You purchase a machine for $80,000 now, with a salvage value of $25,000 in 10 years. The machine will have O&M costs and cost of raw goods totaling $30,000 per year. The machine will produce 5,000 high-quality parts per year. If i = 9% annual rate compounded annually, what is the cost per high-quality part produced?

$8.1639 per unit

Explanation:

The computation of the cost per high-quality part produced is shown below:

= Equivalent cost on annual basis ÷ number of units produced

where,

number of units produced = 5,000 units

And, the Equivalent cost on annual basis is

= Present value ÷ PVIFA factor

It is computed below:

Year        Outflow             PVF at 9%         PVIFA at 9%          Present value

0              $80,000            1                                                      $80,000

1-10          $30,000                                     6.4177                    $192,531

10           -$25,000           0.4225                                            -$10,562.50

Present value                                                                            $261,968.50

Now the equivalent cost

= $261,968.50 ÷ 6.4177

= $40,819.69

Now the cost per high quality part produced is

=  $40,819.69 ÷ 5,000

= $8.1639 per unit

Refer to the PVF and the PVIFA table