You decide to move to the mountains of Colorado and want to know what would be a good offering price on a home, but you know you will only own it a year. Fortunately, you are armed with the simple residential investment equation. You have the following information: the real interest rate is 4 percent; the depreciation rate of homes is 5 percent; average rent is $1,000; there is no expected capital gain; and you will have a 20 percent down payment. You offer the owner, rounding to the nearest dollar:
A) $25,000.
B) $125,000.
C) $4,167.
D) $17,241.
E) $50,000.

Question

Quizplus · Accepted Answer

Using the simple residential investment equation:

Offering price = (Annual rent / Real interest rate) - (Depreciation rate * Price of the house)

Plug in the given values:

Offering price = ($1,000 * 12 months / 0.04) - (0.05 * Price of the house)

We know the down payment will be 20% of the offering price, so the loan amount will be 80% of the offering price.

Loan amount = 0.8 * Offering price

After one year, we will need to sell the house for the remaining loan balance. If there is no expected capital gain, that means we can only sell for the remaining loan balance, which is:

Remaining loan balance = Loan amount * (1 + Real interest rate)

Substitute the loan amount equation:

Remaining loan balance = [0.8 * Offering price] * (1 + 0.04)

Simplify:

Remaining loan balance = 0.832 * Offering price

We only want to break even on this investment, so the remaining loan balance must equal the offering price (minus the down payment):

Offering price - (0.2 * Offering price) = 0.832 * Offering price

Simplify:

0.8 * Offering price = 0.832 * Offering price

Offering price = $17,241 (rounded to the nearest dollar)

Therefore, the best choice is D, $17,241.

You Decide to Move to the Mountains of Colorado and Want