Question

You will put $1200 down on a car and want a 4 year loan. You could buy a new car for $15,000 (interest rate 6%) or the same model car that is 2 years old for $11,500 (interest rate 6.5%). The new car has a monthly payment of $305.31 and the used car has a monthly payment of $244.26. Explain what you would pick and why.

Answer 1

Buying a new car is a better option, which can be explained as follows:

To determine which option is better, we need to calculate the IRR of both the options. The option with lower IRR is bettwer as you will have to pay a lower cost of capital for financing the loan for car.

New Car			Old Car
At the beginning (month 0), you need to take a loan of $15,000 less $1200 down payment, i.e. loan of $13,800 and for the next 4 years, you will make monthly payments of $305.31 i.e. 48 monthly payments			At the beginning (month 0), you need to take a loan of $11,500 less $1200 down payment, i.e. loan of $10,300 and for the next 4 years, you will make monthly payments of $244.26 i.e. 48 monthly payments
Month	Net cash Flows		Month	Net cash Flows
0	13800		0	10300
1	-305.31		1	-244.26
2	-305.31		2	-244.26
3	-305.31		3	-244.26
4	-305.31		4	-244.26
5	-305.31		5	-244.26
6	-305.31		6	-244.26
7	-305.31		7	-244.26
8	-305.31		8	-244.26
9	-305.31		9	-244.26
10	-305.31		10	-244.26
11	-305.31		11	-244.26
12	-305.31		12	-244.26
13	-305.31		13	-244.26
14	-305.31		14	-244.26
15	-305.31		15	-244.26
16	-305.31		16	-244.26
17	-305.31		17	-244.26
18	-305.31		18	-244.26
19	-305.31		19	-244.26
20	-305.31		20	-244.26
21	-305.31		21	-244.26
22	-305.31		22	-244.26
23	-305.31		23	-244.26
24	-305.31		24	-244.26
25	-305.31		25	-244.26
26	-305.31		26	-244.26
27	-305.31		27	-244.26
28	-305.31		28	-244.26
29	-305.31		29	-244.26
30	-305.31		30	-244.26
31	-305.31		31	-244.26
32	-305.31		32	-244.26
33	-305.31		33	-244.26
34	-305.31		34	-244.26
35	-305.31		35	-244.26
36	-305.31		36	-244.26
37	-305.31		37	-244.26
38	-305.31		38	-244.26
39	-305.31		39	-244.26
40	-305.31		40	-244.26
41	-305.31		41	-244.26
42	-305.31		42	-244.26
43	-305.31		43	-244.26
44	-305.31		44	-244.26
45	-305.31		45	-244.26
46	-305.31		46	-244.26
47	-305.31		47	-244.26
48	-305.31		48	-244.26
Monthly IRR	0.248%		Monthly IRR	0.542%

To calculate the monthly IRR, use a financial calulator.

• For new car: CF0 = 13800 Enter, C01 = -305.31 enter, F01 = 48 Enter, Compute IRR = 0.248%
• For old car: CF0 = 10300 Enter, C01 = -244.26 enter, F01 = 48 Enter, Compute IRR = 0.542%

Calculate yearly IRR, using the formula:

Yearly IRR = [(1+monthly IRR)^12]-1

• For new car: Yearly IRR = [(1+0.00248)^12]-1 = 3.02%
• For old car: Yearly IRR = [(1+0.00542)^12]-1 = 6.70%

Thus, if you buy the new car its cost will be much lower at 3.02% per annum as compared to 6.07% per annum for buying the old car. Thus, it is better to purchase a new car.