Question

Suppose you can buy a new car for $15,000 and sell it for $6,000 after six years. Or, you can lease the car to $300 per month for three years and return it at the end of the three years. Assume that lease payments are made yearly instead of monthly (i.e., are $3,600 per year for each of the three years).

a.) If the interest rate, r, is 4 percent, should you lease or buy?

b.) What if the interest rate is 12 percent?

c.) At what interest rate would you be indifferent between buying and leasing the car?

Answer 1

a) Following excel may be obtained:

time, t	Discount factor @4%	Cashflows if car is bought	Present Value	Cashflows if leased	Present Value
0	1	-15000	-15000
1	1.04			-3600	-3461.54
2	1.0816			-3600	-3328.4
3	1.124864			-3600	-3200.39
4	1.16985856
5	1.216652902
6	1.265319018	6000	4741.887
Total Cost			-10258.1		-9990.33

Clearly, price of car comes out to be lower if leased, we should lease it.

b) Following excel is obtained at 12% interest rate

time, t	Discount factor @12%	Cashflows if car is bought	Present Value	Cashflows if leased	Present Value
0	1	-15000	-15000
1	1.12			-3600	-3214.29
2	1.2544			-3600	-2869.9
3	1.404928			-3600	-2562.41
4	1.57351936
5	1.762341683
6	1.973822685	6000	3039.787
Total Cost			-11960.2		-8646.59

Here too, price is lower if car is leased.

c) For indifference, price of buying = price of leasing

Hence, 15000 - 6000 / (1+r)⁶ = 3600 / (1+r) + 3600 / (1+r)² + 3600 / (1+r)³

We solve for r by hit and trial method, to get

r = 4.31%