Question

12. Buy on time or pay cash? You are going to make a substantial purchase. You have enough money to pay cash, but don’t know if that’s the way to make best use of your assets. Maybe you should take out an installment loan to make the purchase and invest the cash you would otherwise have used to pay for it. Use the information provided to complete the following worksheet and analyze how the numbers work out most favorably for you. For simplicity, compounding is ignored in calculating both the cost of interest and interest earnings. [Note: Enter your dollar answers rounded to the nearest two cents and precede numbers that are less than zero (0) with a minus sign (–).] Buy On Time or Pay Cash Cost of Borrowing 1. Terms of the loan a. Amount of the loan $15,000 b. Length of the loan (in years) 5 c. Monthly payment $289.95 2. Total loan payments made ($ per month months) $ 3. Less: Principal amount of the loan $ 4. Total interest paid over life of loan $ 5. Tax considerations: – Is this a home equity loan? yes – Do you itemize deductions on your federal tax return? yes 6. What federal tax bracket are you in? 10% 7. Taxes saved due to interest deductions ($ x %) $ 8. Total after-tax interest cost on the loan $ Cost of Paying Cash 9. Annual interest earned on savings (5% x ) $ 10. Annual after-tax interest earnings ($ x %) $ 11. Total after-tax interest earnings over life of loan ($ x years) $ Net Cost of Borrowing 12. Difference in cost of borrowing versus cost of paying cash $ Based on the numbers alone, you should      because: The interest on a loan will cost you more than the interest you would earn if you invested the principal. If you invest the principal, you’ll earn more interest than you’ll pay on the loan.

Answer 1

First we will calculate the cost of borrowing

Amount of loan = 15000, Length of loan = 5 years = 5 x 12 months = 60 months, Monthly payment = 289.95

Total loan payment made = Length of loan in months x monthly payment = 60 x 289.95 = 17397.00

Total interest paid over life the loan = Total loan payment made - Principal amount of Loan = 17397 - 15000 = 2397.00

Federal tax rate = 10%

Taxes saved due to interest deductions = Total interest paid paid over life of loan x federal tax rate = 2397 x 10% = 239.70

Total after tax interest cost of loan = Total interest paid over life the loan - Taxes saved due to interest deductions = 2397 - 239.70 = 2157.30

Cost of Paying Cash

Rate of interest = 5%

Annual interest earned on savings = Loan x Rate of interest = 15000 x 5% = 750.00

Annual after tax interest earnings = Annual interest earned on savings x (1- tax rate) = 750 x (1-10%) = 750 x 90% = 675.00

Total after tax interest earning over the life of loan = 675 x 5 = 3375

Net cost of borrowing = Cost of borrowing - Cost pf paying cash = 2157.30 - 3375 = -1217.70

We get the following table

Buy On Time or Pay Cash
Cost of Borrowing
1	Terms of the loan
	a. Amount of the loan	$15,000
	b. Length of the loan (in years)	5
	c. Monthly payment	$289.95
2	Total loan payments made
	($ per month months)	17397.00	$
3	Less: Principal amount of the loan	15000.00	$
4	Total interest paid over life of loan	2397.00	$
5	Tax considerations:
	– Is this a home equity loan?	yes
	– Do you itemize deductions on your federal tax return?	yes
6	What federal tax bracket are you in?	10%
7	Taxes saved due to interest deductions
	($ x %)	239.70	$
8	Total after-tax interest cost on the loan	2157.30	$
Cost of Paying Cash
9	Annual interest earned on savings
	(5% x )	750.00	$
10	Annual after-tax interest earnings
	($ x %)	675.00	$
11	Total after-tax interest earnings over life of loan
	($ x years)	3375.00	$
Net Cost of Borrowing
12	Difference in cost of borrowing versus cost of paying cash	-1217.70	$

Based on the numbers alone, you should take out an installment loan because if you invest the principal you'll earn more interest than you'll pay the loan.