Question

A corporation expects to receive $10,000 each year for 8 years from the sale of a product. There will be an initial investment of $40,000. Annual expenses will be $3,707 per year. Assume straight-line depreciation, an 8-year useful life and no salvage value. Use a 46% income tax rate. Determine the projected after-tax rate of return (show IRR calculation using book notation in your answer or handwritten submission).

Answer 1

net income per year = 10000 - 3707 = 6293

SL dep per year = (B-S)/N = (40000 - 0)/8 =5000

Taxable income = 6293 - 5000 = 1293

Tax per year = 1293 * 0.46 = 594.78

ATCF = 6293 - 594.78 = 5698.22

Let i% be the IRR, then

5698.22 * (P/A,i%,8) = 40000

(P/A,i%,8) = 40000 / 5698.22 = 7.019735

using trail and error method

When i = 2%, value of (P/A,i%,8) = 7.325481

When i = 3%, value of (P/A,i%,8) = 7.019692

using interpolaiton

i = 2% + (7.325481-7.019735) /(7.325481-7.019692)*(3%-2%)

i = 2% + 0.9998% ~ 2.9998% ~ 3% (Approx)