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.