A firm can lease a truck for 5 years at a cost of $39,000 annually. It can instead buy a truck at a cost of $89,000, with annual maintenance expenses of $19,000. The truck will be sold at the end of 5 years for $29,000.

A firm can lease a truck for 5 years at a cost of $39,000 annually. It can instead buy a truck at a cost of $89,000, with annual maintenance expenses of $19,000. The truck will be sold at the end of 5 years for $29,000.



a. What is the equivalent annual cost of buying and maintaining the truck if the discount rate is 12%?


Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.
Leasing is the better option.

PV of costs
= $89,000 + [$19,000 × Annuity factor (12%, 5 years)] − [$29,000 / (1.12)⁵]
= $89,000 +  $19,000  ×  [1.12 − 1.12 ×  (1.12)5] −  $29,000(1.12)5

= $89,000 + 68,490.75 − 16,455.38
= $141,035.37

The equivalent annual cost is the payment with the same present value. Solve the following equation for C:

C × [1.12 − 1.12 ×  (1.12)5] =  $141,035.37 ⇒ C= EAC= $39,124.58


Using a financial calculator, enter n = 5; i = 12; FV = 0; PV = (−)141,035.37; compute PMT.

b.
If you can lease instead for $30,000, then leasing is the less costly option.

You can also compare the PV of the lease costs to the total PV of buying:

$39,000 × Annuity factor (12%, 5 years) =
$39,000  ×  [1.12 −  1.12  ×   (1.12)5]  =  $140,586.27


The PV of the lease costs is less than the PV of the costs when buying the truck.

Thank you!