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.