Question

You are evaluating two different silicon wafer milling machines. The Techron 1 costs $550,000, has a three-year life, and has pretax operating costs of $85,000 per year. The Techron II milling costs 650,000, has a five-year life, and has pretax operating costs of $97,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $75,000. If your tax rate is 30 percent and your discount rate is 15 percent, compute the EAC for both machines. Which do you prefer? Why?

Answer 1

EAC = (NPV * r) / (1 - (1 + r)^-n)

where NPV = net present value

r = discount rate

n = life of machine

NPV = sum of present values of cash flows

present value of each cash flow = cash flow / (1 + r)^t, where t = number of years after which the cash flow occurs.

For each machine, the cash flows are calculated as below :

• cash outflow in year 0 = cost of machine
• cash outflow in subsequent years (except final year) = (pretax operating cost * (1 - tax rate)) - (depreciation expense * tax rate)
• cash outflow in final year = (pretax operating cost * (1 - tax rate)) - (depreciation expense * tax rate) - (salvage value * (1 - tax rate))

EAC of  Techron I is $230,369

EAC of  Techron II is $189,019

I prefer Techron II as it has a lower EAC

L M 2 Year A B C D E F G H I K Techron Techron II Pretax Pretax Cost of operating Salvage PV of Cash Cost of operating Salvage machine cost Depreciation value Cash Flow Flow machine cost Depreciation value 0 $(550,000) $(550,000) $(550,000) $ (650,000) $ (85,000) $ 183,333 $ (4,500) $ (3,913) $ 197,000) $ 216,667 $ (85,000) $ 183,333 $ (4,500) $ (3,403) $ (97,000) $ 216,667 $ (85,000) $ 183,333 $ 75,000 $ 48,000 $ 31,561 $ (97,000) $ 216,667 NPV $(525,755) $ (97,000) $ 216,667 EAC $ (230,269) $ (97,000) $ 216,667 $ 75,000 UwN PV of Cash Cash Flow Flow $(650,000) $ (650,000) $ (2,900) $ (2,522) $ (2,900) $ (2,193) $ (2,900) $ (1,907) $ (2,900) $ (1,658) $ 49,600 $ 24,660 NPV $(633,619) EAC $(189,019)

- A B C J K Techron II Pretax operating 2 Year Cost of machine cost 30 -550000 4 1 -85000 -85000 -85000 D E H I Techron Pretax operating Depreciation Salvage value Cash Flow PV of Cash Flow Cost of machine cost =B3 =F3/(1+15%)*A3 -650000 =550000/3 =(C4*(1-30%))+(D4*30%) =F4/(1+15%) A4 -97000 =550000/3 = (C5*(1-30%))+(D5*30%) =F5/(1+15%)*A5 -97000 =550000/ 3 75000 =(C6*(1-30%))+(D6*30%)+(E6*(1-30%)) =F6/(1+15%)A6 -97000 NPV |-SUM(G3:56) -97000 EAC =((G7*15%)/(1-(1+15%)^_3)) -97000 Depreciation Salvage value Cash Flow PV of Cash Flow =H3 =L3/(1+15%)*A3 =650000/3 =(14*(1-30%))+(J4*30%) =L4/(1+15%)^A4 =650000/3 =(15*(1-30%))+(J5*30%) =L5/(1+15%)"A5 =650000/3 =(16*(1-30%))+(J6*30%) =L6/(1+15%)^A6 =650000/3 =(17*(1-30%))+(37*30%) =L7/(1+15%)^A7 =650000/ 3 75000 =(18*(1-30%))+(J8*30%)+(K8*(1-30%)) =L8/(1+15%)A8 NPV | -SUM(M3:M8) EAC 1 =((M9*15%)/(1-(1+15%)^-5))