Principles of
Corporate
Finance
Seventh Edition
Richard A. Brealey
Chapter 6
Making Investment Decisions
with the Net Present Value
Rule
Stewart C. Myers
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
6- 2
Topics Covered
Š What To Discount
Š IM&C Project
Š Project Interaction
Equivalent Annual Cost
Î Replacement
Î Timing
Î Fluctuating Load Factors
Î
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6- 3
What To Discount
Only Cash Flow is Relevant
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6- 4
What To Discount
Points to “Watch Out For”
ÂDo not confuse average with incremental
payoffs
ÂInclude all incidental effects
ÂDo not forget working capital requirements
ÂForget sunk costs
ÂInclude opportunity costs
ÂBeware of allocated overhead costs
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6- 5
Inflation
INFLATION RULE
Š Be consistent in how you handle inflation!!
Š Use nominal interest rates to discount
nominal cash flows.
Š Use real interest rates to discount real cash
flows.
Š You will get the same results, whether you
use nominal or real figures
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6- 6
Inflation
Example
You own a lease that will cost you $8,000 next year,
increasing at 3% a year (the forecasted inflation
rate) for 3 additional years (4 years total). If
discount rates are 10% what is the present value
cost of the lease?
1+ nominal interest rate
1 + real interest rate =
1+inflation rate
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6- 7
Inflation
Example - nominal figures
Year
1
2
3
4
Cash Flow
PV @ 10%
8000
8000
1.10 = 7272.73
8240
8000x1.03 = 8240
= 6809.92
1.102
2
8487 .20
8000x1.03 = 8240
= 6376.56
1.103
.82
8000x1.033 = 8487.20 8741
= 5970.78
1.104
$26,429.99
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Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
6- 8
Inflation
Example - real figures
Year
1
2
3
4
McGraw Hill/Irwin
8000
1.03
8240
1.032
8487.20
1.033
8741.82
1.034
Cash Flow
= 7766.99
= 7766.99
= 7766.99
= 7766.99
7766.99
1.068
7766.99
1.0682
7766.99
1.0683
7766.99
1.0684
PV@6.7961%
= 7272.73
= 6809.92
= 6376.56
= 5970.78
= $26,429.99
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
6- 9
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
present value of costs
Equivalent annual cost =
annuity factor
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6- 10
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower cost machine
using equivalent annual cost method.
Machine
A
B
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Year
0
15
10
1
5
6
2
5
6
3
5
PV@6%
28.37
21.00
EAC
10.61
11.45
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6- 11
Timing
Š Even projects with positive NPV may be
more valuable if deferred.
Š The actual NPV is then the current value of
some future value of the deferred project.
Net future value as of date t
Current NPV =
t
(1 + r )
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6- 12
Timing
Example
You may harvest a set of trees at anytime over the
next 5 years. Given the FV of delaying the harvest,
which harvest date maximizes current NPV?
Net FV ($1000s)
% change in value
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Harvest Year
0
1
2
3
50 64.4
77.5
89.4
28.8
20.3
4
5
100 109.4
15.4 11.9
9.4
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6- 13
Timing
Example - continued
You may harvest a set of trees at anytime over the next 5 years. Given
the FV of delaying the harvest, which harvest date maximizes current
NPV?
64.4
NPV if harvested in year 1 =
= 58.5
1.10
0
1
NPV ($1000s) 50 58.5
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Harvest Year
2
3
64.0
67.2
4
5
68.3 67.9
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6- 14
Aufgaben zu Hause
Q7
PQ10, 18
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