As the text points out, a stock that currently pays no dividends may or may not have value; a stock that will NEVER pay a dividend cannot have any value as long as investors are rational. For a stock that currently pays no dividend, market value derives from (a) the hope of future dividends and/or (b) the expectation of a liquidating dividend. This issue is discussed in more depth in a Lecture Tip in the IM.
Note, the calculation can also be done as: FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = -13.33
If you have taught students how to use uneven cash flow keys, then you can show them how to do this on the calculator. The notation below is for the TI-BA-II+ Or CF 0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I = 20; CPT NPV = 13.33
In equilibrium, the required return, R, is the same as the “expected return.”
Remind the students that if dividends are paid quarterly, then the discount rate must be a quarterly rate. Also, if students have been using a financial calculator for most of their calculations, they often forget to convert the interest rate and they leave it as a percent, i.e., P = .5 / (10/4) = .2. Ask them if this is a reasonable answer – “Would you only be willing to pay $0.20 for an asset that will pay you $0.50 every quarter forever?”
g is the growth rate in dividends; the subscripts denote the period in which the dividend is paid. This is the formula for a growing perpetuity that was developed in chapter 6. An expanded derivation of the model is available in a Lecture Tip in the IM.
The biggest mistake that students make with the DGM is using the wrong dividend. Be sure to emphasize that we are finding a present value, so the dividend needed is the one that will be paid NEXT period, not the one that has already been paid.
Does this result look familiar? The examples used to develop the earlier model were based on a 5% growth rate in dividends.
As the growth rate approaches the required return, the stock price increases dramatically.
As the required return approaches the growth rate, the price increases dramatically. This graph is a mirror image of the previous one.
Point out that the formula is completely general. The dividend in the numerator is always for one period later than the price we are computing. This is because we are computing a Present Value, so we have to start with a future cash flow. This is very important when discussing supernormal growth. We know the dividend in one year is expected to be $4 and it will grow at 6% per year for four more years. So, D 5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06) 4 Lecture Tip : In his book, A Random Walk Down Wall Street , pp. 82 – 89, (1985, W.W. Norton & Company, New York), Burton Malkiel gives four “fundamental” rules of stock prices. Loosely paraphrased, the rules are as follows. Other things equal: - Investors pay a higher price, the larger the dividend growth rate - Investors pay a higher price, the larger the proportion of earnings paid out as dividends - Investors pay a higher price, the less risky the company’s stock - Investors pay a higher price, the lower the level of interest rates
Point out that P 2 is the value, at year 2, of all expected dividends year 3 on. The final step is exactly the same as the 2-period example at the beginning of the chapter. We can look at it as if we buy the stock today and receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2 years and then immediately sell it for $9.66. Calculator: CF 0 = 0; C01 = 1.20; F01 = 1; C02 = 11.04; F02 = 1; NPV; I = 20; CPT NPV = 8.67
Point out that D 1 / P 0 is the dividend yield and g is the capital gains yield
Shareholders have the right to vote for the board of directors and other important issues. Cumulative voting increases the likelihood of minority shareholders getting a seat on the board. Proxy votes are similar to absentee ballots. Proxy fights occur when minority owners are trying to get enough votes to obtain seats on the Board or affect other important issues that are coming up for a vote. Different classes of stock can have different rights. Owners may want to issue a nonvoting class of stock if they want to make sure that they maintain control of the firm. Lecture Tip: Large institutions, such as mutual funds and pension funds, used to remain on the sidelines when it came to corporate control. However, several institutions have become much more active in recent years and have worked to force companies to operate in the shareholders’ best interests. CalPERS, the pension plan for California public employees, has been at the forefront of the corporate governance movement. For more information, see http://www.calpers-governance.org/forumhome.asp.
See the Lecture Tip in the IM for a discussion of the tax law changes regarding dividends received by individuals. (Resource: www.irs.gov “What are Qualified Dividends?” article.) Dividend exclusion: If corporation A owns less than 20% of corporation B stock, then 30% of the dividends received from corporation B are taxable. If A owns between 20% and 80% of B, then 20% of the dividends received are taxable. If A owns more than 80%, a consolidated statement can be filed and dividends received from B are essentially untaxed.
