Andrew Jacobson Financial

Preferred Stock

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Preferred stock is a hybrid—it is similar to bonds in some respects and to common stock in others. The hybrid nature of preferred stock becomes apparent when we try to classify it in relation to bonds and common stock. Like bonds, preferred stock has a par value and a fixed amount of dividends that must be paid before dividends can be paid on the common stock. However, if the preferred dividend is not earned, the directors can omit (or "pass") it without throwing the company into bankruptcy. So, although preferred stock has a fixed payment like bonds, a failure to make this payment will not lead to bankruptcy.

As noted above, a preferred stock entitles its owners to regular, fixed dividend payments. If the payments last forever, the issue is a perpetuity whose value, Vp, is found as follows:

Vp is the value of the preferred stock, Dp is the preferred dividend, and rp is the required rate of return. MicroDrive has preferred stock outstanding that pays a dividend of $10 per year. If the required rate of return on this preferred stock is 10 percent, then its value is $100, found by solving Equation 5-6 as follows:

If we know the current price of a preferred stock and its dividend, we can solve for the rate of return as follows:

Some preferred stocks have a stated maturity date, say, 50 years. If MicroDrive's preferred matured in 50 years, paid a $10 annual dividend, and had a required return of 8 percent, then we could find its price as follows: Enter N = 50, I = 8, PMT = 10, and FV = 100. Then press PV to find the price, Vp = $124.47. If rp = I = 10%, change I = 8 to I = 10, and find P = Vp = PV = $100. If you know the price of a share of preferred stock, you can solve for I to find the expected rate of return, Tp.

Most preferred stocks pay dividends quarterly. This is true for MicroDrive, so we could find the effective rate of return on its preferred stock (perpetual or maturing) as follows:

L Nom

If an investor wanted to compare the returns on MicroDrive's bonds and its preferred stock, it would be best to convert the nominal rates on each security to effective rates and then compare these "equivalent annual rates."

Self-Test Questions

Explain the following statement: "Preferred stock is a hybrid security."

Is the equation used to value preferred stock more like the one used to evaluate a perpetual bond or the one used for common stock?

Summary

Corporate decisions should be analyzed in terms of how alternative courses of action are likely to affect a firm's value. However, it is necessary to know how stock prices are established before attempting to measure how a given decision will affect a specific firm's value. This chapter showed how stock values are determined, and also how investors go about estimating the rates of return they expect to earn. The key concepts covered are listed below.

• A proxy is a document that gives one person the power to act for another, typically the power to vote shares of common stock. A proxy fight occurs when an outside group solicits stockholders' proxies in an effort to vote a new management team into office.

• A takeover occurs when a person or group succeeds in ousting a firm's management and takes control of the company.

• Stockholders often have the right to purchase any additional shares sold by the firm. This right, called the preemptive right, protects the control of the present stockholders and prevents dilution of their value.

• Although most firms have only one type of common stock, in some instances classified stock is used to meet the special needs of the company. One type is founders' shares. This is stock owned by the firm's founders that carries sole voting rights but restricted dividends for a specified number of years.

• A closely held corporation is one that is owned by a few individuals who are typically associated with the firm's management.

• A publicly owned corporation is one that is owned by a relatively large number of individuals who are not actively involved in its management.

• Whenever stock in a closely held corporation is offered to the public for the first time, the company is said to be going public. The market for stock that is just being offered to the public is called the initial public offering (IPO) market.

• The value of a share of stock is calculated as the present value of the stream of dividends the stock is expected to provide in the future.

• The equation used to find the value of a constant growth stock is:

• The expected total rate of return from a stock consists of an expected dividend yield plus an expected capital gains yield. For a constant growth firm, both the expected dividend yield and the expected capital gains yield are constant.

• The equation for rs, the expected rate of return on a constant growth stock, can be expressed as follows:

• A zero growth stock is one whose future dividends are not expected to grow at all, while a supernormal growth stock is one whose earnings and dividends are expected to grow much faster than the economy as a whole over some specified time period and then to grow at the "normal" rate.

• To find the present value of a supernormal growth stock, (1) find the dividends expected during the supernormal growth period, (2) find the price of the stock at the end of the supernormal growth period, (3) discount the dividends and the projected price back to the present, and (4) sum these PVs to find the current value of the stock, Pd.

The horizon (terminal) date is the date when individual dividend forecasts are no longer made because the dividend growth rate is assumed to be constant. The horizon (terminal) value is the value at the horizon date of all future dividends after that date.

The marginal investor is a representative investor whose actions reflect the beliefs of those people who are currently trading a stock. It is the marginal investor who determines a stock's price.

Equilibrium is the condition under which the expected return on a security as seen by the marginal investor is just equal to its required return, r = r. Also, the stock's intrinsic value must be equal to its market price, P0 = P0, and the market price is stable.

