Financial Management: Theory and Practice

Eugene F. Brigham, Michael C. Ehrhardt

Chapter 8

Stocks, Stock Valuation, and Stock Market Equilibrium - all with Video Answers

Educators

Chapter Questions

Problem 1

Thress Industries just paid a dividend of $\$ 1.50$ a share (i.e., $D_{0}=\$ 1.50$ ). The dividend is expected to grow $5 \%$ a year for the next 3 years, and then $10 \%$ a year thereafter. What is the expected dividend per share for each of the next 5 years?

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

Boehm Incorporated is expected to pay a $\$ 1.50$ per share dividend at the end of the year (i.e., $D_{1}=\$ 1.50$ ). The dividend is expected to grow at a constant rate of $7 \%$ a year. The required rate of return on the stock, $r_{s}$, is $15 \% .$ What is the value per share of the company's stock?

Narayan Hari

Numerade Educator

Problem 3

Woidtke Manufacturing's stock currently sells for $\$ 20$ a share. The stock just paid a dividend of $\$ 1.00$ a share (i.e., $D_{0}=\$ 1.00$ ). The dividend is expected to grow at a constant rate of $10 \%$ a year. What stock price is expected 1 year from now? What is the required rate of return on the company's stock?

Nick Johnson

Numerade Educator

Problem 4

Basil Pet Products has preferred stock outstanding which pays a dividend of $\$ 5$ the end of each year. The preferred stock sells for $\$ 50$ a share. What is the prefer stock's required rate of return?

Nick Johnson

Numerade Educator

Problem 5

A company currently pays a dividend of $\$ 2$ per share, $D_{0}=\$ 2 .$ It is estimated that the company's dividend will grow at a rate of $20 \%$ per year for the next 2 years, then the dividend will grow at a constant rate of $7 \%$ thereafter. The company's stock has a beta equal to $1.2,$ the risk-free rate is $7.5 \%$, and the market risk premium is $4 \% .$ What is your estimate of the stock's current price?

Akash M

Numerade Educator

Problem 6

A stock is trading at $\$ 80$ per share. The stock is expected to have a year-end dividend of $\$ 4$ per share $\left(\mathrm{D}_{1}=\$ 4\right),$ which is expected to grow at some constant rate $g$ throughout time. The stock's required rate of return is $14 \%$, If you are an analyst who believes in efficient markets, what is your forecast of $g$ ?

Akash M

Numerade Educator

Problem 7

You are considering an investment in the common stock of Crisp's Cookware. The stock is expected to pay a dividend of $\$ 2$ a share at the end of the year $\left(\mathrm{D}_{1}=\$ 2.00\right)$ The stock has a beta equal to $0.9 .$ The risk-free rate is $5.6 \%$, and the market risk premium is $6 \% .$ The stock's dividend is expected to grow at some cunstant rate $g$. The stuck currently sells fur $\$ 25$ a share. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (Ihat is, what is $\hat{\mathrm{P}}_{3} ?$ )

Akash M

Numerade Educator

Problem 8

What will be the nominal rate of return on a preferred stock with a $\$ 100$ par value, a stated dividend of $8 \%$ of par, and a current market price of (a) $\$ 60,(\mathrm{b}) \$ 80,(\mathrm{c})$ $\$ 100,$ and $(d) \$ 140 ?$

Saad Ali Khan

Numerade Educator

Problem 9

Brushy Mountain Mining Company's ore reserves are being depleted, so its sales are falling. Also, its pit is getting decper cach year, so its costs are rising. As a result, the company's earnings and dividends are declining at the constant rate of $4 \%$ per year. If $\mathrm{D}_{0}=\$ 5$ and $\mathrm{r}_{\mathrm{s}}=15 \%,$ what is the value of Brushy Mountain's stock?

