# fm13 19 - expires We previously calculated the value of the...

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Mini Case: 13 - 19 The indirect approach: Given a current stock price and an anticipated range of possible stock prices at some point in the future, we can use our knowledge of the distribution of stock returns (which is lognormal) to relate the variance of the stock’s rate of return to the range of possible outcomes for stock price. To use this formula, we need the coefficient of variation of stock price at the time the option expires. To calculate the coefficient of variation, we need the expected stock price and the standard deviation of the stock price (both of these are measured at the time the option expires). For the real option, we need the expected value of the project’s cash flows at the date the real option expires, and the standard deviation of the project’s value at the date the real option
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Unformatted text preview: expires. We previously calculated the value of the project at the time the option expires, and we can use this to calculate the expected value and the standard deviation. Value At Expiration Year 1 High \$111.91 Average \$74.61 Low \$37.30 Expected Value =.3(\$111.91)+.4(\$74.61)+.3(\$37.3) = \$74.61. σ value = [.3(\$111.91-\$74.61) 2 + .4(\$74.61-\$74.61) 2 + .3(\$37.30-\$74.61) 2 ] 1/2 = \$28.90. Coefficient Of Variation = CV = Expected Value / σ value CV = \$74.61 / \$28.90 = 0.39. Here is a formula for the variance of a stock’s return, if you know the coefficient of variation of the expected stock price at some point in the future. The CV should be for the entire project, including all scenarios: σ 2 = LN[CV 2 + 1]/T = LN[0.39 2 + 1]/1 = 14.2%....
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