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- 1. CHAPTER 9 Stocks and Their Valuation <ul><li>Features of common stock </li></ul><ul><li>Determining common stock values </li></ul><ul><li>Preferred stock </li></ul>
- 2. Facts about common stock <ul><li>Represents ownership </li></ul><ul><li>Ownership implies control </li></ul><ul><li>Stockholders elect directors </li></ul><ul><li>Directors elect management </li></ul><ul><li>Management’s goal: Maximize the stock price </li></ul>
- 3. Intrinsic Value and Stock Price <ul><li>Outside investors, corporate insiders, and analysts use a variety of approaches to estimate a stock’s intrinsic value (P 0 ). </li></ul><ul><li>In equilibrium we assume that a stock’s price equals its intrinsic value. </li></ul><ul><ul><li>Outsiders estimate intrinsic value to help determine which stocks are attractive to buy and/or sell. </li></ul></ul><ul><ul><li>Stocks with a price below (above) its intrinsic value are undervalued ( overvalued ). </li></ul></ul>
- 4. Determinants of Intrinsic Value and Stock Prices (Figure 1-1)
- 5. Different approaches for estimating the intrinsic value of a common stock <ul><li>Dividend growth model </li></ul><ul><li>Corporate value model </li></ul><ul><li>Using the multiples of comparable firms </li></ul>
- 6. Dividend growth model <ul><li>Value of a stock is the present value of the future dividends expected to be generated by the stock. </li></ul>
- 7. Constant growth stock <ul><li>A stock whose dividends are expected to grow forever at a constant rate, g. </li></ul><ul><li>D 1 = D 0 (1+g) 1 </li></ul><ul><li>D 2 = D 0 (1+g) 2 </li></ul><ul><li>D t = D 0 (1+g) t </li></ul><ul><li>If g is constant, the dividend growth formula converges to: </li></ul>
- 8. Future dividends and their present values $ 0.25 Years (t) 0
- 9. What happens if g > r s ? <ul><li>If g > r s , the constant growth formula leads to a negative stock price, which does not make sense. </li></ul><ul><li>The constant growth model can only be used if: </li></ul><ul><ul><li>r s > g </li></ul></ul><ul><ul><li>g is expected to be constant forever </li></ul></ul>
- 10. If r RF = 7%, r M = 12%, and b = 1.2, what is the required rate of return on the firm’s stock? <ul><li>Use the SML to calculate the required rate of return (r s ): </li></ul><ul><li>r s = r RF + (r M – r RF )b </li></ul><ul><li>= 7% + (12% - 7%)1.2 </li></ul><ul><li>= 13% </li></ul>
- 11. If D 0 = $2 and g is a constant 6%, find the expected dividend stream for the next 3 years, and their PVs. 1.8761 1.7599 D 0 = 2.00 1.6509 r s = 13% g = 6% 0 1 2.247 2 2.382 3 2.12
- 12. What is the stock’s intrinsic value? <ul><li>Using the constant growth model: </li></ul>
- 13. What is the expected market price of the stock, one year from now? <ul><li>D 1 will have been paid out already. So, P 1 is the present value (as of year 1) of D 2 , D 3 , D 4 , etc. </li></ul><ul><li>Could also find expected P 1 as: </li></ul>
- 14. What are the expected dividend yield, capital gains yield, and total return during the first year? <ul><li>Dividend yield </li></ul><ul><ul><li>= D 1 / P 0 = $2.12 / $30.29 = 7.0% </li></ul></ul><ul><li>Capital gains yield </li></ul><ul><ul><li>= (P 1 – P 0 ) / P 0 </li></ul></ul><ul><ul><li>= ($32.10 - $30.29) / $30.29 = 6.0% </li></ul></ul><ul><li>Total return (r s ) </li></ul><ul><ul><li>= Dividend Yield + Capital Gains Yield </li></ul></ul><ul><ul><li>= 7.0% + 6.0% = 13.0% </li></ul></ul>
- 15. What would the expected price today be, if g = 0? <ul><li>The dividend stream would be a perpetuity. </li></ul>2.00 2.00 2.00 0 1 2 3 r s = 13% ...
