WHAT DISCOUNT RATE SHOULD THE FIRM
USE IN CAPITAL BUDGETING?
MANY FIRMS USE OVERALL FIRM COST OF CAPITAL
TO DISCOUNT CASH FLOWS FOR ALL NEW
PROJECTS
WRONG IF NEW PROJECT MORE OR LESS RISKY
THAN ITS EXISTING BUSINESS
EACH PROJECT SHOULD IN PRINCIPLE BE
DISCOUNTED USING ITS OWN OPPORTUNITY COST
OF CAPITAL
1
Copyright 1996 by The McGraw-Hill Companies, Inc
COMPANY COST OF CAPITAL AND
REQUIRED RETURN ON PROJECT
REQUIRED RETURN
Security market line showing
required return on project
Company cost of capital
Average beta
of firm's assets
PROJECT BETA
2
Copyright 1996 by The McGraw-Hill Companies, Inc
COMPANY COST OF CAPITAL RULE
DUKE POWER HAS LOW RISK AND LOW COMPANY
COST OF CAPITAL
MICROSOFT HAS HIGH RISK AND HIGH COMPANY
COST OF CAPITAL
IF BOTH FIRMS USED THE COMPANY COST OF
CAPITAL RULE TO EVALUATE THE SAME PROJECT,
POSSIBLE THAT
– DUKE POWER WOULD ACCEPT THE PROJECT
– MICROSOFT WOULD REJECT THE PROJECT
WRONG!!
3
Copyright 1996 by The McGraw-Hill Companies, Inc
COMPANY COST OF CAPITAL RULE
WIDESPREAD USE OF A UNIFORM COST OF
CAPITAL BY MANY COMPANIES IN EVALUATING
PROJECTS
BUT MANY FIRMS DO REQUIRE DIFFERENT
RETURNS FOR DIFFERENT CATEGORIES OF
INVESTMENT
– EXAMPLE ON NEXT SLIDE
4
Copyright 1996 by The McGraw-Hill Companies, Inc
CATEGORY
DISCOUNT RATE
SPECULATIVE VENTURES
30%
NEW PRODUCTS
20%
EXPANSION OF
EXISTING BUSINESS
15% (company cost of capital)
COST IMPROVEMENT
KNOWN TECHNOLOGY
10%
5
Copyright 1996 by The McGraw-Hill Companies, Inc
USING CAPM AND PROJECT b
MANY LARGE CORPORATIONS USE CAPM AND AN
ESTIMATE OF THE PROJECT b TO ESTIMATE
PROJECT DISCOUNT RATE
EXPECTED PROJECT RETURN = rf + bproject (rm- rf)
6
Copyright 1996 by The McGraw-Hill Companies, Inc
BEGIN WITH PROBLEMS IN
MEASURING COMPANY b
b IS DIFFICULT TO MEASURE FOR INDIVIDUAL FIRM
BETTER ACCURACY BY LOOKING AT AVERAGE OF
SIMILAR COMPANIES
– BUT FIRM’S BORROWING POLICIES AFFECTS ITS
STOCK b
– IBM AND DEC ARE NOT SIMILAR COMPANIES FOR
PURPOSE OF ESTIMATING b BECAUSE THEY USE
DIFFERENT DEGREES OF LEVERAGE
7
Copyright 1996 by The McGraw-Hill Companies, Inc
MEASURING COMPANY b
APPROPRIATE FOR ACROSS-THE-BOARD EXPANSION
COMPARE RETURN ON STOCK WITH MARKET
RETURN OVER 60-MONTH TIME PERIOD
– AT&T
– HEWLETT-PACKARD
SLOPE IS b
VARIES BY PERIOD
ESTIMATES OF b ARE PUBLISHED BY BROKERAGE
HOUSES AND ADVISORY SERVICES
8
Copyright 1996 by The McGraw-Hill Companies, Inc
ESTIMATING BETA
RETURN ON SHARE
RETURN ON SHARE
+
+
+
+
+
+
+ +
+
+
+
+ +
+
+
+
+
+
+
+
+++
+ ++
+
+
+
Beta = .4
+
+
RETURN ON MARKET
+
+
+
+++
+
+ +
+
Beta = 1.6
+
+
+
+
+
+
+
+
+
+
+
RETURN ON MARKET
+
+
+
+
9
Copyright 1996 by The McGraw-Hill Companies, Inc
PFIZER
WHICH IS THE BETTER ESTIMATE OF b FOR PFIZER?
