Question

The Sumitomo Chemical Corporation is considering replacing a 5-year-old machine that originally cost $50,000 and can be sold for $60,000. This machine is totally depreciated. The replacement machine would cost $125,000, and have a 5-year expected life over which it would be depreciated down using the straight-line method and have no salvage value at the end of five years. The new machine would produce savings before depreciation and taxes of $45,000 per year. Assuming a 34 percent marginal tax rate and a required return of 10%, calculate: (a) The internal rate of return and the net present value. (b) Assume now that the machine to be replaced is not totally depreciated. This machine presently has a book value of $25,000 and is being currently depreciated using the straight-line method down to a terminal value of zero over the next five years, generating depreciation of $5,000 per year. If the rest of the variables involved in the problem do not vary, what is now the net present value of substituting the machine?

Answer 1

- Sale value of old machine = $60,000 - This machine is fully depreciated so Book value = 0 - capital gain= sale value - Book value - 60,000 – 0 = 60,000 Tax So rate = 34% Tax on Capital gain= 60,000 x 34% = $20,400 sale value = 60,000 - 20, 400 - $39,600 Net 125,000 39 Goo - Cost of new machine = less Net sale value of = old machine Net out flow Life of new Asset = syears so depreciation = 125000 15 $ 85,400 = 25,000 per annum

calculation of cash flows :- = additional benefits less depreciation 45,ooo 25,800 20,000 less: Tax @ 34% 6800 13200 Add 25000 38,200 Depreciation operating cash flows given r= 107 and n= 5 years PVIFA (n= 5; -10] = 3.190187 so present value of future Cash flows = 36200+ 3.190187 - $144,808.05 N.P. v=144808.05 - 85, you 2 (pov.of future cash flows - cash out flow] $ 59,408-05 So - rate IRR is the where NPV=0 so 0= -85400 + 38200 X {PVIFA (n=5; 2=97 PUIFA (n=S; N= ?] = 85400 = 2.2356 38 200 using PVIFA Table IRR = 34.6091 %

Book value of old machine = $25,000 sale value = $60,000 So capital gain= 60,000 - 25000 = $35,000 Tax on capital gain= 35,000 + 34% = $ 11,900 Net sale value 35000 - 11900 [Net gain] - $23,100 - Cost of new machine - 125000 less Net gain on sale = 23100 of old machine $101900 Net out flow depreciation of new machine = 25000 less depreciation of old machine - ooo Incremental depreciation 20,000 calculation of operating additional benefits cash flows :- = 45,000 less: Incremental deprec Tarion = 20,000 less Tax @ 34% Hold depreciation operating cash flows 25,000 8 JOO 165oo 20,000 36,500

N.p.v So given r= 10% and n=5 PVIFA (n = 5; r=10] = 3.190781 present value of future Cash flows = 36,500 x 3.190787 = 138, 363.73 NPV=p.v. of Future Cashflows - Initial cash out flow - 138, 363.13 - 101900 = $36,463.73