Question

You are evaluating two different silicon wafer milling machines. The Techron I costs $261,000, has a three-year life, and has pretax operating costs of $70,000 per year. The Techron II costs $455,000, has a five-year life, and has pretax operating costs of $43,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $47,000. If your tax rate is 35 percent and your discount rate is 9 percent, compute the EAC for both machines. (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.)

Answer 1

After tax salvage value for both the machines = Salvage value x (1 – tax rate)

= $ 47,000 x (1 – 0.35)

= $ 47,000 x = $ 30,550

Techron I:

Annual operating cash flow = Annual pre-tax operating cash flow x (1- tax rate) + tax rate x annual depreciation

                          = - $ 70,000 x (1 – 0.35) + 0.35 x ($ 261,000/3)

                          = - $ 70,000 x 0.65 + 0.35 x $ 87,000

                         = - $ 45,500 + $ 30,450 = - $ 15,050

NPV = PV of initial cost + PV of annual operating cash flow + PV of after tax salvage value

        = - $ 261,000 - $ 15,050 x PVIFA (9 %, 3) + $ 30,550 x PVIF (9 %, 3)

       = - $ 261,000 - $ 15,050 x 2.5313 + $ 30,550 x 0.7722

= - $ 261,000 - $ 38,096.065 + $ 23,590.71

= - $ 299,096.065 + $ 23,590.71 = - $ 275,505.36

EAC = NPV/PVIFA (r, t)

Rate of interest r is 9 % and time period t is 3 years

EAC = - $ 275,505.36/ PVIFA (9 %, 3)

         = - $ 275,505.36/2.5313 = $ 108,839.4718 or $ 108,839.47

Techron II:

Annual operating cash flow = Annual pre-tax operating cash flow x (1- tax rate) + tax rate x annual depreciation

                          = - $ 43,000 x (1 – 0.35) + 0.35 x ($ 445,000/5)

                          = - $ 43,000 x 0.65 + 0.35 x $ 89,000

                         = - $ 27,950 + $ 31,150 = $ 3,200

NPV = PV of initial cost + PV of annual operating cash flow + PV of after tax salvage value

        = - $ 445,000 + $ 3,200 x PVIFA (9 %, 5) + $ 30,550 x PVIF (9 %, 5)

       = - $ 445,000 + $ 3,200 x 3.8897+ $ 30,550 x 0.6499

       = - $ 445,000 + $ 12,447.04 + $ 19,854.45

       = - $ 445,000 + $ 32,301.485 = - $ 412698.515 or - $ 412,698.52

EAC = NPV/PVIFA (r, t)

Rate of interest r is 9 % and time period t is 5 years

EAC = - $ 412,698.52/ PVIFA (9 %, 5)

         = - $ 275,505.36/2.5313 = - $ 106,100.3458 or - $ 106,100.35

Techron II is preferable as EAC of Techron II is lower than Techron I.