Capital BudgetingFIN 461: Financial Cases & Modeling

George W. GallingerAssociate Professor of FinanceW. P. Carey School of Business

Arizona State University

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Typical Capital Budgeting System

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Calculating Accounting Rate of Return

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Calculating Payback Period

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Calculating Discounted Payback Period

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Calculating NPV

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Calculating NPV…

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Use Nominal or Real WACC?

Nominal return reflects the actual dollar return; real return measures the increase in purchasing power gained by holding a certain investment

Common in capital budgeting is the use of market rates of return at the time of the analysis

Market interest rates have embedded an assumption about inflation

Use nominal cash flows to reflect the same inflation rate as that embedded in discount rate.

1inf1

nom1rate real or,

rate), real(1rate)inflation (1rate) nominal1(

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Risk-Return Tradeoff for Projects

Projects plotting above the security market line (SML) have rates of return in excess of their required market rates

Positive NPVs Projects plotting below

the SML have rates of return less than their required market rates

Negative NPVs Projects plotting on the

SML earn their market rates

Zero NPVs.

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Calculating IRR

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Illustration for Calculating IRR

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IRR & Required Risk-Adjusted Rate

Appropriate rates for comparing project returns are those falling on the upward sloping market risk-return trade-off curve

Not the firm’s horizontal cost of capital line, WACC

WACC is only appropriate for evaluating projects with risk comparable to the level of risk of the firm

“Carbon copy” projects.

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Size Problem

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Cash Flow Pattern Problems

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Multiple IRR Solutions

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Undervaluation of Later Cash Flows

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Calculating the Profitability Index

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Comparison of Project Rankings

Project B is better than project A

Project B continues to earn cash flows longer

Project D is more desirable than project C

Although both projects generate the same amount of cash flows, project D does it earlier

Unanswered question: Is Project D better

than project B?

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Sunk Costs

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Salvage Value Comparisons

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Calculating Initial Investment

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Calculating Annual Operating Cash Flows

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Alternatively, Calculating Annual Operating Cash Flows…

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Calculating Terminal Cash Flows

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Salvage Value: Present vs. Future

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Another Topic:Competing Projects

Assume projects Mutually exclusive On-going Different economic lives

How do you select the correct project?

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Example There are times when application of the NPV rule

can lead to the wrong decision Consider a factory which must have an air

cleaner The equipment is mandated by law, so there is no

“doing without” There are two choices:

The “Cadillac cleaner” costs $4,000 today, has annual operating costs of $100 and lasts for 10 years

The “cheaper cleaner” costs $1,000 today, has annual operating costs of $500 and lasts for 5 years

Which one should we choose?

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Example … At first glance, the cheap cleaner has the “better” NPV (r = 10%):

46.614,4)10.1(

100$000,4$

10

1Cadillac

tt

NPV

39.895,2)10.1(

500$000,1$

5

1cheap

tt

NPV

Overlooks the fact that the Cadillac cleaner lasts twice as long

When we incorporate project life, the Cadillac cleaner is actually cheaper.

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Example … The Cadillac cleaner time line of cash flows:

-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100

0 1 2 3 4 5 6 7 8 9 10

-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500

0 1 2 3 4 5 6 7 8 9 10

The “cheaper cleaner” time line of cash flows over ten years:

20.693,4$)10.1(

500$

)10.1(

000,1$

)10.1(

500$000,1$

10

65

5

1cheap

tt

tt

NPV

46.614,4)10.1(

100$000,4$

10

1Cadillac

tt

NPV

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Investments of Unequal Lives Replacement Chain

Repeat the projects forever, find the PV of that perpetuity

Assumption: Both projects can and will be repeated Matching Cycle

Repeat projects until they begin and end at the same time—like we just did with the air cleaners

Compute NPV for the “repeated projects” The Equivalent Annual Annuity (EAA) Method.

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Equivalent Annual Cost Method

Equivalent Annual Annuity Method Provides the value of the level payment annuity that

has the same PV as the original set of cash flows NPV = EAA × Ar

T

For example, the EAA for the Cadillac air cleaner is $750.98

10

1

10

1 )10.1(

98.750$46.614,4

)10.1(

100$000,4$

tt

tt

The EAA for the cheaper air cleaner is $763.80, which confirms our earlier decision to reject it.

Annuity Table10%, 10 years

= 6.1446

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Another Example:Calculating EAA

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Human Face of Capital Budgeting

NPV of a project based on assumptions Managers must be aware of optimistic bias in these

assumptions made by supporters of the project Companies need control measures to remove bias

Analysis done by a group independent of individual or group proposing the project

Analysts must have a sense of what is reasonable when forecasting a project’s profit margin and its growth potential

Another side of determining which projects receive funding – storytelling

Best analysts not only provide numbers to highlight a good investment, but also can explain why this investment makes sense.

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The End