Question

9. Rent versus buy analysis - Part 2

Which is better: to rent or to buy?

The decision of whether to rent or buy housing is a personal decision that is based on both your lifestyle and your finances. While most financial experts argue that the financial aspect of the decision is important, it is also important not to base your rent-or-buy decision solely on the numbers. Your personal needs and housing market conditions are important.

However, it is still necessary to perform the financial analysis.

Lorenzo and his wife are trying to decide whether to rent or to purchase a new townhouse. After looking for several months, they’ve narrowed their choice down to one particular house, and the builder is willing to lease or sell—depending upon the preference of the buyer.

To perform a rent-or-buy analysis, Lorenzo and his wife have collected the following information:

•	If they rent, the builder will require monthly rental payments of $1,300 and a security deposit equal to two months of rent.
•	Since they want to be protected against the possible loss of their possessions, they will purchase a renters’ policy of $200 every six months, while a more comprehensive homeowners’ policy will cost 0.5% of the home’s value per year.
•	Money used to fund the house’s security deposit could otherwise be invested to earn 5% per year after taxes. Funds expended for a home’s down payment and closing costs also incur an opportunity cost.
•	If the house is purchased, it will cost $247,000 and will require a 20% down payment. The loan will carry an interest rate of 6%, a term of 30 years, and monthly payments of $1,185. The closing costs associated with the house’s mortgage will be $3,500.
•	The property taxes and the maintenance and repair expenses on the house are estimated to be 3% and 2% of the house’s total price, respectively.
•	Your ordinary income is taxed at the rate of 28%, and you’ll be willing to itemize your tax deductions in the event that you purchase your new home.
•	Financial publications report that home values are expected to increase by 3% this year due to inflation.

Complete a rent-or-buy analysis worksheet to determine the total cost of renting and the total cost of purchasing Lorenzo and his wife’s prospective house. To complete the worksheet, enter the appropriate values in their corresponding blanks and round each value to the nearest whole dollar.

RENT-OR-BUY ANALYSIS FOR HOUSING	Amount
COST OF RENTING	($)
Security deposit
Annual rental cost
Renter’s insurance
Opportunity cost on security deposit
Total Annual Cost of Renting:	RENT-OR-BUY ANALYSIS FOR HOUSING Amount COST OF BUYING ($) Monthly mortgage payment Annual mortgage payments Property taxes Homeowner’s insurance Maintenance expenses Opportunity cost of down payment and closing costs Total costs Less Reduction of loan principal Tax savings on mortgage interest deduction Tax saving on property tax deduction Total deductions Annual after-tax cost of homeownership Estimated annual appreciation in home value Total Annual Cost of Purchasing: Based on this analysis, Lorenzo and his wife should: Purchase the home, as the cost of purchasing is greater than the cost of renting. Purchase the home, as the total cost of purchasing is less than the cost of renting. Rent the home, as its total cost is less than the total cost of purchasing.

Answer 1

Answer :

