1. 9-1 CHAPTER 9 Stocks and Their Valuation Methods for valuing common stock Preferred stock We WILL cover Sections 9-1 through 9-5 (pages 269-283) and Section 9-8 (Preferred Stock, pages 291-292). In the interest of time, we will NOT cover (and will NOT be on the final exam) Sections 9-6 and 9-7. Practice problems: Please work end of Chapter 9: 2,3,6,8,10,11, and 13.

2. 9-2 Different approaches for estimating what you think a share of a company’s common stock is worth Dividend growth model Corporate value model (We’ll skip this.) Using the multiples of comparable firms Note: The value you put on the stock could be different from its current price in the market. Example: Suppose IBM is trading for $84/share. But you estimate it is worth $100/share. Based on that belief, you might buy IBM stock. You’d be betting others would figure out you are right and buy IBM stock. If you are right, as others buy IBM, the price could increase.

3. 9-3 Dividend growth model: This is a popular method for estimating the value or worth of common Value of a stock (in $/share) is the present value of the future dividends expected to be generated by the stock. P 0 is price you estimate it is worth now. D t is the dividend ($/share) you expect the company will pay shareholders at time “t”. r s is the rate of return you require to invest in the stock.

4. 9-4 If we believe the dividend will grow at a constant rate, we can use the “Constant Growth” version of the Dividend Growth Model A stock whose dividends are expected to grow forever at a constant rate, g. 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, the dividend growth formula converges to (i.e., approximately equals):

5. 9-5 Constant Growth Model (continued): What if growth (g) > required return (r s )? If g > r s, the constant growth formula leads to a negative stock price, which does not make sense. The constant growth model can only be used if: r s > g g is expected to be constant forever

6. 9-6 CAPM/Security Market Line/Beta approach for estimating required rate of return (r s ): If r RF = 7%, r M = 12%, and beta (b) = 1.2, what is the required rate of return on the firm’s stock? r s = r RF + (r M – r RF )(b) = 7% + (12% - 7%)(1.2) = 13%

7. 9-7 Suppose D 0 = $2 (paid now) and you believe g will be a constant 6%. The PVs of the dividends today plus first 3 years are: 1.8761 1.7599 D 0 = 2.00 1.6509 r s = 13% g = 6% 01 2.247 2 2.382 3 2.12

8. 9-8 Suppose D 0 = $2 (paid yesterday) and you believe g will be a constant 6%. What is the stock’s intrinsic value? (We exclude D 0.) Using the constant growth model:

9. 9-9 What is the expected market price of the stock, one year from now? We assume 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. Could also find expected P 1 as:

10. 9-10 What would we estimate for the value of the stock if g = 0? The dividend stream would be a perpetuity. 2.00 0123 r s = 13%...

11. 9-11 If the stock was expected to have negative growth (g = -6%), would anyone buy the stock, and what is its value? The firm still has earnings and pays dividends, even though they may be declining, they still have value.

12. 9-12 Firm multiples method using financial ratios Analysts often use the following multiples to value stocks. P / E P / CF P / Sales EXAMPLE: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price. Chartered Financial Analysts often use include this analysis as part of their valuations of stock. They themselves often refer to the multiples approach as more of an art than a science.

13. 9-13 Use a little algebra to rewrite the Constant Growth Model with required return on the left- hand side of the equation: Multiply both sides of the equation by (r s - g), Divide both sides by P 0, and Add g to both sides. This expression says that if we expect Dividends will grow at constant growth rate g and we pay P 0, we expect our return (per period) will equal r s.

14. 9-14 What is market equilibrium (using the Constant Growth Model and CAPM/SML/Beta approach)? In equilibrium, stock prices are stable and there is no general tendency for people to buy versus to sell. In equilibrium, two conditions hold: The current market stock price equals what the “marginal investor” thinks it is worth. Expected returns must equal required returns.

15. 9-15 Preferred stock Hybrid security. Like bonds, preferred stockholders receive a fixed dividend that must be paid before dividends are paid to common stockholders. However, companies can omit preferred dividend payments without fear of pushing the firm into bankruptcy.

16. 9-16 If preferred stock with an annual dividend of $5 sells for $50, what is the preferred stock’s expected return? (This is just a perpetuity.) V p = D / r p $50= $5 / r p r p = $5 / $50 = 0.10 = 10% ^