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CHAPTER 8
STOCK VALUATION
Answers to Concepts Review and Critical Thinking Questions
6. The two components are the dividend yield and the capital gains yield. For most companies, the capital
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11. Presumably, the current stock value reflects the risk, timing and magnitude of all future cash flows,
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:
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3. The dividend yield is the dividend next year divided by the current price, so the dividend yield is:
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:
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We can solve for the dividend that was just paid:
8. The price of a share of preferred stock is the dividend divided by the required return. This is the same
9. We can use the constant dividend growth model, which is:
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12. Using the equation to calculate the price of a share of stock with the PE ratio:
13. First, we need to find the sales per share, which is:
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Intermediate
14. This stock has a constant growth rate of dividends, but the required return changes twice. To find the
15. 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:
16. The price of a stock is the PV of the future dividends. This stock is paying five dividends, so the price
of the stock is the PV of these dividends using the required return. The price of the stock is:
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17. With supernormal dividends, we find the price of the stock when the dividends level off at a constant
18. With supernormal dividends, we find the price of the stock when the dividends level off at a constant
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Now we can substitute the previous dividend in Year 4 into this equation as follows:
20. The constant growth model can be applied even if the dividends are declining by a constant percentage,
just make sure to recognize the negative growth. So, the price of the stock today will be:
21. We are given the stock price, the dividend growth rate, and the required return and are asked to find
the dividend. Using the constant dividend growth model, we get:
22. The price of a share of preferred stock is the dividend payment divided by the required return. We
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23. The annual dividend paid to stockholders is $1.28, and the dividend yield is 2.1 percent. Using the
equation for the dividend yield:
24. We can use the two-stage dividend growth model for this problem, which is:
25. We can use the two-stage dividend growth model for this problem, which is:
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26. a. Using the equation to calculate the price of a share of stock with the PE ratio:
c. To find the implied return over the next year, we calculate the return as:
27. We need to find the PE ratio each year, which is:
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Using the equation to calculate the price of a share of stock with the PE ratio:
28. First, we need to find the earnings per share next year, which will be:
Using the equation to calculate the price of a share of stock with the PE ratio, the high target price is:
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29. To find the target price in five years, we first need to find the EPS in five years, which will be:
30. We need to begin by finding the dividend for each year over the next five years, so:
31. To find the target stock price, we first need to calculate the growth rate in earnings. We can use the
sustainable growth rate from a previous chapter. First, the ROE is:
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So, the sustainable growth rate is:
P1 = $86.27
Challenge
32. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks
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33. a. Using the constant growth model, the price of the stock paying annual dividends will be:
34. Here we have a stock with supernormal growth, but the dividend growth changes every year for the
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35. Here we want to find the required return that makes the PV of the dividends equal to the current stock
price. The equation for the stock price is:
36. Even though the question concerns a stock with a constant growth rate, we need to begin with the
equation for two-stage growth given in the chapter, which is:
Since we want the first t dividends to constitute one-half of the stock price, we can set the two terms
on the right hand side of the equation equal to each other, which gives us:
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Solving this equation, we get:
37. To find the value of the stock with two-stage dividend growth, consider that the present value of the
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Now we can rewrite the equation again as:
which can be written as:
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38. To find the expression when the growth rate for the first stage is exactly equal to the required return,
consider we can find the present value of the dividends in the first stage as:
