current liabilities
Bank overdraft
140
250
Trade payables
280
510
Other payables
60
100
––––––––
Total equity and liabilities
480
––––––––
860
––––––––
––––––––
1,530
1,990
––––––––
––––––––
Statements of profit or loss for the year ending 31st March:
Sales
Year 5
Year 6
Rs.000
Rs.000
1,800
2,900
Gross profit
210
260
Profit before tax
120
160
30
40
90
120
Taxation
DON paid dividends of Rs. 40,000 each year to the equity shareholders.
Required
Evaluate whether DON is over-trading.
Over-trading is defined as expanding a business quickly with insufficient longterm finance, and relying excessively on short-term sources of finance. A
business entity is therefore over-trading when it attempts to carry on a growing
volume of business with insufficient working capital.
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29.3
WASEEM LIMITED
Waseem Limited is engaged in manufacture and sale of consumer products. It’s
management is in the process of developing the sales plan for the next year.
The sales director is of the view that the main hurdle in increasing the sales is
the availability of finance.
The summarized statement of financial position as of November 30, 2016 is shown
below:
Rs. in million
ASSETS
Fixed assets
950
Current assets
730
1,680
LIABILITIES AND EQUITIES
Ordinary share capital
250
Retained earnings
450
700
Long term debts
Current liabilities
465
515
1,680
Following additional information is available:
(i)
It has been established from the company’s past record that any increase
in sales require an investment of 140% of the additional sales amount, in
inventories and accounts receivable. Further, the accounts payable of the
company also increase by 25% of the additional sales amount.
(ii)
The current sales of the company is Rs. 1,100 million while the net profit
after tax is 10% of sales.
(iii)
It is the policy of the company to distribute 20% of its profit after tax among
the shareholders of the company.
Required
Assuming that you are the Chief Financial Officer of the company, advise the
management on the following:
(a)
How much additional finance would be required to achieve 20% increase in
sales in the next year?
(b)
What would be the maximum growth in sales that the company can achieve
if:
‰
external finances are not available?
‰
the additional financing is limited to an amount which will maintain the
existing debt equity ratio?
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CHAPTER 30 – INVENTORY MANAGEMENT
30.1
MARX LIMITED
The finance manager of Marx Limited has recognised the need for some
improvements in working capital management, and is looking in particular at inventory.
The company’s main inventory item is Material M. Current policy is to purchase 50,000
units of Material M when the inventory level falls to 25,000 units. Annual demand for
Material M is currently 400,000 units. The cost of holding one unit of Material M in store
is Rs. 0.75 per year, and the cost of placing a purchase order for Material M is Rs. 240.
These costs are expected to remain constant for the foreseeable future. Orders are
delivered exactly two weeks after they are placed with the supplier. You should
assume constant demand throughout the year and a 50-week year.
Required
30.2
(a)
Explain the main objectives of working capital management and the conflict
that may arise between them.
(b)
Calculate the annual cost of the current inventory ordering policy and the
saving that would be achievable if the company switched to using the
Economic Order Quantity (EOQ) model to decide purchase quantities for
Material M.
ENGELS LIMITED
The recently-appointed financial manager of Engels Limited has gathered the following
information as part of an investigation into inventory.
The current policy is to order 100,000 units when the inventory level falls to 35,000
units. Forecast demand to meet production requirements during the next year is
625,000 units. The cost of placing and processing an order is Rs. 250, while the cost of
holding a unit in stores is Rs. 0·50 per unit per year. Both costs are expected to be
constant during the next year. Orders are received two weeks after being placed with
the supplier. You should assume a 50-week year and that demand is constant
throughout the year.
Required
Calculate the cost of the current ordering policy and determine the saving that
could be made by using the economic order quantity model.
30.3
LENIN LIMITED
(a)
Discuss the key factors which determine the level of investment in current
assets.
(b)
Lenin Limited wishes to minimise its inventory costs. Annual demand for a
raw material costing Rs. 12 per unit is 60,000 units per year. Inventory
management costs for this raw material are as follows:
Ordering cost:
Rs. 6 per order
Holding cost:
Rs. 0·5 per unit per year
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The supplier of this raw material has offered a bulk purchase discount of
1% for orders of 10,000 units or more.
If bulk purchase orders are made regularly, it is expected that annual
holding cost for this raw material will increase to Rs. 2 per unit per year.
Required
(i)
Calculate the total cost of inventory for the raw material when using
the economic order quantity.
(ii)
Determine whether accepting the discount offered by the supplier will
minimise the total cost of inventory for the raw material.
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CHAPTER 31 – MANAGEMENT OF RECEIVABLES AND PAYABLES
31.1
TRADE RECEIVABLES MANAGEMENT
Entity M is reviewing its credit policy. It is estimated that if the period of credit
allowed to customers is reduced to 60 days, there will be a 25% reduction in
annual sales, but bad debts would be reduced by Rs. 30,000 each year. It would
also be necessary to spend an extra Rs. 20,000 each year on credit control.
Entity M has cash flow difficulties and relies on overdraft finance, for which the
interest rate is 9%.
Required
Calculate the effect of these changes on the annual profit. Base your answer on
the level of sales in Year 3, and assume that purchases and inventory would be
reduced in the same proportion as the reduction in sales.
Entity M - Extracts from annual accounts
Inventory
Rs.
Raw materials
180,000
Work in progress
31.2
Year 3
93,360
Finished goods
142,875
Purchases
720,000
Cost of goods sold
1,098,360
Sales
1,188,000
Trade receivables
297,000
Trade payables
126,000
BAHAWALPUR BULIDERS LTD
Bahawalpur Buliders Ltd makes annual credit sales of Rs. 4,800,000. Credit
period was 30 days but due to poor credit administration, the average collection
period has been 45 days with 1% sales resulting in bad debts which is normally
written off.
A factor is being considered to take up the administration of the debts and trade
credits at an annual fee of 2.5% of credit sales. In this respect, the company
would save administrative costs of Rs. 96,000 annually and the payment period
is expected to be 30 days.
The factor would provide 80% of invoiced debts in advance at an interest rate of
12% per annum (base rate). The company can obtain overdraft facility to finance
its debtors at a rate of 2.5% over base rate.
Required
(a)
Advise the company’s management on whether or not to accept the
services of a factor.
(b)
“Factoring is one of the popular ways of managing accounts receivable in
corporate organizations”.
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When should factoring be used for debt collection?
(c)
31.3
Briefly explain each of the following factoring terms:
(i)
Full service non-recourse
(ii)
Full service recourse factoring
(iii)
Non-notification factoring
CHISHTIAN CONSTRUCTION PLC
(a)
Chishtian Construction Plc. has just won a big contract and needs
additional working capital of Rs. 9.5 billion to be able to execute the
contract. Investigations carried out by the company revealed the following
three feasible sources of funds:
(i)
Bank Loan: The company’s banker “Apex Bank” has agreed to
extend a loan facility of Rs. 10.6billion at 14%. A 10% compensating
balance will be required.
(ii)
Trade Credit: Chishtian Construction Plc. buys about Rs. 5billion of
materials per month on terms of “3/10, net 90”. Discounts are
currently taken.
(iii)
Factoring: Here, a factor will buy the company’s receivables (Rs. 15
billion per month) which have an average collection period of 30days.
The factor will advance up to 75% of the face value of the receivables
at 12% on an annual basis and 2% fee on all receivables purchased.
It was estimated that the factor’s service will save the company Rs.
250million per month – consisting of both bad debt expenses and
credit department expenses.
Required
Determine, on the basis of annualised percentage cost, which alternative
the company should select.
(b)
31.4
Evaluate FIVE factors that should be considered by an organization when
formulating a policy for credit control.
DISCOUNT AND FACTOR
(a)
A business entity offers its customers trade credit of 90 days. It is
considering whether to offer a settlement discount of 2% for payment within
seven days.
Required
Calculate the cost of offering the discount, as an annual interest cost.
(b)
Entity C has monthly sales of Rs. 100,000. A factor has offered to take over
the administration of Entity C’s trade receivables, on a non-recourse basis
(or without recourse basis). It would charge a fee of 4% of the value of
invoices processed. If the factor takes over this work, Entity C would save
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monthly administration costs of Rs. 2,000 and would avoid its bad debts,
which are 0.75% of sales.
Entity C has been informed by the factor that the average collection period
(the time between issuing an invoice and receiving payment from the
customer) will be reduced from 2 months to 1 month.
The factor will also provide finance by lending 80% of the value of unpaid
invoices, charging interest at an annual rate of 8% on the cash that it lends.
At the moment, Entity C finances its trade receivables with bank overdraft
finance at 9% per year interest.
Calculate the net effect on annual profits of Entity C if the factor took over
the administration of the trade receivables and provided finance on the
terms described above.
31.5
VEHARI IT SOLUTIONS LIMITED
Vehari IT Solutions Limited is a software business owned and managed by two
computer software specialists. Although, sales have remained stable at Rs.
40,000,000 per annum in recent years, the level of trade receivable has
increased significantly. A recent financial report submitted to the owners
indicates an average settlement period of 60 days for trade receivable compared
with an industry average of 40 days. The level of bad debts has also increased
in recent years and the company now writes off approximately Rs. 40,000 bad
debts each year.
The recent problems experienced in controlling credit have led to a liquidity crisis
for the company. At present, the company finances its trade receivables by a
bank overdraft on an interest rate of 14% a year. However, the overdraft limit
has been exceeded on several occasions in recent months and the bank is now
demanding a significant decrease in the size of the overdraft.
To meet this demand, the owners of the company have approached a factor who
has offered to make an advance payment equivalent to 85% of trade receivables
based on the assumption that the level of receivables will be in line with the
industry average.
The factor will charge a rate of interest of 12% a year for this advance. The factor
will take over the sales records of the Company and, for this service, will charge a
fee based on 2% of sales. The company believes that the services offered by the
factor should eliminate bad debts and lead to administrative cost savings of Rs.
52,000 per year.
Required
(a)
Calculate the effect of employing a debt factor on the profit of Vehari IT
Solutions Limited. Comment on your findings.
Note: You may assume 360 days in a year.
(b)
State FIVE potential advantages and TWO disadvantages of using the
services of a debt factor by a business organisation.
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31.6
ULNAD CO
Ulnad Co has annual sales revenue of Rs. 6 million and all sales are on 30 days’
credit, although customers on average take ten days more than this to pay.
Contribution represents 60% of sales and the company currently has no bad
debts. Accounts receivable are financed by an overdraft at an annual interest rate
of 7%.
Ulnad Co plans to offer an early settlement discount of 1.5% for payment within
15 days and to extend the maximum credit offered to 60 days. The company
expects that these changes will increase annual credit sales by 5%, while also
leading to additional incremental costs equal to 0.5% of turnover. The discount is
expected to be taken by 30% of customers, with the remaining customers taking
an average of 60 days to pay.
Required
31.7
(a)
Evaluate whether the proposed changes in credit policy will increase the
profitability of Ulnad Co.
(b)
Identify and explain the key areas of accounts receivable management.
BRUTUS COMPANY
Brutus Company has annual sales revenue of Rs. 8 million. It has a contribution
to sales ratio of 45% and its annual fixed costs are Rs. 2.5 million. These figures
exclude bad debts which are currently 1.25% of sales. All sales are on credit and
standard credit terms are 30 days, although customers take on average 45 days
to pay. Accounts receivable are financed by a bank overdraft on which interest is
payable at 8%.
The company’s management are considering whether to offer a discount of 2.5%
for all customers who pay within 14 days, and to extend the credit period for other
customers to 60 days. It has been estimated that if this policy is introduced, 25%
of customers would take the settlement discount and the rest would take the full
60 days credit offered.
The new policy would result in higher administration costs equal to 0.5% of total
gross sales. It is expected that total (gross) sales would be boosted, and would
increase by 3% per year. It is also expected that bad debts would fall to 1% of
gross sales.
Required
Calculate the effect that the new policy would have on annual profit and
recommend whether the new policy should be introduced. Suggest an alternative
policy for the management of receivables that might improve profit by a larger
amount.
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CHAPTER 32 – CASH MANAGEMENT
32.1
BAUMOL AND MILLER-ORR
(a)
Entity X uses a bank account for its daily expenditures. There are no
payments into the account. Instead, whenever the account needs more
cash, Entity X sells a quantity of marketable securities. These currently
provide an interest yield of 5% per year. The cost of selling securities is Rs.
60 per transaction, regardless of the size of the transaction.
Annual payments from the account are Rs. 3,000,000.
Required
Use the Baumol cash management model to decide the optimal size of
transaction for selling marketable securities, and the frequency with which
securities will be sold. Assume a 365-day year.
(b)
Entity Y uses a bank account for its daily income and expenditures. Each
year, it expects income and expenditure to be Rs. 3,000,000. However,
daily cash flows are variable, and the standard deviation of daily cash flows
is Rs. 2,200. The annual interest rate is 5%.
If the cash balance goes above a certain level, the entity will buy
marketable securities to earn interest on the surplus cash. If the cash
balance reaches a minimum level, the entity will sell some marketable
securities to obtain more cash. The cost of buying or selling securities is
Rs. 60 per transaction.
Entity Y uses the Miller-Orr cash management model. It has decided that it
should have a minimum cash balance of Rs. 20,000.
Calculate:
32.2
(a)
the spread between the lower and upper cash limits
(b)
the upper cash limit
(c)
the return point.
RENPEC CO
Renpec Co has set a minimum cash account balance of Rs. 7,500. The average
cost to the company of making deposits or selling investments is Rs. 18 per
transaction and the standard deviation of its cash flows was Rs. 1,000 per day
during the last year. The average interest rate on investments is 5.11%.
Required
(b)
Determine the spread, the upper limit and the return point for the cash
account of Renpec Co using the Miller-Orr model and explain the relevance
of these values for the cash management of the company.
(d)
Discuss the key factors to be considered when formulating a working
capital funding policy.
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32.3
BAUMOL
Explain how the Baumol cash model can be used to reduce the costs of cash
management and discuss whether the model might be of any assistance to the
finance manager of a travel company.
32.4
CASSIUS COMPANY
Cassius Company is a subsidiary of Brutus. It uses the Miller-Orr model to
manage its cash balances and has set a minimum cash balance of Rs. 12,500.
The average rate received on investments is currently 5.68%. Over the past year,
the standard deviation of daily cash flows has been Rs. 2,800. The cost to the
company of selling investments or making deposits is Rs. 20 per transaction.
Required
(a)
Calculate the spread, the upper limit and the return point for cash balances
using the Miller-Orr model and explain the meaning and purpose of these
amounts for the purpose of cash management.
(b)
Suggest with reasons how Cassius Company might invest its short-term
cash surpluses.
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SECTION
Certified finance and accounting professional
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B
Answers
CHAPTER 1 – AN INTRODUCTION TO STRATEGIC FINANCIAL
MANAGEMENT
1.1
COMPANY OBJECTIVES
(a)
Financial management is concerned with making decisions about the
provisions and use of a firm’s finances. A rational approach to decisionmaking necessitates a fairly clear idea of what the objectives of the
decision maker are or, more importantly, of what are the objectives of those
on behalf of whom the decisions are being made.
There is little agreement in the literature as to what objectives of firms are
or even what they ought to be. However, most financial management
textbooks make the assumption that the objective of a limited company is to
maximise the wealth of its shareholders. This assumption is normally
justified in terms of classical economic theory. In a market economy, firms
that achieve the highest returns for their investors will be the firms that are
providing customers with what they require. In turn these companies,
because they provide high returns to investors, will also find it easiest to
raise new finance. Hence the so-called ‘invisible hand’ theory will ensure
optimal resource allocation and this should automatically maximise the
overall economic welfare of the nation.
This argument can be criticised on several grounds. Firstly it ignores
market imperfections. For example it might not be in the public interest to
allow monopolies to maximise profits. Secondly it ignores social needs like
health, police, defence etc.
From a more practical point of view directors have a legal duty to run the
company on behalf of their shareholders. This however begs the question
as to what do shareholders actually require from firms.
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Another justification from the individual firm’s point of view is to argue that it
is in competition with other firms for further capital and it therefore needs to
provide returns at least as good as the competition. If it does not it will lose
the support of existing shareholders and will find it difficult to raise funds in
the future, as well as being vulnerable to potential take-over bids.
Against the traditional and ‘legal’ view that the firm is run in order to
maximise the wealth of ordinary shareholders, there is an alternative view
that the firm is a coalition of different groups: equity shareholders,
preference shareholders and lenders, employees, customers and suppliers.
Each of these groups must be paid a minimum ‘return’ to encourage them
to participate in the firm. Any excess wealth created by the firm should be
and is the subject of bargaining between these groups.
At first sight this seems an easy way out of the ‘objectives’ problem. The
directors of a company could say ‘Let’s just make the profits first, then we’ll
argue about who gets them at a later stage’. In other words, maximising
profits leads to the largest pool of benefits to be distributed among the
participants in the bargaining process. However, it does imply that all such
participants must value profits in the same way and that they are all willing
to take the same risks.
In fact the real risk position and the attitude to risk of ordinary shareholders,
loan creditors and employees are likely to be very different. For instance, a
shareholder who has a diversified portfolio is likely not to be so worried by
the bankruptcy of one of his companies as will an employee of that
company, or a supplier whose main customer is that company. The
problem of risk is one major reason why there cannot be a single simple
objective which is common to all companies.
(b)
Separate from the problem of which goal a company ought to pursue are
the questions of which goals companies claim to pursue and which goals
they actually pursue. Many objectives are quoted by large companies and
sometimes are included in their annual accounts. Examples are:
‰
to produce an adequate return for shareholders
‰
to grow and survive autonomously
‰
to improve liquidity
‰
to improve productivity
‰
to give the highest quality service to customers
‰
to maintain a contented workforce
‰
to be technical leaders in their field
‰
to be market leaders
‰
to acknowledge their social responsibilities.
Some of these stated objectives are probably a form of public relations
exercise. At any rate, it is possible to classify most of them into four
categories which are related to profitability:
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(i)
pure profitability goals e.g. adequate return for shareholders
(ii)
‘surrogate’ goals of profitability e.g. improving productivity, happy
workforce
(iii)
constraints on profitability e.g. acknowledging social responsibilities,
no pollution, etc.
(iv)
‘dysfunctional’ goals.
The last category is goals which should not be followed because they do
not benefit in the long run. Examples here include the pursuit of market
leadership at any cost, even profitability. This may arise because
management assumes that high sales equal high profits which is not
necessarily so.
In practice, the goals which a company actually pursues are affected to a
large extent by the management. As a last resort, the directors may always
be removed by the shareholders or the shareholders could vote for a takeover bid, but in large companies individual shareholders lack voting power
and information. These companies can, therefore, be dominated by the
management.
There are two levels of argument here. Firstly, if the management do
attempt to maximise profits, then they are in a much more powerful position
to decide how the profits are ‘carved up’ than are the shareholders.
Secondly, the management may actually be seeking ‘prestige’ goals rather
than profit maximisation. Such goals might include growth for its own sake,
including empire building or maximising turnover for its own sake, or
becoming leaders in the technical field for no reason other than general
prestige. Such goals are usually ‘dysfunctional’.
The dominance of management depends on individual shareholders having
no real voting power, and in this respect institutions have usually preferred
to sell their shares rather than interfere with the management of
companies. There is some evidence, however, that they are now taking a
more active role in major company decisions.
From all that has been said above, it appears that each company should
have its own unique decision model. For example, it is possible to construct
models where the objective is to maximise profit subject to first fulfilling the
target levels of other goals. However, it is not possible to develop the
general theory of financial management very far without making an initial
simplifying assumption about objectives. The objective of maximising the
wealth of equity shareholders seems the least objectionable.
1.2
POSSIBLE CONFLICTS
Achievement of the objective of maximisation of the value of a firm might be
compromised by conflicts which may arise between the managers and the other
stakeholders in an organisation. Such conflicts include:
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(i)
Managers might not work industriously to maximise shareholders’ wealth if
they feel that they will not have a fair share in the benefits of their labour.
(ii)
There might be little incentive for managers to undertake significant
creative activities, including looking for profitable new ventures or
developing new technology.
(iii)
Managers might be giving themselves high salaries and perks.
(iv)
Managers might be providing themselves with larger empires, through
merger and organic growth, thus increasing their opportunity for promotion
and social status.
(v)
Reducing risk through diversification which may not necessarily benefit
shareholders, but may well improve the managers’ security and status.
(vi)
Managers might take a more short-term view of the firm’s performance than
the shareholders would wish.
(vii) Management acting on behalf of shareholders, might also reduce the
wealth e.g. by selling off assets of the company.
viii)
1.3
Since senior managers do not own the business, they may be more
concerned with their benefits rather than maximizing the wealth of
shareholders.
OWNERSHIP
(a)
(b)
A publicly quoted company seeks to know the detailed composition of its
shareholders and their objectives in investing in the company for the
following reasons:
(i)
To enable it take various decisions in accordance with the
preferences of such shareholders.
(ii)
To prevent the occurrence of conflict of interest as related to principal
and agents.
Advantages that may accrue to the corporate finance manager include the
following:
(i)
Dividend Policy - The knowledge of shareholders’ preferences with
regards to dividends or capital appreciation and marginal tax rates will
assist in the determination of the company’s optimal dividend policy.
(ii)
Risky Investment - Shareholders’ preferences may assist corporate
management when making decisions concerning risky capital
investments. Depending on their attitude to risk and their specific
circumstances, they may dislike, or prefer the company to undertake
risky investments with the possibility of a higher return.
(iii)
Financing Decisions – With respect to the level of debt to employ,
the risk attitude of shareholders can again be useful; generally
speaking, a risky approach is to employ more and more debt, since in
the event of default, the shareholders are paid last. However, a high
level of risk is matched by a high potential return to equity holders.
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(iv)
Rebuffing a take-over: A company whose shares are held by a few
may find an unwanted take-over bid less easy to rebuff as the bidder
needs to convince only a few shareholders for the bid to be
successful. However, if shares are held by a few key shareholders, it
may be easier to provide these shareholders with the type of return
they require with a possible reduction in their likely acceptance of any
take-over.
(v)
Measurement of performance: Ascertaining how shareholders
judge performance may enable management to optimise this
measure or measures, when making decisions, although this
measure may not be in the prime interest of the company in terms of
value maximisation.
(vi)
Religious belief: Knowing the religious belief of the shareholders will
assist in deciding the type of business to be involved in. For
example, Islam forbids investment in businesses involved in the
manufacture and sale of alcohol. Such information will enable
corporate finance managers to tailor their performance to satisfy the
expectations of the shareholders.
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CHAPTER 2 – RELEVANT CASH FLOWS
2.1
SHOCKLAT CO
(a)
Factors to consider
When making any decision with a financial impact, the relevant costs and
benefits of the decision should be considered.
(b)
(1)
Incremental revenue. By further processing the basic product into
CP1 and CP2, Shoklat will make incremental revenue. The additional
revenue that would be earned is a relevant factor.
(2)
Incremental costs. Further processing will result in incremental costs
and also some opportunity costs. These are the relevant costs of
further processing which must be included in the financial evaluation.
(The relevant costs are the future cash flows arising as a direct
consequence of the further processing decision.) However costs that
have already been incurred, such as the market research costs, are
not relevant.
(3)
Impact on sales of the basic product. By making CP1 and CP2,
production and sales quantities of the basic product will be lost. The
loss of profit must be included in the relevant cost calculation. In
addition the company should consider the possible effect on customer
loyalty in the longer term if supply to the market of the basic product
is reduced. It might provide an opportunity for a rival producer of
chocolate products to increase its share of the market for chocolate
for children.
(4)
Product safety. The company must be fully satisfied about the safety
of the new products CP1 and CP2 before introducing them to the
market. If testing has not yet been carried out, this will have an
incremental cost to take into consideration.
The incremental costs and benefits of further processing would be the
same in each month of the trial period; therefore it is sufficient to make
calculations for just one month.
Workings: opportunity cost of direct labour
Direct labour has an opportunity cost because it is in short supply and using
labour to make CP1 and CP2 means that there will be a reduction in sales
of the basic product.
The proposal is to further process 35,000 kilos of the basic product each
month.
Cost of M1: 3/7 u 35,000 kilos u Rs. 9
Cost of M2: 4/7 u 35,000 kilos u Rs. 7
Material cost of the basic product
Direct labour: 2,000 hours u Rs. 20
Total variable cost
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Rs.
135,000
140,000
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Sales value: 35,000 kilos u Rs. 14
Total contribution from these quantities
Contribution per direct labour hour
(Rs. 175,000/2,000 hours)
Rs.
490,000
175,000
Rs. 87.50
Incremental revenue and costs from further processing
The following costs are not relevant and should be ignored in the
calculation:
(1)
The market research cost is not relevant because it has already been
incurred.
(2)
The cost of the supervisor is not relevant because his salary will be
paid anyway, and there will be no extra cash spending on
supervision.
(3)
The fixed overhead absorption rate is irrelevant because absorbed
fixed overheads are not relevant costs. It is assumed that there will be
no increase in actual cash spending on fixed overhead items as a
consequence of the further processing.
Further processing to make CP1
Rs.
Revenue from 6,800 kilos of CP1 (u Rs.
30)
Rs.
204,000
Revenue from 6,000 kilos of basic
product
(u Rs. 14)
84,000
Incremental revenue from further
processing
120,000
Incremental costs of further processing
800 kilos of M3 (u Rs. 19)
15,200
Direct labour: basic pay for 900 hours (u
Rs. 20)
18,000
Direct labour: opportunity cost of not
selling basic product (900 u Rs. 87.50)
78,750
Total incremental costs
111,950
Incremental profit from further processing
to make CP1, per month
8,050
Over a three-month trial period, there would be incremental profits of Rs.
24,150 from making and selling CP1. This is a fairly small amount given
the volume of processing involved, and comes to an additional profit of
about Rs. 1.34 for each kilo of the basic product that is further processed.
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Further processing to make CP2
Rs.
Rs.
Revenue from 30,200 kilos of CP2 (u Rs.
20.50)
619,100
Revenue from 29,000 kilos of basic product
(u Rs. 14)
406,000
Incremental revenue from further processing
213,100
Incremental costs of further processing
1,200 kilos of M4 (u Rs. 80)
96,000
Direct labour: basic pay for 1,250 hours (u Rs.
20)
25,000
Direct labour: opportunity cost of not selling
basic product (1,250 u Rs. 87.50)
109,375
Total incremental costs
230,375
Incremental loss from further processing to
make CP2, per month
(17,275)
Over a three-month trial period, there would be an incremental loss of Rs.
51,825 from making and selling CP2. This suggests that unless the
product can be sold for a higher price or incremental costs can be
produced, the company should not make and sell CP2.
(c)
2.2
The breakeven selling price per kilo of CP2 would be the initial selling price
of Rs. 20.50 plus Rs.(17,275/30,200) = Rs. 20.50 + Rs.0.572 = Rs. 21.072.
TOPAZ LIMITED
Calculation of unit price to be quoted to Pearl Limited:
Rs.
Material (25,000 u 200)+(53,125 u 225) + 80,000
W1
17,033,125
Labour (20,000 u 45 × 40%) + (210,625 u 45)
W2
9,838,125
Variable overhead (230,625 × Rs. 25)
5,765,625
Incremental fixed cost (Rs. 22m u 10% u 1.5)
W3
3,300,000
35,936,875
Profit margin (25% of cost)
8,984,219
Sale price
44,921,094
Sale price per unit ( Rs. 44,921,094 / 150,000)
299
W1: Material
Input units of material C (150,000 / 96%) × 0.5
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W2: Labour
Labour hours – completed units 150,000 u 1.50
225,000
– lost units
{[(150,000 / 0.96) – 150,000] u 1.5 u 60%}
5,625
230,625
W3: Capacity
2.3
Percentage of existing capacity required by the project
30%
Spare capacity without project (100% – 80%)
20%
Capacity that must be obtained elsewhere
10%
TYCHY LIMITED
Tychy Limited (TL)
Note
Rs.
Technical manager – meeting
1
NIL
Wire – C
2
8,160
Wire – D
3
600
Components
4
2,400
Direct labour
5
3,250
Machine running cost
6
450
Fixed overhead
7
NIL
Total relevant cost
14,860
Notes:
1.
In case of technical manager’s meeting with the potential client, the
relevant cost is NIL because it is not only a past cost but also the
manager is paid an annual salary and therefore TL has incurred no
incremental cost on it.
2.
Since wire-C is regularly used by TL, its relevant value is its
replacement cost. The historical cost is not relevant because it is a past
cost and the resale value is not relevant since TL is not going to sell it.
3.
Since wire-D is to be purchased for the contract therefore its purchase
cost is relevant. TL only requires 50 kg of wire-D but due to the
requirement of minimum order quantity TL will be purchasing 60 kg of
the material and since TL has no other use for this material, the full cost
of purchasing the 60 kg is the relevant cost.
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4.
Since the components are to be purchased from the market at a cost of
Rs. 80 each. Therefore, the entire purchase price is a relevant cost.
5.
The 100 hours of direct labour are presently idle and hence have zero
relevant cost. The remaining 150 hours are relevant. TL has two
choices: either use its existing employees and pay them overtime at
Rs. 23 per hour which is a total cost of Rs. 3,450: or engage the
temporary workers which would cost TL Rs. 3,250 including supervision
cost of Rs. 100. The relevant cost is the cheaper of the two alternatives
i.e. Rs. 3250.
6.
The lease cost of machine will be incurred regardless of whether it is
used for the manufacture of motors or remains idle. Hence, only the
incremental running cost of Rs. 15 per hour is relevant.
7.
Fixed overhead costs are incurred whether the work goes ahead or not
so it is not a relevant cost.
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CHAPTER 3 – DECISION MAKING
3.1
PAKPATTAN ELECTRONICS LIMITED
(a)
(i)
Materials
Rs.
K: 3,000 kg at (Rs. 19,600 ÷ 2,000) u 1.05
L: 200 kg at Rs. 11
30,870
2,200
33,070
(ii)
Skilled labour
Rs.
Labour cost 800 hours at Rs. 9·50
Opportunity cost of labour 800 hours at (Rs. 40 ÷
4)
7,600
8,000
15,600
(iii)
There is no indication of relevant fixed costs so the total relevant cost
of the contract is the sum of relevant labour and materials costs:
Rs.
Labour
15,600
Materials
33,070
Total
48,670
Given that the extra cost of completing the contract in house is Rs.
48,670 the company should not be prepared to pay more than this to
outsource
(b)
Any variable overhead costs associated with the contract would be relevant
because they would represent additional or incremental costs caused
directly by the contract.
Fixed overhead costs would only be relevant if the total fixed overhead
costs of the company increased as a direct consequence of the contract
being undertaken. In that case the relevant amount would be the specific
increase in the total fixed overhead costs caused by the acceptance of the
contract. Arbitrary apportionments of existing fixed overhead costs would
not be relevant. Similarly sunk and committed costs would not be relevant.
(c)
To:
Senior Management Team
From:
Management Accountant
Concerning:
Outsourcing
Introduction
Outsourcing can have a major impact on the structure operation of a
business. If successful it can enhance quality and profitability. If it fails it
can threaten the existence of the business.
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Relevant costing
Outsourcing decisions based on relevant costing can be misleading. If
relevant fixed costs savings are included, for instance, how certain can the
company be that these savings will actually arise? The absence of such
savings may lock a company into higher costs than expected rendering the
outsourcing uneconomic
Reversibility
If a product or service is outsourced, how easy is it for a company to
reverse this process if the relationship proves unsatisfactory or the supplier
goes out of business? Loss of key personnel may the most critical factor
here. If it is difficult/impossible to reverse should the company undertake
the outsourcing?
Impact on remaining business
Closure of a significant part of a business due to outsourcing may have an
adverse effect on staff morale, particularly if significant redundancies are
involved. The impact of this needs to be quantified and included in the
assessment process.
Reaction of customers
Are customers likely to react adversely to an outsourcing decision?
Consider, for example, the negative reaction of UK customers to the
outsourcing of bank account and broadband support to Indian call centres.
Flexibility
Is the outsourcing company able to scale its production to match our
needs? If our business doubles in size in 18 months will the outsource
company be able to cope. Equally, what is the financial cost of this
flexibility? If we don't meet forecast levels of activity are there financial
penalties?
Quality
There is a danger that by focussing on costs we forget quality. What
guarantees of quality do we have. Does the supplier have a track record of
high quality output/service provision?
Summary
Whilst outsourcing potentially offers the company significant benefits, a
wide range of criteria need to be considered. Relevant costing is a useful
tool here but a range of non-financial factors should be considered.
3.2
WAZIR MANUFACTURING LTD
(a)
Tutorial note
Though this question looks complex due to the volume of information, it is
actually relatively straightforward. At its heart this is a limiting factor question.
What production mix maximises return on material R2? Work out the
contribution per unit of R2 used for each of the products – these figures are then
used to prioritise production.
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AR2
GL3
HT4
Rs. per
unit
Rs. per
unit
Rs. per
unit
Material R2
2.5 u 2
5.00
2.5 u 3
7.50
2.5 u 3
7.50
Material R3
2u2
4.00
2 u 2.2
4.40
2 u 1.6
3.20
4 u 0.6
2.40
4 u 1.2
4.80
4 u 1.5
6.00
Labour
Variable overhead
1.10
1.30
1.10
Variable costs
12.50
18.00
17.80
Selling price
21.00
28.50
27.30
Contribution
8.50
10.50
9.50
2
3
3
Rs.
4.25
Rs.
3.50
Rs. 3.17
1
2
3
R (kg per unit)
Contribution per kg
Ranking
Product
Demand
R2 used
Production
Contribution
units
kg
units
Rs.
950
1,900
950
8,075
AR2
1,000
3,000
1,000
10,500
GL3
900
600
200
1,900
HT4
5,500
20,475
The optimum production schedule is 950 units of Product AR2, 1,000 units of
GL3 and 200 units of HT4, giving a total contribution of Rs. 20,475.
Tutorial note:
The fixed production overheads are ignored in this analysis because they are
assumed not to vary with changes in the level of production.
(b)
Further supplies of Material R2 will be used to produce additional units of
Product HT4. The contribution per kg of Material R2 of Product HT4 is Rs.
3.17 and so if Wazir Manufacturing Ltd pays 3.17 + 2.50 = Rs. 5.67 per kg
for Material R2, the additional units of Product HT4 produced will make a
zero contribution towards fixed costs. Rs. 5.67 is therefore the maximum
price.
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(c)
Tutorial note
Any decision cannot just involve comparison of variable costs as there is an
incremental cost of Rs. 50,000 to be accounted for.
Strong answers will also distinguish between short and long-term decisionmaking, together with considering non-financial criteria.
The variable cost of Product XY5:
Rs./unit
Material R3: 3 u 2 =
6.00
Labour: 1.7 u 4 =
6.80
Variable overhead:
1.40
14.20
The substitute offered by Kenzi Chemicals Ltd gives a saving of Rs. 4 per unit.
However, Wazir Manufacturing Ltd would also pay an annual fee of Rs. 50,000
for the right to use the substitute.
The company would need to manufacture more than Rs. 50,000/Rs. 4 = 12,500
units per year of Product XY5, or 1,042 units per month, in order for the offered
substitute to be financially acceptable.
If it needed less than 12,500 units of Product XY5 per year, it would be cheaper
to manufacture the product internally.
This evaluation is from a short-term perspective: in the longer term, buying in
may lead to fixed cost savings and lower investment, increasing the benefits of
buying in and lowering the break-even point.
Wazir Manufacturing Ltd would also need to assure itself that the quality of the
substitute was acceptable and that this quality could be maintained: the lower
price offered by Kenzi Chemicals Ltd might be associated with poorer quality
than the minimum standard of quality considered necessary by Wazir
Manufacturing Ltd. Orders for the substitute product would also need to be
delivered promptly in order to avoid production hold-ups.
Wazir Manufacturing Ltd could also become dependent on Kenzi Chemicals Ltd
for supplies of the substitute product and might be vulnerable to future price
increases by the supplier. Such price increases might reduce or even eliminate
the cost saving of buying in.
(d)
Marginal costing (variable costing) treats fixed costs as a period cost, on
the assumption that fixed costs do not change in the short term. The
difference between selling price and variable costs is the variable
contribution made by units sold towards meeting fixed costs and generating
profit.
Marginal costing has traditionally been used for short-term decisions such as
whether to cease production of a product, whether to make a product or buy it
from a supplier, and how to allocate scarce resources in order to maximise
contribution.
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A major limitation with using marginal costing as the basis for making short-term
decisions is the assumption that fixed costs are irrelevant to short-term
decisions. In the longer term, fixed costs will change: for example, rent is usually
regarded as a fixed cost and in the longer term rent might be expected to
increase due to inflation. However, a change in fixed costs may be the result of a
short-term decision: for example, if a product is discontinued and as a result the
work of the marketing department decreases, in the longer term marketing costs
would be expected to decrease.
This points to the danger of relying on a simplistic analysis of costs into fixed
costs and variable costs, and of assuming that only variable costs are relevant
for decision-making purposes. It is possible for a fixed cost to be a relevant cost.
It is also possible for a variable cost to be irrelevant, for example in the case
where a variable cost is common to two decision alternatives. If fuel costs are
incurred whether a machine is leased or bought, for example, these costs are
not relevant to the decision on whether to lease or buy.
Reliance on marginal costing as a basis for making short-term decisions may
therefore lead to sub-optimal decisions overall for a company, as the analysis
may fail to consider all relevant costs.
3.3
KHOKHAR PERFUMERS LIMITED
(a)
Khokhar Perfumers Limited should consider the following factors when
making a further processing decision.
–
Incremental revenue. The new perfume, once further processed,
should generate a higher price and the extra revenue is clearly
relevant to the decision.
–
Incremental costs. A decision to further process can involve more
materials and labour. Care must be taken to only include those costs
that change as a result of the decision and therefore sunk costs
should be ignored. Sunk costs would include, for example, fixed
overheads that would already be incurred by the business before the
further process decision was taken. The shortage of labour means
that its ‘true’ cost will be higher and need to be included.
–
Impact on sales volumes. Khokhar Perfumers Limited is selling a
‘highly branded’ product. Existing customers may well be happy with
the existing product. If the further processing changes the existing
product too much there could be an impact on sales and loyalty.
–
Impact on reputation. As is mentioned in the question, adding
hormones to a product is not universally popular. Many groups exist
around the world that protest against the use of hormones in
products. Khokhar Perfumers Limited could be damaged by this
association.
–
Potential legal cases being brought regarding allergic reactions to
hormones.
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(b)
Production costs for 1,000 litres of the standard perfume
Aromatic oils
Diluted solvent
10 ltrs x Rs. 18,000/ltr
990 ltrs x Rs. 20/ltr
Material cost
Labour
2,000 hrs x Rs. 15/hr
Total
Cost per litre
Sales price per litre
Rs.
180,000
19,800
––––––––
199,800
30,000
––––––––
229,800
––––––––
229·80
399·80
Lost contribution per hour of labour used on new products
(Rs. 399,800 – Rs. 199,800) ÷ 2,000 hrs = Rs. 100/hr
Incremental costs
Male version
Female version
Rs.
Rs.
Hormone
2 ltr x Rs. 7,750/ltr
15,500 8 ltr x Rs. 12,000/ltr
96,000
Supervisor
Sunk cost
0 Sunk cost
0
Labour
500 hrs x Rs. 100/hr 50,000 700 hrs x Rs. 100/hr 70,000
Fixed cost
Sunk cost
0 Sunk cost
0
Market research Sunk cost
0 Sunk cost
0
–––––––
–––––––––
Total
65,500
166,000
–––––––
–––––––––
Incremental revenues
Male version
Female version
Rs.
Rs.
Standard
200 ltr x Rs. 399·80/ltr 79,960 800 ltr x Rs. 399·80 319,840
Hormone added 202 ltr x Rs. 750/ltr 151,500 808 ltr x Rs. 595/ltr
480,760
–––––––
–––––––––
Incremental revenue
71,540
160,920
–––––––
–––––––––
Net benefit/(cost)
6,040
(5,080)
–––––––
–––––––––
The Male version of the product is worth further processing in that the extra
revenue exceeds the extra cost by Rs. 6,040.
The Female version of the product is not worth further processing in that the
extra cost exceeds the extra revenue by Rs. 5,080.
In both cases the numbers appear small. Indeed, the benefit of Rs. 6,040 may
not be enough to persuade management to take the risk of damaging the brand
and the reputation of the business. To put this figure into context: the normal
output generates a contribution of Rs. 170 per litre and on normal output of
about 10,000 litres this represents a monthly contribution of around Rs. 1·7m
(after allowing for labour costs).
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Future production decisions are a different matter. If the product proves popular,
however, Khokhar Perfumers Limited might expect a significant increase in
overall volumes. If Khokhar Perfumers Limited could exploit this and resolve its
current shortage of labour then more contribution could be created. It is worth
noting that resolving its labour shortage would substantially reduce the labour
cost allocated to the hormone added project. Equally, the prices charged for a
one off experimental promotion might be different to the prices that can be
secured in the long run.
(c)
The selling price charged would have to cover the incremental costs of Rs.
166,000. For 808 litres that would mean the price would have to be
(Rs.166,000 + Rs.319,840)
= Rs.601.29/ ltr
808 ltrs
or about Rs. 60·13 per 100 ml.
This represents an increase of only 1·05% on the price given and so clearly
there may be scope for further consideration of this proposal.
(d)
Outsourcing involves consideration of many factors, the main ones being:
–
Cost. Outsourcing often involves a reduction in the costs of a
business. Cost savings can be made if the outsourcer has a lower
cost base than, in this case, Khokhar Perfumers Limited. Labour
savings are common when outsourcing takes place.
–
Quality. Khokhar Perfumers Limited would need to be sure that the
quality of the perfume would not reduce. The fragrance must not
change at all given the product is branded. Equally Khokhar
Perfumers Limited should be concerned about the health and safety
of its customers since its perfume is ‘worn’ by its customers
–
Confidentiality. We are told that the blend of aromatic oils used in
the production process is ‘secret. This may not remain so if an
outsourcer is employed. Strict confidentiality should be maintained
and be made a contractual obligation.
–
Reliability of supply. Khokhar Perfumers Limited should consider
the implications of late delivery on its customers.
–
Primary Function. Khokhar Perfumers Limited is apparently
considering outsourcing its primary function. This is not always
advisable as it removes Khokhar Perfumers Limited’s reason for
existence. It is more common to outsource a secondary function, like
payroll processing for example.
–
Access to expertise. Khokhar Perfumers Limited may find the
outsourcer has considerable skills in fragrance manufacturing and
hence could benefit from that.
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CHAPTER 4 – LINEAR PROGRAMMING
4.1
PROGLIN
(a)
Linear programme
Let the number of units of Mark 1 be x
Let the number of units of Mark 2 be y.
The objective function is to maximise total contribution: 10x + 15y.
Subject to the following constraints:
Direct materials
Direct labour
Sales demand, Mark 1
Non-negativity
2x + 4y
3x + 2y
x
x, y
≤
≤
≤
≥
24,000
18,000
5,000
0
These constraints are shown in the graph below. The graph also shows an
iso-contribution line (10x + 15y = 60,000).
x = 5,000
₦
9,000
3x + 2y = 18,000
6,000 A
B
4,000
C
D
0
5,000
6,000
12,000
The feasible solutions are shown by the area 0ABCD in the graph.
Using the slope of the iso-contribution line, it can be seen that contribution is
maximised at point B on the graph.
At point B, we have the following simultaneous equations:
(1)
(2)
Multiply (2) by 2
(3)
Subtract (1) from (3)
Therefore
Substitute in equation (1)
2x + 4y
3x + 2y
=
=
24,000
18,000
6x + 4y
=
36,000
4x
x
=
=
12,000
3,000
2 (3,000) + 4y
4y
y
=
=
=
24,000
18,000
4,500
The objective in this problem is to maximise 10x + 15y.
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The total contribution where x = 3,000 and y = 4,500 is as follows:
Rs.
3,000 units of Mark 1 (u Rs. 10)
30,000
4,500 units of Mark 2 (u Rs. 15)
67,500
Total contribution
97,500
(b)
The graph for a linear programming solution is virtually identical to the
graph shown above, and the solution is still at point B. However, at point B:
(1)
2x + 4y
=
24,001
(2)
Multiply (2) by 2
3x + 2y
=
18,000
(3)
Subtract (1) from (3)
6x + 4y
=
36,000
4x
=
11,999
x
=
2,999.75
3 (2,999.75) + 2y
2y
=
=
18,000
9,000.75
y
=
4,500.375
Therefore
Substitute in equation (2)
The objective in this problem is to maximise 10x + 15y.
The total contribution where x = 2,999.75 and y = 4,500.375 is as follows:
Rs.
2,999.75 units of Mark 1 (u Rs. 10)
29,997.500
4,500.375 units of Mark 2 (u Rs. 15)
67,505.625
Total costs
97,503.125
The effect of having Rs. 1 more of direct materials would be an increase of
Rs. 3.125 in total contribution.
The shadow price of direct materials is therefore Rs. 3.125 per Rs. 1 of direct
materials.
4.2
Light Engineering
(a)
Tutorial note: The first step is to make a clear statement of what is taken
to be x and what is taken to be y.
Let x = weekly production of water tanks
Let y = weekly production of water butts
Define the objective function:
The objective is to maximise contribution. Since each water tank (x)
contributes Rs. 50.00 and each water butt (y) contributes Rs. 40.00, the
objective function can be written as:
C = 50x + 40y
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Define the constraints:
(i)
Cutting time:
6x + 3y d 36
(ii)
Assembly time:
4x + 8y d 48
(iii)
Minimum constraints
The company has to produce at least two water tanks and three water
butts.
xt2
yt3
(b)
Constraints can be graphed by treating them as simple linear equations
and working out the value of x when y = 0 and the value of y when x = 0.
(1)
Cutting time constraint:
6x + 3y = 36
When x = 0, y = 12
When y = 0, x = 6
(2)
Assembly time constraint:
4x + 8y = 48
When x = 0 y = 6
When y = 0 x = 12
Together with non-negativity constraints, these lines can then be plotted on
a graph. The feasible region is the region within which values of x and y
meet all of the stated constraints.
12
Butts
6
P
Feasible
Region
3
2
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(c)
Tutorial note: The quickest way to find the contribution maximising mix of
products is to plot an iso-contribution line on to the graph. Slowly move the
line out from the origin – the last point inside the feasible region that it
passes through is the optimum product combination.
In this example this is point P.
P is the intersection of the lines:
(1)
6x + 3y = 36
(2)
4x + 8y = 48
The intersection of these lines can be found by solving the equations
simultaneously.
Step 1: Multiply equation 1 by 4 and equation 2 by 6:
(3)
24x + 12y = 144
(4)
24x + 48y = 288
Step 2: Subtract equation 3 from equation 4 to get:
36y =144
y=4
Step 3: Inserting the value of y into equation 1 gives:
6x + 3y = 36
6x + 12 = 36
6x = 24
x=4
Maximum contribution therefore occurs when 4 water tanks and 4 water
butts are produced.
This gives a contribution of
C = 50x + 40y
C = 4 u Rs. 50 + 4 u Rs. 40 = Rs. 360
(d)
Cutting time shadow price
The cutting time constraint is currently 6x + 3y = 36. An extra hour of
cutting time changes this to 6x + 3y = 37
The profit maximising equation can now be solved as:
(1)
6x + 3y = 37
(2)
4x + 8y = 48
Step 1: Multiply equation 1 by 4 and equation 2 by 6:
(3)
24x + 12y = 148
(4)
24x + 48y = 288
Step 2: Subtract equation 3 from equation 4 to get:
36y =140
y = 3.889
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Step 3: Inserting the value of y into equation 1 gives:
(1)
6x + 3y = 37
6x + 11.667 = 37
6x = 25.33
x = 4.22
Step 4: Calculate the new contribution:
C = 50x + 40y
C = 4.22 u Rs. 50 + 3.889 u Rs. 40 = Rs. 366.56
The shadow price of one extra hour of cutting time is Rs. 6.56 (Rs. 366.56 Rs. 360)
Assembly time shadow price
The cutting time constraint is currently 4x + 8y = 48. An extra hour of
cutting time changes this to 4x + 8y = 49
The profit maximising equation can now be solved as:
(1)
6x + 3y = 36
(2)
4x + 8y = 49
Step 1: Multiply equation 1 by 4 and equation 2 by 6:
(3)
24x + 12y = 144
(4)
24x + 48y = 294
Step 2: Subtract equation 3 from equation 4 to get:
36y =150
y = 4.167
Step 3: Inserting the value of y into equation 1 gives:
(1)
6x + 3y = 36
6x + 12.501 = 36
6x = 23.499
x = 3.917
Step 4: Calculate the new contribution:
C = 50x + 40y
C = 3.927 u Rs. 50 + 4.167u Rs. 40 = Rs. 363.03
The shadow price of one extra hour of cutting time is Rs. 3.03 (Rs. 363.03 Rs. 360)
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CHAPTER 6 – DISCOUNTED CASH FLOW
6.1
BADGER
Cash Flows
Machine
Existing machine
01/01/17
Rs. m
0
(180)
2
31/12/17
Rs. m
1
31/12/18
Rs. m
2
31/12/19
Rs. m
3
31/12/20
Rs. m
4
25
(1)
79
(32)
103
(48)
175
(57)
179
(73)
(6)
(13)
(9)
(10)
(8)
(9)
(8)
(10)
(3)
(3)
(6)
(3)
(3)
2
(3)
(1)
(179)
1.000
25
25
0.909
27
27
0.826
98
98
0.751
109
109
0.683
(179)
23
22
74
74
Operating flows
Sales W1
Purchases W2
Payments to
subcontractors
Fixed overhead
Labour costs:
Promotion
Redundancy
Material
X
Y
Net operating flows
Discount factor (10%
NPV
14
WORKINGS
(1)
Sales
2016
Rs. m
2017
Rs. m
2018
Rs. m
2019
Rs. m
2020
Rs. m
1,100
1,122
1,144
1,167
1,191
0.07
0.09
0.15
0.15
79
103
175
179
Opening payables
Add purchases
Less closing payables
2017
40
(8)
2018
8
50
(10)
2019
10
58
(11)
2020
11
62
-
Cash for purchases
32
Market size
Market share
Sales
(2)
Purchases
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6.2
HASAN AND SONS LIMITED
(a)
Calculation of the annual repayment
A
=
[1 - (1+ r) - n]
r
=
1 - ( 1.12) -20
0.12
=
7.4694
: . Annual repayment
=
=
(b)
•Ǥʹ,5000,000
7.4694
Rs. 334,698.90
Calculation of the NPV of the machine
Year
0
0
1-5
5
Cash flow
(Rs.)
(3,000,000)
(250,000)
540,000
250,000
DF@
12%
1.0000
1.0000
3.6048
0.5674
NPV
PV
(Rs.)
(3,000,000)
(250,000)
1,946,592
141,850
(1,161,558)
Advice:
The machine should not be bought, as its purchase would result in the
reduction of the shareholders’ wealth by Rs. 1,161,558.
6.3
DCF and relevant costs
Year
0
1
2
3
4
5
Rs.000 Rs.000 Rs.000 Rs.00 Rs.000 Rs.000
Sales
7,400 8,300
9,800
5,800
Wages
(550) (580)
(620)
(520)
Materials
(340) (360)
(410)
(370)
Licence fee
(300)
(300)
(300) (300)
(300)
Overheads
(100) (100)
(100)
(100)
Equipment
(5,200) (5,200)
2,000
Specialised equipment
(150)
Working capital
(650)
650
(5,500) (6,150)
5,960 6,960
8,370
7,460
Discount factor at 10%
Present value
1.000
0.909
0.826
0.751
0.683
0.621
(5,500) (5,590)
4,923
5,227
5,717
4,633
NPV = + Rs. 9,409,000
The project has a positive NPV. The project should be undertaken because it will
increase the value of the company and the wealth of its shareholders.
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6.4
Sadeeq Energy Plc
(a)
The difference between mutually exclusive investments and independent
investments is that for mutually exclusive investments, once one project is
selected another must be forgone because the projects are in competition,
whereas for independent investments/projects, the selection of one project
does not foreclose the selection of others.
(b)
(i)
Investment decision is important to organisations as it involves the
identification of viable projects. It deals with the appraisal of projects
using various techniques to determine those that are viable.
(ii)
Techniques that can be used to ensure optimal investments include
Net Present Value (NPV) Internal Rate of Return (IRR), Pay Back
Period and Accounting Rate of Return (ARR).
(c)
Using payback period:
Year
Cash flows
Rs.’000
(260,000)
0
1-12
480,000
i.e. 40m x 12
13 - 20
272,000
i.e. 34m x 8
Payback period
•Ǥʹ60,000,000
=
•ǤͶ0,000,000
=
years
6.5 years
The project should be accepted because it’s payback period is less than
the projects’ life.
(d)
NPV and IRR
Year
Cash flow
DF(15%)
Rs.‘000
Present Value
Rs.‘000
0
(260,000)
1.0000
(260,000)
1 – 12
40,000
5.4206
216,824
13 – 20
34,000
0.8387
28,516
Net Present Value
(14,660)
Using internal rate of return (IRR)
Try 12% discount factor
Year
Cashflow
DF(12%)
Rs.‘000
Rs.‘000
0
(260,000)
1.0000
(260,000)
1 – 12
40,000
6.1944
247,776
13 – 20
34,000
1.2750
43,350
Net Present Value
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Business finance decisions
§ NPVp DFn DFp
DFp ¨
¨ NPVp NPVp
©
IRR
·
¸
¸
¹
·
¸¸
¹
§ 31,126 u 15 12
= 12% + ¨¨
© 31,126 (14,660
= 12% + 2.039%
= 14.039%
6.5
BETA LIMITED
(a)
The summary of investment appraisal results are as follows:
Option I
Option II
82
107.41 (W1)
3.10
3.83 (W2)
Internal rate of return
10.50%
15.11% (W3)
Modified internal rate of return
13.20%
14.30% (W4)
Net present value (Rs. in million)
Payback period (years)
On financial ground, the project to be accepted should be the one with the
higher NPV, i.e. Option 2. NPV shows the absolute amount by which the
project is forecast to increase shareholders' wealth and is theoretically
more sound than the IRR and MIRR. However, In this case, both IRR and
MIRR back up the NPV.
The discounted payback period shows that Option II is more risky as it
takes longer to recover the present value.
WORKINGS
W1: Net present value
Year 0
Year 1
Year 2
Year 3
Year 4
Rs. in million
Outside Pak nominal cash flows
(W1.1)
(2,252.25)
244.23
308.25
348.35
357.65
-
366.30
423.50
551.03
658.85
(2,252.25)
610.53
731.75
899.38 1,016.50
0.885
0.783
0.693
0.613
540.32
572.96
623.27
623.11
Year 3
Year 4
Pak nominal cash flows (10%
inflation)
Total nominal cash flows
Discount factor at 13%
Present value
Net present value
1.000
(2,252.25)
107.41
W1.1: US$ nominal cash flows in Rupees
Exchange rate forecast (PY × 1.03
÷ 1.10)
© Emile Woolf International
A
174
Year 0
Year 1
Year 2
0.0111
0.0104
0.0097
0.0091
0.0085
The Institute of Chartered Accountants of Pakistan
Answers
in million
US$ net cash flows at current
prices
US $ net nominal cash flows (3%
inflation)
US$ nominal cash flows (Rs.)
(25.00)
2.47
2.82
2.90
2.70
B
(25.00)
2.54
2.99
3.17
3.04
B÷A
(2,252.2
5)
244.23
308.25
348.35
357.65
W2 : Discounted payback period
Year 0
Year 1
Year 2
Year 3
Year 4
Present value of cash flow
(Rs. in m)
(2,252.25)
572.96
623.27
623.11
Cumulative discounted cash
flows
(2,252.25) (1,711.93) (1,138.97)
( 515.70)
107.41
540.32
‹• ‘—–‡†’ƒ›„ƒ ’‡”‹‘†
ൌ ‡ƒ”„‡ˆ‘”‡ˆ—ŽŽ”‡ ‘˜‡”›ሺ૜ሻ ൅
Discounted payback
period =
”‡ ‘˜‡”‡† ‘•–ƒ–•–ƒ”–‘ˆ–Š‡›‡ƒ”ሺ૞૚૞Ǥ ૠ૙ሻ
ƒ•ŠˆŽ‘™•†—”‹‰–Š‡›‡ƒ”ሺ૟૛૜Ǥ ૚૚ሻ
3.83 years
W4 : Internal rate of return
Year 0
Year 1
Year 2
Year 3
Year 4
in million
Nominal cash flows in
million Rs.
