Chapter 8 Stock Valuation.

Chapter 8 Stock Valuation

Chapter Outline Bond and Stock Differences Common Stock Valuation
Features of Common Stock Features of Preferred Stock The Stock Markets

Bonds and Stocks: Similarities
Both provide long-term funding for the organization Both are future funds that an investor must consider Both have future periodic payments Both can be purchased in a marketplace at a price “today” With so many students today using social media, introducing the initial price offering (IPO) of Facebook as an example will bring familiarity and relevance to the entire issue of raising capital for the organization.

Bonds and Stocks: Differences
From the firm’s perspective: a bond is a long-term debt and stock is equity From the firm’s perspective: a bond gets paid off at the maturity date; stock continues indefinitely. We will discuss the mix of bonds (debt) and stock (equity) in a future chapter entitled capital structure A brief review of the balance sheet may be in order to reinforce the location of long-term debt on the balance sheet as a liability and common stock as equity on the balance sheet.

Bonds and Stocks: Differences
A bond has coupon payments and a lump-sum payment; stock has dividend payments forever Coupon payments are fixed; stock dividends change or “grow” over time This is a great time to introduce to students the concept of a perpetuity as it applies to a share of common stock. Cleary an investor can “end” the perpetuity by simply selling the stock to another investor, thus ending the stream of future dividends for that first investor. The introduction of stock in this chapter assumes a fixed coupon interest rate producing a constant coupon payment and the stock dividend grows over time. Some firms pay zero dividends and some bonds pay zero coupons but those are the exceptions, not the rule.

A visual representation of a bond with a coupon payment (C) and a maturity value (M)
1 2 3 4 5 $C1 $C2 $C3 $C4 $C5 $M

A visual representation of a share of common stock with dividends (D) forever
∞ 1 2 3 4 5 $D1 $D2 $D3 $D4 $D5 $D∞

Comparison Valuations
1 2 3 Bond C M P0 1 2 3 Common Stock D1 D2 D3 D∞ P0 This important slide demonstrates visually to students the connection between the past chapter of Bonds. Demonstrating both the similarities and the differences of the two financial instruments allows students the opportunity to visualize how finance approaches valuation.

Notice these differences:
The “C’s” are constant and equal The bond ends (year 5 here) There is a lump sum at the end 1 2 3 4 5 $C1 $C2 $C3 $C4 $C5 $M

∞ Notice these differences: The dividends are different
The stock never ends There is no lump sum ∞ 1 2 3 4 5 $D∞ $D1 $D2 $D3 $D4 $D5

To value a share of Common Stock
Our Task: To value a share of Common Stock

And how will we accomplish our task?

Bring All Expected Future Earnings Into Present Value Terms B A E F I

Just remember: BAEFEIPVT

Cash Flows for Stockholders
If you buy a share of stock, you can receive cash in two ways: The company pays dividends 2. You sell your shares, either to another investor in the market or back to the company 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.

One-Period Example Receiving one future dividend and one future selling price of a share of common stock

One-Period Example 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?

Visually this would look like:
1 R = 20% D1 = $2 P1 = $14

Compute the Present Value
1 R = 20% $1.67 D1 = $2 $11.67 P1 = $14 Note, the calculation can also be done as: FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = PV =$13.34

-13.34 TI BA II Plus 1 year = N 20% = Discount rate $2 = Payment (PMT)
$14 = FV 1st PV = ? 2nd 8-22 8-22

HP 12-C 1 year = N 20% = Discount rate $2 = Payment (PMT) PV = ?
$14 = FV -13.34

Two Period Example 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. Now how much would you be willing to pay?

Visually this would look like:
R = 20% 1 2 D1 = $2 D2 = $ 2.10 P2 = $14.70

Compute the Present Value
1 2 $1.67 D1 = $2 D2 = $ 2.10 $1.46 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 CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I = 20; CPT NPV = 13.33 P2 = $14.70 $ 10.21 $ = P0

What is the Observed Pattern?
We value a share of stock by bring back all expected future dividends into present value terms

Future Dividends So the key is to determine the future dividends when given the growth rate of those dividends, whether the growth is zero, constant, or unusual first and then levels off to a constant growth rate.

