Exogenous price uncertainty and the option to invest.
Answer the following questions based on the information in Exhibit T16.1.
a. Draw a decision tree that depicts this investment decision.
b. Calculate the NPV of investing today as if it were a now-or-never alternative.
c. Calculate the NPV (at t = 0) of waiting one year before making a decision.
d. Decompose option value into intrinsic value and time value. Should this investment be made today, in one year, or not at all?
e. Suppose price will be either ¥70,000 or ¥30,000 with equal probability in one year. How does this increase in endogenous price uncertainty affect option value?
Exhibit T16.1
A proposed plant in China will process soybeans for the local (Chinese new yuan, or ¥) market. The sales price of a ton of processed soy will be determined by a government panel, and will be known with certainty in one year. The plant must decide whether to begin production today or in one year.
The following facts apply to the investment decision.
Initial investmentI0 = ¥20,000,000 (rises at 10% per year)
Expected sales price per tonP0 = ¥50,000 per ton in perpetuity
Actual priceP1 = either ¥40,000 or ¥60,000 with equal probability
Variable production costVC = ¥40,000 per ton
Expected productionQ = 500 tons per year forever
Tax rateTC = 0%
Discount ratei = 10%