1. (50 points, in-class example) Mr. Conrad Willig liked the idea of hotels made of ice...

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1. (50 points, in-class example) Mr. Conrad Willig liked the idea of hotels made of ice more than anything else. While he was pretty sure that the initial investment of one ice hotel would cost $12 million, there was some uncertainty concerning annual cash flows. He believed that there was a 75 percent probability that the idea would be successful with an annual cash flows of $3 million and a 25 percent probability that the idea will fail with an annual cash flows of only $1 million. However, if the idea turned out to be successful, Mr. Willig would want to expand, and therefore build 10 hotels in total instead of only one. He felt that 20 percent was an appropriate discount rate, given the risk of this new venture. And he believed that the cash flows would be perpetual. Please compute the value of the option to expand. (Hint: You need to compute the value of the project without expanding option as well as the value with expanding option. The difference of these two values will be the value of the option.) Solution: The NPV calculations for the two forecasts are given here: = $3 million Optimistic forecast: -$12 million + $3 million/.20 Pessimistic forecast: -$12 million+ $1 million/.20 = $7 million Without expanding: the expect NPV is 0.75* 3 + 0.25 * (-7)= $0.5 million With expanding: the expected NPV is 0.75* 30 +0.25 * (-7)= $20.75 million Therefore, the value of the expanding option is $20.25 million. 1. (50 points, in-class example) Mr. Conrad Willig liked the idea of hotels made of ice more than anything else. While he was pretty sure that the initial investment of one ice hotel would cost $12 million, there was some uncertainty concerning annual cash flows. He believed that there was a 75 percent probability that the idea would be successful with an annual cash flows of $3 million and a 25 percent probability that the idea will fail with an annual cash flows of only $1 million. However, if the idea turned out to be successful, Mr. Willig would want to expand, and therefore build 10 hotels in total instead of only one. He felt that 20 percent was an appropriate discount rate, given the risk of this new venture. And he believed that the cash flows would be perpetual. Please compute the value of the option to expand. (Hint: You need to compute the value of the project without expanding option as well as the value with expanding option. The difference of these two values will be the value of the option.) Solution: The NPV calculations for the two forecasts are given here: = $3 million Optimistic forecast: -$12 million + $3 million/.20 Pessimistic forecast: -$12 million+ $1 million/.20 = $7 million Without expanding: the expect NPV is 0.75* 3 + 0.25 * (-7)= $0.5 million With expanding: the expected NPV is 0.75* 30 +0.25 * (-7)= $20.75 million Therefore, the value of the expanding option is $20.25 million.