	RENT-OR-BUY ANALYSIS FOR HOUSING	Amount	Total
	COST OF RENTING	$	$
1	Security deposit	2600	2,600.00
2	Annual rental cost	15600	4,68,000.00
3	Renter’s insurance	400	12,000.00
4	Total ( 1+2+3)		4,82,600.00
5	Opportunity cost on security deposit @ 5%		8,134.01
6	Total Annual Cost of Renting:		4,74,465.99
	Opportunity cost on security deposit for 30 Years
	Formula for calculation of Interest A = P(1 + r/n)^nt
	P = $2600 , t = 30 year , r=5% pa
	A = $8134.01
	RENT-OR-BUY ANALYSIS FOR HOUSING		Total Amount
	COST OF BUYING		$
1	Monthly mortgage payment	1185
2	Annual mortgage payments	14220	4,26,600.00
3	Property taxes ( 3% on Cost of House $2,47,000 )	7410	2,22,300.00
4	Homeowner’s insurance @ 0.5%	1235	37,050.00
5	Maintenance expenses ( 2% on total Cost of House $ 2,47,000)	4940	1,48,200.00
6	Opportunity cost of down payment and closing costs ( 20% of 2,47,000 +3500)		52,900.00
A	Total costs ( 2 to 6)		8,87,050.00
	Less
1	Reduction of loan principal		1,97,600.00
2	Tax savings on mortgage interest deduction		64,090.32
3	Tax saving on property tax deduction		2,22,300.00
B	Total deductions		4,83,990.32
	Annual after-tax cost of homeownership		4,03,059.68
	Estimated annual appreciation in home value @ 3% on $ 247000		5,88,533.83
	Total Annual Cost of Purchasing:		1,85,474.15
B	Working note
1	Estimated annual appreciation in home value @ 3% on $ 247000
	Formula for calculation of Interest A = P(1 + r/n)^nt
	P = $2,47,000 t = 30 year , r=3% pa
	A = $ 599,533.83
	Tax savings on mortgage interest deduction ref Home loan aortization table
	Total interest paid	2,28,894

Home Loan Amortization Table
Year	Opening Balance	EMI*12	Interest paid yearly	Principal paid yearly	Closing Balance
1	1,97,600.00	14,217.00	11,790.00	2,427.00	1,95,173.00
2	1,95,173.00	14,217.00	11,640.00	2,576.00	1,92,597.00
3	1,92,597.00	14,217.00	11,481.00	2,735.00	1,89,862.00
4	1,89,862.00	14,217.00	11,313.00	2,904.00	1,86,958.00
5	1,86,958.00	14,217.00	11,134.00	3,083.00	1,83,875.00
6	1,83,875.00	14,217.00	10,943.00	3,273.00	1,80,602.00
7	1,80,602.00	14,217.00	10,742.00	3,475.00	1,77,127.00
8	1,77,127.00	14,217.00	10,527.00	3,689.00	1,73,438.00
9	1,73,438.00	14,217.00	10,300.00	3,917.00	1,69,521.00
10	1,69,521.00	14,217.00	10,058.00	4,158.00	1,65,363.00
11	1,65,363.00	14,217.00	9,802.00	4,415.00	1,60,948.00
12	1,60,948.00	14,217.00	9,529.00	4,687.00	1,56,261.00
13	1,56,261.00	14,217.00	9,240.00	4,976.00	1,51,285.00
14	1,51,285.00	14,217.00	8,933.00	5,283.00	1,46,002.00
15	1,46,002.00	14,217.00	8,608.00	5,609.00	1,40,393.00
16	1,40,393.00	14,217.00	8,262.00	5,955.00	1,34,438.00
17	1,34,438.00	14,217.00	7,894.00	6,322.00	1,28,115.00
18	1,28,115.00	14,217.00	7,504.00	6,712.00	1,21,403.00
19	1,21,403.00	14,217.00	7,090.00	7,126.00	1,14,277.00
20	1,14,277.00	14,217.00	6,651.00	7,566.00	1,06,711.00
21	1,06,711.00	14,217.00	6,184.00	8,032.00	98,679.00
22	98,679.00	14,217.00	5,689.00	8,528.00	90,151.00
23	90,151.00	14,217.00	5,163.00	9,054.00	81,097.00
24	81,097.00	14,217.00	4,604.00	9,612.00	71,485.00
25	71,485.00	14,217.00	4,011.00	10,205.00	61,280.00
26	61,280.00	14,217.00	3,382.00	10,834.00	50,445.00
27	50,445.00	14,217.00	2,714.00	11,503.00	38,943.00
28	38,943.00	14,217.00	2,004.00	12,212.00	26,731.00
29	26,731.00	14,217.00	1,251.00	12,965.00	13,765.00
30	13,765.00	14,217.00	451.00	13,765.00	0.00
		4,26,510.00	2,28,894.00	1,97,598.00