Problem $1.$ 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?