Question

Bart Simpson is trying to decide whether or not he should lease or buy a new viper. The viper can be leased for $10,000 per year (first payment made right now) for 10 years or he can buy the car outright for a cost of $65,000. Bart has located a bank that will lend him the $65000 at a cost of 15.75%. Bart will drive the car for 10 years and will abuse viper to the point that it will have no resale value. Bart also lives in a world of no uncertainty and pays no taxes.

What is Bart's present value of the lease payments?

A. $65,000 B. $48,786 C. $56,469 D. $63,282 E. None of the above

Barts implied interest rate in the lease payment is?

A. 10% B. 12.71% C. 8.71% D. 11.17% E. None of the above

Answer 1

A) Since the payments are beginning at each year, we need to multiply the lease payments with the present value interest factor annuity (PVIFA) of 9 years (since after today their will be 9 more payments) plus present value interest factor of today (which is always 1).

PV of lease payments = $10000 x [1 + PVIFA (15.75%, 9)] = $10000 x [1 + 4.646929] = $56,469 (option C)

B) To compute the Implied interest rate we equate the present value of lease payments with the cost of the viper. Let interest rate be r.

$65000 = $10000 [1 + PVIFA (r, 9)]

or, $65000 = $10000 + $10000 x PVIFA (r, 9)

or, PVIFA (r, 9) = 5.5

We refer this value in the PVIFA table in the 9th year, and get -

At 11% - 5.5370

At 12% - 5.3282

Our value lies between 11% to 12% (it lies close to 11%). We need to interpolate -

Difference required (from 11%) = 5.5370 - 5.5 = 0.0370

Total difference (between 11% and 12%) = 5.5370 - 5.3282 = 0.2088

Implied rate = Lower rate + Difference in rates x (Difference required / Total difference)

or, Implied rate = 11% + 1% x (0.0370 / 0.2088) = 11.17% (option D)