– PFIZER HAS A b OF 1.02 WITH A STANDARD ERROR
OF 0.14
– A MARKET VALUE-WEIGHTED INDUSTRY
PORTFOLIO OF LARGE PHARMACEUTICAL
COMPANIES HAS A b OF 0.98 WITH A STANDARD
ERROR OF 0.07
DIFFERENCE BETWEEN ESTIMATE OF COMPANY
BETA AND INDUSTRY BETA IS PROBABLY NOISE
– UNLESS YOU HAVE REASON TO BELIEVE THAT
PFIZER IS RISKIER THAN INDUSTRY AVERAGE
10
Copyright 1996 by The McGraw-Hill Companies, Inc
HOW CAPITAL STRUCTURE AFFECTS
EXPECTED RETURNS
IF YOU OWN ALL OF THE EQUITY AND ALL OF THE
DEBT OF A COMPANY, YOU WOULD ALSO RECEIVE
ALL CASH FLOWS FROM THE COMPANY
COMPANY’S COST OF CAPITAL IS EXPECTED
RETURN ON THIS PORTFOLIO
11
Copyright 1996 by The McGraw-Hill Companies, Inc
HOW CHANGING CAPITAL
STRUCTURE AFFECTS b
AFTER REFINANCING, RISK OF TOTAL PORTFOLIO
OF DEBT AND EQUITY IS UNCHANGED
– BUT BOTH DEBT AND EQUITY ARE INDIVIDUALLY
LESS RISKY
FIRM’S ASSET BETA IS WEIGHTED AVERAGE OF
PORTFOLIO OF DEBT AND EQUITY BETAS
b assets  b portfolio

D
E
bdebt  b equity
V
V
12
Copyright 1996 by The McGraw-Hill Companies, Inc
HOW CHANGING CAPITAL
STRUCTURE AFFECTS b
AFTER REFINANCING, RISK OF TOTAL PORTFOLIO
OF DEBT AND EQUITY IS UNCHANGED
– BUT BOTH DEBT AND EQUITY ARE INDIVIDUALLY
LESS RISKY
FIRM’S ASSET BETA IS WEIGHTED AVERAGE OF
PORTFOLIO OF DEBT AND EQUITY BETAS
b assets  b portfolio

D
E
bdebt  b equity
V
V
SUPPOSE bdebt FALLS TO .1
.8 = (.3 X .1) + (.7 X b equity )
bequity = 1.1
13
Copyright 1996 by The McGraw-Hill Companies, Inc
UNLEVERING BETAS
GOING FROM AN OBSERVED bequity TO bassets
WE KNOW bequity
bdebt
MARKET WEIGHTS OF DEBT AND
EQUITY, (D/V )AND (E/V)
b assets  b portfolio
D
E
 bdebt  b equity
V
V
14
Copyright 1996 by The McGraw-Hill Companies, Inc
UNLEVERING BETAS
GOING FROM AN OBSERVED bequity TO bassets
WE KNOW bequity
bdebt
MARKET WEIGHTS OF DEBT AND
EQUITY, (D/V )AND (E/V)
b assets  b portfolio
D
E
 bdebt  b equity
V
V
WE WILL ADD TAX EFFECTS LATER
15
Copyright 1996 by The McGraw-Hill Companies, Inc
REVIEW
COST OF CAPITAL IS RELEVANT IN CAPITAL
BUDGETING DECISIONS
– NOT EXPECTED RETURN ON COMMON STOCK
COMPANY COST OF CAPITAL IS WEIGHTED AVERAGE
RETURN THAT INVESTORS EXPECT ON FIRM’S DEBT
AND EQUITY
– RELATED TO FIRM’S ASSET BETA, NOT TO EQUITY
BETA
ASSET BETA CALCULATED AS WEIGHTED AVERAGE
OF BETAS OF DEBT AND EQUITY
WHEN FIRM CHANGES ITS CAPITAL STRUCTURE
– RISK AND EXPECTED RETURNS OF DEBT AND
EQUITY CHANGE
– ASSET BETA AND COMPANY COST OF CAPITAL 16
Copyright 1996 by The McGraw-Hill Companies, Inc
DO NOT CHANGE
WHAT DETERMINES ASSET BETAS?
