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Selling or purchasing problem

Atlas Realty Company is interested in buying a house and renting it out for $12,000 a year, collecting the rent in advance each year. This will depreciate the house over 25 years; however sell it after 15 years at twice its purchase price. The maintenance expenditures and real estate taxes, at the end of each year, are $1000 annually. The risk-adjusted discount rate for Atlas is 10% and its income tax rate 25%. Find the price of the house that Atlas should pay so that it can make $5000, in current dollars, from this project.

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Let P be the purchase price of the house. Book value of house after 15 years = P - (P/25)*15 = 0.4P
Excess on book value = 2P – 0.4P = 1.6P
Tax on residual value = 1.6P*0.25 = 0.4P

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-P + 9000 + 60777.75 + 0.07367P – 179.25 + 0.38P = 5000
69598.5 – 0.54633P = 5000
P = $118,241

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