1. CHAPTER 8 Stocks and Their Valuation
Features of common stock
Determining common stock values
Efficient markets
Preferred stock

2. Facts about common stock
Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the stock price

3. Types of stock market transactions
Secondary market
Primary market
Initial public offering market (“going public”)

4. Different approaches for valuing common stock
Dividend growth model
Corporate value model
Using the multiples of comparable firms

5. Terms used in stock valuation
Dt = Dividend expected to receive at the end of year t.
Po = Actual market price of the stock today
= Expected price of the stock at the end of year t
=Intrinsic or theoretical value

6. Terms used in stock valuation
g= Expected growth rate in dividends.
= Required rate of return
= Expected rate of return
= Actual or realized rate of return
D1/P0 =Dividend Yield during the coming year
(P1-P0)/P0 = Capital Gain Yield.

7. Dividend growth model
Value of a stock is the present value of the future dividends expected to be generated by the stock.

8. Constant growth stock
A stock whose dividends are expected to grow forever at a constant rate, g.
D1 = D0 (1+g)1
D2 = D0 (1+g)2
Dt = D0 (1+g)t
If g is constant, the dividend growth formula converges to:

9. What happens if g > ks?
If g > ks, the constant growth formula leads to a negative stock price, which does not make sense.
The constant growth model can only be used if:
ks > g
g is expected to be constant forever

10. If kRF = 7%, kM = 12%, and β = 1.2, what is the required rate of return on the firm’s stock?
Use the CAPM to calculate the required rate of return (ks):
ks = kRF + (kM – kRF)β
= 7% + (12% - 7%)1.2
= 13%

11. If D0 = $2 and g is a constant 6%, find the expected dividend stream for the next 3 years, and their PVs. 1
2.247 2
2.382 3
2.12
ks = 13%
g = 6%
1.8761
1.7599
D0 = 2.00
1.6509

12. What is the stock’s market value?
Using the constant growth model:

13. What is the expected market price of the stock, one year from now?
D1 will have been paid out already. So, P1 is the present value (as of year 1) of D2, D3, D4, etc.
Could also find expected P1 as:

14. What is the expected dividend yield, capital gains yield, and total return during the first year?
= D1 / P0 = $2.12 / $30.29 = 7.0%
Capital gains yield
= (P1 – P0) / P0
= ($ $30.29) / $30.29 = 6.0%
Total return (ks)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%

15. What would the expected price today be, if g = 0?
The dividend stream would be a perpetuity.
2.00 1 2 3
ks = 13%
...

16. Self testing:1
Cook company is expected to pay a $0.50 per share dividend at the end of the year. The dividend is expected to grow at a constant rate of 7% per year. The required rate of return on the stock,Ks, is 15%. What is the value per share of the company’s stock?

17. Self testing:2
Dozier Corporation’s share currently sell for $20 per share. The stock just paid a dividend of $1 per share. The dividend is expected to grow at a constant rate of 10% a year. What stock price is expected 1 year from now? What is the required rate of return on the company’s stock?

18. Supernormal/Nonconstant growth: What if D0 = $2 & g = 30% for 3 years before achieving long-run growth of 6%?
Can no longer use just the constant growth model to find stock value.
However, the growth does become constant after 3 years.

19. Valuing common stock with nonconstant growth1 2 3 4
D0 =
...
4.658
ks = 13%
g = 30%
g = 6%
2.301
2.647
3.045
46.114
= P0 =
0.06
$66.54 3
4.658
0.13 - $ P ^

20. Find expected dividend and capital gains yields during the first and fourth years.
Dividend yield (first year)
= $2.60 / $54.11 = 4.81%
Capital gains yield (first year)
= 13.00% % = 8.19%
During nonconstant growth, dividend yield and capital gains yield are not constant, and capital gains yield ≠ g.
After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%.

21. Nonconstant growth: What if g = 0% for 3 years before long-run growth of 6%?1 2 3 4
D0 =
...
2.12
ks = 13%
g = 0%
g = 6%
1.77
1.57
1.39
20.99
= P0 ^
0.06 $
$30.29 P 3
2.12
0.13 = -

22. Dividend yield (first year) Capital gains yield (first year)
Find expected dividend and capital gains yields during the first and fourth years.
Dividend yield (first year)
= $2.00 / $25.72 = 7.78%
Capital gains yield (first year)
= 13.00% % = 5.22%
After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%.

23. 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.

24. Find expected annual dividend and capital gains yields.
Dividend yield
D1 / P0 = $1.88/$9.89 = 19.00%
Since the stock is experiencing constant growth, dividend yield and capital gains yield are constant. Dividend yield is sufficiently large (19%) to offset a negative capital gains.

25. Corporate value model
Also called the free cash flow method. Suggests the value of the entire firm equals the present value of the firm’s free cash flows.
Free cash flow is the firm’s after-tax operating income less the net capital investment
FCF = NOPAT – Net capital investment

26. Issues regarding the corporate value model
Often preferred to the dividend growth model, especially when considering number of firms that don’t pay dividends or when dividends are hard to forecast.
Similar to dividend growth model, assumes at some point free cash flow will grow at a constant rate.
Terminal value (TVn) represents value of firm at the point that growth becomes constant.

27. Given the long-run gFCF = 6%, and WACC of 10%, use the corporate value model to find the firm’s intrinsic value.
21.20 1 2 3 4
...
g = 6%
k = 10%
-4.545
8.264
15.026
21.20
530 = = TV3
0.10
0.06 -

28. What is market equilibrium?
In equilibrium, stock prices are stable and there is no general tendency for people to buy versus to sell.
In equilibrium, expected returns must equal required returns.

29. Market equilibrium
Expected returns are obtained by estimating dividends and expected capital gains.
Required returns are obtained by estimating risk and applying the CAPM.

30. What is the Efficient Market Hypothesis (EMH)?
Securities are normally in equilibrium and are “fairly priced.”
Investors cannot “beat the market” except through good luck or better information.
Levels of market efficiency
Weak-form efficiency
Semistrong-form efficiency
Strong-form efficiency

31. Weak-form efficiency
The weak form of the EMH states that all information contained in past price movements is fully reflected in current market prices.

32. Semistrong-form efficiency
The semistrong-form of the EMH states that current market prices reflect all publicly available information.

33. Strong-form efficiency
The strong form of the EMH states that current market prices reflect all related information, whether publicly available or privately held.

34. 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.

35. If a preferred stock with an annual dividend of $5 sells for $50, what is the preferred stock’s expected return?
Vp = D / kp
$50 = $5 / kp
kp = $5 / $50
= 0.10 = 10%