So how do you compute the future dividends?
Three scenarios: A constant dividend (zero growth) The dividends change by a constant growth rate We have some unusual growth periods and then level off to a constant growth rate

1. Constant Dividend – Zero Growth
The firm will pay a constant dividend forever This is like preferred stock The price is computed using the perpetuity formula: P0 = D / R

2. Constant Growth Rate of Dividends
Dividends are expected to grow at a constant percent per period. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + … P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R) D0(1+g)3/(1+R)3 + …

With a little algebra this reduces to: 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.

Student caution: If g > R we get a negative number in the denominator which would yield a negative price (which is nonsense)! If g = R then we get a zero in the denominator and Euclidian algebra cannot handle that and the fraction blows up. A. What happens if g > R? B. What happens if g = R?

Dividend Growth Model (DGM) Assumptions
To use the Dividend Growth Model (aka the Gordon Model), you must meet all three requirements: The growth of all future dividends must be constant, The growth rate must be smaller than the discount rate ( g < R), and The growth rate must not be equal to the discount rate (g ≠ R)

DGM – Example 1 Suppose Big D, Inc., just paid a dividend (D0) 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?

DGM – Example 1 Solution P0 = .50 ( 1 + .02) .15 - .02 P0 = .51
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. P0 = .51 .13 = $3.92

DGM – Example 2 Suppose Moore Oil 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?

DGM – Example 2 Solution P0 = 2.00 .20 - .05 P0 = 2.00 = $13.34 .15
Does this result look familiar? The examples used to develop the earlier model using Moore Oil Inc. were based on a 5% growth rate in dividends. Notice that the $2.00 figure given was the next dividend, D1, and NOT the past dividend, D0 as was the case in DGM Example 1. P0 = .15 = $13.34

3. Unusual Growth; Then Constant Growth
Just draw the time line with the unusual growth rates identified and determine if/when you can use the Dividend Growth Model. Deal with the unusual growth dividends separately.

Non-constant Growth Problem Statement
Suppose a firm is expected to increase dividends by 20% in one year and by 15% for 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?

Draw the time line and compute each dividend using the corresponding growth rate: 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% D1 D2 D3

Draw the time line and compute each dividend using the corresponding growth rate: 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% D1 =1.20 D2 D3 D1 = ($1.00) (1 + 20%) = $1.00 x 1.20 = $1.20

Draw the time line and compute each dividend using the corresponding growth rate: 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% D1 D2 =1.38 D3 D2 = ($1.20) (1 + 15%) = $1.20 x 1.15 = $1.38

Draw the time line and compute each dividend using the corresponding growth rate: 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% D1 D2 D3 =1.59 D3 = ($1.38) (1 + 15%) = $1.38 x 1.15 = $1.59

Now we can use the DGM starting with the period of the constant growth rate at our time frame of year 3: R = 20% 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% D1 D2 D3 P3 = D4/R – g P3 = D3 (1 + g) / R - g

Now we can use the DGM starting with the period of the constant growth rate at our time frame of year 3: R = 20% 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% D1 D2 D3 P3 = D3 (1 + g) / R - g P3 = 1.59 (1.05)/ = $11.13

We now have all of the dividends accounted for and we can compute the present value for a share of common stock: R = 20% 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% Recognize that at this point we have dividends 1 – 3 computed individually as we do not meet the criteria for the DGM because the growth is NOT constant from time zero and in year one the growth equals the discount rate R, both violations of the DGM model. The value at time 3 is the present value of all future dividends from that point forth which represents dividends 4 through infinity. Now we must bring all expected future earnings into present value time using the discount rate (required rate of return) of 20%. Many students try to use dividend three for the DGM but we start the constant growth of 5% at time 3, thus the NEXT period for the model is dividend 4. If P0 requires D1, then P3 requires D4. D1 D2 D3 P3 = 11.13

BAEFEIPVT! R = 20% 1 2 3 4 D0 = $1.00 ∞ g = 20% g = 15% g = 15% g = 5% The individual present values are 1.00 for PV of D1; .96 for the PV of D2; .92 for the PV of D3; 6.44 for the PV of P3 totaling $9.32 D1 D2 D3 $9.32 P3 = 11.13

Stock Price Sensitivity to Dividend Growth, g
D1 = $2; R = 20% 50 100 150 200 250 0.05 0.1 0.15 0.2 Growth Rate Stock Price As the growth rate approaches the required return, the stock price increases dramatically.

Stock Price Sensitivity to Required Return, R
D1 = $2; g = 5% 50 100 150 200 250 0.05 0.1 0.15 0.2 0.25 0.3 Growth Rate Stock Price As the required return approaches the growth rate, the price increases dramatically. This graph is a mirror image of the previous one.

