8-39: Frequently we read in the newspaper that one should lease a car rather tha

Question

8-39: Frequently we read in the newspaper that one should lease a car rather than buying it. For a typical 24-month lease on a car costing $9400, the monthly lease charge is about $267. At the end of the 24 months, the car is returned to the lease company (which owns the car). As an alternative, the same car could be bought with no down payment and 24 equal monthly payments, with interest at a 12% nominal annual percentage rate. At the end of 24 months the car is fully paid for. The car would then be worth about half its original cost.

(a) Over what range of nominal before-tax interest rates is leasing the preferred alternative?

(b) (b) What are some of the reasons that would make leasing more desirable than is indicated?

Explanation / Answer

Lease: Pay $267 per month for 24 months.

Purchase:

      A = $9,400 (A/P, 1%, 24) = $9,400 (0.0471) = $442.74

      Salvage (resale) value = $4,700

(a) Purchase Rather than Lease

Monthly payment = $442.71 - $267       = $175.74

Salvage value     = $4,700 - $0   = $4,700

Rate of Return

                  PW of Cost = PW of Benefit

                  $175.74 (P/A, i%, 24) = $4,700

                  (P/A, i%, 24)    = $4,700/$175.74 = 26.74

                   i = 0.93% per month

Thus, the additional monthly payment of $175.74 would yield an 11.2% rate of return. Leasing is therefore preferred at all interest rates above 11.2%.

(b) Items that might make leasing more desirable:

1.   One does not have, or does not want to spend, the additional $175.74 per month.

2.   One can make more than 11.2% rate of return in other investment.

3. One does not have to be concerned about the resale value of the car at the end of two years.

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