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- 1. CHAPTER 8 Stocks, Stock Valuation, and Stock Market Equilibrium
- 2. Topics in Chapter <ul><li>Features of common stock </li></ul><ul><li>Determining common stock values </li></ul><ul><li>Efficient markets </li></ul><ul><li>Preferred stock </li></ul>
- 3. Common Stock: Owners, Directors, and Managers <ul><li>Represents ownership. </li></ul><ul><li>Ownership implies control. </li></ul><ul><li>Stockholders elect directors. </li></ul><ul><li>Directors hire management. </li></ul><ul><li>Since managers are “agents” of shareholders, their goal should be: Maximize stock price. </li></ul>
- 4. Classified Stock <ul><li>Classified stock has special provisions. </li></ul><ul><li>Could classify existing stock as founders’ shares, with voting rights but dividend restrictions. </li></ul><ul><li>New shares might be called “Class A” shares, with voting restrictions but full dividend rights. </li></ul>
- 5. Initial Public Offering (IPO) <ul><li>A firm “goes public” through an IPO when the stock is first offered to the public. </li></ul><ul><li>Prior to an IPO, shares are typically owned by the firm’s managers, key employees, and, in many situations, venture capital providers. </li></ul>
- 6. Seasoned Equity Offering (SEO) <ul><li>A seasoned equity offering occurs when a company with public stock issues additional shares. </li></ul><ul><li>After an IPO or SEO, the stock trades in the secondary market, such as the NYSE or Nasdaq. </li></ul>
- 7. Different Approaches for Valuing Common Stock <ul><li>Dividend growth model </li></ul><ul><li>Using the multiples of comparable firms </li></ul><ul><li>Free cash flow method (covered in Chapter 15) </li></ul>
- 8. Stock Value = PV of Dividends What is a constant growth stock? One whose dividends are expected to grow forever at a constant rate, g. P 0 = ^ (1+r s ) 1 (1+r s ) 2 (1+r s ) 3 (1+r s ) ∞ D 1 D 2 D 3 D ∞ + + +…+
- 9. For a constant growth stock: D 1 = D 0 (1+g) 1 D 2 = D 0 (1+g) 2 D t = D 0 (1+g) t If g is constant and less than r s , then: P 0 = ^ D 0 (1+g) r s - g = D 1 r s - g
- 10. Dividend Growth and PV of Dividends: P 0 = ∑( PVof D t ) $ 0.25 Years (t) D t = D 0 (1 + g) t PV of D t = D t (1 + r) t If g > r, P 0 = ∞ !
- 11. What happens if g > r s ? P 0 = ^ (1+r s ) 1 (1+r s ) 2 (1+r s ) ∞ D 0 (1+g) 1 D 0 (1+g) 2 D 0 (1+r s ) ∞ + +…+ (1+g) t (1+r s ) t If g > r s , then P 0 = ∞. ^ > 1, and So g must be less than r s to use the constant growth model.
- 12. Required rate of return: beta = 1.2, r RF = 7%, and RPM = 5%. r s = r RF + (RP M )b Firm = 7% + (5%) (1.2) = 13%. Use the SML to calculate r s :
- 13. Projected Dividends <ul><li>D 0 = 2 and constant g = 6% </li></ul><ul><li>D 1 = D 0 (1+g) = 2(1.06) = 2.12 </li></ul><ul><li>D 2 = D 1 (1+g) = 2.12(1.06) = 2.2472 </li></ul><ul><li>D 3 = D 2 (1+g) = 2.2472(1.06) = 2.3820 </li></ul>
- 14. Expected Dividends and PVs (r s = 13%, D 0 = $2, g = 6%) 0 1 2.2472 2 2.3820 3 g=6% 4 1.8761 1.7599 1.6508 13% 2.12
- 15. Intrinsic Stock Value: D 0 = 2.00, r s = 13%, g = 6%. Constant growth model: = = $30.29. 0.13 - 0.06 $2.12 $2.12 0.07 P 0 = ^ D 0 (1+g) r s - g = D 1 r s - g
- 16. Expected value one year from now: <ul><li>D 1 will have been paid, so expected dividends are D 2 , D 3 , D 4 and so on. </li></ul>P 1 = ^ D 2 r s - g = $2.2427 0.07 = $32.10
- 17. Expected Dividend Yield and Capital Gains Yield (Year 1) Dividend yield = = = 7.0%. $2.12 $30.29 D 1 P 0 CG Yield = = P 1 - P 0 ^ P 0 $32.10 - $30.29 $30.29 = 6.0%.
