Mariposa Inc is considering improving its production process by acquiring a new machine. There are two machines management is analyzing to determine which one it should purchase. The company requires a 14% rate of return and uses straight-line depreciation to a zero book value. Machine A has a cost of $290,000, annual operating costs of $8,000, and a 3-year life. Machine B costs $180,000, has annual operating costs of $12,000, and has a 2-year life. Whichever machine is purchased will be replaced at the end of its useful life. Which machine should Mariposa purchase and why?

Machine B should be purchased because it has a lower equivalent annual cost

Explanation:

To determine the better of the two options, we would compare the equivalent annual cost of each options using a discount rate of 14% per annum

Equivalent annual cost = Total PV of cost / Annuity factor

Total PV of cost = Initial cost + PV of annual operating cost

PV of annual operating cost = Annual operating cost * Annuity factor

Annuity factor = (1 - (1+r) ^ (-n)) / r

r - rate, n - years

Machine A

PV of annual operating cost = 8,000 * (1 - 1.14^ (-3) / 0.14 = 18573.05622

PV of total cost = 290,000 + 18573.05622 = 308,573.06

Uniform Annual cost = 308,573.06 / 2.321632027 = 132,912.13

Equivalent annual cost = $132,912.13

Machine B

PV of annual operating cost = 12,000 * (1 - 1.14^ (-2) / 0.14 = 19759.92613

PV of total cost = 180,000 + 19759.92613 = 199,759.93

Equivalent annual cost = 199,759.93 / 1.6466=$121,312.15

Equivalent annual cost = $121,312.15

Machine B should be purchased because it has a lower equivalent annual cost

Total PV of cost