Using the DGM to Find R Start with the DGM and then algebraically rearrange the equation to solve for R: Point out that D1 / P0 is the dividend yield and g is the capital gains yield. This will be explored further in the chapter on Dividend Policy.

Finding the Required Return - Example
Suppose a firm’s stock is selling for $ It just paid a $1 dividend, and dividends are expected to grow at 5% per year. What is the required return? R = [1(1.05)/10.50] = 15% What is the dividend yield? 1(1.05) / = 10% An alternative computation is that if the required return totals 15% and the dividend yield is 10%, then the capital gains yield is = 5%. What is the capital gains yield? g =5%

Stock Valuation Alternative
But my company doesn’t pay dividends! How can I value the stock?

Valuation Using Multiples
We can use the PE ratio and/or the price-sales ratio: Pt = Benchmark PE ratio X EPSt Pt = Benchmark price-sales ratio X Sales per sharet

Stock Valuation Summary

Features of Common Stock
Voting Rights Proxy voting Classes of stock 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

Features of Common Stock
Other Rights Share proportionally in declared dividends Share proportionally in remaining assets during liquidation Preemptive right – first shot at new stock issue to maintain proportional ownership if desired 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

Dividend Characteristics
Dividends are not a liability of the firm until a dividend has been declared by the Board Consequently, a firm cannot go bankrupt for not declaring dividends

Dividend Characteristics
Dividends and Taxes Dividend payments are not considered a business expense; therefore, they are not tax deductible The taxation of dividends received by individuals depends on the holding period Dividends received by corporations have a minimum 70% exclusion from taxable income See the Lecture Tip in the IM for a discussion of the tax law changes regarding dividends received by individuals. (Resource: “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.

Features of Preferred Stock
Dividends Stated dividend that must be paid before dividends can be paid to common stockholders Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely 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.

Dividends Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid 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.

Preferred stock generally does not carry voting rights

Stock Market, Dealers vs. Brokers
Dealer: trades with inventory for bid and ask prices Broker: matches buyers and sellers for a fee 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.”

Stock Market New York Stock Exchange (NYSE) Largest stock market
in the world License holders (1,366) Commission brokers Specialists Floor brokers Floor traders Operations Floor activity 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.

NASDAQ Not a physical exchange – it is a computer-based quotation system Multiple market makers Electronic Communications Networks 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.

NASDAQ Three levels of information:
Level 1 – median quotes, registered representatives Level 2 – view quotes, brokers & dealers Level 3 – view and update quotes, dealers only A large portion of technology stocks are bought and sold each day on NASDAQ

Work the Web Electronic Communications Networks provide trading in NASDAQ securities Click on the web surfer and visit Instinet

Reading Stock Quotes 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.

Work the Web Click on the web surfer to go to Bloomberg for current stock quotes. Reminding students

Ethics Issues 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?

Quick Quiz What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%? What if the company starts increasing dividends by 3% per year, beginning with the next dividend? The required return stays at 15%. Zero growth: 2 / .15 = 13.33 Constant growth: 2(1.03) / ( ) = $17.17

Comprehensive Problem
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? Expected return = 2/ = .10 Price = 2/ ( ) = $33.33 Dividend yield = 2 / = 6%

Terminology Bonds versus Common Stock Cash Dividends
Capital Gain Yield & Dividend Yield Dividend Growth Model (DGM) Preferred Stock Stock Market – NYSE Electronic Exchange – NASDAQ Stock Quotes

Formulas P0 = D R Value of a Perpetuity:
Value of a Share of Common Stock using the DGM:

Value of a Share of Common Stock
Formulas Value of a Share of Common Stock using Multiples Pt = Benchmark PE ratio X EPSt Pt = Benchmark price-sales ratio X Sales per sharet

Key Concepts and Skills
Compute the future dividend stream based on dividend growth Use the Dividend Growth Model (DGM) to determine the price of stock Explain how stock markets work Describe the workings of a stock exchange

What are the most important topics of this chapter?
A stock’s value is the present value of all expected future earnings. 2. Computing the future dividends of a stock is the key to understanding its value 3. Issuing stock provides the firm long-term funding

What are the most important topics of this chapter?
The Dividend Growth Model (DGM) provides us help with infinite dividend streams 5. Stocks are bought and sold each business day with reporting via stock quotes

Questions?

Chapter 8 Stock Valuation.

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