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CHAPTER 7 The Valuation and Characteristics of Stock
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Common Stock <ul><li>Background </li></ul><ul><ul><li>Stockholders own the corporation, but in many instances the corporation is widely held </li></ul></ul><ul><ul><ul><li>Stock ownership is spread among a large number of people </li></ul></ul></ul><ul><ul><li>Because of this, most stockholders are only interested in how much money they will receive as a stockholder </li></ul></ul><ul><ul><ul><li>Most equity investors aren’t interested in a role as owners </li></ul></ul></ul>
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The Return on an Investment in Common Stock <ul><li>The future cash flows associated with stock ownership consists of </li></ul><ul><ul><li>Dividends and </li></ul></ul><ul><ul><li>The eventual selling price of the shares </li></ul></ul><ul><li>If you buy a share of stock for price P 0 , hold it for one year during which time you receive a dividend of D 1 , then sell it for a price P 1 , your return, k, would be: </li></ul>A capital gain (loss) occurs if you sell the stock for a price greater (lower) than you paid for it.
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The Intrinsic (Calculated) Value and Market Price <ul><li>A stock’s intrinsic value is based on assumptions made by a potential investor </li></ul><ul><ul><li>Must estimate future expected cash flows </li></ul></ul><ul><ul><ul><li>Need to perform a fundamental analysis of the firm and the industry </li></ul></ul></ul><ul><li>Different investors with different cash flow estimates will have different intrinsic values </li></ul>
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Developing Growth-Based Models <ul><li>Realistically most people tend to forecast growth rates rather than cash flows </li></ul><ul><li>A stock’s value today is the sum of the present values of the dividends received while the investor holds it and the price for which it is eventually sold </li></ul><ul><li>An Infinite Stream of Dividends </li></ul><ul><ul><li>Many investors buy a stock, hold for awhile, then sell, as represented in the above equation </li></ul></ul><ul><ul><ul><li>However, this is not convenient for valuation purposes </li></ul></ul></ul>
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Developing Growth-Based Models <ul><li>A person who buys stock at time n will hold it until period m and then sell it </li></ul><ul><ul><li>Their valuation will look like this: </li></ul></ul><ul><li>Repeating this process until infinity results in: </li></ul><ul><li>Conceptually it’s possible to replace the final selling price with an infinite series of dividends </li></ul>
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What is a constant growth stock? One whose dividends are expected to grow forever at a constant rate, g. Stock Value = PV of Dividends:
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The Constant Growth Model <ul><li>If dividends are assumed to be growing at a constant rate forever and we know the last dividend paid, D 0 , then the model simplifies to: </li></ul><ul><li>Which represents a series of fractions as follows </li></ul><ul><li>If k>g the fractions get smaller (approach zero) as the exponents get larger </li></ul><ul><ul><li>If k>g growth is normal </li></ul></ul><ul><ul><li>If k<g growth is supernormal </li></ul></ul><ul><ul><ul><li>Can occur but lasts for limited time period </li></ul></ul></ul>
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Constant Normal Growth <ul><li>Constant growth model can be simplified to </li></ul>K must be greater than g. <ul><li>D 1 = D 0 (1+g) </li></ul><ul><li>The constant growth model is a simple expression for forecasting the price of a stock that’s expected to grow at a constant, normal rate </li></ul>
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<ul><li>The discount rate (k i ) is the opportunity cost of capital , i.e., the rate that could be earned on alternative investments of equal risk. </li></ul>k i = k * + IP + LP + MRP + DRP. For Bonds: For Stocks: K s = K RF + (K M – K RF ) s
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Constant Normal Growth—Example Q: Atlas Motors is expected to grow at a constant rate of 6% a year into the indefinite future. It recently paid a dividends of $2.25 a share. The rate of return on stocks similar to Atlas is about 11%. What should a share of Atlas Motors sell for today? A: Example
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What happens if g > k s ? <ul><li>We can’t use model unless (1) k s > g and (2) g is expected to be constant forever . </li></ul><ul><li>If k s < g, get negative stock price, which is nonsense . </li></ul>
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The Zero Growth Rate Case—A Constant Dividend <ul><li>If a stock is expected to pay a constant, non-growing dividend, each dollar dividend is the same </li></ul><ul><li>Gordon model simplifies to: </li></ul><ul><li>A zero growth stock is a perpetuity to the investor </li></ul>
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The Expected Return <ul><li>Can recast Constant Growth model to focus on the return (k) implied by the constant growth assumption </li></ul><ul><li>g is the expected capital gains (%) </li></ul><ul><li>The higher the expected growth in dividends the faster the price is expected to grow </li></ul><ul><li>Would this apply to farmland? How? </li></ul>
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Basis for growth expectations <ul><li>Just looking at past dividend growth is not very informative because it can be distorted </li></ul><ul><li>Growth in EPS is the fundamental driver of growth in dividends (get data on EPS growth) </li></ul><ul><li>EPS growth greater than sales growth is not sustainable over a long period (so get data on sales growth) </li></ul><ul><li>Consider industry factors that affect growth and market share </li></ul><ul><li>ROE times the retention rate is the fundamental driver of EPS growth (get data on ROE and retention rate) </li></ul><ul><li>Also look for expert opinion </li></ul>
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What’s the stock’s market value? D 0 = 2.00, k s = 16%, g = 6%. Constant growth model:
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What is the stock’s market value one year from now, P 1 ? <ul><li>D 1 will have been paid, so expected dividends are D 2 , D 3 , D 4 and so on. Then, </li></ul>^
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Constant Growth Implications K s = 16%; g = 6%; 1/(.16-.06) = 10 Year Dividend Multiple Stock Price Growth Rate 0 $2.12 10 $21.20 6% 1 $2.247 10 $22.47 6% 2 $2.382 10 $23.82 6%
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Find the expected dividend yield, capital gains yield, and total return during the first year.