Point out that there are a lot of features of preferred stock that are similar to debt. In fact, many new issues have sinking funds that effectively convert what was a perpetual security into an equity security with a definite maturity. However, for tax purposes, preferred stock is equity and dividends are not a tax deductible expense, unless they meet specific characteristics as discussed in the text. Real-World Tip: Here’s a gruesome-sounding security – the “death spiral.” Actually, the name refers to convertible preferred shares that have a floating conversion ratio. That is, the conversion ratio varies with the price of the firm’s common stock. Also known as “toxic convertibles,” The Wall Street Journal reports that, when the issuer’s common stock falls, more shares must be issued to redeem the convertible securities, so this dilution pushes the common stock price down further. Hence, the “death spiral” appellation.
Dealer: maintains an inventory and stands ready to trade at quoted bid (price at which they will buy) and ask (price at which they will sell) prices. Make their profit from the difference between the bid and ask prices, called the bid-ask spread. The smaller the spread, the more competition and the more liquid the stock. The move to decimalization allows for a smaller bid-ask spread. There will be more discussion of this later. Broker: a broker matches buyers and sellers. They perform the search function for a fee (commission). They do not hold an inventory of securities. Lecture Tip: Some students find it hard to grasp the relative importance of primary and secondary market transactions. Suggest that they consider automobile sales rather than stocks. New automobiles are sold through a network of dealers and salesman (brokers) to the public. In any given year, however, the majority of transactions are between people buying and selling existing automobiles, i.e., the secondary (used) car market. As with secondary market transactions in stocks, used car purchases do not directly benefit the issuer/manufacturer. You can also introduce the notion of information asymmetry and signaling at this point, see the classic article by George Akerlof titled “Market for Lemons.” Video: The Financial Markets video discusses how capital is raised in the market and shows the open-outcry market at the CBOT. www: Check out the NYSE by clicking on the web surfer. Students are often amazed at all of the information that is available. NYSE: Specialists manage the order flow by keeping the limit order book. The limit order book lists the trades that investors have given to their brokers that include desired trading prices. The specialist is also a dealer that holds an inventory in their assigned stock, they post bid and ask prices, and they are supposed to maintain an orderly market. Other participants on the floor of the exchange include floor traders that own exchange seats, commission brokers, and floor brokers.
Point out that the NASDAQ market site in Times Square is NOT an exchange. It is just offices and basically a place for reporters to report on what is happening with Nasdaq stocks.
This quote is the Costco quote from the text. 52 week high = 75.23 52 week low = 54.85 Company is Costco Wholesale Annual dividend = $.64 per share Dividend yield = 0.90% P/E ratio = 27.63 Most recent price = 73.28 Lecture Tip: A useful assignment is to require students to obtain a recent Wall Street Journal and examine the financial section. Have the students examine the dividend column for various stocks and point out the number of non-dividend paying stocks. Also have them identify the information available in each quote. This allows them to see more information at once than they would normally see with online quotes.
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?
Now, what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay?
Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now how much would you be willing to pay?
If dividends are expected at regular intervals forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formula
P 0 = D / R
Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?
Suppose Big D, Inc., just paid a dividend of $0.50 per share. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?
Suppose TB Pirates, Inc., is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?
P 0 = 2 / (.2 - .05) = $13.33
Why isn’t the $2 in the numerator multiplied by (1.05) in this example?
8-
14.
Stock Price Sensitivity to Dividend Growth, g 8- D 1 = $2; R = 20%
15.
Stock Price Sensitivity to Required Return, R 8- D 1 = $2; g = 5%
Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that, dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?
Remember that we have to find the PV of all expected future dividends.
Suppose a firm’s stock is selling for $10.50. It just paid a $1 dividend, and dividends are expected to grow at 5% per year. What is the required return?
The status of pension funding (i.e., over- vs. under-funded) depends heavily on the choice of a discount rate. When actuaries are choosing the appropriate rate, should they give greater priority to future pension recipients, management, or shareholders?
How has the increasing availability and use of the internet impacted the ability of stock traders to act unethically?
XYZ stock currently sells for $50 per share. The next expected annual dividend is $2, and the growth rate is 6%. What is the expected rate of return on this stock?
If the required rate of return on this stock were 12%, what would the stock price be, and what would the dividend yield be?
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