# valpr - Valuation Solutions Problem 1 a False The dividend...

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Valuation: Solutions Problem 1 a. False. The dividend discount model can still be used to value the dividends that the company will pay after the high growth eases. b. False. It depends upon the assumptions made about expected future growth and risk. c. False. This will be true only if the stock market falls more than merited by changes in the fundamentals (such as growth and cash flows). d. True. Portfolios of stocks that are undervalued using the dividend discount model seem to earn excess returns over long time periods. e. True. The model is biased towards these stocks because of its emphasis on dividends. Problem 2 a. Cost of Equity = 6.25% + 0.90 * 5.5% = 11.20% Value Per Share = \$3.56 * 1.055/(.1120 - .055) = \$65.89 b. \$3.56 (1 + g)/(.1120 - g) = \$80 Solving for g, g = (80 * .112 - 3.56)/(80 + 3.56) = 6.46% Problem 3 a. There will be an increasing in the stable growth rate; the discount rate will also go up. b. The stable growth rate will be higher, if the economy is growing faster. c. The stable growth rate will not be affected, but the high growth period for this company will be longer. d. Again the stable growth rate will be unaffected, but the high growth period and growth rate will be higher. Problem 4 A. Expected Earnings Per Share in 1999 = \$2.10 * 1.155 * 1.06 = \$4.48 Expected Dividends Per Share in 1999 = \$4.48 * 0.65 = \$2.91 Cost Of Equity After 1999 = 6.25% + 1.1 * 5.5% = 12.30% Expected Price at the End of 1998 = Expected DPS in 1999/(ke, 1999 - g) = \$2.91/(.1230 - .06) = \$46.19 B. Year EPS DPS 1994 \$2.42 \$0.79 1995 \$2.78 \$0.91 1996 \$3.19 \$1.05 1997 \$3.67 \$1.21 1998 \$4.22 \$1.39 \$46.19 Cost of Equity = 6.25% + 1.40 * 5.5% = 13.95% PV of Dividends and Terminal Price (@ 13.95%) = \$27.59 Problem 5 a. Retention Ratio = 1 - Payout Ratio = 1 - 0.42/1.50 = 72% Return on Assets = (Net Income + Int Exp (1-t))/(BV of Debt + BV of Equity) FALSE Page 1

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Valuation: Solutions Debt/Equity Ratio = 7.6/160 = .0475 Interest Rate on Debt = 0.8/7.6 = 10.53% Expected Growth Rate = 0.72 [.1819 + .0475 (.1819 - .1053 * (1 - 0.385))] = 13.5% Alternatively, and much more simply, Return on Equity = 30/160 = .1875 Expected Growth Rate = 0.72 * .1875 = 13.5% B. Expected payout ratio after 1998: = 1 - g/[ROA + D/E (ROA - i (1-t))] = 1 - .06/(.125+.25(.125 - .07(1-.385)) 58.76% c. Beta in 1993 = 0.85 Unlevered Beta = 0.85/(1 + (1 - 0.385) * 0.05) = 0.8246 Beta After 1998 = 0.8246 * (1 + (1 - 0.385) * 0.25) = 0.95 d. Cost of Equity in 1999 = 7% + 0.95 * 5.5% = 12.23% Expected Dividend in 1999 = ( \$1.50 * 1.1355 * 1.06) * 0.5876 = \$1.76 Expected Price at End of 1998 = \$1.76/(.1223 - .06) = \$28.25 e. Year EPS DPS 1994 \$1.70 \$0.48 1995 \$1.93 \$0.54 1996 \$2.19 \$0.61 1997 \$2.49 \$0.70 1998 \$2.83 \$0.79 \$28.25 Cost of Equity = 7% + 0.85 * 5.5% = 11.68% PV of Dividends and Terminal Price (@ 11.68%) = \$18.47 f. Total Value per Share = \$18.47 Value Per Share Using Gordon Growth Model = \$1.50 * 1.06 * 0.5876/(.1223 - .06) = \$15.00 Value Per Share With No Growth = \$1.50 * 0.5876/.1223 = \$7.21 Value of Extraordinary Growth = \$18.47 - \$15.00 = \$3.47 Value of Stable Growth = \$15.00 - \$7.21 = \$7.79 Problem 6 a. Period EPS DPS 1 \$4.58 \$0.79 2 \$5.32 \$0.92 3 \$6.17 \$1.07 4 \$7.15 \$1.21 Page 2
Valuation: Solutions 5 \$8.30 \$1.43 6 \$9.46 \$2.35 7 \$10.59 \$3.56 8 \$11.65 \$4.94 9 \$12.58 \$6.44 10 \$13.34 \$8.00 b.. Expected Price at End of 2003 = (\$13.34 * 1.06 * 0.60)/(.1175 - .06) = \$147.54 (Cost of Equity = 6.25% = 5.5% = 11.75%) c. PV of Dividends - High Growth = \$3.67 PV of Dividends - Transition = \$9.10 PV of Terminal Price = \$44.59 Value Per Share = \$57.36 Problem 7 a. Value Per Share = \$1.70 * 1.07/(.1203 - .07) = \$36.20 (Cost of Equity = 6.25% + 1.05 * 5.50% = 12.03%) b. Current Earnings per share = \$3.20 - (1 - Desired Debt Fraction) * (Capital Spending - Depreciation) = 83.61%* \$ 1.00 = \$0.84 - (1 - Desired Debt Fraction) * Working Capital = 83.61% * \$0.00 = \$0.00 Free Cash Flow to Equity = \$2.36 Cost of Equity = 6.25% + 1.05 * 5.5% = 12.03% Value Per Share = \$2.36 * 1.07/(.1203 - .07) = \$50.20 This is based upon the assumption that the current ratio of capital expenditures to depreciation is maintained in perpetuity.

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valpr - Valuation Solutions Problem 1 a False The dividend...

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