Automated Manufacturers uses high-tech equipment to produce specialized aluminum products for its customers.Each one of these machines costs $1,480,000 to purchase plus an additional $52,000 a year to operate.The machines have a 6-year life after which they are worthless.What is the equivalent annual cost of one these machines if the required return is 16 percent?
A)-$453,657
B)-$427,109
C)-$301,586
D)-$295,667
E)-$256,947

Question

Quizplus · Accepted Answer

The equivalent annual cost of the machine is the sum of the annual operating cost and the capital recovery cost. The capital recovery cost is the annual payment that will repay the purchase cost of the machine over its 6-year life, plus interest on the unpaid balance. The capital recovery cost can be calculated using the following formula:```Capital recovery cost = Purchase cost * (interest rate / (1 - (1 + interest rate)^-life))```In this case, the purchase cost is $1,480,000, the interest rate is 16%, and the life is 6 years. Plugging these values into the formula, we get:```Capital recovery cost = $1,480,000 * (0.16 / (1 - (1 + 0.16)^-6))= $1,480,000 * (0.16 / (1 - 0.5645))= $1,480,000 * (0.16 / 0.4355)= $1,480,000 * 0.3675= $543,657```The equivalent annual cost of the machine is therefore $543,657 + $52,000 = $595,657.

Automated Manufacturers Uses High-Tech Equipment to Produce Specialized Aluminum Products