A family currently live in an apartment whose monthly rent is $950. They are thi

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.

Should they buy this house or continue to rent?

Buy since IRR is 5.47%

Rent since IRR is 4.16%

Buy since IRR is 5.51%

Buy since IRR is 6.28%

Part 2 of Problem

Calculate the Post tax Mortgage Cost (principal repayment plus after tax interest cost) for year 1.

$44,078

$43,679

$42,925

$42,896

Buy since IRR is 5.47%

Rent since IRR is 4.16%

Buy since IRR is 5.51%

Buy since IRR is 6.28%

Part 2 of Problem

Calculate the Post tax Mortgage Cost (principal repayment plus after tax interest cost) for year 1.

$44,078

$43,679

$42,925

$42,896

Explanation / Answer

0 1 2 3 4 5 Annual Mortgage payments (as per Amortsn.Table) -44296 -44296 -44296 -44296 -44296 Taxes ,ins.Maint(1500+5500+1200),increasing at 2.5% p.a. -8200 -8405 -8615.1 -8830.5 -9051.3 After-tax Int.lost on down payment(20000*5%*(1-20%) -800 Tax savings in mortg. Interest(20%*int.as per amortsn.table) 1400 1139 869 589 300 Tax savings on (Taxes ,ins.Maint)(20%*above ) 1640 1681 1723 1766 1810 Rent exp. Saved(950*12)increasing at 2.5% p.a. 11400 11685 11977 12277 12583 Tax -saving lost on above rent at 20% -2280 -2337 -2395 -2455 -2517 Down payment -20000 Sale value at end Yr.5 248910 -20800 -40336 -40533 -40738 -40950 207739 IRR 4.53% As IRR of Buying is less than the required return of 5% , Renting is recommended. Using the PV of annuity formula, we calculate the annual payment towards the mortgage as follows: 200000=Annual pmt.*(1-1.035^-5)/0.035 x=44296.3 Mortgage Amortisation Schedule: Year Annuity Tow.int. Tow.Principal Princ. Bal. 0 200000 1 44296 7000 37296 162704 2 44296 5695 38602 124102 3 44296 4344 39953 84149 4 44296 2945 41351 42798 5 44296 1498 42798 0 Post tax Mortgage Cost (principal repayment plus after tax interest cost) for year 1: 37296+(7000*(1-20%))= 42896

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