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

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?

Please can you explain how you got your answer, thank you :)

Solutions

Expert Solution

(a) The calculation of equity in case the land is decided not to be developed is as follows:

Present Value of Equity=(-5/1.10)

=$4.55 Million

Present Value of Debt=(15/1.10)

=$13.64 Million

(b) NPV of the development of land is calculated as follows:

The above table has been derived from following excel formula:

(c) The calculation of equity in case the land is decided to be developed by raising funds through equity, is as follows:

Equity=(Asset-Debt)

=35-20

=15

PV of Equity=(15/1.10)

=$13.64 Million

PV of Debt=(15/.10)

=$13.64 Million

jeff jeffy answered 6 months ago
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