You will put $1200 down on a car and want a 4 year loan. You could...

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.

Expert Solution

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.

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