Discount factor at 16%
Present value
Net present value
By Interpolation, the IRR
is :
(2,252.25)
610.53
731.75
899.38
1,016.5
0
1.000
0.862
0.743
0.641
0.552
(2,252.25)
526.28
543.69
576.50
561.11
(44.67)
15.11% per annum
W3 : Modified Internal rate of return
୰ ଵȀ୬
ൌ ൬ ൰ ሺͳ െ ”ୣ ሻ െ ͳ
୧
where,
୰ (return phase)
4)
(Years 1 2,359.66
୧ (investment phase) (Year 0)
”ୣ
2,252.25
13%
MIRR = 14.3%
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Business finance decisions
CHAPTER 7 – DCF: TAXATION AND INFLATION
7.1
MORE INVESTMENT APPRAISAL AND TAX
Tax allowances on the investment
Tax saving
(35% of allowance)
Year of
claim
0
Rs.
600,000
(150,000)
Cost
Allowance (25%)
Cash
flow year
Rs.
52,500
1
39,375
2
29,531
3
22,148
4
16,611
5
49,834
6
––––––––
1
450,000
(112,500)
Allowance (25%)
––––––––
2
337,500
(84,375)
Allowance (25%)
––––––––
3
253,125
(63,281)
Allowance (25%)
––––––––
4
189,844
(47,461)
Allowance (25%)
––––––––
5
142,383
0
Disposal
––––––––
142,383
––––––––
Note: It is assumed that the company has taxable profits against which it can
claim an allowance in Year 0 (or early in Year 1).
Year
0
1
2
3
4
5
6
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
250
(50)
(25)
250
(55)
(25)
300
(58)
(30)
350
(64)
(30)
400
(70)
(35)
––––––
––––––
––––––
––––––
––––––
175
170
(61)
212
(60)
256
(74)
295
(90)
Sales
Materials
Labour
Cash profits
Tax at 35%
Capital
equipment
Cash effect of
allowances
Net cash flow
DCF factor at
15%
PV of cash flow
NPV
(103)
(600)
53
39
30
22
17
50
––––––
––––––
––––––
––––––
––––––
––––––
––––––
(600)
1.000
228
0.870
148
0.756
182
0.658
204
0.572
222
0.497
(53)
0.432
(600)
198
112
120
117
110
(23)
––––––
––––––
––––––
––––––
––––––
––––––
––––––
34
––––––
© Emile Woolf International
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Answers
The project is just worthwhile, because the NPV is + Rs. 34,000. However, the
NPV is quite small in relation to the size of the capital investment, and in view of
the fact that it is a five-year project.
It might be appropriate to carry out some risk and uncertainty analysis on the
project, before deciding whether or not to undertake it.
7.2
INVESTMENT APPRAISAL AND TAX
Workings
Tax allowances on the investment
Year of
claim
0
Cost
Allowance (25%)
Rs.
250,000
(62,500)
Tax saving
(35% of allowance)
Rs.
Cash flow
year
21,875
1
16,406
2
12,305
3
9,228
4
(7,314)
5
––––––––
1
Allowance (25%)
187,500
(46,875)
––––––––
2
Allowance (25%)
140,625
(35,156)
––––––––
3
Allowance (25%)
105,469
(26,367)
––––––––
4
79,102
100,000
Disposal
––––––––
(20,898)
––––––––
NPV calculation
Year
0
Rs.
1
Rs.
Capital
equipment
(250,000)
Working capital
(38,000)
Cash profits before tax
Tax on profits (35%)
Cash effect of allowances
(12,000)
120,000
Net cash flow
DCF factor at
10%
PV of cash flow
2
Rs.
3
Rs.
4
Rs.
5
Rs.
21,875
120,000
(42,000)
16,406
120,000
(42,000)
12,305
100,000
50,000
120,000
(42,000) (42,000)
9,228 (7,314)
––––––––
––––––––
––––––––
––––––––
––––––––
(288,000)
1.000
129,875
0.909
94,406
0.826
90,305
0.751
237,228 (49,314)
0.683
0.621
(288,000)
118,056
77,979
67,819
162,027 (30,624)
––––––––
–––––––––– ––––––––– ––––––––– ––––––––– ––––––––– –––––––––
NPV
+ 107,257
––––––––––
The NPV is + Rs. 107,257. This indicates that the project should be undertaken.
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Business finance decisions
7.3
ALAWADA LIMITED
(a)
Calculation of net present value (NPV)
Year
CF
PV
DF @
10%
Rs.
Rs.
1
800,000
0.9091
727,280
2
640,000
0.8264
528,896
3
466,000
0.7513
350,106
4
836,700
0.6830
571,466
5
630,675
0.6209
391,586
2,569,334
Less: Initial outlay
(3,000,000)
Net present value
(430,666)
The project is not viable since the NPV shows a negative figure of Rs.
430,666.
Workings
Year
Sales (Rs.)
Less:
Materials
Labour
Net MCF
(b)
(c)
1
2,800,000
2
2,800,000
3
2,800,000
4
3,360,000
5
3,360,000
(800,000)
(1,200,000)
───────
800,000
═══════
(840,000)
(1,320,000)
───────
640,000
═══════
(882,000)
(1,452,000)
───────
466,000
═══════
(926,100)
(1,597,200)
───────
836,700
═══════
(927,405)
(1,756,920)
───────
630,675
═══════
Features of capital budgeting decisions include the following:
(i)
They involve large outlay.
(ii)
The benefits will accrue over a long period of time, usually well over
one year and often much longer, so that the benefits cannot all be set
off against costs in the current year’s Statement of profit or loss.
(iii)
They are very risky.
(iv)
They involve irreversible decision.
(i)
The continued existence of any company is not predicated on its
investment on short-term basis but rather on its long-term investment
strategies.
(ii)
Investment decisions facilitate the identification of viable projects in
order to maximise the wealth of the shareholders.
(iii)
Companies need to undertake long-term investments which are the
pre-requisite to the concept of “on-going concern” basis.
(iv)
Capital budgeting ensures that the management team does not
mortgage the future of the company for their personal individual
financial gains through short-term investments.
(v)
It assists the streamlining of the projects being executed by the
organisation.
© Emile Woolf International
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Answers
7.4
KOHAT LIMITED
Inflation
factor
Investment
Years
0
1
2
3
Rs. in million
4
5
(15,000)
Revenue (Rs.
8,000×1 million)
5%
8,000
8,400
8,820
9,261
9,724
Operating
costs(excluding
wages) (W1)
10.34%
(2,000)
(2,207)
(2,435)
(2,686)
(2,965)
Wages (W2)
11.73%
(1,000)
(1,117)
(1,248)
(1,395)
(1,558)
5,000
5,076
5,137
5,180
5,201
Profit before
taxation
Residual value
(Rs.
15,000×20%)
3,000
Tax @ 30 %
(W3)
Net inflows
(600)
(803)
(965)
(1,093)
(617)
(15,000)
4,400
4,273
4,172
4,087
7,584
1
0.850
0.722
0.614
0.522
0.444
(15,000)
3,740
3,085
2,562
2,125
3,367
Discount factor
(W4)
Net present
value
(121)
Conclusion: The projective has a negative NPV. KL should not invest in the
project.
W1: Compound annual growth rate for CPI
175
CAGR for CPI
(1 i) 5
107
1/5
(1.6355) = 1 + i
1 + i = 1.1034
i = 10.34%
W2: Compound annual growth rate for PPI
CAGR for SPI =
195
= (1 + i) 5
112
(1.7411)1/5 = 1+i
1+i = 1.1173
i = 11.73%
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Business finance decisions
W3: Tax Computation:
Profit before
taxation
Depreciatio
n
Loss on
disposal
Taxable
profit/loss
Tax@ 30%
YEARS
3
1
2
4
5
5,000
5,076
5,137
5,180
5,201
(3000)
(2400)
(1920)
(1536)
(1229)
(1,915)
2,000
600
2,676
803
3,217
965
3,644
1,093
2,057
617
W4: Nominal return
Discount Rate = Required return nominal
1 + nominal return = (1 + real return) × (1 + inflation) = 106% × 111% = 117.7%
Therefore, the nominal return = 17.7%
7.5
JAP RECREATION CLUB
2016
2017
Initial
investment
(7,000,000)
Residual value
1
Restaurant
contribution
5,040,000
Lost contribution
from snack bar
(2,025,000)
(W4)
Salaries
Additional
overheads
Net cash flows
Tax payment
(W1)
Net cash flow
after tax
Discount factor
(W3)
2018
Rupees
2019
2020
510,000
5,544,000
6,098,400
6,708,240
(1,991,250)
(1,942,313)
(1,876,079)
(800,000)
(800,000)
(1,000,000)
(1,000,000)
(595,000)
1,620,000
(595,000)
2,157,750
(595,000)
2,561,087
(595,000)
3,747,161
45,500
(295,838)
(551,849)
(456,413)
(7,000,000)
1,665,500
1,861,912
2,009,238
3,290,748
1
0.940
0.884
0.831
0.781
(7,000,000)
-
(7,000,000) 1,565,570
Present value
1,645,930
1,669,677
2,570,074
Net present
value
451,251
Conclusion:
The company should invest in the project as it would generate higher net cash
flows as compare to existing business.
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Answers
W1: Tax payments
2017
2018
2019
2020
Rupees
Net cash flows
Less: Depreciation for
the year (W2)
Taxable profit
1,620,000
2,157,750
2,561,087
3,747,161
(1,750,000)
(1,312,500)
(984,375)
(2,443,125)
4,595,000
5,806,500
6,786,025
6,773,815
(45,500)
295,838
551,849
456,413
7,000,000
5,250,000
3,937,500
2,953,125
(1,750,000)
(1,312,500)
(984,375)
*(2,443,125)
5,250,000
3,937,500
2,953,125
510,000
Tax payments
(Taxable profit x 35%)
W2 : Depreciation for the year
Opening WDV of
equipment
Less: Depreciation for
the year (WDV x 25%)
Closing WDV of
equipment
* Loss on disposal
W3: Adjustment of inflation in cost of capital
Real discount rate
= ((1+nominal discount rate)/(1+inflation rate))-1
= 6.36%
W4: Lost snack bar contribution
0
1
2
3
4
250
263
276
289
304
No. of members
with restaurant
150
165
181.5
199.65
Lost
members/day
113
111
108
104
Rate (u)
50
50
50
50
No. of days (u)
360
360
360
360
2,025,000
1,991,250
1,942,313
1,876,078
Years
No. of members
without restaurant
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Business finance decisions
7.6
ARG COMPANY
(a)
NPV calculation for Alpha and Beta
Year
Sales revenue
Material cost
Fixed costs
Advertising
Taxable profit
Tax (25%)
Capital
allowance tax
benefit
Non-current
asset sale
Recovery of
working capital
Discount factors
Present values
1
$
3,585,000
(1,395,000)
(1,000,000)
(500,000)
––––––––
690,000
(172,500)
250,000
2
$
6,769,675
(2,634,225)
(1,050,000)
(200,000)
–––––––––
2,885,450
(721,362)
3
4
$
$
6,339,000
1,958,775
(2,466,750) (761,925)
(1,102,500) (1,157,625)
(200,000)
––––––––– –––––––––
2,569,750
39,225
(642,438)
(9,806)
1,200,000
1,000,000
––––––––
767,500
––––––––
0.885
679,237
–––––––––
2,164,088
–––––––––
0.783
1,694,481
–––––––––
1,927,312
–––––––––
0.693
1,335,626
–––––––––
2,229,419
–––––––––
0.613
1,366,634
$
Sum of present values
Initial investment
5,075,978
3,000,000
–––––––––
2,075,978
–––––––––
Net present value
The positive NPV indicates that the investment is financially acceptable.
Workings
Year
Alpha sales revenue
Selling price ($/unit)
Sales (units per year)
Sales revenue ($/year)
Beta sales revenue
Selling price ($/unit)
Sales (units per year)
Sales revenue ($/year)
Total sales revenue
Alpha materials cost
Unit cost ($/unit)
Sales (units per year)
Total cost ($/year)
© Emile Woolf International
1
2
3
4
31.00
31.93
32.89
33.88
60,000
110,000
100,000
30,000
1,860,000 3,512,300 3,289,000 1,016,400
23.00
23.69
24.40
25.13
75,000
137,500
125,000
37,500
1,725,000 3,257,375 3,050,000
942,375
3,585,000 6,769,675 6,339,000 1,958,775
12.00
12.36
12.73
60,000
110,000
100,000
720,000 1,359,600 1,273,000
182
13.11
30,000
393,300
The Institute of Chartered Accountants of Pakistan
Answers
Year
Beta materials cost
Unit cost ($/unit)
Sales (units per year)
Total cost ($/year)
Total materials cost
(b)
1
2
3
4
9.00
9.27
9.55
75,000
137,500
125,000
675,000 1,274,625 1,193,750
1,395,000 2,634,225 2,466,750
9.83
37,500
368,625
761,925
The evaluation assumes that several key variables will remain constant,
such as the discount rate, inflation rates and the taxation rate. In practice
this is unlikely.
(1)
The taxation rate is a matter of government policy and so may
change due to political or economic necessity.
(2)
Specific inflation rates are difficult to predict for more than a short
distance into the future and in practice are found to be constantly
changing. The range of inflation rates used in the evaluation is
questionable, since over time one would expect the rates to
converge. Given the uncertainty of future inflation rates, using a
single average inflation rate might well be preferable to using specific
inflation rates.
(3)
The discount rate is likely to change as the company’s capital
structure changes. For example, issuing debentures with an interest
rate of 9% is likely to decrease the average cost of capital.
Looking at the incremental fixed production costs, it seems unusual that nominal
fixed production costs continue to increase even when sales are falling. It also
seems unusual that incremental fixed production costs remain constant in real
terms when production volumes are changing. It is possible that some of these
fixed production costs are stepped, in which case they should decrease.
The forecasts of sales volume seem to be too precise, predicting as they do the
growth, maturity and decline phases of the product life-cycle. In practice it is
likely that improvements or redesign could extend the life of the two products
beyond five years. The assumption of constant product mix seems unrealistic,
as the products are substitutes and it is possible that one will be relatively more
successful. The sales price has been raised in line with inflation, but a lower
sales price could be used in the decline stage to encourage sales.
Net working capital is to remain constant in nominal terms. In practice, the level
of working capital will depend on the working capital policies of the company, the
value of goods, the credit offered to customers, the credit taken from suppliers
and so on. It is unlikely that the constant real value will be maintained.
The net present value is heavily dependent on the terminal value derived from
the sale of non-current assets after five years. It is unlikely that this value will be
achieved in practice. It is also possible that the machinery can be used to
produce other products, rather than be used solely to produce Alpha and Beta.
(c)
ARG Co currently has $50m of non-current assets and long-term debt of
$10m. The issue of $3m of 9% debentures, and investment in property and
© Emile Woolf International
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Business finance decisions
equipment of $2m will increase non-current assets by $2m. There seems to
be ample security for the new issue.
Interest cover is currently 5.1 times (= 4,560/900) which is less than the sector
average, and this will fall to 3.9 times (= 4,560/(900 + 3m × 9%)) following the
debenture issue.
The new products will increase profit by $440,000 ($690,000 – $250,000
depreciation), increasing interest cover to 4.3 times (= 5,000/1,170). Although on
the low side and less than the sector average, this evaluation ignores any
increase in profits from current activities. Interest cover may not be a cause for
concern.
Current gearing of 32% (measured as debt/equity based on book values, =
10,000/30,900) will rise to 42% (13,000/30,900) after the debenture issue. Both
values are less than the sector average and ignore any increase in reserves due
to next year’s profits.
Financial risk appears to be at an acceptable level and gearing does not appear
to be a problem.
The debentures are convertible after eight years into 20 ordinary shares per
$100 of debentures. The current share price is $4.00, giving a conversion value
of $80. For conversion to be likely, a minimum average annual growth rate of
only 2.83% is needed ((5.00/4.00)0.125 – 1). This growth rate could well be
exceeded, making conversion after eight years a likely prospect. This analysis
assumes that the floor value on the conversion date is the par value of $100: the
actual floor value could well be different in eight years’ time, depending on the
prevailing cost of debt. Conversion of the debentures into ordinary shares will
eliminate the need to redeem them, as well as reducing the company’s gearing.
The current share price may be depressed by the ongoing recovery from the
loss-making magazine publication venture. Annual share price growth may
therefore be substantially in excess of 2.83%, making the conversion terms too
generous (assuming a floor value equal to par value on the conversion date). On
conversion, 600,000 new shares will be issued, representing 23% (= 0.6m/2.6m)
of share capital. The company must seek the views and approval of existing
shareholders regarding this potential dilution of ownership and control.
The maturity of the debentures (12 years) does not match the product life-cycle
(four years). This may be caution on the part of the company’s managers, but a
shorter period could be used.
It has been proposed that $1 million of the debenture issue would be used to
finance the working capital needs of the project. Financing all working capital
from a long-term source is a very conservative approach to working capital
financing. ARG Co might consider financing fluctuating current assets from a
short-term source such as an overdraft. By linking the maturity of the finance to
the maturity of the assets being financed, ARG Co would be applying the
matching principle.
© Emile Woolf International
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Answers
7.7
HAFEEZ LTD
(a)
Bid amount of annual fee
Rupees
NPV of costs (W1)
50,074,626
Target NPV (Rs. 50 million x 15%)
7,500,000
NPV of fees
57,574,626
NPV of fees (W1)
Annual Fees
=
Cum disc factor
57,574,626
=
=
16,770,937
3.433
W1: NPV of Costs
Tax Allowance on
Operating
Costs
Year Capital Cost
Depreciation
and Disposal
(W2)
Operating
Costs
Total Cash
Outflows
Discount
Factor
(14%)
Rupees
0
PV of
Costs
(Rupees)
(50,000,000)
(50,000,000)
1.000
(50,000,000)
1
(6,000,000)
5,687,500
2,100,000
1,787,500
0.877
1,567,638
2
(6,600,000)
1,181,250
2,310,000
(3,108,750)
0.769
(2,390,629)
3
(7,260,000)
1,063,125
2,541,000
(3,655,875)
0.675
(2,467,716)
4
(7,986,000)
956,813
2,795,100
(4,234,087)
0.592
(2,506,580)
(8,784,600)
4,236,312
3,074,610
11,026,322
0.519
5,722,661
5
12,500,000
(50,074,626)
W2: Tax Allowance
Depreciation
Year
Tax Allowance
WDV
Initial
@35%
Normal
Tax
Allowance on
Disposal
Total
Allowance
Rupees
1
50,000,000
2
12,500,000
3,750,000
5,687,500
-
5,687,500
33,750,000
3,375,000
1,181,250
-
1,181,250
3
30,375,000
3,037,500
1,063,125
-
1,063,125
4
27,337,500
2,733,750
956,813
-
956,813
5
24,603,750
2,460,375
861,131
3,375,181
4,236,312
(W3)
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W3: Tax Allowance on Disposal
Rupees
Disposal value (Rs. 50,000,000 x
25%)
WDV
Loss on disposal
Tax allowance @ 35%
(b)
12,500,000
22,143,375
(9,643,375)
(3,375,181)
IRR of the Contract
IRR =
a=
b=
A=
B=
a + [ (A/A-B) (b-a) ]%
14%
20%
7,500,000
(W5)
(426,261)
IRR = 14% + [7,500,000/ [(7,500,000+426,261) (20%-14%)] %
= 19.7%
W5
Inflows/ (Outflows)
excluding fee
Inflows from fee
Rupees
(50,000,000)
Net Cash
Flows
Disc
Factor
Rupees
20%
(50,000,000)
1.00
(50,000,000)
NPV
Rupees
1,787,500
16,770,937
18,558,437
0.83
15,403,503
(3,108,750)
16,770,937
13,662,187
0.69
9,426,909
(3,655,875)
16,770,937
13,115,062
0.58
7,606,736
(4,234,087)
16,770,937
12,536,850
0.48
6,017,688
11,026,322
16,770,937
27,797,259
0.40
11,118,903
(426,261)
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Answers
CHAPTER 8 – DCF: RISK AND UNCERTAINTY
8.1
RISK IN INVESTMENT APPRAISAL
(a) and (b)
Machine A
Year
0
1
2
3
Discounted
cash flows
Year 0
1
2
3
(Rs. 4 - Rs.
1)/unit
Discount factor
at 6%
1.000
0.943
0.890
0.840
2,000
demand
3,000
demand
5,000
demand
Rs.
(15,000)
6,000
Rs.
(15,000)
9,000
Rs.
(15,000)
15,000
6,000
6,000
9,000
9,000
15,000
15,000
PV
PV
PV
Rs.
(15,000)
5,658
5,340
5,040
Rs.
(15,000)
8,487
8,010
7,560
Rs.
(15,000)
14,145
13,350
12,600
––––––––
NPV
––––––––
––––––––
1,038
9,057
25,095
––––––––
––––––––
––––––––
Expected value of NPV = (0.2 × 1,038) + (0.6 × 9,057) + (0.2 × 25,095) = Rs.
10,661
Machine B
2,000
demand
3,000
demand
5,000
demand
Rs.
(20,000)
10,500
10,500
10,500
Rs.
(20,000)
17,500
17,500
17,500
Year
0
1
2
3
(Rs. 4 - Rs.0.5)/unit
Rs.
(20,000)
7,000
7,000
7,000
Discounted
cash flows
Discount factor at
6%
PV
PV
PV
Year 0
1
2
3
1.000
0.943
0.890
0.840
Rs.
(20,000)
6,601
6,230
5,880
Rs.
(20,000)
9,902
9,345
8,820
Rs.
(20,000)
16,503
15,575
14,700
––––––––
––––––––
––––––––
8,067
26,778
––––––––
––––––––
NPV
(1,289)
––––––––
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Expected value of NPV = (0.2 × (1,289)) + (0.6 × 8,067 + (0.2 × 26,778) =
Rs. 9,938
Note: A quicker way of calculating expected values is to:
‰
calculate the EV of annual sales (which is 3,200 units)
‰
calculate the cash flows and NPV for annual sales of 3,200 units.
However, this approach makes it more difficult to carry out risk and uncertainty
analysis.
On the basis of the figures, it would seem that Machine A should be
purchased.
(c)
‰
It has a higher expected value of NPV.
‰
It is also a lower risk option, because the NPV will be positive even when
sales are only 2,000 units each year. With machine B, the NPV would be
negative if the annual sales are just 2,000 units.
‰
Machine A also gives a higher NPV if sales are 3,000 units, which is the
most likely outcome.
Sensitivity analysis on the Machine A investment.
(i)
The NPV is + Rs. 1,038 even when sales are 2,00 units each year. The
probability of a negative NPV is 0%. (With machine B, the risk of a
negative NPV is 20%).
(ii)
The project will achieve a 6% return if the NPV of annual cash profits is
Rs. 15,000.
Discount factor at 6% for years 1 – 3 = 2.673
Annual cash profits to achieve a PV of Rs. 15,000 = Rs. 15,000/2.673 =
Rs. 5,612.
The contribution per unit is Rs. 3.
Therefore minimum annual sales to achieve an NPV of Rs.0 = Rs.
5,612/Rs. 3 per unit
= 1,871 units.
If annual sales exceed 1,871 units, the NPV with Machine A will be
positive at a discount rate of 6%.
8.2
CALM PLC
Calculation of expected sales of the device is based on the probabilities
determined by the analysis of previous experience as given in the question.
Expected sales are obtained as follows:
Year 1 = Rs.(240,000,000 x 0.25) + (140,000,000 X 0.60) + (50,000,000 x 0.15)
= Rs. 151,500,000
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Year 2 = Rs.(500,000,000 x 0.25) + (340,000,000 + 0.60) + (180,000,000 x 0.15)
= Rs. 125 million + Rs. 204 million + Rs. 27 million
= Rs. 356,000,000
Year 3 = Rs.(160,000,000 x 0.25) + (80,000,000 x 0.60) + (50,000,000 + 0.15)
Rs. 40 million + Rs. 48 million + Rs. 7.5 million
= Rs. 95,500,000
Expected value of rent forgone:
If the factory space is let at the beginning of year 2, rent of Rs. 16,000,000 each
will be received in year 1 and Year 2 (rent is payable in advance). This has a
probability of 0.6.
If it is not let in year 2 (probability of 0.4); it could be let at the beginning of year 3
(with a probability of 0.5). This will produce cashflow of Rs. 16 million in year 2.
This event has a joint probability of (0.4 x 0.5) = 0.2.
Summary
Probability
Year 1
Year 2
Year 3
Rs.’m
Rs.’m
Rs.’m
Rs.’m
0.6
=
0.60
16
16
-
0.4 x 0.5
=
0.20
-
16
-
0.4 x 0.5
=
0.20
-
-
-
1.00
9.6
12.8
Nil
Year
0
Rs.’m
1
Rs.’m
2
Rs.’m
3
Rs.’m
4
Rs.’m
Initial Outlay
(190)
-
-
-
-
Advertisement
Fixed cost less depreciation
Scrap value
Rent Forgone
(30)
-
(20)
(10)
(9.6)
(10)
(10)
(12.8)
(10)
-
10
-
Contribution (70% of sales)
106.05
249.2
66.85
Net Cash flow
DCF (20%)
(220)
1.00
66.45
0.83
216.4
0.69
56.85
0.58
10
0.48
PV
(220)
55.154
149.316
32.973
4.8
ENPV
= Rs. 242,243,000 – Rs. 220,000,000
= Rs. 22,243,000
DECISION: Since the Expected Net Present Value is positive, the new product
should be produced all things being equal.
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Business finance decisions
8.3
OUTLOOK PLC
(a)
Calculation of NPV
Year
Items
NCF
(Rs.)
DF@
15%
Initial Outlay
(350,000)
1.0000
(350,000)
1 - 10
1 - 10
Relevant Fixed Cost
Variable Cost
(25,000)
(300,000)
5.0188
5.0188
(125,470)
(1,505,640)
1 - 10
Sales
400,000
5.0188
2,007,520
NPV
26,410
0
NOTE:
PV
(Rs.)
DF@ 15% = (1 – (1 +r)n/r) = (1 – (1.15)10/0.15) = 5.0188
Contribution
=
Sales – Variable Cost
=
Rs. 400,000 – Rs. 300,000
=
Rs. 100,000
PV of contribution is Rs. 100,000 x 5.0188
=
Rs. 501,880
Sensitivity Analysis:
NPV
100
u
PV of Sales
1
(i)
Sales Price =
(ii)
Initial Outlay =
(iii)
Sales Volume =
(iv)
Variable Cost =
NPV
100
u
PV of Outlay
1
(b)
Fixed Cost =
1.32%
26,410 100
u
350,000
1
7.55%
NPV
100
u
PV of Contributi on
1
NPV
100
u
PV of Variable Cost
1
(v)
26,410
100
u
2,007,520
1
NPV
100
u
PV of FC
1
26,410 100
u
501,880
1
26,410
100
u
1,505,640
1
26,410 100
u
125,470
1
5.26%
1.75%
21.05%
The two most sensitive variables are:
(i)
Sales price at 1.32%
(ii)
Variable Cost - 1.75%
These are derived from the sensitivity analysis workings above as these
are the two least NPVs in terms of sensitivity.
The sales price must not fall by more than 1.32% and the variable cost
must not increase by more than 1.75%.
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Answers
8.4
ZAHEER LTD
(a)
Financial feasibility of the proposal
Rupees
Capital cost
(20,000,000)
Present value of tax allowable depreciation
(Rs. 1,200,000 (W1) u 3.352)
4,022,400
PV of net incremental profit for five years
(7,000,000 (W1) x 3.352 (W2))
23,464,000
7,486,400
Net Present Value
Conclusion:
The proposal is financially feasible for the company as it has a positive net
present value.
W1: Tax allowable depreciation
Annual allowance (Rs. 20,000,000 / 5 years)
Tax rate
Tax saving (per annum)
W2: Profit for the year
Profit per unit (1,900 – 800 – 500 – 150 – 200)
No. of units
Net Profit before tax (40,000 x 250)
Less: Taxation @ 30%
Net profit after tax
W3: Cumulative discount factor (15%)
= (1 – (1 +r)n/r) = (1 – (1.15)5/0.15) = 5.0188
(b)
4,000,000
30%
1,200,000
Rupees
250
u40,000
10,000,000
(3,000,000)
7,000,000
3.352
Sensitivity analysis
Material costs Labour costs
800
500
u40,000
u40,000
32,000,000
20,000,000
(9,600,000)
(6,000,000)
22,400,000
14,000,000
Cost per unit
Number of units
Total cost
Tax relief (30%)
Post-tax cost
Cumulative discount factor
(5 years at 15%)
Present value
Sensitivity
NPV of project
PV of costs (see above)
© Emile Woolf International
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3.352
75,084,800
3.352
46,928,000
7,486,400
÷75,084,800
0.0997
9.97%
7,486,400
÷46,928,000
0.1595
15.95%
The Institute of Chartered Accountants of Pakistan
Business finance decisions
Set-up cost
20,000,000
(4,022,400)
15,977,600
Cost
PV of tax saving
Present value
Sensitivity
NPV of project
PV of costs (see above)
7,486,400
÷15,977,600
0.4685
46.85%
Conclusion:
The outcome of the order is most sensitive to material costs.
0.7
0.7
0.3
0.3
1,600
1,800
0.8
0.8
0.5
0.5
0.9
0.9
0.75
1.00
1.25
Expected
incremental
earnings
E
Expected
incremental
Costs
D
Cost of cell
sites
C
Expected
incremental
revenue
B
Probability
Probability
A
Airtime
minutes
No. of
subscribers in
million
JKL PHONE LIMITED
Selling Price
8.5
Rupees in million
0.6
0.4
AxBxCxDx
E
151
113
300
300
54
36
ETR ECOS
97
77
1,600
1,800
0.6
0.4
288
216
300
300
90
60
198
156
0.2
0.2
1,600
1,800
0.6
0.4
540
540
0.5
0.5
0.3
0.3
1,600
1,800
0.6
0.4
130
97
995
144
108
180
180
65
43
348
32
22
65
54
647
112
86
0.6
0.6
0.5
0.5
1,600
1,800
0.6
0.4
288
216
300
300
90
60
198
156
0.8
0.8
0.2
0.2
1,600
1,800
0.6
0.4
300
300
0.3
0.3
0.3
0.3
1,600
1,800
0.6
0.4
154
115
1,025
108
81
180
180
36
24
264
32
22
118
91
761
76
59
0.4
0.4
0.5
0.5
1,600
1,800
0.6
0.4
240
180
180
180
54
36
186
144
0.6
0.6
0.2
0.2
1,600
1,800
0.6
0.4
144
108
861
300
300
36
24
204
108
84
657
H
HxCxE
Conclusion:
Tariff of Re. 1 is most suitable because it gives the highest value of pay-off.
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Answers
KHAYYAM LIMITED (KL)
(a)
Cash Outflow
(Rs. 500
million)
Rs. 250 million
(65%)
Rs. 320 million
(35%)
Rs. 280 million
(20%)
Rs. 330 million
(65%)
Rs. 360 million
(15%)
Rs. 340 million
(5%)
Rs. 380 million
(50%)
Rs. 400 million
(45%)
Path 1
Path 2
Path 3
Path 4
Path 5
Path 6
(b)
Discount
factor
PV
PV of total
inflow
Cash outflow
0.8772
219.30
*330
0.7695
253.94
473.24
500
(26.76)
0.1300
(3.48)
2 250
0.8772
219.30
*380
0.7695
292.41
511.71
500
11.71
0.4225
4.95
3 250
0.8772
219.30
*410
0.7695
315.50
534.80
500
34.80
0.0975
3.39
4 320
0.8772
280.70
*390
0.7695
300.11
580.81
500
80.81
0.0175
1.41
5 320
0.8772
280.70
*430
0.7695
330.89
611.59
500
111.59
0.1750
19.53
6 320
0.8772
280.70
*450
0.7695
346.28
626.98
500
126.98
0.1575
20.00
Probability
Amount
NPV
PV
1 250
Path
Discount
factor
PV of NCIAT of Year
2
Amount
PV of NCIAT of Year
1
Expected NPV
All amount are in million rupees
Joint
8.6
45.80
*including salvage value of Rs. 50 million
Comment: Since the expected net present value of project is positive, it is suggested to accept
investment proposal.
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Business finance decisions
CHAPTER 9 – DCF: SPECIFIC APPLICATIONS
9.1
LEASE OR BUY
(a)
Evaluate the investment decision
Year of
claim
Tax saving
(30% of
allowance)
Rs.
30,000
(7,500)
Cost
Allowance (25%)
1
Cash flow
year
Rs.
2,250
2
1,688
3
1,266
4
949
5
1,048
6
––––––––
2
22,500
(5,625)
Allowance (25%)
––––––––
3
16,875
(4,219)
Allowance (25%)
––––––––
4
12,656
(3,164)
Allowance (25%)
––––––––
5
9,492
6,000
Disposal
––––––––
Balance
(3,492)
––––––––
Year
0
1
2
Rs.
(30,000)
Rs.
Rs.
Equipment
Tax relief
Project cash flows
Tax on these at 30%
–––––––
Net cash
flow
DCF factor
at 10%
Present
value
5
6
Rs.
Rs.
Rs.
1,688
10,000
(3,000)
1,266
10,000
(3,000)
Rs.
6,000
949
10,000
(3,000)
–––––––
–––––––
–––––––
––––––– ––––––––
2,250
10,000 10,000
(3,000)
––––––––
Cash flows
3
4
1,048
(3,000)
(30,000)
10,000
9,250
8,688
8,266
13,949
(1,952)
1.000
0.909
0.826
0.751
0.683
0.621
0.564
7,641
6,525
5,646
8,662
(1,101)
(30,000)
9,090
NPV = + Rs. 6,463
The acquisition is worthwhile.
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Answers
(b)
Evaluate the financing decision:
Now consider how it should be financed. The project cash flows and tax on
these are now irrelevant to this decision. Only the financing cash flows
need to be considered.
The cost of financing is the after-tax cost of borrowing, which is 8%.
Leasing
Cash flows
Year
1
2
3
4
5
6
Rs.
Rs.
Rs.
Rs.
Rs.
Rs.
(7,000)
(7,000)
(7,000)
(7,000)
(7,000)
2,100
2,100
2,100
2,100
2,100
––––––––
––––––––
––––––––
––––––––
––––––––
––––––––
Net cash flow
(7,000)
(4,900)
(4,900)
(4,900)
(4,900)
2,100
DCF factor at
8%
0.926
0.857
0.794
0.735
0.681
0.630
Present value
(6,482)
(4,199)
(3,891)
(3,602)
(3,337)
1,323
Lease
payments
Tax relief
PV of the cost of leasing = Rs. 20,188
Purchase
Year
Cash flows
0
1
Rs.
Equipment
2
Rs.
DCF factor
at 8%
Present
value
Rs.
Rs.
4
Rs.
(30,000)
5
Rs.
6
Rs.
6,000
Tax relief
Net cash
flow
3
2,250
1,688
1,266
949
1,048
––––––––
––––––
––––––
––––––
––––––
––––––
––––––
(30,000)
0
2,250
1,688
1,266
6,949
1,048
1.000
0.857
0.794
0.735
0.681
0.630
(30,000)
1,928
1,340
931
4,732
660
PV of the cost of purchasing = Rs. 20,409
Leasing has the lower PV of costs (although only by about Rs. 200) and is
slightly cheaper.
On this basis, the company might decide to lease the asset. However, the
difference in cost is so small that other non-financial factors might influence the
decision.
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Business finance decisions
9.2
MOHANI LIMITED
I would recommend to the management of the company to consider option B as
this option provides NPV of cash outflow of Rs. 1,988,750 to the company which
is lower by Rs. 455,798 in comparison to option A. Detailed computation is as
follows:
Year
Security
deposits
Salvage
value
Tax
benefits
35%
Lease
payment
Net cash
outflow
PV
Factor
14%
Rupees
0
320,000
860,000
-
1
860,000
2
PV
Rs.
1,180,000
1.000
1,180,000
(301,000)
559,000
0.877
490,243
860,000
(301,000)
559,000
0.769
429,871
3
860,000
(301,000)
559,000
0.675
377,325
4
860,000
(301,000)
559,000
0.592
330,928
-
(301,000)
(701,000)
0.519
(363,819)
5
(400,000)
2,444,548
Alternative answer
Description
Rupees
PV
PV
factor
Rupees
Security deposit
320,000
1
320,000
Lease payments
860,000
3.913
3,365,180
Tax benefit @35%
301,000
3.432
(1,033,032)
Salvage value
400,000
0.519
(207,600)
2,444,548
Installment Amount
Rs. 3,200,000
R
Y
ea
r
Loan
payment
Intere
st @
11%
Principal
Repayme
nt
1 (1 i )n
i
865,825
Depreciation
Balance
Insuran
ce
Initial
PV
Fact
or
@14
%
Norma
l
Tax
Shield @
35%
Salva
ge
value
Outfl
ow
-
-
-
96,000
(772,800)
-
189,025 0.877 165,775
Rupees
PV
(Rs.)
0
-
-
-
3,200,000
96,000
1
865,825
352,000
513,825
2,686,175
96,000
2
865,825
295,479
570,346
2,115,829
96,000
-
144,000
(187,418)
-
774,407 0.769 595,519
3
865,825
232,741
633,084
1,482,023
96,000
-
129,600
(160,419)
-
801,406 0.675 540,949
4
865,825
163,102
702,723
780,023
96,000
-
116,640
(131,510)
-
830,315 0.592 491,547
5
865,825
85,802
780,023
0
-
-
104,976
*(291,081)
© Emile Woolf International
-
1,600,000 160,000
196
1.000
400,000 190,674 0.519
96,000
98,960
The Institute of Chartered Accountants of Pakistan
Answers
*This includes tax benefit / loss on disposal amounted to Rs. 190,674. Computation of this tax
benefit is as follows:
Rs.
3,200,000
2,255,216
944,784
400,000
544,784
Cost of machine
Less: Initial and normal depreciation
Tax WDV
Less: Sales value
Tax loss
Tax benefits @35%
9.3
190,674
DS LEASING COMPANY LIMITED
Years
2
3
4
Rupees in million
(a)
0
1
Principal
repayment
Interest
(Principal
outstanding x 16%)
Tax savings (W1)
Recovery
of
residual
value
(Note)
Net cash outflow to
DS
Discount @ 18%
1.00
PV of net cash
outflow
Total PV of net cash outflow
5
5.00
5.00
5.00
5.00
-
3.20
-
2.40
(3.40)
1.60
(1.31)
0.80
(0.99)
(3.41)
-
-
-
(2.00)
-
8.20
0.85
4.00
0.72
5.29
0.61
2.81
0.52
(3.41)
0.44
6.97
2.88
3.23
1.46
(1.50)
13.04
NPV factor of tax rental income (W2)
2.236
Annual rental
5.83
W1: Tax savings
Years
0
1
2
3
4
5
Rupees in million
WDV at start of year
20.00
13.50
12.15
10.93
Initial depreciation (25%)
5.00
-
-
-
Normal depreciation (10%)
1.50
Loss on disposal (Note)
-
1.35
-
1.22
-
1.09
7.84
Total tax allowance
6.50
1.35
1.22
8.93
WDV at end of year
13.50
12.15
10.93
2.00
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Note: Disposal value i.e. Rs. 2 million (10% of Rs. 20 million) - WDV at the
end of year 4 i.e. 9.84 = Rs. 7.84 million (Loss on disposal)
Years
1
2
3
Rupees in million
0
Total tax allowance as
computed above
Interest payment computed
above
4
5
6.50
1.35
1.22
8.93
3.20
9.70
2.40
3.75
1.60
2.82
0.80
9.73
3.40
1.31
0.99
3.41
4
5
Tax savings @ 35% in next
year
W2 : NPV factor of after tax rental income
Years
0
Income
1
1.00
Tax savings
Discount factor @ 18%
PV factor of income
Total PV of income
(b)
1.00
1.000
1.000
2.236
2
3
Rupees
1.00
1.00
1.00
(0.35)
0.65
0.850
0.553
(0.35) (0.35)
0.65 (0.35)
0.610 0.520
0.397 (0.182)
(0.35)
0.65
0.720
0.468
Years
Leasing
0
1
2
3
4
5
Rupees in million
Annual rental
7.00
7.00
7.00
7.00
(2.45)
(2.45)
(2.45)
(2.45)
7.00
4.55
4.55
4.55
(2.45)
1
0.833
0.694
0.578
0.482
7.00
3.79
3.16
2.63
(1.18)
Tax savings (rental x 35%)
Discount at 20%
PV of cash flow
NPV of leasing option
15.40
Purchase Outright
Years
0
1
2
3
4
5
Rupees in million
Principal outstanding
(Opening - Loan
payment + Interest)
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15.4
20.00
198
16.17
11.65
6.30
0.00
The Institute of Chartered Accountants of Pakistan
Answers
Loan payment (W1)
A
Interest (@18% of
opening principal)
B
Maintenance costs
Tax allowance as
computed above
Tax savings (in next
year)
7.43
7.43
7.43
7.43
3.60
2.91
2.08
1.13
0.60
0.60
0.60
0.60
6.50
1.35
1.22
8.93
10.70
4.86
3.90
10.66
-
(3.75
)
(1.70
)
(1.37
)
(3.73)
-
-
(2.00
)
-
C
Recovery of residual
value
Cash outflow to BP
-
-
-
8.03
4.29
6.33
4.67
(3.73)
Discount at 20%
-
0.833
0.694
0.578
0.482
0.402
PV of cash outflow
-
6.69
2.97
3.66
2.25
(1.50)
A+B+C
NPV of purchase
option
14.07
W1:
Installment amount = Rs. 20 million
4
1 (1 0.18)
0.18
7.43
Conclusion:
The feasible option is the outright purchase.
Note: Insurance costs are ignored in our computation as these are the
same in both options.
9.4
HIN TEXTILE MILLS LIMITED
Proposal of BAL Leasing Company Limited
Cash flow
Security deposit
Amo
unt
(Rs.
in
millio
n)
Interest
rate
/period
(W1)
10.00
Lease rentals
7.46
Lubricants and
filters
1.00
Parts replacement
3.00
Staff cost
0.50
© Emile Woolf International
Frequency
Total no.
of
payment
s (Rs. in
million)
Quarterly
Discoun
t factor
(annuity
factor)
PV
(Rs. in
million)
1.000
10
12
4.00%
*9.385
*70
12
4.00%
*9.385
*9
half yearly
6
8.00%
*4.623
*14
monthly
36
1.33%
*28.460
*14
Quarterly
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Business finance decisions
Overhaul
15.00
Residual value
(20.0
0)
End of 2
year
nd
End of 3
year
0.731
11
0.625
(13)
rd
Total present
value
115
Proposal of PUS Rental Services
Quarter
Quarterly
rental
(Rs. in m)
Discount
factor
(W1) 4%
Present
value
(Rs. in m)
1
2
3
4
5
6
7
8
9
10
11
12
Total
11.
0
11.
0
11.
0
11.
0
12.
1
12.
1
12.
1
12.
1
13.
31
13.
31
13.
31
13.
31
0.96
2
0.9
25
0.8
89
0.8
55
0.8
22
0.7
90
0.7
60
0.7
31
0.7
03
0.6
76
0.6
50
0.6
25
10.5
8
10.
18
9.7
8
9.4
1
9.9
5
9.5
6
9.2
0
8.8
5
9.3
6
9.0
0
8.6
5
8.3
2
112.84
Conclusion
PUS’s option is better as it gives lower overall cost in present value terms
W1 : Finding the rate offered by BAL
PV of inflow = Present value of outflows (annuity) = R × Annuity Factor (AF)
Hence, 80 10 = 7.46 × AF
AF = 70 ÷ 7.46 = 9.383
IRR is 4% per quarter i.e. the figure corresponding to annuity factor of 9.383
and 12 periods, on the annuity table.
9.5
CRANK PLC.
Year
DF
(10%)
1
2
3
Rs.’000
Rs.’000
Rs.’000
0
1.0000
(1,500.00)
(1,500.00)
(1,500.00)
1
0.9091
(272.73)
(272.73)
(272.73)
2
0.8264
(495.84)
(495.84)
3
0.7513
PV of scrap
NPV
Annuity factor
Annual Equivalent Cost:
(563.48)
(1,772.73)
(2,268.57)
(2,832.05)
954.56
619.80
450.78
(818.17)
(1,648.77)
(2,381.27)
0.9091
1.7355
2.4868
(899.98)
(950.02)
(957.56)
The optimal replacement cycle is one-year because it has the lowest cost.
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Answers
ALTERNATIVE SOLUTION
Decision: Replace every 1 year.
Year
Cash Flow
DF@ 10%
PV
Rs.
Rs.
0
(1,500,000) 1.0000
(1,500,000)
1
(300,000) 0.9091
(272,730)
1
1,050,000 0.9091
954,555
(818,175)
Replace every 2 years
Year
Cash Flow
DF@ 10%
PV
Rs.
Rs.
0
(1,500,000) 1.0000
(1,500,000)
1
(300,000) 0.9091
(272,730)
2
(600,000) 0.8264
(495,840)
2
750,000 0.8264
619,800
(1,648,770)
Replace every 3 years
Year
Cash Flow
DF@ 10%
PV
Rs.
0
Rs.
(1,500,000) 1.000
(1,500,000)
1
(300,000) 0.9091
(272,730)
2
600,000 0.8264
(495,840)
3
750,000 0.7513
(563,475)
3
600,000 0.7513
450,780
(2,381,265)
Calculation of Annual Equivalent Value (AEV)
Every 1 year
(818,175)/0.9091
=
(899,984)
Every 2 years
(1,648,770)/1.7355 =
(950,026)
Every 3 years
(2,381,265)/2.4868 =
(957,562)
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Business finance decisions
9.6
Asset replacement
(a)
Replace every year
Cash
flow
Year
Discount
factor at
10%
Rs.
PV
Rs.
0
Purchase cost
(40,000)
1
Running costs
(8,000)
1
Disposal value
25,000
1
Net cash flow, Year 1
17,000
1.000
(40,000)
0.909
15,453
––––––––
(24,547)
––––––––
Annuity factor at 10%, Year 1
0.909
Equivalent annual cost
Rs.(27,004)
––––––––
(b)
Replace every two years
Cash
flow
Year
Discount
factor at
10%
Rs.
PV
Rs.
0
Purchase cost
(40,000)
1.000
(40,000)
1
Running costs
(8,000)
0.909
(7,272)
2
Running costs
(12,000)
2
Disposal value
20,000
2
Net cash flow, Year 2
0.826
6,608
8,000
––––––––
(40,664)
––––––––
Annuity factor at 10%, Years 1 – 2
Equivalent annual cost
1.736
Rs.(23,424)
––––––––
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Answers
(c)
Replace every three years
Cash
flow
Year
Discount
factor at
10%
Rs.
PV
Rs.
0
Purchase cost
(40,000)
1.000
(40,000)
1
Running costs
(8,000)
0.909
(7,272)
2
Running costs
(12,000)
0.826
(9,912)
3
Running costs
(20,000)
3
Disposal value
10,000
3
Net cash flow, Year 3
0.751
(7,510)
(10,000)
––––––––
(64,694)
––––––––
Annuity factor at 10%, Years 1 – 3
2.487
Equivalent annual cost
Rs.(26,013)
––––––––
(d)
Replace every four years
Cash
flow
Year
Discount
factor at
10%
Rs.
PV
Rs.
0
Purchase cost
(40,000)
1.000
(40,000)
1
Running costs
(8,000)
0.909
(7,272)
2
Running costs
(12,000)
0.826
(9,912)
3
Running costs
(20,000)
0.751
(15,020)
4
Running costs
(25,000)
0.683
(17,075)
(89,279)
Annuity factor at 10%, Years 1 – 4
Equivalent annual cost
3.170
Rs.(28,1
64)
Recommendation
The machine should be replaced every two years, because this
replacement policy gives the lowest equivalent annual cost.
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Business finance decisions
9.7
ROTOR PLC
YEAR
DF
(10%)
0
1.0000 (6,000,000) (6,000,000) (6,000,000) (6,000,000)
1
0.9091
(409,095)
(409,095)
(409,095)
(409,095)
2
0.8264
__
(396,672)
(396,672)
(396,672)
3
0.7513
__
__
(428,241)
(428,241)
4
0.6830
__
__
__
(430,290)
PV of costs
1
2
3
4
(6,409,095) (6,805,767) (7,234,008) (7,664,298)
PV of scrap
value
4,090,950
NPV
3,222,960
2,253,900
1,434,300
(2,318,145) (3,582,807) (4,980,108) (6,229,998)
Annuity
factor (÷)
0.9091
Annual
equivalent
cost
1.7355
2.4868
3.1698
(2,549,934) (2,064,424) (2,002,617) (1,965,423)
Conclusion: The machine should be replaced every four years.
9.8
UVW RENTAL SERVICES
Option – 1: Overhaul and continue
(a)
Year
Cost of
overhau
ling
Net
Revenu
e
Residu
al
value
Net cash
flow
Rupees
0
(2,200,000
)
1
-
2
-
Discou
nt rate
@
8.33%
(W1)
Net
present
value
Rupees
-
(2,200,000)
1.0000
(2,200,000)
*13,600,00
0
-
3,600,000
0.9231
3,323,160
3,600,000
787,500
4,387,500
0.8521
3,738,589
4,861,749
*1 (2,000 × 0.94 – 440) × 2,500
Cum discount factor for two years (0.9231 +
0.8521)
Annual equivalent Net Present
© Emile Woolf International
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1.7752
Rs.
The Institute of Chartered Accountants of Pakistan
Answers
Value
2,738,705
Option – 2: Replacement
Year
Capital
Cost
Net
Revenue
Residu
al
value
Net cash
flow
Rupees
0
1
2
3
*1(4,305,000
)
-
(W1)
*23,700,000
3,700,000
3,700,000
Discou
Net
nt rate present
@
value
8.33%
Rs.
1,312,50
0
(4,305,000
)
3,700,000
3,700,000
5,012,500
(4,305,000
)
3,415,470
3,152,770
1.0000
0.9231
0.8521
0.7866
3,942,833
6,206,073
*1 5,250,000 – 945,000 = 4,305,000
*2 (2,000 × 0.94 – 400) × 2,500 =
3,700,000
Cum discount factor for three years (0.9231 + 0.8521 +
0.7866)
2.5618
Rs.
2,422,54
4
Annual equivalent Net Present
Value
W – 1: Calculation of Real Rate for discounting
ª (1 NominalDiscount Rate)º
Real Discount Rate «
» 1
(1 InflationRate)
¬
¼
ª1 17%º
« 1 8% » 1 8.33%
¬
¼
Conclusion:
Since annual equivalent NPV of overhaul and continue option is higher,
this equipment should be overhauled.
Rupees
(b)
Total required NPV of replacement option
(Rs. 2,422,544× 1.7752)
Less: NPV of overhauling and continue option
Difference
% change in overhauling cost at which management would
be indifferent (Rs. 561,249 ÷ Rs. 2,200,000)
© Emile Woolf International
205
4,300,500
4,861,749
(561,249)
25.51%
The Institute of Chartered Accountants of Pakistan
Business finance decisions
CHAPTER 10 – EVALUATING FINANCIAL PERFORMANCE
10.1
EQUITY RATIOS
Earnings per share (EPS)
Rs.
Profit before interest and tax
Interest (10% × Rs. 250,000)
600,000
25,000
Profit before tax
Tax (30%)
575,000
172,500
Profit available to equity (earnings)
402,500
Number of equity shares (÷)
1,000,000
EPS
Rs.0.4025
This is a measure of the profit per equity share.
”ƒ–‹‘ ൌ
•Ǥ ͵Ǥʹ
ൌ ͹Ǥͻͷ–‹‡•
•Ǥ ͲǤͶͲʹͷ
The above ratio shows that investors are ready to pay Rs. 7.95 for an earning of
Rs. 1. The ratio indicates the confidence of investors in a company with a higher
PE ratio implying higher confidence.
‹˜‹†‡†›‹‡Ž† ൌ
•Ǥ ͲǤʹ
ൈ ͳͲͲ ൌ ͸ǤʹͷΨ
•Ǥ ͵ǤʹͲ
This ratio shows how much a company is paying as a dividend for each Rs. 1 of
its market value. The above example shows that the company pays Rs. 0.0625
out of every Rs. 1 of market value.
‹˜‹†‡† ‘˜‡” ൌ
•Ǥ ͲǤͶͲʹͷ
ൌ ʹǤͲͳ–‹‡•
•Ǥ ͲǤʹͲ
This shows that the profit available to the ordinary shareholders covers the
dividend by a factor of 2. In other words, approximately 50% of the earnings for
the year have been paid out as dividends and the remainder reinvested in the
company.
–‡”‡•–›‹‡Ž†‘†‡„‡–—”‡• ൌ
•Ǥ ͳͲ
ൈ ͳͲͲ ൌ ͳͳǤͳΨ
•Ǥ ͻͲ
This shows that the effective interest income on debenture is 11.1%. An investor
earns Rs. 11.1 for each Rs. 100 invested in these debentures.
‡ƒ”‹‰„ƒ•‡†‘ƒ”‡–˜ƒŽ—‡• ൌ
ͻͲ
•Ǥ ʹͷͲǡͲͲͲ ൈ ቀͳͲͲቁ
ͳǡͲͲͲǡͲͲͲ ൈ •Ǥ ͵ǤʹͲ
ൈ ͳͲͲ ൌ ͳͳǤͳΨ
This shows the extent to which the company is financed by outsiders and how
much by the owners. In the above scenario 11.1% of financing is by lenders and
the remaining by equity holders implying that the company has low gearing.
‡ƒ”‹‰„ƒ•‡†‘ƒ”‡–˜ƒŽ—‡• ൌ
© Emile Woolf International
•Ǥ ʹʹͷǡͲͲͲ
ൈ ͳͲͲ ൌ ͹ǤͲ͵Ψ
•Ǥ ͵ǡʹͲͲǡͲͲͲ
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Answers
10.2
AYELAND AND ZEDLAND
(a)
Performance report for companies in Ayeland and Zedland
The performance of the companies may be measured against indicators
from the relevant economies. A simple measure is to compare growth
trends over the four year period.
Ayeland
Indexed trends
% growth
20X0
20X1
20X2
20X3
20X0-1
20X1-2
20X2-3
Revenue
100
131.2
160.4
187.5
31.2
22.2
16.9
Profit
100
138.2
185.5
229.1
38.2
34.2
23.5
RPI
Share price
100
100
135.5
125.7
171.7
153.1
205.2
189.1
35.5
25.7
26.7
21.8
19.5
23.5
Stock market
100
119.9
148.9
189.2
Zedland
19.9
24.1
27.1
Indexed trends
% growth
20X0
20X1
20X2
20X3
20X0-1
20X1-2
20X2-3
Revenue
Profit
100
100
103.6
108.9
109.2
126.1
121.4
138.0
3.6
8.9
5.4
15.8
11.2
9.5
RPI
Share price
Stock market
100
100
100
104.3
81.4
87.2
107.1
86.4
87.2
110.8
97.0
92.7
4.3
(18.6)
(12.8)
2.7
6.2
4.8
3.5
12.3
1.5
The average investment returns, measured by share price change, are:
‰
Ayeland 23·7%
‰
Ayelandian market 23·7%
‰
Zedland (1·0%)
‰
Zedland market (2·4%)
Indicators for the Ayeland company are mixed. Growth in turnover has
lagged behind a broad measure of inflation, the retail price index, yet profit
after tax has performed relatively well. Despite this profit performance the
company’s share price has only increased by a similar amount to the
general stock market index.
