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) = 1 − x. Now assume that the payoff from the biofuel car is higher, A2(x) = 2x. As before, x is a random variable uniformly distributed between 0 and 1, capturing the relative availability of bio-fuels 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) = x.

Compute the option value of a lexible-fuel car that allows the buyer to reproduce the payoff from either single-fuel car.

b. Repeat the option value calculation for a riskaverse buyer with utility function U(x) = !x.

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 lexible-fuel car.