Consider a firm whose only asset is a plot of vacant land, and whose only liabil
ID: 2658602 • Letter: C
Question
Consider a firm whose only asset is a plot of vacant land, and whose only liability is debt of $14.7 million due in one year. If left vacant, the land will be worth $10.2 million in one year. Altematively, the firm can develop the land at an up-front cost of $20.2 million. The developed the land will be worth $34.9 million in one year. Suppose the risk-free interest rate is 9.5%, 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 $20.2 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 d. Given your answer to part (c), would equity holders be willing to provide the S20.2 million needed to develop the land? today?Explanation / Answer
a. Assets = Liability + Equity.
Assets = $10.2 Million in one year , Risk Free Rate = 9.5%
PV of Assets = 10.2 / (1.095) = $9.31
Equity = Aseets - Liability = 9.31 - 14.7 = -$ 5.39 million
Negative Equity arises when value of property fall below the mortgage used to buy the property.
b- Cash Flow after one year = $34.9 million
PV = 34.9 / (1.095) = $31.87 million
Initial Investment = 10.2 + 20.2 = $30.4 million
NPV = -30.4 + 31.87 = 1.47
c- Value of Asset Today after developing the land = 34.9 / (1.095) = 31.87
Liability = $14.7
Equity = $17.17
d. Equity holder is likely not to provide $20.2 million as PV of equity after developing the land is $17.17 (less than $20.2 million)
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