Chapter Stocks and their Valuation Features of Common Stock Common

Chapter 7 – Stocks and their Valuation Features of Common Stock Common Stock Valuation Efficient Markets Preferred Stock Common Stock: Owners, Directors, and Managers Represents ownership. Ownership implies control. Stockholders elect directors. Directors hire management. Since managers are “agents” of shareholders, their goal should be: Maximize stock price. When is a stock sale an initial public offering (IPO)? A firm “goes public” through an IPO when the stock is first offered to the public. Prior to an IPO, shares are typically owned by the firm’s managers, key employees, and, in many situations, venture capital providers. What is a seasoned equity offering (SEO)? A seasoned equity offering occurs when a company with public stock issues additional shares. After an IPO or SEO, the stock trades in the secondary market, such as the NYSE or Nasdaq. Different Approaches for Valuing Common Stock Dividend growth model Constant Growth Two-Stage Growth Model Three-Stage Growth Model Using the multiples of comparable firms Valuing Common Stocks The first question to ask when attempting to value any security is, “What are the expected cash flows?”. In the case of common stocks, there are two types of cash flows: dividends the amount received at the time of the sale (increase in intrinsic value) Valuing Common Stocks Of course in a real-world example we wouldn’t know for sure what the dividends and future selling price are going to be. Companies tend to have somewhat stable dividend policies, so it isn’t such a leap to be estimating future dividends. However advanced knowledge of future stock prices is a different story. Stock prices fluctuate on a daily basis, so trying to predict a stock price years from now would be near impossible. The Constant-Growth Dividend Discount Model To eliminate this problem of uncertainty, we can make certain assumptions: The dividend will change at a constant rate. Therefore, knowing the first dividend allows us to know all of the future dividends. We have an infinite holding period; we will never sell the stock. The Constant-Growth Dividend Discount Model (the Gordon Model) is found by taking the present value of future dividends plus the present value of the selling price, however since the stock will never be sold, the model becomes: N P0 = Σ t=1 Dt (1+g) (1 + rs)t Where P0 is the price of the common stock, the Dt is the dividend in period t, and rs is the required return. t ranges from 1 to infinity since the stock is never sold. The Constant-Growth Dividend Discount Model Because the dividends are growing at a constant rate, they can be expressed as a function of the most recently paid out dividend: N P0 = Σ t=1 Dt (1+g) (1 + rs)t This can be restated in closed form: D1 rs - g Assume beta = 1.2, rRF = 7%, and RPM = 5%. What is the required rate of return on the firm’s stock? Use the SML to calculate rs: rs = rRF + (RPM)bFirm = 7% + (5%) (1.2) = 13%. D0 was $2.00 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. rs = 13%. 0 g=6% 1 2 2.2472 3 2.3820 4 D0=2.00 2.12 13% 1.8761 1.7599 1.6508 What’s the stock’s market value? D0 = 2.00, rs = 13%, g = 6%. Constant growth model: ˆ D (1 + g ) = D1 P0 = 0 rs − g rs − g = $2.12 $2.12 = $30.29. 0.07 0.13 - 0.06 What is the stock’s market value one year ^ from now, P1? D1 will have been paid, so expected dividends are D2, D3, D4 and so on. Thus, D2 P1 = rs - g = $2.2427 = $32.10 0.07 Find the expected dividend yield and capital gains yield during the first year. Dividend yield = $2.12 D1 = = 7.0%. $30.29 P0 ^ P1 - P0 $32.10 - $30.29 CG Yield = = $30.29 P0 = 6.0%. Find the total return during the first year. Total return = Dividend yield + Capital gains yield. Total return = 7% + 6% = 13%. Total return = 13% = rs (found from the SML). For constant growth stock: Capital gains yield = 6% = g. Rearrange model to rate of return form: ˆ P0 = ∧ D1 D to r s = 1 + g . rs − g P0 ^ Then, rs = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%. The Constant-Growth Dividend Discount Model Another Example Suppose you are interested in purchasing a share of GM common stock. GM has decided to