CHAPTER 7 LECTURE (PART I)
In this chapter, we are going to learn to find the price of preferred and common stock. As was true with bonds, the prices of common and preferred stock are just the present values of their expected cash flows when discounted at the appropriate rate of return.
Preferred Stock
Preferred is a hybrid security having characteristics of both bonds and common stocks. It is like a bond in that it pays the same dividend every period just as bonds make the same interest payment every period. Preferred stock is like common stock in that most issues of preferred never mature.
Most issues of preferred stock are cumulative preferred. This means that if a dividend on the preferred stock is skipped, no dividends can be paid on common stock until all dividends in arrears are paid on the preferred. In essence, the unpaid dividends on preferred “accumulate” and remain a liability of the firm until they are paid.
It’s important to note that in the event of bankruptcy, preferred shareholders are next to last to receive funds realized from the sale of assets. This means, in most cases, preferred shareholders will receive nothing.
Like common stock, preferred stock has a par value. Unlike common stock, the par value of preferred actually has a useful purpose: it is used to find the annual dividend paid on the preferred shares. For example, the balance sheet entry for a firm’s preferred stock might be as follows:
6%,Preferred Stock, $100 par,...... $2,000,000
To find the annual dividend offered on these preferred shares, simply multiply the par value ($100) by the 6%:
Annual dividend = $100 X 6% = $6.
This issue of preferred promises to pay a dividend of $6 per year forever. In reality, this annual payment will be paid every three months (quarterly) so the quarterly dividend will be $6/4 = $1.50. Valuing a quarterly dividend is relatively complicated. To simplify the math somewhat, we will assume preferred dividends are paid just once per year. Incidentally, common stocks that pay dividends also pay them quarterly, but we will assume they pay them once per year also.
Because preferred stock pays the same dividend each year into perpetuity, we can value preferred stock using the formula for a perpetual annuity.
Pp = Dividend/Kp Where:
PP = Price of Preferred Stock
KP = Required Return on Preferred Stock.
Notice this formula tells us that there is an inverse relationship between the required return and the price of a share of preferred stock.
Using the 6%, $100 par preferred stock as an example, we can find its price by dividing the $6 annual dividend by the required return on the preferred. Suppose investors require a 10% return as compensation for the perceived risk they are bearing. The price of the preferred would therefore be calculated as follows:
PP = $6/.10 = $60.00.
This means $60 is the most investors would be willing to pay for shares of this preferred stock. They would be willing to pay less (since this would increase their return), but they would not be willing to pay more (since this would decrease their return).
Examine the formula for pricing preferred once again:
Pp = Dividend/Kp
Notice if we use just a little algebra, we can create an equation solving for the required return on preferred stock:
Kp = Dividend/Pp
Using the same issue of preferred stock as above:
Kp = $6/$60 = 10%.
Common Stock
Common shareholders are the residual claimants on the assets of the firm in the event of bankruptcy. This means that if the firm goes bankrupt, they will, in all probability, receive nothing. Common shareholders are the firm’s true owners. As such, they have the right to vote for the Board of Directors at the annual shareholders’ meeting. (preferred shareholders are considered “owners” too although they don’t usually have the right to vote at the annual shareholders meeting). Usually, shareholders can cast one vote per share owned for each open board seat. Thus, a shareholder owning over 50% of the outstanding shares can dominate the election for board members.
Some corporations have more than one class of common stock. One issue may have the right to vote while the other issue may not have voting rights. In this case, the party controlling the voting shares dominates the elections. This scheme is sometimes used by family-controlled firm’s (like Ford Motors) to allow family members or other insiders to retain control of the corporation.
Voting shares of common stock provide the holders with just one right: the right to vote at the annual shareholders’ meeting. Common shareholders do not have the right to manage the firm and they do not have the right to a dividend. The corporation’s Board of Directors appoints the firm’s senior management and decides on the timing and amount of dividends. The Board of Directors can decide to pay no dividend, stop paying dividends (if previously paid), increase or decrease dividends. Corporate boards frequently use dividend policy to “signal” the prospects of the firm to investors. If the board believes the firm will prosper for the foreseeable future, it might increase the dividend on the common stock. If the board believes the firm’s prospects are relatively bleak for the foreseeable future, it might reduce or even eliminate the dividend.
