1. CHAPTER 9 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 stock price.

3. Social/Ethical Question
Should management be equally concerned about employees, customers, suppliers, “the public,” or just the stockholders?
In enterprise economy, work for stockholders subject to constraints (environmental, fair hiring, etc.) and competition.

4. 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.

5. 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.

6. Average Initial Returns on IPOs in Various Countries
100%
75%
50%
25%
Japan
United States
Brazil
Portugal
Sweden
Malaysia
Canada

7. Different Approaches for Valuing Common Stock
Dividend growth model
Free cash flow method
Using the multiples of comparable firms

8. Stock Value = PV of Dividends What is a constant growth stock?
One whose dividends are expected to
grow forever at a constant rate, g.

9. For a Constant Growth Stock
D1 = D0(1 + g)1
D2 = D0(1 + g)2
Dt = Dt(1 + g)t
If g is constant, then:
P0 = =
D0(1 + g)
ks - g D1
ks - g ^

10. $
0.25
Years (t)

11. What happens if g > ks?
If ks< g, get negative stock price, which is nonsense.
We can’t use model unless (1) ks> g and (2) g is expected to be constant forever.

12. Assume beta = 1. 2, kRF = 7%, and kM = 12%
Assume beta = 1.2, kRF = 7%, and kM = 12%. What is the required rate of return on the firm’s stock?
Use the SML to calculate ks:
ks= kRF + (kM – kRF)bFirm
= 7% + (12% – 7%) (1.2)
= 13%.

13. D0 was $2. 00 and g is a constant 6%
D0 was $2.00 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. ks = 13%. 1 2 3
g = 6%
D0 = 2.00
2.12
2.247
2.382
13%
1.8761
1.7599
1.6509

14. What’s the stock’s market value? D0 = 2.00, ks = 13%, g = 6%.
Constant growth model: D1
$2.12
P0 = =
ks – g – 0.06
$2.12
= =
$30.29.
0.07

15. 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,
Could also find P1 as follows: D2
$2.247 ^
P1 = =
ks – g – 0.06
= $32.10. ^ ^
P1 = P0(1.06) = $32.10.

16. Find the expected dividend yield, capital gains yield, and total return during the first year.
$2.12
Dividend yld = = =
7.0%. P0
$30.29 ^
P1 – P0
$32.10 – $30.29
Cap gains yld = = P0
$30.29
= 6.0%.
Total return = 7.0% + 6.0% = 13.0%.

17. $ . P D k g = - + to Rearrange model to rate of return form:s 1 = - + to ^
Then, ks = $2.12/$
= = 13%.

18. What would P0 be if g = 0? PMT k $2.00 0.13^
What would P0 be if g = 0?
The dividend stream would be a perpetuity. 1 2 3
13%
...
2.00
2.00
2.00 ^
PMT k
$2.00
0.13
P0 = = = $15.38.

19. Can no longer use constant growth model.
If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P0? k is still 13%. ^
Can no longer use constant growth model.
However, growth becomes constant after 3 years.

20. Nonconstant growth followed by constant growth:1 2 3 4
ks = 13%
...
g = 30%
g = 30%
g = 30%
g = 6%
D0 =
2.301
2.647
3.045
4.658 . $
46.116 P = =
$66.54 3 . 13 - . 06 ^
= P0

21. What is the expected dividend yield and capital gains yield at t = 0
What is the expected dividend yield and capital gains yield at t = 0? At t = 4?
$2.60
$54.11
Div. yield0 = = 4.81%.
Cap. gain0 = 13.00% – 4.81% = 8.19%.

22. During nonconstant growth, D/P and capital gains yield are not constant, and capital gains yield is less than g.
After t = 3, g = constant = 6% = capital gains yield; k = 13%; so D/P = 13% – 6% = 7%.

23. Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P0?^ 1 2 3 4
ks=13%
...
g = 0%
g = 0%
g = 0%
g = 6%
1.77
1.57
1.39
2.12 $
20.99 P = =
30.29. 3 . 07
25.72

24. What is D/P and capital gains yield at t = 0 and at t = 3?
$2.00
$25.72
= = 7.78%.
t = 0: P0
CGY = 13% – 7.78% = 5.22%.
t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%.

