Question

You are considering buying an apartment complex with 50 units. The units rent for $1000 per month each. Usually, there is a 10% vacancy. You want a 7.5% percent total annual after-tax return on the funds you invest. You do not expect any appreciation of the property value. You also expect the property to not have any economic or real depreciation in value, since the maintenance expenses will keep the property in equal condition year after year.

When fully occupied, there is additional income from laundry, vending machines, and parking (for tenants with more than one car) of $10,000 per year; the actual income is proportional to occupancy.

You will pay a 20% down payment, with a mortgage rate of 5%.

Your mortgage is perpetual, so the entire payment is interest.

Half the property value is land value.

To keep the math simple, the building is depreciated over 25 years.

The total state and federal marginal income tax rate is 50%.

Annual operating expenses are: Property tax: $ 39,000, Insurance $110,000, Maintenance $300,000.

How much should you offer to pay for the apartments to get a 7.5% return on your money?

Suggestion: Use algebra

Let X = purchase price

Calculate interest payment, depreciation as functions of X.

Calculate return on investment as a function of X.

You will have the after-tax cash flow as a function of X.

You should have two different equations; solve for X.

Test your answer when you have X.

Answer 1

Let X=purchase Price

Initial Investment =Down Payment =0.2X

Loan amount =X-0.2X=0.8X

Annual Interest Payment=5%*Loan amount=0.05*0.8X=0.04X

Cost of Land =0.5X

Cost of Building =0.5X

Annual Depreciation of building =0.5X/25=0.02X

Return on investment required =7.5%*0.2X=0.015X

After Tax Cash Flow:

Annual Rental Income considering 10% Vacancy(90% Occupancy)=0.9*50*$1000*12=$540000

Additional Income from Laundry, Vending Machine and Parking =90%*$10000=$9000

Total Annual Income =540000+9000=$549000

Annual Operating Expenses=39000+110000+300000=$449000

Total Annual expenses=449000+Deprection+Interest

Total Annual expenses=449000+0.02X+0.04X=449000+0.06X

Annual Before tax Profit =549000-449000-0.06X=100000-0.06X

Annual After Tax Profit =50%*(100000-0.06X)=$50000-0.03X

Annual Cash Flow=Annual After Tax Profit +Depreciation =$50000-0.03X+0.02X=50000-0.01X

Return on investment required= Annual Cash Flow

0.015X=50000-0.01X

0.025X=50000

X=50000/0.025=$2,000,000

Amount to be paid=$2,000,000