- 18. Total Year-1 Return <ul><li>Total return = Dividend yield + Capital gains yield. </li></ul><ul><li>Total return = 7% + 6% = 13%. </li></ul><ul><li>Total return = 13% = r s . </li></ul><ul><li>For constant growth stock: </li></ul><ul><ul><li>Capital gains yield = 6% = g. </li></ul></ul>
- 19. Rearrange model to rate of return form: Then, r s = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%. ^ P 0 = ^ D 1 r s - g to D 1 P 0 r s ^ = + g.
- 20. If g = 0, the dividend stream is a perpetuity. 2.00 2.00 2.00 0 1 2 3 r s =13% P 0 = = = $15.38. PMT r $2.00 0.13 ^
- 21. Supernormal Growth Stock <ul><li>Supernormal growth of 30% for 3 years, and then long-run constant g = 6%. </li></ul><ul><li>Can no longer use constant growth model. </li></ul><ul><li>However, growth becomes constant after 3 years. </li></ul>
- 22. Nonconstant growth followed by constant growth (D 0 = $2): 0 2.3009 2.6470 3.0453 46.1135 1 2 3 4 r s =13% 54.1067 = P 0 g = 30% g = 30% g = 30% g = 6% 2.60 3.38 4.394 4.6576 ^ P 3 = ^ $4.6576 0.13 – 0.06 = $66.5371
- 23. Expected Dividend Yield and Capital Gains Yield (t = 0) CG Yield = 13.0% - 4.8% = 8.2%. (More…) Dividend yield = = = 4.8%. $2.60 $54.11 D 1 P 0 At t = 0:
- 24. Expected Dividend Yield and Capital Gains Yield (t = 4) <ul><li>During nonconstant growth, dividend yield and capital gains yield are not constant. </li></ul><ul><li>If current growth is greater than g, current capital gains yield is greater than g. </li></ul><ul><li>After t = 3, g = constant = 6%, so the t = 4 capital gains gains yield = 6%. </li></ul><ul><li>Because r s = 13%, the t = 4 dividend yield = 13% - 6% = 7%. </li></ul>
- 25. Is the stock price based on short-term growth? <ul><li>The current stock price is $54.11. </li></ul><ul><li>The PV of dividends beyond year 3 is $46.11 (P 3 discounted back to t = 0). </li></ul><ul><li>The percentage of stock price due to “long-term” dividends is: </li></ul>= 85.2%. $46.11 $54.11
- 26. Intrinsic Stock Value vs. Quarterly Earnings <ul><li>If most of a stock’s value is due to long-term cash flows, why do so many managers focus on quarterly earnings? </li></ul><ul><li>See next slide. </li></ul>
- 27. Intrinsic Stock Value vs. Quarterly Earnings <ul><li>Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This would affect the current stock price. </li></ul><ul><li>Sometimes managers have bonuses tied to quarterly earnings. </li></ul>
- 28. Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. 0 1.7699 1.5663 1.3861 20.9895 1 2 3 4 r s =13% 25.7118 g = 0% g = 0% g = 0% g = 6% 2.00 2.00 2.00 2.12 2.12 P 3 0.07 30.2857
- 29. Dividend Yield and Capital Gains Yield (t = 0) <ul><li>Dividend Yield = D 1 / P 0 </li></ul><ul><li>Dividend Yield = $2.00 / $25.72 </li></ul><ul><li>Dividend Yield = 7.8% </li></ul><ul><li>CGY = 13.0% - 7.8% = 5.2%. </li></ul>
- 30. Dividend Yield and Capital Gains Yield (t = 3) <ul><li>Now have constant growth, so: </li></ul><ul><li>Capital gains yield = g = 6% </li></ul><ul><li>Dividend yield = r s – g </li></ul><ul><li>Dividend yield = 13% - 6% = 7% </li></ul>
- 31. 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: ^ = = = $9.89. $2.00(0.94) 0.13 - (-0.06) $1.88 0.19 P 0 = ^ D 0 (1+g) r s - g = D 1 r s - g
- 32. Annual Dividend and Capital Gains Yields Capital gains yield = g = -6.0%. Dividend yield = 13.0% - (-6.0%) = 19.0%. Both yields are constant over time, with the high dividend yield (19%) offsetting the negative capital gains yield.
