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# bkmsol_ch18 - CHAPTER 18 EQUITY VALUATION MODELS 1 2 3...

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CHAPTER 18: EQUITY VALUATION MODELS 1. Choice (a): P 0 = D 1 /(k – g) = \$2.10/(0.11 – 0) = \$19.09 2. (c) 3. a.k = D 1 /P 0 + g 0.16 = \$2/\$50 + g g = 0.12 = 12% b. P 0 = D 1 /(k – g) = \$2/(0.16 – 0.05) = \$18.18 The price falls in response to the more pessimistic dividend forecast. The forecast for current year earnings, however, is unchanged. Therefore, the P/E ratio falls. The lower P/E ratio is evidence of the diminished optimism concerning the firm's growth prospects. 4. a.g = ROE × b = 16% × 0.5 = 8% D 1 = \$2(1 – b) = \$2(1 – 0.5) = \$1 P 0 = D 1 /(k – g) = \$1/(0.12 – 0.08) = \$25 b. P 3 = P 0 (1 + g) 3 = \$25(1.08) 3 = \$31.49 5. a.This director is confused. In the context of the constant growth model [i.e., P 0 = D 1 /( k g )], it is true that price is higher when dividends are higher holding everything else including dividend growth constant . But everything else will not be constant. If the firm increases the dividend payout rate, the growth rate g will fall, and stock price will not necessarily rise. In fact, if ROE > k , price will fall. b. (i) An increase in dividend payout will reduce the sustainable growth rate as less funds are reinvested in the firm. The sustainable growth rate (i.e., ROE × plowback) will fall as plowback ratio falls. (ii) The increased dividend payout rate will reduce the growth rate of book value for the same reason -- less funds are reinvested in the firm. 6. a.k = r f + β[Ε (r M ) – r f ] = 6% + 1.25(14% – 6%) = 16% 18-1

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g = 2/3 × 9% = 6% D 1 = E 0 (1 + g) (1 – b) = \$3(1.06) (1/3) = \$1.06 60 . 10 \$ 10 . 0 16 . 0 06 . 1 \$ g k D P 1 0 = - = - = b. Leading P 0 /E 1 = \$10.60/\$3.18 = 3.33 Trailing P 0 /E 0 = \$10.60/\$3.00 = 3.53 c. 275 . 9 \$ 16 . 0 18 . 3 \$ 60 . 10 \$ k E P PVGO 1 0 - = - = - = The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%). d. Now, you revise b to 1/3, g to 1/3 × 9% = 3%, and D 1 to: E 0 × 1.03 × (2/3) = \$2.06 Thus: V 0 = \$2.06/(0.16 – 0.03) = \$15.85 V 0 increases because the firm pays out more earnings instead of reinvesting a poor ROE. This information is not yet known to the rest of the market. 7. Since beta = 1.0, then k = market return = 15% Therefore: 15% = D 1 /P 0 + g = 4% + g g = 11% 8. a. 160 \$ 05 . 0 10 . 0 8 \$ g k D P 1 0 = - = - = b. The dividend payout ratio is 8/12 = 2/3, so the plowback ratio is b = 1/3. The implied value of ROE on future investments is found by solving: g = b × ROE with g = 5% and b = 1/3 ROE = 15% c. Assuming ROE = k, price is equal to: 120 \$ 10 . 0 12 \$ k E P 1 0 = = = Therefore, the market is paying \$40 per share (\$160 – \$120) for growth opportunities. 18-2
9. Using a two-stage dividend discount model, the current value of a share of Sundanci is calculated as follows. 2 3 2 2 1 1 0 ) k 1 ( ) g k ( D ) k 1 ( D ) k 1 ( D V + - + + + + = 98 . 43 \$ 14 . 1 ) 13 . 0 14 . 0 ( 5623 . 0 \$ 14 . 1 4976 . 0 \$ 14 . 1 3770 . 0 \$ 2 2 1 = - + + = where: E 0 = \$0.952 D 0 = \$0.286 E 1 = E 0 (1.32) 1 = \$0.952 × 1.32 = \$1.2566 D 1 = E 1 × 0.30 = \$1.2566 × 0.30 = \$0.3770 E 2 = E 0 (1.32) 2 = \$0.952 × (1.32) 2 = \$1.6588 D 2 = E 2 × 0.30 = \$1.6588 × 0.30 = \$0.4976 E 3 = E 0 × (1.32) 2 × = \$0.952 × (1.32) 3 × 1.13 = \$1.8744 D 3 = E 3 × 0.30 = \$1.8743 × 0.30 = \$0.5623 10. a.Free cash flow to equity (FCFE) is defined as the cash flow remaining after meeting all financial obligations (including debt payment) and after covering capital expenditure and working capital needs. The FCFE is a measure of how much the firm can afford to pay out as dividends, but in a given year may be more or less than the amount actually paid out.

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bkmsol_ch18 - CHAPTER 18 EQUITY VALUATION MODELS 1 2 3...

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