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

Solution:

Outsourcing:

Annual overhauling cost for outsourcing for one machine= $35,000

Present value of overhauling cost for 15 years for one machine = $35,000 * cumulative PV factor at 10% for 15 years

= $35,000 * 7.60608 = $266,213

Annual equivalant overhauling cost of machine for outsourcing option = $266,213/15 = $17,748.53

In house maintenance:

Cost of building maintenance facility = $589,000

Annual overhauling cost for In house for one machine= $21,000

Present value of annual overhauling cost for 15 years for one machine = $21,000 * cumulative PV factor at 10% for 15 years

= $21,000 * 7.60608 = $159,728

PV of capital cost of manitenance facility = $589,000 - ($52,000*0.239392) = $576552

Let X is the number of machine that company X must operate to make exonomically feasible to build its own facility

Annual equivalant overhauling cost of machine for In house option = ($576,552/15X) + ($159728/15)

At minimum number of machine annual equivalant cost under both option will be same.

($576,552/15X) + ($159728/15) = $17,748.53

$38436.80/X + $10,648.53 = $17,748.53

$38,436.80 / X = $7,100

X = 5.41, hence X = 6

Therefore company X must operated 6 machines to make economically feasible to build its own facility.