Lord Rayleigh has bought a house for $350,000, of which $50,000 is the value of
ID: 2624057 • Letter: L
Question
Lord Rayleigh has bought a house for $350,000, 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 5% per year. He will rent the house for the next six years and then sell it. He will depreciate the house uniformly over 24 years. The income tax rate of Rayleigh is 32%, and the risk-adjusted discount rate is 11%. The annual expenses on the property (real estate taxes, maintenance, etc.) are $9000, realized at the end of each year. Find the amount of rent that Rayleigh must collect at the end of each year to break even.
please show all work
Explanation / Answer
value of house = 350000-50000= 300,000
Depreciation = 300000/24=12500
Book value of the house at the end of 6 years = 300,000-6*12500=225000
Value of land after 6 years = 50000*1.05^6=$67004.78
Let revenue be x
Free cash flow =( x-9000-12500)*(1-30%) + 12500= 0.7x -2120
for breakeven NPV =0
-350000 + (0.7x -2120)/1.11 + (0.7x -2120)/1.11^2 + (0.7x -2120)/1.11^3 + (0.7x -2120)/1.11^4 + (0.7x -2120)/1.11^5 + (0.7x -2120)/1.11^6 + 225000/1.11^6+ 67004.78/1.11^6=0
x= $70513.59
Rent = $70513.59
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