The Efficient Markets Hypothesis (EMH) holds (1) that stocks are always in equilibrium and (2) that it is impossible for an investor who does not have inside information to consistently "beat the market." Therefore, according to the EMH, stocks are always fairly valued (P0 = P0), the required return on a stock is equal to its expected return (r = r), and all stocks' expected returns plot on the SML. Differences can and do exist between expected and realized returns in the stock and bond markets—only for short-term, risk-free assets are expected and actual (or realized) returns equal.

When U.S. investors purchase foreign stocks, they hope (1) that stock prices will increase in the local market and (2) that the foreign currencies will rise relative to the U.S. dollar.

Preferred stock is a hybrid security having some characteristics of debt and some of equity.

Most preferred stocks are perpetuities, and the value of a share of perpetual preferred stock is found as the dividend divided by the required rate of return:

Maturing preferred stock is evaluated with a formula that is identical in form to the bond value formula.

Questions

5-1 Define each of the following terms:

a. Proxy; proxy fight; takeover; preemptive right; classified stock; founders' shares b. Closely held corporation; publicly owned corporation c. Secondary market; primary market; going public; initial public offering (IPO)

d. Intrinsic value (P0); market price (P0)

e. Required rate of return, rs; expected rate of return, rs; actual, or realized, rate of return, rs f. Capital gains yield; dividend yield; expected total return g. Normal, or constant, growth; supernormal, or nonconstant, growth; zero growth stock h. Equilibrium; Efficient Markets Hypothesis (EMH); three forms of EMH

i. Preferred stock

5-2 Two investors are evaluating AT&T's stock for possible purchase. They agree on the expected value of Dx and also on the expected future dividend growth rate. Further, they agree on the riskiness of the stock. However, one investor normally holds stocks for 2 years, while the other normally holds stocks for 10 years. On the basis of the type of analysis done in this chapter, they should both be willing to pay the same price for AT&T's stock. True or false? Explain.

5-3 A bond that pays interest forever and has no maturity date is a perpetual bond. In what respect is a perpetual bond similar to a no-growth common stock, and to a share of preferred stock?

Self-Test Problems (Solutions Appear in Appendix A)

ST-1 Ewald Company's current stock price is $36, and its last dividend was $2.40. In view of Ewald's CONSTANT GROWTH strong financial position and its consequent low risk, its required rate of return is only 12 percent. If dividends are expected to grow at a constant rate, g, in the future, and if rs is expected to remain at 12 percent, what is Ewald's expected stock price 5 years from now?

ST-2 Snyder Computer Chips Inc. is experiencing a period of rapid growth. Earnings and dividends SUPERNORMAL GROWTH are expected to grow at a rate of 15 percent during the next 2 years, at 13 percent in the third year, and at a constant rate of 6 percent thereafter. Snyder's last dividend was $1.15, and the required rate of return on the stock is 12 percent.

a. Calculate the value of the stock today.

b. Calculate P1 and P2.

c. Calculate the dividend yield and capital gains yield for Years 1, 2, and 3.

STOCK VALUATION

STOCK VALUATION

Problems

DPS CALCULATION

CONSTANT GROWTH VALUATION

CONSTANT GROWTH VALUATION

PREFERRED STOCK VALUATION 5-5

SUPERNORMAL GROWTH VALUATION

CONSTANT GROWTH RATE, G

CONSTANT GROWTH VALUATION

PREFERRED STOCK RATE OF RETURN

DECLINING GROWTH STOCK VALUATION

Warr Corporation just paid a dividend of $1.50 a share (i.e., D0 = $1.50). The dividend is expected to grow 5 percent a year for the next 3 years, and then 10 percent a year thereafter. What is the expected dividend per share for each of the next 5 years?

Thomas Brothers is expected to pay a $0.50 per share dividend at the end of the year (i.e., D1 = $0.50). The dividend is expected to grow at a constant rate of 7 percent a year. The required rate of return on the stock, rs, is 15 percent. What is the value per share of the company's stock?

Harrison Clothiers' stock currently sells for $20 a share. The stock just paid a dividend of $1.00 a share (i.e., D0 = $1.00). The dividend is expected to grow at a constant rate of 10 percent a year. What stock price is expected 1 year from now? What is the required rate of return on the company's stock?

Fee Founders has preferred stock outstanding which pays a dividend of $5 at the end of each year. The preferred stock sells for $60 a share. What is the preferred stock's required rate of return?

A company currently pays a dividend of $2 per share, D0 = 2. It is estimated that the company's dividend will grow at a rate of 20 percent per year for the next 2 years, then the dividend will grow at a constant rate of 7 percent thereafter. The company's stock has a beta equal to 1.2, the risk-free rate is 7.5 percent, and the market risk premium is 4 percent. What would you estimate is the stock's current price?

