Final answer:
The analysis shows that Pharoah Company should keep the old machine instead of purchasing the new one due to its lower total cost over the remaining useful life.
Step-by-step explanation:
To determine whether Pharoah Company should keep the old machine or invest in a new one, we need to compare the costs and benefits of each option. The old machine has a book value of $87,800 and can be sold for $32,000. The new machine costs $455,100 and has a 5-year useful life with no salvage value. The new machine would reduce the annual variable manufacturing costs from $624,400 to $524,400.
To calculate the cost of each option, we'll consider the remaining useful life of the old machine and the annual cost savings from using the new machine.
The total cost of the old machine over its remaining 5-year life would be the book value minus the salvage value, divided by the remaining years:
Total cost of old machine = ($87,800 - $32,000) / 5 = $11,760 per year
The total cost of the new machine would be the upfront cost plus the annual cost savings:
Total cost of new machine = $455,100 + ($624,400 - $524,400) = $555,100
Comparing the total costs, it is more cost-effective for Pharoah Company to keep the old machine at a total cost of $11,760 per year, rather than investing in the new machine at a total cost of $555,100.