A homeowner wants to decide whether he should install an electronic heat pump in his home. Given that the cost of installing a new heat pump is fairly large, the homeowner wants to do so only if he can count on being able to recover the initial expense over five consecutive years of cold winter weather. After reviewing historical data on the operation of heat pumps in various kinds of winter weather, he computes the expected annual costs of heating his home during the winter months with and without a heat pump in operation. These cost figures are shown in the file P09_77.xlsx. The probabilities of experiencing a mild, normal, colder than normal, and severe winter are 0.2(1 - x), 0.5(1 - x), 0.3(1 - x), and x, respectively. In words, we let the last probability vary, we let the other three be in the ratio 2 to 5 to 3, and we force them to sum to 1.
a. Given that x = 0.1, what is the most that the homeowner is willing to pay for the heat pump?
b. If the heat pump costs $500, how large must x be before the homeowner decides it is economically worthwhile to install the heat pump?
c. Given that x = 0.1, calculate and interpret EVPI when the heat pump costs $500.
d. Repeat part c when x = 0.15.
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