Question

The manager of a canned food processing plant must decide between two different labeling machines. Machine A will have a first cost of $42,000, an annual operating cost of $28,000, and a service life of 4 years. Machine B will cost $51,000 to buy and will have an annual operating cost of $17,000 during its 4-year life. At an interest rate of 10% per year, which should be selected on the basis of a annual worth analysis?

Answer 1

Rate of Interest (r) = 10%

Machine A:

First cost = $42,000

Annual operating cost = $28,000

Service life (n) = 4 years

Annual worth = -42,000 * (A/P, 10%, 4) - 28,000

Capital recovery factor (A/P, 10%, 4) = [r * (1 + r))^ⁿ] / [(1 + r)^ⁿ - 1] = [0.1 * (1 + 0.1))^⁴] / [(1 + 0.1)^⁴ - 1] = 0.3154

Annual worth = -42,000 * 0.3154 - 28,000 = -41,249.77

Machine B:

First cost = $51,000

Annual operating cost = $17,000

Service life (n) = 4 years

Annual worth = -51,000 * (A/P, 10%, 4) - 17,000

Capital recovery factor (A/P, 10%, 4) = [r * (1 + r))^ⁿ] / [(1 + r)^ⁿ - 1] = [0.1 * (1 + 0.1))^⁴] / [(1 + 0.1)^⁴ - 1] = 0.3154

Annual worth = -51,000 * 0.3154 - 17,000 = -33,089.01

As annual worth of machine B is more than machine A, it should be selected.