Question

A company is considering two methods for obtaining a certain part. Method A will involve purchasing a machine for $65,000 with a life of 5 years, a $1,600 salvage value, and a fixed annual operating cost of $13,500. Additionally, each part produced by the method will cost $14. Method B will involve purchasing the part from a subcontractor for $19 per part. At an interest rate of 10% per year, determine the number of parts per year required for the two methods to break even. (Enter your answer as a number without the dollar $ sign.)

Answer 1

Interest rate = 10% per year

Method A:

Initial cost = -$65,000

Salvage Value = $1,600

Annual operating cost = -$13,500

Cost of each part = -$14

Life of the machine = 5 years

From the compound interest factor table, we obtain

(A/P, 10%, 5) = 0.2638

(A/F, 10%, 5) = 0.1638

Let us assume that the breakeven parts per year be 'q'

Annual worth of method A = AW of the initial cost + AW of the salvage value + Annual operating costs + Cost of producing 'q' parts

= -$65,000*(A/P, 10%, 5) + $1,600*(A/F, 10%, 5) - $13,500 - $14q

= -$65,000*0.2638 + $1,600*0.1638 -$13,500 - 14q

= -$30,384.92 - 14q

Annual worth of method B = Cost of subcontracting 'q' parts = -$19 * q = -19q

At the breakeven point, the annual worth of both the methods must be equal

i.e., -30,384.92 - 14q = -19q

=> 5q = 30384.92

=> q = 6077 (Rounded off to the nearest whole number)

Ans: Breakeven quantity = 6077 parts per year