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# Stock Valuation (ch 8) 1

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### Stock Valuation (ch 8) 1

1. 1. <ul><li>Common Stock Valuation </li></ul><ul><li>Features of Common and Preferred Stocks </li></ul><ul><li>The Stock Market </li></ul>Stock Valuation
2. 2. 1. Common Stock Valuation <ul><li>In 1938, John Burr Williams postulated what has become the fundamental theory of valuation : </li></ul><ul><li>The value today of any financial asset equals the present value of all of its future cash flows. </li></ul><ul><li>For common stocks, this implies the following (the general case): </li></ul><ul><li> D 1 P 1 D 2 P 2 </li></ul><ul><li>P 0 = + and P 1 = + </li></ul><ul><li>(1 + R) 1 (1 + R) 1 (1 + R) 1 (1 + R) 1 </li></ul><ul><li>substituting for P 1 gives </li></ul><ul><li> D 1 D 2 P 2 </li></ul><ul><li>P 0 = + + . Continuing to substitute, we obtain </li></ul><ul><li>(1 + R) 1 (1 + R) 2 (1 + R) 2 </li></ul><ul><li> D 1 D 2 D 3 D 4 </li></ul><ul><li>P 0 = + + + + … </li></ul><ul><li>(1 + R) 1 (1 + R) 2 (1 + R) 3 (1 + R) 4 </li></ul>
3. 3. Common Stock Valuation: The Zero Growth Case <ul><li>According to the fundamental theory of value, the value of a financial asset at any point in time equals the present value of all future dividends. </li></ul><ul><li>If all future dividends are the same, the present value of the dividend stream constitutes a perpetuity . </li></ul><ul><li>The present value of a perpetuity is equal to </li></ul><ul><li>C/r or, in this case, D 1 /R. </li></ul><ul><li>Question: Cooper, Inc. common stock currently pays a \$1.00 dividend, which is expected to remain constant forever. If the required return on Cooper stock is 10%, what should the stock sell for today? </li></ul><ul><li>Answer: P 0 = </li></ul>
4. 4. Common Stock Valuation: The Constant Growth Case <ul><li>In reality, investors generally expect the firm (and the dividends it pays) to grow over time. How do we value a stock when each dividend differs from the one preceding it? </li></ul><ul><li>As long as the rate of change from one period to the next, g , is constant, we can apply the growing perpetuity model: </li></ul><ul><li> D 1 D 2 D 3 D 0 (1+g) 1 D 0 (1+g) 2 D 0 (1+g) 3 </li></ul><ul><li>P 0 = + + + … = + + + ... </li></ul><ul><li>(1 + R) 1 (1 + R) 2 (1 + R) 3 (1 + R) 1 (1 + R) 2 (1 + R) 3 </li></ul><ul><li>D 0 (1 + g ) D 1 </li></ul><ul><li>P 0 = = . </li></ul><ul><li>R - g R- g </li></ul><ul><li>Now assume that D 1 = \$1.00, r = 10%, but dividends are expected to increase by 5% annually. What should the stock sell for today? </li></ul>
5. 5. Common Stock Valuation: The Constant Growth Case <ul><li>Answer: The equilibrium value of this constant-growth stock is </li></ul><ul><li> D 1 </li></ul><ul><li> = = \$ </li></ul><ul><li>R - g </li></ul><ul><li>Question: What would the value of the stock be if the growth rate were only 3%? </li></ul><ul><li>Answer: </li></ul><ul><li> D 1 </li></ul><ul><li> = = \$ </li></ul><ul><li>R - g </li></ul><ul><li>Why does a lower growth rate result in a lower value? </li></ul>
6. 6. Stock Price Sensitivity to Dividend Growth, g 0 2% 4% 6% 8% 10% 50 45 40 35 30 25 20 Stock price (\$) Dividend growth rate, g D 1 = \$1 Required return, R , = 12% 15 10 5
7. 7. Common Stock Valuation - The Nonconstant Growth Case <ul><li>For many firms (especially those in new or high-tech industries), dividends are low but are expected to grow rapidly. As product markets mature, the dividend growth rate is then expected to slow to a “steady state” rate. How should stocks such as these be valued? </li></ul><ul><li>Answer: We return to the fundamental theory of value - the value today equals the present value of all future cash flows. </li></ul><ul><li>Put another way, the nonconstant growth model suggests that </li></ul><ul><li>P 0 = present value of dividends in the nonconstant growth period(s) </li></ul><ul><li>+ present value of dividends in the “steady state” period. </li></ul>
8. 8. See Examples in page 223 If a firm is not paying dividend currently and it expects to pay \$0.50/share dividend in year 5. Dividend will grow by 10% since then. The required rate of return is 20%. What is the price of the stock today? the starting point is year 0 while first dividend is in year 5. Let’s ignore the period from year 0 to year 5. Assuming year 5 is a new year 0. What would be the stock price of the new stock in the setup: P(5) = D(5)+D(5)*(1+g)/(R-g) = 0.5+0.5*1.1/(.2-.1)=6.0 P(0) = P(5)/(1+R)^5 = 6.0/1.2^5=2.41 Go through the next example (figure 8.1, p223) Go through Table 8.1
9. 9. Example 2 : A company has been growing at a rate of 30% for 3 years and then drops to 10% per year. Its total dividend just paid were \$5 million and required rate of return is 20%. If the growth rate remains constant indefinitely, what is the total value of the stock?
10. 10. The Required Return <ul><li>The required return, r , can be written as the sum of two things: </li></ul><ul><li>R = D 1 /P 0 + g </li></ul><ul><li>where D 1 /P 0 is the dividend yield and g is the capital gains yield (which is the same thing </li></ul><ul><li>as the growth rate in dividends for the steady growth case). </li></ul>
11. 11. 2. Features of Common and Preferred Stock <ul><li>Features of Common Stock </li></ul><ul><li>The right to vote </li></ul><ul><li>The right to share proportionally in dividends paid </li></ul><ul><li>The right to share proportionally in assets remaining after liabilities have been paid, in event of a liquidation </li></ul><ul><li>The preemptive right </li></ul><ul><li>Features of Preferred Stock </li></ul><ul><li>Preferences over common stock - dividends, liquidation </li></ul><ul><li>Dividend arrearages </li></ul><ul><li>Stated/liquidating value </li></ul>
12. 12. 3. The Stock Markets <ul><li>Primary vs. secondary markets </li></ul><ul><li>New York Stock Exchange (NYSE) Operations </li></ul><ul><li>Exchange members </li></ul><ul><li>Commission brokers </li></ul><ul><li>Specialists </li></ul><ul><li>Floor brokers </li></ul><ul><li>Floor traders </li></ul><ul><li>Stated/liquidating value </li></ul><ul><li>Nasdaq Operations </li></ul><ul><li>Dealers vs. brokers </li></ul><ul><li>Multiple market makers </li></ul>