Question

Buy a 900 SF house for $180/SF. Sell in 2 years. Finance 90% of the sale price. At purchase the total closings costs that you pay are $2,500 and 1.00 points on the loan. At resale in 2 years, you pay $3,000 in closing costs and a 5% commission to the broker. Since the purchase, the house has increased in value by 6% per year, compounded once per year. Assume loan payoff is $140,988.

What is the profit on your equity investment, considering the gain in sale price, but subtracting the closing costs at each end of the investment and the broker’s commission? What is your annual rate of return on equity, compounded once per year?

Answer 1

(All caluclation in $)

At t= 0 (initial buying of the house)

P0= Price of the house = 900*180= 162000 (900sf @180/SF)

D0: Debt component= 90%*162000= 145800 (90% financed)

E0: Equity component= 10*162000=16200 (10% own money or equity)

C0: closing costs = 2500

M0: Mortgage point cost=1%*145800=14580 9you pay initial mortage point to reduce your interest rate)

At t =2 (selling of the house after 2 years)

P2= Price of the house= 162000(1+0.06)^2 (6% growth in the housing prices) =182,023.20

C2: closing cost = 3000

CM2: Commision to broker = 0.05*182,023= 9101.16 (5% on the price of the house)

LP2: Loan payoff= 140988

profit on equity = Current price of the house-closing costs-commision to broker - loan payoff - Initial own money invested/equity   

= P2-C0-C2-CM2-LP2- E0

=182,023.20-2500-3000-9101.16-140,988-16200

=10,234.04

(In these kind of problem we just need to focus on how much have we invested from our posket (equity componen. commision, closing cost) and how much we got back( current selling price.)

anuual rate of return = [(final value/ initial value)^0.5]- 1 (just a simple arrangement of compound interest formula:

final value= initial value* (1+ r/100)^n

n: no of years

r: annualised rate of return)

Since, final value= initial value+ profit for the period= 26434.04

annual rate of return = [(26434.04/16200)^0.5]-1

= 0.2774

= 27.74%