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09 ModelHW9 - HW#9 solutions Model Answers Problem 9.10.1...

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HW #9 solutions – Model Answers Problem 9.10.1 Years Expected cash flow Cash flow (w/ delay) 0 -$500,000 -$500,000 1 $200,000 0 2 $200,000 ? 3 $200,000 ? 4 $200,000 ? 5 $200,000 ? Determine the Additional after-tax cash flow that will be needed to maintain the same IRR with the cash flow that has no delay occurred. 1. Find the IRR for expected cash flow: NPW(without delay) = -$500,000 + $200,000(P/A,i,5) = 0 Trial-and -error method: let NPW = 25% and 30% NPW (25%) = -$500,000 + $200,000(P/A, 25%, 5) = $37,856 NPW (30%) = -$500,000 + $200,000(P/A, 30%, 5) = -$12,886.05 Using linear interpolation, i = 25% + 5% [37856 / (37856 + 12866.05)] = 28.65% (This answer is verified using excel function = 28.65%) 2. By using iteration, find the additional cash flow to maintain the same IRR = 28.65% Additional cash flow with increment of $20,000. (Compute the IRR using excel function) Annual Return (n = 2 to 5 years) IRR 220,000 18.11 240,000 21.29 260,000 24.32 280,000 27.21 300,000 29.99 We Notice that the IRR of 28.65 is between annuity of $280,000 and $300,000. Therefore we find the annuity amount using linear interpolation. ($300,000 - X) / (29.99-28.65) = (X - $280,000) / (28.65-27.21) 2.075X = 1.075(300,000) + 280,000 X = $290,250 Therefore the additional amount of $90,250 or annuities of $290,250 are required each year (from 2 nd to 5 th year) in order to have the same IRR rate of 28.65% This can be verified by determine its NPW value at 28.65%
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