ALUM Inc. uses high-tech equipment to produce specialized products. Each one of its machines costs $1,243,000 to purchase plus an additional $78,000 a year to operate. The machines have a five-year life after which they are worthless. What is the equivalent annual cost of one these machines if the required return is 16.5 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 would be required to repay the purchase price of the machine over its five-year life, plus interest on the unpaid balance. The capital recovery cost can be calculated using the following formula:```Capital recovery cost = Purchase price * (Required return / (1 - (1 + Required return)^-Life))```In this case, the purchase price of the machine is $1,243,000, the required return is 16.5%, and the life of the machine is five years. Plugging these values into the formula, we get:```Capital recovery cost = $1,243,000 * (0.165 / (1 - (1 + 0.165)^-5))``````Capital recovery cost = $1,243,000 * (0.165 / (1 - 0.567427))``````Capital recovery cost = $1,243,000 * (0.165 / 0.432573)``````Capital recovery cost = $1,243,000 * 0.381554``````Capital recovery cost = $475,999.92```The equivalent annual cost of the machine is the sum of the annual operating cost and the capital recovery cost, which is $78,000 + $475,999.92 = $553,999.92. However, the question asks for the equivalent annual cost with a negative sign, so the correct answer is -$553,999.92, which is choice A.

ALUM Inc Uses High-Tech Equipment to Produce Specialized Products