Question

Jackson & Sons uses packing machines to prepare its products for shipping. They need to replace their primary packing machine and are considering two different options.

Machine 1 costs $404,700 and lasts 5 years before it needs replaced. The annual aftertax operating cost for the machine is $34,800.
Machine 2 costs $545,900 and should last for 7 years. It has an annual aftertax operating cost of $22,950.
What is the equivalent annual cost of each machine if the required return is 12 percent?
EAC for Machine 1 =
EAC for Machine 2 =

Answer 1

The equivalent annual cost (EAC) for Machine 1 is $519,516.60 and for Machine 2 is $635,220.40 with a required return of 12 percent.

Step-by-step explanation:

To calculate the equivalent annual cost (EAC) of each machine, we can use the formula:

EAC = Initial Cost + (Annual Aftertax Operating Cost) * (Present Worth Factor)

For Machine 1:

EAC for Machine 1 = $404,700 + ($34,800) * (Present Worth Factor)

For Machine 2:

EAC for Machine 2 = $545,900 + ($22,950) * (Present Worth Factor)

Using a required return of 12 percent, we can determine the Present Worth Factor using the following formula:

Present Worth Factor = (1 - (1 + Required Return)-n)/(Required Return)

Where n is the number of years the machine is expected to last.

Plugging in the values, we find:

EAC for Machine 1 = $404,700 + ($34,800) * (3.037)

EAC for Machine 2 = $545,900 + ($22,950) * (4.111)

Calculating the two values, we get:

EAC for Machine 1 = $519,516.60

EAC for Machine 2 = $635,220.40