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) What is the internal rate of return and the net present value?

Answer 1

Initial cost of new machine Sale proceeds from old machine Savings before depreciation Depreciation less: Tax @ 34% Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 -1,25,000 60,000 45000 45000 45000 45000 45000 25000 25000 25000 25000 25000 20000 20000 20000 20000 20000 27200 6800 6800 6800 6800 -7200 13200 13200 13200 13200 25000 25000 25000 25000 25000 -65,000 17800 38200 38200 38200 38200 1.000 0.909 0.826 0.751 0.683 0.621 -65000 16,182 31,570 28,700 26,091 23,719 61,263 =SUM(B84:G84) Add: Depreciation a. Cash flow after tax b. PVF @ 10% c. Present value of cashflow (a x b) d. NPV (sum of c values) =(C78+B75)*0.34 IRR 38.52% =IRR(B82:682)

Note : Sale of existing machine

The book value of existing machine is nil. Hence the entire sale proceeds of 60000 is capital gain. This is subject to tax @ 34%. Now since the sale takes place at the beginning of the year and the tax is normally paid at the end of the year there is a time difference. Hence we compute the tax on sale of existing machine in Year 1 along with the tax on cash inflows of year 1 and discount at the PVF of 10% to arrive at present value. Hence it can be observed that the tax liability computed for Year 1 is higher than the tax liability for other years.

In the computation, IRR is computed using excel formula

In the given computation, the IRR is determined using the excel formula. You can also arrive at IRR using the following formula:

NPV IRR = r +- NPV - NPy. (ro-r) r. = lower discount rate chosen = higher discount rate chosen = NPV atr = NPV atr N N