Lucas Finney

Numerade Educator

Problem 10

The beta coefficient for Stock $\mathrm{C}$ is $\mathrm{b}_{\mathrm{C}}=0.4,$ whereas that for Stock $\mathrm{D}$ is $\mathrm{b}_{\mathrm{D}}=-0.5$ (Stock $D^{\prime}$ s beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative beta stocks, although collection agency stocks are sometimes cited as an example.)
a. If the risk-free rate is $9 \%$ and the expected rate of return on an average stock is $13 \%,$ what are the required rates of return on Stocks $C$ and $D ?$
b. For Stock $C$, suppose the current price, $P_{0}$, is $\$ 25$; the next expected dividend, $\mathrm{D}_{1},$ is $\$ 1.50 ;$ and the stock's expected constant growth rate is $4 \% .$ Is the stock in equilibrium? Explain, and describe what will happen if the stock is not in equilibrium.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 11

Assume that the average firm in your company's industry is expected to grow at a constant rate of $6 \%$ and its dividend yield is $7 \% .$ Your company is about as risky as the average firm in the industry, but it has just successfully completed some $\mathrm{R} \& \mathrm{D}$ work that leads you to expect that its earnings and dividends will grow at a rate of $50 \%\left[\mathrm{D}_{1}=\mathrm{D}_{0}(1 \text { ? } g)=\mathrm{D}_{0}(1.50)\right]$ this year and $25 \%$ the following year, after which growth should match the $6 \%$ industry average rate. The last dividend paid $\left(\mathrm{D}_{0}\right)$ was $\$ 1 .$ What is the value per share of your firm's stock?

Akash M

Numerade Educator

Problem 12

Simpkins Corporation is expanding rapidly, and it currently needs to retain all of its earnings; hence it does not pay any dividends, However, investors expect Simpkins to begin paying dividends, with the first dividend of $\$ 1.00$ coming 3 years from today. The dividend should grow rapidly-at a rate of $50 \%$ per year-during Years 4 and $5 .$ After Year $5,$ the company should grow at a constant rate of $8 \%$ per year. If the required return on the stock is $15 \%$, what is the value of the stock today?

Lucas Finney

Numerade Educator

Problem 13

Rolen Riders issued preferred stock with a stated dividend of $10 \%$ of par. Preferred stock of this type currently yields $8 \%$, and the par value is $\$ 100$. Assume dividends are paid annually.
a. What is the value of Rolen's preferred stock?
b. Suppose interest rate levels rise to the point where the preferred stock now yields $12 \% .$ What would be the value of Rolen's preferred stock?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 14

You buy a share of The Ludwig Corporation stock for $\$ 21.40 .$ You expect it to pay dividends of $\$ 1.07, \$ 1.1449,$ and $\$ 1.2250$ in Years $1,2,$ and $3,$ respectively, and you expect to sell it at a price of $\$ 26.22$ at the end of 3 years.
d. Calculate the gruwth rate in dividends.
b. calculate the expected dividend yield.
c. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected gruwth rate to get the expected total rate of return. What is this stuck's expected total rate of return?

William Semus

Numerade Educator

Problem 15

Investors require a $15 \%$ rate of return on Brooks Sisters' stock $\left(\mathrm{r}_{*}=15 \%\right)$
a. What will be Brooks Sisters' stock value if the previous dividend was $D_{0}=\$ 2$ and if investors expect dividends to grow at a constant compound annual rate of $(1)-5 \%,(2) 0 \%,(3) 5 \%,$ and (4) $10 \% ?$
b. Using data from part a, what is the Gordon (constant growth) model value for Brooks Sisters' stock if the required rate of return is $15 \%$ and the expected growth rate is (1) $15 \%$ or (2) $20 \% ?$ Are these reasonable results? Explain.
c. Is it reasonable to expect that a constant growth stock would have $g>r_{s} ?$

Lucas Finney

Numerade Educator

Problem 16

The risk-free rate of return, $r_{R F}$, is $11 \%$; the required rate of return on the market, $\mathrm{r}_{\mathrm{M}}$ is $14 \%$; and Schuler Company's stock has a beta coefficient of 1.5
a. If the dividend expected during the coming year, $D_{1}$, is $\$ 2.25,$ and if $g=a$ constant $5 \%$, at what price should Schuler's stock sell?
b. Now, suppose the Federal Reserve Board increases the money supply, causing the risk-free rate to drop to $9 \%$ and $\mathrm{r}_{\mathrm{M}}$ to fall to $12 \% .$ What would this do to the price of the stock?
c. In addition to the change in part b, suppose investors' risk aversion declines; this fact, combined with the decline in $\mathrm{r}_{\mathrm{RF}^{\prime}}$ causes $\mathrm{r}_{\mathrm{M}}$ to fall to $11 \%$. At what price would Schuler's stock sell?
d. Now, suppose Schuler has a change in management. The new group institutes policies that increase the expected constant growth rate to $6 \%$. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.5 to $1.3 .$ Assume that $r_{\mathrm{RF}}$ and $r_{\mathrm{M}}$ are equal to the values in part c. After all these changes, what is Schuler's new equilibrium price? (Note:
$D_{1}$ goes to $\$ 2.27 .$ )

