Question

"Company X has been contracting its overhauling work to Company Y for $35,000 per machine per year. Company X estimates that by building a $589,000 maintenance facility with a life of 15 years and a salvage value of $52,000 at the end of its life, it could handle its own overhauling at a cost of only $21,000 per machine per year. What is the minimum annual number of machines (as an integer) that Company X must operate to make it economically feasible to build its own facility? (Assume an interest rate of 10%.) Hint: calculate the annual equivalent cost of the maintenance facility."

Answer 1

The cost of contracting is $35,000 per machine per year. Initial cost of facility is $589,000, a total life of 15 years will result in a salvage value of $52,000. Then the company can use its overhauling at a cost of only $21,000 per machine per year. Assume an interest rate of 10%. Find the annual equivalent cost of ‘X’ machine in both cases, subcontracting as well as using its own facility

AEC of subcontracting = $35000X

AEC of using own facility =589000(A/P, 10%, 15) + 21000X – 52000(A/F, 10%, 15)

= 589000*0.131474 + 21000X – 52000*0.031474

= 75801.54 + 21000X

The minimum number of X is

35000X = 75801.54 + 21000X

X* = 5.41 or approximately 6 machines per year.