finance a new product (an electric car) which they plan on launching in three years, so they have decided not to pay any dividends for the next three years. After three years, GM is expected to pay $1.50 per share (beginning in the fourth year from now). That dividend is expected to grow at 7% per year. If your required return is 15% per year, what is the maximum amount that you should be willing to pay for a share of ABC common stock? We must first find the value of some future time period. For this problem, the future time period we choose is arbitrary as long as it is period 3 or later: P3 = D4 = 1.50 rs – g 0.15 – 0.07 = $18.75 So we know that the stock will be worth $18.75 per share three years from today. The Constant-Growth Dividend Discount Model Another Example We know that the stock will be worth $18.75 per share three years from today. Remembering that the value of the stock is the present value of its cash flows, the value as of today must be: P0 = 18.75 1.153 = $12.33 We could try doing this by beginning the valuation process at period 5 instead of 3, and the result should be approximately the same (might differ slightly due to rounding). Alternatively, you can use the PV function for this second part of the problem: 15% would be the RATE, 3 would be the NPER, and the FV would be your answer from the first part of the problem ($18.75). Your result would be negative to represent a cash outflow if you were to buy the stock now. What happens if g > rs? ˆ P0 = D1 requires rs > g . rs − g If rs< g, get negative stock price, which is nonsense. We can’t use this model unless: g < rs g is expected to be constant forever Non-Constant Growth Rates Assuming that the dividends will grow at a constant rate indefinitely is not very realistic. Other valuation models have been developed that are more realistic. A two-stage growth model allows for a period of above normal (supernormal) growth followed by a period of constant growth. A three-stage growth model allows for a gradual decline into the constant growth stage. Both of these models are still present value calculations, but they change the pattern of the future cash flows. The Two-Stage (Non-Constant) Growth Model A two-stage valuation model allows for the dividend to grow at one rate for several periods and then to grow at a (usually) slower rate from that point on. This is realistic because growth is unlikely to continue forever. Usually companies mature and find that their earnings growth slows (so the dividend growth rate slows as well). The two-stage growth model assumes that this transition will occur instantaneously at some point. The Two-Stage Growth Model Assume: g1 is the dividend growth rate from period 1 to n and g2 is the dividend growth rate for the remainder of time. Assume D0 does not equal 0 and g1 does not equal rs and g2 < rs: P0 = D0 (1+g1) 1 - 1+g1 rs – g 1 1 + rs n + D0 (1+g1)n (1+g2) rs - g 2 (1 + rs)n Present Value of the first n dividends growing at a rate of g1 The present value of all of the remaining dividends growing at a rate of g2 The Two-Stage Growth Model – An Example Due to an immensely popular new product, analysts expect Sirius Satellite Radio’s earnings and dividends to grow at a rate of 15% per year for the next five years. After that, analysts expect the growth rate to decline to 8% per year as competitors produce similar products. If Sirius recently paid a dividend of $0.35 and your required return is 12%, what is the value of the stock today? P0 = D0 (1+g1) 1 - 1+g1 rs – g 1 1 + rs n + D0 (1+g1)n (1+g2) rs - g 2 (1 + rs)n P0 = $0.35, g1 = 15%, g2 = 8%, rs = 12% P0 = .35 (1.15) .12 – .15 1 - 1.15 1.12 5 + .35 (1.15)5 (1.08) .12 - .08 (1.12)5 P0 = $12.68 The Two-Stage Growth Model – Performed in Excel There is no built-in function in Excel to do this complex calculation. Timothy Mayes and Todd Shank, the authors of a textbook, have created a macro to do the work. Their macro is called: FAME_TwoStageValue. The macro is defined as: FAME_TwoStageValue(DIV1,REQRATE, GROWTHRATE1, GROWTHRATE2, G1PERIODS) Where DIV1 = dividend in period 1 REQRATE = required rate of return GROWTHRATE1 = g1 GROWTHRATE2 = g2 G1PERIODS = length of the first