Question

You are evaluating two different silicon wafer milling machines. The Techron I costs $294,000, has a 3-year life, and has pretax operating costs of $81,000 per year. The Techron II costs $510,000, has a 5-year life, and has pretax operating costs of $48,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $58,000. If your tax rate is 22 percent and your discount rate is 10 percent, compute the EAC for both machines.

Answer 1

Calculating EAC for Techron I

Initial cost = $294000, Useful life = 3 years. Since Machine is depreciated to zero,hence Book value after 3 year = 0

Per year Depreciation = (Initial cost - Book value after 3 year) / Useful life = (294000 - 0) / 3 = 294000 / 3 = 98000

Cash flow in year 0 = - Initial cost = -294000

Cash flow in year 1 = Cash flow in year 2 = After tax operating cash flow = [Revenue - Operating costs - Depreciation][1-tax rate] + depreciation = [ 0 - 81000 - 98000]]1-22%] + 98000 = -179000 x 78% + 98000 = -139620 + 98000 = -41620

Terminal cash flow in year 3 = Salvage value - tax rate(salvage value - Book value after 3 years) = 58000 - 22%(58000 - 0) = 45240

Cash flow in year 3 = After tax operating cash flow + Terminal cash flow = -41620 + 45240 = 3620

Net Present value of Techron I = Cash flow in year 0 + Sum of present value of cash flow for year 1 to year 3 = -294000 - 41620 / (1+10%)¹ - 41620 / (1+10%)² + 3620 / (1+10%)³ = -294000 - 37836.3636 - 34396.6942 + 2719.7595 = -363513.2983

Now will calculate equivalent annual cash flow using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get equivalent annual cash flow = -146174.0785

EAC of Techron 1 = Equivalent annual cost =146174.0785 = 146174.08 (rounded to two decimal places)

Calculating EAC for Techron II

Initial cost = $510000, Useful life = 5 years. Since Machine is depreciated to zero,hence Book value after 3 year = 0

Per year Depreciation = (Initial cost - Book value after 3 year) / Useful life = (510000 - 0) / 5 = 510000 / 5 = 102000

Cash flow in year 0 = - Initial cost = -510000

Cash flow in year 1 = Cash flow in year 2 = Cash flow in year 3 = Cash flow in year 4 = After tax operating cash flow = [Revenue - Operating costs - Depreciation][1-tax rate] + depreciation = [ 0 - 48000 - 102000]]1-22%] + 102000 = -150000 x 78% + 102000 = -117000 + 102000 = -15000

Terminal cash flow in year 5 = Salvage value - tax rate(salvage value - Book value after 5 years) = 58000 - 22%(58000 - 0) = 45240

Cash flow in year 5 = After tax operating cash flow + Terminal cash flow = -15000 + 45240 = $30240

Net Present value of Techron II = Cash flow in year 0 + Sum of present value of cash flow for year 1 to year 5 = -510000 - 15000 / (1+10%)¹ - 15000 / (1+10%)² -15000 / (1+10%)³ -15000 / (1+10%)⁴ + 30240 / (1+10%)⁵ = -510000 - 13636.3636 -12396.6942 - 11269.7220 - 10245.2018 + 18776.6608 = -538771.3208

Now will calculate equivalent annual cash flow using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get Equivalent annual cash flow = -142126.5171

EAC of Techron II = Equivalent annual cost =142126.5171 = 142126.52 (rounded to two decimal places)