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# Chap018 - Chapter 18 Equity Valuation Models CHAPTER 18...

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Chapter 18 - Equity Valuation Models CHAPTER 18: EQUITY VALUATION MODELS PROBLEM SETS 1. Theoretically, dividend discount models can be used to value the stock of rapidly growing companies that do not currently pay dividends; in this scenario, we would be valuing expected dividends in the relatively more distant future. However, as a practical matter, such estimates of payments to be made in the more distant future are notoriously inaccurate, rendering dividend discount models problematic for valuation of such companies; free cash flow models are more likely to be appropriate. At the other extreme, one would be more likely to choose a dividend discount model to value a mature firm paying a relatively stable dividend. 2. It is most important to use multi-stage dividend discount models when valuing companies with temporarily high growth rates. These companies tend to be companies in the early phases of their life cycles, when they have numerous opportunities for reinvestment, resulting in relatively rapid growth and relatively low dividends (or, in many cases, no dividends at all). As these firms mature, attractive investment opportunities are less numerous so that growth rates slow. 3. The intrinsic value of a share of stock is the individual investor’s assessment of the true worth of the stock. The market capitalization rate is the market consensus for the required rate of return for the stock. If the intrinsic value of the stock is equal to its price, then the market capitalization rate is equal to the expected rate of return. On the other hand, if the individual investor believes the stock is underpriced (i.e., intrinsic value < price), then that investor’s expected rate of return is greater than the market capitalization rate. 4. 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. 18-1

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Chapter 18 - Equity Valuation Models 5. 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 6. a.k = r f + β[Ε (r M ) – r f ] = 6% + 1.25(14% – 6%) = 16% g = 2/3 × 9% = 6% D 1 = E 0 (1 + g) (1 – b) = \$3(1.06) (1/3) = \$1.06 60 \$10. 0.06 0.16 \$1.06 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% 18-2
Chapter 18 - Equity Valuation Models 8. a.

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