Question

The Supreme Show Company is considering the purchase of a new, fully automated machine to replace a manually operated one. The machine being replaced, now five years old, originally had an expected life of 10 years, is being depreciated using the straight-line method from $40,000 down to $0 and can now be sold for $22,000. It takes one person to operate the machine and he earns $29,000 per year in salary and benefits.

The annual costs of maintenance and defects on the old machine are $6,000 and $4,000, respectively. The replacement machine being considered has a purchase price of $75,000 and an expected salvage value of $15,000 at the end of its five-year life. There will also be shipping and installation expenses of $6,000. Because the new machine would work faster, investment in raw materials would increase by a total of $3,000. The company expects that annual maintenance costs on the new machine will be $5,000 while defects will cost $2,000.

The required return for this project is 15% and the tax rate is 34%. What is the NPV of the project based on the incremental cash flows? Please show all your work to earn full credits. In particular, construct the capital budgeting tables consistent with major components.

Answer 1

Tax rate 34.00% Cost Dep-year 1-5 (40000*5/10) WDV Sale price Gain/(Loss), (22000-20000) Tax benefit Sale price after tax Old equipment 40,000 20.000 20,000 22,000 2,000 680 =2000*34% 21,320 =22000-680 Cost of new machine Installation Total cost Less sale proceed of old equipment Net investment 75,000 6.000 81,000 (21,320) 59,680 Total cost Less Salvage value Depreciable cost Useful life in years Annual depreciation 81,000 (15,000) 66,000 5.00 13,200 Tax shield Year Incremental Depreciation Depreciation-old Depreciation 1 $ 13,200 $ 4,000 $ 2 $ 13,200 $ 4,000 $ 3 $ 13,200 $ 4,000 $ 4 $ 13,200 $ 4,000 $ 5 $ 13,200 $ 4,000 $ Tax shield 9,200 9200*34% 9,200 9200*34% 9,200 9200*34% 9,200 9200*34% 9,200 9200*34% Tax shield 3,128 3,128 3,128 3,128 3,128

Maintenance Defects Total cost Saving Old machine cost New machine cost 6,000 $ 5,000 4,000 $ 2,000 10,000 $ 7,000 3,000 After tax value of operating profits Year Cost saving Salary saving Cost saving 1 $ 3,000 $ 29,000 $ 2 $ 3,000 $ 29,000 $ 3 $ 3,000 $ 29,000 $ 4 $ 3,000 $ 29,000 $ 5 $ 3,000 $ 29,000 $ Dep rate 32,000 =32000*(1-34%) 32,000 =32000*(1-34%) 32,000 =32000*(1-34%) 32,000 =32000*(1-34%) 32,000 =32000*(1-34%) Total After tax saving $ 21,120 $ 21,120 $ 21,120 $ 21,120 $ 105,600 Old equipment New equipment 15,000 $ 15,000 A A A WDV Sale price Gain/(Loss), (0-0) Tax benefit Sale price after tax Incremental salvage value Incremental salvage value 15,000 A II = 15000-0 15,000 Calculation of NPV 15% Year Capital Annual free PV factor, commitment Working capital Annual benefit Dep tax shield cashflow 1/(1+r)^time Total * PV factor OS (59,680.00) $ (3,000.00) $ $ (62,680) 1.00000 $ (62,680) 21,120 $ 3,128 $ 24,248 0.86957 $ 21,120 $ 3,128 $ 24,248 0.75614 $ 18,335 3 21,120 $ 3,128 $ 24,248 0.65752 $ 15,943 21,120 $ 3,128 $ 24,248 0.57175 $ 13,864 5 $ 15,000.00 $ 3,000.00 21,120 $ 3,128 $ 42.248 0.49718 $ 21,005 NPV 27,552

Since NPV is positive, replacement is suggested