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## CHAPTER 7 Valuation Models: Stocks

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**CHAPTER 7Valuation Models: Stocks**• Features of common stock • Determining common stock values • Security market equilibrium • Efficient markets • Preferred stock S05**Facts about Common Stock?**• Represents ownership? • Ownership implies control? • Agency problem • Stockholders elect directors? • Directors elect management? • Management’s goal: Maximize stock price.**What’s classified stock? How might classified stock be**used? • Classified stock has special provisions. • Could classify existing stock as founders’ shares, with voting rights but dividend restrictions. • New shares might be called “Class A” shares, with voting restrictions but full dividend rights.**What is tracking stock?**• The dividends of tracking stock are tied to a particular division, rather than the company as a whole. • Investors can separately value the divisions. • Its easier to compensate division managers with the tracking stock. • But tracking stock usually has no voting rights, and the financial disclosure for the division is not as regulated as for the company.**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 • Using the multiples of comparable firms • Free cash flow method (covered in Chapter 12)**Stock value = PV of dividends**D1 (1 + r) D2 (1 + r)2 D (1 + r) ^ P0 = + + . . . . ABSOLUTELY FUNDAMENTAL!**Future Dividend Stream:**D1 = D0(1 + g1) D2 = D1(1 + g2) . . .**WHAT IS A CONSTANT GROWTH STOCK? HOW ARE CONSTANT GROWTH**STOCKS VALUED? • A stock whose dividends grow at a constant rate. • In application, doesn’t mean that each year must have precisely a growth rate equal to the constant rate, but rather that our best guess is that that dividends will grow at a constant rate. Slide T7-14.**WHAT IS A CONSTANT GROWTH STOCK? HOW ARE CONSTANT GROWTH**STOCKS VALUED? • D1 = D0(1+g) • D2 = D1(1+g)=D0(1+g)2 • . • . • . • Dn = D0(1+g)n**If growth of dividends g is**constant, then: D1 rs - g D0 (1 + g) rs - g ^ P0 = = . • Model requires: • rs > g (otherwise results in negative price). • g constant forever.**$**0.25 0 Years (t)**What happens if g > rs?**• If rs< g, get negative stock price, which is nonsense. • We can’t use model unless (1) g rs and (2) g is expected to be constant forever. Because g must be a long-term growth rate, it cannot be rs.**Bon Temps Company: What is the required rate of return?** = 1.2. rRF = 7%. rM = 12%. Use SML equation to calculate rs: rs = rRF + (rM - rRF) = 7% + (12% - 7%)(1.2) rs = 13%.**What is the value of Bon Temps’ stock, P0, given rs =**13%, D0 = 2.00? Last dividend = $2.00; Dividend is expected to grow at 6%, i.e. g = 6%. . Hint: D0 = 2.00 (already paid). D1 = D0(1.06) = $2.12 D2 = D1(1.06) = $2.247 D3 = D2(1.06) = $2.382 T7-16,7-17.**What’s the stock’s market value? D0 = 2.00, rs = 13%, g**= 6%. Constant growth model: $2.12 $2.12 = = =$30.29. 0.13 - 0.06 0.07**What is Bon Temps’ value one year from now?**^ P1 = D2/(rs - g) = 2.247/0.07 = $32.10. ^ Note: Could also find P1 as follows: P1 = D2 /(rs - g) = D1 (1 + g)/(rs - g) = P0 (1 + g) = $30.29(1.06) = $32.10. So, price grows at rate = g. ^**P0 = D1/(rs - g) P1 = D2/(rs - g) BUT, D2 = D1( 1+g)So, P1 =**D1( 1+g)(rs - g)OR: P1 = P0( 1+g)**Find the expected dividend yield, capital gains yield, and**total return during the 1st, 2nd and 3rd years.**Find the expected dividend yield, capital gains yield, and**total return during the first year. Dn Pn - 1 Dividend yield in Year n = . ^ In 1st year: D1 P0 $2.12 $30.29 = = 7.00%. ^**Find the expected dividend yield, capital gains yield, and**total return during the first year. Dn Pn - 1 Dividend yield in Year n = . ^ In 2nd year: D2 P1 $2.247 $32.10 = = 7.00%. ^**So, in CGR models, Dividend and Price both grow at a rate =**g; consequently the dividend yield is: ?