25. If g = -6%, would anyone buy the stock? If so, at what price?
Firm still has earnings and still pays
dividends, so P0 > 0: ( ) D D 1 + g $ P = 1 = k - g k - g s s
$2.00(0.94) $1.88
0.13 – (-0.06)
= = = $9.89.

26. What is the annual D/P and capital gains yield?
Capital gains yield = g = -6.0%,
Dividend yield= 13.0% – (-6.0%) = 19%.
D/P and cap. gains yield are constant,
with high dividend yield (19%) offsetting
negative capital gains yield.

27. NOPAT – Net capital investment.
Free Cash Flow Method
The free cash flow method suggests that the value of the entire firm equals the present value of the firm’s free cash flows (calculated on an after-tax basis).
Recall that the free cash flow in any given year can be calculated as:
NOPAT – Net capital investment.

28. Using the Free Cash Flow Method
Once the value of the firm is estimated, an estimate of the stock price can be found as follows:
MV of common stock (market capitalization) = MV of firm – MV of debt and preferred stock.
P = MV of common stock/# of shares. ^

29. Issues Regarding the Free Cash Flow Method
Free cash flow method is often preferred to the dividend growth model--particularly for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends.
(More...)

30. FCF Method Issues Continued
Similar to the dividend growth model, the free cash flow method generally assumes that at some point in time, the growth rate in free cash flow will become constant.
Terminal value represents the value of the firm at the point in which growth becomes constant.

31. FCF estimates for the next 3 years are -$5, $10, and $20 million, after which the FCF is expected to grow at 6%. The overall firm cost of capital is 10%. 1 2 3 4
k = 10%
...
g = 6%
-4.545
8.264
15.026
21.20
0.04
530 = = *TV3
*TV3 represents the terminal value of the firm, at t = 3.

32. If the firm has $40 million in debt and has 10 million shares of stock, what is the price per share?
Value of equity = Total value – Value of debt
= $ – $40
= $ million.
Price per share = Value of equity/# of shares
= $376.94/10
= $37.69.

33. Using the Multiples of Comparable Firms to Estimate Stock Price
Analysts often use the following multiples to value stocks:
P/E
P/CF
P/Sales
P/Customer
Example: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price.

34. What is market equilibrium?
In equilibrium, stock prices are stable.
There is no general tendency for
people to buy versus to sell.
In equilibrium, expected returns must
equal required returns: ^
ks = D1/P0 + g = ks = kRF + (kM – kRF)b.

35. Required returns are obtained from the CAPM.
Expected returns are obtained by estimating dividends and expected capital gains (which can be found using any of the three common stock valuation approaches).
Required returns are obtained from the CAPM. ^
ks = D1/P0 + g = ks = kRF + (kM – kRF)b.

36. How is equilibrium established?P0 ^
If ks = g > ks, then
P0 is “too low” (a bargain).
Buy orders > sell orders;
P0 bid up; D1/P0 falls until
D1/P0 + g = ks = ks. ^

37. Why do stock prices change?
ki – g ^
P0 =
1. ki could change:
ki = kRF + (kM – kRF )bi.
kRF = k* + IP.
2. g could change due to
economic or firm situation.

38. 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 better information.

39. 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.

40. 2. Semistrong-form EMH:
All publicly available information is reflected in stock prices, so doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true, but superior analysts can still profit by finding and using new information.

41. 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.

42. Markets are generally efficient because:
1. 15,000 or so trained analysts; MBAs, CFAs, Technical PhDs.
2. Work for firms like Merrill, Morgan, Prudential, which have a lot of money.
3. Have similar access to data.
4. Thus, news is reflected in P0 almost instantaneously.

43. Preferred Stock
Hybrid security.
Similar to bonds in that preferred stockholders receive a fixed dividend that must be paid before dividends can be paid on common stock.
However, unlike interest payments on bonds, companies can omit dividend payments on preferred stock without fear of pushing the firm into bankruptcy.

44. What’s the expected return of preferred stock with Vp = $50 and annual dividend = $5?