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Ch07 Solutions

# Ch07 Solutions - Chapter 7 Stocks Stock Valuation and Stock...

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r s = 13% g n = 6% g 2 = 25% g 1 = 50% g = 50% g = 8% r s = 15% g = 5% r = 12% g = 15% g = 5% Stocks, Stock Valuation, and Stock Market Equilibrium 7-1 D 0 = \$1.50; g 1-3 = 5%; g n = 10%; D 1 through D 5 = ? D 1 = D 0 (1 + g 1 ) = \$1.50(1.05) = \$1.5750. D 2 = D 0 (1 + g 1 )(1 + g 2 ) = \$1.50(1.05) 2 = \$1.6538. D 3 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 ) = \$1.50(1.05) 3 = \$1.7364. D 4 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 )(1 + g n ) = \$1.50(1.05) 3 (1.10) = \$1.9101. D 5 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 )(1 + g n ) 2 = \$1.50(1.05) 3 (1.10) 2 = \$2.1011. 7-2 D 1 = \$1.50; g = 7%; r s = 15%; = ? = = = \$18.75. 7-3 P 0 = \$20; D 0 = \$1.00; g = 10%; = ?; s = ? = P 0 (1 + g) = \$20(1.10) = \$22. s = + g = + 0.10 = + 0.10 = 15.50%. s = 15.50%. 7-4 D ps = \$5.00; V ps = \$50; r ps = ? Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS

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r ps = = = 10%. 7-5 0 1 2 3 | | | | D 0 = 2.00 D 1 D 2 D 3 Step 1: Calculate the required rate of return on the stock: r s = r RF + (r M - r RF )b = 7.5% + (4%)1.2 = 12.3%. Step 2: Calculate the expected dividends: D 0 = \$2.00 D 1 = \$2.00(1.20) = \$2.40 D 2 = \$2.00(1.20) 2 = \$2.88 D 3 = \$2.88(1.07) = \$3.08 Step 3: Calculate the PV of the expected dividends: PV Div = \$2.40/(1.123) + \$2.88/(1.123) 2 = \$2.14 + \$2.28 = \$4.42. Step 4: Calculate : = D 3 /(r s – g) = \$3.08/(0.123 – 0.07) = \$58.11. Step 5: Calculate the PV of : PV = \$58.11/(1.123) 2 = \$46.08. Step 6: Sum the PVs to obtain the stock’s price:
= \$4.42 + \$46.08 = \$50.50. Alternatively, using a financial calculator, input the following: CF 0 = 0, CF 1 = 2.40, and CF 2 = 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to solve for NPV = \$50.50. 7-6 The problem asks you to determine the constant growth rate, given the following facts: P 0 = \$80, D 1 = \$4, and r s = 14%. Use the constant growth rate formula to calculate g: s = + g 0.14 = + g g = 0.09 = 9%.

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7-7 The problem asks you to determine the value of , given the following facts: D 1 = \$2, b = 0.9, r RF = 5.6%, RP M = 6%, and P 0 = \$25. Proceed as follows: Step 1: Calculate the required rate of return: r s = r RF + (r M – r RF )b = 5.6% + (6%)0.9 = 11%. Step 2: Use the constant growth rate formula to calculate g: s = + g 0.11 = + g g = 0.03 = 3%. Step 3: Calculate : = P 0 (1 + g) 3 = \$25(1.03) 3 = \$27.3182 ≈ \$27.32. Alternatively, you could calculate D 4 and then use the constant growth rate formula to solve for : D 4 = D 1 (1 + g) 3 = \$2.00(1.03) 3 = \$2.1855. = \$2.1855/(0.11 – 0.03) = \$27.3188 \$27.32. 7-8 V ps = D ps /r ps ; therefore, r ps = D ps /V ps . a. r ps = \$8/\$60 = 13.3%. b. r ps = \$8/\$80 = 10%.
c. r ps = \$8/\$100 = 8%. d. r ps = \$8/\$140 = 5.7%. 7-9 = = = = = \$25.26. 7-10 a. r i = r RF + (r M - r RF )b i . r C = 9% + (13% – 9%)0.4 = 10.6%. r D = 9% + (13% – 9%)-0.5 = 7%. Note that r D is below the risk-free rate. But since this stock is like an insurance policy because it “pays off” when something bad happens (the market falls), the low return is not unreasonable.

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