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

Answer:

EAC Techron I = -$141,050

EAC Techron II = -$138,181

Explanation:

Techron I costs $285,000, has a three-year life, and has pretax operating costs of $78,000 per year. Salvage value $55,000, use straight line depreciation.

annuity factor = [1 - 1/(1 + r)ⁿ] / r = [1 - 1/(1 + 0.11)³] / 0.11 = 2.4437

depreciation expense per year = ($285,000 - $55,000) / 3 = $76,667

cash outflow years 1 and 2 = [($78,000 + $76,667) x (1 - 24%)] - $76,667 = ($154,667 x 0.76) - $76,667 = $40,880

cash outflow year 3 = [($78,000 + $76,667) x (1 - 24%)] - $76,667 - $55,000 = ($154,667 x 0.76) - $76,667 - $55,000 = -$14,120

NPV = -285,000 - 40,880/1.11 - 40,880/1.11² + 14,120/1.11³ = -285,000 - 36,829 - 33,179 + 10,324 = -344,684

EAC = NPV / annuity factor = -344,684 / 2.4437 = -$141,050

Techron II costs $495,000, has a five-year life, and has pretax operating costs of $45,000 per year. Salvage value $55,000, use straight line depreciation.

annuity factor = [1 - 1/(1 + r)ⁿ] / r = [1 - 1/(1 + 0.11)⁵] / 0.11 = 3.6959

depreciation expense per year = ($495,000 - $55,000) / 5 = $88,000

cash outflow years 1 through 4 = [($45,000 + $88,000) x (1 - 24%)] - $88,000 = ($133,000 x 0.76) - $88,000 = $13,080

cash outflow year 5 = [($45,000 + $88,000) x (1 - 24%)] - $88,000 - $55,000 = ($133,000 x 0.76) - $88,000 - $55,000 = -$41,920

NPV = -495,000 - 13,080/1.11 - 13,080/1.11² - 13,080/1.11³ - 13,080/1.11⁴ + 41,920/1.11⁵ = -495,000 - 11,784 - 10,616 - 9,564 - 8,616 + 24,877 = -510,703

EAC = NPV / annuity factor = -510,703 / 3.6959 = -$138,181