5. David Livingston has bought a house for $250,000, of which $50,000 is the val

Question

5. David Livingston has bought a house for $250,000, of which $50,000 is the value of the land. Livingston expects that the value of the property will increase at the compound rate of 4% per year. He will rent the house for the next five years and then sell it. He will depreciate the house uniformly over 25 years. The income tax rate of Livingston is 30%, and the risk-adjusted discount rate is 12%. The annual expenses on the property (real estate taxes, maintenance, etc.) are $6000, realized at the end of each year. Find the amount of rent that Livingston must collect at the end of each year to break even.

Explanation / Answer

value of house = 350000-50000= 300,000

Depreciation = 300000/25=12000

Book value of the house at the end of 6 years = 300,000 - 6 * 12000=228000

Value of land after 6 years = 50000 * 1.04^6 = $63,265.95.

Let revenue be x

Free cash flow =( x-6000-12000) * (1-30%) + 12000= 0.7x - 600

for breakeven NPV =0

-350000 + (0.7x -600)/1.12 + (0.7x -600)/1.12^2 + (0.7x -600)/1.12^3 + (0.7x -600)/1.12^4 + (0.7x -600)/1.12^5 + (0.7x -600)/1.12^6 + 228000/1.12^6+ 63,265.95/1.12^6=0

x= $71,196.49

Rent = $71,196.49

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