P 16-29 ISINIllar to) estl Help Consider a firm whose only asset is a plot of va
ID: 2791926 • Letter: P
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P 16-29 ISINIllar to) estl Help 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. Alternatively, the firm can develop the land at an up-front cost of $20.1 million. The developed the land will be worth $35.7 million in one year. Suppose the risk-free interest rate is 10.5%, 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 $20.1 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
The following information is given
· The value of land which is an asset is $ 10.2 million if sold after one year from now
· The value of liability is 14.7 million payable after one year
· The risk free interest is 10.5%
If land is developed than
· The upfront cost of development will be $20.1 million
· The value of land after one year if sold will be $ 35.7 million
A ) what is the value of the firm’s equity today? What is the value of the debt today?
As there is no information of equity given only value of asset and liability is given hence
Value of equity is $0
Value of debt is will be only asset value which is sold at $10.2 million after one year at 10.5% interest rate
The present value of cash inflow of asset at 10.5% interest rate or discount rate will be value of debt
Value of debt = $ 10.2 million / (1+ interest rate)
= $10.2 million / (1+0.105)
= $10.2 / 1.105
= $ 9.23 million ( rounding off two decimals)
B) NPV of land will be calculated as below
· The expense of today to develop land is $ 20.1 million
· The cash inflow of developed land after one year is $ 35.7 million . the net cash inflow after one year for developed land = $ 35.7 million - $10.2 Million = $25.5 million
The net present value of developed land
A) present value of net Cash inflow after one year for developed land
= 25.5 / 1.105
= $23.08 million
B ) – present value of expense for land development is $ 20.1 million
NPV = $23.08 - $20.10
= $2.98
C) the following information is given if firm raises equity
· The amount of equity infused is $20.1
· The amount of debt will be $14.7 million after one year payable
· The amount of land value after one year is $35.7 million
The value of debt today = amount of debt / (1+ interest rate)
= $14.7 / (1+0.105)
= $14.7 / 1.105
= $13.30 million
The value of equity today is = (income on sale of land – amount of debt) / (1+ interest rate)
=( $ 35.7 - $ 14.7 ) / (1+0.105)
= $21 /1.105
= $19.00 million
D ) the present value of equity today is $19 million and investment is $20.1 million . which is negative NPV hence equity investors will not provide the money
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