FIRMS WITH HIGH ACCOUNTING OR CASH FLOW
BETAS ALSO TEND TO HAVE HIGH STOCK BETAS
– CYCLICAL FIRMS WHOSE EARNINGS ARE
STRONGLY RELATED TO THE BUSINESS CYCLE
TEND TO BE HIGH BETA FIRMS
DEMAND A HIGHER RATE OF RETURN FROM
SECURITIES WHOSE PERFORMANCE MOVES WITH
THE ECONOMY
17
Copyright 1996 by The McGraw-Hill Companies, Inc
OPERATING LEVERAGE
WE KNOW FINANCIAL LEVERAGE INCREASES BETA
FOR SIMILAR REASONS, OPERATING LEVERAGE
ALSO INCREASES BETA
– PRESENCE OF FIXED COSTS OF PRODUCTION
 CASH FLOWS FROM THE ASSET
= REVENUES - FIXED COST - VARIABLE COST
 PV(CASH FLOWS FROM THE ASSET) = PV(ASSET)
=PV(REVENUE) - PV(FIXED COST) - PV(VARIABLE COST)
 PV(REVENUE)
=PV(FIXED COST) + PV(VARIABLE COST) + PV(ASSET)
18
Copyright 1996 by The McGraw-Hill Companies, Inc
OPERATING LEVERAGE
bFIXED COST = 0
 ALSO bREVENUES @ bVARIABLE COST
– AS THEY ARE BOTH PROPORTIONAL TO OUTPUT
b ASSET
 b REVENUE
PV(REVENUE) - PV(FIXED COST)
PV(ASSET)
 b REVENUE [1  PV(FIXED COST) ]
PV(ASSET)
19
Copyright 1996 by The McGraw-Hill Companies, Inc
NET PRESENT VALUE RULE
WHY DOES THE NPV OF A PROJECT SHOW UP AS
INCREASE IN MARKET VALUE?
IMAGINE THE CASH FLOWS OF THE PROJECT ARE
PAID OUT AS DIVIDENDS
THE SHARE PRICE WOULD INCREASE BY THE
PRESENT VALUE OF THE DIVIDENDS LESS THE
COST OF THE PROJECT (DIVIDENDS FOREGONE)
THIS IS THE NPV OF THE PROJECT
20
Copyright 1996 by The McGraw-Hill Companies, Inc
INTERNAL RATE OF RETURN,
IRR
C1
C2
CT

 . . . .
0
NPV = C0 
2
T
(1  IRR) (1  IRR)
(1  IRR)
IRR IS THE DISCOUNT RATE FOR WHICH NPV=0
21
Copyright 1996 by The McGraw-Hill Companies, Inc
CALCULATING IRR
FINANCIAL CALCULATOR
.
TRIAL AND ERROR
– EXAMPLE:
C0 = - 4,000
C1 = +2,000
C3 = +4,000
TRY IRR = 0,
NPV = +2,000, IRR > 0
TRY IRR = 50%, NPV = - 889, IRR < 50
TRY IRR = 25%, NPV = +160, IRR >25
TRY IRR = 28%, NPV =
0
22
Copyright 1996 by The McGraw-Hill Companies, Inc
NET PRESENT VALUE PROFILE
C0 = - 4
C1 = +2
C3 = +4
NPV
+2
IRR = 28%
0
-1
50
DISCOUNT
RATE (%)
23
Copyright 1996 by The McGraw-Hill Companies, Inc
INTERNAL RATE OF RETURN RULE
ACCEPT PROJECT
IF IRR IS GREATER THAN
THE OPPORTUNITY COST OF CAPITAL
LOOKING AT THE NET PRESENT VALUE PROFILE
FOR A CONVENTIONAL PROJECT,
WE WILL BE ACCEPTING PROJECTS
WITH POSITIVE NPV
24
Copyright 1996 by The McGraw-Hill Companies, Inc
CONVENTIONAL PROJECT
CASH OUTFLOWS FOLLOWED BY CASH INFLOWS
NPV DECLINES WITH INCREASING DISCOUNT RATES
25
Copyright 1996 by The McGraw-Hill Companies, Inc
WARNING
DISTINGUISH BETWEEN IRR AND OPPORTUNITY COST
OF CAPITAL
– BOTH APPEAR AS DISCOUNT RATES IN NPV FORMULA.
