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CH 11Capital Budgeting and Risk Analysis

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Three Measures of a Projects Risk

Project Standing

Alone Risk Riskdiversified away

within firm as thisproject is combined

with firms other

projects and assets.

Risk

diversified away

by shareholders as

securities are combined

to form diversified

portfolio.

Projects

Contribution-to-Firm Risk

Systematic Risk

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Incorporating Risk into Capital

Budgeting

Certainty Equivalent Approach

Adjust free cash flows (FCF)

Use risk-free rate to discount

CFs

Risk-Adjusted DiscountRate Adjust discounting rate

Two Approaches

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Certainty Equivalent Approach

Adjusts the risky after-tax cash flowsto certain cash flows.

The idea:

Risky Certainty Certain

Cash X Equivalent = CashFlow Factor (a) Flow

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Certainty Equivalent Approach

Risky Certainty Certain

Cash X Equivalent = Cash

Flow Factor (a) FlowRisky safe

$1000 .70 $700

Risky safe

$1000 .95 $950

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The greater the risk associated

with a particular cash flow,

the smaller the CE factor.

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Certainty Equivalent Method

tNPV = - IOt FCFt(1 + krf)

n

t=1S

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Certainty Equivalent Approach

Steps:

1) Adjust all after-tax cash flows by

certainty equivalent factors to getcertain cash flows.

2) Discount the certain cash flows by

the risk-free rate of interest.

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Incorporating Risk into

Capital Budgeting

Risk-Adjusted Discount Rate

Approach

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Risk-Adjusted Discount Rate

Simply adjust the discount rate (k)

to reflect higher risk.

Riskier projects will use higherrisk-adjusted discount rates.

Calculate NPV using the new risk-

adjusted discount rate.

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Risk-Adjusted Discount Rate

NPV = - IOFCFt

(1 + k*)t

n

t=1S

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Risk-Adjusted Discount Rates

How do we determine the

appropriate risk-adjusted discount

rate (k*) to use? Many firms set up risk classes to

categorize different types of

projects.

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Risk Classes

Risk RADRClass (k*) Project Type

1 12% Replace equipment,

Expand current business

2 14% Related new products

3 16% Unrelated new products

4 24% Research & Development

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Yr FCF(t) Alpha PV at 0.06 PV of FCF(t)

0-

800000 1.0000

-800000

1 100000 0.92 0

.9434 86957

2 100000 0.85 0

.8900 75614

3 100000 0.78 0

.8396 65752

4 100000 0.72 0.7921 57175

5 100000 0.67 0

.7473 49718

6 100000 0.61 0

.7050 43233

7 100000 0.57 0

.6651 37594

8 100000 0.52 0

.6274 32690

9 100000 0.48 0

.5919 28426

10 100000 0.44 0

.5584 24718

NPV ( , . )

CE Approach (with alpha)

RAA approach impliesthat risk becomesgreater as cash flows

are further away.Reducing alphaindicates that risk isgreater.(Alpha = 1 = Sure

thing!

Yr FCF(t) PV at 0.15 PV of FCF(t) Yr FCF(t) PV at 0.06 PV of FCF(t)

0-

800000 1.0000

-800000 0

-800000 1

.0000

-800000

1 100000 0.8696 86957 1 100000 0

.9434 94340

2 100000 0.7561 75614 2 100000 0

.8900 89000

3 100000 0

.6575 65752 3 100000 0

.8396 83962

4 100000 0.5718 57175 4 100000 0

.7921 79209

5 100000 0.4972 49718 5 100000 0

.7473 74726

6 100000 0.4323 43233 6 100000 0

.7050 70496

7 100000 0.3759 37594 7 100000 0

.6651 66506

8 100000 0.3269 32690 8 100000 0

.6274 62741

9 100000 0.2843 28426 9 100000 0

.5919 59190

10 100000 0.2472 24718 10 100000 0

.5584 55839

NPV ( , . ) NPV ( , . )

Risk Adjusted Approach CE Approach (w/o alpha)