A stock is trading at $80 per share. The stock is expected to have a year-end dividend of $4 per share (D1 = 4), which is expected to grow at some constant rate g throughout time. The stock's required rate of return is 14 percent. If you are an analyst who believes in efficient markets, what would be your forecast of g?

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. 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 P3?)

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

Martell Mining Company's ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising. As a result, the company's earnings and dividends are declining at the constant rate of 5 percent per year. If D0 = $5 and rs = 15%, what is the value of Martell Mining's stock?

5-10

RATES OF RETURN AND EQUILIBRIUM

5-11

SUPERNORMAL GROWTH STOCK VALUATION

5-12

SUPERNORMAL GROWTH STOCK VALUATION

5-13

PREFERRED STOCK VALUATION

5-14

CONSTANT GROWTH STOCK VALUATION

5-15

RETURN ON COMMON STOCK

The beta coefficient for Stock C is bC = 0.4, whereas that for Stock D is bD = —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.)

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.

Assume that the average firm in your company's industry is expected to grow at a constant rate of 6 percent and its dividend yield is 7 percent. Your company is about as risky as the average firm in the industry, but it has just successfully completed some R&D work that leads you to expect that its earnings and dividends will grow at a rate of 50 percent [D1 = D0(1 + g) = D0(1.50)] this year and 25 percent the following year, after which growth should match the 6 percent industry average rate. The last dividend paid (D0) was $1. What is the value per share of your firm's stock?

Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings, hence it does not pay any dividends. However, investors expect Microtech 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 percent per year—during Years 4 and 5. After Year 5, the company should grow at a constant rate of 8 percent per year. If the required return on the stock is 15 percent, what is the value of the stock today?

Ezzell Corporation issued preferred stock with a stated dividend of 10 percent of par. Preferred stock of this type currently yields 8 percent, and the par value is $100. Assume dividends are paid annually.

a. What is the value of Ezzell's preferred stock?

b. Suppose interest rate levels rise to the point where the preferred stock now yields 12 percent. What would be the value of Ezzell's preferred stock?

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.

a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that D0 = $2.

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 P3 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?

e. Use Equation 5-2 to calculate the present value of this stock. Assume that g = 5%, and it is constant.

f. Is the value of this stock dependent 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, P0?

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.

a. Calculate the growth 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 growth rate to get the expected total rate of return. What is this stock's expected total rate of return?

5-16 Investors require a 15 percent rate of return on Levine Company's stock (rs = 15%).

CONSTANT GROWTH a. What will be Levine's stock value if the previous dividend was Dd = $2 and if investors exSTOCK VALUATION pect dividends to grow at a constant compound annual rate of (1) —5 percent, (2) 0 percent, (3) 5 percent, and (4) 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 (1) 15 percent or (2) 20 percent? Are these reasonable results? Explain.

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

5-17 Wayne-Martin Electric Inc. (WME) has just developed a solar panel capable of generating SUpERNORMAL GROWTH 200 percent more electricity than any solar panel currently on the market. As a result, WME STOCK VALUATION is expected to experience a 15 percent annual growth rate for the next 5 years. By the end of

5 years, other firms will have developed comparable technology, and WME's growth rate will slow to 5 percent per year indefinitely. Stockholders require a return of 12 percent on

WME's stock. The most recent annual dividend (D0), which was paid yesterday, was $1.75

per share.

a. Calculate WME's expected dividends for t = 1, t = 2, t = 3, t = 4, and t = 5.

b. Calculate the value of the stock today, P0. Proceed by finding the present value of the dividends expected att = 1, t = 2, t = 3, t = 4, and t = 5 plus the present value of the stock price which should exist at t = 5, P5. The P5 stock price can be found by using the constant growth equation. Notice that to find P5, you use the dividend expected at t = 6, which is 5 percent greater than the t = 5 dividend.

c. Calculate the expected dividend yield, D1/P0, 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 P0 = P0, and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Also calculate these same three yields for t = 5

5-18 Taussig Technologies Corporation (TTC) has been growing at a rate of 20 percent per year in SUpERNORMAL GROWTH recent years. This same growth rate is expected to last for another 2 years.

STOCK VALUATION a. If dd = $1.60, rs = 10%, and gn = 6%, what is TTC's stock worth today? What are its expected dividend yield and capital gains yield at this time?

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? (Hint: 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?