IRR IS A MEASURE OF PROFITABILITY, DEPENDS ON
AMOUNT AND TIMING OF CASH FLOWS
OPPORTUNITY COST OF CAPITAL MEASURES WHAT
WE COULD EARN BY INVESTING IN FINANCIAL
ASSETS OF SIMILAR RISK
– SET BY CAPITAL MARKETS
– IT IS A COST OF FINANCING THE PROJECT
26
– IT PROVIDES US WITH A MINIMUM ACCEPTABLE
Copyright 1996 by The McGraw-Hill Companies, Inc
LEVEL OF PROFITABILITY
LENDING OR BORROWING?
Year:
A
B
0
-1,000
+1,000
1
IRR(%)
+1,500
-1,500
+50
+50
NPV
At 10% ($)
+364
+364
BOTH PROJECTS HAVE IRR OF 50%
NPV PROFILE FOR PROJECT B INCREASES WITH
INCREASING DISCOUNT RATES
ACCEPT PROJECT B WHEN IRR IS LESS THAN
THE OPPORTUNITY COST OF CAPITAL
27
Copyright 1996 by The McGraw-Hill Companies, Inc
MULTIPLE RATES OF RETURN
DESCARTES’ RULE OF SIGNS SAYS THERE ARE
AS THERE ARE CHANGES IN SIGN
– BUT SOME OF THE ROOTS MAY BE THE SAME!
OFTEN HAVE CASH OUTCASH OUTFLOWS FROM
INITIAL INVESTMENT,
FOLLOWED BY POSITIVE CASH FLOWS
DURING PROJECT LIFE,
FOLLOWED BY CASH OUTFLOWS
AT END OF PROJECT LIFE
– DECOMMISSIONING COSTS OF NUCLEAR POWER PLANT
– RECLAMATION COSTS AFTER STRIPMINING COAL
– DELAY BETWEEN EARNING INCOME AND PAYING TAX
28
Copyright 1996 by The McGraw-Hill Companies, Inc
MULTIPLE RATES OF RETURN
Year:
C
0
1
2
-4
+25
-25
IRR
25% & 400%
NPV @ 10
-1.9
TWO CHANGES IN SIGN OF CASH FLOWS
TWO INTERNAL RATES OF RETURN
 r < 25%, NPV < 0
29
Copyright 1996 by The McGraw-Hill Companies, Inc
MULTIPLE RATES OF RETURN
Year:
C
0
1
2
-4
+25
-25
IRR
25% & 400%
NPV @ 10
-1.9
TWO CHANGES IN SIGN OF CASH FLOWS
TWO INTERNAL RATES OF RETURN
 r < 25%, NPV < 0
25% < r < 400%, NPV > 0
ACCEPT PROJECT
30
Copyright 1996 by The McGraw-Hill Companies, Inc
IRR MAY GIVE THE WRONG DECISION
WITH MUTUALLY EXCLUSIVE PROJECTS
WHICH DIFFER IN:
SCALE
PATTERN OF CASH FLOWS OVER TIME
– COMPARE PROJECTS G AND H
0
1
2
3
G
-9
+6
+5
+4
H
-9
+1.8
+1.8
+1.8
4
0
5
IRR
NPV @ 10%
0 ........ 33%
3,592
+1.8 +1.8...... 20%
9,000
31
Copyright 1996 by The McGraw-Hill Companies, Inc
IRR MAY GIVE THE WRONG DECISION
WITH MUTUALLY EXCLUSIVE PROJECTS
WHICH DIFFER IN:
SCALE
PATTERN OF CASH FLOWS OVER TIME
– COMPARE PROJECTS G AND H
0
1
2
3
G
-9
+6
+5
+4
H
-9
+1.8
+1.8
-6
+1.2
I
4
0
5
IRR
NPV @ 10%
0 ........ 33%
3,592
+1.8
+1.8 +1.8...... 20%
9,000
+1.2
+1.2
6,000
+1.2...... 20%
PROJECT H HAS HIGHER NPV THAN PROJECT G
32
Copyright 1996 by The McGraw-Hill Companies, Inc
– BUT LOWER IRR
NPV($)
6,000
15.6
33.3
DISCOUNT RATE
G
20
H
33
Copyright 1996 by The McGraw-Hill Companies, Inc
MUTUALLY EXCLUSIVE PROJECTS
PROJECT G HAS IRR OF 33%
PROJECT H HAS IRR OF 20%
NPVG = NPVH AT CROSSOVER POINT OF 15.6%
CASH FLOWS OF PROJECT H ARE LARGER BUT
OCCUR LATER
– FOR DISCOUNT RATES < 15.6%, PROJECT H HAS
HIGHER NPV
– FOR DISCOUNT RATES > 15.6%, PROJECT G HAS
HIGHER NPV
34
Copyright 1996 by The McGraw-Hill Companies, Inc
Real Options
35
Copyright 1996 by The McGraw-Hill Companies, Inc
Topics Covered
 Sensitivity Analysis
 Break Even Analysis
 Monte Carlo Simulation
 Decision Trees
36
Copyright 1996 by The McGraw-Hill Companies, Inc
How To Handle Uncertainty
Sensitivity Analysis - Analysis of the effects of
changes in sales, costs, etc. on a project.
