A firm can lease a truck for 5 years at a cost of $49,000 annually. It can instead buy a truck at a cost of $99,000, with annual maintenance expenses of $29,000. The truck will be sold at the end of 5 years for $39,000. a. What is the equivalent annual cost of buying and maintaining the truck if the discount rate is 12%

Leasing or Buying a Truck:

The equivalent annual cost of buying and maintaining the truck (if the discount rate is 12%) is:

= $50,328

Explanation:

a) Data and Calculations:

Interest rate = 6% per year

                            Lease             Purchase

Initial Cost                                   $99,000

Annual Cost      $49,000           $29,000

Salvage Value                             $39,000

Useful Life (years)        5                        5

Annuity factor = 3.605 for 5 years at 12%.

Present value factor = 0.567 for 5 years at 12%.

                                      Lease          Purchase

Present value of  costs:

Initial cost                                          $99,000 (1 * $99,000)

Annuity costs             $176,645        104,545 (3.605 * $29,000)    

PV of salvage value                            (22,113) (0.567 * $39,000)

NPV cost                    $176,645       $181,432

The equivalent annual cost:

= Total NPV cost/PV annuity factor

                             ($176,645/3.605)   ($181,432/3.605)

Equivalent annual cost $49,000      $50,328

Difference:

Purchase =  $50,328

Lease =       $49,000

Difference =  $1,328

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