The Ecology Group wishes to purchase a piece of equipment for recycling of various metals. Ma­chine 1 costs $123,000, has a life of 10 years, an annual cost of $5000, and requires one operator at a cost of $24 per hour. It can process 10 tons per hour. Machine 2 costs $70,000, has a life of 6 years, an annual cost of $2500, and requires two operators at a cost of $24 per hour each to process 6 tons per hour. Assume i = 7% per year and 2080 hours per work year. Determine the annual break­even tonnage of scrap metal at i = 7% per year and select the better machine for a processing level of 1500 tons per year.

Question

What will be an ideal response?

Answer 1

Let T = number of tons/year. Solve relation AW1 = AW2 for T

Variable costs (VC) for each machine:
VC1: 24T/10 = 2.4T VC2: 2(24)T/6 = 8T

-123,000(A/P,7%,10) – 5000 – 2.4T = -70,000(A/P,7%,6) – 2500 – 8T
(8-2.4)T = -70,000(0.20980) – 2500
+ 123,000(0.14238) + 5000
5.6T = 5327
T = 951 tons/year

If tonnage is less than breakeven, select machine 2 since the slope is steeper. At 1500 tons, select machine 1.