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Then, k s = $2.12/$21.20+ 0.06 = 0.10 + 0.06 = 16%. Dividend yield+capital gain Why do the dividend and capital gains returns add-up to the required rate of return? Rearrange model to rate of return form:
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What would P 0 be if g = 0? The dividend stream would be a perpetuity. 2.00 2.00 2.00 0 1 2 3 16%
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Two Stage Growth <ul><li>At times a firm’s future growth may not be expected to be constant </li></ul><ul><ul><li>For example, a new product may lead to temporary high growth </li></ul></ul><ul><li>The two-stage growth model allows us to value a stock that is expected to grow at an unusual rate for a limited time </li></ul><ul><ul><li>Use the Gordon model to value the constant portion </li></ul></ul><ul><ul><li>Find the present value of the non-constant growth periods </li></ul></ul>
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Problem 9 from lab <ul><li>Frazier Inc. paid a dividend of $4 last year (D 0 ). The firm is expecting dividends to grow at 21% in years 1–2 and 10% in Year 3. After that growth will be constant at 8% per year. Similar investments return 14%. Calculate the value of the stock today. </li></ul><ul><li>a.$71.49b.$88.31c.$91.47d.$116.10 </li></ul>
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<ul><li>ANS: C </li></ul><ul><li>D 1 = 4(1.21) = 4.84 </li></ul><ul><li>D 2 = D 1 (1.21) = 5.8564 </li></ul><ul><li>D 3 = D 2 (1.10) = 6.442 </li></ul><ul><li>D 4 = D 3 (1.08) = 6.9574032 </li></ul><ul><li>P 3 = [D 4 ]/(.14 – .08) = 115.95672 </li></ul><ul><li>6.44 + 115.96 = 122.40 </li></ul><ul><li>Calculator Steps: </li></ul><ul><li>CFo = 0, C 01 = 4.84, C 02 = 5.86, C 03 = 122.40; I = 14 </li></ul><ul><li>Solve for NPV = $91.37 </li></ul>
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Two Stage Growth—Example Q: Zylon Corporation’s stock is selling for $48 a share according to The Wall Street Journal. We’ve heard a rumor that the firm will make an exciting new product announcement next week. By studying the industry, we’ve concluded that this new product will support an overall company growth rate of 20% for about two years. After that, we feel growth will slow rapidly and level off at about 6%. The firm currently pays an annual dividend of $2.00, which can be expected to grow with the company. The rate of return on stocks like Zylon is approximately 10%. Is Zylon a good buy at $48? A: We’ll estimate what we think Zylon should be worth given our expectations about growth. Example
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Two Stage Growth—Example We’ll develop a schedule of expected dividend payments: Next, we’ll use the constant growth model at the point in time where the growth rate changes and constant growth begins. That’s year 2, so: Example 6% $3.05 3 20% $2.88 2 20% $2.40 1 Growth Expected Dividend Year
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Do time line and PV on the board <ul><li>CF 0 = 0 </li></ul><ul><li>CF 1 = 2.40 </li></ul><ul><li>CF 2 = 2.88 + 76.32 = 79.20 </li></ul><ul><li>K s = 10% </li></ul><ul><li>NPV =?= 67.64 </li></ul>
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<ul><li>Have to project out the assumptions on a time line. </li></ul><ul><li>Apply the constant growth model after 3 years. </li></ul>Another example: If we have supernormal growth of 30% for 3 yrs, then a long-run constant g=6%, what is P 0 ? k s is still 16%. ^
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High growth followed by constant lower growth: 0 NPV = 37.410 = P 0 g = 30% g = 30% g = 30% g = 6% D 0 = 2.00 2.60 3.380 4.394 4.658 46.58 CF 0 =0 CF 1 =2.6 CF 2 =3.38 CF 3 =50.97 I=16 1 2 3 4 k s =16%
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What is the expected dividend yield and capital gains yield at t = 0? At t = 4?