The performance of the company in Zedland appears to be better, with
turnover, profit and share price all growing faster than the relevant country
indices.
However, comparisons such as this ignore the risk of the two companies.
The company in Ayeland appears to be much more risky, as evidenced by
its relatively high beta. Performance measures incorporating risk would be
much more useful.
A possible performance measure is the historic alpha coefficient associated
with the investment, the actual return less the required return for the risk of
the investment.
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Business finance decisions
Using CAPM, the required return for Ayeland was:
19% + (23·7% – 19%) 1·55 = 26·3%
The actual return was 23·7%. The investment has performed worse than
would be expected over the period.
For Zedland the required return was: 4% + (–2·4% – 4%) 0·98 = (2·3%)
Actual return was (1·0%). Although the company’s share price return was
negative, it was still better than might have been expected given the
general poor performance of the Zedland stock market. However, historic
alphas are unlikely to persist in the future, and negative expected market
returns over a long period make little economic sense.
Possible alternative performance measures include excess return to beta,
which is useful for a well-diversified investor, and is measured by:
investmentreturn - risk free rate
investmentbeta
For an investor who is not well diversified, a measure using total risk (the
standard deviation of returns) is more appropriate.
investmentreturn - risk free rate
standard deviationof returns
Based upon the available data, the company in Zedland appears to have
been the more successful during the last four years.
(b)
Other useful information might include:
(i)
A benchmark with which to draw comparisons, preferably data for
companies in the same industries as the two companies in Ayeland
and Zedland.
(ii)
The objectives and risk aversion of the client.
(iii)
Information about whether or not profits, RPI and other data are
calculated in the same way in the two countries.
(iv)
Total returns from the relevant stock markets and for investors in the
companies. The data provided only shows the return from share price
movements, and excludes the dividend yield, which might be
significant.
(v)
Exchange rate movements between the two countries and the UK.
The client is likely to be interested in returns in sterling, not in foreign
currencies.
(vi)
Any tax implications of investing in the two countries.
(vii) Information about the future prospects of the companies. Historic
returns do not provide an accurate guide to future performance. What
are the future strategies of the two companies, what are their
strengths and weaknesses, what is their competition?
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Answers
(viii) Macro economic information about the two countries and their
prospects. Ayeland is a relatively high inflation country. Is the
government likely to bring this under control? What are key economic
indicators and trends?
(ix)
10.3
How stable are the governments in the two countries and would there
be significant political risk with the investments?
Khan Industries plc
The data provided does not provide the basis for a thorough analysis, but ratios
and growth rates give an indication of the divisions' performance.
Last
year
Current
year
Last
year
Current
year
A
A
B
B
Operating profit
Sales
11.3%
12.2%
12.8%
14.5%
Operating profit
Capital employed
14.4%
15.8%
15.6%
18.4%
Current ratio
1.38
1.35
1.39
1.41
Gearing (medium and long-term
debt/equity)
6%
22%
12%
12%
A
B
Revenue
19%
6.6%
Taxable profit
17%
23%
Non-current assets
17%
2%
12.5%
Division
Growth rates:
Working capital
Based upon the above financial ratios and growth rates the two divisions have
both improved their performance during the last year. There is, however, no data
allowing comparisons with similar operations to allow assessment of whether the
improved performance is of the standard that might be expected in the
industry(ies) concerned.
The only detrimental elements are the small reduction in the current ratio of
division A, and the increase in gearing of division A to 22% probably in order to
finance the purchase of fixed assets. It is unlikely that either of these factors
would be of major concern.
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These results have, however, been achieved in different ways. Division A seems
to be taking a longer term perspective and has expanded its operations and
invested heavily in new fixed assets. Division B's apparent good performance, for
example in return on capital employed, has been achieved using existing assets.
Division B is more likely to have ensured that the short-term results look good
without considering the long-term implications of the lack of investment. It
depends on companies objectives as to whether it would like to increase its short
term profits or be inclined towards long term benefits.
The board of Khan Industries should be much more explicit in what is meant by
'an improvement in performance'. Controls should be introduced to ensure that
the development of the divisions is in line with the long-term strategic plans of
Khan Industries, including the nature of products in the divisions, and the markets
to be served by the divisions.
The short termism approach of division B should be discouraged, and divisions
should be encouraged to focus on the cash flows of their activities. Investments
should be judged on their likely effect on cash flows and the value of the
business (e.g. through the expected NPV of investments) rather than accounting
ratios.
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CHAPTER 11 – CAPITAL RATIONING
11.1
CAPITAL RATIONING
(a)
Assume that all the investments are divisible
Total NPV is maximised by maximising the NPV per Rs. 1 invested.
Investment
A
B
C
D
E
Capital
investment
NPV per
Rs. 1
invested
NPV
Rs.
60,000
80,000
50,000
45,000
55,000
Rs.
12,000
21,600
8,500
10,800
9,900
Ranking
Rs.
0.20
0.27
0.17
0.24
0.18
3rd
1st
5th
2nd
4th
Investments to maximise NPV
Investment
Capital investment
NPV
Rs.
80,000
45,000
125,000
25,000
150,000
Rs.
21,600
10,800
B
D
A
Total
(b)
(balance)
5,000
37,400
Assume that all investments are indivisible
The combination to maximise total NPV is found by identifying possible
combinations of investments within the Rs. 150,000 investment limit and
calculating the total NPV from that combination.
Capital
investment
Investments
A+B
B+D
C+D+E
(60,000 + 80,000)
(80,000 + 45,000)
(50,000 + 45,000 + 55,000)
Rs.
140,000
125,000
150,000
Total
NPV
Rs.
33,600
32,400
29,200
Notes:
If A is undertaken there would only be enough cash left to undertake any
one of the remaining investments. B has the highest NPV so other
combinations involving A can be ignored.
Similarly, if B is undertaken there would only be enough cash left to
undertake any one of the remaining investments. A + B has already been
considered. Of the remainder, D has the highest NPV so other
combinations involving B can be ignored.
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Clearly, other combinations involving pairs of projects chosen from C, D
and E could be considered but as all give positive NPVs it is obviously
better to do all three rather than two put of the three projects.
Conclusion
(A + B) is clearly better than (C + D + E) and (B + D).
If the projects are indivisible, the combination of investments to maximise
total NPV is investment in A and B.
11.2
BASRIL COMPANY
(a)
(i)
Year
Analysis of projects assuming they are divisible
DCF
factor
Project 1
12%
Project 3
Cash flow
PV
Cash flow
PV
Rs.
Rs.
Rs.
Rs.
0
1.000
(300,000)
1
0.893
85,000
2
0.797
3
(300,000)
(400,000)
(400,000
)
75,905
124,320
111,018
90,000
171,730
128,795
102,650
0.712
95,000
167,640
133,432
195,004
4
0.636
100,000
163,600
138,236
187,918
5
0.567
95,000
153,865
143,212
181,201
NPV
32,740
Profitability index
32,740/300,000:
0.109 or
10.9%
77,791
77,791/400,000:
0.194 or
19.4%
Project 2 NPV at 12% = Rs.(140,800 × 3.605) – 450,000 = Rs.
57,584
Project 2 profitability index = 57,584/450,000 = 0.128 or 12.8%
The optimum investment schedule involves investment in projects 3
and 2:
Project
Profitability
index
Ranking Investment
NPV
Rs.
Rs.
3
19.4%
1st
400,000
77,791
2
12.8%
2nd
400,000
51,186 ( 57,584 × 400/450)
800,000
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Answers
(ii)
If the projects are assumed to be indivisible, the total NPV of
combinations of projects must be considered.
Projects
Investment
NPV
Rs.
Rs.
1 and 2
750,000
90,324 (= 32,740 + 57,584)
1 and 3
700,000 110,531 (= 32,740 + 77,791)
The optimum combination is now projects 1 and 3.
(b)
The NPV decision rule requires that a company invest in all projects that
have a positive net present value. This assumes that sufficient funds are
available for all incremental projects, which is only true in a perfect capital
market. When insufficient funds are available, that is when capital is
rationed, projects cannot be selected by ranking them in order of their NPV.
Choosing a project with a large NPV may mean not choosing smaller
projects that, in combination, give a higher NPV. Instead, if projects are
divisible, they can be ranked using the profitability index in order to make
the optimum selection. If projects are not divisible, different combinations of
available projects must be evaluated to select the combination with the
highest NPV.
(c)
The NPV decision rule, to accept all projects with a positive net present
value, requires the existence of a perfect capital market where access to
funds for capital investment is not restricted. In practice, companies are
likely to find that funds available for capital investment are restricted or
rationed.
Hard capital rationing is the term applied when the restrictions on raising
funds are due to causes external to the company. For example, potential
providers of debt finance may refuse to provide further funding because
they regard a company as too risky. This may be in terms of financial risk,
for example if the company’s gearing is too high or its interest cover is too
low, or in terms of business risk if they see the company’s business
prospects as poor or its operating cash flows as too variable. In practice,
large established companies seeking long-term finance for capital
investment are usually able to find it, but small and medium-sized
enterprises will find raising such funds more difficult.
Soft capital rationing refers to restrictions on the availability of funds that
arise within a company and are imposed by managers. There are several
reasons why managers might restrict available funds for capital investment.
Managers may prefer slower organic growth to a sudden increase in size
arising from accepting several large investment projects. This reason might
apply in a family-owned business that wishes to avoid hiring new
managers. Managers may wish to avoid raising further equity finance if this
will dilute the control of existing shareholders. Managers may wish to avoid
issuing new debt if their expectations of future economic conditions are
such as to suggest that an increased commitment to fixed interest
payments would be unwise.
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One of the main reasons suggested for soft capital rationing is that
managers wish to create an internal market for investment funds. It is
suggested that requiring investment projects to compete for funds means
that weaker or marginal projects, with only a small chance of success, are
avoided. This allows a company to focus on more robust investment
projects where the chance of success is higher1. This cause of soft capital
rationing can be seen as a way of reducing the risk and uncertainty
associated with investment projects, as it leads to accepting projects with
greater margins of safety.
11.3
CB INVESTMENT LIMITED
Project duration
Forecasted net cash inflows start
from year
A
B
C
D
E
F
4
5
3
6
3
2
1
2
1
3
1
1
Discount rate
10%
11%
12%
11%
13%
14%
Annuity factor for total period
3.487
4.102
2.690
4.696
2.668
1.877
Less: Annuity factor for zero cash
inflow period
-
Adjusted annuity factor
(1.000)
3.487
3.102
-
(1.901)
-
-
2.690
2.795
2.668
1.877
Forecasted annual net cash inflows
150.00
50.00
140.00
256.00
440.00
300.00
Present value of inflows
523.05
155.10
376.60
715.55
1,173.92
563.10
376.60
715.55
1,173.92
563.10
(240.00)
(512.00)
(800.00)
(400.00)
Adjustment for mutually compulsory
projects
Less: Initial investment required
today
678.15
(300.00)
Adjustment for mutually compulsory
projects (a)
(120.00)
(420.00)
(240.00)
(512.00)
(800.00)
(400.00)
Net present value (b)
258.15
136.60
203.55
373.92
163.10
Profitability index (b ÷ a)
0.615
0.569
0.398
0.467
0.408
Ranking
1
2
5
3
4
Option 1 : Invest in the highest ranked projects
In this combination only up to Rs. 660 million is invested leaving Rs. 340
unused. This is not enough to undertake any other of the projects.
Investment
NPV
Rs. in million
Rank 1
420.00
258.15
Rank 2
240.00
136.60
660.00
394.75
However, the company might be able to increase the available NPV by investing
more of its available funds.
Hence other options should be considered. While selecting other options the
basic presumption should be to select the last project (balancing amount) which
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can be scaled down i.e. Project C. Considering the above, there are four more
options as shown below:
Option 2: Invest in Rank 4 ahead of Rank 2 which can be scaled down
If we consider the rank 4 project which requires lesser investment as compare to
rank 5 project, we would be able to utilize about 75% of rank 2 project, as
against option 3 in which Project C is only 28% utilized.
Investment
NPV
Rs. in million
Rank 1
420.00
258.15
Rank 4
400.00
163.10 Because it cannot be scaled down.
Rank 2 (balance)
180.00
102.45
1,000.00
523.70
Option 3 : Invest in Rank 5 ahead of Rank 2 which can be scaled down
Rank 1
Rank 5
Rank 2 (balance)
Investment
NPV
Rs. in million
420.00
258.15
512.00
203.55 Because it cannot be scaled down.
68.00
38.70
1,000.00
500.40
Option 4: Invest in Rank 3 and Rank 2 which can be scaled down
Rank 3
Rank 2(balance)
Investment
NPV
Rs. in million
800.00
373.92 Because it cannot be scaled down.
200.00
113.83
1,000.00
487.75
Option 5: Invest in Rank 4, Rank 5 and Rank 2 which can be scaled down
Rank 4
Rank 5
Rank 2(balance)
Investment
NPV
Rs. in million
400.00
163.10
512.00
203.55 Because it cannot be scaled down.
88.00
50.09
1,000.00
416.74
Conclusion:
The most beneficial mix for the company is to invest in Projects A, B, F and C
(balancing amount) which gives the highest NPV to the company.
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CHAPTER 12 – SOURCES OF FINANCE
12.1
RIGHTS
(a)
Rs.
4 shares
1 new share
22.00
4.50
have a current market value of (u Rs. 5.50)
- issue price
––––––
5 shares
Have a theoretical value of
26.50
––––––
Theoretical ex-rights price = Rs. 26.50/5 = Rs. 5.30 per share.
(b)
Value of rights
Rs.
Current market price
Theoretical ex-rights price
5.50
5.30
––––
Value of rights
0.20
––––
This is the theoretical value of the rights, for each existing share.
12.2
KAMALIA CARRIERS PLC
(a)
Rights Issue –This is an offer to the existing shareholders of securities
listed in the primary market to subscribe for additional shares in the
proportion of their existing shareholdings at a price generally lower than the
current market price of the shares. It is the most common method of raising
capital by private and public companies.
(b)
Differences between “rights issue” and “public issue”
(i)
Rights issue is usually more successful than public issue because it is
made to investors who are familiar with the operations of the
company.
(ii)
A rights issue involves selling of ordinary shares to the existing
shareholders while a public issue involves raising of share capital
directly from the public.
(iii)
The flotation costs of a rights issue are significantly lower than those
of a public issue because a rights issue is not underwritten.
(iv)
A rights issue may be made by private companies as well as public
companies whereas a public issue can only be made by public
companies.
(v)
A rights issue does not lead to dilution of control except the rights are
not fully taken up by the shareholders whereas a public issue can
lead to dilution of control.
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(c)
(i)
Finance required:
The finance required to redeem the debenture and finance the new
project is the addition of the current price of the debenture and the
cost of the new project. This is obtained as follows:
Calculation of the current value of the debenture
15% Redeemable debenture
= Rs. 6,000,000
Annual interest
=
Rs. 900,000
Year
Item
Cashflow
Rs.
DCF @
9%
PV
(Rs.)
1 – 10
10
Interest
Debt redeemed
900,000
6,000,000
6.4177
0.4224
5,775,930
2,534,400
Current value
8,310,330
Current value of the 15% redeemable debenture =
Rs. 8,310,330
Cost of the proposed project (given)
=
Rs. 1,600,000
Therefore, the finance required is
=
Rs. 9,910,330
= Rs. 10,000,000
approx.
(ii)
Calculation of issue price per share
Finance required=
Rs. 10,000,000 (c (i) above)
No of shares issued (6,000,000/3)
= 2,000,000 shares
Issue price
=
•Ǥͳ0,000,000
2,000,000
= Rs. 5.00
(iii)
Calculation of theoretical ex-rights price
Rs.
3 shares at N6.20
1 share at N5.00
18.60
5.00
4 shares
23.60
Theoretical ex-rights price
(iv)
=
Rs.
23.60/4
=
Rs. 5.90
=
Rs. 5.90
Calculation of right per share
Theoretical ex-rights price
Less:
Issue price
5.00
0.90
Right per share
© Emile Woolf International
217
=
0.90/3
=
Rs.0.30
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Business finance decisions
12.3
RIGHTS ISSUE
(a)
Calculations
(i)
Number of shares in issue = total earnings/EPS
= Rs. 1,200,000/Rs.0.15 = 8,000,000
Rs. m
Value of the existing shares = 8,000,000 × Rs. 2.70
Cash raised from new shares
21.6
3.8
––––––
Total
25.4
––––––
Number of shares issued = Rs. 3,800,000/Rs. 1.90 per share
= 2,000,000 shares
The rights issue is therefore a 1 for 4 rights issue
(2,000,000:8,000,000)
The number of shares after the issue = 10 million
Rs.
Current value of 4 existing shares
Rights issue price of 1 share
(u Rs. 2.70)
10.80
1.90
–––––––
Theoretical value of 5 shares
12.70
–––––––
Theoretical ex-rights price
(12.70/5)
Rs. 2.54
(ii)
Rs.
Current market value of existing share
Theoretical ex-rights price
2.70
2.54
––––––
The value of a right
0.16
––––––
(iii)
Existing P/E ratio = Rs. 2.70/Rs.0.15 = 18.0
The revised profit after tax = Rs. 1.8 million
The revised total market value = 18 × Rs. 1.8 million = Rs. 32.4
million
Therefore, the market value per share =
•Ǥ͵2.4 million
= •Ǥ͵.24
10 million shares
(b)
The shareholder can do any of the following:
‰
© Emile Woolf International
Buy all the shares offered to him in the rights issue. This would
maintain his percentage shareholding in the company.
218
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12.4
‰
Sell the rights. Rights can be sold on the stock market. The
theoretical market price is Rs.0.16 for the rights attached to one
existing share.
‰
Buy some of the shares offered to him in the rights issue and sell
some rights.
‰
Do nothing. This is a bad choice. Shareholders will see a fall in the
value of their shares because the new shares will be issued at a
discount to the current market price. The company may try to sell any
rights that are not taken up on behalf of the shareholder, but the
shareholder should not rely on getting any money from the company.
STOCK EXCHANGE LISTING
Advantages
A stock market quotation might have the following advantages:
(i)
Access to outside finance. It provides the opportunity to raise equity
finance from other than existing shareholders. It should also be easier to
raise additional debt finance.
(ii)
Once well-established, a company via a better credit rating can obtain
cheaper debt finance.
(iii)
Marketability of shares. Existing shareholders are given the opportunity to
sell their shares more easily and at better prices.
(iv)
Incentive schemes including share ownership can be offered to
management and employees.
(v)
Status of company. A publicly quoted company may achieve greater status
than a similar unlisted company: this could improve staff morale and result
in increased publicity and sales.
(vi)
Take-overs. Other businesses can be acquired by using shares as
consideration rather than having to use cash.
Disadvantages
A stock market quotation has the following disadvantages:
(i)
Costs. It is expensive e.g. in terms of advisers and advertising, to achieve
a listing plus routine costs of conforming to requirements of the Stock
Exchange.
(ii)
Accountability. It makes it necessary for the board to report to 'outside
shareholders'; this would be particularly important, for example, in the case
of a family-owned company where most shareholders are board members.
(iii)
Dilution of control of existing shareholders.
(iv)
Take-overs. With shares in the hands of the public, risk of take-over may
be increased.
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12.5
CONVERTIBLE BONDS
Earnings = profit after interest and tax.
Rs.
Current total annual earnings (2,000,000 × Rs.0.25)
On conversion:
Reduction in interest cost (Rs. 1,000,000 × 4%)
Minus increase in taxation (30%)
Rs.
500,000
40,000
(12,000)
––––––––
Increase in annual earnings
28,000
––––––––
528,000
––––––––
Total annual earnings after conversion
Shares
Shares currently in issue
New shares on conversion of the bonds
(Rs. 1,000,000 u 40/Rs. 100)
2,000,000
400,000
2,400,000
EPS after conversion = Rs. 528,000/2,400,000 shares = Rs.0.22 per share.
There will be dilution in EPS from Rs.0.25 to Rs.0.22 per share.
12.6
SHOAIB INVESTMENT COMPANY
(a) Fresh equity required to be injected on June 30, 2016
Market value of equity on March 31, 2016
Market value of equity as at June 30, 2016
Fresh equity required
Rupees in
million
2,800 Working 1
700 Working 2
2,100
Since the market value of debt on June 30, 2016 is the same as the
market value of debt on March 31, 2016, the company has to maintain the
same level of equity also.
Working 1: Market value of net equity and debt as of March 31, 2016
Rupees in
million
2,000
Net equity at book value
Market value of the company's shares
(2,000 x 1.4)
2,800
Existing debt (2,800 x 70/30)
6,533
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Working 2: Market value of net equity as at June 30, 2016
Rupees in
million
Book value of net equity as of
March 31, 2016
Less: Loss on listed securities portfolio
Net Equity as at June 30, 2016
2,000
1,222 Working 3
778
Market value of equity as at June 30, 2016
(Rs. 778 x 0.9)
700
Working 3: Loss on listed securities portfolio
Rupees in
million
20%
1.1
22%
Decline in Stock
Correlation
Decline in company’s portfolio value
Listed portfolio value as at March 31, 2016
(Rs. in million)
Loss on portfolio (5,555 x 22%)
(Rs. in million)
5,555 Working 4
1,222
Working 4: Listed portfolio value as at March 31, 2016
Value of long term debt
Value of other liabilities (6,533 ÷ 90 x 10)
Value of equity
Listed securities (60% of total assets)
Rupees in
million
6,533 Working 1
726
2,000 Given
9,259
5,555
(b) % holding of Mr. Alam
Market value of required new equity (Rs. in million)
Current market price (700 ÷ 100) (Rs.)
7.00
Number of shares [2,100 ÷ (7 x 90%)] (shares in million)
Already issued shares (shares in million)
Total number of shares (shares in million)
Equity stake of new owner (333.33 ÷ 433.33)
© Emile Woolf International
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2,100
333.33
100.00
433.33
76.92%
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Business finance decisions
12.7
SAJAWAL SUGAR MILLS LIMITED
(a)
Right Ratio
Rs.
1,076.39
Rs. 20.00
Market value of the company after expansion (W1)
Current market price of SSML’s Share (given)
Number of shares to be issued to maintain Market Value Rs. 1,076.39
at Rs. 20 desired price:
Share in
million
Total number of shares after right issue (Market value /
Price)
53.82
Less: Present number of shares
40.00
Number of right shares to be issued
13.82
Right ratio - one right share will be issued for every 2.89 (40÷13.82) shares
held.
(b)
Right offer price
To maintain Debt : Equity ratio, amount to be
raised as equity (Rs. 300 million × (100% - 52%)
Rs. 144
[W7])
Offer price of right shares (Rs. 144 ÷ 13.82)
Rs.
(c)
10.42
per share
Theoretical Ex-Rights price
The market value of 40 million shares (already issued to date)
Capital to be raised through right issue
Theoretical Ex - rightsprice
(d)
Million
Rs. in
million
800
144
944
944
17.54
53.82
Value of Right
Valueof right
Ex - right price issue price
No. of rightsrequiredto buy one share
Valueof right (applicable to each existingshare)
20 - 10.42
2.89
= 3.31
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Workings
W1 : Market value after expansion
MV
d1
r-g
MV =
Rs. 155 (W 2) × 70%
= 1,076.39
16.9% (W 5) - 6.82% (W 6)
W2: Expected profit
Expected Profit = Total assets × ROA
= 1,550 (W3) × 10% (W4) = 155
W3: Total assets after capital increase
Existing assets
Total capital to be raised
Total assets after capital increase
Rs. in million
1,250
300
1,550
W4 : Existing return on assets
Existing ROA
Net profit
Total Assets
125
10.00%
1,250
W5: Required return (r)
r = Rf + (Rm-Rf) × B
= 12% + (16% - 12%) × 1.23
= 16.9%
W6: Growth (g)
g=rxb
Net Profit
u (1 - pay out%)
Equity
125
u (1 - 70%)
550
= 6.82%
W7: Debt: Equity ratio
D/E ratio =
© Emile Woolf International
Debt
600,000
52%
Debt Equity 600,000 550,000
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12.8
PSD ENGINEERING LIMITED
(a) (i)
ƒ Theoretical ex-right price
Value of 5 original shares @ Rs. 16
Value of 2 right share @ Rs. 12.5)
Ex-right price (Rs. 105 ÷ 7)
Rupees
80.00
25.00
105.00
15.00
ƒ Value of the right
(ii)
Ex-right share price
Cost of acquiring right share
15.00
12.50
2.50
Value of right per original share (Rs. 2.5 ÷ 5 share)
0.500
Yield adjusted theoretical ex-right price
Current shares market value
(20 million share of Rs. 16 each)
Value of right shares (8 million shares of Rs. 12.5 each)
NPV
Yield adjusted theoretical ex-right price
(Rs. 516 million ÷ 28 million shares)
(iii) Current earnings per share
Profit before interest and taxation
Less: Interest on debentures (Rs. 350 million @ 10%)
Profit before taxation
Less: taxation @ 35%
Earnings per share (Rs. 39 million ÷ 20)
Price earnings ratio (Rs. 16 ÷ Rs. 1.95)
© Emile Woolf International
224
Rupees
in
million
320
100
96
516
18.43
95.00
(35.00)
60.00
(21.00)
39.00
Rs.
1.95
8.21
The Institute of Chartered Accountants of Pakistan
Answers
New earnings per share and share price
Right
Debenture
issue
issue
Rupees in million
Profit before interest and taxation
(95.00 x 1.1)
Less: Debenture interest (10% × 350)
(9% × 100)
Profit before tax
Less: Taxation at 35%
EPS
Rs. 45.17 million / 28 million shares
Rs. 39.32 million / 20 million shares
New share price
Rs. 1.61 x 8.21
Rs. 1.97 x 8.21 x 70%
104.50
(35.00)
69.50
24.33
45.17
104.50
(35.00)
(9.00)
60.50
21.18
39.32
Rs.
Rs.
1.61
1.97
13.22
11.31
(b) PSD already has a gearing level of 37% (350 ÷ 940). If it is at or near its
optimal level of gearing, shareholders may take negatively to the additional
debt which would push the gearing level up to 43% (450 ÷ 1,040).
Accordingly the cost of equity would rise and the ordinary share price
would fall.
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Business finance decisions
CHAPTER 13 – COST OF CAPITAL
13.1
COST OF CAPITAL
(a)
Dividend valuation model
(i)
(ii)
(iii)
(iv)
No growth therefore:
Total MV
ൌ
†ଵ ܴ‫ݏ‬Ǥ ͳͲ ൈ ͷͲǡͲͲͲ
ൌ
ൌ ܴ‫ݏ‬Ǥ ͷǡͲͲͲǡͲͲͲ
ͲǤͳͲ
”ୣ
MV per share
ൌ
†ଵ ܴ‫ݏ‬Ǥ ͳͲ
ൌ
ൌ ܴ‫ݏ‬Ǥ ͳͲͲ
ͲǤͳͲ
”ୣ
No growth therefore:
†ଵ ܴ‫ݏ‬Ǥ ͷͲͲǡͲͲͲ
ൌ
ൌ ܴ‫ݏ‬Ǥ ͵ǡ͵͵͵ǡ͵͵͵
ͲǤͳͷ
”ୣ
Total MV
ൌ
MV per share
ൌ ܴ‫ݏ‬Ǥ ͵ǡ͵͵͵ǡ͵͵͵ ൊ ͳͲǡͲͲͲ‫ ݏ݁ݎ݄ܽݏ‬ൌ ܴ‫ݏ‬Ǥ ͵͵͵
Constant growth
Therefore use:
ൌ †ଵ
†଴ ൈ ሺͳ ൅ ݃ሻ
ൌ
”ୣ െ ݃
”ୣ െ ݃
Total MV
ൌ ܴ‫ݏ‬Ǥ ͳͲ ൈ ͳ݉ ൈ ሺͳǤͲͷሻ
ൌ ܴ‫ݏ‬Ǥ ͳͲͷ݉
ͲǤͳͷ െ ͲǤͲͷ
MV per share
ൌ ܴ‫ݏ‬Ǥ ͳͲ ൈ ሺͳǤͲͷሻ
ൌ ܴ‫ݏ‬Ǥ ͳͲͷ
ͲǤͳͷ െ ͲǤͲͷ
No growth for first five years and then growth at 5% pa in perpetuity.
The PV of the cash flows from 1 to 5 and those from 6 to infinity must
be calculated separately and then summed.
Rs.
ͳ െ ሺͳ ൅ ͲǤͳͷሻିହ
ൌ
ͲǤͳͷ
1 to 5
•Ǥ ͳͲͲǡͲͲͲ ൈ 6 to f
ͳ
•Ǥ ͳͲͲǡͲͲͲ ൈ ሺͳǤͲͷሻ
ൈ
ൌ
ͳǤͳͷହ
ͲǤͳͷ െ ͲǤͲͷ
Total MV
521,850
857,066
MV per share (÷10,000)
(b)
335,216
85.71
Cost of equity
(i)
re
=
7 .5
× 100
150
= 5%
(ii)
re
=
15
× 100
165 15
= 10%
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Answers
Note: The dividend valuation model always uses the ex-div price. Rs.
15 is deducted from the cum-div price of Rs. 165 in order to arrive at
the ex-div price.
(c)
(iii)
re
=
24 u (1 0.05)
× 100 + 5
120
= 26%
(iv)
re
=
1 .5
× 100
10
= 15%
Cost of debt (pre-corporation tax)
(i)
Cost of debt
ൌ
݅
ܴ‫ݏ‬Ǥ ͳͲ
ൌ
ൌ ͳͲΨ
”ୢ ܴ‫ݏ‬Ǥ ͳͲͲ
(ii)
Cost of debt
ൌ
݅
ܴ‫ݏ‬Ǥ ͳͲ
ൌ
ൌ ͳͳǤ͹͸Ψ
”ୢ ܴ‫ݏ‬Ǥ ͺͷ
(iii)
Cost of debt is the IRR of the following cash flows.
Try 20%
Yr.
Cash flow
Discount
factor
PV
Discount
factor
PV
0
Market value
(74)
1.000
(74.00)
1.000
(74.00)
1
Interest
10
0.833
8.33
0.800
8.00
2
Interest
10
0.694
6.94
0.640
6.40
3
Interest +
redemption
110
0.579
63.69
0.512
56.32
NPV
?
(iv)
Try 25%
kd
4.97
= 20% +
ൌ
Cost of debt
(3.28)
4.97
× (25% – 20%) = 23%
4.97 3.28
݅
ܴ‫ݏ‬Ǥ ͳͲ
ൌ
ൌ ͳͲΨ
”ୢ ܴ‫ݏ‬Ǥ ͳͲͲ
Tutorial note: If debt is trading at par and is to be redeemed at
par, the cost of debt is the nominal interest rate.
(v)
(d)
ൌ
Cost of pref.
݅
ܴ‫ݏ‬Ǥ ͷ
ൌ
ൌ ͹Ǥ͹Ψ
”୮ ܴ‫ݏ‬Ǥ ͸ͷ
Cost of debt (post-corporation tax)
(i)
Cost of debt
ൌ
݅
ܴ‫ݏ‬Ǥ ͳͲሺͳ െ ͲǤ͵ሻ
ൌ
ൌ ͹Ψ
”ୢ
ܴ‫ݏ‬Ǥ ͳͲͲ
or simply multiply the pre-tax cost (found in part c) by
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Business finance decisions
(1 t)
10% u (1 0.3) = 7%
(ii)
Cost of debt
ൌ
݅
ܴ‫ݏ‬Ǥ ͳͲሺͳ െ ͲǤ͵ሻ
ൌ
ൌ ͺǤʹ͵Ψ
”ୢ
ܴ‫ݏ‬Ǥ ͺͷ
or simply multiply the pre-tax cost (found in part c) by
(1 t)
11.76% u (1 0.3) = 8.23%
(iii)
Cost of debt is the IRR of the following cash flows.
Try 15%
Discount
Cash flow
factor
Yr.
0
Market value
1
Try 20%
PV
Discount
factor
PV
(74)
1.000
(74.00)
1.000
(74.00)
Interest less tax
7
0.870
6.09
0.833
5.83
2
Interest less tax
7
0.756
5.29
0.694
4.86
3
Interest less tax +
redemption
107
0.658
70.41
0.579
61.95
NPV
7.79
(1.36)
Using interpolation, the after-tax cost of the debt is:
15% +
(iv)
7.79
× (20 15)% = 19.26% ?
(7.79 + 1.36)
Cost of debt
ൌ
݅
ܴ‫ݏ‬Ǥ ͳͲ ൈ ሺͳ െ ͲǤ͵ሻ
ൌ
ൌ ͹Ψ
”ୢ
ܴ‫ݏ‬Ǥ ͳͲͲ
or simply multiply the pre-tax cost (found in part c)
by (1 t)
10% u (1 0.3) = 7%
(v)
Cost of pref.
ൌ
݅
ܴ‫ݏ‬Ǥ ͷ
ൌ
ൌ ͹Ǥ͹Ψ
”୮ ܴ‫ݏ‬Ǥ ͸ͷ
Note: There is no tax relief on preference dividends so this is the
same as the answer in part c
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Answers
13.2
WACC
Cost of equity
18 1.03
0.03
155
= 0.1496 or 14.96%.
WACC
ª
350
« 1,200 350 u7.8 1 0.30
¬
º ª
º
1,200
» « 1,200 350 u14.96 »
¼
¼ ¬
= 1.23 + 11.58
= 12.81%.
13.3
REDSKINS PLC
Post-tax weighted average cost of capital
(i)
Cost of debt
3% irredeemable debentures
For irredeemable stock kd
=
Cost of 3% irredeemable stock
=
Interest (1 - T)
Ex interest market value
Rs.3.00 × (1 - 0.30)
= 7.34%
Rs.(31.60 - 3.00)
Note: Rs. 3 is deducted from the cum-div price of Rs. 31.6 in order to arrive
at the ex-div price.
9% redeemable debentures
Calculate the internal rate of return of the after-tax cash flows.
Time 0 Ex-interest market price
Time 1-10 Interest (post-tax)
Time 10 Repayment of capital
Net present values
By linear interpolation: IRR = 5% +
Cash
flows
Rs.
(94.26)
6.30
100.00
PV
at 5%
Rs.
(94.26)
48.65
61.40
———
15.79
———
PV
at 10%
Rs.
(94.26)
38.71
38.60
———
(16.95)
———
Rs.15.79
× 5% = 7.41%
Rs.(15.79 + 16.95)
Cost of 6% unquoted stock
The value of the stock is the present value of the pre-tax cash flows
discounted at 10%, i.e.
(Rs. 6.00 × 6.145) + (Rs. 100 × 0.386) = Rs. 75.47
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Business finance decisions
The after-tax cost is the discount rate which equates the after-tax cash
flows to a present value of Rs. 75.47, i.e.
Cash
flows
Rs.
(75.47)
4.20
100.00
Time 0 Current value
Time 1-10 Post-tax interest
Time 10 Repayment
Net present values
By linear interpolation: IRR = 5% +
PV
at 5%
Rs.
(75.47)
32.43
61.40
———
18.36
———
PV
at 10%
Rs.
(75.47)
25.81
38.60
———
(11.06)
———
18.36
× 5% = 8.12%
29.42
Bank loans
After-tax cost of bank loan
=
(11% + 2%) × (Rs. 1 – 0.30) = 9.10%
Cost of equity
”ୣ ൌ †ሺͳ ൅ ‰ሻ
ͳͲሺͳǤͲͻሻ
൅‰ൌ
൅ ͲǤͲͻ ൌ ͲǤͳͻ‘”ͳͻΨ
ͳͳͲ
Cost of equity
The values of the various sources of finance are as follows.
MV
Cost (%)
Weighted
average
Rs.000
3% debt
1,400 × 0.286
400
7.34
0.21
9% debt
1,500 × 0.9426
1,414
7.41
0.77
6% debt
2,000 × 0.7547
1,509
8.12
0.90
1,540
9.10
1.03
8,800
19.00
12.24
Bank loan
Equity
8,000 × 1.1
Total
1,540
15.14
WACC = 15.14%
13.4
CHASANDA AGATES PLC.
(a)
The net dividend has increased by 1.5 times from the end of 2013 to the
end of 2017, a period of 5 years. This represents an approximate
annualized growth rate of:
g
© Emile Woolf International
=
Latest dividend
൬n-1 ටEarliest divident-1 x 100%൰
230
The Institute of Chartered Accountants of Pakistan
Answers
300
=
൬S-1 ට200-1 x 100%൰
=
ቆ4 ට1.5-1 x 100%ቇ
=
10.6%
d1
+g
po
k3
Where d1 = do (1 + g)
Ke
=
do (1 g )
g
po
=
30 (1.1067)
0.1067
376
=
0.195 OR
19.5%
Cost of debenture (kd) (Tax Ignored)
Workings: determination of relevant cashflows.
Year
MV
Interest
Cashflow
Rs.
0
Rs.
(75)
8
(67)
8
8
100
100
1-20
20
Using 10% and 20% discount rates for the IRR
Year
CF
DF
PV
DF
PV
(Rs.)
(10%)
Rs.
(20%)
Rs.
0
67
1.00
1-20
8
8.5136
68.11
4.8696
38.96
100
0.1486
14.86
0.0261
2.61
20
(67)
1.00
15.97
୒୔୚ఽ
ቁൈ
ఽ ି୒୔୚ా
ୢ ൌ ൌ Ψ ൅ ቀ୒୔୚
? Kd
© Emile Woolf International
(25.43)
ሺ െ ሻΨ
Rs. 15.97
15.97 + Rs. 25.53
=
10% + Rs.
=
10 + 0.3857 (10)
=
13.86%
231
(67)
× (20 -10)%
The Institute of Chartered Accountants of Pakistan
Business finance decisions
WACC Computation
Market
Value
Rs.’000
Source of capital
Equity (1m x Rs. 3.76)
Cost (%)
Total
Rs.’000
3,760
19.50
733.20
469
13.86
65.00
Debenture (700,000 x 0.67)
4,229
•Ǥ͹98.20
WACC
(b)
(c)
=
•ǤͶ,229.00
798.20
100
x
= 18.87%
1
Difficulties and uncertainties are:
(i)
Will the growth rate in dividend remain the same as in previous
years?
(ii)
Should a premium for risk be added to the weighted average cost of
capital?
(iii)
The existing gearing ratio will be maintained and the optimal capital
structure of the company already attained.
(iv)
The market values used for the computation of the WACC can never
remain constant but subject to changes due to market forces
particularly that of debentures when approaching the redemption
time.
(v)
Equity valuation is based only on the basis of dividends, ignoring
other factors.
Calculation of NPV of the project
Year
CF
DF
PV
(Rs.)
(18.87%)
Rs.
0
Initial outflow
(1,500,000)
1.00
(1,500,000)
1-f
Cash inflows
500,000
1/r = 1/.1887
2,658,161
1,658,161
Recommendation: The NPV of the project is positive, hence its acceptance
is worthwhile (NPV of Rs. 1,158,161).
(d)
Company’s dividend policy.
Year
Dividends
Rs.’000
Earnings
before tax
Rs.’000
Earnings
after tax
Rs.’000
Dividend as a
% of earnings
after tax (%)
2013
200
575
350
57
2014
230
723
452
51
2015
2016
230
260
682
853
410
536
56
49
2017
300
906
606
50
© Emile Woolf International
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Answers
The policy is only suitable when a company achieves a stable EPS or
steady EPS growth.
This appears not to be the case with this company as the earnings have
revealed, particularly that of year 2015.
13.5
MISTERI COMPANY
Workings
WACC
WACC = (70% u 10%) + [(30%) u (8.9%)(1 – 0.25)] = 7% + 2% = 9%.
Capital allowances
Year
Tax
1
Rs.
1,200,000
(300,000)
Allowance
WDV
Capital
allowance
Year of
saving
Rs.
Tax
saved
at 25%
Rs.
300,000
75,000
2
225,000
56,250
3
168,750
42,188
4
306,250
76,562
5
––––––––––
2
900,000
(225,000)
Allowance
––––––––––
3
675,000
(168,750)
Allowance
––––––––––
4
506,250
(200,000)
Disposal value
––––––––––
4
Balancing allowance
306,250
––––––––––
Year 1
Sales (units)
400,000
Contribution per unit: Rs. 2
Rs.
Total contribution
800,000
Fixed costs (cash)
(500,000)
––––––––
Cash profit
Tax at 25%
Year 2
600,000
Year 3
700,000
Year 4
700,000
Rs.
1,200,000
(520,000)
Rs.
1,400,000
(540,000)
Rs.
1,400,000
(560,000)
––––––––
––––––––
––––––––
300,000
680,000
860,000
880,000
––––––––
––––––––
––––––––
––––––––
(170,000)
(215,000)
(220,000)
Year 4
Rs.
880,000
Year 5
Rs.
(75,000)
Project cash flows
Cash profits
© Emile Woolf International
Year 1
Rs.
300,000
Year 2
Rs.
680,000
233
Year 3
Rs.
860,000
The Institute of Chartered Accountants of Pakistan
Business finance decisions
Tax on profits
Tax benefit of cap.
allowances
Disposal of machine
(75,000) (170,000)
75,000
56,250
(220,000)
76,562
200,000
––––––––
Net cash flow
(215,000)
42,188
––––––––
––––––––
––––––––
––––––––
300,000
680,000
746,250
907,188
(143,438)
––––––––
––––––––
––––––––
––––––––
––––––––
NPV calculation
Year
Net cash
flow
Rs.
(1,200,000)
300,000
680,000
746,250
907,188
(143,438)
0
1
2
3
4
5
Discount
factor at 9%
1.000
0.917
0.842
0.772
0.708
0.650
Present
value
Rs.
(1,200,000)
275,100
572,560
576,105
642,289
(93,235)
––––––––
NPV
+ 772,819
––––––––
Recommendation
The NPV of the project is + Rs. 772,819.
The project would appear to provide a DCF return well in excess of the WACC,
and on financial considerations (assuming that the estimates of costs and
revenues are reasonably reliable) the project should be undertaken.
13.6
FAIZ LIMITED
(a) Market Price of share
K eg
R f Equity Premium x Equity Beta
= 9% + 6.25% x 1.6
= 19%
Current dividend expected (Rs. 1.25 x (1+10%)
Rupees
1.375
Present value of all future dividends
Do (1 g)
K eg - g
1.375 x (1 10%)
19% - 10%
16.806
Market price of share
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Answers
Market price of TFCs
Calculation of TFCs’ market price (cum interest)
Factor
PV of 1st coupon today
PV of 5 coupons today @ 11%
PV of redemption today @ 11%
1.000
3.696
0.593
Amount
(Rs.)
6.00
6.00
130.98
(W1)
PV
(Rs.)
6.00
22.18
77.67
Market price today (cum interest)
105.84
*KIBOR + 2% i.e. prevailing commercial rate
W1 Calculation of redemption price
Rs.
100.00
Issue price
(4.355[Factor] x
Less: Present value of coupons at 10%
Rs. 6)
Hence PV of redemption price must be
Price on redemption @ 10% (Rs. 73.87 / 0.564 [Factor])
26.13
73.87
130.98
(b) Weightage average cost of capital
Equity (ex-dividend)
TFCs (ex-interest)
Bank loan
(equals to book value)
Price
Rs.
No. of
shares
16.806
*99.84
40,000,000
**5,410,000
Value
Rs.
Million
672
540
80
1,292
Cost %
19.00%
11.00%
12.00%
* Rs. 105.84 – 6 = 99.84
** Rs. 595/1.1 = 541m / Rs. 100 = 5.41 million shares
WACC = W eks + W dkd (1-T) + W dkd (1-T)
80
540
672
x 11% x 65% x 19% 12% x 65% = 13.35%
1292
1292
1292
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CHAPTER 14 – PORTFOLIO THEORY AND THE CAPITAL ASSET PRICING
MODEL
14.1
TWO-ASSET PORTFOLIO
(a)
Security X
EV of return ( x )
= (0.25 x 15) + (0.60 x 10) + (0.15 x 2) = 10.05.
(b)
Probability
Return
x– x
p(x – x )2
p
0.25
0.60
0.15
x
15
10
2
4.95
(0.05)
(8.05)
6.1256
0.0015
9.7204
Variance V2
15.8475
Standard deviation of return V x
Security Y
15.8475 3.98 .
EV of return ( x )
= (0.25 x 20) + (0.60 x 8) + (0.15 x (6)) = 8.90
Probability
Return
y– y
p(y – y )2
p
0.25
0.60
0.15
y
20
8
(6)
11.10
(0.90)
(14.90)
30.8025
0.4860
33.3015
Variance V 2
64.5900
Standard deviation of return V y
(c)
(d)
8.04 .
64.59
Covariance
Probability (p)
x– x
y– y
0.25
0.60
0.15
4.95
(0.05)
(8.05)
11.10
(0.90)
(14.90)
13.7363
0.0270
17.9917
Cov x,y
31.7550
p(x – x )( y – y )
Correlation coefficient
U x,y
31.7550
= + 0.992.
3.98 u 8.04
This shows a high level of positive correlation between the returns from
Security X and the returns from Security Y.
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Answers
(e)
The EV of the return from a portfolio consisting of 50% Security X and
50% Security Y
= (0.50 x 10.05) + (0.50 x 8.90) = 9.475%.
The variance of the returns from this portfolio would be:
[(0.50)2 × 15.8475] + [(0.50)2 × 64.5900] + [2 × 0.50 × 0.50 × 31.7550]
= 3.9619 + 16.1475 + 15.8775 = 35.9869.
The standard deviation of the portfolio returns =
(f)
35.9869 6.0%.
For a portfolio consisting of 80% Security X and 20% Security Y:
The EV of the return
= (0.80 × 10.05) + (0.20 × 8.90) = 9.82%.
The variance of the returns from this portfolio would be:
[(0.80)2 × 15.8475] + [(0.20)2 × 64.5900] + [2 × 0.80 × 0.20 × 31.7550]
= 10.1424 + 2.5836 + 10.1616 = 22.8876.
The standard deviation of the portfolio returns = √22.8876 = 4.78%.
Note: In this example, since Security Y has a lower expected return than
Security X and a higher standard deviation, expected returns will be highest
and risk lowest with a ‘portfolio’ consisting of Security X only, and none of
Security Y.
14.2
COEFFICIENT OF VARIATION
Portfolio
Expected
return
50% Country A, 50% Country B
50% Country A, 50% Country C
50% Country B, 50% Country C
(0.5 × 16) + (0.5 × 22)
(0.5 × 16) + (0.5 × 30)
(0.5 × 22) + (0.5 × 30)
19.0
23.0
26.0
The standard deviation of a portfolio is:
VU
2
2
V A x 2 V B 1 x 2x 1 x UA, BV A V B
2
However, since the returns from each country are independent of each other, the
covariance of returns (ρA,B ) is 0; therefore the second half of the formula can be
ignored because its value is zero.
Standard
deviation
of returns
Portfolio
[(252 × 0.52) + (362 × 0.52)]1/2
[(252 × 0.52) + (452 × 0.52)]1/2
[(362 × 0.52) + (452 × 0.52)]1/2
50% Country A, 50% Country B
50% Country A, 50% Country C
50% Country B, 50% Country C
21.9
25.7
28.8
(Tutorial note: ‘To the power of ½’ is the same as ‘the square root’.)
© Emile Woolf International
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Business finance decisions
Coefficient of variation
The coefficient of variation is the ratio of the risk (standard deviation of returns) to
the expected return.
Portfolio
Coefficient of
variation
50% Country A, 50% Country B
50% Country A, 50% Country C
50% Country B, 50% Country C
21.9/19.0 =
25.7/23.0 =
28.8/26.0 =
1.15
1.12
1.11
The ratio of risk to expected returns is roughly the same for all three portfolios.
14.3
PORTFOLIO RETURN
(i)
Calculation of beta factors for each of the security:
σx u Cox
Standard deviation x Correlatio n coefficient
=
σm
Market standard deviation
Security:
X
=
0.05 x 0.8
0.08
=
0.5
Y
=
0.15 x 0.4
0.08
=
0.75
Z
=
0.14 x 0.6
0.08
=
1.05
Expected Return for each security
=
E(Ri) = Rf +
E (Rm –Rf)
where: E(Ri) is expected return on the security
Rf is the risk-free return
Rm is the expected market return
E is the beta (risk) of the security
X
=
15% + 0.5 (20−15)%
=
17.5%
Y
=
15% + 0.75 (20−15)%
=
18.75%
Z
=
15% + 1.05 (20−15)%
=
20.25%
Expected return on the portfolio is derived from the following formula.
E(Rp) = W x E(Rx) + W y E(Ry) + W z E(Rz)
where: X, Y, and Z are the securities
E(Rp) is the expected return on portfolio
E(Rx) is the expected return of security X and
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Answers
W x is the proportion of the available investment funds invested in
security X.
Therefore the expected return on the portfolio using the above
formula is:
(0.3 x 17.50)% + (0.3 x 18.75)% + (0.4 x 20.25)%
(ii)
=
5.250% + 5.625% + 8.100%
=
18.975% = 19%
The risk of the portfolio is the addition of the Beta factor for each
security X proportion of the available investment funds invested in
each security.
i.e.
E p = E x x Wx + E y x Wy + E z x Wz
which is:
(0.5 x 0.3) + (0.75 x 0.3) + (1.05 x 0.4)
=
0.150 + 0.225 + 0.420
=
0.795
=
79.5% = 80%.
Determination of Rf
14.4
Rm –Rf
=
Premium
i.e.
0.20 – Rf
=
0.05
−Rf
=
0.05 – 0.20
Rf
=
0.15
=
15%
DOLPHIN PLC.
(a)
Calculation of cost of equity capital using:
CAPM
Ke = Rf + β(Rm – Rf)
Ke = 9% + 0.7 (17% - 9%)
= 9% + 5.6% = 14.6% ≈ 15%
Dividend Growth Model
Ke =
=
ୈ೚ ାሺଵା୥ሻ
ெೡ
ଵହሺଵǤଵ଴ሻ
ଵହ଴
+ 0.10
= 0.11 + 0.10 = 0.21 i.e. 21%
Evaluation of the projects i.e. computation of NPV
(i)
Using CAPM
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Business finance decisions
Year
Details
Project A
Project B
Cash flows
PV
DF
(15%)
Cash flow
PV
Rs.
Rs.
Rs.
Rs.
Rs.
(10,000,000)
(10,000,000)
1.0000
(24,000,000)
(24,000,000)
0
Initial Outlay
1–3
Inflow
4,800,000
10,959,360
2.2832
7,800,000
17,008,960
4&5
Inflow
5,600,000
5,986,400
1.069
8,900,000
7,514,100
5
Inflow
1,000,000
497,200
0.4972
1,000,000
497,200
NPV
(ii)
Year
7,442,960
3,820,260
Using Dividend Growth Model
Details
Project A
Project B
Cash flows
PV
DF
(21%)
Cash flow
PV
Rs.
Rs.
Rs.
Rs.
Rs.
(10,000,000)
(10,000,000)
1.0000
(24,000,000)
(24,000,000)
0
Initial Outlay
1–3
Inflow
4,800,000
9,954,720
2.0739
7,800,000
16,176,420
4&5
Inflow
5,600,000
4,771,760
0.8521
8,900,000
7,583,690
5
Inflow
1,000,000
385,600
0.3856
1,000,000
385,600
NPV
5,112,080
145,710
(b)
Under the two methods, i.e. the CAPM and the DGM, Project A has a
higher Net Present Value and should therefore be selected. Assuming the
two projects are not mutually exclusive, both would have been accepted on
the basis of positive Net Present Values.
(c)
The three factors are explained as follows:
(i)
Life of the Asset: The life of assets can differ. For instance, bonds
have a fixed maturity life, while equity has no fixed maturity life.
(ii)
The expected stream of cash flows/returns: for bond, the stream of
return can easily be determined because it is fixed, whereas those of
equity are difficult to estimate because of the discretionary nature of
the dividends.
(iii)
Appropriate discount rate: This will reflect the risk attached to the
asset. The higher the risk, the higher the discount rate. The rate of
equity is subjective, but that of bond is typically determined.
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Answers
14.5
RISK AND RETURN
(a)
Expected return
Project 3
(0.6 × 6) + (0.4 × 1) = + 4.0
Return
r
Probability
p
p(r- r )2
6.0
1.0
Variance (σ)2
2.40
3.60
6.00
σ
2.45
(b)
0.6
0.4
Project 4
(0.5 × 8) + (0.5 × –1) = + 3.5
Return
r
Probability
p
8.0
– 1.0
0.5
0.5
p(r- r )2
10.125
10.125
20.250
4.5
The divisional manager will invest in projects that are more risky provided
that they offer a higher return.
The manager will not invest in Project 4 because it offers a lower expected
return than Project 3 but higher risk.
The expected return from Project 1 is (0.8 × 4) + (0.2 × 2) = + 3.6.
The expected return from Project 2 is (0.7 × 5) + (0.3 × 1.5) = + 3.95.
The highest expected return is offered by Project 3, which has a higher risk
than Project 1 and Project 2. It would seem that the divisional manager will
invest in Project 3 because he is prepared to take the higher risk for a
higher expected return. However, Project 2 might seem more attractive: its
expected return is almost as high as for Project 3 and the risk is much less.
14.6
OBTAINING A BETA FACTOR
(a)
Standard deviations
Month
Market portfolio
Security Y
x– x
(x – x )2
y– y
(y – y
)2
1
+ 1.5
2.25
+2
4
2
(1.5)
2.25
(3)
9
3
(2.5)
6.25
(3)
9
4
+ 2.5
6.25
+4
16
17.00
Standard deviation of market returns =
38
17.00 4.123%.
Standard deviation of Security Y returns =
© Emile Woolf International
241
38
6.164%.
The Institute of Chartered Accountants of Pakistan
Business finance decisions
(b)
Correlation coefficient
Month
x– x
y– y
+ 1.5
(1.5)
(2.5)
+ 2.5
+2
(3)
(3)
+4
1
2
3
4
(x –
x ) (y – y )
+ 3.0
+ 4.5
+ 7.5
+ 10.0
+ 25.0
Covariance of returns = 25.0
Correlation coefficient U m, y
U x,y
(c)
25.0
= + 0.984.
4.123u 6.164
Beta factor for Security Y
E
Cov m, y
25
1.47
17
Var m
Alternatively
E
14.7
U m, y xV y
0.984u 6.164
1.47
4.123
Vm
SODIUM PLC
(a)
(i)
Computation of NPV using WACC
Hotel & Tourism (H & T)
Year
Cash Flow
0
1
2
3
Rs.‘m
(300)
85
170
150
Discount
Factor
@17%
1
0.8547
0.7305
0.6244
NPV
PV
Rs.‘m
(300.00)
72.65
124.19
93.66
(9.50)
Food & Beverages (F & B)
Year
0
1
2
3
© Emile Woolf International
Cash Flow
Rs.‘m
(400)
190
180
200
242
Discount Factor
@17%
1
0.8547
0.7305
0.6244
NPV
PV
Rs.‘m
400.00
162.39
131.49
124.88
(18.76)
The Institute of Chartered Accountants of Pakistan
Answers
(ii)
Projects’ NPVs using CAPM
Hotel & Tourism (H & T)
Year
Cash Flow
Discount
Factor
PV
Rs.‘m
@15%
Rs.‘m
0
(300)
1
(300.00)
1
85
0.8696
73.92
2
170
0.7561
128.54
3
150
0.6575
98.63
NPV
(1.09)
Food & Beverages (F & B)
Year
(iii)
(b)
Cash Flow
Discount
Factor
PV
Rs.‘m
@20%
Rs.‘m
0
400
1
400.00
1
190
0.8333
158.33
2
180
0.6944
124.99
3
200
0.5787
115.74
NPV
(0.94)
In view of the high risk inherent in the Food and Beverages project,
the Hotel and Tourism project should be selected. The positive NPV
before the incorporation of the risk factor on the F&B project should
not be taken for viability as the NPV became negative after adjusting
for risk.
Uses of CAPM
(i)
To evaluate projects taking risk into account.
(ii)
To determine an optimal capital structure.
(iii)
It is a device for understanding the risk-return relationship.
