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 $49,000 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?

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 price 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 price * (interest rate / (1 - (1 + interest rate)^-number of years))```In this case, the purchase price is $1,480,000, the interest rate is 16%, and the number of years is 6. 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= $543,600```The equivalent annual cost of the machine is therefore:```Equivalent annual cost = Annual operating cost + Capital recovery cost= $49,000 + $543,600= $592,600```The closest answer choice to this value is A) -$450,657.

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