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78106_11_Web_Ch11A_p01-07 - WEB EXTENSION 11A Certainty...

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W E B E X T E N S I O N 11A Certainty Equivalents and Risk-Adjusted Discount Rates T wo alternative methods have been developed for incorporating project risk into the capital budgeting decision process. One is the certainty equivalent method , in which the expected cash flows are adjusted to reflect project risk: Risky cash flows are scaled down because the riskier the flows, the lower their certainty equivalent values. The second is the risk-adjusted discount rate method , where differ- ential project risk is dealt with by changing the discount rate: Average-risk projects are discounted at the firm s corporate cost of capital, above-average-risk projects are discounted at a higher cost of capital, and below-average-risk projects are discounted at a rate below the corporate cost of capital. The risk-adjusted discount rate method is used by most companies, so we focused on it in earlier chapters. However, the certainty equiv- alent approach does have some advantages, so financial managers should be familiar with it as well. It is not always possible to find existing models for financial options that corre- spond to all real options. In such a situation, the analyst must use financial engineer- ing techniques. One technique, risk-neutral valuation , is analogous to the certainty equivalent method, except it is applied using simulation. 11.1 T HE C ERTAINTY E QUIVALENT M ETHOD The certainty equivalent (CE) method follows directly from the concept of utility theory. Under the CE approach, the decision maker must first evaluate a cash flow s risk and then specify how much money, to be received with certainty, will make him indifferent between the riskless and the risky cash flows. To illustrate, suppose a rich eccentric offered you the following two choices: 1. Flip a fair coin. If heads comes up you receive $1 million, but if tails comes up you get nothing. The expected value of the gamble is (0.5)($1,000,000) + (0.5)($0) = $500,000, but the actual outcome will be either $0 or $1 million, so this choice is risky. 2. Do not flip the coin and simply pocket $300,000 cash. If you find yourself indifferent between the two alternatives, then $300,000 is your certainty equivalent for this particular risky $500,000 expected cash flow. The certain (or riskless) $300,000 thus provides you with the same utility as the risky $500,000 expected return. Now ask yourself this question: In the preceding example, exactly how much cash- in-hand would it actually take to make you indifferent between a certain sum and the risky $500,000 expected return? If you are like most people, your certainty equivalent would be significantly less than $500,000, indicating that you are risk averse. In 1
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general, people are risk averse, and the lower the certainty equivalent, the greater the decision maker s risk aversion. The certainty equivalent concept can be applied to capital budgeting decisions, at least in theory, in the following way.
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78106_11_Web_Ch11A_p01-07 - WEB EXTENSION 11A Certainty...

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