- 33. Using Stock Price Multiples to Estimate Stock Price <ul><li>Analysts often use the P/E multiple (the price per share divided by the earnings per share). </li></ul><ul><li>Example: </li></ul><ul><ul><li>Estimate the average P/E ratio of comparable firms. This is the P/E multiple. </li></ul></ul><ul><ul><li>Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price. </li></ul></ul>
- 34. Using Entity Multiples <ul><li>The entity value (V) is: </li></ul><ul><ul><li>the market value of equity (# shares of stock multiplied by the price per share) </li></ul></ul><ul><ul><li>plus the value of debt. </li></ul></ul><ul><li>Pick a measure, such as EBITDA, Sales, Customers, Eyeballs, etc. </li></ul><ul><li>Calculate the average entity ratio for a sample of comparable firms. For example, </li></ul><ul><ul><li>V/EBITDA </li></ul></ul><ul><ul><li>V/Customers </li></ul></ul>
- 35. Using Entity Multiples (Continued) <ul><li>Find the entity value of the firm in question. For example, </li></ul><ul><ul><li>Multiply the firm’s sales by the V/Sales multiple. </li></ul></ul><ul><ul><li>Multiply the firm’s # of customers by the V/Customers ratio </li></ul></ul><ul><li>The result is the total value of the firm. </li></ul><ul><li>Subtract the firm’s debt to get the total value of equity. </li></ul><ul><li>Divide by the number of shares to get the price per share. </li></ul>
- 36. Problems with Market Multiple Methods <ul><li>It is often hard to find comparable firms. </li></ul><ul><li>The average ratio for the sample of comparable firms often has a wide range. </li></ul><ul><ul><li>For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers? </li></ul></ul>
- 37. Preferred Stock <ul><li>Hybrid security. </li></ul><ul><li>Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock. </li></ul><ul><li>However, unlike bonds, preferred stock dividends can be omitted without fear of pushing the firm into bankruptcy. </li></ul>
- 38. Expected return, given V ps = $50 and annual dividend = $5 V ps = $50 = $5 r ps ^ r ps $5 $50 ^ = = 0.10 = 10.0%
- 39. Why are stock prices volatile? <ul><li>r s = r RF + (RP M )b i could change. </li></ul><ul><ul><li>Inflation expectations </li></ul></ul><ul><ul><li>Risk aversion </li></ul></ul><ul><ul><li>Company risk </li></ul></ul><ul><li>g could change. </li></ul>P 0 = ^ D 1 r s - g
- 40. Consider the following situation. D 1 = $2, r s = 10%, and g = 5%: P 0 = D 1 / (r s -g) = $2 / (0.10 - 0.05) = $40. What happens if r s or g change?
