Consider a firm whose only asset is a plot of vacant land, and whose only liabil

Question

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 $9.7 million in one year. Alternatively, the firm can develop the land at an up-front cost of $20.1 million. The developed the land will be worth $34.8 million in one year. Suppose the risk-free interest rate is 9.9%, cash flows are risk-free, and 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 $20.1 million from the 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 $20.1 million needed to develop the land? 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? If the firm chooses not to develop the land, the value of the equity is million. (Round to two decimal places.)

Explanation / Answer

a.) Value of firms equity today =$ 9.7/1.099 =$ 8.83 million

Value of Debt today =$ 15/1.099 =$ 13.65 million

b.) NPV of Land development =$ -20.10 + (34.80 - 9.70)/1.099 =$ -20.10 + 22.84 =$ 2.74 million

c.) Value of Firm's Equity today =$34.80/1.099 =$31.67 million

Value of Debt today =$ 15/1.099 =$ 13.65 million

d.) Yes, the equity holders will be willing to give $20.10 million since the NPV of the land development project is positive. Moreover, the debt equity ratio is 0.43, which is in the comfortable zone.

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