STOCK VALUATION: PRACTICE QUESTIONS

QUESTION 1

You are considering buying the stocks of two companies that operate in the same industry; they have very similar characteristics except for their dividend payout policies. Both companies are expected to earn $6 per share this year. However, Company D (for “dividend”) is expected to pay out all of its earnings as dividends, while Company G (for “growth”) is expected to pay out only one-third of its earnings, or $2 per share. D’s stock price is $40. G and D are equally risky.

Required

Which of the following is most likely to be true?

a. Company G will have a faster growth rate than Company D. Therefore, G’s stock price should be greater than $40.

b. Although G’s growth rate should exceed D’s, D’s current dividend exceeds that of G, and this should cause D’s price to exceed G’s.

c. An investor in Stock D will get his or her money back faster because D pays out more of its earnings as dividends. Thus, in a sense, D is like a short-term bond, and G is like a long-term bond. Therefore, if economic shifts cause kd and ks to increase, and if the expected streams of dividends from D and G remain constant, both Stocks D and G will decline, but D’s price should decline further.

d. D’s expected and required rate of return is kˆs = ks = 15%. G’s expected return will be higher because of its higher expected growth rate.

e. If we observe that G’s price is also $40, the best estimate of G’s growth rate is 10 percent.

QUESTION 2

Reen Company’s current stock price is $36, and its last dividend was $2.40. In view of Reen strong financial position and its consequent low risk, its required rate of return is only 12 percent. Assume dividends are expected to grow at a constant rate, g, in the future, and k s is expected to remain at 12 percent.

Required

What is Reen expected stock price 5 years from now?

QUESTION 3

Hart Enterprises recently paid a dividend, D0, of $1.25. The company expects to have supernormal growth of 20 percent for 2 years before the dividend is expected to grow at a constant rate of 5 percent. The firm’s cost of equity is 10 percent.

Required

a. What year is the terminal, or horizon, date?

b. What is the firm’s horizon, or terminal, value?

c. What is the firm’s intrinsic value today Pˆ0?

QUESTION 4

You are considering an investment in the common stock of Keller Corp. The stock is expected to pay a dividend of $2 a share at the end of the year (D1 = $2.00). The stock has a beta equal to 0.9. The risk-free rate is 5.6 percent, and the market risk premium is 6 percent. The stock’s dividend is expected to grow at some constant rate g. The stock currently sells for $25 a share.

Required

Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is Pˆ3?)

QUESTION 5

The beta coefficient for Stock C is βC = 0.4, whereas that for Stock D is βD = - 0.5. (Stock D’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.)

Required

a. If the risk-free rate is 9 percent and the expected rate of return on an average stock is 13 percent, what are the required rates of return on Stocks C and D?

b. For Stock C, suppose the current price, P0, is $25; the next expected dividend, D1, is $1.50; and the stock’s expected constant growth rate is 4 percent. Is the stock in equilibrium? Explain, and describe what will happen if the stock is not in equilibrium.

QUESTION 6

Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $2 yesterday. You expect the dividend to grow at the rate of 5 percent 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.

Required

a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that D0 = $2.00.

b. Given that the appropriate discount rate is 12 percent 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 D1, D2, and D3, 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 Pˆ3

to equal $34.73. Discounted at a 12 percent 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 today?

e. Calculate the present value of this stock. Assume that g = 5% and it is constant.

f. Is the value of this stock dependent upon how long you plan to hold it? In other words, if your planned holding period were 2 years or 5 years rather than 3 years, would this affect the value of the stock today, Pˆ0?

QUESTION 7

Investors require a 15 percent rate of return on Levine Company’s stock (ks = 15%).

Required

a. What will be Levine’s stock value if the previous dividend was D0 = $2 and if investors expect dividends to grow at a constant compound annual rate of (i) 5 percent, (ii) 0 percent, (iii) 5 percent, and (iv) 10 percent?

b. Using data from part a, what is the Gordon (constant growth) model value for Levine’s stock if the required rate of return is 15 percent and the expected growth rate is (i) 15 percent or (ii) 20 percent? Are these reasonable results? Explain.

c. Is it reasonable to expect that a constant growth stock would have g = ks?

QUESTION 8

The risk-free rate of return, kRF, is 11 percent; the required rate of return on the market, kM, is 14 percent; and Upton Company’s stock has a beta coefficient of 1.5.

Required

a. If the dividend expected during the coming year, D1, is $2.25, and if g is a constant 5%, at what price should Upton’s stock sell?

b. Now, suppose the Federal Reserve Board increases the money supply, causing the risk-free rate to drop to 9 percent and kM to fall to 12 percent. 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 kRF, causes kM to fall to 11 percent. At what price would Upton’s stock sell?

d. Now, suppose Upton has a change in management. The new group institutes policies that increase the expected constant growth rate to 6 percent. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.5 to 1.3. Assume that kRF and kM are equal to the values in part c. After all these changes, what is Upton’s new equilibrium price? (Note: D1 is now $2.27.)

QUESTION 9

Suppose Chance Chemical Company’s management conducts a study and concludes that if Chance expanded its consumer products division (which is less risky than its primary business, industrial chemicals), the firm’s beta would decline from 1.2 to 0.9. However, consumer products have a somewhat lower profit margin, and this would cause Chance’s constant growth rate in earnings and dividends to fall from 7 to 5 percent.

Required

a. Should management make the change? Assume the following: kM = 12%; kRF = 9%; D0 = $2.00.

b. Assume all the facts as given above except the change in the beta coefficient. How low would the beta have to fall to cause the expansion to be a good one? (Hint: Set Pˆ0 under the new policy equal to Pˆ 0 under the old one, and find the new beta that will produce this equality.)

QUESTION 10

Use the following February 12, 1998 quotation for Merck & Co. to answer the question.

52 Weeks Yld. Vol. Current Net.Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg

120. 80.19

Merck MRK 1.80 ? 30 195111 115.9 114.5

115 -1.25

Required

Which of the following statements is false?

a. The dividend yield was about 1.6%.

b. The 52 weeks’ trading range was $39.81.

c. The closing price per share on February 10, 1998, was $113.75.

d. The closing price per share on February 11, 1998, was $115.

e. The earnings per share were about $3.83.

QUESTION 11

You own $100,000 worth of Smart Money stock. At the end of the first year you receive a dividend of $2 per share; at the end of year 2 you receive a $4 dividend. At the end of year 3 you sell the stock for $50 per share. Only ordinary (dividend) income is taxed at the rate of 28 percent. Taxes are paid at the time dividends are received. The required rate of return is 15 percent.

Required

How many shares of stock do you own?

QUESTION 12

Rite Bite Enterprises sells toothpicks. Gross revenues last year were $3 million, and totalcosts were $1.5 million. Rite Bite has 1 million shares of common stock outstanding. Gross revenues and costs are expected to grow at 5 percent per year. Rite Bite pays no income taxes, and all earnings are paid out as dividends.

Required

a. If the appropriate discount rate is 15 percent and all cash flows are received at year’s end, what is the price per share of Rite Bite stock?

b. The president of Rite Bite decided to begin a program to produce toothbrushes. The project requires an immediate outlay of $15 million. In one year, another outlay of $5 million will be needed. The year after that, net cash inflows will be $6 million. This profit level will be maintained in perpetuity. What effect will undertaking this project have on the price per share of the stock?