Question

Precision Plumbus is analyzing two machines to determine which one it should purchase. The company requires a 15 percent rate of return and uses straight-line depreciation to a zero book value over the life of its equipment. Machine A has a cost of $905,000, annual operating costs of $27,000, and a 4-year life. Machine B costs $1,025,000, has annual operating costs of $20,000, and has a 5-year life. Whichever machine is purchased will be replaced at the end of its useful life. Which machine should be purchased?

Answer 1

As the tax rate is not given, assume the tax rate is 0%

For Machine A;

Depreciation = Cost of the System / Useful life years = $905,000 / 4 = $226,250

OCF = [-Costs * (1 - t)] + [Depreciation * t]

= [-$27,000 * (1 - 0)] + [$226,250 * 0] = -$27,000 + $0 = -$27,000

NPV = PV of Cash Inflows - PV of Cash Outflows

PV of Cash Outflows = Annual OCF * [{1 - (1 + r)-n} / r] + Cost

= $27,000 * [{1 - (1 + 0.15)^-4} / 0.15] + $905,000

= $27,000 * [0.4282 / 0.15] + $905,000

= [$27,000 * 2.8550] + $905,000 = $77,084.42 + $905,000 = $982,084.42

NPV = $0 - $982,084.42 = -$982,084.42

EAC = NPV / [{1 - (1 + r)^-n} / r]

= -$982,084.42 / [{1 - (1 + 0.15)^-4} / 0.15]

= -$982,084.42 / [0.4282 / 0.15] = -$982,084.42 / 2.8550 = -$343,990.14

For Machine B;

Depreciation = Cost of the System / Useful life years = $1,025,000 / 5 = $205,000

OCF = [-Costs * (1 - t)] + [Depreciation * t]

= [-$20,000 * (1 - 0)] + [$205,000 * 0] = -$20,000 + $0 = -$20,000

NPV = PV of Cash Inflows - PV of Cash Outflows

PV of Cash Outflows = Annual OCF * [{1 - (1 + r)-n} / r] + Cost

= $20,000 * [{1 - (1 + 0.15)^-5} / 0.15] + $1,025,000

= $20,000 * [0.5028 / 0.15] + $1,025,000

= [$20,000 * 3.3522] + $1,025,000 = $67,043.10 + $1,025,000 = $1,092,043.10

NPV = $0 - $1,092,043.10 = -$1,092,043.10

EAC = NPV / [{1 - (1 + r)^-n} / r]

= -$1,092,043.10 / [{1 - (1 + 0.15)^-5} / 0.15]

= -$1,092,043.10 / [0.5028 / 0.15] = -$1,092,043.10 / 3.3522 = -$325,773.44

If the machine will be continually replaced, we should choose Machine B since it has the more positive EAC.