Question

A forklift will last for only 2 more years. It costs $5,000 a year to maintain. For $20,000 you can buy a new lift that can last for 10 years and should require maintenance costs of only $2,000 a year. a-1. Calculate the equivalent cost of owning and operating the forklift if the discount rate is 4% per year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) a-2. Should you replace the forklift

Answer 1

The equivalent cost of owning and operating the forklift is $4,465.82

We should replace the forklift.

Step-by-step explanation:

The Equivalent annual cost can be calculated using the following formula

Equivalent annual cost = PV of cost / Annuity factor

Old forklift

PV of Cost = Annual cost x 2 years Annuity factor at 4% / 2 years Annuity factor at 4%

Hence

PV of cost = Annual cost = $5,000

New forklift

10 years Annuity factor at 4% = 1 - ( 1 + 4%)^-10 )/4% = 8.11090

PV of cost = ( Annual Cost x 10 years Annuity factor at 4% ) + Initial cost

PV of cost = ( $2,000 x 8.11090 ) + $20,000

PV of cost = 16,221.79 + $20,000

PV of cost = 36,221.79

Placing values in the formula

Equivalent annual cost = $36,221.79 / 8.11090

Equivalent annual cost = $4,465.82

As the equivalent annual cost of the new lift is lower than the the old one, we should replace the forklift