Limitations of CAPM
(i)
It is based on unrealistic assumptions.
(ii)
It is difficult to test its validity.
(iii)
It only considers systematic risk which does not remain stable over
time.
(iv)
Many times, the risk of an asset is not captured by beta alone.
(v)
It only examines investments from the shareholders point of view.
(vi)
It is a theoretically one-period model and should therefore be used
with caution in the appraisal of multi-period projects.
© Emile Woolf International
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Business finance decisions
Workings
Cost of capital using CAPM:
Hotel & Tourism (HT)
Rs.
=
Rf + B(Rm – Rf)
=
9% + 1.2 (14% - 9%)%
=
9% + 6%
=
15%
Food and Beverages (F&B)
Rs.
=
Rf + B(Rm – Rf)
=
9% + 2.2 (14% - 9%)%
=
9% + 11% =
20%
Cost of capital using WACC:
=
ට
g
=
n-1ටாௗ - 1
=
5-1ට
Ke
14.8
ௗሺ௟ା௚ሻ
ெ௏
Ke
+g
௅ௗ
଴Ǥଶହ
଴Ǥଵ଼
଴Ǥଶହ
-1
1ൗ
4
=
ቀ଴Ǥଵ଼ቁ
=
0.085 or 8.5%
=
0.25(1.085 )
0.085
3.20
=
0.169 = 16.9%
-1
DR JAMAL
(a)
(i)
The Beta Factor for the portfolio can be calculated by means of a
weighted average of the Beta values of the individual shares. Market
values should be used in the weightings.
Number
of Shares
Black Plc.
Blue Plc.
Yellow Plc.
Purple Plc.
White Plc.
Total
© Emile Woolf International
Market
Price
Rs.
2.50
2.20
1.90
1.50
0.60
15,000
18,000
10,000
12,000
20,000
244
Market
Value
(MV)
Rs.
37,500
39,600
19,000
18,000
12,000
126,100
Beta
Factor
(B)
1.32
1.20
0.80
1.05
0.80
MVx
Rs.
49,500
47,520
15,200
18,900
9,600
140,720
The Institute of Chartered Accountants of Pakistan
Answers
‫׵‬The portfolio Beta
=
(MVxߚ)/MV
=
140,720/126,100
ߚ =
(ii)
1.11594
The required return on the portfolio can be calculated by establishing
the required rate of return for each share, and then applying this to
the market value of the holding.
The formula used is: R
where
=
Rf + ߚ (Rm – Rf)
R
=
Return on the individual share
ߚ
=
Beta factor
Rm =
Rf
=
Market rate of return
Risk free rate of return
A quicker way to calculate this is to calculate ‘Rs.’ for the portfolio as
a whole using the Beta factor previously derived, and then to apply
this rate of return to the market value of the portofolio:
R
=
Rf +ߚ(Rm – Rf)
R
=
8% + 1.11594 (14% - 8%)
R
=
14.6956%
‫׵‬Selected return
=
Rs. 126,100 x 14.6956%
=
Rs. 18,531
Alternatively, we can calculate the ‘R’ for each security and have an
aggregate value for the portfolio as demonstrated below:
Market
Value
Beta
factor
R (%)
(MV)
R x MV
Rs.
Black Plc.
Blue Plc.
1.32
1.20
15.92
15.20
37,500
39,600
5,970
6,019
Yellow Plc.
Purple Plc.
White Plc.
0.80
1.05
0.80
12.80
14.30
12.80
19,000
18,000
12,000
2,432
2,574
1,536
Total
(b)
18,531
Portfolio theory will assist Dr Jamal with a formal means of evaluating the
systematic risk profile of his portfolio. He can decide the level of risk that
he is happy to accept and express this in terms of a target beta factor for
his portfolio as a whole. He can then select securities which will provide
him with this risk/return profile. As has been demonstrated above, he can
© Emile Woolf International
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Business finance decisions
also use the theory to indicate whether an individual security is correctly
priced in the market, as this will influence his buying and selling decisions.
At the same time, however, the portfolio manager must be aware of the
theoretical shortcomings of this form of analysis as stated below:
(i)
The theory assumes that transactions costs can be ignored. In
practice, the costs of buying and selling shares, particularly in
relatively small quantities may become significant.
(ii)
It further assumes that investors hold a well diversified portfolio and
they are, therefore, protected against unsystematic risk and need only
be concerned with systematic risk.
(iii)
The theory is based upon a single period time horizon. This is
unrealistic in terms of the way business decisions within firms are
made.
In practice, the portfolio manager must also take other factors as well
as the risk/return profile into account. The factors include the
following:
‰
Liquidity
The manager must ensure that liquid funds are available to
meet current commitments. This may mean that the portfolio at
any one time contains a higher than predicted element of riskfree securities which are being held in anticipation of a known
payment.
‰
Purpose
The purpose for which the portfolio is being held will influence
its make-up. For instance, if the overall fund is small and
transaction costs are significant, and the fund is being invested
with the intention of providing a regular income, then the
manager will select high income securities in preference to
growth stocks. This may mean that the optimum portfolio from
the point of view of the theory may not be the one which should
be selected in practice.
‰
Investment Criteria
The owners of the fund may lay down investment criteria such
as the ethical status of the companies in which to invest. This
may restrict the choice available to the portfolio manager.
Again, this may mean that the “optimum portfolio” is not chosen.
Thus, it can be seen that the theory does have relevance to a
portfolio manager in his selection of securities, but it does not
provide the complete answer to the structuring of a portfolio.
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Answers
14.9
MR. FARAZ
(a)
COST OF EQUITY OF MR. FARAZ (UNDER CAPM MODEL)
CAPM=RF+(RM-RF) x Beta
Beta =
Co variance with Market
Market Variance
Market
Standard
Deviation
Market
Varianc
e
Covariance
with
market
Beta
A
B=A2
C
C/B
A
15%
0.0225
2.10%
0.93
8%
12%
19.16%
B
15%
0.0225
3.00%
1.33
8%
12%
23.96%
C
15%
0.0225
2.60%
1.16
8%
12%
21.92%
D
15%
0.0225
1.90%
0.84
8%
12%
18.08%
E
15%
0.0225
2.80%
1.25
8%
12%
22.88%
Compan
y Name
(i)
RM-RF
20%-8%
Estimated Value of portfolio as at December 31, 2016
*Price at
Dec 31
Required
Return
Price on
Jan. 1,
2016
Dividend
yield
Co. Name
(b)
RF
Require
d.
Return
%
(P)
(y)
(x)
(A)
(B)
AXB
A
60
3.50%
19.16%
69.40
15m/60 =
250,000
17,350,000
B
245
3.00%
23.96%
296.35
18m/245 =
73,469
21,772,538
C
225
2.50%
21.92%
268.70
22m/225 =
97,778
26,272,949
D
130
8.00%
18.08%
143.10
25m/130 =
192,308
27,519,275
E
210
5.00%
22.88%
247.55
20m/210 =
95,238
23,576,167
(Rs.)
(Rs.)
P[1 + (x –y)]
No. of
Shares
Portfolio
Value on
Dec 31 (Rs.)
116,490,929
© Emile Woolf International
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The Institute of Chartered Accountants of Pakistan
Business finance decisions
(ii)
Portfolio beta as at December 31, 2016
Compa
ny
Name
Portfolio Value on
Dec 31
New
Investment
Weightage
Beta
Weighted
Beta
Rs.
A
B
AXB
A
17,350,000
14.89%
0.93
0.14
B
21,772,538
18.65%
1.33
0.25
C
26,272,949
22.55%
1.16
0.26
D
27,519,275
23.62%
0.84
0.20
E
23,576,167
20.24%
1.25
0.25
116,490,929
Estimated Total return on portfolio
Co. Name
(iii)
1.10
Beg. Price
End Price
Capital Gain
Dividend
(A)
(B)
B-A
A x Div. yield
Total
Return
Rs.
Rs.
Rs.
Rs.
Rs.
A
15,000,000
17,350,000
2,350,000
525,000
2,875,000
B
18,000,000
21,772,538
3,792,538
540,000
4,312,538
C
22,000,000
26,272,949
4,272,949
550,000
4,822,949
D
25,000,000
27,519,275
2,519,275
2,000,000
4,519,275
E
20,000,000
23,576,167
3,576,167
1,000,000
4,576,167
4,615,000
21,105,92
9
16,490,929
OR
Company
Name
Portfolio Value on
January 1
Required
return
Rs.
Rs.
A
15,000,000
19.16%
2,875,000
B
18,000,000
23.96%
4,312,538
C
22,000,000
21.92%
4,822,949
D
25,000,000
18.08%
4,519,275
E
20,000,000
22.88%
4,576,167
100,000,000
© Emile Woolf International
Total Return
248
21,105,929
The Institute of Chartered Accountants of Pakistan
Answers
14.10
MUSHTAQ LIMITED
Computation of market variance
Probability
Market
Return
1
2
Probable
Market
Return
3 =1 x 2
p1
Rm
pRm
Rm R m
0.25
30
7.5
0
0
0.5
25
12.5
-5
12.5
0.25
40
10
10
25
Deviation from
Mean
Market
Variance
2
4
5 = 1x (4)
p(Rm - Rm) 2
30
37.5
Return and cost of project 1
Probability
Project
Return
1
2
Probable
Project
Return
3=1 x 2
p1
Rp1
pRp1
0.25
0.5
0.25
20
30
40
5
15
10
30
Deviation
from Mean
Market
Variance
Covariance
4
5 ( above)
1x 4 x 5
Rp1 Rp1
p(Rm - Rm)
-10
0
10
2
*
0
12.5
25
37.5
0
0
25
25
* p(Rm - Rm) (Rp1- Rp1)
ß (project1)
Covariancebetweenproject and market
Variancemarket
ß (project1) = 25 / 37.5 = 0.67
Required Return from new project =
Risk free rate + ß (Market rate – Risk free rate)
= 10% + 0.67 (30% - 10%)
= 23.4
Return and cost of project 2
Probability
Project
Return
1
2
Probable
Project
Return
3=1 x 2
Deviation
from Mean
Market
Variance
Covariance
4
5 (above)
1x4x5
p2
Rp2
pRp2
Rp 2 Rp2
p(Rm - Rm)
0.25
0.50
0.25
22
28
40
5.50
14.00
10.0
29.50
-7.5
-1.5
10.5
0
12.5
25
37.5
2
*
0
3.75
26.25
30.00
* p(Rm - Rm) (Rp2 - Rp2)
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The Institute of Chartered Accountants of Pakistan
Business finance decisions
ß (project2)
Covariancebetweenproject and market
Variancemarket
ß (project2) = 30 / 37.5 = 0.8
Required Return from new project =
Risk free rate + ß (Market rate – Risk free rate)
= 10% + 0.8 (29.5% - 10%)
= 25.6%
Conclusion:
Since the project 1 has higher return over its cost of capital worked out under
CAPM, the company should undertake this project.
14.11
ATTOCK INDEX TRACKER FUND
(a)
Systematic risk is measured by Beta.
Beta = Co-relation of returns x σ of the fund ÷ σ of the market
=
0.737 × 0.22 ÷ 0.18 = 0.9
Assessment of AITF Performance
Beta of 0.9 shows that AITF substantially (90%) matches the
performance of KSE 100 Index.
(b)
AITF's actual return is 11% which is less than the return which AITF
should achieve according to its risk profile i.e. 11.6% (W1) as per its
current systematic risk.
W1: Required return of the fund
The required return of AITF in terms of CAPM would be
R = Rf + (Rm – Rf) × β
= 8% + (12% - 8%) × 0.901
= 11.60%
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The Institute of Chartered Accountants of Pakistan
a
25
15
C
D
d=(b+c-
Remarks
return (W1)
=Rf+β(R
2
m-Rf)
(e)
a)÷a
Required
Co-variance
Variance
Market
share
(Rs.) per
Dividend
next year (Rs.)
(σ)
Beta
(f)
g=f ÷
h
e
27
2.0
16.0%
0.0324
0.024
1
11.0%
-
17
1.0
20.0%
0.0324
0.039
4
12.8%
-
13.4%
-
1.35
46
52
2.5
18.5%
0.0324
0.044
7
under
1.01
106
111
4.0
8.5%
0.0324
0.033
9
12.1%
performing
10.2%
-
13.1%
performing
0.55
E
75
85
2.0
16.0%
0.0324
0.018
114
125
3.0
12.3%
0.0324
0.041
6
under
1.26
F
G
H
(d)
c
return
1.20
B
J
b
Total
0.74
A
I
after one year
per share
Forecasted price
(c)
Name of company
Current price
Answers
5
under
0.98
239
220
5.5
-5.6%
0.0324
0.032
8
12.0%
under
1.23
156
168
3.0
9.6%
0.0324
0.040
5
performing
12.9%
performing
12.2%
-
12.1%
-
1.04
145
170
2.5
19.0%
0.0324
0.034
9
1.01
67
Name
of
compan
75
1.0
Current
price
13.4%
No. of
shares
0.0324
0.033
Value Rs.
in ‘000’
‘000’
9
Beta
Weighted
beta
y
A
b
c=axb
d
(c) x d / ∑(c)
A
25
150
3,750
0.741
0.088
B
15
230
3,450
1.204
0.132
C
46
190
8,740
1.357
0.376
E
75
100
7,500
0.556
0.132
I
145
35
5,075
1.049
0.169
J
67
45
3,015
1.019
0.097
31,530
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The Institute of Chartered Accountants of Pakistan
Business finance decisions
14.12
IRON LIMITED
(a)
A
14.12%
16%
Required rate of return (W1)
Expected return
Decision
Excess return index (Expected
/Required return)
Preference
(b)
Projects
B
C
13.84% 16.16%
14%
17%
Invest
Invest
Invest
1.13
1.01
1.05
1
3
2
W1: Required rate of return
Risk free rate of return (Rf)
10%
Market return (Rm)
14%
β (W2)
1.03
Required rate of return Rf + (Rm Rf)β
14.12%
W2: Computation of β
Estimated correlation of returns
with market return
a
0.82
Project standard deviation of
returns
b
20%
Market Standard Deviation
c
16%
β (a x b ÷ c)
1.03
Combined portfolio beta
Project
A
B
C
PV
Net annual cash flows (Rs. in millions)
*Cumulative discount factor at required rate
of return
Present value of cash flows (Rs. in
millions)
*
10%
14%
0.96
10%
14%
1.54
13.84%
16.16%
10%
14%
1.46
15.8
4%
0.85
0.91
0.78
18%
16%
0.96
27%
16%
1.54
30%
16%
1.46
Weighted
β
0.34
0.32
0.52
1.18
β
1.03
0.96
1.54
197.20
202.71
201.60
601.51
D
15.84%
15%
Not to
invest
85.00
87.00
90.00
2.32
2.33
2.24
197.20
202.71 201.60
1 (1 i)n
i
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Answers
14.13
FR CO-OPERATIVE HOUSING SOCIETY
(a)
(b)
Computing the effective annual yield
Investment
Public Offer Price per unit
(NAV at acquisition × (1 +
Buy Load)
a
A
500,000
B
1,000,000
C
500,000
b
10.82
10.20
9.85
No of units acquired
Bonus units received
(10%, 5%, 5%)
Total units at year end
Redemption value per unit
(NAV at 31-Mar-2016 ÷ (1
+ Sales Load))
c=a÷b
46,210.72
98,039.22
50,761.42
d
e=c+d
4,621.07
50,831.79
4,901.76
102,940.98
2,538.07
53,299.49
10.30
10.00
9.71
f
Value of investment at
year end
g= e x f
523,567
1,029,410
517,538
Increase in NAV
Cash dividend received
Total return
No. of days
Effective annual yield
h=g-a
i
j=h+i
k
(j ÷a)x365÷k
23,567
9,500
33,067
183
13.19%
29,410
15,000
44,410
152
10.66%
17,538
17,538
121
10.58%
A
12.15%
B
11.08%
C
10.92%
13.19%
Over
performe
d
10.66%
10.58%
Under
performed
Under
performed
B
C
Evaluation of each investment
Required rate of return (W1)
Effective annual yield (Computed in
(a) above)
Decision
Calculation of required rate of
return
Rm
Sharpe Ratio
Rp (effective annual yield, computed
above)
Rf
Investment SD=[(Rp - Rf)÷Sharpe
Ratio]
Correlation with Index
Market SD
β = Inv. SD × Corr. with index ÷
Market SD
Required Return=Rf + β (Rm - Rf)
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A
16%
0.71
17%
0.31
12%
0.16
13.19%
9%
10.66%
9%
10.58%
9%
0.06
0.75
0.10
0.05
0.92
0.18
0.10
0.83
0.13
0.45
12.15%
0.26
11.08%
0.64
10.92%
The Institute of Chartered Accountants of Pakistan
Business finance decisions
CHAPTER 15 – DIVIDEND POLICY
15.1
DIVIDENDS AND RETENTIONS
The dividend growth model will be used to estimate what share price might be
expected.
It is assumed that the growth rate in earnings and dividends will be br, where b is
the proportion of earnings that is retained and r is the return on new investment.
(a)
Dividends are 25% of earnings and 75% of earnings are retained:
Growth rate = 0.75% × 0.09 = 0.0675.
Expected share price
(b)
0.50 (1.0675)
=
(0.09 – 0.0675)
=
Rs. 23.72
Dividends are 50% of earnings and 50% of earnings are retained:
Growth rate = 0.50% × 0.09 = 0.045.
Expected share price
(c)
1.00 (1.045)
=
(0.09 – 0.045)
=
Rs. 23.22
Dividends are 70% of earnings and 30% of earnings are retained:
Growth rate = 0.30% × 0.09 = 0.027.
Expected share price
15.2
1.40 (1.027)
=
(0.09 – 0.027)
=
Rs. 22.82
ACKERS PLC
(a)
Year
Net Earnings
per share
(Rs.)
Net dividend
per share
(Rs.)
Dividend as %
of Earnings
%
2012
1.40
0.84
60
2013
1.35
0.88
65
2014
2015
2016
1.36
1.30
1.25
0.90
0.95
1.00
67
73
80
Change in EPS =
0.15
0.16
u 100 = 10.7% DPS
u 100 = 19%
1.40
0.84
During this period, earnings per share have declined by 10.7%, while at the
same time, dividend per share has increased by 19.0%
The payment ratio has increased from 60% in 2009 to 80% in 2013, and
thus the proportion of earnings retained has fallen to 20%. If it is assumed
that the capital structure has not changed over the period, then it can be
seen that both actual earnings and return on capital employed have
declined over the period.
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Answers
One possible implication of this policy is that insufficient earnings have
been retained to finance the investment required to at least, maintain the
rate of return on capital employed. It then means that the Company is
falling behind its competitors, which could have a serious impact on the
long-term profitability of the business. However, Rs. 1.00 dividend per
share in the current year will result in a fall in the share price.
(b)
Rate of return
For the purposes of calculation, it is assumed that any new investment will
earn a rate of return equivalent to that required by the shareholders (i.e.
15%), and that this will also be the level of return that is earned on existing
investments for the foreseeable future. It is further assumed that investors
are indifferent as to whether they receive their returns in the form of
dividend or as capital appreciation.
Option 1
The amount of dividend per share is Rs. 1.00 with no growth forecast. The
rate of return required by shareholders is 15%. The theoretical share price
can be estimated using the dividend valuation model.
k3
d1
po
where ke
=
Cost of equity
d1
=
Dividend per share
Po
=
Market price per share
0.15Po
=
Rs. 1.00
? Po
=
•Ǥͳ.00
0.15
= Rs. 6.67 ex-div or Rs. 7.67 cum-div
100% of the total return will be paid as dividend.
Option 2
In this case, 50% of the expected return is in the form of dividend and 50%
as capital appreciation.
A numerical example will clarify the position.
The rate of growth of dividend g may be expressed as:
g = rb
where r
=
required rate of return
b
=
proportion of profits retained
Therefore, with dividend at 0.50 rupee per share;
g
=
0.15 x 0.5 = 0.075
NOTE Po
=
d1
r g
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Business finance decisions
where d1
=
do (1+g)
Po
=
0.5 u 1.075
= Rs. 7.17
0.15 0.075
or Rs. 7.17 plus 0.50 rupee = Rs. 7.67 cum-div
Option 3
In this case, 25% of the expected return is paid in form of dividend while
75% is retained.
Therefore,
g
=
0.15 x 0.75 = 0.1125
Po
=
0.25 u 1.1125
= Rs. 7.416
0.15 0.1125
=
Rs. 7.42 ex-div.
or
Rs. 7.42 plus 0.25 rupee dividend
=
Rs. 7.67 cum-div.
Option 4
In this case, for a share price of Rs. 6.67, investors would need to believe
that retained profits will be invested in projects yielding annual growth of
15% and that the share price will be at this rate. 100% of the expected
return is provided in the form of capital appreciation under this option.
15.3
Dividend policy
(a)
The factors that determine the dividend policy of a large public company
whose shares are quoted on the stock exchange include:
(i)
Legal Constraints: The management of a company must recognise
the existence of laws guiding payment of dividends. For example, the
Companies Ordinance 1984 rules that dividends:
‰
may only be paid out of profits but not those from the sale of
capital assets (unless that is the business of the company): and
‰
may not exceed the amount recommended by directors.
(ii)
Future Financial Requirement: Once the legal constraints have
been cleared, management should focus on its future financial needs
including future investment opportunities. This should be done via
budgeted sources and application of funds statements, budgeted
cash flow statements and cash budget.
(iii)
Liquidity: Dividends are usually paid out of cash. Therefore, the
amount of dividend paid by the company is largely influenced by the
available cash resources. Cash has alternative uses within the firm;
management may, therefore, want to recognise these important
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Answers
alternatives (and also be protected against the future) and may,
therefore, decide not to have a high target dividend-payment.
(iv)
Capacity for borrowing: A firm may not be liquid, but may be in a
strong position to borrow at short notice. This ability can be by
arranging a line of credit. The ability of a firm to borrow often largely
influences its ability to meet its short-term obligations as and when
due, including payment of cash dividends.
(v)
Access to the capital market: If the company is large enough and
has good access to the corporate bond market, it needs not bother
much about its liquidity situation for the purpose of paying cash
dividends.
(vi)
Existence of Restrictive Covenants: Restrictions on payment of
cash dividends may be entrenched in a loan agreement.
(vii) Dilution of Control: Payment of cash dividends, supported by
subsequent rising of external finance may dilute the controlling
interest of the existing shareholders, if they do not partake in the
provision of such finance.
(viii) Dividend policy decisions of other similar firms
(ix)
Stock market reaction
(x)
Taxation
(xi)
Attitude of company’s board of directors
(xii) Repayment of debt
(xiii) Liquidity preference of the dominant shareholder
(b)
A stable dividend policy is expected to lead to a higher market valuation of
a company’s share because this policy usually attracts a premium due to
preference for current regular income by certain investors. It gives rise to
positive signalling effects and also facilitates conformity with directives
issued by regulatory authorities to certain institutions like the Pension Fund
Administrators.
(c)
(i)
Determination of market value of the firm based on retention of 20%
of earnings.
Dividend payable
=
80% of Rs. 2,250,000
=
Rs. 1,800,000
‫ ׵‬MV
=
D0 (1+ g)
Ke - g
MV
=
=
•Ǥͳ,800,000 (1.05)
0.14-0.05
Rs. 21,000,000
Where MV is Market Value, D0 is Initial Dividend, g is dividend growth
rate, Ke is cost of capital
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Business finance decisions
(ii)
Retain 10%
Dividend payable
‫׵‬MV
=
90% of Rs. 2,250,000
=
Rs. 2,025,000
•Ǥʹ,Ͳʹͷ,000 (1.0ʹ)
=
0.14-0.02
=
Rs. 17,212,500
Advice:
The retention policy that favours the company is that of the retention of
20% as it will make the market value of the company higher than when
10% is retained.
15.4
YB PAKISTAN LIMITED
YEARS
(a)
1
2
3
4
5
Rupees in million
Existing operating profit
from current projects
[67.79(W1)x1.12]
75.92
Operating profit from new
investment plan (W2)
-
85.03
95.23
5.85
13.05
106.66 119.46
22.95
32.85
Less: Depreciation for the
year (W3)
(15.12) (18.70) (23.10) (29.53) (35.00)
Less: Interest on debt (W5)
(12.58) (13.05) (14.10) (15.73) (16.92)
Net profit before tax
Tax (38%, 36%, 34%, 34%,
34%)
48.22
71.08
84.35 100.39
(18.32) (21.29) (24.16) (28.68) (34.13)
Net profit after tax
Less: Retained for CAPEX
(A × 60%)
59.13
29.90
37.84
46.91
55.67
66.26
(23.40) (28.80) (39.60) (39.60) *(48.60)
Residual income for
dividend distribution
6.50
9.04
7.31
16.07
17.66
*(Rs. 300 m x 27% x 60%)
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(b)
The company would have surplus cash of Rs. 79.55 million (W5) which is
less than Rs. 90 million. However, the company may pay the amount by
obtaining the balance amount from its short term running finance facility.
WORKINGS
Rs. in
millions
W1: Existing operating profit
Net profit before tax and interest (190 - 110 - 30)
50.00
Add: Depreciation for current year (100.8 × 15 ÷ 85)
17.79
Operating profit
67.79
W2: Operating profit from new projects
YEARS
1
Year wise
CAPEX in
terms
2
3
4
5
13%
16%
22%
22%
outlay for
percentage
0%
Rs. in million
Year wise planned
CAPEX (Rs. 300m ×
CAPEX %)
A
B
Cumulative new CAPEX
Yield from new projects :
(B) × 15% pre-tax cash
flow
-
39.00
48.00
66.00
66.00
39.00
87.00
153.0
0
219.00
5.85
13.05
22.95
32.85
-
W3: Depreciation for
the year
WDV at the beginning of
year
100.8
0
85.68
105.9
8
130.8
8
167.35
Addition during the year
(A)
-
39.00
48.00
66.00
66.00
Depreciable value
100.8
0
124.6
8
153.9
8
196.8
8
233.35
Depreciation for the
year
15.12
18.70
23.10
29.53
35.00
WDV at the end of year
85.68
105.9
8
130.8
8
167.3
5
198.35
90.00
90.00
W4: Interest on debts
Long term debt at the
beginning of year (Rs.
135m÷60×40)
© Emile Woolf International
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105.6
0
124.8
0
151.20
The Institute of Chartered Accountants of Pakistan
Business finance decisions
New debt during the year
(A × 40%)
-
15.60
Long Term debt at the
end of year
105.6
90.00
0
Interest on long term debt
(15- (20 x 0.16)) ÷ 90=
13.11%
11.80
13.84
19.20
124.8
0
16.36
26.40
151.2
0
19.82
26.40
177.6
23.28
Interest on short term
debt (W5)
0.78
Interest income (W5)
-
(0.79)
(2.26)
(4.09)
(6.36)
12.58
13.05
14.10
15.73
16.92
-
-
-
-
YEARS
1
2
3
4
5
(W5) Interest on short term running finance
Opening outstanding
balance / (Cash)
20.00
Additional working capital
(10% of additional
CAPEX)
(9.92) (28.22) (51.15)
3.90
Less: Additional cash
flow generated
(Depreciation)
4.80
6.60
6.60
(15.12) (18.70) (23.10) (29.53) (35.00)
Debt / (balance) at the
end of year
4.88
Interest on short term
running finance
0.78
Interest income
15.5
4.88
-
(9.92) (28.22) (51.15) (79.55)
-
(0.79)
-
(2.26)
-
(4.09)
-
(6.36)
AL-GHAZALI PAKISTAN LIMITED (AGPL)
(a) Under dividend irrelevance theory, Modigliani and Miller argued that the
value of the firm depends only on the income produced by its assets, not on
how this income is split between dividends and retained earnings.
Arguments against the theory
(i)
Differing rates of taxation on dividends and capital gains can create a
preference for a high dividend or one for high earnings retention.
(ii)
Dividend retention should be preferred by companies in a period of
capital rationing.
(iii)
Due to imperfect markets and the possible difficulties of selling shares
easily at a fair price, shareholders might need high dividends in order
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Answers
to have funds to invest in opportunities outside the company.
(iv)
Markets are not perfect. Because of transaction costs on the sale of
shares, investors who want some cash from their investments will
prefer to receive dividends rather than to sell some of their shares to
get the cash they want.
(v)
Information available to shareholders is imperfect and they are not
aware of the future investment plans and expected profits of their
company. Even if management were to provide them with profit
forecasts, these forecasts would not necessarily be accurate or
believable.
(vi)
Perhaps the strongest argument against the MM view is that
shareholders will tend to prefer a current dividend to future capital
gains (or deferred dividends) because the future is more uncertain.
(b) Market price per share
Calculation of market price per share under MM dividend irrelevance theory
P1 D1
1 Ke
Po
OR
P1
Po u (1 Ke) - D1
Market price if dividend
Declared
Po
Rs. 80.00
D1
Rs. 2.00
Ke (W1)
P1 {80x(1+0.144)-2} {80x(1+0.144)-0}
Not
declared
Rs.
80.00
-
14.4%
14.4%
Rs. 89.52
Rs.
91.52
W1: Cost of equity under CAPM
Ke = Rf + (Rm – Rf) β
= 0.075 + (0.129 – 0.075) 1.28 (W2)
= 14.4%
W2: β Computation
β
AGPL' s StandardDeviationwith Market Return
u Correlation of Return with Market Returns
Market StandardDeviation
8%
u 0.8 1.28
5%
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(c) Justification of MM Dividend Irrelevance Theory
No of shares to be
issued
Not
Declared declared
Rs. in million
250.00
250.00
40.00
210.00
250.00
(600.00) (600.00 )
Net income
Less: Dividend paid
Retained earnings
Less: New investments
Amount to be raised through right
issue
A
390.00
350.00
Market price per share (as computed
in (b) above
B
89.52
91.52
C=A÷B
D
4.36
20.00
3.82
20.00
E=C+D
24.36
23.82
B×E
2,180
2,180
Number of new shares to be issued
(in million)
Already issued share capital
Total number of shares to be
outstanding
Market capitalization
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Answers
CHAPTER 16 – FINANCING OF PROJECTS
16.1
GEARING
(a)
Increase in earnings from increase in sales
Company A
Rs.
Sales
Variable costs
Contribution
Fixed operating costs
Earnings before interest
and tax
Interest costs
Profit before tax
Tax at 20%
Earnings after interest
and tax
(b)
100,000
12,500
87,500
60,000
%
increase
25%
Company B
Rs.
100,000
75,000
25,000
10,000
%
increase
25%
27,500
7,000
20,500
4,100
175%
15,000
0
15,000
3,000
50%
16,400
583.3%
12,000
50%
Further calculations
Company A
Operational gearing
= Increase in earnings before
interest and tax/increase in sales
Company B
(175/25)
7.0
(50/25)
2.0
Financial gearing
= Increase in earnings after interest
and tax/ increase in earnings
before interest and tax
(583.3/175)
3.3
(50/50)
1.0
Combined gearing effect
= Increase in earnings after interest
and tax/ increase in sales
(583.3/25)
23.3
(50/25)
2.0
The combined gearing effect is the operational gearing effect multiplied by
the financial gearing effect.
For company A, a combination of high operational gearing and high
financial gearing will result in a 583% increase in earnings for shareholders,
as a consequence of a 25% increase in sales.
For company B, a combination of operational gearing and financial gearing
will result in a 50% increase in earnings for shareholders, as a
consequence of a 25% increase in sales.
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16.2
FINANCING SCHEMES
(a)
Projected statements of profit or loss for the year ended 30th November
Financing method
i
ii
iii
Rs. m
Rs. m
Rs. m
22.9
22.9
22.9
Interest payable
1.5
2.1
2.1
Profit before tax
21.4
20.8
20.8
Taxation (25%)
5.4
5.2
5.2
Profit after tax
16.0
15.6
15.6
0.0
1.4
0.0
16.0
14.2
15.6
Profit before interest and tax: (17.9 + 5.0)
Preference dividend
Profit available to ordinary shareholders
Number of shares
20.0 + 9.0
29.0m
20.0m
20.0 + 6.0
26.0m
Earnings per share =
Rs.0.552
Rs.0.71
Rs.0.60
Rs. m
Rs. m
Rs. m
Accumulated profit at start of the year
17.8
17.8
17.8
Profit available to equity for the year
16.0
14.2
15.6
Dividend payments (Rs.0.30 per share)
(8.7)
(6.0)
(7.8)
Accumulated profit at end of the year
25.1
26.0
25.6
Equity shares
14.5
10.0
13.0
Share premium
13.5
0.0
9.0
General reserve
4.6
4.6
4.6
57.7
40.6
52.2
15.0
21.0
21.0
0.0
12.0
0.0
72.7
73.6
73.2
Total share capital and reserves
Fixed rate long-term capital:
10% debentures
Preference shares
Total long-term capital
Gearing
15.0/72.7 33.0/73.6 21.0/73.2
20.6%
44.8%
28.7%
Other methods of calculating the gearing ratio would be acceptable.
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(b)
Financing scheme (i) produces the lowest EPS of the three options. This
EPS is also lower than the current EPS of Rs.0.615.
Financing scheme (ii) produces the highest EPS. It is also the only option
that produces a higher EPS than the current EPS. However the gearing
ratio is substantially higher than the current gearing ratio or the gearing
ratios of the other options. The projected statements of profit or loss show a
high level of coverage for interest payments under this option and therefore
the relatively high level of gearing is unlikely to be a problem.
Financing option (iii) produces an EPS that is lower than the current EPS
and lower than the EPS of option (ii). However the gearing ratio is fairly low,
indicating a relatively low level of financial risk.
16.3
MM, GEARING AND COMPANY VALUATION
Value of geared company = Value of company ungeared + (Value of debt × Tax
rate)
Vg = Vu + Dt
Vg = (4,000,000 × Rs. 10) + (Rs. 15,000,000 × 30%) = Rs. 44,500,000
Rs.
million
Total value of geared company (equity + debt)
Value of debt
Therefore value of equity in geared company
44.5
(15.0)
29.5
The total value of the equity in the geared company is lower than when the
company was geared, but there are fewer shares left in issue and the value per
share will be higher.
16.4
DIVERSIFY
(a)
The first step is to use the equity betas of the three chemical manufacturing
companies (proxy companies) to estimate an asset beta for the business risk in
chemicals manufacturing.
Company
Estimated asset beta
A
2.66 u [40/40 + 60(1 – 0.25%)]
= 2.66 u 0.4706 = 1.25
B
1.56 u [75/75 + 25(1 – 0.25%)]
= 1.56 u 0.80 = 1.25
C
1.45 u [80/80 + 20(1 – 0.25%)]
= 1.45 u 0.8421 = 1.22
It is assumed that the asset beta is a simple average of these three values:
(1.25 + 1.25 + 1.22)/3 = 1.24.
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This asset beta can be used to calculate an equity beta for Bustra, for the
investment in chemicals manufacturing:
1.24 =
βE u
60
60 + 40 (1 – 0.25)
0.667 βE = 1.24
βE = 1.86
If an appropriate equity beta for Bustra in chemicals manufacturing is 1.86, the
cost of equity (using the CAPM) is:
5% + 1.86 (9 – 5)% = 12.44%
(b)
If the cost of equity is 12.44%, the pre-tax cost of debt is 5% (= risk-free rate) and
tax is 25%, a suitable discount rate (WACC) for evaluating the proposed
investment would be:
(60% u 12.44%) + [40% u 5 (1 – 0.25)%] = 8.964%, say 9%.
16.5
FINANCIAL AND OPERATING GEARING
(a)
Existing earnings per share =
Net profitaftertax
Number of equity shares
$344,000/8 00,000
$0.43
Earnings per share with new production process:
Rs.0
00
Sales
Minus:
Variable costs: (60,000 × Rs. 5)
Fixed costs: (360 + 120)
1,800
300
480
Net profit before interest and taxation
Interest payable [190 + (12.5% × Rs. 2 million)]
Net profit before taxation
Tax at 35%
Net profit after taxation
EPS
$377,000
800,000
Rs.00
0
780
1,020
440
580
203
377
$0.4713
There is an increase in EPS of Rs.0.0413
(b)
(i)
The degree of operating gearing
Contribution
Profit before interest and tax
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1800 300
1020
1.47 times
(ii)
The degree of financial gearing
Profit before interest and tax
Profit after interest but before tax
1020
1020 440
1.76 times
(iii)
16.6
The combined gearing effect = 1.47 × 1.76 = 2.59
OPTIMAL WACC
The optimal WACC is the lowest WACC, because this will maximise the value of
the company and the wealth of shareholders.
Step 1
Calculate the geared beta for equity at each level of gearing.
Gearing
Geared beta
20%
0.90 u
30%
0.90 u
40%
0.90 u
50%
0.90 u
60%
0.90 u
80 + 20 (1 - 0.30)
80
70 + 30 (1 - 0.30)
70
60 + 40 (1 - 0.30)
60
50 + 50 (1 - 0.30)
50
40 + 60 (1 - 0.30)
40
=
1.057
5
=
1.170
=
1.320
=
1.530
=
1.845
Step 2
Use the geared beta value and the CAPM to calculate a cost of equity at each
gearing level.
Gearing Cost of equity (4% + E (9 – 4)%
20%
30%
40%
50%
60%
4 + 1.0575 × 5
4 + 1.170 × 5
4 + 1.320 × 5
4 + 1.530 × 5
4 + 1.845 × 5
=
=
=
=
=
7.17%
7.51%
7.96%
8.59%
9.54%
Step 3
Calculate the WACC at each level of gearing, and identify the gearing level with
the lowest WACC.
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Gearing
WACC
20%
[20% × 5.0 (1 – 0.30)]
+ [80% × 7.17]
= 6.44%
30%
[30% × 5.4 (1 – 0.30)]
+ [70% × 7.51]
= 6.39%
40%
[40% × 5.8 (1 – 0.30)]
+ [60% × 7.96]
= 6.40%
50%
[50% × 6.5 (1 – 0.30)]
+ [50% × 8.59]
= 6.58%
60%
[60% × 7.2 (1 – 0.30)]
+ [40% × 9.54]
= 6.84%
Conclusion
The optimal gearing level is 30%, because the WACC is lowest at this gearing
level. However, the WACC is almost as low at a gearing level of 40%.
16.7
GEARED BETA
(a)
The current proportion of equity in the capital structure is 1,500/(1,500 +
500) = 0.75 or 75%.
The current proportion of debt in the capital structure is 500/(1,500 + 500) =
0.25 or 25%.
Cost of equity = 5% + 1.126 (11 – 5)% = 11.756%.
Since the beta factor of debt is 0, the debt must be risk-free, with a pre-tax
cost of 5%.
WACC = [0.25 × 5.0 (1 – 0.30)] + [0.75 × 11.756] = 9.692%, say 9.7%
(b)
The asset beta of a company is a measure of the systematic business risk
in the company’s business operations. This is a measure of systematic risk
assuming that the company is all-equity financed.
To convert the current geared beta into an asset beta given that debt
capital is risk-free:
βA = βE u
E
E + D (1 – T)
75
75 + 25 (1 – 0.30)
βA = 1.126 u
βA = 0.913
(c)
If the company is geared differently, its equity beta will not be 1.126
because its financial risk will be different. A geared beta can be calculated
for the new gearing level.
0.913 Bgeared u
Bgeared
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60 40 1 0.30
0.913
1.339
0.6818
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This geared beta factor can now be used to calculate the cost of equity at
this gearing level.
Cost of equity = 5% + 1.339 (11 – 5)% = 13.03%.
WACC at this gearing level. It is assumed that the cost of debt remains
risk-free.
WACC = (60% u 13.03%) + [40% u 5%(1 – 0.30)] = 9.218%, say 9.2%
16.8
ADJUSTED PRESENT VALUE
Capital allowances: Workings
Year of
claim
0
1
2
3
(a)
Tax saving at
35%
Rs.
450,000
(315,000)
135,000
(45,000)
90,000
(45,000)
45,000
(45,000)
0
Year of
cash flow
Rs.
110,250
1
15,750
2
15,750
3
15,750
4
Current WACC
Cost of equity = 10% + 1.8(15 – 10)% = 19%.
WACC
0.80u19% >0.20u10% 1 0.65 @ = 16.5%
Year
Machine
Tax saved, tax
allowances
Cash profits
Tax on cash profits
(35%)
Net cash flow
Discount factor at
16.5%
Present value
NPV = + Rs.
17,420
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1
2
3
4
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
110.25
220.00
15.75
220.00
15.75
220.00
15.75
(450)
330.25
(77.0)
158.75
(77.0)
158.75
(77.00)
(61.25)
1.000
0.858
0.737
0.632
0.543
(450)
283.35
117.00
100.33
(33.26)
(450)
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Business finance decisions
(b)
WACC adjusted for business risk and financial risk
Step 1
Calculate an ungeared beta for the plastics industry.
1.356u
5
= 1.20
5 1 1 0.35
The company’s gearing is 60% equity and 40% debt; therefore we need to
re-gear the equity beta for the company.
1.20 Beta geared u
60
60 40 1 0.35
Betageared = 1.72
The cost of equity for the project is therefore 10% + 1.72 (15% – 10%) =
18.6%.
WACC = (0.60 × 18.6%) + (0.40 × 10% (1 – 0.35)) = 13.76%, say 14%.
Year
Net cash flows
(as in (a))
(c)
0
1
2
3
4
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
(450.00)
330.25
158.75
158.75
(61.25)
DCF factor at 14%
1.000
0.877
0.769
0.675
0.592
Present value
NPV = Rs. 32,610
(450.00)
289.63
122.08
107.16
(36.26)
APV method
Step 1
The ungeared beta for the plastics industry is 1.20 (see above)
The cost of ungeared equity in the industry is 10% + 1.20 (15% – 10%) =
16%.
The cash flows of the project are discounted at this cost of capital, to obtain
the base case NPV.
Year
Net cash flow
DCF factor at 16%
Present value
Base case NPV =
Rs. 20,580
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1
2
3
4
Rs.000
(450.00)
Rs.000
330.25
Rs.000
158.75
Rs.000
158.75
Rs.000
(61.25)
1.000
0.862
0.743
0.641
0.552
(450.00)
284.68
117.95
101.76
(33.81)
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Step 2: PV of issue costs
Issue costs before tax
Net finance
obtained
Issue
costs
Rs.
180,000
270,000
Rs.
3,600
13,500
17,100
Debt: (40% × 450,000)
Equity: (60% × 450,000)
Total issue costs
2%
5%
The PV of issue costs is calculated using the risk-free rate of 10% as the
discount rate.
Year
Item
Cash flow
Discount
factor at 10%
Rs.
(17,100)
5,985
0
Issue costs
1
Tax saved at 35%
PV of issue costs
PV
Rs.
(17,100)
5,440
(11,660)
1.000
0.909
Step 3: PV of tax shield
The amount borrowed will be Rs. 180,000 + Rs. 3,600 = Rs. 183,600.
The interest rate will be 10%.
If the loan is repaid in three equal annual instalments, the annual
repayments will be:
Loan
PV factor, years 1 3 at 10%
Year
$183,600
$73,824
2, 487
Balance at
beginning of
year
Loan
payment
Interest at
10%
Rs.
73,824
Rs.
18,360
Rs.
55,464
73,824
12,814
61,010
67,126
73,824
6,713
(67,111)
15 (rounding error)
67,111
Rs.
(183,600)
(55,464)
128,136
(61,010)
1
2
3
Balance
Year of
interest cost
1
2
3
Interest
Year of
tax
saving
Rs.
18,360
12,814
6,713
2
3
4
PV of tax shield
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Tax saving
at 35%
Rs.
6,426
4,485
2,350
Loan
repayment
DCF
factor at
10%
0.826
0.751
0.683
PV of
tax
saving
Rs.
5,308
3,368
1,605
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Adjusted present value
Rs.
Base case NPV
PV of issue costs
PV of tax shield
APV
16.9
20,580
(11,660)
10,281
+ 19,201
APV METHOD
(a)
Modigliani-Miller formula approach
Ungeared beta for the telecommunications industry:
1.30625u
80
80 20 1 0.25
= 1.10
The company’s gearing is 70% equity and 30% debt; therefore we need to
re-gear the equity beta for the company.
1.10 Beta geared u
70
70 30 1 0.25
Betageared = 1.45
The cost of equity for the project is therefore 4% + 1.45 (9% – 4%) =
11.25%.
WACC = (0.70 × 11.25%) + (0.3 × 4% (1 – 0.25))
= 7.875% + 0.9%
= 8.775%, say 8.8%
Year
0
Capital expenditure
Cash profits
Tax at 25%
Net cash flow
DCF factor at 8.8%
Present value
Rs.
(200,000)
1
2
3
4
Rs.
Rs.
Rs.
Rs.
100,000
(200,000)
100,000
165,000
(25,000)
140,000
120,000
(41,250)
78,750
(30,000)
(30,000)
1.000
1/(1.088)
1/(1.088)2
1/(1.088)3
1/(1.088)4
(200,000)
91,912
118,269
61,145
(21,409)
NPV = Rs. 49,917
(b)
APV method
The ungeared beta for the telecommunications industry is 1.10 (see above)
The cost of ungeared equity in the industry is 4% + 1.10 (9% - 4%) = 9.5%.
The cash flows of the project are discounted at this cost of capital, to obtain
the base case NPV.
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Year
Capital
expenditure
Cash profits
Tax at 25%
0
1
2
3
4
Rs.
(200,000)
Rs.
Rs.
Rs.
Rs.
100,000
165,000
(25,000)
120,000
(41,250)
(30,000)
Net cash flow
(200,000)
100,000
140,000
78,750
(30,000)
DCF factor at
8.8%
1.000
1/(1.095)
1/(1.095)2
1/(1.095)3
1/(1.095)4
Present value
(200,000)
91,324
116,762
59,980
(20,867)
Base case NPV = Rs. 47,199
6
PV of issue costs
Issue costs before tax:
Rs.
Equity
Rs. 1,000,000 ×
4/96
Rs. 1,000,000 ×
3/97
Debt
Total issue costs
41,667
30,928
72,595
The PV of issue costs is calculated using the risk-free rate of 4% as the
discount rate.
Year
Item
Cash flow
Rs.
(72,595)
18,149
0
Issue costs
1
Tax saved at 25%
PV of issue costs
7
Discount
factor at 4%
1.000
0.962
PV
Rs.
(72,595)
17,459
(55,136)
PV of tax shield
The amount borrowed will be Rs. 1,000,000 + Rs. 30,928 = Rs. 1,030,928.
The interest rate will be 4%.
The annual interest cost will be Rs. 1,030,928 × 4% = Rs. 41,237 each year,
years 1 – 3.
The reduction in tax due to the interest payments = Rs. 10,309 (= 25% ×
Rs. 41,237) each year, years 2 – 4.
Discount factor at 4%, years 1 – 4
Discount factor at 4%, year 1
Discount factor at 4%, years 2 – 4
3.630
0.962
2.668
PV of tax shield = Rs. 10,309 × 2.668 = Rs. 27,504.
8
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Rs.
Base case NPV
PV of issue costs
PV of tax shield
APV
16.10
47,199
(55,136)
27,504
+ 19,567
MORE APV
It is assumed that the company’s debt capital will be risk-free.
The asset beta for the industry is 1.39 × 80/[80 + 20(1 – 0.25)] = 1.17
The cost of ungeared equity in the industry is 6% + 1.17 (10 – 6)% = 10.68%.
This will be rounded up to 11%.
Only relevant cash flows should be included in the DCF analysis. Non-relevant
costs are the market research cost (already incurred, so a sunk cost) and head
office allocated charges (a non-cash cost).
Note: an increase in head office spending as a result of undertaking a project
would be a relevant cost.
Year
0
1
2
3
4
5
6
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
Rs.000
Revenue
6,800
7,800
8,800
9,200
9,476
9,760
Operating costs
5,500
6,600
7,100
7,500
7,725
7,957
50
50
50
60
60
60
500
400
300
200
200
200
Lost contribution
100
100
Tax-allowable
dep’n
600
480
480
480
480
480
600
6,750
7,630
7,930
8,240
8,465
8,697
(600)
50
270
870
960
1,011
1,063
150
(13)
(68)
(218)
(240)
(253)
(266)
(450)
37
202
652
720
758
797
-
600
480
480
480
480
480
Head office
Royalty
payments
Taxable profit
Tax at 25%
Add back dep’n
Equipment
Working capital
Net cash flow
DCF factor 11%
Present value
600
(3,000)
(400)
400
(3,850)
637
682
1,132
1,200
1.000
0.901
0.812
0.731
0.659
(3,850)
574
554
827
791
1,238
0.593
734
1,277
0.535
897
The base case NPV, discounting the cash flows at the ungeared cost of equity, is
(in Rs.000) + 527.
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Issue costs
Issue costs will be 2%. The net borrowing after issue costs needs to be Rs.
3,400,000; therefore the gross amount borrowed will need to be Rs. 3
million/0.98 = Rs. 3,469,400. Issue costs will be (2%) Rs. 69,000. It is assumed
that this is a Year 0 cost.
There is no tax relief on issue costs
Tax shield
The annual interest cost will be Rs. 3,469,400 × 6% = Rs. 208,164.
Tax relief each year will be (25%) Rs. 52,041
Annuity factor at 6% (the risk-free cost of capital), Years 1 – 6 = 4.917.
Present value of tax shield = Rs. 255,886, say Rs. 256,000.
Rs.000
527
(69)
256
+ 714
Base case NPV
PV of issue costs
PV of tax shield
Adjusted present value
16.11
JALIB LIMITED
Rs. in
million
672
599
(a)
Existing value of equity
Existing value of debt
Total MV of the company before investments
1,271
Increase in MV if the new project to be undertaken
NPV of new project, if funded from all equity
Investment required
60
399
Total Market Value of the company after investment
(ungeared)
1,730
Benefit of tax shield on debt funding (D x t)
(Assume the value of debt = X)
35% of X
Total market value of the company after investments
(geared)
Rs. 1,730 +
35% of X
Maximum debt will be half of the above i.e.
Rs. 865 +
17.5% of X
Existing debt
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Rs. 266 +
17.5% of X
Hence, new debt should be
New debt will be (Rs. 266 / 82.5%)
322
Less: Total investments required
399
Minimum increase in equity required
(b)
77
Rs. in
million
(i)
Existing equity
New equity
NPV of the new project (ungeared)
672
77
60
Benefit of tax shield on debt funding (Rs. 322 x 35%)
113
Value of equity after investment is taken up
922
Price to remain the same
Rs. 16.8
Hence, number of new total shares
54,880,952
Existing shares (given)
40,000,000
New shares to be issued
14,880,952
Right shares ratio (14,880,952 / 40,000,000)
Amount to be raised through equity
Right share price (Rs. 77,000,000 / 14,880,952)
(ii)
Value of equity after investment is taken up
No. of shares already issued
3.72:10
Rs.
77,000,000
Rs. 5.17
Rs.
922,000,000
40,000,000
New issue of ordinary shares (Rs. 77,000,000 / Rs.
14)
5,500,000
45,500,000
Market value of shares after new share issue
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16.12
JAVED LIMITED
Weighted average cost of capital
Value
Cost
Cost
rupees
%
rupees
Equity
(W3)120,000,000
(W1)24.09
28,905,120
Debt
(W5)152,538,000
15.00
22,880,700
272,538,000
WACC
51,785,820
51,785,820
272,538,000
= 19%
W1: Cost of equity
Ke(g) = Ke(u) + [(Ke(u)-Kd) x D/E)]
Ke(g) = 19% + [(19% - 15%) x 1.27115 (W2)
Ke(g) = 24.09%
W2: Debt Equity Ratio
152,538,000 (W5)
=
120,000,000 (W3)
= 1.27115
W3: Market value of equity
Market value of equity = Profit × P/E ratio
= 15,000,000 × 8 = 120,000,000
W4: Market value of TFC’s
Cost of debt (6 months KIBOR +1%) i.e. (14% + 1%)
15.00%
Actual markup (6 months KIBOR + 2%) i.e. (14% + 2%)
16.00%
W5 Present value of outflows against TFCs
Markup at
16%
Discount
factor 15.00%
Date
Description
PV
31-Dec-08
Markup payment
12,000,000
0.930
11,160,000
30-Jun-09
Markup payment
12,000,000
0.865
10,380,000
31-Dec-09
Markup payment
12,000,000
0.805
9,660,000
30-Jun-10
Markup payment
12,000,000
0.749
8,988,000
30-Jun-10
Redemption
150,000,000
0.749
112,235,000
152,538,000
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Business finance decisions
16.13
GHI LIMITED
Advise:
Debt ratio of 40% is the optimal debt structure as at this level the WACC is at
the lowest.
Weighted Average Cost of Capital (WACC)
Debt ratios
10%
40%
10.00%
40.00%
8.00%
10.00%
90.00%
60.00%
50%
50.00%
12.00%
50.00%
10.80%
35.00%
11.20%
35.00%
12.00%
35.00%
12.80%
35.00%
10.80%
10.60%
9.80%
10.30%
Beta
Rf
Rm
0%
1.20
6.00%
10.00%
Debt ratios
10%
40%
1.30
1.50
6.00%
6.00%
10.00%
10.00%
50%
1.70
6.00%
10.00%
Re = Rf + E(Rm - Rf)
10.80%
11.20%
12.80%
Wd
Kd
We
Ke
(Working 1)
Tax
WACC =
WdKd (1-t) + WeKe
0%
0.00%
0.00%
100.00%
Working 1: Cost of equity
16.14
12.00%
NS TECHNOLOGIES LIMITED
(a) APV separates project value into one component associated with the
unlevered operating cash flows and another associated with financing the
project. Each component is evaluated separately.
The disaggregation of cash flows is undertaken so that different discount
rates may be used. As operating cash flows are more risky, they are
discounted at higher rate.
Comparative advantages of APV over WACC
(i)
Unbundles major components of value – drivers of value are much
more apparent under APV than WACC.
(ii)
Miscalculation in WACC, sometimes, produces large errors in the
estimates of value. APV is less prone to such miscalculations.
(iii) Show better result when there are significant changes in capital
structure.
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Answers
(b) Adjusted present value
Net present value on the basis of revised Ke
Years
Investments
After tax cash flows (180 x 0.65)
Cash flows
(Rs. in
million)
0
Rs in million
Discount
@
18.72%
(W1)
(600.00)
1.00
1
Present
value
(Rs. in
million)
(600)
1-8
117.00
* 3.99
467
8
90.00
0.30
27
Residual value
Net present value on the basis of revised Ke
(106)
2
Tax shield [(600 x 55% x 9% x 35% x * 6.21]
Issue
- Right shares (3% x 600 x 45% x (1 0.35))
costs
- Loan (1% x 600 x 55% x (1 0.35))
65
(5)
(2)
(48)
1
*
1 (1 0.1872)8
0.1872( W 1)
2
*
1 (1 0.06)8
0.06
Conclusion
The project is not feasible for the company as the APV of the project is
negative.
