# BD_SM09 - Chapter 9 Valuing Stocks 9-1 a b c P(0 = 2.80...

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Chapter 9 Valuing Stocks 9-1. a. P(0) = 2.80 / 1.10 + (3.00 + 52.00) / 1.10 2 = \$48.00 b. P(1) = (3.00 + 52.00) / 1.10 = \$50.00 c. P(0) = (2.80 + 50.00) / 1.10 = \$48.00 9-2. Dividend Yield = 0.88 / 22.00 = 4% Capital gain rate = (23.54 – 22.00) / 22.00 = 7% Total expected return = r E = 4% + 7% = 11% 9-3. With simplifying assumption (as was made in the chapter) that dividends are paid at the end of the year, then the stock pays a total of \$2.00 in dividends per year. Valuing this dividend as a perpetuity, we have, P \$2.00 / 0.15 \$13.33 = = Alternatively, if the dividends are paid quarterly, we can value them as a perpetuity using a quarterly discount rate of 1 4 (1.15) 1 3.556% - = (see Eq. 5.1) then, P \$0.5010.03556 \$14.06 = = . 9-4. P = 1.50 / (11% – 6%) = \$30 9-5. a. Eq 9.7 implies r E = Div Yld + g , so 8% – 1.5% = g = 6.5% b. With constant dividend growth, share price is also expected to grow at rate g = 6.5% (or we can solve this from Eq 9.2) 9-6. a. Eq 9.12: g = retention rate × return on new invest = (2/5) × 15% = 6% b. P = 3 / (12% – 6%) = \$50 c. g = (1/5) × 15% = 3%, P = 4 / (12% – 3%) = \$44.44. No, projects are positive NPV (return exceeds cost of capital), so don’t raise dividend. 9-7. Estimate r E : r E = Div Yield + g = 4 / 50 + 3% = 11% New Price: P = 2.50/(11% – 5%) = \$41.67

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84 Berk/DeMarzo • Corporate Finance In this case, cutting the dividend to expand is not positive NPV. 9-8. Value if the first 5 dividend payments ( 29 5 1 5 0.65 1.12 PV 1 \$3.24 0.08 0.12 1.08 - = - = - Value on date 5 of the rest of the dividend payments ( 29 4 5 0.65 1.12 1.02 PV 17.39 0.08 0.02 = = - Discounting this value to the present gives ( 29 0 5 17.39 PV \$11.83 1.08 = = So the value of Gillette is: 1 5 0 P PV PV 3.24 11.83 \$15.07 - = + = + = 9-9. PV of the first 5 dividends ( 29 5 first 5 0.96 1.11 1.11 PV 1 5.14217 0.085 0.11 1.085 = - = - PV of the remaining dividends in year 5 ( 29 ( 29 5 remaining in year 5 0.96 1.11 1.052 PV 51.5689 0.085 0.052 = = - Discounting back to the present ( 29 remaining 5 51.5689 PV 34.2957 1.085 = = Thus the price of Colgate is first 5 remaining P PV PV 39.4378
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BD_SM09 - Chapter 9 Valuing Stocks 9-1 a b c P(0 = 2.80...

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