Figure 147

Expected Rates of Return on Investments X and Y

Investments X and Y both have continuous distributions of returns around their expected values.

Probability of occurrence

Probability of occurrence

Rate of return

lation for two alternative projects, X and Y, each with an expected cost of $20 million. The expected rate of return on investment X is 15 percent, and 20 percent on investment Y. However, these are only average rates of return derived by the computer simulation. The range of simulated returns is from -10 percent to 45 percent for investment Y, and from 5 percent to 25 percent for investment X. The standard deviation for X is only 4 percent; that for Y is 12 percent. Based on this information, the coefficient of variation is 0.267 for investment X and 0.60 for investment Y. Investment Y is clearly riskier than investment X. A decision about which alternative to choose can be made on the basis of expected utility, or on the basis of a present value determination that incorporates either certainty equivalents or risk-adjusted discount rates.

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