Exogenous price uncertainty and the option to abandon. $2.$ 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?