Scenario Analysis - Project analysis given a
particular combination of assumptions.
Simulation Analysis - Estimation of the
probabilities of different possible outcomes.
Break Even Analysis - Analysis of the level of
sales (or other variable) at which the company
breaks even.
37
Copyright 1996 by The McGraw-Hill Companies, Inc
Monte Carlo Simulation
Modeling Process
 Step 1: Modeling the Project
 Step 2: Specifying Probabilities
 Step 3: Simulate the Cash Flows
38
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
960 (.8)
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
140(.6)
800(.8)
-150
+100(.6) or
410(.8)
0
Piston
-250
NPV=
?
100(.2)
180(.2)
220(.4)
+50(.4)
100(.6)
39
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
960 (.8)
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
-150
+100(.6) or
NPV=
?
100(.2)
410(.8)
0
-250
456
140(.6)
800(.8)
Piston
812
180(.2)
660
364
220(.4)
+50(.4)
100(.6)
148
40
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
960 (.8)
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
-150
+100(.6) or
NPV=
?
100(.2)
410(.8)
0
-250
456
140(.6)
800(.8)
Piston
812
180(.2)
660
364
220(.4)
960  .80+50(.4)
 220  .20  812
100(.6)
148
41
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
Turboprop
-550
NPV=
?
960 (.8)
660 +150(.6)
 150  450
1.10
220(.2)
930(.4)
+30(.4)
800(.8)
-150
+100(.6) or
0
?
100(.2)
410(.8)
Piston
NPV=
456
140(.6)
*450
331
-250
812
180(.2)
660
364
220(.4)
+50(.4)
100(.6)
148
42
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
960 (.8)
NPV=888.18
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
800(.8)
*450
-150
or
NPV=
?
100(.2)
410(.8)
0
Piston
331
-250
456
140(.6)
NPV=444.55
812 NPV=550.00
 150  888+100(.6)
.18
1.10
812
180(.2)
660
364
220(.4)
+50(.4)
NPV=184.55
100(.6)
148
43
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
960 (.8)
NPV=888.18
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
710.73
930(.4)
NPV=550.00
800(.8)
-150
+100(.6) or
100(.2)
410(.8)
NPV=
?
660
  444180(.2)
 888403.82
.18  .60
.55  .40
331
0
-250
456
140(.6)
NPV=444.55
*450
Piston
812
364
220(.4)
+50(.4)
NPV=184.55
100(.6)
148
44
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
Turboprop
-550
NPV=96.12
220(.2)
710.73
930(.4)
+30(.4)
NPV=550.00
+100(.6) or
-250
NPV=117.00
800(.8)
-150
100(.2)
410(.8)
0
710.73
180(.2)
331
 550  96.12
403.82
220(.4)
1.10
+50(.4)
NPV=184.55
456
140(.6)
NPV=444.55
*450
Piston
812
100(.6)
660
364
148
45
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
Turboprop
-550
NPV=96.12
220(.2)
710.73
930(.4)
+30(.4)
800(.8)
*450
-150
NPV=550.00
+100(.6) or
0
NPV=117.00
+50(.4)
NPV=184.55
100(.2)
410(.8)
Piston
403.82
456
140(.6)
NPV=444.55
-250
812
331
180(.2)
660
364
220(.4)
100(.6)
148
46
Copyright 1996 by The McGraw-Hill Companies, Inc