W1: Cost of equity
Ke = Rf + (Rm – Rf) x βe
Ke = 6% + (14% – 6%) x 1.59 (W2)
= 18.72%
W2: Calculating Equity Beta for Telecommunication Industry
βa
βe
1.5 βe
βe
16.15
D (1 - t)
E
βd
E D(1 t)
E D(1 t)
40(1 0.35)
60
1.3
60 40(1 0.35)
60 40(1 0.35)
1.59
COPPER INDUSTRIES LIMITED
(a) (i) Weighted average cost of capital
ƒ
Existing WACC =
(Equity % (W1) x Ke (W2)) + (Debt % (W1) x Kd (1-t))
= (60% x 17%(W2) ) + (40% x 9% x 65%) = 12.54%
ƒ
70% equity 30% debt
WACC = (70% x 15.9% (W2)) + (30% x 8% (W3) x 65%) = 12.70%
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ƒ
50% equity 50% debt
WACC = (50% x 18.5% (W2)) + (50% x 11% (W3) x 65%) = 12.83%
(ii) Value of the company
ƒ
Current value of the company (825+550) = Rs. 1.375 million
ƒ
Value of the company at 70% equity 30% debt
WACC (Computed above) = 12.70%
Valuation
ƒ
112.55 x 1.0403
0.1270 0.0403(W 5)
1350 million
Value of the company at 50% equity 50% debt
WACC (Computed above) = 12.83%
Valuation
112.55 x 1.0403
0.1283 0.0403(W 5)
1330 million
W1: Existing debt equity ratio
Equity
Debt
825
60%
1375
550
40%
1375
W2: Cost of equity
ƒ
Existing
Ke = rf + (rm - rf)β
Ke = 7% + (15% - 7%) x 1.25 = 17%
ƒ
At 70% equity 30% debt
Ke = 7% + (15% - 7%) x 1.115 = 15.9%
βe
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βa
E D(1 - t)
E
* 0.872
70% 30% x 65%
= 1.115
70%
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Answers
ƒ
At 50% equity 50% debt
Ke = 7% + (15% - 7%) x 1.439 = 18.5%
βe
*
βa
βa
E D(1 - t)
E
βe
1.25
* 0.872
50% 50% x 65%
= 1.439
50%
D(1 t)
E
βd
E D(1 t)
E D(1 t)
825
0 = 0.872
825 550 x 65%
W3 : Cost of debt
ƒ
At 70% equity 30% debt
Since interest cover has an inverse relationship, we assume decline in
debt moves the CIL to lower category of interest rate:
30% debt in existing market value of the company (30% x 1375) = 412.5
Cost of debt = (8% x 412.5) = 33
Interest cover = (327* ÷ 33) = 9.91
? Kd = 8%
* Profit before interest and tax
ƒ
At 50% equity 50% debt
Since interest cover has an inverse relationship, we assume increase in
debt moves the CIL to upper category of interest rate:
50% debt in existing market value of the company (50% x 1375) = 687.5
Cost of debt is = (11% x 687.5) = 75.63
Interest cover = (327 ÷ 75.63) = 4.32
Kd = 11%
W4: Current Free cash flow (FCFo)
Profit before tax
Rs. in million
272.00
Add: Interest
55.00
Profit before tax and interest
327.00
Less: Income tax @ 35%
114.45
Profit after tax
212.55
Add:
Depreciation
Less
:
Capital expenditures
50.00
(150.00)
Free cash flow
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W5 Computation of growth factor
Current valuation 1375
1375
FCF1
Ÿ 1375
(k - g)
FCF1
(k - g)
112.55(1 g )
0.1254 g
1375(0.1254 g) 112.55(1 g) Ÿ J ŸJ (b) Evaluation of the above options
(i)
The existing debt equity structure gives the lowest WACC i.e. 12.54%.
If debt equity ratio is decreased, some of the benefits of tax shield on
(ii) debt are lost.
If debt equity ratio is increased, the financial risks cause an increase in
(iii) the cost of debt.
Since the existing debt equity ratio gives the lowest WACC and resultantly
the highest valuation to the company, the capital structure of the company
should not be changed.
16.16
MAC FERTILIZER LIMITED
DIRECTOR A's RECOMMENDATION : Evaluation on the basis of Existing
WACC
ܹ‫ ܥܥܣ‬ൌ ‫ܭ‬௘ ൈ
ܸ௘
ܸௗ
൅ ݇ௗ ൈ
ܸ௘ ൅ ܸௗ
ܸ௘ ൅ ܸௗ
ܸ௘ ൌ ͹ͲͲ ൈ ͺͲǤͲͲ ൌ ܴ‫ݏ‬Ǥͷ͸ǡͲͲͲ݈݈݉݅݅‫݊݋‬
ܸௗ ൌ ʹͺͲ ൈ ͳͲʹǤͷͲ ൌ ܴ‫ݏ‬Ǥʹͺǡ͹ͲͲ݈݈݉݅݅‫݊݋‬
ͺͶǡ͹ͲͲ
ܹ‫ ܥܥܣ‬ൌ ͳͶǤͷΨሺࢃ૚ሻ ൈ ͷ͸ǡͲͲͲ
ʹͺǡ͹ͲͲ
൅ ͹ǤͷΨሺࢃ૛ሻ ൈ
ൌ ͳʹǤͳΨ
ͺͶǡ͹ͲͲ
ͺͶǡ͹ͲͲ
W1: Cost of equity
݇௘ ൌ ܴ௙ ൅ ൫ܴ௠ െ ܴ௙ ൯ ൈ ߚ
ൌ ͺΨ ൅ ሺͳ͵Ψ െ ͺΨሻͳǤ͵ ൌ ͳͶǤͷΨ
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Answers
W2: Cost of debt
Ye
ar
0
(102.5
0)
Interest
(Rs. 100 × 11.5% × (130%)
Repayment
Price of TFC
1-5
5
Cash
flows
(Rs.)
Description
Discoun
t factor
(6%)
PV
(Rs.)
Discoun
t factor
(9%)
PV
(Rs.)
1.000
(102.50
)
1.000
(102.50)
8.05
4.212
33.91
3.890
31.31
100
0.747
74.70
0.650
65.00
6.11
(6.19)
Calculating the cost of debt using IRR
͸Ǥͳͳ
ൈ ͵Ψ ൌ ͹ǤͶͻΨ
ሺ͸Ǥͳͳ ൅ ͸Ǥͳͻሻ
݇ௗ ൌ ͸Ψ ൅
DIRECTOR B's RECOMMENDATION: Evaluation on the basis of Project
Specific Cost of Capital
ܹ‫ ܥܥܣ‬ൌ ‫ܭ‬௘ ൈ ܸ௘
ܸௗ
൅ ݇ௗ ൈ ሺͳ െ ‫ݐ‬ሻ
ܸ௘ ൅ ܸௗ
ܸ௘ ൅ ܸௗ
ܹ‫ ܥܥܣ‬ൌ ͳͻǤͺʹΨሺࢃ െ ૜ሻ ൈ ͳǡ͸ʹͲ
ͳǡͻͺͲ
൅ ͺǤͶΨሺࢃ െ ૝ሻ ൈ
ൌ ͳ͵ǤͷͶΨ
͵ǡ͸ͲͲ
͵ǡ͸ͲͲ
W3: Cost of equity
݇௘ ൌ ͺΨ ൅ ሺͷΨሻ ൈ ʹǤ͵͸Ͷሺࢃ െ ૞ሻ ൌ ͳͻǤͺʹΨ
W4: Cost of debt
݇ௗ ൌ ͳʹǤͲΨ ൈ ሺͳ െ ͵ͲΨሻ ൌ ͺǤͶΨ
W5: Computation of project specific beta
Un-geared Steel Company Beta
‫ܤ‬௨ ൌ ‫ܤ‬௚ ൈ ܸ௘
ܸௗ ሺͳ െ ‫ݐ‬ሻ
൅ ‫ܤ‬ௗ ൈ
ܸ௘ ൅ ܸௗ ሺͳ െ ‫ݐ‬ሻ
ܸ௘ ൅ ܸௗ ሺͳ െ ‫ݐ‬ሻ
where,
ܸ௘ ൌ ͻͲͲ ൈ ͵ͷ ൌ ͵ͳǡͷͲͲ,
ܸௗ ሺͳ െ ‫ݐ‬ሻ ൌ ͺǡͲͲͲ ൈ ͹ͲΨ ൌ ͷǡ͸ͲͲ
‫ܤ‬௚ ൌ ͳǤͷ
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‫ܤ‬௨ ൌ ͳǤͷ ൈ
͵ͳǡͷͲͲ
൅ Ͳ ൌ ͳǤʹ͹Ͷ
ሺ͵ͳǡͷͲͲ ൅ ͷǡ͸ͲͲሻ
Get the project beta on the basis of steel company un-geared beta
‫ܤ‬௚ ൌ ‫ܤ‬௨ ൅ ሺ‫ܤ‬௨ െ ‫ܤ‬ௗ ሻ ൈ
‫ܤ‬௚ ൌ ͳǤʹ͹Ͷ ൅ ͳǤʹ͹Ͷ ൈ
ܸௗ ሺͳ െ ‫ݐ‬ሻ
ܸ௘
ͳǡͻͺͲ ൈ ͹ͲΨ
ൌ ʹǤ͵͸Ͷ
ͳǡ͸ʹͲ
Appropriateness of discount rate
The view expressed by the Director A is not worthwhile because:
‰
existing WACC only reflects the current business and financial risk. It does
not incorporate the additional risk of the new sector as well as additional
return required by the company's shareholders.
‰
the proportion of debt in the investment i.e. 55% is quite high as compare to
existing debt proportion i.e. 34%. The financial risk has therefore increased
and it could therefore be argued that current WACC is not an acceptable
discount rate.
‰
rate used for evaluation of the project i.e. 17% is too high as it is based only
on the relatively high cost of equity and ignores the amount of debt that will
be used to finance the project.
The suggestion given by the Director B is worthwhile as the project specific cost
of capital (based on steel industry's risk) incorporates the business and financial
risk of the new sector, in which MFL intends to invest and also incorporates the
higher return expectation of the shareholder because of increase in financial risk.
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Answers
CHAPTER 17 – BUSINESS VALUATION
17.1
VALUATION MODEL
(a)
Expected share price = Rs. 24/0.08 = Rs. 300
(b)
Expected share price = Rs. 24(1.03)/(0.08 – 0.03) = Rs. 494
(c)
Expected growth rate in dividends = 60% × 9% = 5.4%.
Expected share price=
17.2
•Ǥʹ4(1.054)
=•Ǥͻ73
(0.08-0.054)
VALUATION
The dividend growth model:
800
38 1 g
0.10 g
800 (0.10 – g)
80 – 800g
838g
g = 0.05 or 5%.
=
=
=
38 (1 + g)
38 + 38g
42
An expected dividend growth rate of 5% per year is required to achieve a share
price of 800.
17.3
VALUATION OF BONDS
(a)
7.5% irredeemable bonds
(7.5/9.0) × 100 = 83.33. (Rs. 83.33 market value for each Rs. 100 nominal
value of bonds.)
(b)
6% redeemable bond
Year
Item
1 – 3 Interest
4
Interest plus capital
Cash flow
Discount
factor at 9%
6
106
2.531
0.708
PV
15.19
75.05
90.24
The market value of the bonds should be 90.24 for each Rs. 100 nominal
value of bonds.
(c)
10% redeemable bond
Period
Item
1–7
8
Interest
Interest plus capital
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Cash flow
Discount
factor at 4.4%
5
105
5.914
1/(1.044)8
PV
29.57
74.40
103.97
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Business finance decisions
The market value of the bonds should be 103.97 for each Rs. 100 nominal
value of bonds.
(d)
Convertible bond
Year
Item
1 – 3 Interest
3
Value of shares acquired
(20 shares u Rs. 7)
Cash
flow
Discount
factor at 9%
PV
5
2.531
12.66
140
0.772
108.08
120.74
The market value of the bonds should be 120.74 for each Rs. 100 nominal
value of bonds.
17.4
ANNUITIES AND BOND PRICES
Tutorial note
You might be required in the examination to remember and use the formula for
the present value of an annuity. This is:
PV of annuity
(a)
(i)
1ª
1
Annuityu «1 r «¬
1 r
º
n »
»¼
Valueof zerocouponbond
100u
1
1.05
10
= 100 ×0.6139
= 61.39.
(ii)
PV of interest payments to maturity of the bond: interest = 4 every 6
months for 10 years.
PV of annuity
4u
1 ª
1
«1 0.025 ¬«
1.025
20
º
»
¼»
= 160 ×[0.3897]
= 62.35
Cash
flow
Period
1 – 20
Interest
20
Redemption
Value of bond
(b)
4
100
Discount
factor (2.5%)
See above
1/(1.025)20
PV
62.35
61.03
123.38
When interest yields rise, bond prices fall. Edit: the below boxes needs the
‘x’ replaced
(i)
Valueof zerocouponbond
100u
1
1.06
10
= 100 ×0.5584
= 55.84.
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Answers
(ii)
PV of annuity
4u
1 ª
1
«1 0.03 «¬
1.03
º
20 »
»¼
= 133.33 ×[0.4463]
= 59.51
Cash
flow
Period
1 – 20 Interest
20
Redemption
Value of bond
17.5
Discount factor
at 3%
4
100
See above
1/(1.03)20
PV
59.51
55.37
114.88
WARRANTS AND CONVERTIBLES
(a)
Convertibles
Share
price
Value of equity if
converted per Rs.
100 of bonds
(20 shares)
Value as
debt if not
converted
Value of
convertibles
Convert?
Rs. 88
Rs. 104
Rs. 120
Rs. 136
Rs. 105
Rs. 105
Rs. 105
Rs. 105
Rs. 105
Rs. 105
Rs. 120
Rs. 136
No
No
Yes
Yes
Rs. 4.40
Rs. 5.20
Rs. 6.00
Rs. 6.80
Warrants
Share price
Rs. 4.40
Rs. 5.20
Rs. 6.00
Rs. 6.80
(b)
Exercise
price
Value of
warrant
Rs. 5
Rs. 5
Rs. 5
Rs. 5
Rs.0
Rs.0.20
Rs. 1.00
Rs. 1.80
Exercise?
No
Yes
Yes
Yes
Convertibles
Before
conversion
After
conversion
Rs.000
1,200
300
900
450
450
Rs.000
1,200
1,200
600
600
Number of shares
2,000,000
2,500,000
Earnings per share
Rs.0.225
Rs.0.24
Profit before interest
Interest (Rs. 2.5 million × 12%)
Tax at 50%
Earnings (profit after tax)
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Warrants
Before
exercise
After
exercise
Rs.000
1,200
-
Rs.000
1,200
250
1,200
600
600
2,000,000
1,450
725
725
2,500,000
Rs.0.30
Rs.0.29
Profit before interest
Plus return on additional funds raised: 10%
× Rs. 2,500,000
Tax at 50%
Number of shares
Earnings per share
17.6
KENCAST LIMITED
(a)
Computation of the value of Kencast Limited’s share capital as at
30/12/2017
(i)
Price/Earnings’ Basis:
Value of Business
= P/E ratio x Earnings
= 6 x Rs. 4,050,000
= Rs. 24,300,000
Computation of earnings:
Profit
Overvaluation of opening
inventory
Overcharge of directors
remuneration
Undercharged depreciation
(3000 – 2250)
Adjusted Profit
Earnings (Average)
2015
Rs.‘000
3,250
2016
Rs.‘000
3,600
2017
Rs.‘000
4,175
600
-
-
625
1 025
1 125
(750)
(750)
(750)
3,725
3,875
4550
•Ǥ͵,725 + •Ǥ͵,875 + •ǤͶ,550
3
= Rs. 4,050,000
Computation of P/E ratio:
Company 1
5.4
Company 2
6.6
Total
Average
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12
/2 =
6.0
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Answers
(Note: It would have been better to calculate a PE ratio as the
weighted average of the ratios of the two companies based on their
market values. However, the information necessary to do this was not
available in the question
(ii)
Liquidation/break-up basis as at 31/12/2017
Non-Current Assets:
Freehold Properties
Equipment
Current Assets:
Inventories
Account Receivables
Cash Equivalent/Bank
Less: Liabilities
(iii)
Rs.’000
15,000
5,400
8,000
4,825
650
33,875
4,150
29,725 i.e. Rs. 29,725,000
Dividend Yield Basis:
Computation of dividend yield
Company 1
9%
Company 2
11%
Total
20%
Average
12
/2 =
Value of business:
(b)
(i)
(ii)
© Emile Woolf International
10%
Total Dividend
Dividend Yield
=
Rs. 2,250,000
ȗ10%
ൌ •Ǥ ʹʹǡͷͲͲǡͲͲͲ
Limitations of P/E ratio method
‰
It assumes that current earnings will continue. The value
computed will be overstated if there is reduction in earnings.
‰
It used the P/E ratio of a similar company. This may not
correctly reflect the true position of Kencast Ltd.
‰
It makes use of accounting profit whereas cash profit is more
useful.
‰
It ignores the time value of money.
Limitations of Liquidation basis
‰
It ignores the future potential earnings of an entity.
‰
It is only used when a company’s going concern is threatened.
It cannot be used for a continuing business.
‰
The break up values may not be readily available.
‰
Liquidation costs that need to be deducted may be omitted.
289
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Business finance decisions
(iii)
17.7
Limitations of Dividend Yield basis
‰
Value may be understated if earnings are substantially higher
than dividend.
‰
It used the dividend yield of a similar entity which may not
reflect the true position of Kencast Ltd.
‰
It is only useful for the valuation of non-controlling interest or
small holding
‰
It will not be usable if a company pays no dividend
‰
There may be difficulty of finding a comparable firm.
A PLC’S AND B PLC
Calculation of offer price by A Plc to shareholders of B Plc based on :
(a)
Net asset basis
Net Asset Value (NAV)
=
NAV for Company A
=
=
NAV for Company B
=
=
Value attributab le to equity
No of ordinary shares
•Ǥͳ,380,000,000
1,000,000,000
Rs. 1.38
•Ǥͷ60,000
500,000,000
Rs. 1.12
Comment
A Plc is expected to issue 112 of its own shares in exchange for every 138
of those in B Plc, which it acquires
To acquire the whole of the issued share capital of B Plc, A Plc should
issue.
500,000,00 0
u 112 = 405,797,101 new Rs. 1 shares
138
(b)
Earnings Basis
Earnings per share (EPS) =
EPS for A Plc
=
Total earnings attributab le to equity
No. of shares
•Ǥʹ40,000,000
1,000,000,000
1,000,000,000
=
EPS for B Plc
=
=
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Rs.0.24
•Ǥͳ50,000,000
500,000,000
Rs. 0.30
The Institute of Chartered Accountants of Pakistan
Answers
Comment
A Plc is expected to issue 30 new shares in exchange for 24 existing
shares in B Plc. This leads to a total issue of
500,000,00 0
u 30 = 625,000,000 new Rs. 1 shares
24
(c)
Market value Basis
The current market price of A Plc share is Rs. 2.40 and that of B Plc’s
share is Rs. 2.70. To maintain the market value of the holdings, A Plc
should issue 9 new shares for each 8 of Bayela’s shares (i.e. 270 for 240).
Therefore, the total number of shares to be issued is
•Ǥͷ00,000ǡͲͲͲ
x 9 = 562,500,000 new Rs. 1 shares
8
(d)
Financial Analysis
A Plc current cost of equity (assuming no expected growth) is:
Maintainab le annual profit 100%
u
Market value of equity
1
=
=
A Plc cost of debt is:
•Ǥʹ40,000,000
•Ǥʹ,400,000,000
x
100%
1
10% per annum
Coupon rate x
=
10% x
=
8%
Nominal value
Market value
100
125
The after tax cost of debt is therefore 8 (1-tax rate)
=
8 (0.7)
=
5.6% per annum
A Plc WACC is:
(10
x •Ǥʹ,400,000,000) + [5.6 x (•Ǥͳ50,000,000x1.25]
•Ǥʹ,587,500,000
=
9.68% per annum
The maximum price that A Plc would be prepared to pay to B Plc for this to
be an acceptable “project” under conventional capital project appraisal
methods
is:
Earning of B PŽ
Cost of capital of Ž
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=
=
•Ǥͳ50,000,000
0.0968
Rs. 1.549,586,777
•Ǥͳ,549,586,777
This implies issuing
•Ǥʹ.40
=
645,661,157 new shares in A Plc
for the equity in B Plc
This is an offer of about 129 new shares in A Plc for 100 shares in B Plc as
follows:
645,661,157
500,000,000
17.8
= 1.29 : 1 or 129 : 100
MNO CHEMICALS LIMITED
Merger
with PQ
Merger
with RS
Rupees in million
Investment required to be made (W – 1)
848.00
1,888.75
Net profit after tax
124.80
169.00
37.05
47.39
161.85
216.39
19.09%
11.46%
Synergy impact (W5)
Return on investment
Conclusion:
By acquiring PQ (Pvt.) Ltd., the shareholders of MNO Chemicals will earn a
higher return on investment as compared to the acquisition of RS. Hence,
acquisition of PQ is financially feasible for the shareholders of MNO Chemicals.
W1: Value of equity i.e. investment required to be made by MNO
PQ
RS
Rupees in million
Total value of the company (W – 2)
1,248.00
2,388.75
Less: Value of TFCs
(400.00)
(500.00)
848.00
1,888.75
Value of equity i.e. investment to be made by
MNO
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W2: Total value of company
Yo x (1 g)
Re - g
Total Valueof PQ (Pvt.) Ltd.
Total Valueof RS Ltd.
156 (W - 3) x (1 4%)
17% (W - 4) - 4%
204.75(W - 3) x (1 5%)
14% (W - 4) - 5%
1,248
2,388.75
W3: Maintainable earnings (Yo)
PQ
RS
Rupees in million
Net profit after tax
Add Interest (PQ : 48 × 0.65) (RS : 55 × 0.65)
Maintainable earnings
124.80
169.00
31.20
35.75
156.00
204.75
W4: Cost of equity (Re)
Ke = Rf + (Rm – Rf)E
Cost of equity of RS = 8% + (13% – 8%) x 1.2 = 14%
Cost of equity of PQ (Pvt.) Ltd.
= Ke of RS Ltd. + Illiquidity premium
= 14% + 3% = 17%
W5 Synergy Impact
PQ
RS
Rupees in million
Net profit after tax of MNO
585.00
Maintainable earnings of PQ (W3)
156.00
Maintainable earnings of RS (W3)
204.75
Combined profit of merged entities
Synergies impact on profitability
Synergy impact
17.9
585.00
741.00
789.75
5%
6%
37.05
47.39
FREE CASH FLOW
Rs.
Profit before interest and tax
Interest
Taxation
Depreciation charges
Increase in working capital
Essential capital expenditure
Free cash flow
© Emile Woolf International
3,000,000
(440,000)
(600,000)
550,000
(150,000)
(1,000,000)
1,360,000
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17.10
FINANCIAL PLAN
(a)
Tutorial note. Many of the figures for the financial plan can be calculated
by increasing the amount by 8% each year, in line with sales growth. The
bank overdraft interest each year is calculated by taking the bank overdraft
at the end of the previous year. The bank overdraft is a balancing figure in
the statement of financial position, that makes the equity and liabilities add
up to the total assets.
Statements of profit or loss
Year 5
Year 6
Year
7
Year 8
Rs. m
Rs. m
Rs. m
Rs. m
EBITDA
(+ 8% per year)
583
630
680
735
Depreciation
(+ 8% per year)
(173)
(187)
(202)
(218)
410
443
478
517
(86)
(95)
(106)
(118)
Profit before tax
324
348
372
399
Tax (30%)
(97)
(104)
(112)
(120)
Profit after tax
227
244
260
279
(145)
(159)
(166)
(179)
82
85
94
100
(+ 8% per
year)
2,182
2,356
2,545
2,748
(+ 8% per
Inventory +
receivables – trade year)
payables
767
828
894
966
(+ 8% per
year)
32
35
38
41
2,981
3,219
3,477
3,755
450
450
450
450
1,283
1,368
1,462
1,562
1,733
1,818
1,912
2,012
800
800
800
800
2,533
2,618
2,712
2,812
448
601
765
943
2,981
3,219
3,477
3,755
Earnings before
interest
(see workings)
Interest
(64%)
Dividends
Retained earnings
Plant and
equipment
Cash
Share capital
(add retained
profit)
Reserves
Long-term loan
Bank overdraft
(balancing
figure)
Workings
(1)
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At the end of year 4, inventory + receivables – trade payables = 710
(in Rs. million). This amount will increase by 8% each year.
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(2)
Interest charges
Long-term loan
Bank overdraft
(b)
(8% × 800)
(7% × previous
year)
Year
5
Rs. m
64
Year
6
Rs. m
64
Year
7
Rs. m
64
Year
8
Rs. m
64
22
86
31
95
42
106
54
118
There are several definitions of free cash flow. Other definitions are
acceptable for your answer.
Year 5
Rs. m
EBIT (1 – t)
Earnings
interest less
30%
Year 7
Rs. m
Year 8
Rs. m
287
173
(162)
310
187
(174)
335
202
(189)
362
218
(203)
(57)
241
(61)
262
(66)
282
(72)
305
before
tax at
Depreciation
Increase in plant and equipment
Increase in inventory + receivables payables
Free cash flow
(c)
Year 6
Rs. m
A feature of the financial plan that might need review is the cash position of
the company. The bank overdraft is forecast to increase from Rs. 310,000
to Rs. 943,000, although the company expects to make a profit each year.
The free cash flow each year, as measured, is not much more than the
interest payments and dividend payments.
This suggests that the company might need to reconsider its dividend
policy, and pay lower dividends. In addition, the company might possible
consider alternative sources of finance, so that it does not have to rely so
much on an overdraft facility. More long-term debt might be appropriate, if
this can be obtained at a suitable interest rate.
(d)
A possible value of the company’s shares at the end of the financial
planning period can be estimated using the dividend growth model,
assuming that dividends will grow by about 8% per year (in line with sales
growth) and the cost of equity will remain at 12%.
Expected equity value in Rs.
millions
179 (1.08)
(0.12 – 0.08)
= Rs. 4,833 million.
There are 9,000,000 shares of Rs.0.05 each . This gives a valuation of Rs.
537 per share.
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Business finance decisions
17.11
TAKEOVER
(a)
Cost of equity in Flat Company, using the CAPM = 5% + 1.20 (11 – 5)% =
12.2%
WACC in Flat Company = (12.2 × 75%) + (7 (1 – 0.30) × 25%) = 10.375%,
say 10.4%
Cost of equity in Slope Company, using the CAPM = 5% + 1.35 (11 – 5)%
= 13.1%
WACC in Slope Company = (13.1 × 60%) + (8 (1 – 0.30) × 40%) = 10.1%.
Free cash flow is defined here as EBIT less tax, plus tax-allowable
depreciation minus replacement capital expenditure.
Free cash flows and valuation of Flat Company based on free cash
flows
Year
1
2
3
4
Rs.000
Rs.000
Rs.000
Rs.000
Earnings before interest
and tax
1,918
2,014
2,115
2,221
Tax at 30%
(575)
(604)
(635)
(666)
1,343
1,410
1,480
1,555
872
915
961
1,009
Less: Replacement
capital spending
(966)
(1,014)
(1,065)
(1,118)
Free cash flow
1,249
1,311
1,376
1,446
Discount factor at 10.4%
0.906
0.820
0.743
0.673
Present value
1,132
1,075
1,022
973
Add back tax-allowable
depreciation
End-of-year 4 value of free cash flows from Year 5
onwards
1,446 (1.03)
=
(0.104 – 0.03)
= (in Rs.000) 20,322
Present value of Year 5 onward cash flows(Year 0 value) = 20,322 × 0.673
= 13,677.
Total valuation of Flat Company equity, using the free cash flow method, is
(1,132 + 1,075 + 1,022 + 973 + 13,677) = Rs. 17,879,000.
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Answers
Free cash flows and valuation of Slope Company based on free cash
flows
Year
1
2
3
4
Rs.000
Rs.000
Rs.000
Rs.000
Earnings before
interest and tax
1,893
1,969
2,047
2,129
Tax at 30%
(568)
(591)
(614)
(639)
1,325
1,378
1,433
1,490
728
757
787
819
Less: Replacement
capital spending
(822)
(854)
(889)
(924)
Free cash flow
1,231
1,281
1,331
1,385
Discount factor at
10.1%
0.908
0.825
0.749
0.681
Present value
1,118
1,057
997
943
Add back taxallowable depreciation
End-of-year 4 value of free cash flows from
Year 5 onwards
=
1,385 (1.02)
(0.101 – 0.02)
= (in Rs.000) 17,441
Present value of Year 5 onward cash flows(Year 0 value) = 17,441 × 0.681
= 11,877.
Total valuation of Slope Company equity, using the free cash flow method,
is (1,118 + 1,057 + 997 + 943 + 11,877) = Rs. 15,992,000.
Combined group WACC
Market
Cost of
value
capital
MV ×
Cost
Rs. m
Flat equity
(6m × 3.20)
Flat debt
(19.2m/0.75) × 25%
Slope equity
(9m × 1.54)
Slope debt
(13.86m/0.60)
40%
×
19.20
0.104
1.9968
6.40
0.049
0.3136
13.86
0.101
1.3999
9.24
0.056
0.5174
48.70
4.2277
WACC = 4.2277/48.70 = 0.068 or 8.68%, say 8.7%.
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Free cash flows and valuation of combined company based on free
cash flows
Tax-allowable depreciation in the year just ended (combined) was 1,530
and replacement capital expenditure combined was 1,710.
Year
1
2
3
4
Rs.000
Rs.000
Rs.000
Rs.000
4,100
4,305
4,520
4,746
(1,230)
(1,292)
(1,356)
(1,424)
2,870
3,013
3,164
3,322
1,607
1,687
1,771
1,860
(1,860)
(1,885)
(1,980)
(2,079)
Free cash flow
2,617
2,815
2,955
3,103
Discount factor at 8.7%
0.920
0.846
0.779
0.716
Present value
2,408
2,381
2,302
2,222
Earnings before interest
and tax
Tax at 30%
Add back tax-allowable
depreciation
Less: Replacement capital
spending
End-of-year 4 value of free cash flows from
Year 5 onwards
=
3,103 (1.04)
(0.087 – 0.04)
= (in Rs.000) 68,662
Present value of Year 5 onward cash flows(Year 0 value) = 68,662 × 0.716
= 49,162.
Total valuation of equity in the combined company, using the free cash flow
method, is (2,408 + 2,381 + 2,302 + 2,222 + 49,162) = Rs. 58.475 million
Summary of free cash flow valuations
Value of Flat Company equity
Value of Slope Company equity
Value of equity in combined company
Increase in equity value
Rs. m
17.879
15.992
33.871
58.475
24.604
On the basis of these estimates, the value of equity (as valued on a free
cash flow basis) will increase by about 72.6% as a result of the takeover.
(b)
The estimates of equity value might not be reliable, for several reasons.
(1)
© Emile Woolf International
The WACC used for the combined company, based on current
market values, is lower than the WACC used for each separate
company valuation. This lower WACC is questionable, and if a WACC
of over 10% were used, the valuation of the company after the
takeover would be much lower.
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(2)
(3)
(c)
The estimates for the increase in the combined Year 1 EBIT might be
unrealistic, and the estimates of higher growth in sales and earnings
should also be questioned.
Valuations based on a dividend growth model, rather than a free cash
flow model, would produce a lower valuation.
Shareholders in Slope are being offered 2 shares in Flat (current value Rs.
6.40) for every three shares they hold (current value Rs. 4.62). On the
basis of current market values, they are being offered a price that is 38.5%
above the current share price. This is a very high premium in a takeover
bid, and is likely to be very attractive to them.
For the same reason, shareholders in Flat might oppose the takeover bid,
because ‘value’ is being given to the shareholders of Slope and a very high
premium is being offered for the shares. The shareholders in Flat will only
support the bid if they believe that it will ‘unlock value’ in the shares or
result in substantial synergy gains through higher sales, cost savings or
faster business growth.
17.12
MK LIMITED
(a)
VALUE OF MK LIMITED
Years
1
2
Rupees in million
Sales
4%
12,480
12,979
75%
(9,360)
(9,734)
3,120
3,245
35%
(1,092)
(1,136)
Add back depreciation
4%
1,357
1,411
Annual capital expenditure
4%
(728)
(757)
2,657
2,763
0.911
0.830
Present value
2,421
2,292
Present value 1 - 2 years
4,713
Operating costs including
depreciation
Profit before interest and tax
Taxation
Free cash flow
Discount factor (W1)
9.8%
Free cash flow after year 2 =
2,763(1.05)
x 0.83 = Rs. 50,166 million
0.098 0.05
Total free cash flows = (4,713 +
50,166)
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W1: Weighted Average Cost of
Capital
D/E Ratio
Rate
WACC
ke (8% + (13% -8%) x 1.1)
60%
13.50%
8.1%
kd (6.5% x 0.65)
40%
4.23%
1.7%
WACC
9.8%
VALUE OF ZA LIMITED
Years
1
2
Rupees in million
Sales
5.5%
8,925
9,416
Operating costs including
depreciation
5.5%
(6,219)
(6,561)
2,706
2,855
Profit before interest and tax
Taxation
35%
(947)
(999)
Add back depreciation
5.5%
1,044
1,101
Annual capital expenditure
5.5%
(686)
(724)
2,117
2,233
0.916
0.839
Present value
1,939
1,873
Present value 1 - 2 years
3,812
Free cash flow
Discount factor (W2)
Free cash flow after year 2 =
9.2%
2,233(1.05)
x 0.839 = Rs. 46,837 million
0.092 0.05
Total free cash flows = (3,812 +
46,837)
Rs. 50,649 million
W2: Weighted Average Cost of
Capital
Rate
ke - (8% + (13% - 8%) x 1.3
kd - (7.5% x 65%)
WACC
© Emile Woolf International
D/E %
WACC
14.5%
45%
6.5%
4.9%
55%
2.7%
9.2%
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VALUE OF PROPOSED MERGED COMPANY
Years
1
2
Rupees in million
Combined Sales
5%
21,483
22,557
Operating costs including
depreciation
70%
(15,038)
(15,790)
6,445
6,767
Profit before interest and tax
Taxation
35%
(2,256)
(2,368)
Add back depreciation
5%
2,410
2,531
Annual capital expenditure
5%
(1,418)
(1,489)
5,181
5,441
0.911
0.830
Present value
4,720
4,516
Present value 1 - 2 years
9,234
Free cash flow
Discount factor (W3)
Free cash flow after year 2 =
9.8%
5,441(1.055)
x 0.83 = Rs. 110,800 million
0.098 0.055
Total free cash flows = (9,234 +
110,800)
Rs. 120,036 million
W3: Weighted Average Cost of
Capital
Equity - MK (100 x 20)
Equity - ZA (90 x 7/9 x 20)
Debt - MK (2,000 x 40% / 60%)
Debt - ZA (90 x 12 x 55% / 45%)
Total equity + debt of merged
company
2,000
1,400
1,333
1,320
6,053
WACC = 594 ÷ 6,053
(b)
13.50%
14.5%
4.23%
4.98%
270.00
203.00
56.00
65.00
594
9.8%
Synergy effect of acquisition
Rupees in million
Total free cash flow of Merged
Co.
120,036
Total free cash flow of MK
Limited
54,879
Total free cash flow of ZA
Limited
50,649
105,528
Synergy effect of acquisition
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Business finance decisions
17.13
PLATINUM LIMITED
(a) Synergistic effects can arise from five sources:
(i)
Operating economies, which result from economies of scale in
management, marketing, production, or distribution.
(ii)
Financial economies, including lower interest costs etc.
(iii) Tax effects, where the combined enterprise pays less in taxes than the
separate firms would pay.
(iv) Differential efficiency, which implies that management of one firm is
more efficient and that the weaker firm’s assets will be more productive
after the merger.
(v)
(b) (i)
Increased market power, due to reduced competition.
The number of shares in Platinum Limited offered to shareholders of
Diamond Limited are:
No. of shares to be issued to DL (7/6 x 19.2) =
22.4 million shares
Existing earnings per share of PL (Rs. 231m /
90m) =
Rs. 2.57
Value of shares in PL (Rs. 2.57 x 15) =
Rs. 38.55
Total value of bid
(22.4 million shares x Rs. 38.55) =
Rs. 863.52 million
(ii)
EPS of PL following a successful acquisition:
Rs. in
million
Earnings of PL before acquisition
231.00
Earnings of DL before acquisition
58.00
Post takeover synergy
24.00
313.00
Shares in issue following acquisition (90+22.4) (in million)
EPS after acquisition (Rs. 313m / 112.4m) =
Share price after acquisition (Rs. 2.78 x 18)
112.40
Rs. 2.78
50.04
(iii) Cost of each debenture
Rupees
EPS of DL before acquisition (Rs. 58 ÷ 19.2)
Value of a share in DL (Rs. 3.02 x 19)
3.02
57.38
Value of 2 shares of DL (2 X 57.38)
114.76
Present Value of
each (W1)
130.17
3 redeemable debentures of Rs. 100
Since the present value of debentures is greater than the current
market price of DL shares, the offer is expected to be worth considering
by shareholders of DL. In case these debentures are marketable, there
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Answers
will be high chance that it will satisfy those shareholders too who are
interested in equity instrument.
Such shareholders will be able to
swap debentures with PL’s shares in market.
W1
PV of 3 debentures
of Rs. 100 each
17.14
Redeemable value
(Rs.)
8 year DF @ 11% PV
300
0.4339
130.17
EMH
(a)
Capital markets are said to be efficient when prices of securities in such
markets fully reflect all information about the company, the industry to
which it belongs and the economy as a whole. This means that any new
information about a company coming into the market is immediately
reflected in the price of the share of the company such that no investor can
make above average return on an investment.
In a supposedly efficient market, the price of a security is expected to
fluctuate randomly around its true or intrinsic value. Efficient simply means
security is price efficient. The price is right and represents the best
estimate of the security’s true value based on the available information.
Forms of efficiency:
The Weak Form: This form of efficiency implies that information about
past share price movement is already reflected in the current market price.
Therefore, the ability to forecast future prices cannot be enhanced based
on the use of past information alone.
The Semi-Strong Form: This form states that the current market price of
a security, fully and immediately reflects all publicly available information
including information from financial statements, Chairman’s report and
news items. Here, insider information is excluded.
The Strong Form: This form of efficiency implies that all pieces of
information both public and private (including insider information) are fully
and immediately reflected in the current market price of the security.
Insider information is said to be information that is known to management
but unknown to the public.
(b)
(i)
Weak form efficiency
The share price will not react to the announcement by the directors.
Share prices in a market with weak-form efficiency react to historical
data, not future expectations.
(ii)
Semi-strong form efficiency
If investors believe the estimate of an NPV of + Rs. 4,000,000, the
value of the company’s shares will increase by this amount (Rs.0.08
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per share) and rise to Rs. 4.08 on 12th May – the date that the
announcement is made to the market.
(iii)
Strong form efficiency
If investors believe the estimate of an NPV of + Rs. 4,000,000, the
value of the company’s shares will increase by this amount (Rs.0.08
per share) and rise to Rs. 4.08 on 1st May – the date that the
investment decision is taken and before it is formally announced to
the market.
17.15
X PLC AND Y PLC
(a)
(i)
Semi-Strong form efficient – Cash Offer
In semi-strong form efficient, shareholders know all the relevant
historical data and publicly available current information.
DAY 2
Value of X Plc. shares = (Rs. 3 x 30,000,000) i.e. Rs. 90,000,000
Value of Y Plc. shares (Rs. 6 x 80,000,000)
= Rs. 480,000,000
The decision of the private meeting does not reach the market, hence
share-prices will remain unchanged.
DAY 5
The takeover bid was announced, but no information is available yet
about the operating savings, hence, value of X Plc. shares will be
(Rs. 5 x 30,000,000) = Rs. 150,000,000
Value of Y Plc.
Rs.
Previous value (Rs. 6 x 80,000,000)
Value of X Plc acquired (Rs. 3 x 30,000,000)
480,000,000
90,000,000
570,000,000
Less purchase consideration for X Plc
150,000,000
420,000,000
Number of shares (÷)
80,000,000
Price per share
Rs. 5.25
The number of shares in Y Plc. after acquisition remains unchanged
since cash is paid.
DAY 10
The market learns of the potential savings of Rs. 80,000,000. Value
of X Plc. remains unchanged at Rs. 5 per share but the value of Y
Plc. will be as follows:
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Answers
Value of Y Plc.
Rs.
Previous value (R
420,000,000
Potential savings
80,000,000
500,000,000
(ii)
Number of shares (÷)
80,000,000
Price per share
Rs. 6.25
Semi-Strong form Efficient-Share Exchange Offer
Day 5
Value of Y Plc.
Rs.
Previous value (Rs. 6 x 80,000,000)
480,000,000
Value of X Plc. acquired (Rs. 3 x 30,000,000)
90,000,000
570,000,000
Less purchase consideration for X Plc
150,000,000
420,000,000
Number of shares in Y Plc
80,000,000 + (5/6 u 30,000,000)
105,000,000
Price per share
Rs. 5.43
Price per share of X Plc. will be 5/6 x 5.43 = Rs. 4.53
DAY 10
Rs.
Value of Y Plc
500,000,000
Value of X Plc. acquired (Rs. 3 x 30,000,000)
150,000,000
650,000,000
Number of shares in Y Plc
80,000,000 + (5/6 u 30,000,000)
105,000,000
Price per share
Rs. 6.29
Price per share of X Plc. will be 5/6 x 6.19 = Rs. 5.16
© Emile Woolf International
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The Institute of Chartered Accountants of Pakistan
Business finance decisions
(b)
(i)
Strong Form Efficient – Cash Offer
In strong form efficient, the market would become aware of all the
relevant information when the private meeting takes place. The value
per share would change as early as day 2 to
X Plc. = Rs. 5.00
Y Plc. = Rs. 6.25
The share prices would then remain unchanged until day 20.
(ii)
Strong Form Efficient-Share Exchange Offer
Also, for the same reason, the price per share would change on day 2
to
X Plc. = Rs. 5.16, Y Plc. = 6.19 and these prices would remain
unchanged till day 20.
© Emile Woolf International
306
The Institute of Chartered Accountants of Pakistan
Answers
CHAPTER 18 – MERGERS AND ACQUISITIONS
18.1
ACQUISITION
(a)
The earnings of Little next year are expected to be Rs. 86,000. A forward
P/E multiple of 8.0 could be applied to this estimate, and the valuation of
the equity shares in Little would be:
Rs. 86,000 × 8.0 = Rs. 688,000.
(b)
The cost of equity of Big is expected to be:
6% + 1.60 (11 – 6)% = 14%.
The WACC of Big is expected to be:
[35% × 7.4 (1 – 0.30)] + (65% × 14)
= 10.913%.
(c)
Since Little is in the same industry as Big, it is probably appropriate to use
the WACC of Big to obtain a DCF-based valuation of Little. The WACC of
10.913% will be rounded to 11%.
The cash flows from the acquisition of Little must be calculated.
Sales
Cash costs
Year 1
Rs.
200,000
(120,000)
Year 2
Rs.
280,000
(160,000)
Year 3
Rs.
320,000
(180,000)
––––––––
––––––––
––––––––
120,000
(30,000)
(10,000)
140,000
(40,000)
(10,000)
––––––––
––––––––
80,000
(20,000)
(10,000)
Capital allowances
Interest
––––––––
Taxable profit
Tax at 30%
50,000
(15,000)
––––––––
Profit after tax
Profit after tax
Add back capital allowances
––––––––
Cash flow
90,000
(27,000)
––––––––
35,000
56,000
63,000
––––––––
––––––––
––––––––
35,000
20,000
56,000
30,000
63,000
40,000
––––––––
––––––––
––––––––
55,000
(25,000)
Asset replacement
80,000
(24,000)
86,000
(30,000)
103,000
(35,000)
––––––––
––––––––
30,000
56,000
––––––––
68,000
––––––––
––––––––
––––––––
Cash flows will increase by 4% each year from Year 4 onwards.
The dividend growth valuation model can be used to calculate the Year 3
value of these cash flows, using a growth rate of 4% and a cost of capital of
11%:
Year 3 value of cash flow s from Year 4
© Emile Woolf International
307
$68,000 1.04
= Rs. 1,010,286
0.11 0.04
The Institute of Chartered Accountants of Pakistan
Business finance decisions
The expected cash flows can now be converted in to a present value:
Year
Cash flow
Discount
factor at
11%
PV
Rs.
1
2
3
4 onwards
Rs.
30,000
56,000
68,000
1,010,286
0.901
0.812
0.731
0.731
27,030
45,472
49,708
738,519
–––––––
Total value
860,729
–––––––
18.2
ADAM PLC
(a)
(i)
Market Value of Adam Plc
Using the Gordon’s growth model: g = rb
where
r
=
return on investment
b
=
retention ratio
g
=
rb, r = 0.16, b = 0.25
g
=
0.16 x 0.25
= 4%
Future dividend in one year
=
Rs. 300m x 1.04 =
Rs. 312 million
=
•Ǥ͵12,000,000
d
=
0.12-0.04
r g
=
Rs. 3.9 billion
r
=
0.21, b = 2/3
g
=
0.21 x 2/3 = 14%
Market Value
Market value of Eve Plc
Future dividend in one year = 50m x 1.4 = Rs. 57 million
MV
=
=
(ii)
•Ǥͷ7,000,000
0.18-0.14
Rs. 1.425 billion
Adam Plc earning in 1 year
Rs.’m
Rs. 400m x 1.04
416
Eve Plc earning in 1 year
Rs. 150 m x 1.14
171
587
Dividend in 1 year
© Emile Woolf International
308
=
Rs. 587m x 0.4
=
Rs. 234,800,000
The Institute of Chartered Accountants of Pakistan
Answers
If r = 0.2 and b = 0.6
g = 0.2 x 0.6 = 0.12
Market Value =
Maximum Price
•Ǥʹ34,800,000
0.16-0.12
=
Payable for Eve Plc =
=
(b)
(i)
= Rs. 5,870,000,000
Rs. 5,870,000,000 – Rs. 3,900,000,000
Rs. 1,970,000,000 or
Rs. 1.97 billion
White Knight
A situation in which the target company looks for a friendly company
whose offer is more appealing for the takeover bid.
(ii)
Shark Repellant
This involves amending the company’s memorandum and articles of
association in such a way that makes the takeover difficult for the
acquiring company.
An example is increasing the margin of majority votes required at an
Annual General Meeting called to approve such a take-over.
(iii)
Pac-man Defence
An anti-takeover strategy in which the target company tries to buy up
the shares of the acquiring company.
(iv)
Poison-Pill
A strategy sometimes employed by target companies in a take-over
bid to reduce the attractiveness of their securities to the prospective
acquiring companies. This is often done by enlarging the outstanding
shares of a target company through a new issue of shares to its
shareholders at a discount to the market price, thus making the takeover quite expensive to the prospective acquiring company.
(v)
Golden Parachutes
This refers to provisions in the executives’ employment contract that
call for payment of severance pay or other compensation should they
lose their jobs as a result of a successful takeover.
18.3
D LIMITED
(a)
The following are the various options available to D Limited:
(i)
© Emile Woolf International
Merger: The term merger is normally used to describe a situation
where two businesses come together by agreement to form a single
entity. Here, the two companies go into liquidation and an entirely
new one is formed to acquire their shares. Alternatively, the life of
one company is, in law, terminated (still in physical existence as a
division or branch) and the other one remains.
309
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Business finance decisions
(ii)
Take over: This describes a situation where one business acquires
control of another business. This usually occurs when one company
buys shares in another company substantial enough to acquire a
controlling interest in the other company. The former is called the
bidding company while the latter is called the target company.
(iii)
Consolidation: This is a combination of two or more companies into
a new company.
‰
Exchange ratio = 40/80 = 1:2 (one share of D Limited exchanges for
every two shares of F Limited.)
‰
Number of shares to be issued to shareholders of F Limited =
3,000,000/2 = 1,500,000
‰
Combined post merger number of shares = 5,500,000 (i.e. 4,000,000
+1,500,000)
‰
Combined post acquisition earnings = Rs. 29,000,000 (i.e. Rs.
20,000,000 + Rs. 9,000,000)
‰
Post merger earnings per share of enlarged company –D Limited =
Rs. 29,000,000/5,500,000 = Rs. 5.27
(b)
Comment:
The merger improves the Earnings Per Share (EPS) of D Limited from Rs.
5.00 to Rs. 5.27. However, the shareholders of F Limited suffer a drop in
their EPS from Rs. 3.00 to Rs. 2.64 (i.e. Rs. 5.27/2)
18.4
CLOONEY PLC AND PITT PLC
(a)
Price Earnings, P/E ratio computation before merger:
EPS
=
PAT
§
·
¨
¸
No
of
shares
©
¹
=
150
600
P/E
ratio
=
Share price
EPS
=
•Ǥͷ
•Ǥ0.25
Clooney
Plc
Pitt Plc
Rs.’m
Rs.’m
= 0.25
= 20 times
(b)
30
150
= 0.2
•Ǥʹ
•Ǥ0.2Ͳ
= 10 times
P/E ratio computation for the group after merger
P/E ratio =
© Emile Woolf International
Share price
Earning Per Share
310
Total market value
Total Earnings
The Institute of Chartered Accountants of Pakistan
Answers
EPS
=
Total Earnings
No of shares
No of shares = (600 + 75)m = 675 million shares.
Total earnings
Rs.’m
Clooney Plc
150.0
Pitt Plc
30.0
Increased cash flow
4.5
184.5
Therefore EPS
=
184,500,00 0
= Rs.0.27
675,000,00 0
If EPS
=
Rs.0.27 and
Share price
=
Rs. 5.50 (given)
Then, the Price Earning (P/E) Ratio of the group would be:
•Ǥͷ.50
=
•Ǥ0.27
(c)
20.37 times
Calculation of market capitalisation of Clooney Plc (after merger)
Rs.
million
Capitalisation of Clooney Plc (pre-merger)
= 600m x Rs. 5.0
Capitalisation of Pitt Plc (pre-merger)
= 150m x Rs. 2.0
Value of merger benefit (given)
Therefore, capitalisation of group after merger
(d)
=
3,000
=
=
=
300
45
3,345
Calculation of dividend income of the holder of 1 share in Pitt Plc before
and after merger assuming Clooney Plc maintains the same dividend per
share as before the merger.
Dividend per share (DPS) of holder of 1 share in Pitt Plc:
Before merger:
DPS
=
=
•Ǥʹ1,000,000
150,000,000
Rs.0.14
After merger: assuming Clooney Plc maintains the same dividend per
share as before the merger:
DPS
=
=
© Emile Woolf International
60,000,000
600,000,000
Rs.0.10
311
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Business finance decisions
Therefore, a holder of 1 share in Pitt Plc will now get Rs.0.1 ÷2 = Rs.0.5
since the ratio of offer is 2:1.
Comment:
The shareholders of Pitt Plc would be losing Rs.0.09, that is, (0.14 – 0.5) on
each of their shareholding since they were earning Rs.014 on each holding,
before the merger.
18.5
NELSON PLC
(a)
Calculation of market values of the two companies using Gordon’s growth
model (rb)
(i)
Nelson Plc:
Using rb model where:
r=
return on investment
b=
proportion of earnings retained
r=
21% or 0.21
b
2
/3
growth = rb = 21% x 2/3 = 14%
Future dividend in one future year
=
Rs. 75,000 x 1.14
=
Rs. 85,500
Market Value (MV)
=
=
=
=
(ii)
•Ǥͺ5,500
18%-14%
•Ǥͺ5,500
4%
•Ǥͺ5,500
0.4
Rs. 2,137,500
Drake Plc
g = rb where: r = 16%
b = ¼ (or 0.25)
‫ ׵‬g = 0.16 x 0.25 = 0.04
= 4%
Dividend in the next one year
= Rs. 450,000 x 1.04
= Rs. 468,000
Market Value
=
=
=
© Emile Woolf International
312
•ǤͶ68,000
12%-14%
•ǤͶ68,000
0.08
Rs. 5,850,000
The Institute of Chartered Accountants of Pakistan
Answers
(b)
Maximum Price Nelson Plc should pay for Drake Plc:
Earnings in the next one year:
Rs.
Nelson Plc Rs. 225,000 x 1.14
=
256,500
Drake Plc Rs. 600,000 x 1.04
=
624,000
880,500
Dividend in the next one year (100% - 60%) = 40%
=
Rs. 880,500 x 0.4 = Rs. 352,200
r
=
20%; b = 60%
‫׵‬
g = rb = 20% x 60%
=
12%
Market Value after Merger
M/V
=
=
=
•Ǥ͵52,200
0.16-0.12
•Ǥ͵52,200
0.04
Rs. 8,805,000
Maximum Price = Market Value after merger – Market value before merger
18.6
=
Rs. 8,805,000 – Rs. 2,137,000
=
Rs. 6,667,500
HALI LTD
(a)
To:
Board of Directors
From: XYZ
Date: June 4, 2016
Sub: Report on Demerger Scheme
Dear Sirs,
My comments on demerger scheme are as follows:
a) If the company opts for demerger scheme, the ordinary shareholder
will get a surplus of Rs. 28.64 million details of which are as follows:
Rupees
in million
Value of OCX
276.59
Annexure ‘A’
Value of OCY
281.05
Annexure ‘B’
Total value of both the companies
557.64
© Emile Woolf International
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Business finance decisions
Current market value of HL
Equity (5 million shares of Rs. 90)
Debt (40+30*130/100)
450.00
79.00
Surplus
529.00
28.64
As the demerger of two separate divisions has increased the value of two
companies by approx. 5.4% as compare to current market value, it
appears that HL should float the two divisions separately.
(b)
The following additional information and analysis would be relevant in the
process of decision making:
(i)
Other details of items included in the profit and loss statement and
information such as expected future growth could have been
useful in determining the operating cash flows more accurately.
(ii)
The model uses operating cash flows. A more reliable estimate of
value might be free cash flows, taking into account the investment
needs of both divisions.
(iii)
The cash flow forecasts as they stand, appear to take no account
of uncertainty. It would have been helpful to see best-worst
estimates, simulations or other techniques that incorporate
uncertainty.
(iv)
The risk profiles of the companies have not been considered.
(v)
Individual divisions might be more vulnerable to takeovers
because of their smaller size.
(vi)
The views of the shareholders shall be important in reaching a final
decision.
(vii)
How will the decision impact on the company’s ability to negotiate
better terms with the suppliers, financial institutions, etc?
(viii)
The interests of other stakeholders may have to be taken into
account – what will employees feel about the split, will there be
fewer management opportunities available, and how will creditors
view their security?
Annexure A – Value of HX
Year
1
2
3 onward
Total
Rupees in million
Profit before tax and depreciation
39.00
42.00
44.00
Depreciation
12.00
11.00
13.00
Profit before tax
27.00
31.00
31.00
Tax (30%)
(8.10)
(9.30)
(9.30)
Profit after tax
18.90
21.70
21.70
© Emile Woolf International
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Answers
Add back depreciation
12.00
11.00
13.00
One time costs
(8.50)
-
-
Net cash inflow
22.40
32.70
34.70
Discount factors (12% [W1])
0.8929
0.7972
6.6432
Present value of net cash inflows
20.00
26.07
230.52
2
3 onward
W2
276.59
W1: Adjustment of inflation in the discount rate
1 money rate
1 inf lationrate
1.18
1.05
12.38% say 12%
W2: Present value factor from year 3 to infinity
1
0.8929 0.7972
0.12
6.6432
Annexure B – Value of HY
Year
1
Total
Rupees in million
Profit before tax and depreciation
26.00
34.00
36.00
9.00
10.00
11.00
Profit before tax
17.00
24.00
25.00
Tax (30%)
(4.25)
(6.00)
(6.25)
Profit after tax
12.75
18.00
18.75
Add back depreciation
9.00
10.00
11.00
One time costs
(8.50)
-
-
Net cash inflow
13.25
28.00
29.75
Discount factors (10% [W3])
0.9091
0.8265
8.2644
Present value of net cash inflows
12.05
23.14
245.87
Depreciation
W4
281.05
`
W3: Adjustment of inflation in the discount rate
1 money rate
1 inf lationrate
1.18
1.07
10.28% say 10%
W4: Present value factor from year 3 to infinity
1
0.9091 0.8265 8.2644
0.1
© Emile Woolf International
315
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Business finance decisions
18.7
URD PAKISTAN LIMITED
To: The Management
From: Chief Financial Officer
Date: June 8, 2016
Subject: Report on selection of financing option
In response to your advice to explore the financing options for the acquisition of
100 % shareholding in CHI Limited, we have carried out an analysis to
determine the debt equity ratio and price of our shares after the acquisition
under the following options:
‰
Where the acquisition is financed through debt only
‰
Where the acquisition is financed by debt and equity in the ratio of 60:40.
Analysis of financing options
The following calculations suggest that both the options are feasible to the
company as the acquisition of CHI Limited would result in increase in the
shareholders wealth as shown below.
Existing
(Without
acquisition)
Option 1
(acquisition
thru 100%
debt)
Option 2
(acquisition
thru 60% debt
and 40%
equity)
Debt equity ratio after
acquisition
W1
42 : 58
59 : 41
47 : 53
Per share price (Rs.)
