7.9 Return to Example 7.5, in which we computed the value of the real option provided by a flexible-fuel car. Continue to assume that the payoff from a fossil-fuel–burning car is A1(x) ¼ 1 % x. Now assume that the payoff from the biofuel car is higher, A2(x) ¼ 2x. As before, x is a random variable uniformly distributed between 0 and 1, capturing the relative availability of biofuels versus fossil fuels on the market over the future lifespan of the car.

a. Assume the buyer is risk neutral with von Neumann–Morgenstern utility function U(x) ¼ x. Compute the option value of a flexible-fuel car that allows the buyer to reproduce the payoff from either single-fuel car.

b. Repeat the option value calculation for a risk-averse buyer with utility function UðxÞ ¼ ffiffi x p .

c. Compare your answers with Example 7.5. Discuss how the increase in the value of the biofuel car affects the option value provided by the flexible-fuel car.