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# ch_13_sol - CHAPTER 13 EQUITY VALUATION 1 2 3(a P = 2.10.11...

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CHAPTER 13: EQUITY VALUATION 1. (a) P = 2.10/.11 = 19.09 2. (c) 3. a. k = D 1 /P 0 + g .16 = 2/50 + g g = .12 b. P 0 = D 1 /(k – g) = 2/(.16 – .05) = 18.18 The price falls in response to the more pessimistic dividend forecast. The forecast for current earnings, however, is unchanged. Therefore, the P/E ratio must fall. The lower P/E ratio is evidence of the diminished optimism concerning the firm's growth prospects. 4. a. False. Higher beta means that the risk of the firm is higher and the discount rate applied to value cash flows is higher. For any expected path of earnings and cash flows the present value of the cash flows, and therefore, the price of the firm will be lower when risk is higher. Thus the ratio of price to earnings will be lower. b. True. Higher ROE means more valuable growth opportunities. c. Uncertain. The answer will depend on a comparison of the expected rate of return on reinvested earnings versus the market capitalization rate. If the expected rate of return on the firm's projects is higher than the market capitalization rate, then P/E will increase as the plowback ratio increases. 5. a. g = ROE × b = 20% × .30 = 6% D 1 = \$2(1 – b) = \$2(1 – .30) = \$1.40 P 0 = D 1 /(k – g) = \$1.40/(.12 – .06) = \$23.33 P/E = 23.33/2 = 11.67 b. PVGO = P 0 = 23.33 – = \$6.67 c. g = ROE × b = 20% × .20 = 4% D 1 = \$2(1 – b) = \$2(1 – .20) = \$1.60 P 0 = D 1 /(k – g) = \$1.60/(.12 – .04) = \$20 P/E = 20/2 = 10 PVGO = P 0 = 20 – = \$3.33 13-1

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6. a. g = ROE × b = 16% × .5 = 8% D 1 = \$2(1 – b) = \$2.00 × (1 – .5) = \$1.00 P 0 = D 1 /(k – g) = \$1/(.12 – .08) = \$25 b. P 3 = P 0 (1 + g) 3 = \$24(1.08) 3 = \$31.49 7. a. E(r) = k = + g = + .08 = .11 = 11% b. The model assumes that the dividend growth rate is forever constant. Therefore, the model cannot be applied to firms that currently do not pay dividends. Second, the model is inappropriate when g > k (which presumably cannot persist indefinitely). Third, the model cannot handle firms with variable dividend growth paths. c. One can use either P/E multiples or market-to-book multiples exhibited by other firms in the same industry.
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