A forklift will last for only 2 more years. It costs $5,100 a year to maintain. For $21,000 you can buy a new lift that can last for 10 years and should require maintenance costs of only $2,100 a year.

A forklift will last for only 2 more years. It costs $5,100 a year to maintain. For $21,000 you can buy a new lift that can last for 10 years and should require maintenance costs of only $2,100 a year.



a-1.  Calculate the equivalent cost of owning and operating the forklift if the discount rate is 5% per year.



Explanation

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

a.
The equivalent annual cost (EAC) of the new machine over its 10-year life is found by solving as follows:

C ×  [1.05 −  1.05 ×  (1.05)10]  =  $21,000


C × Annuity factor (5%, 10 years) = $21,000
C × 7.72173 = $21,000 ⇒
C = EAC = $2,719.60

Together with maintenance costs of $2,100 per year, the equivalent cost of owning and operating is $4,819.60.

The old machine costs $5,100 per year to operate and is already paid for. (We assume it has no scrap value and therefore no opportunity cost.) The new machine is less costly. You should replace.

b.
If r = 10%, then the equivalent annual cost (EAC) is computed as follows:

C × [1.10 − 1.10 ×  (1.10)10] =  $21,000


C × Annuity factor (10%, 10 years) = $21,000
C × 6.14457 = $21,000 ⇒
C = EAC = $3,417.65

The equivalent cost of owning and operating the new machine is now $5,517.65. This is higher than that of the old machine. Do not replace.