W3
52.50
64.00
57.75
Increase in
shareholders’ wealth
because of acquisition
(Rs. in million)
W4
460.00
388.50
-
The relevant workings are enclosed as annexure.
Under option 1, the shareholders’ wealth would increase by Rs. 460 million as
compared to the projected position under the existing conditions. However,
accepting option 1 would increase the debt equity ratio of the company.
If we are willing to accept the higher gearing level, option 1 should be selected.
Otherwise, we should opt for option 2 as in that case there is only a slight
increase in debt equity ratio which is more than adequately compensated by a
significant increase in the shareholders’ wealth.
© Emile Woolf International
316
The Institute of Chartered Accountants of Pakistan
Answers
Other factors to be considered
Besides the increase in profitability and shareholders wealth, URD should also
consider the following aspects:
Stability of cash flows/high risk due to financial leverage
A company with stable cash flows can handle more debt because there is
constant stream of cash inflows to cover periodic interest payments. Hence, in
case the company is satisfied with the stability of future cash flows, it can opt for
option 2.
Future plans
The company may have future plans of further expansion. While comparing the
option (i) and (ii) the management should assess that if it plans to obtain further
financing in the near future, it may not be feasible to opt for 100% debt financing
at this stage.
Stock market conditions
In case the company decides to go for option 2, it should study the stock market
conditions to ensure that it would be able to generate sufficient interest in the
right issue, before making any commitments as regards investment in the new
venture.
Due Diligence
It seems that URD is relying on the audited accounts for making the above
decision. Even if the audited accounts show a true and fair view, it is not
necessary that CHI would be in a position to repeat the performance in future
years. It is therefore recommended that URD should carry out a proper due
diligence exercise before making a final decision.
ANNEXURE TO THE REPORT
W1:
Debt equity ratio after acquisition
Existing
(Without
acquisition)
Debt (Rs.
million)
Equity (Rs.
million)
Option 1
(acquisition
thru 100% debt)
in
1,500
*13,075
*22,445
(W2) 2,100
2,100
*32,730
59 : 41
47 : 53
in
Debt equity ratio
42 : 58
*1
1,500 + 1,575 (W2)
*2
1,500 + 1,575 (W2) x 60% = 2,445
*3
© Emile Woolf International
Option 2
(acquisition thru
60% debt and
40% equity)
2,100 + 1,575 (W2) x 40% = 2,730
317
The Institute of Chartered Accountants of Pakistan
Business finance decisions
W2:
Value of URD and CHI
Rs. in million
URD
Net profit after tax
Number of shares outstanding (Rs. 400m
÷ Rs. 10)
300.00
250.00
40.00
7.50
Earnings per share (300 ÷ 40)
P/E ratio (Rs. 52.5m/Rs. 7.5)
7.00
Value of the company
W3:
CHI
x
90
%
2,100.00
6.30
1,575.00
Post-acquisition price under each option
If the acquisition is financed by debt only
Net profit after tax-URD
Net profit after tax-CHI
Additional Interest expense (Rs. 1,575m (W2) x 18% x 65%
Rs. in
million
300.00
250.00
(184.28)
Revised profit after tax
365.72
Value of URD after acquisition (Rs. 365.72 x 7 (W2))
2,560.0
4
Post-acquisition value
40m shares)
per share after (Rs. 2,560.04m ÷
64.00
If the acquisition is financed by debt and equity in the ratio
of 60:40.
Rs. in
million
300.00
Net profit after tax-URD
Net profit after tax-CHI
Additional interest expense (Rs. 1,575 (W2) x 60% x 17%
(W4) x 65%)
Revised profit after tax
250.00
(104.42)
445.58
Shares in
million
Existing shares in issue
Number of right shares to be issued (Rs. 1,575 (W2) × 40%
© Emile Woolf International
318
40.00
14.00
The Institute of Chartered Accountants of Pakistan
Answers
÷ 45)
Total number of shares to be outstanding after right issue
54.00
Revised EPS after right issue (Rs. 445.58 million (W4) ÷
54m shares)
Revised market value after right issue (Rs. 8.25 x 7)
W4:
PKR
57.75
Market Capitalization
Option 1
(acquisition
thru 100%
debt)
Market capitalization
– Option 1: (40 x 64)
Option 2
(acquisition
thru 60% debt
and 40%
equity)
2,560.00
– Option 2: (54 x 57.75)
Less: Funds injected by the shareholders
(14 × 45 )
Less: Existing market capitalization
Increase in shareholders wealth
18.8
PKR
8.25
3,118.50
-
(630.00)
(2,100.00
)
(2,100.00)
460.00
388.50
FF INTERNATIONAL
Advantages of growth by acquisition
(a)
(i)
The company may be able to grow much faster than would be
possible through purely organic development. This is particularly
true if the company is seeking to expand into a new product or
market area when acquisition will allow the company to gain
technical skills, goodwill and customer contracts which would take it
a long time to develop by itself.
(ii)
A larger company with a better spread of products, customers and
markets faces a lower level of operating risk than a small company
which may be more dependent on a small number of customers and
suppliers. Acquisition will therefore allow the company to reduce its
operating risk more quickly. This effect is enhanced if the company
is using acquisition as a mean of diversification into new
product/market areas.
(iii)
Acquisition may permit the company to make operating economies
through the rationalization and elimination of duplication in areas
such as research and development, debt collection and corporate
relations.
© Emile Woolf International
319
The Institute of Chartered Accountants of Pakistan
Business finance decisions
(iv)
Acquisition may allow the company to achieve a better level of asset
backing if it has a high ratio of sales to assets.
Disadvantages of growth by acquisition
(b)
(i)
If the acquisition is being made for strong strategic reasons, there
may be competition between bidding companies which may force
the price to rise to a level which may not be justifiable on financial
grounds.
(ii)
Acquisition may involve significant reorganizations cost which may
result in lower earnings at least in the short term.
(iii)
The acquisition may lead to inequalities in returns between the
shareholders of the bidding and the target companies. Quite often
the shareholders in the target company do disproportionately well as
compared to the shareholders in the bidding company.
Determination of Optimal Sales Level
Existing
sales
Market share
Market size (Rs. 1,000 ÷
30%) x 1.1
Price increased
by
Price
decreased
by
5%
10%
10%
30%
23%
20%
45%
Rs. m
Rs. m
Rs. m
Rs. m
3,667
3,667
3,667
3,667
1,100.00
843.41
733.40
1,650.15
-
42.17
73.34
(165.02)
1,100.00
885.58
806.74
1,485.13
(363.00)
(278.33)
(242.02)
(544.55)
(55.00)
(42.17)
(36.67)
682.00
565.08
528.05
858.07
Depreciation - New plant &
mach. (150m ÷ 5)
-
-
-
(30.00)
Interest expense (Rs. 150m
-
-
-
Sales (Market Share ×
Market Size) x 1.1
Add/(Less): Effect of price
change
Net sales
Less: Variable cost of sales
(Rs. 363 ÷ 1,100) × Sales
without price effect
Less: Variable selling and
admin exp
(Rs. 250 × 20% *1.1) ÷
1,100 × Sales
(82.51)
Less: Incremental fixed
costs
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× 15%)
(22.50)
Incremental profit
682.00
565.08
528.05
805.57
* (Rs. 430m - Rs. 100m)
The company can achieve the optimal sale level by reducing
10% price.
Determination of cash flow gap
Cash flow
Year 1
Growth rate
Operating profit excluding
depreciation (W1)
One time cost of
employees lay off
Net operating cash flow
Fin. charges - Long term
loan (W2)
Financial charges - Short
term loan (1,000 × 14%)
Net cash flow before
taxation
Taxation (W3)
Net cash flow
Year 2
Year 3
Year 4
Year 5
10%
10%
10%
10%
10%
634.52
697.97
767.77
844.55
929.01
-
-
-
-
767.77
844.55
(102.00)
(76.50)
(51.00)
(140.00)
(140.00)
(140.00)
267.02
455.97
(17.11)
(97.79)
249.91
358.18
(100.00)
534.52
(127.50)
697.97
551.27
(126.38)
(140.00)
653.55
(157.07)
424.89
496.48
-
-
-
Reduction in short term
debt
(300.00)
Reduction in long term
debt (W2)
(170.00)
(170.00)
(170.00)
Increase in working
capital (W4)
(194.05)
(59.40)
(65.34)
(Deficit ) to be filled in by
cash
(414.14)
128.78
Net deficit
(414.14)
(285.36)
189.55
(170.00)
(71.88)
254.60
929.01
(25.50)
(140.00)
763.51
(190.05)
573.46
-
(170.00)
(79.07)
324.39
(95.81)
W1: Determination of operating profit at optimal sales level
Rs. in million
Contribution margin
805.57
Less: Fixed costs of sales (other than depreciation) (Rs.
25m ×1.1)
(27.50)
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Less: Selling and admin expenses
Payroll costs [Rs. 160m × 75% × 1.1)
(132.00)
Other fixed costs ((Rs. 250m × 80%) - 25m 160m) × 1.1 × 70%
(11.55)
Operating profit (excluding depreciation)
634.52
W2: Financial charges on long term loan
Year 1
Opening balance – principal
700.00
Addition
150.00
850.00
Repayment
Year 2
Year 3
680.00
Year 5
510.00
340.00
170.00
-
-
-
510.00
340.00
170.00
680.00
Year 4
(170.00)
(170.00)
(170.00)
(170.00)
(170.00)
Closing balance
680.00
510.00
340.00
170.00
-
Mark-up expense @ 15%
127.50
102.00
76.50
51.00
25.50
W3: Taxation
Year 1
Net cash flow before taxation
Less: Depreciation (75+25+30)
Year 2
267.02
(130.00)
Taxable income
137.02
Carry forward tax losses
(80.00)
455.97
(130.00)
325.97
Year 3
Year 4
551.27
653.55
(130.00)
(130.00)
(130.00)
421.27
523.55
633.51
-
-
421.27
523.55
633.51
-
Year 5
763.51
-
Tax profit/(loss)
57.02
Tax @ 30%
17.11
97.79
126.38
157.07
190.05
Existing
Year 1
Year 2
Year 3
Year 4
Year 5
1,000.00
1,485.13
1,797.00
1,976.70
325.97
W4: Increase in working capital
Sales
1,633.64
Increase in sales
485.13
148.51
163.36
179.70
Additional working
capital required (40%
of increased sales)
194.05
59.40
65.34
71.88
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(c)
Determination of maximum bid price
Year 0
Net operating cash flows
(from above)
-
Add: Financial charges
Add: Cash flow deficit
-
Add: Changes in working
capital
Year 1
Year 2
Year 3
Year 4
Year 5
249.91
358.18
424.89
496.48
573.46
267.50
242.00
216.50
191.00
165.50
(414.14)
128.78
189.55
95.81
-
(194.05)
(59.40)
(65.34)
(71.88)
(79.07)
Terminal value*
-
-
-
-
-
5,968.52
Cash flows
-
(90.78)
669.56
765.60
711.41
6,628.41
Discounting factor at
18%
1
0.8475
0.7182
0.6086
0.5158
0.4371
PV
-
(76.94)
480.88
465.94
366.95
2,897.28
NPV (Maximum bid
price)
4,134.11
*(573.46 + 165.5) x (1+5%) ÷ (18% - 5%)
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CHAPTER 19 – FOREIGN EXCHANGE RATES
19.1
INTEREST RATE PARITY
The rates are quoted as direct rates.
The direct quotes interest rate parity formula is as follows:
ൌൈ
(a)
ͳ ൅ ‹ୢ
ͳ ൅ ‹୤
GBP/USD = 1.8000 × (1.035/1.05) = 1.7743
(Note: the interest rate is lower for the dollar than for sterling, therefore the
dollar should increase in value over time against sterling.)
GBP/EUR = 1.5000 × (1.025/1.05) = 1.4643
EUR/USD = 1.2000 × (1.035/1.025) = 1.2117
(b)
GBP/USD = 1.8000 × (1.035/1.05)3 = 1.7240
GBP/EUR = 1.5000 × (1.025/1.05)3 = 1.3954
EUR/USD = 1.2000 × (1.035/1.025)3 = 1.2355
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CHAPTER 20 – INTERNATIONAL INVESTMENT DECISIONS
20.1
CASH FLOWS FROM A FOREIGN PROJECT
Year
0
1
2
3
4
Expected exchange rate
5.00 × (1.05/1.03)1
5.00 × (1.05/1.03)2
5.00 × (1.05/1.03)3
5.00 × (1.05/1.03)4
5.00
5.10
5.20
5.30
5.40
Cash flows in
francs
Cash flows in £
(45,000,000)
10,000,000
20,000,000
25,000,000
10,000,000
(9,000,000)
1,960,784
3,846,154
4,716,981
1,851,852
Tutorial note: You may have calculated the exchange rate to three or more
decimal places. Here, the exchange rate has been estimated to just two decimal
places.
These cash flows in sterling should be discounted at the WACC.
Year
0
1
2
3
4
NPV
Cash flow
Discount factor
PV
£
(9,000,000)
1,960,784
3,846,154
4,716,981
1,851,852
9%
1.000
0.917
0.842
0.772
0.708
£
(9,000,000)
1,798,039
3,238,462
3,641,509
1,311,111
+ 989,121
The NPV in sterling is positive. The project is financially viable and should be
undertaken.
20.2
LAHORE PHARMA PLC
(a)
Determination of the expected future exchange rates based on the
information that ringgit is expected to appreciate by 2% per annum. Value
of ringgit today in terms of rupees is Rs. 22 per ringgit. This is expected to
appreciate by 2% per annum. Therefore:
Year
0
Spot
1
22(1.02)
2
2
3
22 (1.02)
22(1.02)3
=
Rs.
22.00
=
22.44
=
=
22.89
23.35
In order to determine the cost of capital in ringgit using Interest Rate Parity,
the following formula is adopted.
ଵାோி
ଵାோ஽
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where RF= Foreign Rate, RD = Domestic Rate, S = Spot Rate and F =
Future Rate
ଵାோி
ଵା଴Ǥଵ଴
ଶଶ
= ଶଶǤସସ
22.44 (1+RF) = 22(1.1)
22.44RF = 22(1.1) − 22.44
:. RF =
ଶଶሺଵǤଵሻିଶଶǤସସ
ଶଶǤସସ
=
ଶସǤଶିଶଶǤସସ
ଶଶǤସସ
RF = 7.8% ؆ 8%
Computation of NPV in ringgits.
Cash flow
Year (ringgit’m)
Discount factor
(8%)
Present
value
(ringgit’m)
0
(160)
1.0000
(160.000)
1
80
0.9259
74.072
2
96
0.8573
82.301
3
64
0.7938
50.803
Net present value
47.176
Since the NPV at the required rate of return gives a positive value, the
project is viable.
(b)
Reasons why business organisations engage in cross-border investment
include the following:
(i)
To take advantage of new markets e.g coca-cola, electronics etc
(ii)
To seek raw material e.g. Us Oil companies establishing business in
nations where there are oil deposits.
(iii)
In search of new technology.
(iv)
Avoidance of political and regulatory hurdles.
(v)
Diversification.
(vi)
Tax avoidance.
(vii) Possible benefits from variations in exchange rates.
(viii) Protection of profit margin.
(ix)
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20.3
FOREIGN INVESTMENT
(a)
Calculate the NPV of the project in the currency of the investment, using a
discount rate appropriate to the investment.
The annual tax allowance on the cost of the equipment is 25% of 1,000,000
Francs = 250,000 Francs each year for 4 years.
This will result in tax savings of 100,000 Francs (40% × 250,000 Francs)
each year in years 2 – 5.
Year
Equipment
Tax saved
on capital
allowances
Cash profit
Tax on cash
profit
Net cash
flow
0
1
2
3
4
5
FR
(1,000,000)
FR
FR
FR
FR
FR
100,000
500,000
100,000
500,000
100,000
500,000
100,000
500,000
(200,000)
(200,000)
(200,000)
(200,000)
400,000
400,000
400,000
(100,000)
(1,000,000)
DCF factor
at 16%
Present
value
500,000
1.000
0.862
0.743
0.641
0.552
0.476
(1,000,000)
431,000
297,200
256,400
220,800
(47,600)
NPV = + 157,800
(b)
Dividend payments
Year
1
2
3
4
5
FR
500,000
FR
500,000
FR
500,000
FR
500,000
(200,000)
(200,000)
(200,000)
(200,000)
100,000
100,000
100,000
100,000
400,000
400,000
400,000
400,000
Dividend
(50%)
Retained
200,000
200,000
200,000
200,000
200,000
200,000
200,000
200,000
Year
1
2
3
4
5
FR
FR
FR
FR
FR
200,000
200,000
200,000
200,000
800,000
Cash profit
Tax on profit
Tax saving
from capital
allowance
Profit after tax
FR
800,000
(c)
Dividend
in FR
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Exchange
rate
Dividend
in $
(d)
3×
(1.10/1.04)
3×
2
(1.10/1.04)
3×
3
(1.10/1.04)
3×
4
(1.10/1.04)
3×
5
(1.10/1.04)
= 3.1731
= 3.3561
= 3.5498
= 3.7546
= 3.9712
63,030
59,593
56,341
53,268
201,450
The cost of buying the equipment in Year 0 = FR1,000,000/3.00 =
$333,333
Year
0
1
2
3
4
5
NPV
Cash flow
Equipment
Dividend
Dividend
Dividend
Dividend
Dividend
PV
Discount factor at
10%
$
(333,333)
63,030
59,593
56,341
53,268
201,450
$
(333,333)
57,294
49,224
42,312
36,382
125,100
(23,021)
1.000
0.909
0.826
0.751
0.683
0.621
The project is not worthwhile because it has a negative NPV in dollars,
even though it has a positive NPV in Francs. This is because:
20.4
‰
the restriction on dividend payments delays returns to the parent
company
‰
the Franc is expected to fall in value against the dollar over the next
five years
GOLD LIMITED
Years
0
1
2
3
4
5
Evaluation of
investment in
Bangladesh
BDT in million
Total contribution (W1)
490.05
Less: Fixed overhead
(Expense x Inflation %)
Operating cash flows
Tax at 35%
Tax savings on depreciation
(W3)
Land
(80.00)
Building
(30.00)
Plant and machinery
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718.74
790.62
869.68
(423.50) (465.85) (512.44)
(563.68)
66.55
252.89
278.18
306.00
(23.29)
(88.51)
(97.36)
(107.10)
16.73
13.38
10.71
8.56
(82.50)
(126.50)
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Working capital (W4)
(22.00) (111.10)
(13.31)
(14.64)
After tax realizable value (W7)
Net cash flow
(16.11)
322.16
(51.11)
164.45
176.89
513.48
0.8250
0.8103
0.7958
0.7816
0.7676
Net cash flow (PKR in million) (130.95) (280.00)
(63.68)
206.65
226.32
668.94
0.87
0.75
0.66
0.57
0.49
Present value (PKR in million) (130.95) (243.22)
(47.76)
136.39
129.00
327.78
Exchange rate BDT / PKR
(W2)
(110.00) (231.00)
0.8400
Discount factor (@ 15.12%)
(PKR in million) (W5)
Net present value (PKR in
million)
1.00
171.24
Evaluation of investment in Sri Lanka
LKR in million
Pre-tax cash flow
(annual increase by 8% from
year 0)
29.16
40.82
44.09
47.62
51.43
Tax @ 25%
(7.29)
(10.21)
(11.02)
(11.91)
(12.86)
(2.88)
(3.11)
(3.36)
(3.63)
(3.92)
Cost of acquisition
(90.00)
Plant and machinery
(18.00)
Working capital (W4)
(36.00)
After tax net realizable value
Net cash flow
167.9
(144.00)
18.99
27.50
29.71
32.08
202.55
Exchange rate LKR / PKR
(W2)
1.3250
1.2777
1.2320
1.1880
1.1456
1.1047
Net cash flow from SISL in
(PKR in million)
(108.68)
14.86
22.32
25.01
28.00
183.35
-
(1.14)
(1.66)
(1.85)
(2.07)
(2.34)
Net cash flow (PKR in million) (108.68)
13.72
20.66
23.16
25.93
181.01
1.00
0.87
0.75
0.66
0.57
0.49
Present value (PKR in million) (108.68)
11.94
15.49
15.29
14.78
88.70
Additional tax @ 5% (W6)
(PKR in million)
Discount factor (@
15.12)(W5)(PKR in million)
Net present value (PKR in
million)
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W1: Contribution margin – Bangladesh
Sales price
300,000
Less: Variable costs
(165,000)
Contribution margin per unit
(BDT)
-
135,000
163,350
179,685
197,654
217,419
3,000
4,000
4,000
4,000
490.05
718.74
790.62
869.68
Production / sales units
Total contribution (BDT in
million)
W2: Computation of exchange rates for the next 5 years
BDT / PKR
0.8400
0.8250
0.8103
0.7958
0.7816
0.7676
LKR / PKR
1.3250
1.2777
1.2320
1.1880
1.1456
1.1047
4
5
Average mid market exchange rate BDT / PKR
Year 0:
0.8300 + 0.8500 = 1.680 ÷ 2 = 0.8400
Year 1-5:
Previous year x 1.10/1.12
Average mid market exchange rate LKR / PKR
Year 0:
1.3100 + 1.3400 = 2.650 ÷ 2 = 1.3250
Year 1-5:
Previous year x 1.08 / 1.12
Years
0
1
2
3
W3: Tax depreciation (BDT in million)
Opening balance
30.00
Machinery
-
Building
30.00
82.50
30.00
239.00
191.20
152.96
122.37
239.00
191.20
152.96
122.37
47.80
38.24
30.59
24.47
191.20
152.96
122.37
97.90
16.73
13.38
10.71
8.56
126.50
Less: 20%
depreciation
allowance
30.00
239.00
239.00
Tax saved at the rate
of 35%
W4 : Working capital
Bangladesh
BDT in million
Working capital ×
inflation factor
22.00
133.10
146.41
161.05
177.16
Increase in working
capital
22.00
111.10
13.31
14.64
16.11
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Sri Lanka
Working capital ×
inflation factor
LKR in million
36.00
38.88
41.99
45.35
48.98
52.90
36
2.88
3.11
3.36
3.63
3.92
Increase in working
capital
W5: WACC as discount factor
Cost of equity
Cost of debt
0.70 x 18% = 12.60%
0.30 x 12% x 70% = 2.52%
WACC
15.12%
W6 : Additional tax for income from Sri Lanka
Tax rate applicable in Pakistan is 5% higher than Sri Lanka. So income from Sri
Lanka will be subject to 5% additional tax.
----- LKR in million ----Pre-tax cash flow in
LKR (as above)
-
Exchange rate (W2)
Pre-tax cash flow in
PKR
1.33
-
Additional Tax in
Pakistan @ 5%
29.16
40.82
44.09
47.62
51.43
1.28
1.23
1.19
1.15
1.10
22.78
33.19
37.05
41.41
46.75
1.14
1.66
1.85
2.07
2.34
W7: After tax realizable value
Bangladesh
(BDT)
Sri Lanka
(LKR)
After tax realizable value of investment
145.00
115.00
Realization of working capital
177.16
52.90
322.16
167.90
Conclusion:
Gold Limited should invest in Bangladesh as it gives higher NPV.
20.5
GHAZALI LIMITED
To: Board of Directors
Date: 7 December 2016
Subject: Evaluation of proposed investment in Country Y
(a)
Net present value of the investment
The financial evaluation of the Country Y Project is based on estimates of
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the future nominal cash flows of the investment, in both Country X and Y. All
foreign cash-flows are converted to CX and total is discounted at a
shareholders' required rate i.e. 22% per annum. The theory of purchasing
power parity has been used to estimate future currency exchange rates.
This predicts that if currencies are allowed to float freely on the market, they
will adjust in the long run to compensate for differences in countries' inflation
rates.
The results show that the investment has an expected net present value of
approximately CX 81.252 million, which indicates that it is worthwhile and
should add to shareholder value.
Calculations
Growth Inflation
YEARS
0
Exchange rate (PY x 1.2 /
1.07)
1
2
3
45.000 50.470 56.600 63.480
CX in million
Cash flows in Country X
5%
Cash flows in Country Y
7%
(7.000) (0.535) (0.601) (0.675)
20% (17.778)
4.042
6.360
7.894
Total nominal cash flows
(24.778)
3.507
5.759
7.219
Discount factor @ 30.54%
[(1.22x1.07)-1]
1.000
0.766
0.587
0.450
Present value
(24.778)
2.686
3.381
3.249
Net present value as computed
above
(15.462)
Country X - NPV from Year 2 to
perpetuity
[(0.675 x 1.1235) ÷ (0.3054 *0.1235)] × 0.450
(1.876)
Country Y - NPV from Year 4 to
perpetuity
[(7.894 x 1.26) ÷ (0.3054 **0.26)] x 0.450
98.59
81.252
*Growth rate for Country X from year 4 to perpetuity [(1.07x1.05)1]=12.35%
**Growth rate for Country Y from year 4 to perpetuity [(1.20x1.05)1]=26%
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(b)
(c)
Risks and uncertainties
(i)
Large margins of potential error in the exchange rate prediction
(ii)
A slow payback: in present value terms the project will probably not
break even until Year 8 or 4.
(iii)
The economic uncertainties in Country Y which may affect adversely
on rate of inflation.
(iv)
Inappropriate projection of future cash flows specially the cash flows to
be generated in Country Y and cash flows expectation to perpetuity.
Management strategies
To counter the increase in local taxes
(i)
Negotiate tax concessions in advance
(ii)
Use transfer price strategies including royalties and management, to
minimize the impact of variation in Country Y taxable profits and
dividends
To counter the imposition of exchange controls
(i)
Make extensive use of local currency loans for financing
(ii)
Arranging currency swaps
(iii)
Back to back loans with other multinational companies and banks with
complimentary cash needs
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CHAPTER 21 – MANAGING FOREIGN EXCHANGE RISK (I)
21.1
FOREIGN EXCHANGE
(a)
A hedge against the risk can be obtained by entering into a forward rate
agreement to buy $750,000. The forward rate is the forward rate that
favours the bank. This is 1.8535 (and not 1.8543).
The cost of buying the dollars will be $750,000/1.8535 = £404,639.87.
(b)
Subtract a premium, add a discount.
Spot rate
Premium
Forward rate
1.3025
(0.0018)
1.3007
The $450,000 will be sold in exchange for €345,967.56 (450,000/1.3007).
(c)
Forward rates = 1.9757 – 1.9763
The rate for a company to buy sterling (sell dollars) is 1.9763.
Cost of buying £750,000 = 750,000 u 1.9763 = $1,479,750.
21.2
MONEY MARKET HEDGE
(a)
The company will receive $600,000 in six months, and will want to receive
sterling and pay dollars.
It can do this with a money market hedge by borrowing US dollars now.
The interest rate for six months in dollars is 3.5% × 6/12 = 1.75%. It will
need to borrow now:
$600,000/1.0175 = $589,680.59.
It can immediately exchange these dollars into sterling at the spot rate of
1.8800, to obtain:
$589,680.59/1.8800 = £313,659.89.
After six months, the dollar loan will be repayable with interest. The total
repayment will be $600,000, and the payment can be made from the
$600,000 received from the customer.
(b)
The company can do anything with the sterling it receives now from the
hedging transaction. If it chose to invest the cash for six months at 5% per
year (2.5% for six months), the investment of £313,659.89 would increase
to:
£313,659.89 × 1.025 = £321,501.39.
To avoid opportunities for arbitrage between the money markets and the
forward FX markets, the six-month forward exchange rate would therefore
need to be:
$600,000/£321,501.39 = 1.8662.
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21.3
DUNBORGEN
Forward exchange contract
The six-month forward rate is 1.566 – 1.574.
Dunborgen would need to buy $500,000, and the bank would charge a rate of
$1.566.
The cost to Dunborgen in euros in six months’ time = 500,000/1.566 = €319,285.
Money market hedge
The spot exchange rate is 1.602 – 1.606
Dunborgen could borrow euros now, convert them into dollars and put the dollars
on deposit for six months.
The six month interest rate for US dollar deposits = 2.0% u 6/12 = 1.0%.
To have $500,000 in six months time, Dunborgen would need to deposit:
$500,000 u (1/1.01) = $495,050.
The cost in euros of buying $495,050 spot = 495,050/1.602 = €309,020.
It is assumed that the euros to purchase the dollars spot would be obtained by
borrowing for six months at 4.8%. Interest for six months would be 4.8% u 6/12 =
2.4%.
The cost in euros to Dunborgen of a money market hedge, for comparison with
the cost of a forward contract, would therefore be:
€309,020 u 1.024 = €316,436.
Comparison of hedging methods
A money market hedge would be less expensive in this case, and is therefore
recommended as the method of hedging the currency risk exposure.
21.4
CURRENCY SWAP
(a)
Small company will want to borrow 3 million zants, but can borrow in
sterling at a rate that is 2% lower than the rate that the Zantland
counterparty can obtain. The Zantland counterparty presumably wants to
borrow in sterling (the equivalent of 3 million zants), but can borrow in zants
at a rate that is 0.5% lower than the rate that Small Company can obtain.
This provides an opportunity for credit arbitrage of 2% + 0.5% = 2.5%.
The bank would take 0.5% in fees, leaving 2% of net credit arbitrage for the
swap counterparties to share. Small Company would have three-quarters of
this amount, which is 1.5%.
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The swap arrangement might therefore be as follows:
Small Company
Zantland
counterparty
%
%
(6.5)
(ZIBOR + 1.5)
ZIBOR
6.5
Receive
6.0
ZIBOR
Net cost
ZIBOR + 0.5%
8.0
Borrow direct
Swap
Pay
Small company would pay 1.5% less than by borrowing direct (at ZIBOR +
2%) and the Zantland counterparty would borrow at 0.5% less than by
borrowing sterling direct at 8.5%.
(b)
It is assumed that 15% is the appropriate discount rate for evaluating the
project’s cash flows in sterling. (A DCF rate of 15% would be very low for
evaluating the cash flows in zants, considering the expected high rate of
inflation in Zantland.)
It is also assumed that the swap will be undertaken, and in Year 0 Small
Company will spend £333,333 (3 million zants at the spot rate of 9.00). At
the end of Year 3, it is assumed that Small Company will receive the same
amount (£333,333) on the termination of the currency swap, and a further
3,000,000 zants for the remainder of the sale price of the operations centre.
The project cash flows will therefore be as follows:
Year
0
£(333,333)
1
200,000 zants
at the end of Year 1 spot rate
2
200,000 zants
at the end of Year 2 spot rate
3
200,000 zants
at the end of Year 3 spot rate
3
3,000,000 zants
at the end of Year 3 spot rate
3
3,000,000 zants
at the swap rate of 9.00, therefore £333,333.
Year
Spot rate
Best case
Worst case
10% inflation
50% inflation
0
9.00
9.00
1
9.90
13.50
2
10.89
20.25
3
11.98
30.38
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Year
Cash
flow
DCF
factor
at
15%
zants
0
1
2
3
3
NPV
200,000
200,000
3,200,000
3,000,000
1.000
0.870
0.756
0.658
0.658
Best case
Worst case
Cash
PV
Cash
PV
flow
flow
£
£
£
£
(333,333) (333,333) (333,333) (333,333)
20,202
17,576
14,815
12,889
18,365
13,884
9,877
7,467
267,112
175,760
105,332
69,308
333,333
219,333
333,333
219,333
+ 93,220
(24,336)
Conclusion
On the basis of the assumptions used, the project would have a positive
NPV if inflation in Zantland exceeds inflation in the UK by 10% per year, but
will have a negative NPV if inflation in Zantland exceeds inflation in the UK
by 50% per year.
There is consequently an element of risk in the project due to uncertainty
about the spot exchange rate, and this risk element should be assessed
more closely before a decision is taken about the investment.
21.5
MOMIN INDUSTRIES LIMITED
(a) If shipment is made in accordance with the Schedule
Purchases
Month
Per ton
cost
(bhat)
Qty.
(ton)
Amount
(bhat)
Conv.
rate
Rupees
June (Buy
one month
forward)
50,000
4,000
200,000,000
2.33
466,000,000
July (Buy two
month
forward)
50,000
6,000
300,000,000
2.31
693,000,000
1,159,000,000
Sales
Month
Per ton
revenue
(US $)
Qty.
(ton)
Amount
(US$)
Conv.
rate
Rupees
July (Sell two
month fwd.)
2,000
4,000
8,000,000
65.77
526,160,000
Aug. (Sell three
month fwd.)
2,000
6,000
12,000,000
66.10
793,200,000
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1,319,360,000
Profit on transactions
(sales minus purchases)
160,360,000
Less: Commission costs (0.01%)
(247,836)
160,112,164
(b) If the shipment is delayed for a period of two month
Purchases
Month
Per ton
cost
(bhat)
Qty.
(ton)
Amount
(bhat)
Conv.
rate
Rupees
June (Buy
one month
forward)
50,000
4,000
200,000,000
2.33
466,000,000
July (Buy two
month
forward)
50,000
6,000
300,000,000
2.31
693,000,000
July
(Cancelled at
spot)
50,000
2.29
(687,000,000)
July (Buy 2
months
forward)
50,000
2.28
684,000,000
(6,000) (300,000,000)
6,000
300,000,000
1,156,000,000
Sales
Month
Per ton
revenue
(US $)
Qty.
(ton)
Amount
(US$)
Conv.
rate
Rupees
July (Sell two
month
forward)
2,000
4,000
8,000,000
65.77
526,160,000
Aug. (Sell
three month
forward)
2,000
6,000
12,000,000
66.10
793,200,000
July (Buy 1
month
forward)
2,000
(6,000)
(12,000,000)
65.96
(791,520,000)
July (Sell 3
month
forward)
2,000
6,000
12,000,000
66.38
796,560,000
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1,324,400,000
Profit on transactions
(sales minus purchases)
168,400,000
Less: Commission costs (0.01%)
(475,044)
167,924,956
(c) If shipment is cancelled on July 31, 2016
Purchases
Month
Per ton
cost
(Bhat)
Qty.
(ton)
Amount
(bhat)
Conv.
Rate
Rupees
June (Buy one
month
forward)
50,000
4,000
200,000,000
2.33
466,000,000
July (Buy two
month
forward)
50,000
6,000
300,000,000
2.31
693,000,000
July
(Cancelled
at spot)
50,000
2.29
(687,000,000)
(6,000) (300,000,000)
472,000,000
Sales
Month
Per ton
revenue
(US $)
Qty.
(ton)
Amount
(US$)
Conv.
rate
Rupees
July (Sell two
month forward)
2,000
4,000
8,000,000
65.77
526,160,000
Aug. (Sell three
month fwd.)
2,000
6,000
12,000,000
66.10
793,200,000
July (Buy 1
month
forward)
2,000
(6,000)
(12,000,000)
65.96
(791,520,000)
527,840,000
Profit on transactions (sales minus purchases)
Less: Commission costs (0.01%)
55,840,000
(247,836)
55,592,164
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21.6
QALAT INDUSTRIES LIMITED
Net Position
Three months
Export – Receivable
€98,500
Import - (Payable)
€77,000
€(223,500)
Net position – Receivable/(Payable)
(i)
Six months
€98,500
€ (146,500)
Forward Market
Three months contract
Rs.
Receipt of export amount at the end
of third month
€ 98,500 x
123.62
12,176,570
€ 146,500 x
123.54
18,098,610
Six months contract
Net payment at the end of sixth
month
(ii)
Money Market
Three months payment
Since the company is expecting to receive €. Therefore, to hedge currency
rate risk we need to convert the same into definite Rupee receivables.
Borrow in Euro and invest in Rupee, so that at the end of third month repay
Euro borrowing from export proceeds and receive a definite Rupee
amount.
€
Borrow a sum which has a compound value of € 98,500
at the end of third month: 98,500 ÷ (1 + 5% ÷ 4)
97,284
Rs.
Convert € to Rupees at spot (€ 97,284 × Rs. 124.22) for
investment
12,084,618
Invest for three months now which after 3 months would
amount to:
Rs. 12,084,618 × (1 + 6.5% ÷ 4)
12,280,993
Six month payments
Since the company is expecting to pay €. Therefore, to hedge currency
rate risk we need to convert this payable into definite Rupee payables.
Borrow in Rupee a sum equivalent to the present value of € 146,500.
Invest that Euro sum, so that at the end of sixth month Euro will be
available for net import payment and we will have a definite Rupee
payable.
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Investment required for a sum which has compound
value of € 146,500 at the end of sixth month:
€
146,500 ÷ (1 + 3% ÷ 2)
144,335
Rs.
To invest, borrow equivalent Rupee to buy Euro at spot (€
144,335× Rs. 124.52)
17,972,594
Rs. 17,972,594 used for buying € 145,335 would require a
definite rupee repayment of compound value at the end
of sixth month:
17,972,594 × (1 + 11% ÷ 2))
18,961,087
Recommendation:
Feasible option for 3 month net payment -------------------------------> Money Market
Feasible option for 6 month net payment -------------------------------> Forward Cover
21.7
SILVER LIMITED
(a)
Net receipt due at the end of first quarter
US $
Receipt due
1,020,000
Payment due
(775,000)
245,000
(i) Net receipt under forward contract
= 245,000 x (MYR 3.03 – MYR 0.071)
= 245,000 x 2.959
= 724,955
(ii) Net receipt under money market hedge
Borrowed in US $ =
245,000
§ 7.2% ·
1 ¨
¸
© 4 ¹
245,000
1.018
Received now in MYR =
240,668 x 3.03 = MYR 729,224
Received in 3 months time =
729,224 (1+(6.6%/4) = MYR
741,256
240,668
Net payment due at the end of second quarter
US $
Receipt due
1,224,000
Payment due
(1,347,000)
(123,000)
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(i) Net payment under forward contract
= 123,000 x (MYR 3.11 – MYR 0.164)
= 123,000 x 2.946
= 362,358
(ii) Net payment under money market hedge
Lent in US $ =
123,000
§ 5.8% ·
1 ¨
¸
© 2 ¹
123,000
1.02900
Paid now in MYR =
119,534 x 3.11 = 371,751
Paid in 6 months time =
§ § 7.9% · ·
371,751x ¨¨1 ¨
¸ ¸¸
© © 2 ¹¹
119,534
386,435
Conclusion:
‰
For the first quarter, SL would be better off with money market hedge
as it would receive more MYR than with a forward contract.
‰
For the second quarter, forward exchange contract produces a lower
net payment in MYR.
(b) SL wishes to lend and so will buy 5 (MYR 15,000,000 / MYR 3,000,000) interest
rate February Futures.
(i) If interest rates fall by 0.75% and March Futures price increases by 1%, the
net hedging position of the interest rate future would be as follows:
MYR
Future outcome
MYR 15,000,000 x 6/12 x 1%
75,000
Receipt in spot market
(MYR 15,000,000 x 5.25% x
6/12)
393,750
Net outcome
468,750
Target outcome (6% x 6/12 x MYR 15,000,000).
450,000
Gain on hedging through interest rate futures
18,750
(ii) If interest rates rise by 1% and March Futures price decreases by 1%, the
net hedging position of the interest rate future would be as follows:
MYR
Future outcome
15,000,000 x 6/12 x 1%
(75,000)
Receipt in spot market
(MYR 1,500,000 x 7% x 6/12)
525,000
Net outcome
450,000
Target outcome
450,000
No gain or loss (100% efficient)
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21.8
KHALDUN CORPORATION
(a) USA
The full receipt i.e. US $ 1.50 will be hedged.
Hedging through Forward Contract
KC would sell US $ 1.5 million three months forward at Rs. 87.0 per US $
and receive
Rs. 130.5 million.
Hedging through Money Market
To obtain US $ 1.5 million, borrow now: (1.5 million ÷
[1+(5.20%x3/12)] =
$ 1.48
US $ will be converted into Rs. at spot: US $ 1.48 million x
Rs. 86.56 =
Rs. 128.11
Rs. 128.11 million will be invested in Pakistan: Rs.
128.11x[1+(8.5%x3/12)]
Rs. 130.83
UK
The receipts and payments can be netted off : (£ 5.10 - £ 4.0) = £1.10
Hedging through Forward Contract
KC should buy £ 1.1 million three months forward at Rs. 136.18 per £
and pay Rs. 149.8 million.
Hedging through Money Market
To earn £ 1.1 million, invest now: £ 1.1 million ÷ [1+(5.00%
x 3/12)] =
£1.09
Purchase £ at spot rate : £ 1.09 x Rs. 135.13
Rs. 147.29
Borrow Rs. 147.29 million in Pak at 10.5%: Rs. 147.29m x
[1+(10.5% x 3/12) =
Rs. 151.16
Payments
(b)
Receipts
KC-(Pak)
KA-(USA)
Total
KB-(UK)
Rs. in million
KC-(Pak)
-
131.00
688.30
819.30
KA-(USA)
130.02
-
390.06
520.08
KB-(UK)
539.84
242.93
-
782.77
Total receipts
669.86
373.93
1,078.36
2,122.15
(819.30 )
(520.08 )
(782.77 )
(2,122.15)
149.44
146.15
(295.59)
Total
payments
Net payment
/ (receipts)
-
Without multilateral netting, the group companies would have required to
pay Rs. 2,122.15 million as shown in the above table. On account of
multilateral netting, the amounts payable and receivable were netted and
as a result the amount required to be paid/received was reduced to Rs.
295.59 million i.e. 13.93% of the gross amount, resulting in savings of
transaction/hedging costs.
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CHAPTER 22 – MANAGING FOREIGN EXCHANGE RISK (II): CURRENCY
FUTURES
22.1
CURRENCY FUTURES
(a)
The company must make a payment in US dollars in May. It must therefore
buy dollars to make the payment.
Using futures, the company will therefore buy dollars and sell euros. It will
therefore sell euro/US dollar futures, which are for €125,000 each.
At the futures price of 1.2800, the amount of euros to sell in exchange for
$640,000 is:
$640,000/1.2800 = $500,000.
The number of contracts to sell is therefore: $500,000/$125,000 per
contract = 4.0 contracts.
The company will sell 4 June contracts at 1.2800.
(b)
It will close its position in May, when the futures price is 1.2690.
The value of 1 tick for this contract is 125,000 × $0.0001 = $12.50.
Original selling price
1.2800
Buying price to close the position
1.2690
Gain per contract
0.0110
Total gain on futures position = 4 contracts × 0.011 × $125,000 = $5,500.
The French company must pay $640,000 to its supplier. It has $5,500 profit
from closing the futures position. It therefore needs an additional ($640,000
– $5,500) = $634,500.
It must buy these dollars at the spot rate of 1.2710. The cost in euros will
be $634,500/1.2710 = €499,213.
The effective exchange rate for the payment of $640,000 is therefore:
$640,000/€499,213 = US$1.2820/€1.
This is close to the price at which the futures were originally sold. However,
the hedge is not perfect because the position was closed before the
settlement date for the contract.
22.2
MORE CURRENCY FUTURES
(a)
The US company must make a payment in sterling in January. It will sell
the sterling it receives in exchange for dollars.
Using futures, the company will therefore sell sterling and buy dollars. It will
therefore sell sterling/US dollar futures, which are for £62,500 each.
The number of contracts to sell is therefore: £400,000/£62,500 per contract
= 6.4 contracts.
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The company will therefore sell either 6 or 7 March contracts at 1.8600.
In the answer in (b), it is assumed that the company will sell 6 March
sterling/US dollar futures.
(b)
The US company will close its position in January, when the futures price is
1.8420.
The value of 1 tick for this contract is 62,500 × $0.0001 = $6.25.
Original selling price
Buying price to close the position
Gain per contract
1.8600
1.8420
0.0180
Total gain on futures position = 6 contracts × 180 ticks × $6.25 = $6,750.
The US company will receive £400,000 which it will sell at the spot rate of
1.8450.
$
From sale of £400,000 spot at $1.8450/£1
Profit on futures position
Total income
738,000
6,750
744,750
The effective exchange rate for the £400,000 received is therefore:
$744,750/£400,000 = US$1.8619/£1.
This is close to the price at which the futures were originally sold. However,
the hedge is not perfect because the position was closed before the
settlement date for the contract.
22.3
BASIS
(a)
On 1st March: Days to settlement of the June futures contracts = 31 + 30 +
31 + 60 = 122 days.
On 1 March
Spot rate
Futures price
Basis
1.8540
1.8760
0.0220
The basis is 220 points, with the futures rate higher than the spot rate.
The basis at the end of June when the futures reach settlement will be 0.
It is assumed that basis will decrease to zero at a constant rate per day.
The basis will therefore reduce by (220 points/122 days) = 1.80328 points
per day.
At close of trading on 30th April, there are (31 + 30) 61 days remaining to
the settlement of the June futures. The expected basis at this date is
therefore:
1.80328 points per day × 61 days = 110 points.
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At the end of 30th April
Spot rate
Expected basis
Expected futures price (higher)
(b)
1.8610
0.0110
1.8720
At close of trading on 15th June, there are 15 days remaining to the
settlement of the June futures. The expected basis at this date is therefore:
1.80328 points per day × 15 days = 27 points.
At the end of 30th April
Spot rate
Expected basis
Expected futures price (higher)
22.4
1.8690
0.0027
1.8717
IMPERFECT HEDGE AND BASIS
(a)
There is a loss on the underlying currency exposure, because sterling
weakens in value between 20th April and 20th July.
$
At 20th April: expected value of £625,000 receivable (at
1.8050)
At 20th July: actual value of £625,000 received (at
1.7700)
Loss on underlying currency exposure
1,128,125
1,106,250
21,875
The futures position is opened on 20th April by selling futures contracts
(selling British pounds and buying dollars). The US company should sell 10
contracts (£625,000/£62,500 per contract). When the position is closed on
20th July, there is a gain on the position.
$
20th April: Open position – Sell at
20th July: Close position – Buy at
Gain on underlying currency exposure
1.7800
1.7600
0.0200
Total gain (10 contracts) = 10 contracts × 200 ticks per contract × £6.25 per
tick = $12,500.
The futures position has failed to provide a perfect hedge, resulting in a net
‘loss’ of $9,375.
Effective exchange rate
$
Revenue from sale of £625,000 spot on 20th July
(at 1.7600)
Gain on futures position
Total dollar income
1,100,000
12,500
1,112,500
Effective exchange rate = $1,112,500/£625,000 = $1.7800.
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(b)
22.5
The reason why the hedge is not perfect in this case is explained by the
existence of basis. When the futures position was opened, the basis was
250 points (1.8050 – 1.7800). When the position was closed, the basis was
100 points (1.7700 – 1.7600). The spot price has moved in value during the
three months by more than the movement in the futures price, by 150
points. The value of this difference is $9,375 (10 contracts × 150 ticks per
contract × £6.25 per tick).
CURRENCY HEDGE
(a)
Hedging with a forward exchange contract
Only the net exposure should be hedged. This is a net payment of
€(2,650,000 – 540,000) = €2,110,000.
The entity will need to buy euros in three months’ time. The three-month
forward rate for the contract would be 1.4443 (the rate more favourable to
the bank).
Cost in sterling = €2,110,000/1.4443 = £1,460,915.
(b)
Money market hedge
The company must pay €2,110,000 in three months’ time. To create a
money market hedge, it must therefore buy euros spot and invest them for
three months at 3.4% per year. The amount of euros invested, plus
accumulated interest, must be worth €2,110,000 after three months.
It is assumed that the three-month investment rate for euros is 3.4% × 3/12
= 0.85%.
The amount of euros to invest now is therefore €2,110,000/1.0085 =
€2,092,216.
These must be purchased spot at 1.4537, and the cost in sterling will be:
€2,092,216/1.4537 = £1,439,235.
With a forward FX contract, the payment of £1,460,915 will be made in
three months’ time. With a money market hedge, the payment of
£1,439,235 would happen immediately. It can therefore be argued that an
additional cost of a money market hedge is the loss of interest (opportunity
cost) from investing £1,439,235 for three months at 5.6% per year. The lost
interest would be £1,439,235 × 5.6% × 3/12 = £20,149.
The overall cost of a money market hedge would therefore be £1,439,235 +
£20,149 = £1,459,384.
(c)
Currency futures hedge
The company must pay euros. It needs to buy euros to make the payments.
The futures are denominated in euros; therefore the company will buy
futures.
The number of contracts required = €2,110,000/€100,000 per contract =
21.1 contracts. The company should probably buy 21 contracts.
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The payments are due in October. The company should therefore buy
futures with the next settlement date following. It should buy December
contracts at 0.6929.
The remaining €10,000 that is not hedged by futures can be purchased
forward at 1.4443, at a cost of £6,924.
If the basis is 0 when the futures position is closed in October, the effective
exchange rate for the €2,100,000 will be £0.6929 = €1, or £1 = €1.4432.
The net cost in sterling will be:
£
€2,100,000 at $1.4432/£1
€10,000 at €1.4443/£1
Total cost in sterling
1,455,100
6,924
1,462,024
The money market hedge is the cheapest method of hedging.
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CHAPTER 23 – MANAGING FOREIGN EXCHANGE RISK (III): OPTIONS
23.1
TRADED EQUITY OPTIONS
(a)
The investor should buy put options on TBA shares.
Strike
price
950
1,000
Number of options
purchased with £12,000
Cost per option
(2,000 shares × £0.15)
(2,000 shares × £0.50)
£
300
1,000
40
12
The investor could purchase 12 put options at a strike price of 1,000 (£10)
or 40 put options at a strike price of 950 (£9.50).
Tutorial note:
The investor’s decision will depend on how far he expects the share price
to fall. The options with a strike price of 1,000 (£10) are currently in the
money but the investor can only buy 12 such contracts. As the share price
falls, the intrinsic value of these options rise but the intrinsic value of the
options with a strike price of 950 (£9.50) will remain at zero until the share
price falls below £9.50. For any fall below this the investor will gain more
from these 40 contracts than he would from the 12 other contracts.
The share price at which the investor would be indifferent between the two
options can be found as follows:
Let x = the share price at which each course of action would yield the same
return.
The investors return would be equal when:
12(1,000 – x) = 40 (950 – x)
12,000 – 12x = 38,000 – 40x
28x = 26,000
x = 928.57 (£9.29)
If the investor expects the share price to fall below this he should invest in
40 put options with a strike price of 950.
If the investor expects the share price to fall but not below £9.29 he should
invest in 12 put options with a strike price of 1,000.
(b)
If the share price is 910 at expiry and the investor still holds the options, the
options will be exercised. It is assumed that he buys the options at 950.
Traded equity options are settled by physical delivery. The investor would
need to buy shares at 910 and exercise the option to sell them at 950.
£
Buy 40 × 2,000 shares at 910
Buy 40 × 2,000 shares at 950
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728,000
760,000
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Profit on exercise
Cost of options
Net profit on speculative investment
32,000
12,000
20,000
(Note: This calculation of the profit ignores the time value of money. The
options are paid for when they are bought, but the profit is made only when
the options are exercised).
Traded equity options can be bought and sold on the exchange, and the
investor is likely to sell the put options before they expire, making a profit
on the sale. As the options become increasingly in-the-money, their market
value will increase.
23.2
Currency options
(a)
Hedging risk exposure
In September, the UK company will want to sell dollars and buy sterling (to
convert its dollar receipts into sterling).
Since it wants to buy sterling in six months’ time, it should buy call options
with a September expiry.
If the strike price is $1.8500, the sterling equivalent of $2 million =
£1,081,081 (2,000,000/1.85).
The contract size is £31,250; therefore for a perfect hedge, the company
would want to buy 34.6 contracts (1,081,081/31,250).
Since this is not possible, it should buy either 34 or 35 contracts. In the
answer that follows, it is assumed that the company will buy 35 options.
Premium cost = 35 × 31,250 × $0.019 = $20,781.25.
To pay the premium, the company would have to buy $20,781.25 spot, at a
sterling cost of £11,340.38.
(b)
Expiry
At the expiry date, the options are in-the-money if the spot exchange rate is
1.9200. They will therefore be exercised, at a profit of $0.07 per £1 (1.9200
– 1.8500).
Gain on exercise of 35 option contracts = 35 × 31,250 × $0.07 =
$76,562.50.
The total dollar income of the company will therefore be $2,076,562.50.
This can be exchanged into sterling at the spot rate, to obtain £1,081,543
($2,076,562.50/1.9200).
The option premium cost was £11,340, therefore ignoring the time value of
money, the net revenue for the company is £1,081,543 – £11,340 =
£1,070,203.
This gives an effective exchange rate for the $2 million dollar receipts of
1.8688 (2,000,000/1,070,203).
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23.3
DEF SECURITIES LIMITED (DEF)
DEF is not hedging a position but has entered into options contracts with a view
to making a profit on the deal.
For a call option, this would involve exercising the call option (buying the shares)
and then selling the shares at the spot rate on the open market.
For a put option, this would involve exercising the option (selling the shares) and
then buying shares at the spot rate on the open market in order to complete the
deal.
This is referred to as squaring a position. Of course DEF would only do this if the
options were in the money at the date that they are exercisable. It must
determine this by comparing the prices at which the option is exercised to the
spot price of the underlying security.
Complications
This example provides information about futures rates. Thus the company could
square off the transactions with actual shares or by entering into futures contracts
(which in effect result in actual shares at a locked in price).
Note that the call option on the SPL shares is an American option. This means
that it can be exercised at any time up to the end of its duration.
The put option on the DESC shares is a European option. This means that it can
only be exercised at a specified date.
Workings
Call option on SPL shares
SPL
(spot rate)
Rupees
Sale proceeds on the open market
(Rs. 170 x 100,000)
(Rs. 173 × 100,000)
Less: Cost of acquisition
(from exercising the option)
(Rs. 155 x 100,000)
Gain/ (loss) if option is exercised
SPL
(future rate)
Rupees
17,000,000
17,300,000
(15,500,000)
(15,500,000)
1,500,000
1,800,000
Put option on DESC shares
DESC
(spot rate)
Rupees
Sale proceeds
(from exercising the option)
(Rs. 3.50 × 5,000,000)
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DESC
(future rate)
Rupees
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Less: Cost of acquisition on the open market
(Rs. 4.25 x 5,000,000)
(Rs. 4.35 × 5,000,000)
(21,250,000)
Gain/ (loss) if option is exercised
(21,750,000)
(3,750,000)
(4,250,000)
Conclusion:
The best strategy for the company is:
DEF should square its position in SPL shares by exercising the option and
selling the shares at the future price as it gives the highest return.
DEF should not exercise option of DESC shares as this will result in loss to the
company.
23.4
ALPHA AUTOMOBILES LIMITED
Method 1: Hedge using forward contract
AAL will have to buy JPY to make this payment
Amount to pay in three months’ time
JPY
175,000,000
Forward contract amount ሾ ͳ͹ͷǡͲͲͲǡͲͲͲ ൈ ͳǤͻͶͻ͵ሿ ൌ
Rs.
341,127,500
Method 2: Hedge using money market
To earn JPY 1 million, invest now ൣ ͳ͹ͷǡͲͲͲǡͲͲͲ ൊ
൫ͳ ൅ ሺ͵Ψ ൊ ͵ሻ൯൧
JPY
173,267,327
Purchase JPY at spot ሺ•Ǥ ͳ͹͵ǡʹ͸͹ǡ͵ʹ͹ ൈ •Ǥ ͳǤͻ͵͵ͻሻ
Rs.
335,081,683
Borrow rupees to buy JPY ሺ•Ǥ ͵͵ͷǡͲͺͳǡ͸ͺ͵ ൈ ሺͳ ൅ ሺͺΨ ൊ ͵ሻሻ
Rs.
344,017,195
Method 3: Futures market hedge
Futures can mature at the given dates only. Since the amount is to be paid on
September 30, the contract with maturity date of October 2016 would be chosen.
No of futures contracts to buy ሺ ͳ͹ͷǡͲͲͲǡͲͲͲ ൊ
ͳͲͲǡͲͲͲሻ
1,750
Buy 1,750 futures of Sep. 2016 ሺ•Ǥ ͳǤͻͶʹͳ ൈ ͳͲͲǡͲͲͲ ൈ
ͳǡ͹ͷͲሻ
Rs.
