Question

Congratulations - it's time for a new car, to be used for business use, of course. You only need it for 3 years before you'll want to start looking for something else, and you've got three options, described below. In options A and B, the car may be sold at the end of 3 years for $7500. Given a 12% interest rate, compounded MONTHLY (so think about how many periods you have, too), compute the EUAC for option A:

Option A: Buy it: Just buy the car with cash - $26,000.

Option B: Lease-to-own: Lease the car at a monthly charge of $720 per month, payable at the end of each month, for 36 months. You can buy the car at the end of the lease period for a cost of $7000. <Remember, you can sell the car for $7500 in this and the previous option>

Option C: Lease-and-return: Lease the car for $700 per month, payable at the end of each month, with no money down. At the end of the lease, the car is returned to the leasing company.

Answer 1

Monthly (nominal) interest rate = 12%/12 = 1%

Number of months = 3 x 12 = 36

Option A

EUAC ($) = 26,000 x A/P(1%, 36) - 7,500 x P/F(1%, 36) x A/P(1%, 36)

= 26,000 x 0.0332 - 7,500 x 0.6989 x 0.0332

= 863 - 174

= 689

Option B

If I buy the car after 36 months, Net opportunity cost = Potential sale value - Potential buying price

= $7,500 - $7,000 = $500

EUAC ($) = 720 + 500 x P/F(1%, 36) x A/P(1%, 36)

= 720 + 500 x 0.6989 x 0.0332

= 720 + 12

= 732

Option C

EUAC ($) = 700

Since Option A has lowest UEAC, this is the preferred option.