Exhibit Table $1$ 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 investment I$0=20,000,000($rises at $10\%$ per year$)$

Expected sales price per ton P$0=50,000$ per ton in perpetuity

Actual price P$1=$ either $40,000$ or $60,000$ with equal probability

Variable production cost $40,000$ per ton Fixed production cost $0$ per year

Expected production $500$ tons per year forever

Tax rate $0\%$ Discount rate i $=10\%$

Management has gone ahead with the investment in Exhibit Table $1,$but the market is very competitive and several competitors are considering abandoning the market. If they do not abandon, price will remain at the current level of $30,000/$ ton in perpetuity. It is equally likely that they will abandon, in which case the price will rise to $40,000/$ ton $.$As a result, price will be either $30,000$or $40,000$with equal probability in one year. Because of labor agreements, management must either produce at capacity or close the plant, at a cost of $2$million$.$ This abandonment cost rises at $10\%$per year. Assume the plant $$ s abandonment decision does not influence competitors $$abandonment decisions, so price uncertainty is exogenous. Other facts are as in Exhibit Table $1.$

a $.$Calculate the NPV of abandoning today as if it were a now $-$ or $-$ never alternative.

b $.$Calculate the NPV $($ as of t $=0)$of waiting one year before making a decision.

c $.$Suppose price will be either $20,000$or $50,000$with equal probability in one year. How does this increase in price uncertainty affect option value?