period Open the FAMEFNCS.XLS file (download from the course website) to use this macro. Then choose the function from the Insert Function Box under User-Defined functions. The Three-Stage Growth Model The three-stage growth model is very similar to the two-stage model except that the three-stage model assumes that the change in growth rates assumes a linear decline rather than an instantaneous transition. This is a more realistic assumption as the growth rate will likely decline slowly. P0 = D0 (1+g1) rs – g 2 (1+g2) + n1 + n2 2 (g1 – g2) The term in brackets represents a factor by which the constant growth model must be multiplied to account for the higher initial growth rates. N2 is the number of years until the growth rate becomes constant. The Three-Stage Growth Model – An Example We can use the example from the two-stage model (Sirius) but here the growth rate is transitioning from 15% to 8% over a three year period. That makes the time in n1 = 5 years and the time in until constant growth (n2) = 8 years. P0 = 0.35 0.12 – 0.08 (1.08) + (5+8)/2 (0.15 – 0.08) P0 = $13.43 The Three-Stage Growth Model – Performed in Excel There is no built-in function in Excel to do this complex calculation. Again, the authors of that text have created a macro to do the work. Their Macro is called: FAME_ThreeStageValue and it is defined as: FAME_ThreeStageValue(DIV1,REQRATE, GROWTHRATE1, GROWTHRATE2, G1PERIODS, TRANSPERIODS) Where DIV1 = dividend in period 1 REQRATE = required rate of return GROWTHRATE1 = g1 GROWTHRATE2 = g2 G1PERIODS = length of the first period TRANSPERIODS = length of the transition period between growth rates Open the FAMEFNCS.XLS file (download from the website) to use this macro. Then choose the function from the Insert Function Box under User-Defined functions. Why are stock prices volatile? ^ P = r D1g 0 s− rs = rRF + (RPM)bi could change. Inflation expectations (change rRF) Risk aversion (∆ in risk premium) Company risk (bi) g could change. Stock value vs. changes in rs and g D1 = $2, rs = 10%, and g = 5%: P0 = D1 / (rs-g) = $2 / (0.10 - 0.05) = $40. What if rs or g change? g g g 4% 5% 6% 40.00 50.00 66.67 33.33 40.00 50.00 28.57 33.33 40.00 rs 9% 10% 11% Are volatile stock prices consistent with rational pricing? Small changes in expected g and rs cause large changes in stock prices. As new information arrives, investors continually update their estimates of g and rs. If stock prices aren’t volatile, then this means there isn’t a good flow of information. What is market equilibrium? In equilibrium, stock prices are stable. There is no general tendency for people to buy versus to sell. The expected price, P, must equal the actual price, P. In other words, the fundamental value must be the same as the price. (More…) ^ In equilibrium, expected returns must equal required returns: ^ rs = D1/P0 + g = rs = rRF + (rM - rRF)b. How is equilibrium established? ^ ^ If rs = D1 + g > rs, then P0 is “too low.” P0 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, and D1/P0 falls until ^ D1/P0 + g = rs = rs. Idea for Stock Picking Strategy One can check a stock’s price using the appropriate dividend growth model and the required return from the SML. Compare the price to the actual stock’s price in the market. If the dividend model’s price > than the market price, this may be a buying opportunity. Example D1 rs – g XOM stock: Step 1 – Find rs by using the SML equation (looking up the risk free rate, return on the market, and beta) Step 2 – Look up the dividend growth rate and most recently paid annual dividend Step 3 - Find the price under the constant growth model To find Risk Free Rate: http://www.bankrate.com/brm/ratewatch/treasury.asp To find beta and Recent Dividend: http://moneycentral.msn.com/detail/stock_quote?Symbol=XOM Dividend Growth Rate & S&P rate: http://moneycentral.msn.com/investor/invsub/results/compare.asp?Symbol=xom Alternatively you can Compare Rates of Return rather than Price rs = D1 + g P0 XOM stock: Step 1 – Find SML’s rs by looking up the risk free rate, return on the market, and beta Step 2 – Look up the dividend growth rate, most recently paid annual dividend, and the current market price. Step 3 – Compare the SML’s required return to that of the Constant Growth Dividend Discount Model above. Market Multiple Analysis Using the Stock Price Multiples to Estimate Stock Price Analysts often use the P/E multiple (the price per share divided by the earnings per share) Example: Estimate the average P/E ratio of comparable firms. This is the P/E multiple. Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price. Using Entity Multiples to Estimate Stock Price The entity value (V) is: the market value of equity (# shares of stock multiplied by the price per share) plus the value of debt. Pick a measure, such as EBITDA, Sales, Customers, Eyeballs, etc. Calculate the average entity ratio for a sample of comparable firms. For example, V/EBITDA V/Customers Using Entity Multiples (Continued) Take the entity value (V) of the firm in question (total value of the firm). Subtract the firm’s debt to get the total value of equity. Divide by the number of shares to get the price per share. P/E Multiple Approach : An Example XOM stock: Step 1 – Calculate the Earnings Per Share (using Net Income and # shares outstanding) Step 2 – Find the P/E Ratio for a similar company or industry average Step 3 – Multiply this average P/E Ratio by the EPS for XOM stock If actual price < the Multiple Approach Price there is a potential buying opportunity. Alternatively, calculate the P/E ratio for you stock and compare it to the industry average. If your stock’s P/E is lower than the industry, there is a potential buying opportunity. Problems with Market Multiple Methods It is often hard to find comparable firms. The average ratio for the sample of comparable firms often has a wide range. 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? What’s the Efficient Market Hypothesis (EMH)? Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or inside information. (More…) 1. Weak-form EMH: 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. 2. Semistrong-form EMH: 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. 3. Strong-form EMH: 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. Markets are generally efficient because: 1. 100,000 or so trained analysts--MBAs, CFAs, and PhDs--work for firms like Fidelity, Merrill, Morgan, and Prudential. 2. These analysts have similar access to data and megabucks to invest. 3. Thus, news is reflected in P0 almost instantaneously. Preferred Stock Valuation Preferred stock is a hybrid security. It represents ownership on assets of the firm, like common stock. But it also generally pays a fixed dividend payment each period, like a bond. Preferred stock is actually easier to value than common stock or bonds. Consider the following example: The XYZ Corporation has issued preferred stock which pays a 10% annual dividend on its $50 par value. If your required rate of return is 12%, what is the maximum amount that you should be willing to pay for a share of XYZ preferred? As usual, the first step is to determine the cash flows. Here we have an infinite stream of dividends which are 10% of the par value. That is, we have a perpetual annuity, or perpetuity, of $5 per year. Preferred Stock Valuation Preferred stock pays a dividend and never matures, just like common stock. The only difference is that the dividends never change (the growth rate is 0). So: VP = D0 (1+g) rP – g Since g = 0: VP = D0 rP Preferred Stock Valuation Alternatively, we can value a perpetuity as if it were a bond with an infinite life: VP = D 1- (1/ (1+ rP)∞) rP + FV / (1+ rP)∞ Any number greater than 1 raised to infinity = infinity and any number divided by infinity is effectively = 0, so the equation reduces to: VP = D0 rP If we treat preferred stock as common stock or bonds we arrive at exactly the same valuation formula. To fins the value of a share of preferred stock, we simply divide the dividend payment by our required rate of return. Preferred Stock Valuation So, considering our example: The XYZ Corporation has issued preferred stock which pays a 10% annual dividend on its $50 par value. If your required rate of return is 12%, what is the maximum amount that you should be willing to pay for a share of XYZ preferred? VP = 5 .12 = $41.66