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Making Investment Decisions

with the Net Present Value

Rule

Principles of

Corporate

Finance

Seventh Edition

Richard A. Brealey

Stewart C. Myers

Slides by

Matthew Will

Chapter 6

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Topics Covered

What To Discount

Inflation

Equivalent Annual Cost

Project Interaction

Timing

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What To Discount

Only Cash Flow is Relevant

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What To Discount

Do not confuse average with incremental

payoffs

Include all incidental effects

Do not forget working capital requirements

Forget sunk costs

Include opportunity costs

Beware of allocated overhead costs

Points to Watch Out For

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Be consistent in how you handle inflation!!

Use nominal interest rates to discount

nominal cash flows.

Use real interest rates to discount real cash

flows.

You will get the same results, whether you

use nominal or real figures

Inflation

INFLATION RULE

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Inflation

Example

You own a lease that will cost you $8,000 next year,

increasing at 3% a year for three years there after.

The forecasted inflation rate for the 4 years is 3 %per annum. If discount rates are 10% what is the

present value cost of the lease?

1 real interest rate =1+nominal interest rate

1+inflation rate

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Inflation

Example - nominal figures

Year Cash Flow PV @ 10%

1 80002 8000x1.03 = 8240

8000x1.03 = 8240

8000x1.03 = 8487.20

8000

1.10

2

3

7272 736809 92

3 637656

4 5970 78

429 99

8240

1 10

8487 20

1 10

8741 821 10

2

3

4

..

.

.

$26, .

.

.

.

..

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Inflation

Example - real figures

Year Cash Flow PV@6.7961%

1 = 7766.992 = 7766.99

= 7766.99

= 7766.99

8000

1.03

7766.99

1.068

8240

1.03

8487.20

1.03

8741.821.03

2

3

4

7272 736809 92

3 6376 56

4 5970 78

26 429 99

7766 99

1 068

7766 99

1 068

7766 991 068

2

3

4

.

.

.

.

.

.

.

.

..

= $ , .

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Equivalent Annual Cost

Equivalent Annual Cost - The cost per periodwith the same present value as the cost of

buying and operating a machine.

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Equivalent Annual Cost

Equivalent Annual Cost - The cost per period

with the same present value as the cost of

buying and operating a machine.

Equivalent annual cost =present value of costs

annuity factor

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ExampleGiven the following costs of operating two machines

and a 6% cost of capital, select the lower cost machine

using equivalent annual cost method.

Year

Machine 0 1 2 3 PV@6% EAC

A 15 5 5 5 28.37 10.61B 10 6 6 21.00 11.45

Equivalent Annual Cost

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Timing

Even projects with positive NPV may be

more valuable if deferred.

The actual NPV is then the current value of

some future value of the deferred project.

tr

t

)1(dateofasvaluefutureNetNPVCurrent

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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?

9.411.915.420.328.8valueinchange%

109.410089.477.564.450($1000s)Net FV

543210

YearHarvest

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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?

5.581.10

64.41yearinharvestedif NPV

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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?

5.581.10

64.41yearinharvestedif NPV

67.968.367.264.058.550($1000s)NPV

543210

YearHarvest