339,867,500
Financing cost of margin ሺͳǡͲͲͲ ൈ ͳǡ͹ͷͲ ൈ ͺΨ ൈ ͵Ȁͳʹሻ
Rs. 35,000
Rs.
339,902,500
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Method 4: Hedging using an option
Since we need to pay in JPY, we would have to buy call option expiring after the
transaction date i.e. October 31, 2016.
No. of options contracts to buy ሺ ͳ͹ͷǡͲͲͲǡͲͲͲ ൊ
ʹͷͲǡͲͲͲሻ
700
Buy 700 contracts of Sep 2016 ሺ•Ǥ ʹͷͲǡͲͲͲ ൈ ͳǤͻ͵ͳͷሺ െ
ͳሻ ൈ ͹ͲͲሻ
Rs.
338,012,500
Financing cost of premium ሺͲǤͲͳͳͷ ൈ ʹͷͲǡͲͲͲ ൈ ͹ͲͲ ൈ ͺΨ ൈ
͵Ȁͳʹሻ
Rs. 40,250
Rs.
338,052,750
W1: Determination of Exercise Price
The cheapest option including premium cost from October 2016 contracts is
worked out as follows:
Exercise
price
Total
cost
Premium
Remarks
Rs
1.90
0.0355
1.9355
1.91
0.0232
1.9332
1.92
0.0115
1.9315 Cheapest
Conclusion
Hedging using option is the cheapest option and should be selected.
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CHAPTER 24 – MANAGING INTEREST RATE RISK
24.1
FRA
(a)
The company wants to borrow in three months’ time for a period of six
months; therefore to create a hedge with an FRA, it must buy a 3v9 FRA.
The interest rate for the FRA is 3.97%.
‰
The company will borrow in three months’ time at the current LIBOR
rate plus 0.50%.
‰
The FRA will be settled in three months’ time.
x
If the six-month LIBOR rate is higher than 3.97%, the company
will receive a payment from the bank to settle the FRA. The
amount of this payment is the value of the difference between
the FRA rate of 3.97% and the LIBOR rate.
x
If the six-month LIBOR rate is lower than 3.97%, the company
will make a payment to the bank to settle the FRA, for the value
of the difference between the two rates.
The effect of the FRA is therefore to ‘lock in an effective interest rate
of 3.97% + 0.50% = 4.47%.
Tutorial note: For example, if the LIBOR rate in three months is
5.5%, the situation will be as follows:
%
Company borrows at LIBOR + 0.50%
Company receives from settlement of FRA (5.50 – 3.97)
Effective interest cost
6.00
(1.53)
4.47
This is the FRA rate + 0.50%.
(b)
24.2
An FRA works on the same principles as an interest rate coupon swap. The
main difference is that an FRA is for one interest period only, although a
company can arrange a series of FRAs. A coupon swap is longer-term, and
covers several settlement dates.
SWAP
The company should enter into a four-year interest rate coupon swap in which it
receives the floating rate and pays the fixed rate (5.25%).
The effective interest rate will change from floating rate to fixed rate, as follows:
%
Bank loan interest
Swap
Pay
Receive
Effective rate
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(5.25)
LIBOR
(6.50)
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24.3
CREDIT ARBITRAGE
%
Entity A can borrow more cheaply at a fixed rate by (7.25 – 6.35)
0.90
Entity A can borrow more cheaply at a floating rate by (1.25 – 0.75)
Difference
Bank’s profit
Net benefit to share between the two entities
0.50
0.40
0.10
0.30
If the entities share the benefit equally, each will be able to reduce its effective
cost of borrowing by (0.30/2) 0.15%.
‰
Entity A wants to borrow at a floating rate. It can borrow directly at LIBOR +
0.75%. By borrowing at a fixed rate and swapping into a floating rate, its
effective interest rate will be LIBOR + 0.75% – 0.15% = LIBOR + 0.60%.
‰
Entity B wants to borrow at a fixed rate. It can borrow directly at 7.25%. By
borrowing at a floating rate and swapping into a fixed rate, its effective
interest rate will be 7.25% – 0.15% = 7.10%.
For Entity A, the arrangement could be as follows:
%
Borrow at a fixed rate
Swap payments
Pay
Receive (balancing figure)
Effective interest cost
(6.35)
(LIBOR)
5.75
(LIBOR + 0.60)
For Entity A, the arrangement would be as follows:
%
Borrow at a fixed rate
Swap payments
Pay (balancing figure)
Receive
Effective interest cost
(LIBOR + 1.25)
(5.85)
LIBOR
(7.10)
The bank’s profit would come from the difference between the fixed rate received
from Entity B (5.85%) and the fixed rate paid to Entity A (5.75%).
This assumes that the two Entities each arrange their swap with the bank, and
not directly with each other.
24.4
CREDIT ARBITRAGE
Company X
%
Borrow:
Fixed rate
Swap
Receive fixed
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6.27
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Company Y
%
Borrow:
Floating rate
Swap
Pay fixed
(LIBOR + 1.50)
(6.30)
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Pay floating
Net cost
Cost of variable rate
borrowing
(LIBOR)
Receive floating
LIBOR
(LIBOR + 0.98)
Net cost
Cost of fixed rate
borrowing
(7.80)
(LIBOR + 1.25)
Saving in cost
24.5
0.27
Saving in cost
(8.00)
0.20
HEDGING WITH STIRS
The company wants a hedge against the risk of higher interest rates. It should
therefore sell short-term interest rate futures.
The borrowing period will begin in February; the company should therefore buy
March futures, which have the next settlement date following the start of the loan
period.
The planned borrowing period is 5 months, but with futures, the notional deposit
period is only 3 months. To get round this difficulty, the number of futures
contracts should be adjusted.
The number of March futures to sell =
£4.5 million 5 months
u
£500,000 3 months
= 15 contracts.
Conclusion
The company should sell 15 March short sterling futures.
24.6
MORE HEDGING WITH STIRS
(a)
The company wants a hedge against the risk of higher interest rates. It
should therefore sell short-term interest rate futures.
The borrowing period will begin in February; the company should therefore
buy March futures, which have the next settlement date following the start
of the loan period.
The planned borrowing period is 4 months, but with futures, the notional
deposit period is only 3 months. To get round this difficulty, the number of
futures contracts should be adjusted.
The number of March futures to sell =
$12 million 4 months
u
3 months
$1 million
= 16 contracts.
Conclusion
The company should sell 16 March eurodollar futures at 93.70.
(b)
When the futures are sold, the basis is:
Spot LIBOR rate (100 – 5.5)
Futures price
Basis
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0.9450
0.9370
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It is now the end of October. The March futures will reach settlement date
in five months’ time.
If we assume that the basis will reduce from 80 points at the end of October
to 0 by the end of March at an equal amount each month, by the end of
January the basis should be:
2 months to settlement
u 80 points = 32 points
5 months original time to settlement
The futures price is lower than the spot price.
At the beginning of February, if the three-month LIBOR rate is 7.5%, the
futures price should be:
Spot LIBOR rate (100 – 7.5)
Basis
Futures price
0.9250
0.0032
0.9218
The futures position will be closed out, as follows:
Selling price in October
Buying price to close
Gain
0.9370
0.9218
0.0152
The gain is 152 points or 1.52%
The futures hedge is a perfect hedge, and the effective cost of borrowing
can therefore be calculated as follows:
$
Borrow $12 million at
Gain on futures position
Net effective borrowing cost
7.50
(1.52)
5.98
The net effective borrowing cost is 5.98%.
(Note: This differs from the rate in the futures contracts sold in October. In
October, the interest rate in the sold futures was 6.30% (100 – 93.70). The
difference is 32 points, which is the amount of the basis risk. Here, the
company has benefited from the basis to obtain a lower borrowing cost).
24.7
FRAS AND FUTURES
(a)
FRAs
The company can use an FRA to fix the interest rate receivable on £8.2
million. A 4v9 FRA is required, and the bank will offer a rate of 4.52%.
The company will therefore fix a rate of 4.52% for LIBOR and if it can invest
at LIBOR + 0.40% this means that the effective investment rate will be
4.92%.
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Futures
The company wants to fix an interest rate for income, so it should buy
futures. The money for investment will be received at the end of July, so
September futures should be used.
The company should buy (£8.2 million /£500,000) × (5 months/3 months) =
27.33 futures contracts, say 27 futures, and the price is 95.35.
(b)
FRAs
At the end of July when the £8.2 million, the company will invest the money
for 5 months. If it can still obtain a rate of LIBOR + 0.40%, it will invest the
money at 4.65%.
The FRA contract must also be settled, as follows:
%
(4.25)
4.52
0.27
Pay LIBOR
Receive
Profit on settlement
The company will receive a payment on settlement of the FRA equivalent to
0.27% in interest, which means that its effective interest income from
investing the money for 5 months will be 4.65% + 0.27% = 4.92%.
Futures
When the futures contracts were purchased on 1st April, basis was 95.35 –
95.00 = 0.35. This is 0.05833 per month (0.35/6 months). Assuming basis
changes by a constant amount each month, the expected basis at the end
of July (2 months to the end of September) is 0.117.
The expected futures price at the end of July if LIBOR is 4.25% is therefore:
95.75 + 0.117 = 95.867.
The futures position will be closed as follows:
Close: sell at
Purchase price
Profit
95.867
95.350
0.517
Total profit on 27 contracts = 51.7 × £12.50 × 27 = £17,449.
The company can invest £8.2 million + £17,449 for 5 months at 4.65%
(LIBOR + 0.40%) and total interest will be £159,213 (£8,217,449 × 4.65% ×
5/12).
On the money received of £8.2 million, this represents an effective interest
rate of (£159,213/£8.2 million) × (12/5) = 0.047 or 4.7%.
In this particular case, FRAs would be a better way of hedging the interest
rate risk than futures.
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24.8
INTEREST RATE HEDGE
(a)
Futures
The company wants a hedge against the risk of a rise in two-month interest
rates. It should therefore sell futures. Since the interest period will be 2 months
and futures are for a three-month deposit, the quantity of futures sold should
be:
(£21 million/£500,000) × 2/3 = 28 contracts.
The loan period will begin in mid-June; therefore sell 28 June contracts, at
a price of 94.610.
Options on futures
The company will want options to sell futures; therefore it should buy put
options on 28 June futures. The premium cost will depend on the strike
price chosen. (Since the options are needed for two months, apply a factor
of × 2/12).
Strike price
94750
95000
Premium
(£21,000,000 × 0.500% × 2/12)
(£21,000,000 × 0.850% × 2/12)
£17,500
£29,750
FRA
The company should buy a 3v5 FRA, for a notional principal amount of £21
million. The FRA rate will be 5.38%.
(Note: The FRA rate is more favourable than the futures rate of 5.39% (100
– 94.610). The company would therefore prefer to buy an FRA than sell
futures. However, it might prefer to buy put options on futures rather than
buy an FRA).
In mid-June, the company will borrow £21 million for two months. If the
LIBOR rate is 6%, it will borrow at 6.75% (LIBOR + 0.75%) for two months.
Futures
The futures price in mid-June can be estimated as follows:
June futures price in mid-March
LIBOR rate in mid-March
Basis in mid-March
94.610
95.000
0.390
In mid-March, there were 3.5 months to settlement of the June futures. In
mid-June, there are 0.5 months remaining to settlement. Basis is assumed
to have reduced in size by mid-June to:
(0.5/3.5) × 39 points = 5.6 points, say 5 points.
LIBOR rate in mid-June
Basis in mid-June
Estimated futures price in mid-June
94.000
00.005
93.995
The company will close its position by buying 28 June futures at 93.995.
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Original selling price
Buying price to close
Gain (ticks)
94.610
93.995
00.615
The total gain on the futures position:
= 28 contracts × 61.5 ticks per contract × £12.50 per tick
= £21,525.
(The gain on the futures position offsets the cost of the increase in the
interest rate above the rate fixed by the futures contract (6% - 5.39% =
0.61%). The extra borrowing cost is £21 million × 0.61% × 2/12 = £21,350.
The difference of £175 is due to the basis risk).
Options on futures
The company will exercise its options to sell futures at the strike price for
the option, and will then close the futures position, giving a gain on closing
the futures position.
Option strike price to sell
Buying price to close
Gain (ticks)
Total gain:
28 × 75.5 ticks × £12.50
Strike price
94750
Strike price
95000
94.750
93.995
0.755
95.000
93.995
1.005
£26,42
5
28 × 100.5 ticks × £12.50
£35,175
However, after taking into account the cost of the option premiums, the net
gain is reduced.
FRA
The company’s FRA bank will make a payment equivalent to (6% - 5.38%)
= 0.62% per year on £21 million for two months, to settle the FRA.
The gain on the FRA will offset the higher interest cost of borrowing.
24.9
DEFINITIONS
(a)
Interest rate swaps
An interest rate swap is an agreement between two parties to exchange
interest rate payments. The objective might be to:
‰
Switch from paying one type of interest to another
‰
Raise less expensive loans
‰
Securing better deposit rates
In essence, party A agrees to pay the interest on party B’s loan, whilst party
B agrees to pay the interest on party A’s loan.
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(b)
Forwards
A forward contract is a binding agreement to exchange a set amount of
goods at a set future date at a price agreed today.
Forward contracts are used by business to set the price of a commodity
well in advance of the payment being made. This brings stability to the
company who can budget with certainty the payment they will need to raise.
Forwards are particularly suitable in commodity markets such as gold,
agriculture and oil where prices can be highly volatile.
Forward contracts are tailor-made between the two parties and therefore
difficult to cancel (as both sides need to agree). A slightly more flexible
approach would be to use futures
(c)
Futures
Futures share similar characteristics to Forward contracts i.e.:
‰
Prices are set in advance
‰
Futures hedges provide a fixed price
‰
Futures are available on commodities, shares, currencies and interest
rates.
However, futures are standardised contracts that are traded on an open
futures market (unlike forward contracts which are unique to the two
counterparties).
(d)
Options
An option gives the owner the right, but not the obligation to trade
‘something’. The ‘something’ might be shares, a foreign currency or a
commodity.
There are two types of options:
‰
Exchange traded options – these are standardised and traded in an
open market
‰
Over the counter (OTC) options – these are bespoke and the terms
are agreed specifically between the two counterparties.
Options have both an intrinsic value and a time value.
The holder of an option has two choices:
(e)
‰
Exercise the right to buy (a call option) or sell (a put option) at the
pre-determined price (the exercise price)
‰
Not exercising this right – i.e. allowing the option to lapse.
Caps, collars and floors
‰
A cap is a ceiling agreed to an interest rate
‰
A floor is a lower limit set for an interest rate
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‰
24.10
A collar combines both caps and floors thus maintaining the interest
rate within a particular range.
IMRAN LIMITED
(a) Rate of interest is
KIBOR+2
Since KIBOR is swapped at
11%
So the fixed rate of interest to Imran Limited (11% + 2%)
13%
Monthly payment = 70 million x 13% x 6/12
(b) (i)
4,550,000
If KIBOR is 13.5% then:
Rupees
The bank which has provided the credit will receive
(70 million x 15.5% x 6/12)
5,425,000
The bank which has offered the Swap
arrangement will pay to Imran Limited (70 million x
2.5% x 6/12)
(A)
875,000 (B)
Imran Limited
Net payable by Imran Limited
A-B
4,550,000
Rupees
(ii) If KIBOR is 9% then
The bank which has provided the credit will receive
(70 million x 11% x 6/12)
The bank which has offered the Swap
arrangement will receive from Imran Limited (70
million x 2% x 6/12)
3,850,000
(A)
700,000 (B)
Imran Limited
Net payable by Imran Limited
A+B
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Answers
CHAPTER 25 – FORECASTING AND BUDGETING
25.1
GAZELLE LIMITED
(a)
Sales budget
Sales budget for year ending 31/12/2017
Quarter
1
2
3
Forecast trend
1600
1700
1800
Seasonal variation
-150
+200
+300
1450
1900
2100
Forecast sales (Units)
Sales price per unit
Rs. 250
Rs. 250
Rs. 250
Sales value (Rs.)
(b)
362,500
475,000
525,500
4
1900
-350
1550
Rs. 250
387,500
Production budget
Production budget for year ending 31/12/2017
Quarter
1
2
Forecast sales (units)
1,450
1,900
Add planned closing inventory
950
1,050
Forecast sales (Units)
Less: Planned opening
inventory
2,400
Forecast production units
1,675
NOTE:
2,950
(725)
3
2,100
775
4
1,550
925
2,875
2,475
(950)
(1,050)
(775)
2000
1825
1700
Closing inventory for Q4
Assumed 2015 quarter 1 sales (units)
Less Variation
2000
(150)
1,850
Closing inventory for 2017 Q4 = 50% of 1850 = 925 units
(c)
Labour budget for year Ending 31/12/2017
Q1
Q2
Q3
Production Budget (units)
1,675
2,000
1,825
Hrs per unit
u6
u6
u6
Q4
1,700
u6
Hrs used
Labour cost per hour
10,050
u Rs. 1
12,000
u Rs. 1
10,950
u Rs. 1
10,200
u Rs. 1
Total labour cost (Rs.)
150,750
180,000
164,250
153,000
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25.2
FUNCTIONAL BUDGETS (1)
Sales budget
Sales quantity
Sales price
A
50,000
Rs. 2.50
Rs. 125,000
B
80,000
Rs. 4.00
Rs. 320,000
Product
Sales
revenue
Rs. 445,000
Total
Production budget
Units
Sales budget in units
20,000
2,000
Plus budgeted closing inventory
(2,500)
Less closing inventory
19,500
Labour budget
Grade I
Grade II
hours
hours
100,000
175,000
Rs. 12
Rs. 15
Rs.
1,200,000
Rs.
2,625,000
To make 25,000 units DOY
Labour cost per hour
Total labour cost
Total
275,000
Rs.
3,825,000
Materials budget
Production budget
Units
Closing inventory
4,000
Sales
25,000
29,000
Opening inventory
(2,000)
Budgeted production
27,000
Materials usage budget, material X
= 27,000 units of product × 5 kilos per unit = 135,000 kilos.
Materials purchases budget
Closing inventory
Usage in production
Kilos of material X
15,000
135,000
150,000
Opening inventory
(30,000)
Budgeted production
120,000
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Answers
25.3
FUNCTIONAL BUDGETS (LL)
(a) Principal budget factor
That factor which at a particular time, or over a period, will limit the activities
of an organisation. The limiting factor is usually the level of demand for the
product or service of the undertaking but it could be a shortage of one of the
products resources e.g. skilled labour, raw materials or machine capacity. In
order to ensure that the functional budgets are reasonably capable of
fulfilment, the extent of the influence of this factor must first be assessed.
(b) Budgets
(i)
Sales quantity and value budget
Products
G
B
Sales quantities
1000
2000
1500
Selling prices
£110
£115
£120
£110,000
£230,000
Sales value
(ii)
D
Total
£180,000
£520,000
Production quantities budget
Products
(iii)
G
B
D
Sales quantities
1000
2000
1500
Add: Closing stock
1200
1450
480
2200
3450
1980
Deduct opening stock
1100
1050
520
Units to be produced
1100
2400
1460
Material usage budget (quantities):
Production
Materials
Quantities
X1
Units
per
product
G 1100
X2
Total
Units
per
product
3
3300
B 2400
2
D 1460
4
Total
Units
per
product
Total
3
3300
1
1100
4800
3
7200
2
4800
5840
-
-
2
2920
13940
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Business finance decisions
(iv)
Material purchases budget (quantities and value):
X1
X2
X3
Material usage budget
13,940
10,500
8,820
Add closing stock
33,400
26,000
16,000
47,340
36,500
24,820
Less: Opening stock
22,000
18,000
14,000
Purchase in quantities
25,340
18,500
10,820
£5
£8
£7
£126,700
£148,000
Price per unit
Value of purchases
25.4
Total
£75,740 £350,440
FLEXED BUDGET
Workings
The high low method will be used to estimate fixed and variable costs.
Production
labour
Production
overhead
Rs.
Rs.
Total cost of 13,000 units
81,500
109,000
Total cost of 10,000 units
74,000
88,000
7,500
21,000
Variable cost of 3,000 units
Variable production labour cost per unit = Rs. 7,500/3,000 units = Rs. 2.50.
Variable production overhead cost per unit = Rs. 21,000/3,000 units = Rs. 7.00.
Production
labour
Production
overhead
Rs.
Rs.
Total cost of 10,000 units
74,000
88,000
Variable cost of 10,000 units (u Rs. 2.50/Rs.
7)
25,000
70,000
Fixed costs
49,000
18,000
Selling and distribution overhead
Rs.
Total cost of 14,000 units
36,200
Total cost of 9,000 units
29,700
Variable cost of 5,000 units
6,500
Variable selling and distribution overhead cost per unit = Rs. 6,500/5,000 units =
Rs. 1.30.
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Selling and distribution overhead
Rs.
Total cost of 9,000 units
29,700
Variable cost of 9,000 units (u Rs. 1.30)
11,700
Fixed costs
18,000
Fixed cost
Variable
cost per unit
Rs.
Rs.
-
13.00
Direct labour (excluding overtime)
49,000
2.50
Production overhead
18,000
7.00
Administration overhead (all fixed)
26,000
-
Selling and distribution overhead
18,000
1.30
Summary
Direct materials (Rs. 130,000/10,000
units)
Budgeted cost allowance – quarter 3
Production units: 15,000
Sales units: 14,500
Rs.
Materials (15,000 u Rs. 13)
195,000
Labour (Rs. 49,000 + (15,000 u Rs. 2.50))
86,500
Overtime (1,000 u Rs. 2.50 u 50%)
1,250
Production 0verhead (Rs. 18,000 + (15,000 u Rs. 7))
123,000
Administration overhead
26,000
Selling and distribution (Rs. 18,000 + (14,500 u Rs. 1.30))
36,850
468,600
25.5
NORTON CARE HOME
(a)
The rate per patient for the variable overheads on the basis of experience
during January –June are as follows:
Expense
Salaries &Wages
Maintenance
Printing & Stationery
Miscellaneous
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Amount for 5,600 Amount/P
patients
atient
Rs.
Rs.
79,500
14.20
35,000
6.25
65,000
11.61
10,000
1.79
189,500
33.85
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Business finance decisions
Since the expected level of activity in the full year is 10,000, the expected
level of activity for July- December is 4,400 (i.e10,000 −5,600). Thus, the
budget for July− December will be as follows:
Variable cost
Rs.
Salaries & wages
(4,400 x 14.20)
62,480
Maintenance
(4,400 x 6.25)
27,500
Printing /Stationery
(4,400 x 11.61)
51,084
Miscellaneous
(4,400 x 1.79)
7,876
Total variable overhead
148,940
Rs.
Fixed Cost:
Supervision
6/12 (300,000)
150,000
Depreciation
6/12 (197,500)
98,750
Miscellaneous
6/12 (150,000)
75,000
Total fixed cost
323,750
Total overhead Budget (Jan- Dec)
472,690
Total Budgeted overhead/patient
(b)
Rs. 107.43
For July-December 2016, the actual activity was 6,400 patients. For a valid
comparison with the actual outcome, the budget will need to be revised to
reflect this activity as follows:
Rs.
Rs.
Rs.
Variable Cost
206,000
216,640 (Note 1)
10,640 F
Fixed Cost
380,000
323,750 (Note 2)
56,250 A
586,000
540,390
45,610 A
The company is able to control its variable costs per patient, however the
company could not control its fixed costs, as a result of the number of
patients attended to.
This led to a total adverse variance of Rs. 45,610.
Note 1
Variable cost: 6,400 units @ Rs. 33.85 = Rs. 216,640
Note 2: Fixed cost: as computed in the budget above.
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Answers
25.6
THREE SERVICES
(a)
Budgeted statement of profit or loss
Budgeted statement of profit or loss for the year to 31 December Year 2
Service A
Service B
Service C
Total
Revenue:
Contract customers
Non-contract
customers
Rs.
1,946,700
Rs.
2,317,500
Rs.
4,944,000
Rs.
9,208,200
1,687,140
2,317,500
1,483,200
5,487,840
Total revenue
3,633,840
4,635,000
6,427,200
14,696,040
Costs:
Salaries
Fuel:
Services A and B
Service C
4,016,250
2,400,000
2,592,000
4,992,000
4,200,000
Sundry operational costs
Total costs
13,208,250
Net profit
1,487,790
Workings
Revenue:
Service A: contract customers – 350,000 u 60% u Rs. 9 u 1.03 = Rs.
1,946,700
Service A: non-contract customers – 350,000 u 40% u Rs. 9 u 1.30 u 1.03
= Rs. 1,687,140
Service B: contract customers – 250,000 u 60% u Rs. 15 u 1.03 = Rs.
2,317,500
Service B: non-contract customers – 250,000 u 40% u Rs. 15 u 1.50 u 1.03
= Rs. 2,317,500
Service C: contract customers – 20,000 u 80% u Rs. 300 u 1.03 = Rs.
4,944,000
Service C: non-contract customers 20,000 u 20% u Rs. 300 u 1.20 u 1.03 =
Rs. 1,483,200
Salaries: Rs. 45,000 u 85 employees u 1.05 = Rs. 4,016,250
Sundry operational costs: Rs. 4,000,000 u 1.05 = Rs. 4,200,000
Fuel
Services A and B – 400 km u 50 vehicles u 300 days u Rs.0.40 = Rs.
2,400,000
Service C – 600 km u 18 vehicles u 300 days u Rs.0.80 = Rs. 2,592,000
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(b)
Vehicle utilisation
There is no information about weight carried, only about distance travelled.
All vehicles were used for 300 days in the year. Presumably, vehicles might
be used for 365 days per year, indicating an overall utilisation ratio for all
vehicles of 82.2%.
Other utilisation measure: a revenue measure might be used as an
indication of the utilisation of vehicles.
Revenue per vehicle
Services A and B
Service C
(Rs. 8,268,840/50)
Rs. 165,377
(Rs. 6,427,200/18)
Rs. 357,067
Kilometres travelled each year might also be a measure of utilisation:
25.7
‰
Service A and B vehicles travel on average (400 u 300) = 120,000
kilometres each year.
‰
Service C vehicles travel on average (600 u 300) = 180,000
kilometres each year.
Private medical practice
Budgeted statement of profit or loss for the year to […]
Adults
Children
Aged 65 +
Revenue:
No treatment
Minor treatment
Major treatment
Total revenue
Rs.
93,150
1,304,100
558,900
1,956,150
Rs.
31,050
434,700
144,900
610,650
Costs:
Salaries
Doctors
(5 u Rs. 240,000)
Assistants
(5 u Rs. 100,000)
Administrators
(2 u Rs. 80,000)
Rs.
161,460
2,260,440
877,680
3,299,580
1,200,000
500,000
160,000
1,860,000
93,000
Bonus
1,953,000
414,300
733,600
Materials costs
Other costs
Total costs
Net profit
© Emile Woolf International
Rs.
37,260
521,640
173,880
732,780
Total
3,100,900
198,680
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Answers
Workings
Total number of patients per year = 5 doctors u 18 patients per day u 5 days per
week u 46 weeks per year = 20,700.
Total
20,700
Treatment
None: 20%
Minor: 70%
Major: 10%
Patients
Adults
Children
65 years and
over
(45%) =
9,315
(25%) =
5,175
(30%) = 6,210
1,863.0
6,520.5
931.5
1,035.0
3,622.5
517.5
1,242
4,347
621
Revenue:
Adults, no treatment: 1,863 u Rs. 50 = Rs. 93,150
Adults, minor treatment: 6,520.5 u Rs. 200 = Rs. 1,304,100
Adults, major treatment: 931.5 u Rs. 600 = Rs. 558,900
Children, no treatment: 1,035 u Rs. 30 = Rs. 31,050
Children, minor treatment: 3,622.5 u Rs. 120 = Rs. 434,700
Children, major treatment: 517.5 u Rs. 280 = Rs. 144,900
65 years and over, no treatment: 1,242 u Rs. 30 = Rs. 37,260
65 years and over, minor treatment: 4,347 u Rs. 120 = Rs. 521,640
65 years and over, major treatment: 621 u Rs. 280 = Rs. 173,880.
25.8
HEADGEAR LIMITED
(a)
The following comments are relevant to budget revisions that would
produce both favourable and adverse planning variances, although in
practice requests for budget revisions are more likely to occur when the
planning variance will be adverse (because operational variances would be
improved).
Budgeting and budgetary control provide a system for monitoring operational
performance. It is therefore important that actual performance should be
compared with a realistic budget. At the same time, however, revisions to the
budget should not be permitted when they would disguise poor operational
performance.
The general rule should be as follows.
(1)
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Budget revisions should be permitted when they are caused by a
circumstance beyond the control of operational management, so that
the original budget is no longer a fair basis for judging operational
performance. All revisions to the budget, however, must be approved
at senior management level, perhaps at board of director level.
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(2)
Budget revisions should not be permitted when they are caused by
circumstances within the control of operational management
In practice, however, it might not be clear whether changes in
circumstances are due to factors inside or outside the control of operational
management, and each request for a budget revision should be judged on
the facts of the case.
(b)
Situation 1
Argument in favour of a budget revision
The board approved the request for a change in recruitment policy. It might
therefore be argued that the change in policy is outside the influence of
operational management in the sales and marketing department.
Arguments against a budget revision
The board approved a request from the departmental manager. The
problem with the existing staff in the department was an operational matter,
within the control of the departmental managers. The increase in the
departmental labour costs is therefore due to operational factors for which
management should be held responsible in performance reports.
If there is any improvement in the efficiency and effectiveness of the
department as a result of the new recruitment policy, the departmental
management will receive the credit in the departmental performance
(variance) reports. It is inappropriate to allow a budget revision for one
aspect of a policy change (higher staff costs) and at the same time give
management credit for other aspects of the policy change (improving
efficiency and/or effectiveness).
Situation 2
Argument in favour of a budget revision
The insolvency of the original cloth supplier was outside the control of the
purchasing department.
The buying department could argue that they did what they could under the
circumstances to maintain supplies of cloth to the company, and it is
unreasonable to ‘blame’ the department for adverse price variances in the
three-month period.
The department was aware that the short-term solution was not adequate
for the longer term, and after further searching a cheaper source of supply
was found. It may therefore be argued that the performance of the buying
department should be commended and not ‘criticised’ with an adverse price
variance.
Arguments against a budget revision
The management of any department need to be fully aware if the risks that
they face, including the risks of insolvency of a major supplier. Contingency
plans should have been in place to respond to the insolvency of the original
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supplier, and an alternative cheap supplier should already have been
identified.
The first supplier who was found charged high prices and delivery costs,
but there was little or no negotiation by Headgear’s buyer. It is the job of a
buyer to negotiate on price, if possible, whatever the circumstances. In this
case the buyer did not perform his task as well as he might have done.
Recommendations
There are arguments both in favour and against a budget revision in each
situation. My own view is that in each case, the longer-term planning of the
department was at fault in both cases. The sales and marketing department
was inadequately staffed and the buying department had no contingency
plans for using an alternative supplier
I would therefore recommend in each case that the request for a budget
revision should be refused.
(c)
Rs.
10,900 units should sell for (u Rs. 225)
2,452,500
They did sell for (u Rs. 200)
2,180,000
Sales price variance (u Rs. 225 - Rs. 200)
272,500 (A)
units
Budgeted sales volume
11,200
Actual sales volume
10,900
Sales volume variance in units
300 (A)
Budgeted contribution per unit
Rs. 125
Sales volume (contribution) variance
Rs. (A)
37,500
(d)
units
Budgeted sales volume
11,200
Expected market share of actual market size
(10% of 100,000)
10,000
Market size variance in units
1,200 (A)
Budgeted contribution per unit
Rs. 125
Market size variance
Rs. (A)
150,000
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units
Expected market share of actual market size
(10% of 100,000)
10,000
Actual market share
10,900
Market share variance in units
(e)
900 (F)
Budgeted contribution per unit
Rs. 125
Market share variance
Rs. (F)
112,500
The analysis of the sales volume variance shows that there has been a fall
in sales volume due to a fall in the total market share, and if Headgear
Limited had maintained its market share the decline in the size of the
market would have caused a fall in contribution and profit of Rs. 150,000.
This is the market size variance.
However the company was able to gain a larger share of the market than
expected, which had the effect of boosting contribution and profit by Rs.
112,500, in spite of the decline in market size. This is the market share variance.
The net effect was an adverse overall sales volume variance of Rs. 37,500.
25.9
DASKA DESIGN LIMITED
(a)
Tutorial note
Being provided with moving average totals speeds up the process of forecasting
considerably.
In order to make the forecast the first step is to calculate seasonal variations
(actual – trend). These can then be averaged to work out seasonal factors for
each quarter.
The slope of the trend (moving average) line also ha to be forecast.
Using these data it is then possible to make forecasts.
Remember the question asks for the additive model (Y=T+S) not the
multiplicative model Y =TxS. If you use the wrong model both working and right
answer mars will be lost.
Quarter
Year 5
Q3
Q4
Year 6
Q1
Q2
Q3
Q4
© Emile Woolf International
Actual
sales (Y)
Rs.000
3,400
3,000
3,100
3,900
3,600
3,400
Centred moving
average (T)
Rs.000
3,200
3,300
3,375
3,450
3,562.5
3,687.5
374
Seasonal
variation (Y-T)
Rs.000
200
(300)
(275)
450
37.5
(287.5)
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Answers
To make a forecast the slope of the trend (moving average) line has to be
calculated.
(3,687·5 – 3,200)/5 = Rs. 97,500 increase per quarter
The average seasonal variations and the residual error term can now be
calculated.
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Rs.000
Rs.000
Rs.000
Rs.000
200
(300)
Year 5
Year 6
(275)
450
37.5
(287.5)
Average
(275)
450
118.75
(293.75)
Total
Rs.000
nil
Making forecasts is now a two-step process:
Predict the trend line (moving average line).
Adjust the trend line using the appropriate seasonal factor.
The sales forecast for Quarter 3 of Year 7:
Forecast centred moving average = 3,687.5 + (3 u 97.5) = Rs. 3,980,000
Forecast sales for Quarter 3 = 3,980,000 + 118,750 = Rs. 4,098,750
The sales forecast for Quarter 4 of Year 7:
Forecast centred moving average = 3,687.5 + (4 u 97.5) = Rs. 4,077,500
Forecast sales for Quarter 4 = 4,077,500 – 293,750 = Rs. 3,783,750
Both forecasts are higher than those made by the Sales Director (7.9% more for
the Quarter 3 forecast and 5.1% for the Quarter 4 forecast). This may be
because the Sales Director built some slack into his forecasts, or because the
forecasts were made using data prior to the current year (although applying the
additive model to earlier sales data does not support this).
(b)
Independence of trend and seasonal factors
The additive model assumes that the trend and seasonal variations are
independent of each other, and that an increasing trend is not linked to
increasing seasonal variations. There is no evidence of an increasing
seasonality in the sales of Daska Design Limited, and in such circumstances
use of the additive model may be acceptable.
Stable trend and seasonality
The model assumes that the historical pattern of the trend and the seasonal
variations will continue in the future. This may not happen for a number of
reasons, for example because of the occurrence of unexpected events or
because of changes in consumer preferences. The forecast sales figures should
be compared with the expectations and opinions of sales staff, who may have a
more detailed knowledge of likely sales and market factors.
Quantity and accuracy of data
The reliability of the forecasting method is linked to the amount and accuracy of
the data analysed. Since only two years of data has been considered, the
forecast is unlikely to be reliable. The reliability of the forecast will also decrease
as the forecasting period increases, but the forecast period here is only six
months.
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(c)
Top-down approach: advantages
The top-down approach to budget setting implies that budgets are imposed by
senior management. This has the advantage that budgets are more likely to
support the strategic objectives of the company, and the operations of different
divisions are more likely to be co-ordinated. It may be an appropriate form of
budget setting in small organisations, where senior managers are likely to have
a detailed knowledge of all aspects of the business, or in situations where close
control of planned costs is called for, such as business start up or difficult
economic conditions. It also has the advantage of decreasing the amount of time
taken, and the resources consumed, by budget preparation.
Top-down approach: disadvantages
There are number of difficulties with the top-down approach that make it likely
that it will not regularly be used in isolation. Staff may be demotivated if they
have not been involved in the formulation of budgets that produce targets they
are expected to achieve, especially if their rewards and incentives are linked to
their performance against budget. This reduction in motivation could result in
strategic objectives and organisational goals being less than fully supported at
the operational level, with company performance and profitability suffering as a
result. Initiative and innovation could also be lost as staff simply ‘work to budget’,
rather than making creative suggestions for improving performance that they
feel are unlikely to be rewarded, or form part of future plans.
Bottom up approach: advantages
The bottom-up approach to budget setting implies that functional and other
junior managers participate in the preparation of budgets. This approach is likely
to lead to more realistic and more co-ordinated budgets than the top-down
approach if these managers have a more detailed knowledge of the operations
and markets of the organisation. It is also likely to be useful in large, established
companies where the complexity of the budget-setting process calls for detailed
input from lower levels of the organisation. This approach will also lead to higher
levels of motivation and commitment, since managers will have contributed
towards the targets against which their performance will be measured.
Bottom up approach: disadvantages
There are a number of difficulties with the bottom-up approach. For example, it
can be more time-consuming than the top-down approach because of the
larger number of participants in the budget-setting process. Participants may
become dissatisfied if their budget proposals are subsequently amended by
senior managers. Managers may introduce an element of budgetary slack into
their budget estimates, giving them a ‘zone of comfort’ in reaching budget
targets. Any variances between planned and actual performance are then likely
to be favourable ones. The bottom-up approach also requires detailed planning
and co-ordination of the budget-setting process, perhaps supported by a budget
manual. The top-down and bottom-up approaches represent two extremes of
the budget-setting process. In practice, a compromise or negotiated approach is
likely to be used, with senior management reviewing and amending the budget
proposals of junior or operational managers in the light of the organisation’s
strategic plan, and junior or operational managers negotiating amendments to
aspects of the budget they find unacceptable.
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CHAPTER 26 – VARIANCE ANALYSIS
26.1
GOOD HARVEST LIMITED
(a)
Materials price variance: based on quantities purchased since
inventories are valued at standard cost
6,600 kg of materials should cost (u Rs. 4)
They did cost
Material price variance
Rs.
26,400
29,700
3,300 (A)
Materials usage variance
1,100 units produced should use (u 5kg)
They did use
Usage variance in kg
Standard price per kg
Usage variance in Rs.
kg
5,500
6,300
800 (A)
Rs. 4
Rs. 3,200 (A)
Labour rate variance
3,600 hours of labour should cost (u Rs. 4)
They did cost
Labour rate variance
Rs.
14,400
14,220
180 (F)
Labour efficiency variance
1,100 units produced should take (u 3 hours)
They did take
Efficiency variance in hours
Standard rate per hour
Efficiency variance in Rs.
hours
3,300
3,600
300 (A)
Rs. 4
Rs. 1,200 (A)
Fixed overhead expenditure variance
Rs.
6,000
4,000
2,000 (F)
Budgeted fixed overhead costs
Actual fixed overhead costs
Fixed overhead expenditure variance
Variable overhead expenditure variance
3,600 hours should cost (u Rs. 3)
They did cost
Variable overhead expenditure variance
Rs.
10,800
11,700
900 (A)
Variable overhead efficiency variance
300 hours (A) u Rs. 3 per hour = Rs. 900 (A).
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Sales price variance
Rs.
55,000
57,200
2,200 (F)
1,100 units should sell for (u Rs. 50)
They did sell for
Sales price variance
Sales volume (contribution margin) variance
Budgeted sales volume in units
Actual sales volume in units
Sales volume variance in units
1,300
1,100
200 (A)
u Standard contribution per unit
Sales volume variance in Rs.contribution
Rs. 9
Rs. (A)
1,800
Budgeted profit
Budgeted contribution
Budgeted fixed costs
Budgeted profit
Rs. 9.00 u 1,300 units
Rs.
11,700
(6,000)
5,700
Actual profit
Rs.
Sales
Materials
Less closing inventory (300kg u Rs. 4.00)
Rs.
57,200
29,700
(1,200)
28,500
14,220
11,700
4,000
Labour
Variable overheads
Fixed costs
Total
Actual loss in the period
(58,420)
(1,220)
Operating statement
Rs.
5,700
1,800 (A)
2,200 (F)
6,100
Budgeted profit
Sales volume variance
Sales price
Cost variances
F
Rs.
Materials price
Materials usage
Labour rate
Labour efficiency
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Rs.
3,300
3,200
180
1,200
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Variable overhead rate
Variable overhead efficiency
Fixed overhead expenditure
Total
Total cost variances
Actual loss
(b)
900
900
2,000
2,180
9,500
7,320 (A)
(1,220)
Tutorial note
If the company uses absorption costing with a direct labour hour absorption
rate, we can calculate an expenditure, capacity and efficiency variance for
fixed production overheads.
The first step is to calculate a budgeted absorption rate per hour
Budgeted fixed cost
Budgeted labour hours (1,300 u 3)
Budgeted absorption rate per hour
Rs. 6,000
3,900 hrs
Rs. 1.5384
Budgeted fixed cost
Budgeted production
Budgeted absorption rate per unit
Rs. 6,000
1,300 units
Rs. 4.6254
Fixed overhead expenditure variance
Same as in (a): Rs. 2,000 (F).
Fixed overhead volume variance
units
Budgeted production
1,300
Actual production
1,100
Under production
200 (A)
Standard fixed overhead rate per unit
Rs. 4.6154
Fixed overhead capacity variance in Rs.
Rs. 923 (A)
This may be analysed as follows
Fixed overhead capacity variance
hours
Budgeted hours of work
3,900
Actual hours worked
3,600
Capacity variance in hours
300 (A)
Standard fixed overhead rate per hour
Rs. 1.54
Fixed overhead capacity variance in Rs.
Rs. 462 (A)
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Fixed overhead efficiency variance
Efficiency variance in hours = 300 hours (A) – see answer to (a).
Fixed overhead efficiency variance = 300 hours (A) u Rs. 1.54 = Rs. 462 (A).
(c)
Labour rate
The labour rate variance is favourable indicating a lower rate per hour was paid
than expected. This is perhaps because more junior or less experienced staff
were used during production. Though less likely, it is possible that staff had a
pay cut imposed upon them. Finally, an incorrect or outdated standard could
have been used.
Labour efficiency
This is significantly adverse, indicating staff took much longer than expected to
complete the output. This may relate to the favourable labour rate variance,
reflecting employment of less skilled or experienced staff. Staff demotivated by
a pay cut are also less likely to work efficiently.
It may also relate to the reliability of machinery as staff may have been
prevented from reaching full efficiency by unreliable equipment.
26.2
MOONGAZER
(a)
Tutorial note
A good place to start with an operating statement is to calculate the
budgeted and actual profits for the period and then from this to calculate
variances.
Budgeted profit
Budgeted gross profit = (Rs. 100 – Rs. 77) u 450 = Rs. 10,350.
Actual gross profit
Rs.
Sales
Materials
Less closing inventory (125 u Rs. 15)
Labour
Variable overheads
Fixed costs
Cost of sales
Actual profit
Rs.
47,300
17,700
(1,875)
15,825
14,637
3,870
2,400
36,732
10,568
Sales price variance
430 units should sell for (u Rs. 100)
Rs.
43,000
They did sell for
47,300
Sales price variance
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Sales volume (profit) variance
units
450
Budgeted sales volume
Actual sales volume
430
Sales volume variance in units
20 (A)
Budgeted profit per unit
Rs. 23
Sales volume (profit) variance
Rs. 460 (A)
Materials price variance
Rs.
1,200 kg of materials should cost (u Rs. 15)
18,000
They did cost
17,700
Materials price variance
300 (F)
Materials usage variance
kg
430 units of output should use (u 2)
860
They did use
1,075
Materials usage variance in kg
215
Standard price per kg of materials
(A)
Rs. 15
Materials usage variance (Rs.)
3,225
(A)
Labour rate variance
1,700 labour hours should cost (u Rs. 8.50)
Rs.
14,450
They did cost
14,637
Labour rate variance
187 (A)
Labour efficiency variance
hours
430 units of output should take (u 4)
1,720
They did take
1,700
Labour efficiency variance in hours
Standard rate per labour hour
Labour efficiency variance in Rs.
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20
(F)
Rs. 8.50
170 (F)
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Variable overheads expenditure variance
Rs.
1,700 hours should cost (u Rs. 2)
3,400
They did cost
3,870
Variable overhead expenditure variance
470 (A)
Variable overhead efficiency variance (same in hours as labour
efficiency variance)
= 20 hours (F) u Rs. 2 per hour = Rs. 40 (F).
Fixed overheads expenditure variance
Rs.
Budgeted fixed overhead expenditure (450 u Rs. 5)
2,250
Actual fixed overhead expenditure
2,400
Fixed overhead expenditure variance
150 (A)
Fixed overheads volume variance
units
Budgeted production
450
Actual production
430
Volume variance in units
20 (A)
Standard fixed overhead cost per unit
Fixed overhead volume variance
Rs. 5
Rs. 100 (A)
Operating statement
Rs.
10,350
460 (A)
9,890
4,300 (F)
14,190
Budgeted gross profit
Sales volume
Sales price
Actual sales less standard cost of sales
Cost variances
Materials price
Materials usage
Labour rate
Labour efficiency
Variable overhead expenditure
Variable overhead efficiency
Fixed overhead expenditure
Fixed overhead volume
Total
Actual gross profit:
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F
Rs.
300
A
Rs.
3,225
187
170
470
40
510
150
100
4,132
3,622 (A)
10,568
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26.3
ABC LIMITED
Operating statement
Rs.000
Budgeted gross profit
107,500
Sales volume
(4,300)
(A)
103,200
Sales price
7,000
Actual sales less standard cost of sales
Cost variances
(F)
110,200
F
A
Rs.000
Rs.000
Materials price
7,500
Materials usage
12,500
Labour rate
6,000
Labour efficiency
3,000
Variable overhead expenditure
1,250
Variable overhead efficiency
750
Fixed overhead expenditure
Fixed overhead volume
100
200
Total
12,500
18,800
(6,300)
Actual gross profit:
(A)
103,900
Budgeted profit
Per unit
.
Sales price
Rs.
600
Direct material
2.5 kg per unit at Rs. 50 per kg
125
Direct labour
Variable overheads
2.0 hrs per unit at Rs. 100 per hr
2.0 hrs per unit at Rs. 25 per hr
200
50
Fixed overheads
Rs. 10 per unit
10
Cost of sales
385
Budgeted profit
215
Budgeted sales (units)
500,000
Budgeted profit (Rs. 000)
107,500
Actual gross profit
Rs.000
Sales
295,000
Materials
55,000
Labour
105,000
Variable overheads
26,000
Fixed costs
5,100
Cost of sales
191,000
Actual profit (Rs. 000)
103,900
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The inventory level and how it is measured (standard cost) does not change so
can be ignored in the above calculations
Sales price variance
Rs.000
480,000 units should sell for (u Rs. 600)
288,000
They did sell for
295,000
Sales price variance
7,000 (F)
Sales volume (profit) variance
units
Budgeted sales volume
500,000
Actual sales volume
480,000
Sales volume variance in units
20,000 (A)
Budgeted profit per unit (Rs.)
215
Sales volume (profit) variance (Rs. 000)
(4,300) (A)
Materials price variance
Rs.000
950,000 kg of materials should cost (u Rs. 50)
They did cost
47,500
Materials price variance
(7,500) (A)
55,000
Materials usage variance
kg
1,200,000
480,000 units of output should use (u 2.5)
They did use
950,000
Materials usage variance in kg
250,000 (F)
Standard price per kg of materials (Rs.)
Rs. 50
Materials usage variance (Rs. 000)
12,500 (F)
Labour rate variance
Rs.000
990,000 labour hours should cost (u Rs. 100)
They did cost
99,000
105,000
Labour rate variance
(6,000) (A)
Labour efficiency variance
480,000 units of output should take (u 2)
hours
960,000
They did take
990,000
Labour efficiency variance in hours
(30,000)
Standard rate per labour hour
Rs. 100
Labour efficiency variance in Rs. 000
(3,000)
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Variable overheads expenditure variance
Rs.000
990,000 labour hours should cost (u Rs. 25)
They did cost
24,750
Variable overhead expenditure variance
(1,250) (A)
26,000
Variable overhead efficiency variance (same in hours as labour efficiency
variance)
= 30,000 hours (A) u Rs. 25 per hour = Rs. 750,000 (A).
Fixed overheads expenditure variance
Rs.000
Budgeted fixed overhead expenditure (500,000 u Rs. 10)
5,000
Actual fixed overhead expenditure
5,100
Fixed overhead expenditure variance
100 (A)
Fixed overheads volume variance
units
Budgeted production
500,000
Actual production
480,000
Volume variance in units
20,000 (A)
Standard fixed overhead cost per unit
10
Fixed overhead volume variance (Rs.000)
26.4
200 (A)
KASUR MF LIMITED
(a)
Tutorial note
Remember that in a flexed budget, fixed costs do not change with the volume of
activity.
The flexed budget will be based on the actual activity level of 90,000 units.
Rs.
Sales: Rs. 950,000 u 90/95 =
Rs.
900,000
Cost of sales
Raw materials: 133,000 u 90/95 =
126,000
Direct labour: 152,000 u 90/95 =
144,000
Variable production overheads: 100,700 u 90/95 =
Fixed production overheads:
95,400
125,400
490,800
409,200
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(b)
Raw materials cost variance
Rs.
90,000 units produced: material cost should be
(see above)
126,000
Actual material cost
130,500
Materials: total cost variance
4,500 (A)
Direct labour cost variance
Rs.
90,000 units produced: material cost should be
(see above)
144,000
Actual direct labour cost
153,000
Direct labour: total cost variance
9,000 (A)
Fixed overhead variances
Tutorial note
The first step here is to calculate the budgeted absorption rate.
Fixed overhead absorption rate = 125,400/28,500 budgeted machine hours =
Rs. 4.40 per machine hour.
Budgeted machine hours per unit = 28,500 hours/95,000 units = 0.3 machine
hours per unit.
Fixed overhead efficiency variance
hours
90,000 units of output should take (u 0.3)
27,000
They did take
27,200
Efficiency variance in machine hours
200 (A)
Standard fixed overhead rate per machine hour
Rs.
4.40
Labour efficiency variance in Rs.
Rs. 880 (A)
Fixed overhead capacity variance
hours
Budgeted machine hours
28,500
Actual machine hours
27,200
Capacity variance in machine hours
1,300 (A)
Standard fixed overhead rate per machine hour
Fixed overhead capacity variance in Rs.
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5,720 (A)
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Fixed overhead expenditure variance
Rs.
Budgeted fixed overhead expenditure
125,400
Actual fixed overhead expenditure
115,300
Fixed overhead expenditure variance
(c)
10,100 (F)
Raw materials cost variance
The budgeted raw material cost for production of 95,000 units was Rs. 1.40 per
unit (133,000/95,000) but the actual raw material cost for production of 90,000
units was Rs. 1.45 per unit (130,500/90,000). The raw material cost per unit may
have increased either because more raw material per unit was used than
budgeted, or because the price per unit of raw material was higher than
budgeted. Calculation of the raw material price and usage sub-variances would
indicate where further explanation should be sought.
Fixed overhead efficiency variance
The fixed overhead efficiency variance measures the extent to which more or
less standard hours were used for the actual production than budgeted. In this
case, a total of 27,200 machine hours were actually used, when only 27,000
standard machine hours should have been used. The difference may be due to
poorer production planning than expected or to machine breakdowns.
Fixed overhead expenditure variance
The fixed overhead expenditure variance measures the extent to which
budgeted fixed overhead differs from actual fixed overhead. Here, actual fixed
overhead is Rs. 10,100 less than budgeted. This could be due to an error in
forecasting fixed production overheads such as rent and power costs, or to a
decrease in fixed production overheads, such as changing to a cheaper
cleaning contractor.
(d)
Tutorial note
The question makes it clear that only three purposes are needed. Select three
from planning, motivating, communicating, co-ordinating, evaluating, rewarding
and controlling. The scope of the answer below is for illustration purposes only.
Planning
One of the key purposes of a budgeting system is to require planning to occur.
Strategic planning covers several years but a budget represents a financial plan
covering a shorter period, i.e. a budget is an operational plan. Planning helps an
organisation to anticipate key changes in the business environment that could
potentially impact on business activities and to prepare appropriate responses.
Planning also ensures that the budgeted activities of the organisation will
support the achievement of the organisation’s objectives.
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Co-ordination
Many organisations undertake a number of activities which need to be coordinated if the organisation is to meet its objectives. The budgeting system
facilitates this co-ordination since organisational activities and the links between
them are thoroughly investigated during budget preparation, and the overall
coherence between the budgeted activities is reviewed before the master
budget is agreed by senior managers. Without the framework of the budgeting
system, individual managers may be tempted to make decisions that are not
optimal in terms of achieving organisational objectives.
Communication
The budgeting system facilitates communication within the organisation both
vertically (for example between senior and junior managers) and horizontally (for
example between different organisational functions). Vertical communication
enables senior managers to ensure that organisational objectives are
understood by employees at all levels. Communication also occurs at all stages
of the budgetary control process, for example during budget preparation and
during investigation of end-of-period variances.
Control
One of the most important purposes of a budgeting system is to facilitate cost
control through the comparison of budgeted costs and actual costs. Variances
between budgeted and actual costs can be investigated in order to determine
the reason why actual performance has differed from what was planned.
Corrective action can be introduced if necessary in order to ensure that
organisational objectives are achieved. A budgeting system also facilitates
management by exception, whereby only significant differences between
planned and actual activity are investigated.
Motivation
The budgeting system can influence the behaviour of managers and employees,
and may motivate them to improve their performance if the target represented
by the budget is set at an appropriate level. An inappropriate target has the
potential to be demotivating, however, and a key factor here is the degree of
participation in the budget-setting process. It has been shown that an
appropriate degree of participation can have a positive motivational effect.
Performance evaluation
Managerial performance is often evaluated by the extent to which budgetary
targets for which individual managers are responsible have been achieved.
Managerial rewards such as bonuses or performance-related pay can also be
linked to achievement of budgetary targets. Managers can also use the budget
to evaluate their own performance and clarify how close they are to meeting
agreed performance targets.
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CHAPTER 27 – ADVANCED VARIANCE ANALYSIS
27.1
TOXIC KEMS
(a)
Tutorial note
Planning variances compare the old and new sstandards. Operational
variances compare actual results are compared with the revised (ex post)
standard.
Material A price planning variance
Rs.
9,000 tonnes should cost at ex ante standard price
(u Rs. 200)
1,800,000
They should cost at ex post standard price (u Rs. 220)
1,980,000
Material A price planning variance
180,000 (A)
Material B price planning variance
Rs.
4,000 tonnes should cost at ex ante standard price
(u Rs. 350)
1,400,000
They should cost at ex post standard price (u Rs. 385)
1,540,000
Material B price planning variance
140,000 (A)
Material C price planning variance
Rs.
7,000 tonnes should cost at ex ante standard price
(u Rs. 450)
3,150,000
They should cost at ex post standard price (u Rs. 495)
3,465,000
Material C price planning variance
315,000 (A)
Total materials price planning variances = Rs.(180,000 + 140,000 + 315,000)
(A) = Rs. 635,000 (A).
Material A price operational variance
Rs.
9,000 tonnes should cost at ex post standard price
(u Rs. 220)
1,980,000
They did cost
1,935,000
Material A price operational variance
45,000 (F)
Material B price operational variance
Rs.
4,000 tonnes should cost at ex post standard price
(u Rs. 385)
1,540,000
They did cost
1,368,000
Material B price operational variance
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Material C price operational variance
Rs.
7,000 tonnes should cost at ex post standard price
(u Rs. 495)
3,465,000
They did cost
3,164,000
Material C price operational variance
301,000 (F)
Total materials price operational variances = Rs.(45,000 + 172,000 + 301,000)
(F) = Rs. 518,000 (F).
(b)
Tutorial note
Remember that a separate mix variance is needed for each material and
that these are calculated using the revised standard costs.
