Question

A family currently live in an apartment whose monthly rent is $950. They are thinking of buying a house which would cost $220,000. They plan to live in this house for 5 years and sell it at the end of the 5th year. They would put a downpayment of $20,000 and finance the balance through a mortgage at 3.5% interest rate. The mortgage is to be repaid in 5 annual installments (which include both principal and interest) at the end of each year for the next 5 years The house will have the following additional expenses: annual maintenance: $1500; Property taxes:$5500; Insurance: $1200. Assume they are in tax bracket of 20% and the price of home, rent and expenditure increases by 2.5% per year. Their opportunity cost or required rate of return is 5% per year. Note that property taxes are tax deductible and there no tax payable on capital gains. Use annual compounding for amortization schedule of mortgage.

Calculate Ownership Operating Advantage in year 2.

		($39,924)
		($39,631)
		($39,350)
		($39,775)

Answer 1

In order to determine the owership operating advantage, we would need to determine the Annual payment amount (including principal + Interest) on the new property.

Annual payment = (r(p)) / (1-(1+r)^-n)

where r = rate of interest (3.5% or 0.035 in this case)

p = principal amount (200000 in this case)

n = number of payments (5 in this case)

Substituting these values in the above equation, we get Annual payment = 44296.27

Below table shows the calculation of values for year 2:

Description Annual Rent of current apartment Annual Rent of current apartment year 1 Annual Rent of current apartment year 2 Annual maintenance year 0 Annual maintenance year 1 Annual maintenance year 2 Property Taxes year 0 Property Taxes year 1 Property Taxes year 2 Insurance Year 0 Insurance Year 1 Insurance Year 2 Amount Comments 11400 Monthly Rent of current apartment 12 11685 increased by 2.5% from year 0 11977.125 increased by 2.5% from vear 1 1500 Input Data 1537.5 increased by 2.5% from year 0 1575.9375 increased by 2.5% from year 1 5500 Input Data 5637.5 increased by 2.5% from year o 5778.4375 increased by 2.5% from year 1 1200 Input Data 1230 increased by 2.5% from year 0 1260.75 increased by 2.5% from year 1

From the values calculate above, we can find out the Ownership Operating Advantage for year 2 by finding out the incremental costs and benefits in year 2 as shown in the below table: