BA 180-1Stock Valuation, Chapter 8 1 Introduction to Stock Valuation By now you have seen that the value of an asset depends on the magnitude, timing, and risk of the cash flows. Equity securities have the feature that the cash flows are uncertain. We will also need to account for risk more carefully. Remember that we are interested in cash flows, not accounting earnings. By now you have seen that the value of an asset depends on the magnitude, timing, and risk of the cash flows. Equity securities have the feature that the cash flows are uncertain. We will also need to account for risk more carefully. Remember that we are interested in cash flows, not accounting earnings.

BA 180-1Stock Valuation, Chapter 8 2 Features of Common Stock Residual claimants Limited Liability Voting Rights Eligible for dividends, but no guarantee Residual claimants Limited Liability Voting Rights Eligible for dividends, but no guarantee

BA 180-1Stock Valuation, Chapter 8 3 Valuation Approach To determine the value of a stock we need to know something about the cash flows. Let’s start by assuming we will hold the stock for one year. If we pay P 0 today and get a dividend D 1 when we sell for P 1 we have: It seems that both the future stock price and the dividend matter. To determine the value of a stock we need to know something about the cash flows. Let’s start by assuming we will hold the stock for one year. If we pay P 0 today and get a dividend D 1 when we sell for P 1 we have: It seems that both the future stock price and the dividend matter.

BA 180-1Stock Valuation, Chapter 8 4 Valuation Approach Now step forward to time 1 Substitute into the Time 0 price Repeating this substitution, Now step forward to time 1 Substitute into the Time 0 price Repeating this substitution,

BA 180-1Stock Valuation, Chapter 8 5 Zero Dividend Firms If a firm is not currently paying dividends, does this mean the stock is valueless?  NO: Just because a firm is not paying dividends now does not mean it will never pay dividends in the future.  If you knew a stock would never pay dividends (or some other form of distribution) it would be worthless. Why would a firm not pay dividends?  Investing the cash in profitable opportunities.  This will make future dividends even larger. If a firm is not currently paying dividends, does this mean the stock is valueless?  NO: Just because a firm is not paying dividends now does not mean it will never pay dividends in the future.  If you knew a stock would never pay dividends (or some other form of distribution) it would be worthless. Why would a firm not pay dividends?  Investing the cash in profitable opportunities.  This will make future dividends even larger.

BA 180-1Stock Valuation, Chapter 8 6 Special Cases in Stock Valuation There are certain dividend patterns that make the application of our valuation formula easier  Constant Dividends  Constant Growth in Dividends  Supernormal Dividend Growth For the third case we split the problem into pieces and use the tools we have already learned. There are certain dividend patterns that make the application of our valuation formula easier  Constant Dividends  Constant Growth in Dividends  Supernormal Dividend Growth For the third case we split the problem into pieces and use the tools we have already learned.

BA 180-1Stock Valuation, Chapter 8 7 Constant Dividends Constant Dividend is simply a perpetuity: This is based on getting the first dividend payment at the end of period. r is effective rate of return per period. Again, we should use rate ‘matching’ frequency of dividend payment. Constant Dividend is simply a perpetuity: This is based on getting the first dividend payment at the end of period. r is effective rate of return per period. Again, we should use rate ‘matching’ frequency of dividend payment.

BA 180-1Stock Valuation, Chapter 8 8 Constant Dividends Example Coca Cola pays and will pay dividends of $0.56 per share end of each year. Using a 15% yearly rate of return, what is the value of a share? P 0 = D/r = 0.56/15% =$3.73 Coca Cola pays and will pay dividends of $0.56 per share end of each year. Using a 15% yearly rate of return, what is the value of a share? P 0 = D/r = 0.56/15% =$3.73

BA 180-1Stock Valuation, Chapter 8 9 Constant Dividend Growth Now suppose that the Dividends grow at a constant rate g per period. Here we have a perpetuity with a constant growth rate: Remember this only works if r > g. Now suppose that the Dividends grow at a constant rate g per period. Here we have a perpetuity with a constant growth rate: Remember this only works if r > g.

BA 180-1Stock Valuation, Chapter 8 10 Constant Dividend Growth Example Historically, Coca Cola has annual dividend growth of 13%. What is the value of a share with last dividend $0.56 and constant future growth equal to the historic average? (assume the required rate of return 15% per year) G = 13% D 0 =0.56 D 1 = (1+g) D 0 =(1+13%) 0.56 = P 0 = D 1 /(r-g) = $31.64 Historically, Coca Cola has annual dividend growth of 13%. What is the value of a share with last dividend $0.56 and constant future growth equal to the historic average? (assume the required rate of return 15% per year) G = 13% D 0 =0.56 D 1 = (1+g) D 0 =(1+13%) 0.56 = P 0 = D 1 /(r-g) = $31.64

BA 180-1Stock Valuation, Chapter 8 11 Supernormal Dividend Growth If the expected dividend growth rate is higher than the discount rate (g > r), our perpetuity formula does not work. This kind of growth is not sustainable but may occur for some period of time. We break the problem into pieces, value them separately, then add them together.  Value the “normal” growth period (g < r) with existing formulas.  Value the supernormal period (g > r) by simply calculating the present value of each cash flow and adding them up. If the expected dividend growth rate is higher than the discount rate (g > r), our perpetuity formula does not work. This kind of growth is not sustainable but may occur for some period of time. We break the problem into pieces, value them separately, then add them together.  Value the “normal” growth period (g < r) with existing formulas.  Value the supernormal period (g > r) by simply calculating the present value of each cash flow and adding them up.

BA 180-1Stock Valuation, Chapter 8 12 Supernormal Growth Example Coca Cola had 18% dividend growth over the last 5 years. Assume this growth continues for the next 5 years, then reverts to 13% growth. D 1 = How much is the stock worth (what is P 0 )? (assume the rate of return 15% per year)

BA 180-1Stock Valuation, Chapter 8 13 The Rate of Return We have recognized that the riskiness of the cash flows affects the value of an asset. The rate of return is what makes this adjustment.  Riskier cash flows require a higher return.  Risky cash flows are worth less than safe ones. Where do we get the Rate of Return?  Capital Asset Pricing Model (CAPM) or other model  Historical or Peer Group We have recognized that the riskiness of the cash flows affects the value of an asset. The rate of return is what makes this adjustment.  Riskier cash flows require a higher return.  Risky cash flows are worth less than safe ones. Where do we get the Rate of Return?  Capital Asset Pricing Model (CAPM) or other model  Historical or Peer Group

BA 180-1Stock Valuation, Chapter 8 14 A Warning Determination of the rate of return is far from perfect. Be aware that the answer to any present value analysis is highly sensitive to the rate of return. In the case of stocks, the cash flows themselves are also very difficult to forecast accurately. DO NOT OVER-EMPHASIZE THE ANSWER YOU GET FROM A STOCK VALUATION MODEL. IF IT IS DIFFERENT FROM THE MARKET PRICE, YOUR ASSUMPTIONS ARE PROBABLY NOT GOOD. Determination of the rate of return is far from perfect. Be aware that the answer to any present value analysis is highly sensitive to the rate of return. In the case of stocks, the cash flows themselves are also very difficult to forecast accurately. DO NOT OVER-EMPHASIZE THE ANSWER YOU GET FROM A STOCK VALUATION MODEL. IF IT IS DIFFERENT FROM THE MARKET PRICE, YOUR ASSUMPTIONS ARE PROBABLY NOT GOOD.

BA 180-1Stock Valuation, Chapter 8 15 Example 1: Stable Growth A mature company paid a $2.10 dividend this year (=D 0 ) and you expect the future dividends to grow 4% annually. What is the value of the stock if the market demand a 10% rate of return?

BA 180-1Stock Valuation, Chapter 8 16 Example 2: Technology Company Suppose a tech company will pay no dividends for the next five years. It will then (t=6) start paying a $1 dividend which will increase 15% annually for the next five years before it reaches its perpetual growth rate of 10%. How much is a share worth if the market demand a 15% rate of return?

BA 180-1Stock Valuation, Chapter 8 17 Example 3: Finding the Dividend A stock is trading for $75 per share on the basis of 6% dividend growth and a 15% rate of return. What must the current (time zero) dividend be on the stock?

BA 180-1Stock Valuation, Chapter 8 18 Example 4: Negative Growth A company in a declining industry currently pays a $5 dividend. Because the industry prospects are poor, you expect a negative growth of 10% annually. With a 10% rate of return, what is the value of a share?