**So, in CGR models, Dividend and Price both grow at a rate =**g; consequently the dividend yield is: CONSTANT!**Capital gains yield in any Year n:**^ ^ Pn - Pn - 1 Pn - 1 = . ^ In 1 year: $32.10 - $30.29 $30.29 = 6%. In CGR models, Capital gains yield = g**Total yield = Div. yield + Cap. gains yield**= 7% + 6% = 13% = rs.**Find the total return during thefirst year.**• Total return = Dividend yield + Capital gains yield. • Total return = 7% + 6% = 13%. • Total return = 13% = rs. • For constant growth stock: Capital gains yield = 6% = g.**Rearrange model to rate of return form:**^ Then, rs = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%.**Points to Remember**• If a stock is in equilibrium, then: • Price = Value. (P0 = P0) • Required return = Expected return. (rs = rs) ^ ^**For any stock, the expected total return in any year equals**dividend yield + capital gains yield.**For constant growth stocks:**• Dividend yield is constant, D1/P0 = D2/P1 = D3/P2. • Capital gains yield is constant = g. (P1 - P0)/P0 = (P1/P0) - 1 = (1+g) - 1 = g. • Stock price grows at constant rate = g.**DIGRESSION: PRICE-EARNINGS RATIO**• Po = D1/(rs - g) • D1 = E1( 1-b) • Where b = retention ratio, and (1-b) = payout ratio.**PRICE-EARNINGS RATIO**• Po = E1(1-b)/(rs - g) • Po = (1-b) • E1 (rs - g) • A greater g implies a larger P/E.**WHAT WOULD THE STOCK PRICE OF BON TEMPS BE IF DIVIDENDS**HAVE ZERO GROWTH?**What would P0 be if g = 0?**The dividend stream would be a perpetuity. 0 1 2 3 rs=13% 2.00 2.00 2.00 PMT $2.00 ^ P0 = = = $15.38. r 0.13**Subnormal or Supernormal Growth**• Non-constant growth followed by constant growth in dividends. (e.g. after some point, best we can do is estimate a constant growth in dividends.) • Cannot use constant growth model alone • Value the nonconstant & constant growth periods separately**If we have supernormal growth of 30% for 3 years, then a**long-run constant g = 6%, what is P0? ^ 0rs=16% 1 2 3 4 g = 30% g = 30% g = 30% g = 6% D0 =$2.00**Nonconstant growth followed by constant**growth: 0 1 2 3 4 rs=13% g = 30% g = 30% g = 30% g = 6% D0 = 2.00 2.60 3.38 4.394 4.6576 2.3009 2.6470 3.0453 46.1135 ^ 54.1067 = P0 n.b. P3= D4/(rs - g)**What is the expected dividend and capital gains yields at t**= 0? At t = 4?**What is the expected dividend yield and capital gains yield**at t = 0? At t = 4? At t = 0: D1 $2.60 Dividend yield = = = 4.81%. P0 $54.11 CG Yield = 13.0% - 4.8% = 8.19%. (More…)**Check on Capital gains yield:**• Capital Gains yield = (P1 - P0)/P0 • P1= PV(D2) + PV(D3) + PV(P3) • = 3.38/1.13 + 4.394/(1.13)2 + 66.53/(1.13)2 = $58.53 • Capital Gains yield = (P1 - P0)/P0 = (58.53- 54.11)/54.11 = 8.19% 42**During nonconstant growth, dividend yield and capital gains**yield are not constant. • If current growth is greater than g, current capital gains yield is greater than g. • After t = 3, g = constant = 6%, so the t t = 4 capital gains gains yield = 6%. • Because rs = 13%, the t = 4 dividend yield = 13% - 6% = 7%.**At Year 4, stock is constant growth, so**CG yield4 = 6% = g. Div. yield4 = 7%.**$46.11**= 85.2%. $54.11 Is the stock price based onshort-term growth? • The current stock price is $54.11 • The PV of dividends beyond year 3 is $66.53/(1.13)^3 (P3 discounted back to t = 0) =46.11. • The percentage of stock price due to “long-term” dividends is:**If most of a stock’s value is due to long-term cash flows,**why do so many managers focus on quarterly earnings? • Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This would affect the current stock price. • Sometimes managers have bonuses (or options) tied to quarterly earnings.