5-19 The risk-free rate of return, rRF, is 11 percent; the required rate of return on the market, rM, is EQUILIBRIUM STOCK pRICE 14 percent; and Upton Company's stock has a beta coefficient of 1.5.

a. If the dividend expected during the coming year, D1, is $2.25, and if g = 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 rM 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 rRF, causes rM 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 rRF and rM are equal to the values in part c. After all these changes, what is Upton's new equilibrium price? (Note: D1 goes to $2.27.)

Spreadsheet Problem

5-20 Start with the partial model in the file Ch 05 P20 Build a Model.xls from the textbook's

BUILDA MODEL: web site. Rework Problem 5-18, parts a, b, and c, using a spreadsheet model. For part b,

SUpERNORMAL GROWTH AND calculate the price, dividend yield, and capital gains yield as called for in the problem. CORPORATE VALUATION f > F

Robert Balik and Carol Kiefer are senior vice-presidents of the Mutual of Chicago Insurance Company. They are co-directors of the company's pension fund management division, with Balik having responsibility for fixed income securities (primarily bonds) and Kiefer being responsible for equity investments. A major new client, the California League of Cities, has requested that Mutual of Chicago present an investment seminar to the mayors of the represented cities, and Balik and Kiefer, who will make the actual presentation, have asked you to

See Ch 05 Show.ppt and ^elp them Ch 05 Mini Case.xls.

To illustrate the common stock valuation process, Balik and Kiefer have asked you to analyze the Bon Temps Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following questions.

a. Describe briefly the legal rights and privileges of common stockholders.

b. (1) Write out a formula that can be used to value any stock, regardless of its dividend pat tern.

(2) What is a constant growth stock? How are constant growth stocks valued?

(3) What happens if a company has a constant g which exceeds its rs? Will many stocks have expected g > rs in the short run (i.e., for the next few years)? In the long run (i.e., forever)?

c. Assume that Bon Temps has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7 percent, and that the market risk premium is 5 percent. What is the required rate of return on the firm's stock?

d. Assume that Bon Temps is a constant growth company whose last dividend (D0, which was paid yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6 percent rate.

(1) What is the firm's expected dividend stream over the next 3 years?

(2) What is the firm's current stock price?

(3) What is the stock's expected value 1 year from now?

(4) What are the expected dividend yield, the capital gains yield, and the total return during the first year?

e. Now assume that the stock is currently selling at $30.29. What is the expected rate of return on the stock?

f. What would the stock price be if its dividends were expected to have zero growth?

g. Now assume that Bon Temps is expected to experience supernormal growth of 30 percent for the next 3 years, then to return to its long-run constant growth rate of 6 percent. What is the stock's value under these conditions? What is its expected dividend yield and capital gains yield in Year 1? In Year 4?

h. Is the stock price based more on long-term or short-term expectations? Answer this by finding the percentage of Bon Temps' current stock price based on dividends expected more than 3 years in the future.

i. Suppose Bon Temps is expected to experience zero growth during the first 3 years and then to resume its steady-state growth of 6 percent in the fourth year. What is the stock's value now? What is its expected dividend yield and its capital gains yield in Year 1? In Year 4?

j. Finally, assume that Bon Temps' earnings and dividends are expected to decline by a constant 6 percent per year, that is, g = —6%. Why would anyone be willing to buy such a stock, and at what price should it sell? What would be the dividend yield and capital gains yield in each year?

Selected Additional References and Cases

k.	What is market multiple analysis?
l.	Why do stock prices change? Suppose the expected D1 is $2, the growth rate is 5 percent, and rs is 10 percent. Using the constant growth model, what is the price? What is the impact on stock price if g is 4 percent or 6 percent? If rs is 9 percent or 11 percent?
m.	What does market equilibrium mean?
n.	If equilibrium does not exist, how will it be established?
o.	What is the Efficient Markets Hypothesis, what are its three forms, and what are its implications?
P.	Bon Temps recently issued preferred stock. It pays an annual dividend of $5, and the issue price was $50 per share. What is the expected return to an investor on this preferred stock?

Many investment textbooks cover stock valuation models in depth, and some are listed in the Chapter 3 references.

For some recent works on valuation, see

Bey, Roger P., and J. Markham Collins, "The Relationship between Before- and After-Tax Yields on Financial Assets," The Financial Review, August 1988, 313-343.

Brooks, Robert, and Billy Helms, "An N-Stage, Fractional Period, Quarterly Dividend Discount Model," Financial Review, November 1990, 651-657.

Copeland, Tom, Tim Koller, and Jack Murrin, Valuation: Measuring and Managing the Value of Companies, 3rd ed. (New York: John Wiley & Sons, Inc., 2000).

The following cases in the Cases in Financial Management series cover many of the valuation concepts contained in this chapter: Case 3, "Peachtree Securities, Inc. (B)"; Case 43, "Swan-Davis"; Case 49, Beatrice Peabody"; and Case 101, "TECO Energy."

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