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# chap006 - Solutions to Chapter 6 Valuing Stocks 1 No this...

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Solutions to Chapter 6 Valuing Stocks 1. No, this does not invalidate the dividend discount model. The dividend discount model allows for the fact that firms may not currently pay dividends. As the market matures, and Amazon’s growth opportunities moderate, investors may justifiably believe that Amazon will enjoy high future earnings and will then pay dividends. The stock price today can still reflect the present value of the expected per share stream of dividends. 2. Dividend yield = Dividend/Price = DIV 1 /P 0 0.08 = 2.40/P 0 P 0 = \$30 3. The preferred stock pays a level perpetuity of dividends. The expected dividend next year is the same as this year’s dividend (\$8). a. \$8/0.12 = \$66.67 b. \$8/0.12 = \$66.67 c. Dividend yield = \$8/\$66.67 = 0.12 =12% Capital gains yield = 0 Expected rate of return = 12% 4. r = DIV 1 /P 0 + g = 8% + 5% = 13% 5. The value of a share of common stock equals the present value of dividends received out to the investment horizon, plus the present value of the forecast stock price at the horizon. But the stock price at the horizon date depends on expectations of dividends from that date forward. So, even if an investor plans to hold a stock for only a year for two, the price ultimately received from another investor depends on dividends to be paid after the date of purchase. Therefore, the stock’s present value is the same for investors with different time horizons. 6. a.P 0 = DIV 1 /(r - g) \$30 = \$3/(r - 0.04) r =0.14 = 14% b. P 0 = \$3/(0.165 - 0.04) = \$24 6-1

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7. The annual dividend is: \$2 × 4 = \$8 DIV 1 /P 0 = 0.048 \$8/P 0 = 0.048 P 0 = \$8/0.048 = \$166.67 8. weak, semistrong, strong, fundamental, technical 9. The statement is correct. The search for information and insightful analysis makes investor assessments of stock values as reliable as possible. Since the rewards accrue to the investors who uncover relevant information before it is reflected in stock prices, competition among these investors means that there is always an active search for mispriced stocks. 10. a.DIV 1 = \$1 × 1.04 = \$1.04 DIV 2 = \$1 × 1.04 2 = \$1.0816 DIV 3 = \$1 × 1.04 3 = \$1.1249 b. P 0 = 00 . 13 \$ 04 . 0 12 . 0 04 . 1 \$ g r DIV 1 = - = - c.P 3 = 6237 . 14 \$ 04 . 0 12 . 0 04 . 1 1249 . 1 \$ g r DIV 4 = - × = - d. Your payments will be: Year 1 Year 2 Year 3 DIV \$1.04 \$1.0816 \$1.1249 Selling Price 14.6237 Total Cash Flow \$1.04 \$1.0816 \$15.7486 PV of Cash Flow \$0.9286 \$0.8622 \$11.2095 Sum of PV = \$13.00, the same as the answer to part (b). 11. g = return on equity × plowback ratio = 0.15 × 0.40 = 0.06 = 6.0% % 0 . 16 16 . 0 06 . 0 40 4 r 06 . 0 r 4 40 = = + = - = 12. a. 50 . 31 \$ 05 . 0 15 . 0 05 . 1 3 \$ g r DIV P 1 0 = - × = - = b. 45 \$ 05 . 0 12 . 0 05 . 1 3 \$ P 0 = - × = 6-2
The lower discount rate makes the present value of future dividends higher. 13. g 14 . 0 5 \$ 50 \$ - = % 0 . 4 04 . 0 50 \$ 5 \$ 14 . 0 g = = - = 14. a. r = DIV 1 /P 0 + g = [(\$1.64 × 1.03)/27] + 0.03 = 0.0926 = 9.26% b. If r = 0.10, then: 0.10 = [(\$1.64 × 1.03)/27] + g g = 0.0374 = 3.74% c. g = return on equity × plowback ratio 5% = return on equity × 0.4 return on equity = 0.125 = 12.5% 15. P 0 = DIV 1 /(r - g) = \$2/(0.12 – 0.06) = \$33.33 16. a.P 0 = DIV 1 /(r - g) = \$3/[0.15 – ( - 0.10)] = \$3/0.25 = \$12 b. P 1 = DIV 2 /(r - g) = \$3(1 - 0.10)/0.25 = \$10.80 c. expected rate of return = % 0 . 15 150 . 0 12 \$ ) 12 \$ 80 . 10 (\$ 3 \$ P gain Capital DIV 0 1 = = - + = + d. ‘Bad companies’ may be declining, but if the stock price already reflects this fact, the investor can still earn a fair rate of return, as we saw in part (c).

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chap006 - Solutions to Chapter 6 Valuing Stocks 1 No this...

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