- 41. Stock Prices vs. Changes in r s and g 66.67 50.00 40.00 9% 40.00 33.33 28.57 11% 50.00 40.00 33.33 10% 6% 5% 4% r s g
- 42. Are volatile stock prices consistent with rational pricing? <ul><li>Small changes in expected g and r s cause large changes in stock prices. </li></ul><ul><li>As new information arrives, investors continually update their estimates of g and r s . </li></ul><ul><li>If stock prices aren’t volatile, then this means there isn’t a good flow of information. </li></ul>
- 43. What is market equilibrium? <ul><li>In equilibrium, stock prices are stable. There is no general tendency for people to buy versus to sell. </li></ul><ul><li>The expected price, P, must equal the actual price, P. In other words, the fundamental value must be the same as the price. </li></ul>(More…)
- 44. In equilibrium, expected returns must equal required returns: r s = D 1 /P 0 + g = r s = r RF + (r M - r RF )b. ^
- 45. How is equilibrium established? If r s = + g > r s , then P 0 is “too low.” If the price is lower than the fundamental value, then the stock is a “bargain.” Buy orders will exceed sell orders, the price will be bid up until: D 1 /P 0 + g = r s = r s . ^ ^ D 1 P 0 ^
- 46. What’s the Efficient Market Hypothesis (EMH)? <ul><li>Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or inside information. </li></ul>(More…)
- 47. Weak-form EMH <ul><li>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. Evidence supports weak-form EMH, but “technical analysis” is still used. </li></ul>
- 48. Semistrong-form EMH <ul><li>All publicly available information is reflected in stock prices, so it doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true. </li></ul>
- 49. Strong-form EMH <ul><li>All information, even inside information, is embedded in stock prices. Not true--insiders can gain by trading on the basis of insider information, but that’s illegal. </li></ul>
- 50. Markets are generally efficient because: <ul><li>100,000 or so trained analysts--MBAs, CFAs, and PhDs--work for firms like Fidelity, Merrill, Morgan, and Prudential. </li></ul><ul><li>These analysts have similar access to data and megabucks to invest. </li></ul><ul><li>Thus, news is reflected in P 0 almost instantaneously. </li></ul>
- 51. Security Valuation <ul><li>In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return . </li></ul>
- 52. Preferred Stock <ul><li>A hybrid security : </li></ul><ul><li>it’s like common stock - no fixed maturity. </li></ul><ul><ul><li>technically, it’s part of equity capital. </li></ul></ul><ul><li>it’s like debt - preferred dividends are fixed. </li></ul><ul><ul><li>missing a preferred dividend does not constitute default, but preferred dividends are cumulative . </li></ul></ul>
- 53. <ul><li>Usually sold for $25, $50, or $100 per share. </li></ul><ul><li>Dividends are often quoted as a percentage of par. </li></ul><ul><ul><li>Example: In 1988, Xerox issued $75 million of 8.25% preferred stock at $50 per share. </li></ul></ul><ul><ul><li>$4.125 is the fixed, annual dividend per share. </li></ul></ul>Preferred Stock
- 54. <ul><li>May be callable and convertible . </li></ul><ul><li>Is usually non-voting . </li></ul><ul><li>Priority : lower than debt, higher than common stock. </li></ul><ul><li>Usually includes protective provisions . </li></ul><ul><li>May include a sinking fund provision. </li></ul>Preferred Stock
- 55. Preferred Stock Valuation <ul><li>A preferred stock can usually be valued like a perpetuity: </li></ul>V = D k ps ps
- 56. Example: <ul><li>Xerox preferred pays an 8.25% dividend on a $50 par value. </li></ul><ul><li>Suppose our required rate of return on Xerox preferred is 9.5% . </li></ul>V ps = 4.125 .095 = $43.42
- 57. Expected Rate of Return on Preferred <ul><li>Just adjust the valuation model: </li></ul>D P o k ps =
