Question

Scenario 1: Mrs. Rogers is considering purchasing a rental home property. The annual income from the rental house is $26,400 and the annual expenses are $7,200 (both at the end of each year). Assume the house is to be sold at the end of 12 years for $255,000 and that the interest rate is 8% per year. (Note: for simplicity, ignore taxes and depreciation).

What is the maximum Mrs. Rogers is willing to pay for the rental house today?

Assume Mrs. Roger's purchases the home for $200,000 today. What is the benefit/cost ratio of the rental home (including all income/expenses mentioned above and the price of the home today)?

Assume Mrs. Rogers' borrows $180,000 via a 10-year mortgage to help pay for the rental home. The bank has an interest rate of 6% per year, compounded monthly. What is Mrs. Rogers' monthly mortgage payment?

Answer 1

Maximum purchase price should be equal to PV of future cash flows.Let it is X.

Net annual Income=R=26400-7200=$19200

Salvage =S=$255,000

Rate of interest=i=8%

X=PV of future cash flows=R*(P/A,0.08,12)+S*(P/F,0.08,12)

Let us calculate the interest factors

(P/F,0.08,12)=1/(1+0.08)^12=0.397114

X=PV of future cash flows=19200*7.536078+255000*0.397114=$245,956.77

Let let us assume that price of house be $200000

PV of rental income=PVB=26400*(P/A,0.08,12)=26400*7.536078=$198,952.46

PV of annual cost=PVOC=7200*(P/A,0.08,12)=7200*7.536078=$54,259.76

PV of salvage=PVS=255000*(P/F,0.08,12)=255000*0.397114=$101,264.07

B-C Ratio=PVB/(C+PVOC-PVS)=198952.46/(200000+54259.76-101264.07)=1.3004

Loan amount=PV=$180000

Rate of interest=i=6%/12=0.005 per month

Tenure=n=10*12=120 months

Monthly mortgage payment=PV*(A/P,i,n)=180000*(A/P,0.005,120)

Let us calculate the interest factor

Monthly mortgage payment=180000*(A/P,0.005,120)=180000*0.011102=$1998.36