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<ul><li>During nonconstant growth, dividend and cap. gains yields are not constant, and capital gains yield is less than g. </li></ul><ul><li>After t = 3, g = constant = 6% = capital gains yield; k = 16%; so D/P = 16 - 6 = 10% . </li></ul>
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If g = -6%, would anyone buy the stock? If so, at what price? Firm still has earnings and still pays dividends, so P 0 > 0: ^
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What is the annual D/P and capital gains yield? <ul><li>Capital gains yield = g = - 6.0%, </li></ul><ul><li>Dividend yield = 16.0% - (-6.0%) = 22% . </li></ul><ul><li>D/P and cap. gains yield are constant, with high dividend yield (22%) offsetting negative cap. gains yield. </li></ul>
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super normal growth example The XYZ corporation has had annual earnings and dividends increase at the rate of 75% recently and recently paid dividends of $4/share. The outlook is for continued high growth at 50% per year for the next three years, then a more modest growth rate of 5% per year for all future years. The required return for a company of this risk is 15%.
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SUPER NORMAL GROWTH ANSWER <ul><li>D 1 =6, D 2 =9, D 3 =13.50, D 4 =13.5(1.05)=14.175 </li></ul><ul><li>P 3 =price of the stock at time 3, when the constant growth begins </li></ul><ul><li>P 3 =14.175[1/.15-.05]=14.175(10) </li></ul><ul><li>=$141.75 </li></ul><ul><li>Draw a time line. </li></ul><ul><li>Using the CF j part of your calculator: </li></ul><ul><li>CF 0 =0, CF 1 =6, CF 2 =9, CF 3 =13.5+141.75=155.25, I=15 </li></ul><ul><li>NPV=P 0 =$114.10 </li></ul>
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Super Normal Growth Base Dividend Growth rate Num-ber of years Constant growth rate k s $1 20% 5 3% 15% $30 40% 3 4% 16% $2 30% 2 5% 14% 2 30% 3 5% 14%
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What is market equilibrium? In equilibrium, stock prices are stable. There is no general tendency for people to buy versus sell. In equilibrium, expected returns must equal required returns :
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How is equilibrium established? If k = (D 1/ P 0 ) + g > k, then P 0 is “too low,” a bargain. Buy orders > sell orders; P 0 bid up; D 1 /P 0 falls until D 1 /P 0 + g = k = k. ^ ^
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Why do stock prices change? <ul><li>1. k i could change: </li></ul><ul><li>k i = k RF + (k M - k RF )b i </li></ul><ul><li>k RF = k * + IP </li></ul><ul><li>g could change due to economic or firm </li></ul><ul><li>situation </li></ul><ul><li>3. D could change – usually due to earnings </li></ul><ul><li>4. Super-normal growth expectations could </li></ul><ul><li>be formed or change. </li></ul>
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Feb. 4, 1994: Fed announced increase in interest rates at 11 a.m. Result: Dow Jones fell 95 points. k i = k RF + (k M - k RF )b i k RF = k * + IP
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Securities Analysis <ul><li>Securities analysis is the art and science of selecting investments </li></ul><ul><li>Fundamental analysis looks at a company and its business to forecast value </li></ul><ul><li>Technical analysis bases value on the pattern of past prices and volumes </li></ul><ul><li>The Efficient Market Hypothesis says information moves so rapidly in financial markets that price changes occur immediately, so it is impossible to consistently beat the market to bargains </li></ul>
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What’s the Efficient Market Hypothesis? EMH: Securities are normally in equilibrium and are “fairly priced,” given what is currently known. One cannot “beat the market” except through good luck or inside info.
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1. Weak-form EMH: Can’t profit by looking at past trends. A recent decline is no reason to think stocks will go up (or down) in the future. Seems empirically true, but “technical analysis” is still used.
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2. Semi-strong form EMH: All publicly available info. is reflected in stock prices, so doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true, but superior analysts can still profit by finding and using new information. It is VERY hard to tell good luck from superior stock picking/timing ability.
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All information, even inside info, is embedded in stock prices. Not true--insiders can gain by trading on the basis of insider information, but that’s illegal. 3. Strong-form EMH:
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Markets are efficient because: 1. 15,000 or so trained analysts; MBAs, CFAs, Technical PhDs. 2. Work for firms like Merrill, Morgan, Prudential, which have much money. 3. Have similar access to data. 4. Thus, news is reflected in P 0 almost instantaneously.
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