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%

Buy since IRR is 5.51%
Rent since IRR is 4.16%
Buy since IRR is 6.28%

please show work

Thank you

Answer 1

Annuity on the mortgage
200000=Pmt.*(1-1.035^-5)/0.035
44296.27

1	2	3=Prev.5*3.5%	4=2-3	5=Prev.5-4	6=3*20%
Year	Annuity	Tow.Int.	Tow.Mortg.	Mortg. Bal.	Int.tax shield
0				200000
1	44296.27	7000	37296.27	162703.7	1400
2	44296.27	5694.63	38601.64	124102.09	1138.93
3	44296.27	4343.57	39952.70	84149.39	868.71
4	44296.27	2945.23	41351.04	42798.35	589.05
5	44296.27	1497.94	42798.33	0.02	299.59
	221481.35	21481.37	199999.98		4296.27

	0	1	2	3	4	5
Cost	-220000					248909.8
Opportunity cost of after-tax int.income lost on down pmt.(20000*5%*(1-20%)	-800
After-tax Maintenance(1500*(-20%))		-1200	-1230	-1260.75	-1292.27	-1324.575
After-tax Property taxes(5500*1-20%))		-4400	-4510	-4622.75	-4738.32	-4856.777
After- tax insurance(1200*(1-20%))		-960	-984	-1008.6	-1033.82	-1059.66
After-tax savings in annual rent(950*12)*(1-20%)		9120	9348	9581.7	9821.243	10066.77
Int. tax shields(as per amortsn. Table)		1400	1138.93	868.71	589.05	299.59
Total annual cash flows	-220800	3960	3762.93	3558.31	3345.89	252035.16
IRR	3.97%
Decision:
Rent since IRR 3.97% < reqd. return 5%