Heather Duong

Numerade Educator

Problem 17

Suppose a firm's common stock paid a dividend of $\$ 2$ yesterday. You expect the dividend to grow at the rate of $5 \%$ per year for the next 3 years, and, if you buy the stock, you plan to hold it for 3 years and then sell it.
a. Find the expected dividend for cach of the next 3 years; that is, calculate $D_{1}$ $\mathrm{D}_{2},$ and $\mathrm{D}_{3},$ Note that $\mathrm{D}_{0}=\$ 2$
b. Given that the appropriate discount rate is $12 \%$ and that the first of these dividend payments will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PV of $D_{1}, D_{2},$ and $D_{3}$ and then sum these PVs.
c. You expect the price of the stock 3 years from now to be $\$ 34.73 ;$ that is, you expect $\mathrm{P}_{3}$ to equal $\$ 34.73 .$ Discounted at a $12 \%$ rate, what is the present value of this expected future stock price? In other words, calculate the PV of $\$ 34.73$
d. If you plan to buy the stock, hold it for 3 years, and then sell it for $\$ 34.73,$ what is the most you should pay for it?
e. Use Equation $8-2$ to calculate the present value of this stock. Assume that $g=$ $5 \%,$ and it is constant.
f. Is the value of this stock dependent on how long you plan to hold it? In other words, if your planned ho:ding period were 2 years or 5 years rather than 3 years, would this affect the value of the stuck tuday, ?

Dale Sanford

Numerade Educator

Problem 18

$200 \%$ more electricity than any sular panel currently on the market. As a result, RT is expected to experience a $15 \%$ annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and $\mathrm{RT}^{\prime}$ s growth rate will slow to $5 \%$ per year indefinitely. Stockholders require a return of $12 \%$ on $\mathrm{RT}^{\prime}$ s stock. The most recent annual dividend (D $_{0}$ ), which was paid yesterday, was $\$ 1.75$ per share.
a. Calculate RT's expected dividends for $t=1, t=2, t=3, t=4,$ and $t=5$
b. Calculate the value of the stock today, $\hat{P}_{0}$. Proceed by finding the present value of the dividends expected at $t=1, t=2, t=3, t=4,$ and $t=5$ plus the present value of the stock price which should exist at $t=5, \hat{P}_{5}$. The $\hat{P}_{5}$ stock price can be found by using the constant growth equation. Notice that to find $\hat{\mathrm{P}}_{5},$ you use the dividend expected at $t=6,$ which is $5 \%$ greater than the $t=5$ dividend.
c. Calculate the expected dividend yield, $D_{1} / \hat{P}_{0}$, the capital gains yield expected during the first year, and the expected total return (dividend yield plus capital gains yield) during the first year. (Assume that $\hat{\mathrm{P}}_{0}=\mathrm{P}_{0}$, and recognize that the capital gains yicld is equal to the total return minus the dividend yicld.) Also calculate these same three yiclds for $t=5\left(\mathrm{c} . \mathrm{g}, . \mathrm{D}_{6} / \hat{\mathrm{P}}_{5}\right)$

Dale Sanford

Numerade Educator

Problem 19

Taussig Technologies Corporation (TTC) has been growing at a rate of $20 \%$ per year in recent years. This same growth rate is expected to last for another 2 years.
a. If $D_{0}=\$ 1.60, r_{s}=10 \%,$ and $g_{n}=6 \%,$ what is TTC's stock worth today? What are its expected dividend yield and capital gains yield at this time?
Copyright 2008 Thomson Leaming, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
b. Now assume that TTC's period of supernormal growth is to last another 5 years rather than 2 years. How would this affect its price, dividend yield, and capital gains yield? Answer in words only.
c. What will be TTC's dividend yield and capital gains yield once its period of supernormal growth ends? (I lint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the calculations are very easy.)
d. Of what interest to investors is the changing relationship between dividend yield and capital gains yield over time?

Lucas Finney

Numerade Educator