Exercise $16\mathrm{.}4$

Consider a firm whose only asset is a plot of vacant land, and whose only liability is debt of $$15$ million due in one year. If left vacant, the land will be worth $$10$ million in one year. Alternatively, the firm can develop the land at an upfront cost of $$20$ million. The developed land will be worth $$35$ million in one year. Suppose the risk$-$free interest rate is $10\%,$ assume all cash flows are risk$-$free, and assume there are no taxes.

a$.$ If the firm chooses not to develop the land, what is the value of the firm's equity today? What is the value of the debt today?

b$.$ What is the NPV of developing the land?

c$.$ Suppose the firm raises $$20$ million from equity holders to develop the land. If the firm develops the land, what is the value of the firm's equity today? What is the value of the firm's debt today?

d$.$ Given your answer to part $($c$),$ would equity holders be willing to provide the $$20$ million needed to develop the land?