- 16. Supernormal growth: What if g = 30% for 3 years before achieving long-run growth of 6%? <ul><li>Can no longer use just the constant growth model to find stock value. </li></ul><ul><li>However, the growth does become constant after 3 years. </li></ul>
- 17. Valuing common stock with nonconstant growth P ^ r s = 13% g = 30% g = 30% g = 30% g = 6% 0.06 $66.54 3 4.658 0.13 2.301 2.647 3.045 46.114 54.107 = P 0 0 1 2 3 4 D 0 = 2.00 2.600 3.380 4.394 ... 4.658
- 18. Find expected dividend and capital gains yields during the first and fourth years. <ul><li>Dividend yield (first year) </li></ul><ul><ul><li>= $2.60 / $54.11 = 4.81% </li></ul></ul><ul><li>Capital gains yield (first year) </li></ul><ul><ul><li>= 13.00% - 4.81% = 8.19% </li></ul></ul><ul><li>During nonconstant growth, dividend yield and capital gains yield are not constant, and capital gains yield ≠ g. </li></ul><ul><li>After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%. </li></ul>
- 19. Nonconstant growth: What if g = 0% for 3 years before long-run growth of 6%? r s = 13% g = 0% g = 0% g = 0% g = 6% 0.06 $30.29 P 3 2.12 0.13 1.77 1.57 1.39 20.99 25.72 = P 0 ^ 0 1 2 3 4 D 0 = 2.00 2.00 2.00 2.00 ... 2.12
- 20. Find expected dividend and capital gains yields during the first and fourth years. <ul><li>Dividend yield (first year) </li></ul><ul><ul><li>= $2.00 / $25.72 = 7.78% </li></ul></ul><ul><li>Capital gains yield (first year) </li></ul><ul><ul><li>= 13.00% - 7.78% = 5.22% </li></ul></ul><ul><li>After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%. </li></ul>
- 21. If the stock was expected to have negative growth (g = -6%), would anyone buy the stock, and what is its value? <ul><li>The firm still has earnings and pays dividends, even though they may be declining, they still have value. </li></ul>
- 22. Find expected annual dividend and capital gains yields. <ul><li>Capital gains yield </li></ul><ul><ul><li>= g = -6.00% </li></ul></ul><ul><li>Dividend yield </li></ul><ul><ul><li>= 13.00% - (-6.00%) = 19.00% </li></ul></ul><ul><li>Since the stock is experiencing constant growth, dividend yield and capital gains yield are constant. Dividend yield is sufficiently large (19%) to offset a negative capital gains. </li></ul>
- 23. Corporate value model <ul><li>Also called the free cash flow method. Suggests the value of the entire firm equals the present value of the firm’s free cash flows. </li></ul><ul><li>Remember, free cash flow is the firm’s after-tax operating income less the net capital investment </li></ul><ul><ul><li>FCF = NOPAT – Net capital investment </li></ul></ul>
- 24. Applying the corporate value model <ul><li>Find the market value (MV) of the firm, by finding the PV of the firm’s future FCFs. </li></ul><ul><li>Subtract MV of firm’s debt and preferred stock to get MV of common stock. </li></ul><ul><li>Divide MV of common stock by the number of shares outstanding to get intrinsic stock price (value). </li></ul>
- 25. Issues regarding the corporate value model <ul><li>Often preferred to the dividend growth model, especially when considering number of firms that don’t pay dividends or when dividends are hard to forecast. </li></ul><ul><li>Similar to dividend growth model, assumes at some point free cash flow will grow at a constant rate. </li></ul><ul><li>Terminal value (TV N ) represents value of firm at the point that growth becomes constant. </li></ul>
- 26. Given the long-run g FCF = 6%, and WACC of 10%, use the corporate value model to find the firm’s intrinsic value. g = 6% r = 10% 21.20 0 1 2 3 4 -5 10 20 ... 416.942 -4.545 8.264 15.026 398.197 21.20 530 = = TV 3 0.10 0.06 -
- 27. If the firm has $40 million in debt and has 10 million shares of stock, what is the firm’s intrinsic value per share? <ul><li>MV of equity = MV of firm – MV of debt </li></ul><ul><li>= $416.94 - $40 </li></ul><ul><li>= $376.94 million </li></ul><ul><li>Value per share = MV of equity / # of shares </li></ul><ul><li>= $376.94 / 10 </li></ul><ul><li>= $37.69 </li></ul>
- 28. Firm multiples method <ul><li>Analysts often use the following multiples to value stocks. </li></ul><ul><ul><li>P / E </li></ul></ul><ul><ul><li>P / CF </li></ul></ul><ul><ul><li>P / Sales </li></ul></ul><ul><li>EXAMPLE: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price. </li></ul>
- 29. What is market equilibrium? <ul><li>In equilibrium, stock prices are stable and there is no general tendency for people to buy versus to sell. </li></ul><ul><li>In equilibrium, two conditions hold: </li></ul><ul><ul><li>The current market stock price equals its intrinsic value (P 0 = P 0 ). </li></ul></ul><ul><ul><li>Expected returns must equal required returns. </li></ul></ul>^
- 30. Market equilibrium <ul><li>Expected returns are determined by estimating dividends and expected capital gains. </li></ul><ul><li>Required returns are determined by estimating risk and applying the CAPM. </li></ul>
- 31. How is market equilibrium established? <ul><li>If price is below intrinsic value … </li></ul><ul><ul><li>The current price (P 0 ) is “too low” and offers a bargain. </li></ul></ul><ul><ul><li>Buy orders will be greater than sell orders. </li></ul></ul><ul><ul><li>P 0 will be bid up until expected return equals required return. </li></ul></ul>
- 32. How are the equilibrium values determined? <ul><li>Are the equilibrium intrinsic value and expected return estimated by managers or are they determined by something else? </li></ul><ul><ul><li>Equilibrium levels are based on the market’s estimate of intrinsic value and the market’s required rate of return, which are both dependent upon the attitudes of the marginal investor. </li></ul></ul>
- 33. Preferred stock <ul><li>Hybrid security. </li></ul><ul><li>Like bonds, preferred stockholders receive a fixed dividend that must be paid before dividends are paid to common stockholders. </li></ul><ul><li>However, companies can omit preferred dividend payments without fear of pushing the firm into bankruptcy. </li></ul>
- 34. If preferred stock with an annual dividend of $5 sells for $50, what is the preferred stock’s expected return? <ul><li>V p = D / r p </li></ul><ul><li>$50 = $5 / r p </li></ul><ul><li>r p = $5 / $50 </li></ul><ul><li>= 0.10 = 10% </li></ul>^

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