The price of a share of preferred stock is the

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Unformatted text preview: s risky because of the dividend and liquidation preference, so it is possible the preferred could be worth more, depending on the circumstances. 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. Yes. If the dividend grows at a steady rate, so does the stock price. In other words, the dividend growth rate and the capital gains yield are the same. The three factors are: 1) The company’s future growth opportunities. 2) The company’s level of risk, which determines the interest rate used to discount cash flows. 3) The accounting method used. It wouldn’t seem to be. Investors who don’t like the voting features of a particular class of stock are under no obligation to buy it. 4. 5. 6. 7. 8. 9. 10. Presumably, the current stock value reflects the risk, timing and magnitude of all future cash flows, both short-term and long-term. If this is correct, then the statement is false. 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 1. The constant dividend growth model is: Pt = Dt × (1 + g) / (R – g) So, the price of the stock today is: P0 = D0 (1 + g) / (R – g) = $1.90 (1.05) / (.12 – .05) = $28.50 The dividend at year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so: P3 = D3 (1 + g) / (R – g) = D0 (1 + g)4 / (R – g) = $1.90 (1.05)4 / (.12 – .05) = $32.99 We can do the same thing to find the dividend in Year 16, which gives us the price in Year 15, so: P15 = D15 (1 + g) / (R – g) = D0 (1 + g)16 / (R – g) = $1.90 (1.05)16 / (.12 – .05) = $59.25 There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today. The stock price in three years will be: P3 = P0(1 + g)3 = $28.50(1 + .05)3 = $32.99 And the stock price in 15 years will be: P15 = P0(1 + g)15 = $28.50(1 + .05)15 = $59.25 2. 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 = (D1 / P0) + g = ($2.85 / $58) + .06 = .1091 or 10.91% 240 3. The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = D1 / P0 = $2.85 / $58 = .0491 or 4.91% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 6% 4. Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R – g) = $3.05 / (.11 – .0525) = $53.04 5. 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 = .047 + .058 = .1050 or 10.50% 6. We know the stock has a required return of 13 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.13) = .065 = 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: D1 = .065($64) = $4.16 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: D1 = D0(1 + g) We can solve for the dividend that was just paid: $4.16 = D0 (1 + .065) D0 = $4.16 / 1.065 = $3.91 7. The price of any financial instrument is the PV of the future cash flows. The future dividends of this stock are an annuity for 9 years, so the price of the stock is the PVA, which will be: P0 = $11(PVIFA10%,9) = $63.35 8. The price of 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 that 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/P0 = $6.40/$103 = .0621 or 6.21% 241 9. The growth rate of earnings is the return on equity times the retention ratio, so: g = ROE × b g = .15(.70) g = .1050 or 10.50% To find next year’s earnings, we simply multiply the current earnings times one plus the growth rate, so: Next year’s earnings = Current earnings(1 + g) Next year’s earnings = $28,000,000(1 + .1050) Next year’s earnings = $30,940,000 Intermediate 10. This stock has a constant growth rate of dividends, but the r...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of Texas-Tyler.

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