Suppose that the risk-free interest rate is 2.29%. The analyst uses the Black-Scholes option-pricing model to value the flexible project that would invest in one machine today but retain the option to buy five additional machines in one year should the companys experience with the first machine prove successful. She assembles the following information:

Discount rate for machine cash flows 13%

Riskless discount rate 2.29%

S 935.58

X 1000.00

r 2.29%

Sigma 30%

T = 1

(e) What is the value of the option to replace one additional machine in one year according to the Black-Scholes model?

(f) What is the NPV of the total project, including the investment in one machine today and the option to buy five additional machines in one year? Assume that the values attributable to each of the additional five machines are independent. What should the analyst recommend to the line manager?

(g) Is the recommendation given in (f) the same as or different from the conclusion reached based on static NPV? Explain.

(h) Sigma ( ) has been estimated to be 30%, but its value is uncertain since sigma is not observed directly in the marketplace. Calculate the NPV of the total project, including the investment in one machine today, at the following values for sigma: 15%, 20%, and 40%. Explain the effect that sigma has on the NPV of the total project