Common stock is more difficult to value than preferred stock since the dividends (if paid) on common stock can vary. Theoretically, the price of common stock could be determined by estimating all future dividends and then discounting these at stock’s required rate of return:
Pc = DIV1 + DIV2 + DIV3 + . . .
(1 + Ks) (1 + Ks) (1 + Ks)
Clearly, if dividend payments are paid over an infinite time horizon, this formula is not very practical.
In 1959, Myron Gordon introduced an alternative method of pricing common stocks which assumes that dividends grow at a constant rate forever. His formula, called the Gordon growth model (AKA the constant growth model) is shown below:
Pc = DIV0(1 + g) Limitation: KS g
(Ks – g)
Where:
Pc = the price of the common stock
Ks = the required return on the common stock
DIV0 = the last dividend paid on the common stock
g = constant growth rate in dividends
Notice the limitation on this model. For this model to “work” the required return must be more than the dividend growth rate. For if the growth rate were greater than the required return,
KS < g, the denominator would be negative and the result would be a negative price. What would be the interpretation of a negative price? Suppose the negative price were -$50. This would mean sellers of GE would pay investors $50 to take their stock. Clearly that would be nonsense.
Let’s spend some time analyzing this formula.
What does the formula predict will happen to the stock price if the growth rate, g, rises? (ans. The stock price would rise. The reverse is also true).
What does the formula predict will happen to the stock price if the required return, Ks, rises? (ans. The stock price would fall. The reverse is also true).
How do we find Ks? What causes it to rise? (ans. CAPM, an increase in Beta, the market risk premium, or the inflation premium would cause Ks to rise)
To illustrate the Gordon growth model, assume the General Electric just paid a $1 dividend on its common stock and that investors believe GE’s dividends will grow at a constant rate of 6% per year forever. Further, assume investors’ required return for GE is 10% per year. Using the constant growth model, GE’s price would be:
Pc = DIV0(1 + g)
(Ks – g)
Pc = $1 (1 + .06) = $26.50
(.10 - .06)
In other words, given the expected 6% growth rate and the 10% required return, investors in GE would be willing to pay, at most, $26.50 per share. They would be willing to pay less (since this would increase their return), but they would not be willing to pay more (since this would lower their return).
You might be wondering how the constant growth rate in dividends is estimated. Actually, there are two ways to estimate g:
- Examine the historical growth rate in dividends
- Use the sustainable growth rate formula.
Estimating g Using Historical Dividends
To illustrate the first way, refer to problem 7-11 on page 314 of your text. Elk County Telephone’s dividends have risen from $2.25 in 2004 to $2.87 in 2009 (we don’t need the other dividends). We can use these two dividends to find the average annual rate at which Elk County’s dividends have grown. Using this estimate for g will only be valid, however, if we expect the dividends to continue to grow at this rate in the future and if this growth rate is less than the stock’s required rate of return.
To estimate the growth rate in dividends, use the present value formula from chapter 4 (the future value formula could be used too).
PV = FV(PVIF, N, g%)
-$2.25 = $2.87(PVIF, 5, g%)
Notice N is 5 and not 6. N is the number of years of growth, not the number of dividends. N will equal the number of dividends – 1.
Also notice the 2004 dividend is written as a negative number. This is required whenever we want the calculator to compute either a rate or the number of periods.
To find g, make the following entries in the calculator:
2nd CLR TVM
2nd P/Y (verify P/Y = 1, if not, hit 1 ENTER)
2nd QUIT
2.25 +/- PV
2.87 FV
5 N
CPT I/Y
g = 4.99% which I would round up to 5%.
Estimating g Using the Sustainable Growth Model
The second way of estimating the growth rate in dividends utilizes the sustainable growth model:
g = ROE X Retention Ratio Where:
ROE = Return on equity
Retention ratio = Additions to Retained Earnings which is just the percentage of net income
Net Income
retained by the firm (that is, not paid out as dividends).
For example: let ROE = 20% and the retention ratio = .60.
G = 20% X .60 = 12%