The first step is to work out the proportion of each chemical in the standard
mix:
Material
Tonnes Percentage
A
460
40%
B
345
30%
C
345
30%
1,150
100%
Total
tonnes
tonnes
Mix variance
in value
tonnes
Standard
price per
kilo
Mix variance
in quantities
Standard
mix
Material
Actual mix
Mix variance (operational variance)
Rs.
Rs.
A
9,000
(40%)
8,000
1,000 (A)
220
220,000 (A)
B
4,000
(30%)
6,000
2,000 (F)
385
770,000 (F)
C
7,000
(30%)
6,000
1,000 (A)
495
495,000 (A)
20,000
0
20,000
55,000 (F)
Yield variance (operational variance)
In the standard cost, 1,150 tonnes of input produce 1,000 tonnes of output.
The weighted average standard cost of a tonne of output is calculated using the
ex post standard prices as follows:
(Rs. 220 u 460 tonnes + Rs. 385 u 345 tonnes + Rs. 495 u 345 tonnes) / 1,150
tonnes = Rs. 352 per tonne of input.
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The total yield variance can now be calculated as:
Tonnes of
input
17,000 tonnes of output should use (u 1,150/1,000)
19,550
They did use
20,000
Yield variance in tonnes of input
450 (A)
Standard price per tonne of input
Rs. 352
Yield variance in Rs.
(c)
Rs. 158,400 (A)
Historical standards
These are standards that were set some time ago and have not been
subsequently up-dated. These are used to measure progress in the long term
and they do not have a motivational impact on staff as current performance will
be well in excess of the standard.
Current standards
These are standards that take into account current levels of performance e.g.
staff training, efficiency, equipment levels and so on. They are the standard staff
should achieve at the present time. Again they have little motivational impact on
staff as they are already achieving the standard.
Attainable standards
To reach these standards staff will have to improve on current performance.
However, they are set in a way that staff can reach them in the foreseeable
future. This is the most motivational form of standard and can lead to significant
improvement in output.
Ideal standards
These are the standards that should be reached under perfect operating
conditions. Clearly perfect operating conditions are unlikely to occur. The level
of improvement required to reach this type of standard is often so great that it
can be demotivational. Perfect standards can be held out as long-term
aspirational targets but they should not be used to reward staff in the short term.
27.2
BRK
Variances
Before sales volume variances can be calculated standard profits have to be
determined.
Calculation of standard profit
Budgeted machine hours:
(10,000 × 0·3) + (13,000 × 0·6) + (9,000 × 0·8) = 18,000 hours
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Overhead absorption rate
81,000
/18,000 = Rs. 4·50 per machine hour
Product
B (Rs.)
R (Rs.)
K (Rs.)
Total
Direct material
3 × 1·80
5·40
1·25 × 3·28
4·10
1·94 × 2·50
4·85
Direct labour
0·5 × 6·50
3·25
0·8 × 6·50
5·20
0·7 × 6·50
4·55
Fixed production
overhead
0·3 × 4·50
1·35
0·6 × 4·50
2·70
0·8 × 4·50
3·60
Standard cost
10·00
12·00
13·00
Selling price
14·00
15·00
18·00
Standard profit per unit
4·00
3·00
5·00
Budgeted sales volume
10,000
13,000
9,000
32,000
40,000
39,000
45,000
Rs.
124,000
Weighted average profit per unit
Budgeted profit
Rs. 124,000
Budgeted sales volume
32,000
= Rs. 3.875
per unit
(i)
Sales price variance
Actual sales
9,500 × Rs. 14.5
B
R
K
Total
Rs.
Rs.
Rs.
Rs.
137,750
13,500 × Rs. 15.5
209,250
8,500 × Rs. 19
161,500
Should have sold
for
9,500 × Rs. 14
133,000
13,500 × Rs. 15
202,500
8,500 × Rs. 18
153,000
4,750 (F)
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(ii)
Sales volume
R
K
Actual sales
31,500
9,500
13,500
8,500
Budgeted sales
32,000
10,000
13,000
9,000
(500)
500
(500)
4
3
5
(2,000)
1,500
(2,500)
Standard profit per
unit
(iii)
B
(3,000)
(A)
Sale mix variance
Tutorial note
The first step is to work out the standard mix:
Total budgeted sales: 10,000 + 13,000 + 9,000 = 32,000 units
Budgeted sales mix
B:
10,000 / 32,000 u 100% =
31.25%
R:
13,000 / 32,000 u 100% =
40.625%
K:
9,000 / 32,000 u 100% =
28.125%
Product
B
(31.25%)
(iv)
Actual
sales mix
Standard
sales mix
Mix
variance in
quantities
Standard
profit per
unit
Mix
variance in
profit
units
units
units
Rs.
Rs.
9,500
9,843.750
343.750 (A)
4
1,375.000
(A)
R
(40.625%)
13,500
12,796.875
703.125 (F)
3
2,109.375
(F)
K
(28.125%)
8,500
8,859.375
359.375 (A)
5
1,796.875
(A)
31,500
31,500.000
0
1,062.500
(A)
Sales quantity variance
Total
Actual sales quantity in total
31,500
Budgeted sales quantity in total
32,000
Sales quantity variance in units
500
Weighted average standard profit per unit
Rs. 3.875
Sales quantity variance in Rs.
Rs.
1,937.50
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Tutorial note: Sales volume variance
The sales mix and sales quantity variances are sub-variances of the sales
volume variance.
Rs.
Sales mix variance
1,062.50
(A)
Sales quantity variance
1,937.50
(A)
Sales volume variance
3,000.00
(A)
Reconciliation
Rs.
Rs.
Budgeted sales at standard profit
Sales price variance
124,000
20,000 (F)
Sales mix profit variance
1,064 (A)
Sales quantity variance
1,936 (A)
3,000 (A)
17,000 (F)
141,000
Actual sales at actual price less standard cost
27.3
CARAT
(a)
Sales volume contribution per unit
Rs. /unit
Rs. /unit
Standard sales price
12·00
Material A (Rs. 1·70 × 2·5)
Material B (Rs. 1·20 × 1·5)
4·25
1·80
Labour (Rs. 6·00 × 0·45)
2·70
8·75
Standard contribution
3·25
Units
Sales volume variance
Budgeted volume of sales
50,000
Actual volume of sales
48,000
Variance
2,000
Unit contribution
Rs. 3.25
Variance (Rs. )
Rs. 6,500
Sales price variance
(A)
Rs.
Budgeted revenue for actual sales (Rs. 12 × 48,000)
576,000
Actual sales revenue for actual sales:
580,800
Variance:
4,800 (F)
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Direct material price variances
Material A price variance
Rs.
Actual quantity × actual price
200,000
Actual quantity × standard price (Rs. 1·70 × 121,951)
207,317
Price variance
7,317
Material B price variance
Rs.
Actual quantity × actual price
84,000
Actual quantity × standard price (Rs. 1·20 × 67,200)
80,640
Price variance
3,360
(F)
(A)
Materials mix and yield variances
Standard cost of input and output
kg
Rs. /kg
Standard cost
Material A = Rs. 1·70 × 2·5 =
2.5
Rs. 1.7
4·25
Material B = Rs. 1·20 × 1·5 =
1.5
Rs. 1.2
1·80
4.0
6·05
Standard cost of input = Rs. 6.05/4kg
Standard cost of output = Rs. 6.05/unit
Material mix
Actual
mix
Standard Standard
Mix
ratio
mix
variance
(kg)
Standard
cost per
kg
Mix
variance
(Rs)
A
121,951
2.5
118,220
3,731
1.7
6,343 (A)
B
67,200
1.5
70,931
(3,731)
1.2
(4,477) (F)
189,151
189,151
1,866 (A)
Material yield variance
Units
189,151 did yield
48,000
189,151 should have yielded (÷ 4kg)
47,288
Extra yield
712
Standard cost of a unit
Rs. 6.05
Yield variance
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Alternative calculation
AQ AM SC
A
121,951
× Rs. 1.7/kg
207,317
B
67,200
× Rs. 1.2/kg
80,640
189,151
287,957
MIX
(1,866)
(A)
AQ SM SC
189,151 × Rs. 6.05/4kg
286,091
YIELD
4,309 (F)
SQ SM SC
192,000 × Rs. 6.05/4kg
290,400
48,000 × 4kg
or 48,000 units × 6.05
Labour variances
Labour rate
Actual hrs × actual rate
Rs.
117,120
Actual hrs × standard rate (19,200 × Rs. 6)
115,200
Rate:
1,920 (A)
Labour efficiency
Rs.
Actual hrs worked × standard rate
18,900 hours × Rs. 6
113,400
Standard hrs × standard rate
48,000 units × .45 hrs × Rs. 6
129,600
Efficiency:
16,200 (F)
Labour idle time
Actual hrs paid for
Hours
19,200
Actual hrs worked
18,900
Idle time (hours)
300
Standard rate
Rs. 6
Idle time (Rs. )
1,800 (A)
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(b)
Budgeted profit: (50,000 units x Rs. 3.25) - Rs. 62,500 Rs. 100,000
Actual profit Rs. 580,800 – (Rs. 200,000 + Rs. 84,000 + Rs. 117,120 + Rs.
64,000) = Rs. 115,680
Rs.
Budgeted gross profit
Rs.
(50,000 units x Rs. 3.25) - Rs.
62,500
Sales volume contribution
variance (A)
Rs.
100,000
(6,500)
Sales price variance (F)
4,800
98,300
Cost variances
F
Materials price A
7,317
Materials price B
3,360
Material mix
1,866
Material yield
4,309
Labour rate
1,920
Labour idle time
1,800
Labour efficiency
16,200
Fixed overhead expenditure
Total
Actual profit
(c)
A
1,500
27,827
10,446
Rs. 580,800 – (Rs. 200,000 + Rs. 84,000 +
Rs. 117,120 + Rs. 64,000)
17,380
115,680
The favourable material A price variance indicates that the actual price per
kilogram was less than standard. Possible explanations include buying
lower quality material, buying larger quantities of material A and thereby
gaining bulk purchase discounts, a change of supplier, and using an out-ofdate standard.
The adverse material A mix variance indicates that more of this material
was used in the actual input than indicated by the standard mix. The
favourable material price variance suggests this may be due to the use of
poorer quality material (hence more was needed than in the standard mix),
or it might be that more material A was used because it was cheaper than
expected.
The favourable material A yield variance indicates that more output was
produced from the quantity of material used than expected by the standard.
This increase in yield is unlikely to be due to the use of poorer quality
material: it is more likely to be the result of employing more skilled labour,
or introducing more efficient working practices.
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It is only appropriate to calculate and interpret material mix and yield
variances if quantities in the standard mix can be varied. It has also been
argued that calculating yield variances for each material is not useful, as
yield is related to output overall rather than to particular materials in the
input mix. A further complication is that mix variances for individual
materials are inter-related and so an explanation of the increased use of
one material cannot be separated from an explanation of the decreased
use of another.
The unfavourable labour rate variance indicates that the actual hourly rate
paid was higher than standard. Possible explanations for this include hiring
staff with more experience and paying them more (this is consistent with
the favourable overall direct material variance), or implementing an
unexpected pay increase. The favourable labour efficiency variance shows
that fewer hours were worked than standard. Possible explanations include
the effect of staff training, the use of better quality material (possibly on
Material B rather than on Material A), employees gaining experience of the
production process, and introducing more efficient production methods. The
adverse idle time variance may be due to machine breakdowns; or a higher
rate of production arising from more efficient working (assuming employees
are paid a fixed number of hours per week).
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CHAPTER 28 – TRANSFER PRICING
28.1
TWO DIVISIONS
(a)
An optimal transfer price (or range of transfer prices) is a price for an
internally-transferred item at which:
‰
the selling division will want to sell units to the other profit centre,
because this will add to its divisional profit
‰
the buying division will want to buy units from the other profit centre,
because this will add to its divisional profit
‰
the internal transfer will be in the best interests of the entity as a
whole, because it will help to maximise its total profit.
(b)
When Division X has spare capacity, its only cost in making and selling
extra units of Product B is the variable cost per unit of production, Rs. 48.
Division Y can buy the product from an external supplier for Rs. 55.
It follows that a transfer that is higher than Rs. 48 but lower than Rs. 55, for
additional units of production, will benefit both profit centres as well as the
company as a whole. (It is in the best interests of the company to make the
units in Division X at a cost of Rs. 48 than to buy them externally for Rs.
55.)
(c)
When Division X is operating at full capacity and has unsatisfied external
demand for Product A, it has an opportunity cost if it makes Product B for
transfer to Division Y. Product A earns a contribution of Rs. 16 per unit (Rs.
62 – Rs. 46). The minimum transfer price that it would require for Product B
is:
Rs.
Variable cost of production of Product B
48
Opportunity cost: lost contribution from sale of Product A
16
Minimum transfer price to satisfy Division X management
64
Division Y can buy the product from an external supplier for Rs. 55, and will
not want to buy from Division X at a price of Rs. 64. The maximum price it
will want to pay is Rs. 55.
The company as a whole will benefit if Division X makes and sells Product
A.
It makes a contribution of Rs. 16 from each unit of Product A.
If Division X were to make and sell Product B, the company would benefit
by only Rs. 7. This is the difference in the cost of making the product in
Division X (Rs. 48) and the cost of buying it externally (Rs. 55).
The same quantity of limited resources (direct labour in Division X) is
needed for each product, therefore the company benefits by Rs. 9 (Rs. 16 –
Rs. 7) from making units of Product A instead of units of Product B.
On the basis of this information, the transfer price for Product X should be
Rs. 64 as long as there is unsatisfied demand for Product A. At this price,
there will be no transfers of Product B.
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28.2
SHADOW PRICE
(a)
The shadow price of the special chemical is the amount by which total
contribution would be reduced (or increased) if one unit less (or more) of
the chemical were available.
1 kilogram = 1,000 grams; therefore one kilogram of special chemical will
produce 100 tablets (1,000/10 grams per tablet).
Shadow price of the chemical
Rs.
1,000
Sales value of 100 tablets (u Rs. 10)
Further processing costs in B (u Rs. 2)
200
800
(b)
Variable cost of making the chemical in A
500
Shadow price per kilogram of chemical
300
The special chemical does not have an intermediate market.
The ideal transfer price for A is therefore any price above the variable cost
of making the chemical, which is Rs. 500 per kilogram.
The ideal transfer price for B is anything below the net increase in
contribution from processing a kilogram of the chemical. This is Rs. 1,000 –
Rs. 200 = Rs. 800 per kilogram.
There is no single ideal price. Any price in the range above Rs. 500 and
below Rs. 800 should make the managers of both profit centres want to
produce up to the capacity in division A.
A transfer price in the middle of the range, say Rs. 650, might be agreed.
(c)
The transfer price is needed to share the profit from selling the tablets
between divisions A and B. It is an internally negotiated price. Changing the
price will not affect the total profit for the company as a whole, provided that
division A produces the chemical up to its production capacity.
The transfer price itself should not be used as a basis for judging
performance. Having agreed a transfer price, key financial measures of
performance will be control over costs for division A and control over costs
and the selling price for tablets for division B.
(The divisions are profit centres, and so the performance of the divisional
managers should not be assessed on the basis of ROI or residual income.)
28.3
FROOM PLC
(a)
Objectives of Transfer pricing include the following:
(i)
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Goal congruence: The price should be set so that the divisional
management’s desire to maximize divisional profit is consistent with
the objectives of the company as a whole.
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(b)
(ii)
Performance evaluation: The transfer price should be set such that
it enables central management to effectively determine the
contribution of each of the division towards corporate profit.
(iii)
Divisional authority: The transfer price should maintain the
maximum divisional autonomy.
(iv)
Tax minimisation: The transfer price should lead to minimization of
tariffs and income taxes
(v)
Motivation: Transfer price should encourage divisional manager to
put in their best.
The company’s contribution as a whole
DIVISION A
DIVISION B
Rs.
Selling price
Incremental Cost (A)
Rs.
Rs.
20,000
30,000
30,000
(12,000)
(20,000)
(12,000)
(15,000)
(15,000)
(5,000)
3,000
െ
Incremental Cost (B)
Contribution
COMPANY
8,000
(i)
It is better to sell as intermediate product to earn a contribution of
N8,000 per unit than to transfer and earn a contribution of Rs. 3,000
per unit. Therefore, transfer should not be made to division B.
(ii)
If there is excess capacity, the excess capacity would be 200 units.
The total contribution from excess capacity of 200 units =
Rs. 3,000 x 200 units = Rs. 600,000
The overall profit would be as follows:
Rs.
Contribution from excess capacity (200 x Rs. 3,000)
Contribution from 800 units = 800 x Rs. 8,000
600,000
6,400,000
7,000,000
The 200 units which would be the excess capacity should be
transferred at between Rs. 12,000 and Rs. 20,000 per unit.
28.4
TRAINING COMPANY
(a)
If the Lahore centre has spare capacity, it will be in the best interest of the
company for the Karachi centre to use Lahore trainers, at a variable cost of
Rs. 450 per day including travel and accommodation, instead of hiring
external trainers at a cost of Rs. 1,200.
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Since the Lahore centre will have to pay Rs. 450 per trainer day, any
transfer price per day/daily fee in excess of Rs. 450 would add to its profit.
Since the Karachi centre can obtain external trainers for Rs. 1,200 per day,
any transfer price below this amount would add to its profit.
An appropriate transfer price would therefore be a price anywhere above
Rs. 450 per day and below Rs. 1,200 per day.
(b)
If the Lahore centre is operating at full capacity and is charging clients Rs.
750 per trainer day, there will be an opportunity cost of sending its trainers
to work for the Karachi centre. The opportunity cost is the contribution
forgone by not using the trainers locally in Lahore. Assuming that the
variable cost of using trainers in Lahore would be Rs. 200 per day, the
opportunity cost is Rs. 550 (Rs. 750 – Rs. 200).
The minimum transfer price that the manager of the Lahore centre would
want is:
Rs.
Variable cost of trainer day
200
Travel and accommodation
250
Opportunity cost: lost contribution
550
Minimum transfer price
1,000
The maximum price that the Karachi centre would be willing to pay is Rs.
1,200, which is the cost of using an external trainer.
The company should encourage the use of Lahore trainers by the Karachi
centre, because this will add to the total company profit.
The optimal transfer price is above Rs. 1,000 per day, so that the Lahore
centre will benefit from sending trainers to Karachi, but below Rs. 1,200 so
that the Karachi centre will also benefit.
A transfer price of Rs. 1,000 per day might be agreed.
(c)
If the Lahore centre is operating at full capacity and is charging clients Rs.
1,100 per trainer day, the opportunity cost of sending its trainers to work for
the Karachi centre is Rs. 900 (Rs. 1,100 – Rs. 200).
The minimum transfer price that the manager of the Lahore centre would
want is:
Rs.
Variable cost of trainer day
200
Travel and accommodation
250
Opportunity cost: lost contribution
900
Minimum transfer price
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The maximum price that the Karachi centre would be willing to pay is Rs.
1,200, which is the cost of using an external trainer.
It would be in the best interests of the company as a whole to use the
Lahore trainers to work for Lahore clients, earning a contribution of Rs. 900
per day, rather than use them in Karachi to save net costs of Rs. 750 per
day (Rs. 1,200 – Rs. 200 – Rs. 250).
The transfer price should be set at Rs. 1,350 per trainer day. At this rate,
the Karachi centre will use external trainers, and all the Lahore trainers will
be used in Lahore.
28.5
BRICKS
(a)
Profit statements
(i)
Operating at 80% capacity
Transfer price Rs. 200
Transfer price Rs. 180
Group
X
Group
Y
Total
Group
X
Group
Y
Total
External
180
240
420
180
240
420
Transfers
120
-
0
108
-
0
Total
300
240
420
288
240
420
-
(120)
0
-
(108)
0
Variable
(112)
(36)
(148)
(112)
(36)
(148)
Fixed
(100)
(40)
(140)
(100)
(40)
(140)
Total
(212)
(196)
(288)
(212)
(184)
(288)
Profit
88
44
132
76
56
132
Sales:
Costs
Transfers
(ii) Operating at 100% capacity
Transfer price Rs. 200
Transfer price Rs. 180
Group
X
Group
Y
Total
Group
X
Group
Y
Total
External
180
320
500
180
320
500
Transfers
200
-
0
180
-
0
Total
380
320
500
360
320
500
-
(200)
0
-
(180)
0
Variable
(140)
(60)
(200)
(140)
(60)
(200)
Fixed
(100)
(40)
(140)
(100)
(40)
(140)
Total
(240)
(300)
(340)
(240)
(280)
(340)
Profit
140
20
160
120
40
160
Sales:
Costs
Transfers
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(b)
The effect of a change in the transfer price from Rs. 200 to Rs. 180 will
result in lower profit for Group X and higher profit for Group Y, but the total
profit for the company as a whole will be unaffected.
A reduction in the transfer price to Rs. 180 (or possibly lower) is
recommended, because this is the price at which Group Y can buy the
materials externally. At any price above Rs. 180, Group Y will want to buy
externally, and this would not be in the interests of the company as a
whole.
Significantly, at a transfer price of both Rs. 200 and Rs. 180, Division Y
would suffer a fall in its divisional profit if it reduced the selling price of
bricks to Rs.0.32 and increased capacity by 400,000 bricks each month. A
reduction in price would be in the best interests of the company as a whole,
because total profit would rise from Rs. 132,000 per month to Rs. 160,000.
(c)
Ignoring the transfer price, the effect on Division Y of reducing the sale
price of bricks to Rs.0.32 would be to increase external sales by Rs. 80,000
and variable costs in Division Y by Rs. 24,000 (400 tonnes u Rs. 60). Cash
flows would therefore improve by Rs. 56,000 per month. To persuade
Division Y to take the extra 400 tonnes, the transfer price should not
exceed Rs. 140 (Rs. 56,000/400). This is below the current external market
price, although there is strong price competition in the market.
The transfer price for Division X should not be less than the variable cost of
production in Division X, which is Rs. 70 per tonne.
However, if the transfer price is reduced to Rs. 140 per tonne or less,
Division X might try to sell more materials in the external market, by
reducing the selling price.
It would appear that although the ideal transfer price might be Rs. 140 or
below, this will not be easily negotiated between the group managers. An
imposed settlement may be necessary. Intervention by head office might be
needed to impose a transfer price, and require Division Y to reduce its
sales price to Rs.0.32.
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CHAPTER 29 – WORKING CAPITAL MANAGEMENT
29.1
CASH OPERATING CYCLE
(a)
Working capital cycle:
Year
1
Year
2
Year
3
days
days
days
76
76
91
(61)
(55)
(64)
15
21
27
37
37
31
42
49
47
73
88
91
167
195
196
Raw materials inventory cycle
(Raw materials/Purchases) × 365 days
Minus Credit from suppliers
(Trade payables /Credit purchases) × 365 days
Production cycle
(Work-in-progress/Cost of sales) × 365 days
Finished goods inventory cycle
(Finished goods/Cost of sales) × 365 days
Credit to customers
(Trade receivables/Credit sales) × 365 days
Total length of working capital cycle
All sales and purchases are considered to be on credit.
(b)
A long working capital cycle means that a large amount of capital will be
tied up in working capital.
Actions to reduce the length of the cycle
‰
Reduce raw materials inventory cycle – review the inventory levels
and quantities purchased.
Possible disadvantages of reducing inventory levels:
‰
x
Risk of stock-outs and production hold-ups
x
Loss of bulk discounts.
Delay payment to suppliers (increase finance from creditors)
Possible disadvantages of delaying payments
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Loss of cash discounts
x
A bad business relationship with suppliers
x
Possible loss of reliable suppliers of supply
x
Suppliers might decide to charge higher prices.
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‰
Speed up the production cycle (reducing production cycle)
Possible disadvantages of making the production cycle shorter
‰
‰
x
Investment may be required in new technology and training
x
Higher rates of pay may be necessary
x
More efficient production should not be allowed to lead to a
build-up of finished goods inventories.
Reduce inventories of finished goods (Inventory level management).
x
Possible disadvantage of reducing finished goods inventories
x
Possible loss of profit due to stock-outs
Reduce the period of credit allowed to customers (receivables
(debtors) management)
Possible disadvantage of reducing credit
29.2
x
Improved credit control will cost more
x
Cash discounts may be expensive to encourage prompt
payment
x
Some loss of sales, because customers might buy from
competitors offering better credit terms.
WORKING CAPITAL
Overtrading (sometimes referred to as under-capitalisation) occurs when a
business entity attempts to expand its sales rapidly without adequate finance,
especially medium and long-term finance.
There are several symptoms of overtrading. These are:
(a)
Very rapid growth in sales.
(b)
An increase in inventory levels as a proportion of sales. This means slower
inventory turnover.
(c)
Sometimes there are also initial increases in trade receivables. However,
as the cash flow problems of the entity get worse, there might be an effort
to collect debts more quickly in order to improve the cash flow. If this
happens, the average credit period allowed to customers will fall.
(d)
Payments to suppliers and other creditors are delayed. The total of trade
payables therefore increases significantly.
(e)
Short-term bank borrowing increases. There is a rise in the bank overdraft.
Interest payments therefore increase.
(f)
The proportion of total assets financed by equity will decline.
(g)
The current ratio and liquidity ratio get worse.
(h)
There is a rapid increase in sales relative to the entity’s total assets.
(i)
Profit margins fall, and new investment may be delayed.
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There is some evidence of over-trading in the case of DON:
(a)
Sales have increased by 61% during the year.
(b)
Inventory levels have increased by 23%. However, this is much less than
the increase in sales turnover.
Trade receivables have increased by 58%, which is slightly less than the
growth in sales. The average credit period for customers has fallen from 73
days to 72 days (an insignificant change).
(c)
Payments to both suppliers have been delayed. Trade payables in Year 5
(measured as payables/sales × 365 days) were paid in 57 days, but this
increased to 64 days in Year 6. However, the increase in the time taken to
pay is probably not excessive.
(d)
Short-term borrowing (the bank overdraft) increased from Rs. 140,000 to
Rs. 250,000.
(e)
Assets were financed by:
Equity
Trade payables
Bank overdraft
Medium-term bank loan
Year 5
Year 6
%
56
22
9
13
%
47
31
13
10
The percentage of total assets financed by equity has fallen by a large
amount.
(f)
Current ratio
Liquidity ratio
Year 5
Year 6
1.48
0.77
1.15
0.66
Liquidity has worsened.
(g)
Sales/gross assets
Year 5
Year 6
1.18
1.46
Sales are being supported by a lower amount of assets per Rs. 1 of sales.
This might indicate overtrading, but it might also be the result of increased
efficiency.
(h)
Gross margin
Profit before tax/sales
Year 5
Year 6
11.7%
6.7%
8.96%
5.5%
From the above data it is appears that DON is showing many of the
symptoms of overtrading.
Although DON is profitable, it is likely to experience cash flow problems if
the overtrading gets worse.
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29.3
WASEEM LIMITED
Rupees in
million
(a)
Additional finance required:
Expected increase in assets (1,100 x 20% x 140%)
308.00
Expected increase in liabilities (1,100 x 20% x 25%)
(55.00)
Retained earnings for the year (1,100 x 120% x 10% x 80%)
(105.60)
Additional finances required
(b)
147.40
In this case, increase in assets less liabilities must be equal to the
increase in retained earnings.
(i)
Let x be the required growth rate
(1,100x × 140%) – (1,100x × 25%) = 1,100 × (1+x) × 10% ×
(1 – 20%)
1,540x – 275x – 88x= 88
x = 7.48%
(ii)
Existing debt equity ratio = 465 / 700 = 66.43%
In this case, the company must obtain an additional loan of 66.43%
of the additional earnings in order to maintain the current debt equity
ratio.
Now, the revised equation is as follows:
(1,100x × 140%) – (1,100 x × 25%) = [1,100 × (1 + x ) × 10% (1 –
20%)] + [1,100 × (1 + x) × 10% × (1 – 20%) x 66.43%]
1,540x – 275x – 88x – 58.46x= 88 + 58.46
x = 13.09%
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CHAPTER 30 – INVENTORY MANAGEMENT
30.1
MARX LIMITED
(a)
There are two main objectives of working capital management:
(i)
To ensure that the entity has sufficient working capital to conduct its
operations efficiently. In order to achieve this objective, there must be
sufficient working capital to provide adequate liquidity.
(ii)
To avoid over-investment in working capital, because excessive
finance invested in working capital does not provide any financial
return.
The two requirements of liquidity and profitability may conflict with each
other. The need for liquidity suggests having sufficient working capital,
whereas the need to maximise profitability suggests a need to avoid too
much investment in working capital. Working capital management involves
finding a balance between the two objectives.
(b)
Current policy
Demand per week = 400,000/50 = 8,000 units
Re-order level = 25,000 units
Demand during the re-order period = 8,000 u 2 weeks = 16,000 units.
Buffer inventory = 25,000 – 16,000 = 9,000 units.
Average inventory = 50,000/2 + 9,000 = 34,000 units.
Annual costs
Rs.
Ordering costs (400,000/50,000) u Rs. 240
1,920
Holding costs: 34,000 u Rs. 0.75
25,500
27,420
EOQ
2 x 240 x 400,000
0.75
= 16,000 units.
It is assumed that the buffer inventory will remain the same, 9,000 units.
Average inventory = 16,000/2 + 9,000 = 17,000 units.
Annual costs
Rs.
Ordering costs (400,000/16,000) u Rs. 240
6,000
Holding costs: 17,000 u Rs. 0.75
12,750
18,750
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(Tutorial note: The annual holding costs and the annual ordering costs are not
equal, because of the buffer inventory of 9,000 units, which adds Rs. 6,750 to
annual holding costs.)
Conclusion
If the company changes to using the EOQ to decide the order quantity,
annual savings would be Rs. 8,670 (= 27,420 – 18,750). However, reducing
the buffer inventory would reduce costs further by up to Rs. 6,750 per year.
30.2
ENGELS LIMITED
Cost of current ordering policy of Engels Limited
Ordering cost = Rs. 250 x (625,000/100,000) = Rs. 1,563 per year
Weekly demand = 625,000/50 = 12,500 units per week
Consumption during 2 weeks lead time = 12,500 x 2 = 25,000 units
Buffer stock = re-order level less usage during lead time = 35,000 – 25,000 = 10,000
units
Average stock held during the year = 10,000 + (100,000/2) = 60,000 units
Holding cost = 60,000 x Rs. 0·50 = Rs. 30,000 per year
Total cost = ordering cost plus holding cost = Rs. 1,563 + Rs. 30,000 = Rs. 31,563 per
year
Economic order quantity = ((2 x 250 x 625,000)/0·5)1/2 = 25,000 units
Number of orders per year = 625,000/25,000 = 25 per year
Ordering cost = Rs. 250 x 25 = Rs. 6,250 per year
Holding cost (ignoring buffer stock) = Rs. 0·50 x (25,000/2) = Rs. 0·50 x 12,500 = Rs.
6,250 per year
Holding cost (including buffer stock) = Rs. 0·50 x (10,000 + 12,500) = Rs. 11,250 per
year
Total cost of EOQ-based ordering policy = Rs. 6,250 + Rs. 11,250 = Rs. 17,500 per
year
Saving for Engels Limited by using EOQ-based ordering policy = Rs. 31,563 – Rs.
17,500 = Rs. 14,063 per year
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30.3
LENIN LIMITED
(a)
There are a number of factors that determine the level of investment in
current assets and their relative importance varies from company to
company.
Length of working capital cycle
The working capital cycle or operating cycle is the period of time between
when a company settles its accounts payable and when it receives cash
from its accounts receivable. Operating activities during this period need to
be financed and as the operating period lengthens, the amount of finance
needed increases. Companies with comparatively longer operating cycles
than others in the same industry sector, will therefore require comparatively
higher levels of investment in current assets.
Terms of trade
These determine the period of credit extended to customers, any discounts
offered for early settlement or bulk purchases, and any penalties for late
payment. A company whose terms of trade are more generous than
another company in the same industry sector will therefore need a
comparatively higher investment in current assets.
Policy on level of investment in current assets
Even within the same industry sector, companies will have different policies
regarding the level of investment in current assets, depending on their
attitude to risk. A company with a comparatively conservative approach to
the level of investment in current assets would maintain higher levels of
inventory, offer more generous credit terms and have higher levels of cash
in reserve than a company with a comparatively aggressive approach.
While the more aggressive approach would be more profitable because of
the lower level of investment in current assets, it would also be more risky,
for example in terms of running out of inventory in periods of fluctuating
demand, of failing to have the particular goods required by a customer, of
failing to retain customers who migrate to more generous credit terms
elsewhere, and of being less able to meet unexpected demands for
payment.
Industry in which organisation operates
Another factor that influences the level of investment in current assets is
the industry within which an organisation operates. Some industries, such
as aircraft construction, will have long operating cycles due to the length of
time needed to manufacture finished goods and so will have comparatively
higher levels of investment in current assets than industries such as
supermarket chains, where goods are bought in for resale with minimal
additional processing and where many goods have short shelf-lives.
(b)
(i)
Economic order quantity = (2 x 6 x 60,000/0·5)1/2 = 1,200 units
Number of orders = 60,000/1,200 = 50 order per year
Annual ordering cost = 50 x 6 = Rs. 300 per year
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Average inventory = 1,200/2 = 600 units
Annual holding cost = 600 x 0·5 = Rs. 300 per year
Inventory cost = 60,000 x 12 = Rs. 720,000
Total cost of inventory with EOQ policy = 720,000 + 300 + 300 = Rs.
720,600 per year
(ii)
Order size for bulk discounts = 10,000 units
Number of orders = 60,000/10,000 = 6 orders per year
Annual ordering cost = 6 x 6 = Rs. 36 per year
Average inventory = 10,000/2 =5,000 units
Annual holding cost = 5,000 x 2 = Rs. 10,000 per year
Discounted material cost =12 x 0·99 = Rs. 11·88 per unit
Inventory cost = 60,000 x 11·88 = Rs. 712,800
Total cost of inventory with discount = 712,800 + 36 + 10,000 = Rs.
722,836 per year
The EOQ approach results in a slightly lower total inventory cost
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CHAPTER 31 – MANAGEMENT OF RECEIVABLES AND PAYABLES
31.1
TRADE RECEIVABLES MANAGEMENT
Loss of sales based on Year 3 = 25% × Rs. 1,188,000 = Rs. 297,000
However, the cost of these sales will be avoided.
Gross profit percentage = (1,188,000 – 1,098,360)/1,188,000
= 0.755. Gross profit is 7.55% of sales. It is assumed that the loss from the
reduction in sales will be: 7.55% × Rs. 297,000 = Rs. 22,424
Rs.
Loss of profit from fall in sales
Additional cost of credit control
(22,424)
(20,000)
(42,424)
30,000
(12,424)
Reduction in bad debts
Reduction in profit, before savings in interest
Working capital changes
Reduction in inventories
Rs.
Raw materials
Work in progress
Finished goods
(25% × 180,000)
(25% × 93,360)
(25% × 142,875)
Reduction in trade payables
(25% × 126,000)
Reduction in trade receivables
Current trade receivables
297,000
Receivables after the change= (60/365) u 75% u Rs.
146,466
1,188,000
45,000
23,340
35,719
104,059
(31,500)
Reduction in working capital
Cost of financing working capital
Saving per year in interest from reduction
150,534
223,093
9%
Rs.
20,078
Net effect on annual profit
Rs.
Reduction in profit, before savings in interest (see above)
Reduction in interest cost
Net increase in annual profit
(12,424)
20,078
7,654
Reducing the credit period to 60 days will result in annual savings of Rs. 7,654.
To achieve these savings, there would have to be a fall in sales by 25%.
Senior management might decide that the size of the savings does not justify
such a large fall in annual sales, because of the longer-term consequences this
might have for the business.
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31.2
BAHAWALPUR BULIDERS LTD
(a)
Credit sales
Rs. 4,800,000 per annum
Average credit period
45 days
The annual cost is as follows:
Rs.
45
x Rs. 4,800,000 x 14.5%
365
85,808
Bad debts: 1% x Rs. 4,800,000
48,000
133,808
The cost of the factor
80% of credit sales financed by the factor would be 80% of Rs. 4,800,000 =
Rs. 3,840,000. For a consistent comparison, we must assume that 20% of
credit sales would be financed by a bank overdraft.
The average credit period would be only 30 days.
The annual cost would be as follows,
Rs.
Factor’s finance
30
x Rs. 3,840,000 x 12%
365
37,874
Overdraft
30
x Rs. 960,000 x 14.5%
365
11,441
Cost of factor’s services: 2.5% x Rs. 4,800,000
Less savings in company’s administrative costs
Net cost/(benefit) of the factor
49,315
120,000
(96,000)
73,315
Conclusion
The factor option is cheaper by Rs. 60,493 (Rs. 133,808 – Rs. 73,315)
based on the above calculations. Management is therefore advised to
accept the services of the factor.
NOTE:
**Rs. 3,840,000 = 80% of Rs. 4,800,000
*
(b)
Rs. 960,000 = Rs. 20% of Rs. 4,800,000
Factoring can be used under the following situations
(i)
When a company has a substantial amount of its working capital tied
up in debtors which it cannot collect easily.
(ii)
When a company is faced with liquidity problems due to failure of
customers to meet the credit period allowed to them.
(iii)
When the credit control system is becoming increasingly expensive to
maintain.
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(c)
31.3
(iv)
When the company’s fixed assets are limited and it cannot obtain
additional finance without offering security.
(v)
When a company wishes to raise finance without further borrowing or
diluting equity.
(i)
Full service non-recourse factoring is where book debts are
purchased by the factor assuming 100% credit risk. Full amount of
invoices have to be paid to the client in the event of any debt
becoming bad. Factor also advances 80 – 90% of the book debt
immediately to the client.
(ii)
Full service recourse factoring is where the client is not protected
against the risk of bad debt. The client has no indemnity against
unsettled or uncollected debts. Where the factor has advanced fund
against book debts which eventually become bad, the client has to
refund such advance.
(iii)
Non-Notification factoring is where customers are not informed
about the factoring agreement. The factor deals with customers
through the client company.
CHISHTIAN CONSTRUCTION PLC
(a)
Consideration of the three available finance options:
(i)
Bank loan option
The cost of obtaining bank loan with 10%
௜
compensating balance is ଵ଴଴ି௖ x 100%
where i = bank interest rate
c = compensating balance
Cost of obtaining bank loan
=
ଵସ
ଵ଴଴ିଵ଴
x 100
= 14/90 x 100
= 15.56%
(ii)
Trade credit option
If discounts are not taken, up to 97% x Rs. 5 billion per month x 2
months can be raised after the second month.
The cost, which is the same as the cost of lost cash discounts, can be
estimated using the formula: cost =
ௗ
ଵ଴଴ିௗ
ൈ
ଷ଺ହ
௧
where d = discount percentage
t = reduction in the payment period in days which would be necessary
to obtain the early payment. i.e. 90 – 10 = 80
i.e.
cost
=
=
ଷ
ଷ଺ହ
ଵ଴଴ିଷ
ଷ
ଽ଻
ൈ
ൈ ଽ଴ିଵ଴
ଷ଺ହ
଼଴
= 14.11%
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(iii) Cost of factoring
Factors fee per annum i.e. 2% x Rs. 15,000,000,000 x 12
= Rs. 3,600,000,000
Factor’s finance cost: 12% x 9,500,000,000
= Rs. 1,140,000,000
Rs. 4,740,000,000
Less savings in cost per annum
(Rs. 250,000,000 x 12)
= Rs. 3,000,000,000
Rs. 1,740,000,000
Rate Per Annum
=
1,740,000,000
9,500,000,000
×
100
1
= 18.3%
Decision:
From the computations above, trade credit is the cheapest source of
finance, hence Chishtian Construction Plc should take advantage of
the discount.
(b)
31.4
Factors that should be considered when formulating credit control policy
are stated as follows:
(i)
Cost (administrative) of debt collection.
(ii)
Procedures for controlling credit to individual customers and for debt
collection.
(iii)
Any saving or additional cost of operating the credit policy.
(iv)
The amount of extra capital required to finance total credit
extended/extension.
(v)
Way of implementing the credit policy e.g. credit could be eased by
giving debtors longer period for settling their accounts.
(vi)
The cost of additional finance required for any increase in the volume
of receivables (or the savings from a reduction in receivables). The
cost might be bank overdraft interest, or the cost of long-term finance.
DISCOUNT AND FACTOR
(a)
Cost of offering the discount for early payment =
[1 + 2/ (100 – 2] 365/(90- 7) - 1
= (1.02041)4.39759 – 1
= 1.093 – 1 = 0.093 or 9.3%.
(b)
Annual sales = = Rs. 100,000 × 12 months = Rs. 1,200,000.
Average trade receivables without the factor = Rs. 1,200,000 u 2 months/12
months = Rs. 200,000.
Average trade receivables with the factor = Rs. 1,200,000 u 1 month/12
months = Rs. 100,000.
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Annual costs
Without the factor
Administration (12 u Rs. 2,000)
Bad debts (0.75% u Rs. 1,200,000)
Interest cost of finance (9% u Rs. 200,000)
Rs.
Rs.
24,000
9,000
18,000
51,000
With the factor
Fees (4% u Rs. 1,200,000)
Interest cost of finance
Factor finance (8% u 80% u Rs. 100,000)
Overdraft finance (9% u 20% u Rs. 100,000)
48,000
6,400
1,800
56,200
5,200
Net extra cost of the factor per year
31.5
VEHARI IT SOLUTIONS LIMITED
(a)
(i)
Cost of current policy – Credit sales
Credit sales
Rs. 40 million per annum
Average credit period
60 days
Rs.
The annual cost is as follows:
଺଴
Cost of financing receivables: ଷ଺଴ x
ேସ଴௠௜௟௟௜௢௡௫଴Ǥଵସ
ଵ
Bad debts: 0.5% x Rs. 1,500,000
933,333
40,000
Total cost
(ii)
=
973,333
Cost of using a factor
80 percent of credit sales financed by the factor would be 85 percent of Rs.
40,000,000 = Rs. 34,000,000.
For a consistent comparison, we must assume that 15% of credit sales
would be financed by a bank overdraft.
The average period would be only 60 days (but 40 days – industry averageis to be adopted)
In view of the above, the annual cost of using a factor would be as follows:
Rs.
ସ଴
ሺ଴Ǥ଼ହ௫ேସ଴௠ሻ௫଴Ǥଵଶ
Factor’s finance charges: ଷ଺଴ x
ଵ
ସ଴
ሺ଴Ǥଵହ௫ேସ଴௠ሻ௫଴Ǥଵସ
Bank overdraft (interest) ଷ଺଴ x
ଵ
453,333
93,333
546,666
Factor’s service charge: 0.02 x Rs. 40m
800,000
1,346,666
Less: Savings in company’s administration cost
Cost of using a factor
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Comment:
Factoring is more expensive in this case because of the 2 percent charge
on sales that is Rs. 800,000. This appears too high . However, since the
service charge cannot be eliminated or reduced (in this case), the resulting
difference of Rs. 321,333 (Rs. 1,294,666- Rs. 973,333) makes factoring of
the company’s debt unattractive hence it is not advisable for Vehari IT
Solutions Limited to engage the services of a factor.
(b)
31.6
Potential advantages of using the services of a debt factor include the
following:
‰
Savings in the cost of credit administration
‰
Releasing key staff engaged in debt recovery exercise for other tasks
‰
Greater certainty in cash inflow.
‰
Receiving advice on the credit worthiness of customers.
‰
In the case of full service non-recourse factoring, the company will be
provided with full or partial protection against bad debts.
‰
The fear customers have for factors may prompt the debtors to pay
up.
‰
Receiving information on market trends, competitors and customers.
(ii)
Potential disadvantages of using the services of a debt factor include
the following:
‰
It is an indication that the business is experiencing financial
difficulties which may have an adverse effect on the confidence
of customers, suppliers and staff.
‰
It may increase the operating cost of the company.
‰
In the case of full service recourse factoring, the company is not
protected against the risk of bad debts.
ULNAD CO
(a)
Evaluation of change in credit policy
Rs.
Increase in financing cost:
New receivables (W2)
Current receivables (W1)
Cost of finance
Incremental costs = 6.3m × 0.005 =
Cost of discount = 6.3m × 0.015 × 0.3 =
Increase in costs
Contribution from increased sales = 6m × 0.05 × 0.6 =
Net benefit of policy change
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802,603
(657,534)
145,069
7%
10,155
31,500
28,350
70,005
180,000
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The proposed policy change will increase the profitability of Ulnad Co
W1: Existing receivables
Current credit sales
Rs. 6 million
Current average collection period (30 days + 10 days)
Current accounts receivable (6m × 40/ 365)
W2 New receivables
New credit sales
(b)
40 days
Rs. 657,534
Rs. 6.3 million
New level of trade receivables
15 days credit utilisation:
(6,300,000 x 0.3 x 15/365)
60 days credit utilisation
(6,300,000 x 0.7 x 60/365)
Rs 724,932
Total investment in receivables under new policy
Rs 802,603
Rs 77,671
There are four key areas of accounts receivable management: policy
formulation, credit analysis, credit control and collection of amounts due.
Policy formulation
This is concerned with establishing the framework within which
management of accounts receivable in an individual company takes place.
The elements to be considered include establishing terms of trade, such as
period of credit offered and early settlement discounts: deciding whether to
charge interest on overdue accounts; determining procedures to be
followed when granting credit to new customers; establishing procedures to
be followed when accounts become overdue, and so on.
Credit analysis
Assessment of creditworthiness depends on the analysis of information
relating to the new customer. This information is often generated by a third
party and includes bank references, trade references and credit reference
agency reports. The depth of credit analysis depends on the amount of
credit being granted, as well as the possibility of repeat business.
Credit control
Once credit has been granted, it is important to review outstanding
accounts on a regular basis so overdue accounts can be identified. This
can be done, for example, by an aged receivables analysis. It is also
important to ensure that administrative procedures are timely and robust,
for example sending out invoices and statements of account,
communicating with customers by telephone or e-mail, and maintaining
account records.
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Collection of amounts due
Ideally, all customers will settle within the agreed terms of trade. If this does
not happen, a company needs to have in place agreed procedures for
dealing with overdue accounts. These could cover logged telephone calls,
personal visits, charging interest on outstanding amounts, refusing to grant
further credit and, as a last resort, legal action. With any action, potential
benefit should always exceed expected cost.
31.7
BRUTUS COMPANY
Rs.
Contribution from higher sales (45% × Rs. 240,000)
108,000
Decrease in bad debts
Current bad debts (1.25% × Rs. 8 million)
Bad debts with new policy (1% × Rs. 8.24 million)
Reduction in bad debts
100,000
82,400
17,600
Benefits
125,600
Increase in financing cost:
New receivables (W2)
1,094,904
Current receivables (W1)
(986,301)
108,603
Cost of finance
8%
Cost of discount = 8.24m × 0.025 × 0.25 =
Increase in administration costs per year (0.005 × Rs.
8.24 m)
Increase in costs
8,688
51,500
41,200
(101,388)
Net benefit of policy change
24,212
If all the estimates are correct the discount policy will increase annual profit by
about Rs. 24,000. This is a fairly small amount in relation to the company’s
annual profits of Rs. 1 million after bad debts, and management should consider
the reliability of the estimates before deciding whether or not to introduce the
discount policy. The expected increase in total annual sales would seem to be a
key estimate.
By improving the collection of receivables and reducing the average collection
period to the expected current 30 days, the company could reduce average
receivables by Rs. 328,767 (Rs. 8 million × 15/365) and this would reduce annual
interest costs (at 8%) by about Rs. 26,300 per year – more than the expected
benefit from the discount policy.
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Workings
W1: Existing receivables
Current credit sales
Rs. 8 million
Current accounts receivable (8m × 45/ 365)
Rs. 986,301
W2 New receivables
New credit sales (8 Million u1.03)
Rs. 8,240,000
New level of trade receivables
14 days credit utilisation:
(8,240,000 x 0.25 x 14/365)
60 days credit utilisation
(8,240,000 x 0.75 x 60/365)
Rs 1,015,890
Total investment in receivables under new policy
Rs 1,094,904
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CHAPTER 32 – CASH MANAGEMENT
32.1
BAUMOL AND MILLER-ORR
(a)
Optimum size of transaction for investment sales =
2 u 60u 3,000,000
0.05
= Rs. 84,852, say Rs. 85,000.
The frequency of investment sales
ൌ
(b)
•ǤͺͷǡͲͲͲ
ൈ͵͸ͷ†ƒ›•ൌ‡˜‡”›ͳͲ†ƒ›•
•Ǥ͵ǡͲͲͲǡͲͲͲ
Standard deviation of daily cash flows = 2,200.
Therefore the variance of daily cash flows = (2,200)2 = 4,840,000.
Daily interest cost = 5%/365 days = 0.0137%.
(i)
Spread =
¾ u 60 u 4,840,000
0.000137
3u
1/3
(Note: ‘to the power of 1/3 = the cube root)
Spread = 3 u Rs. 11,671 = Rs. 35,013, say Rs. 35,000.
(ii)
Upper limit = Minimum cash balance + Spread
= Rs. 20,000 + Rs. 35,000 = Rs. 55,000.
(iii)
Return point = Rs. 20,000 + (1/3 u Rs. 35,000) = Rs. 31,667.
When the cash balance reaches Rs. 55,000, the entity will buy Rs.
23,333 of investments, and the cash balance will return to Rs. 31,667.
Similarly, when the cash balance reaches Rs. 20,000, the entity will
sell Rs. 11,667 of investments, to return the cash balance to Rs.
31,667.
32.2
RENPEC CO
(a)
Determination of spread:
Daily interest rate = 5.11/ 365 = 0.014% per day
Variance of cash flows = (1,000)2 = Rs. 1,000,000 per day
Transaction cost = Rs. 18 per transaction
Spread
= 3 × ((0.75 x transaction cost x variance)/interest rate)1/3
= 3 × ((0.75 × 18 × 1,000,000)/ 0.00014)1/3
= 3 × 4,585.7 = Rs. 13,757
Lower limit (set by Renpec Co) = Rs. 7,500
Upper limit = 7,500 + 13,757 =Rs. 21,257
Return point = 7,500 + (13,757/ 3) = Rs. 12,086
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The Miller-Orr model takes account of uncertainty in relation to receipts and
payment. The cash balance of Renpec Co is allowed to vary between the
lower and upper limits calculated by the model. If the lower limit is reached,
an amount of cash equal to the difference between the return point and the
lower limit is raised by selling short-term investments. If the upper limit is
reached an amount of cash equal to the difference between the upper limit
and the return point is used to buy short-term investments. The model
therefore helps Renpec Co to decrease the risk of running out of cash,
while avoiding the loss of profit caused by having unnecessarily high cash
balances.
(b)
When considering how working capital is financed, it is useful to divide
assets into non-current assets, permanent current assets and fluctuating
current assets. Permanent current assets represent the core level of
working capital investment needed to support a given level of sales. As
sales increase, this core level of working capital also increases. Fluctuating
current assets represent the changes in working capital that arise in the
normal course of business operations, for example when some accounts
receivable are settled later than expected, or when inventory moves more
slowly than planned.
The matching principle suggests that long-term finance should be used for
long-term assets. Under a matching working capital funding policy,
therefore, long-term finance is used for both permanent current assets and
non-current assets. Short-term finance is used to cover the short-term
changes in current assets represented by fluctuating current assets.
Long-term debt has a higher cost than short-term debt in normal
circumstances, for example because lenders require higher compensation
for lending for longer periods, or because the risk of default increases with
longer lending periods. However, long-term debt is more secure from a
company point of view than short-term debt since, provided interest
payments are made when due and the requirements of restrictive
covenants are met, terms are fixed to maturity. Short-term debt is riskier
than long term debt because, for example, an overdraft is repayable on
demand and short-term debt may be renewed on less favourable terms.
A conservative working capital funding policy will use a higher proportion of
long-term finance than a matching policy, thereby financing some of the
fluctuating current assets from a long-term source. This will be less risky
and less profitable than a matching policy, and will give rise to occasional
short-term cash surpluses.
An aggressive working capital funding policy will use a lower proportion of
long-term finance than a matching policy, financing some of the permanent
current assets from a short-term source such as an overdraft. This will be
more risky and more profitable than a matching policy.
Other factors that influence a working capital funding policy include
management attitudes to risk, previous funding decisions, and organisation
size. Management attitudes to risk will determine whether there is a
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Business finance decisions
preference for a conservative, an aggressive or a matching approach.
Previous funding decisions will determine the current position being
considered in policy formulation. The size of the organisation will influence
its ability to access different sources of finance. A small company, for
example, may be forced to adopt an aggressive working capital funding
policy because it is unable to raise additional long-term finance, whether
equity of debt.
32.3
BAUMOL
The Baumol cash model is similar in concept to the economic order quantity
model for inventory.
It can be used when an entity has a continual demand for cash to make
payments, and the cash requirements are obtained regularly by cashing in
interest-bearing investments. The cash is transferred into a current bank account,
on which it is normally assumed that the interest rate is zero. The demand for
cash should be constant and predictable.
The Baumol model calculates the optimal amount of cash to transfer on each
occasion, in order to minimise cash management costs. Cash management costs
are the combined costs of:
(1)
making the transactions to transfer the cash to the current bank account
and
(2)
the difference in interest income obtainable by holding the cash in a current
account (until it is needed) and the income obtainable by investing in shortterm investments.
The optimal cash transfer is calculated as: [(2 × C × D)/(r1 – r2)]0.5
where
C = the cost of a transaction to transfer cash from interest-bearing
investments to the current bank account
D = the annual demand for cash for spending
r1 =
the interest rate on interest-bearing investments
r2 = the interest rate receivable, if any, on money held in the current bank
account.
The Baumol model is unlikely to be of any assistance to a travel company
because of the assumptions that are used in the model. In particular, the model
assumes a constant rate of demand for cash for spending. In practice, most
companies have varying cash needs through the course of each week, month or
year. In particular, a travel company will experience peaks of demand, for
example, in holiday seasons.
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Answers
32.4
CASSIUS COMPANY
(a)
It is assumed that the volatility of daily cash flows will continue the same as
in the past.
Standard deviation of cash flows per day = Rs. 2,800
Variance of daily cash flows = Rs.(2,800)² = Rs. 7,840,000.
Annual interest yield on investments = 5.68%
Daily interest yield on investments = 5.68%/365 = 0.0155616%
Using the Miller-Orr model, the spread should be:
¾ × 20 × 7.84 million
3×
1/3
0.000155616
= 3 × Rs. 9,108.6 = Rs. 27,326.
Minimum cash balance = Rs. 12,500
Spread = Rs. 27,326
Upper limit = Rs. 12,500 + Rs. 27,326 = Rs. 39,826
Return point = Rs. 12,500 + (1/3 × Rs. 27,326) = Rs. 21,609.
In practice, the spread and the return point might be rounded to a
convenient whole number.
The company has established a minimum cash holding as a matter of
policy. It will manage its cash so that cash holdings do not become too
high. When cash holdings exceed the upper cash limit of Rs. 39,826, some
cash will be invested in interest-earning investments. The amount of cash
invested will be an amount to reduce cash holdings to the return point of
Rs. 21,609.
When cash holdings fall to the minimum cash balance, some investments
will be sold to restore the amount of cash held. The amount of investments
sold should be sufficient to restore cash holdings to the return point.
(b)
The company would invest its surplus cash in investments that provide
some interest yield. Normally, the company would want the investments to
be convertible into cash at fairly short notice and without any significant risk
of capital loss.
A bank might be willing to offer cash deposit facilities, although there might
be a penalty payment if cash is withdrawn without a minimum notice period.
A bank might not want to provide a bank deposit facility to a corporate
customer if the company intends to withdraw cash regularly
An alternative would be to invest in short-term money market instruments
such as Treasury bills or short-dated government bonds. These can be sold
at short notice although there would be some risk of capital loss (in the
event that interest rates rise).
The company is unlikely to invest surplus cash in short-term equities, if it
wants to avoid the risk of capital losses.
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Business finance decisions
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BUSINESS FINANCE
DECISIONS
PRACTICE KIT