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Capital Budgeting and Risk Analysis

Introduction

- Future CFs are estimate based on what is

expected to happen not necessarily what will

happen in the future! - Example
- Cokes replacement of what is now Classic Coke

with New Coke

General Definition

- Risk Potential variability in future CFs

Variability

- Fact that variability reflects risk can be

demonstrated with a simple coin toss

Coin Toss Example

- Consider the possibility of flipping a coin.
- Heads you win 0.25 and tails you loose 0.25.

Most likely you would play because the utility of

winning 0.25 is the same as the utility of

losing 0.25. - Now consider playing for 100 per flip. Now you

would only play if you could win more on a flip

(say 1500) than you could lose on a flip. - Probability is the same in each case however

the width of the dispersion changes making the

second coin toss more risky. - Therefore you may not take the chance unless

the payoffs are altered

Power Ball

- Odds of winning 80 million to 1
- Why do people play this game if the odds of

winning are so low?

Example Conclusion

- The key here is the fact that only the dispersion

changes. Probability of winning remains the same.

Thus the potential variability in futures returns

reflects RISK !

What measure of risk is relevant in capital

budgeting?

- Systematic Risk
- Risk for which shareholders are compensated
- Hard to measure making implementation difficult

Methods for Incorporating Risk into the Capital

Budgeting Process

- Initially we ignored any risk difference between

projects - Now we want to examine 2 methods for

incorporating risk into capital budgeting

- Two Methods
- Certainty Equivalent Approach
- Attempts to incorporate the managers utility

function into the analysis - Risk-Adjusted Discount Rate
- Based on the notion that investors require higher

rates of return on more risky projects

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- Adjust the After-tax Cash Flows (ACFs), or
- Adjust the discount rate (k).

- Adjusts the risky after-tax cash flows to certain

cash flows. - The idea
- Manager is allowed to substitute the certain

amount that he feels is equivalent to the

expected but risky cash flow offered by the

investment for that risky cash flow in the

capital budget analysis

Certainty Equivalent Approach

- LETS MAKE A DEAL!
- Trade certain outcomes for uncertain outcomes

Example

- Look at coin toss again
- Can only play once
- H-win 10,000
- T-lose 0 get nothing
- Probability of winning 10,000 0.5
- Probability of winning 0 0.5
- Thus 5,000 is your uncertain expected value out

come - CE then becomes the amount you would demand to

make you indifferent with regard to playing or

not playing. - If you are indifferent with respect to receiving

3,000 for certain not playing the game. 3,000

is your CE. - Not everyone has the same CE. Your CE depends on

your fear of risk.

- Adjusts the risky after-tax cash flows to certain

cash flows. - The idea
- Risky Certainty Certain
- Cash X Equivalent Cash
- Flow Factor (a) Flow

Certainty Equivalent Coefficient or Factor

- Ratio of the certain outcome to the risky or

expected outcome between which the decision maker

is indifferent

Previous Coin Toss Example

- In our previous example
- (Simple Coin Toss)
- Certain CF 3000
- Risky CF 5000 (EV of coin toss)
- CE 3000/5000 0.6
- After risk is taken out CFs are discounted back

to PV with risk free discount rate to get NPV.

at

- 1 at 0
- 0 Extreme Risk
- 1 Certainty

- Risky Certainty Certain
- Cash X Equivalent Cash
- Flow Factor (a) Flow
- Risky

safe - 1000 .95

950

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- Risky Certainty Certain
- Cash X Equivalent Cash
- Flow Factor (a) Flow
- Risky

safe - 1000 .4

400

- Steps
- 1) Adjust all after-tax cash flows by certainty

equivalent factors to get certain cash flows. - 2) Discount the certain cash flows by the

risk-free rate of interest.

- Simply adjust the discount rate (k) to reflect

higher risk. - Riskier projects will use higher risk-adjusted

discount rates. - Calculate NPV using the new risk-adjusted

discount rate.

n t1

S

t ACFt (1 krf)

NPV - IO

t

Example

- A firm is considering building a new research

facility with a 5 year expected life. The

initial capital investment is 120,000. The

firms RRR is 10 and the risk free rate is 6.

What is the projects NPV?

Example

- To determine the projects NPV using the CE

approach we must first remove risk from future

cash flows. We do this by multiplying each

expected CF by the corresponding CE coefficient.

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- 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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n t1

S

ACFt (1 k)

NPV - IO

t

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