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suggestedProblems_ch08_sol.doc

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Department
Business
Course
BUSI 2504
Professor
Robert Riordan
Semester
Fall

Description
CHAPTER 8 STOCK VALUATION Learning Objectives LO1 How stock prices depend on future dividends and dividend growth. LO2 The characteristics of common and preferred stocks. LO3 The different ways corporate directors are elected to office. LO4: The stock market quotations and the basics of stock market reporting. Answers to Concepts Review and Critical Thinking Questions 2. (LO1) Investors believe the company will eventually start paying dividends (or be sold to another company). 4. (LO1) The general method for valuing a share of stock is to find the present value of all expected future dividends. The dividend growth model presented in the text is only valid (i) if dividends are expected to occur forever, that is, the stock provides dividends in perpetuity, and (ii) if a constant growth rate of dividends occurs forever. A violation of the first assumption might be a company that is expected to cease operations and dissolve itself some finite number of years from now. The stock of such a company would be valued by the methods of this chapter by applying the general method of valuation. A violation of the second assumption might be a start-up firm that isn’t currently paying any dividends, but is expected to eventually start making dividend payments some number of years from now. This stock would also be valued by the general dividend valuation method of this chapter. 6. (LO1) The two components are the dividend yield and the capital gains yield. For most companies, the capital gains yield is larger. This is easy to see for companies that pay no dividends. For companies that do pay dividends, the dividend yields are rarely over five percent and are often much less. 8. (LO3) In a corporate election, you can buy votes (by buying shares), so money can be used to influence or even determine the outcome. Many would argue the same is true in political elections, but, in principle at least, no one has more than one vote. 10. (LO2) Investors buy such stock because they want it, recognizing that the shares have no voting power. Presumably, investors pay a little less for such shares than they would otherwise. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 2. (LO1) We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find: R = (D 1 P 0 + g = ($2.50 / $48.00) + .05 = .1021 or 10.21% 4. (LO1) Using the constant growth model, we find the price of the stock today is: P 0 D /1(R – g) = $3.60 / (.11 – .045) = $55.38 S8-1 5. (LO1) The required return of a stock is made up of two parts: The dividend yield and the capital gains yield. So, the required return of this stock is: R = Dividend yield + Capital gains yield = .036 + .065 = .1010 or 10.10% 6. (LO1) We know the stock has a required return of 12 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.12) = .06 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so: D = .06($60) = $3.60 1 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year: D 1 D (10+ g) We can solve for the dividend that was just paid: $3.60 = D (10+ .06) D 0 $3.60 / 1.06 = $3.40 7. (LO1) The price of any financial instrument is the PV of the future cash flows. The future dividends of this stock are an annuity for eight years, so the price of the stock is the PVA, which will be: P = $11.00(PVIFA ) = $58.68 0 10%,8 8. (LO1) The price a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the price per share of the preferred stock is: R = D/P =0$6.50/$113 = .0575 or 5.75% Intermediate 9. (LO1) This stock has a constant growth rate of dividends, but the required return changes twice. To find the value of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So: P 6 D (16+ g) / (R – g) = D (1 +0g) / (R – g) = $3.50 (1.05) / (.11 – .05) = $82.08 Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is: 4 5 2 6 3 3 P 3 $3.50(1.050) / 1.14 + $3.50(1.050) / 1.14 + $3.50(1.05) / 1.14 + $82.08 / 1.14 P 3 $65.74 Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is: S8-2 P = $3.50(1.050) / 1.16 + $3.50(1.050) / (1.16) + $3.50(1.050) / (1.16) + $65.74 / (1.16)3 3 0 P0= $50.75 10. (LO1) Here we have a stock that pays no dividends for 10 years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember that general constant dividend growth formula is: Pt= [D ×t(1 + g)] / (R – g) This means that since we will use the dividend in Year 10, we will be finding the stock price in Year 9. The dividend growth model is similar to the PVA and the PV of a perpetuity: The equation gives you the PV one period before the first payment. So, the price of the stock in Year 9 will be: P9= D / 10 – g) = $10.00 / (.13 – .06) = $142.86 The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: P0= $142.86 / 1.13 = $47.55 12. (LO1) With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4, at the beginning of the constant dividend growth, as: P4= D (14+ g) / (R – g) = $2.00(1.05) / (.11 – .05) = $35.00 The price of the stock today is the PV of the first four dividends, plus the PV of the Year 3 stock price. So, the price of the stock today will be: 2
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