Question

You are considering buying a new​ car, because you think it will save you money. Your think your old car will cost​ $2,200 in gas and maintenance next year​ (Year 1), and you expect that to increase by​ 6% every year until the end of Year 10. A new car will cost you​ $16,500 now​ (Year 0). You think it will cost​ $500 in gas and maintenance next year​ (Year 1), and you expect that to increase by​ 4% every year until the end of Year 10. You need to decide if the new car is worth the investment. Assume an annual interest rate of​ 5% a. What is the equivalent present value of the maintenance costs of the old​ car? b. What is the equivalent present value of the maintenance costs of the new​ car? c. Is the new car worth the​ investment?

Answer 1

a.

Old Car
Year	Maintenance Cost	Present Value Factor @5%	Present value
0	$             -	1	$                  -
1	$ 2,200.00	0.9524	$      2,095.24
2	$ 2,332.00 (2200*106%)	0.9070	$      2,115.19
3	$ 2,471.92 (2332*106%)	0.8638	$      2,135.34
4	$ 2,620.24 (2471.91*106%)	0.8227	$      2,155.67
5	$ 2,777.45	0.7835	$      2,176.20
6	$ 2,944.10	0.7462	$      2,196.93
7	$ 3,120.74	0.7107	$      2,217.85
8	$ 3,307.99	0.6768	$      2,238.98
9	$ 3,506.47	0.6446	$      2,260.30
10	$ 3,716.85	0.6139	$      2,281.83
	Present Value		$   21,873.53

b.

New Car
Year	Maintenance Cost	Present Value Factor @5%	Present value
0	16500	1	$ 16,500.00
1	$        500.00	0.9524	$       476.19
2	$        520.00 (500*104%)	0.9070	$       471.66
3	$        540.80 (520*104%)	0.8638	$       467.16
4	$        562.43 (540.80*104%)	0.8227	$       462.71
5	$        584.93	0.7835	$       458.31
6	$        608.33	0.7462	$       453.94
7	$        632.66	0.7107	$       449.62
8	$        657.97	0.6768	$       445.34
9	$        684.28	0.6446	$       441.10
10	$        711.66	0.6139	$       436.89
	Present Value		$ 21,062.92

c.

Yes, the new car is worth the investment

Since Present value of maintenance cost of the New car is lower than maintenance cost of old car, the new car is worth the investment