Question

You are evaluating two different silicon wafer milling machines. The Techron I costs $285,000, has a three-year life, and has pretax operating costs of $78,000 per year. The Techron II costs $495,000, has a five-year life, and has pretax operating costs of $45,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $55,000. If your tax rate is 24 percent and your discount rate is 11 percent, compute the EAC for both machines.

Answer 1

Techron I

Initial cost, C₀ = $ 285,000

Pre tax operating costs = $ 78,000

Annual depreciation = Initial cost / useful life = 285,000 / 3 = $  95,000

Tax rate, T = 24%

Post tax operating cash flows, C = - (Pre tax operating costs + Depreciation) x (1 - T) + Depreciation = - (78,000 + 95,000) x (1 - 24%) + 95,000 =  - 36,480

Post tax salvage value, S = Pre tax salvage value - tax on gain on sale = 55,000 - (55,000 - 0) x T = 55,000 - 55,000 x 24% =  41,800

Discount rate = R = 11%

NPV = -C₀ + Sum of PV of C over N = 3 years + PV of S = -C₀ + C / R x [1 - (1+R)^-N] + S x (1 + R)^-N = - 285,000 -36,480 / 0.11 x [1 - (1 + 0.11)^-3] + 41,800 x (1 + 0.11)^-3 = - $ 343,582.91

Let it's EAC be called EAC_I, then PV of EAC_I over three years should be equal to the NPV calculated above.

Hence, EAC_I x Sum of PV factors (over t = 1 to t = 3) = NPV

Sum of PV factors (over t = 1 to t = 3) = 1 / R x [1 - (1+R)^-N] = 1 / 0.11 x [1 - (1 + 0.11)^-3] = 2.443714715

Hence, EAC_I x 2.443714715 = - $ 343,582.91

Hence, EAC_I = - $ 343,582.91 / 2.443714715 = - $140,598.62

Please note the negative sign signifies cost. As long as you understand it, you can remove the negative sign from the final answer.

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Techron II

Initial cost, C₀ = $ 495,000

Pre tax operating costs = $ 45,000

Annual depreciation = Initial cost / useful life = 495,000 / 5 = $  99,000

Tax rate, T = 24%

Post tax operating cash flows, C = - (Pre tax operating costs + Depreciation) x (1 - T) + Depreciation = - (45,000 + 99,000) x (1 - 24%) + 99,000 =  - 10,440

Post tax salvage value, S = Pre tax salvage value - tax on gain on sale = 55,000 - (55,000 - 0) x T = 55,000 - 55,000 x 24% =  41,800

Discount rate = R = 11%

NPV = -C₀ + Sum of PV of C over N = 5 years + PV of S = -C₀ + C / R x [1 - (1+R)^-N] + S x (1 + R)^-N = - 495,000 - 10,440 / 0.11 x [1 - (1 + 0.11)^-5] + 41,800 x (1 + 0.11)^-5 = - $ 508,778.90

Let it's EAC be called EAC_II, then PV of EAC_I over three years should be equal to the NPV calculated above.

Hence, EAC_II x Sum of PV factors (over t = 1 to t = 5) = NPV

Sum of PV factors (over t = 1 to t = 5) = 1 / R x [1 - (1+R)^-N] = 1 / 0.11 x [1 - (1 + 0.11)^-5] = 3.695897018

Hence, EAC_II x 3.695897018 = - $ 508,778.90

Hence, EAC_II = - $ 508,778.90 / 3.695897018 = - $ 137,660.46

Please note the negative sign signifies cost. As long as you understand it, you can remove the negative sign from the final answer.

If the next part of your question is (even though you have not stated it) which machine should we choose, the answer is:

Since EAC_II is lower in magnitude than EAC_I, hence we will prefer Techron II.