Question

Letang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $360,000, has a four-year life, and requires $149,000 in pretax annual operating costs. System B costs $440,000, has a six-year life, and requires $143,000 in pretax annual operating costs. Suppose the company always needs a conveyor belt system; when one wears out, it must be replaced. Assume the tax rate is 24 percent and the discount rate is 10 percent. Calculate the EAC for both conveyor belt systems. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) System A System B Which conveyor belt system should the firm choose? System A System B

Answer 1

a). For System A;

Depreciation = Cost of the System / Useful life years = $360,000 / 4 = $90,000

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

= [-$149,000 * (1 - 0.24)] + [$90,000 * 0.24] = -$113,240 + $21,600 = -$91,640

NPV = PV of Cash Inflows - PV of Cash Outflows

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

= $91,640 * [{1 - (1 + 0.10)^-4} / 0.10] + $360,000

= $91,640 * [0.3170 / 0.10] + $360,000

= [$91,640 * 3.1699] + $360,000 = $290,486.47 + $360,000 = $650,486.47

NPV = $0 - $650,486.47 = -$650,486.47

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

= -$650,486.47 / [{1 - (1 + 0.10)^-4} / 0.10]

= -$650,486.47 / [0.3170 / 0.10] = -$650,486.47 / 3.1699 = -$205,209.49

For System B;

Depreciation = Cost of the System / Useful life years = $440,000 / 6 = $73,333.33

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

= [-$143,000 * (1 - 0.24)] + [$73,333.33 * 0.24] = -$108,680 + $17,600 = -$91,080

NPV = PV of Cash Inflows - PV of Cash Outflows

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

= $91,080 * [{1 - (1 + 0.10)^-6} / 0.10] + $440,000

= $91,080 * [0.4355 / 0.10] + $440,000

= [$91,080 * 4.3553] + $440,000 = $396,677.14 + $440,000 = $836,677.14

NPV = $0 - $836,677.14 = -$836,677.14

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

= -$836,677.14 / [{1 - (1 + 0.10)^-6} / 0.10]

= -$836,677.14 / [0.4355 / 0.10] = -$836,677.14 / 4.3553 = -$192,107.25

b). If the conveyor belt system will be continually replaced, we should choose System B since it has the more positive EAC.