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ch5.measuring return on investment

# ch5.measuring return on investment - Chapter 5 Measuring...

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Chapter 5: Measuring Return on Investments 1. The after-tax earnings is 120000(1-0.34) = 79200. The average book value of capital invested is \$250,000, since the book value is depreciated from 500,000 to zero in 10 years. Hence, the after-tax return on capital equals 79200/250000 = 19.80% 2. a. Year Beginning Value Ending value Average Book Value After-tax earnings After-tax ROC 1 1200 800 1000 132 0.132 2 800 400 600 132 0.22 3 400 0 200 132 0.66 4 0 0 0 132 n/a 5 0 0 0 132 n/a Average 360 132 The market value is not used, since it is irrelevant for the purpose of defining the book- value of the investment. For the last two years, the denominator is zero, and hence the ROC is undefined. To get around this problem, we use the average book value and after tax earnings over the 5 years. Return on Capital = 132/360 = 36.67% b. The geometric average cannot be defined, since the after-tax ROC for the last two years is undefined: the book value for the denominator being zero. c. Using the return on capital of 36.67% estimated from using the averages, we would accept the project since it is high enough to exceed a cost of capital of 25%. 3. If we compute the average return on equity over the entire period, we have an average equity investment of \$300,000 [\$1m.x(1-0.40) = \$600,000 going down to zero in 5 years]. The yearly net income equals 50,000. Hence the before-tax return on equity = 50000/300000 = 16.67%. 4. If the debt-equity ratio is 100%, the debt-to-capital ratio is 50%. Hence, we need Minimum return on capital = (0.5)(after-tax interest rate) + (0.5)(minimum return on equity). Solving, the implied minimum return on equity = 19%.

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5. a. Year Cash Flow Cumulated cash flow 1 250000 250000 2 500000 750000 3 750000 1500000 4 750000 2250000 5 750000 3000000 6 750000 3750000 7 750000 4500000 In year 5, the cumulated cash flow equals the initial investment of \$3m. Hence, the payback period = 5 years. b. The net present value = present value of the inflows - \$3b. = 5,724,015.7 - 3 = \$2.72b. 6. Year FCFF PV @ 10% PV @ 15% 0 (2,000,000.00) 2,000,000.00) (2,000,000.00) 1 100,000.00 90,909.09 86,956.52 2 300,000.00 247,933.88 226,843.10 3 300,000.00 225,394.44 197,254.87 4 300,000.00 204,904.04 171,525.97 5 300,000.00 186,276.40 149,153.02 6 300,000.00 169,342.18 129,698.28 7 300,000.00 153,947.44 112,781.11 8 300,000.00 139,952.21 98,070.53 9 300,000.00 127,229.29 85,278.72 10 300,000.00 115,662.99 74,155.41 NPV (338,448.05) (668,282.46) The project should not be accepted at either discount rate. 7. The present value of the annual free cash flow to equity can be computed using the annuity formula: PV = 50000 0.14 (1 - 1 (1.14) 10 ) = \$260,805.78 . This would be the maximum initial investment.
8. The entire benefit of the NPV should accrue to the shareholders. Hence the share price should rise by \$2 m./1 m. = \$2 per share. However, to the extent that such projects have already been foreseen by the market and incorporated into the stock price, there will be no current impact. 9., 10. Assuming that the discount rates given only apply to the corresponding year, the present values of the flows would be 300,000/(1.1) = \$272,727.27and 350,000/(1.1)(1.12) = \$284,090.91. The NPV = \$56818.18 11. Year Project A Cash flows Project B Cash flows NPV(A) @ 5% NPV(B) @ 5% NPV(A) @ 7.5% NPV(B) @ 7.5% 0 -500 -2000 -500 -2000 -500 -2000 1 50 190 47.61905 180.9524 44.29679 168.3278 2 50 190 45.35147 172.3356 39.24411 149.1276 3 50 190 43.19188 164.1291 34.76776 132.1175 4 50 190 41.13512 156.3135 30.802 117.0476 5 50 190 39.17631 148.87 27.2886 103.6967 6 50 190 37.31077 141.7809 24.17594 91.86858 7 50 190 35.53407 135.0295 21.41833 81.38966 8 50 190 33.84197 128.5995 18.97527 72.10601 9 50 190 32.23045 122.4757 16.81087 63.8813 10 50 190 30.69566 116.6435 14.89335 56.59473 11 50 190 29.23396 111.0891 13.19455 50.13929 12 50 190 27.84187 105.7991 11.68952 44.42019 13 50 190 26.51607 100.7611 10.35617 39.35344 14 50 190 25.2534 95.96291 9.1749 34.86462 15 50 190 24.05085 91.39325 8.128372 30.88781 16 50 190 22.90558 87.04119 7.201215 27.36462 17 50 190 21.81483 82.89637 6.379814 24.24329 18 50 190 20.77603 78.94892 5.652106 21.478 19 50 190 19.7867 75.18945 5.007402 19.02813 20 100 340 37.68895 128.1424 8.872474 30.16641 IRR 8% 7% NPV 141.955 424.3534 -141.67 -641.897

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