8.19 An investor group wants to purchase a firm whose primary asset is ownership of the exclusive rights to develop a parcel of undeveloped land sometime during the next five years. Without considering the value of the option to develop the property, the investor group believes the net present value of the firm is $(10)

million. However, to convert the property to commercial use (i.e., exercise the option), the investors have to invest $60 million immediately in infrastructure improvements. The primary uncertainty associated with the property is how rapidly the surrounding area will grow. Based on their experience with similar properties, the investors estimate that the variance of the projected cash flows is 5% of NPV, which is $55 million.
Assume the risk-free rate of return is 4%. What is the value of the call option the investor group would obtain by buying the firm? Is it sufficient to justify the acquisition of the firm? Show your work.
Answer: The value of the option is $13.47 million. The investor group should buy the firm, since the value of the option more than offsets the $(10) million NPV of the firm if the call option were not exercised.