Look again at Table 22.2. How does the value in 1982 of the option to invest in the Mark II change if:

(a)?The investment required for the Mark II is $800 million (vs. $900 million)?

(b)?The present value of the Mark II in 1982 is $500 million (vs. $467 million)?

(c) The standard deviation of the Mark II?s present value is only 20 percent (vs. 35 percent)?

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Assumptions 1. The decision to invest in the Mark Il must be made after 3 years, in 1985. 2. The Mark Il investment is double the scale of the Mark I (note the expected rapid growth of the industry). Investment required is $900 million (the exercise price), which is taken as fixed. 3. Forecasted cash inflows of the Mark Il are also double those of the Mark I, with present value of $807 million in 1985 and 807/(1.2) = $467 million in 1982. 4. The future value of the Mark II cash flows is highly uncertain. This value evolves as a stock price does with a standard deviation of 35 percent per year. (Many high- technology stocks have standard deviations higher than 35 percent.) 5. The annual interest rate is 10 percent. Interpretation The opportunity to invest in the Mark Il is a three-year call option on an asset worth $467 million with a $900 million exercise price. Valuation 900 PV(exercise price) = (1.1)3 Call value = [N(di) x P] - [Nd2) x PV(EX)] di - log [P/PV(EX)]/Vt+aVt/2 = log [.691]/.606 + .606/2 = -.3072 dz = di - o Vt = -3072 - .606 = - 9134 N(di) = .3793, N(d2) .1805 676 I3! Call value = [.3793 x 467] - [.1805 x 676] = $55.12 million