- 58. Example <ul><li>If we know the preferred stock price is $40 , and the preferred dividend is $4.125 , the expected return is: </li></ul>D P o k ps = = = .1031 4.125 40
- 59. The Financial Pages: Preferred Stocks <ul><li>52 weeks Yld Vol </li></ul><ul><li>Hi Lo Sym Div % PE 100s Close </li></ul><ul><li>29 3 / 8 25 1 / 8 GenMotor pfG 2.28 8.8 … 27 25 7 / 8 </li></ul><ul><li>Dividend: $2.28 on $25 par value </li></ul><ul><li>= 9.12% dividend rate. </li></ul><ul><li>Expected return: 2.28 / 25.875 = 8.8%. </li></ul>
- 60. Common Stock <ul><li>is a variable-income security. </li></ul><ul><ul><li>dividends may be increased or decreased, depending on earnings. </li></ul></ul><ul><li>represents equity or ownership. </li></ul><ul><li>includes voting rights . </li></ul><ul><li>Priority : lower than debt and preferred. </li></ul>
- 61. Common Stock Characteristics <ul><li>Claim on Income - a stockholder has a claim on the firm’s residual income. </li></ul><ul><li>Claim on Assets - a stockholder has a residual claim on the firm’s assets in case of liquidation. </li></ul><ul><li>Preemptive Rights - stockholders may share proportionally in any new stock issues. </li></ul><ul><li>Voting Rights - right to vote for the firm’s board of directors. </li></ul>
- 62. <ul><li>You expect XYZ stock to pay a $5.50 dividend at the end of the year. The stock price is expected to be $120 at that time. </li></ul><ul><li>If you require a 15% rate of return, what would you pay for the stock now? </li></ul>Common Stock Valuation (Single Holding Period) 0 1 ? 5.50 + 120
- 63. Common Stock Valuation (Single Holding Period) <ul><li>Financial Calculator solution: </li></ul><ul><li>P/Y =1, I = 15, n=1, FV= 125.50 </li></ul><ul><li>solve: PV = -109.13 </li></ul><ul><li>or: </li></ul><ul><li>P/Y =1, I = 15, n=1, FV= 120, </li></ul><ul><li>PMT = 5.50 </li></ul><ul><li>solve: PV = -109.13 </li></ul>
- 64. The Financial Pages: Common Stocks <ul><li>52 weeks Yld Vol Net </li></ul><ul><li>Hi Lo Sym Div % PE 100s Hi Lo Close Chg </li></ul><ul><li>139 81 IBM .48 .5 26 56598 108 106 106 5 / 8 -2 </li></ul><ul><li>119 75 MSFT … 60 254888 96 93 95 3 / 8 + 1 / 4 </li></ul>
- 65. Common Stock Valuation (Multiple Holding Periods) <ul><li>Constant Growth Model </li></ul><ul><li>Assumes common stock dividends will grow at a constant rate into the future. </li></ul>V cs = D 1 k cs - g
- 66. <ul><li>Constant Growth Model </li></ul><ul><li>Assumes common stock dividends will grow at a constant rate into the future. </li></ul><ul><li>D 1 = the dividend at the end of period 1. </li></ul><ul><li>k cs = the required return on the common stock. </li></ul><ul><li>g = the constant, annual dividend growth rate. </li></ul>V cs = D 1 k cs - g
- 67. Example <ul><li>XYZ stock recently paid a $5.00 dividend. The dividend is expected to grow at 10% per year indefinitely. What would we be willing to pay if our required return on XYZ stock is 15% ? </li></ul>D 0 = $5, so D 1 = 5 (1.10) = $5.50
- 68. Example <ul><li>XYZ stock recently paid a $5.00 dividend. The dividend is expected to grow at 10% per year indefinitely. What would we be willing to pay if our required return on XYZ stock is 15% ? </li></ul>V cs = = = $110 D 1 5.50 k cs - g .15 - .10
- 69. Expected Return on Common Stock <ul><li>Just adjust the valuation model </li></ul>V cs = D k cs - g k = ( ) + g D 1 V cs
- 70. Expected Return on Common Stock <ul><li>Just adjust the valuation model </li></ul>V cs = D k cs - g k = ( ) + g D 1 P o
- 71. Example <ul><li>We know a stock will pay a $3.00 dividend at time 1, has a price of $27 and an expected growth rate of 5% . </li></ul>k cs = ( ) + g D 1 P o k cs = ( ) + .05 = 16.11% 3.00 27

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