1. CHAPTER 9 Stocks and Their Valuation
Features of common stock
Determining common stock values
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. Intrinsic Value and Stock Price
Investors, corporate insiders, and analysts use a variety of approaches to estimate a stock’s intrinsic value (P0).
In equilibrium, stock’s price equals its intrinsic value.
Outsiders estimate intrinsic value to determine
stocks are attractive to buy
Stocks to be sold
Stocks with a price below (above) its intrinsic value are undervalued (overvalued).

4. Determinants of Intrinsic Value and Stock Prices (Figure 1-1)

5. Different approaches for estimating the intrinsic value of a common stock
i Dividend growth model
ii Corporate value model
iii Compare multiples of similar firms

6. i Dividend growth model
Value of stock: present value of the future dividends expected to be generated by the stock.
[ r – return of stock D – dividend ]

7. 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:

8. Future dividends and their present values$
0.25
Years (t)

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

10. If rRF = 7%, rM = 12%, and b = 1.2, what is the required rate of return on the firm’s stock?
Use the SML to calculate the required rate of return (rs):
rs = rRF + (rMkt – rRF)b
= 7% + (12% - 7%)1.2
= 13%
SML: Security Market Line

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
rs = 13%
g = 6%
1.8761
1.7599
D0 = 2.00
1.6509

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

13. 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. Expected dividend yield, capital gains yield, and total return during first year
= D1 / P0 = $2.12 / $30.29 = 7.0%
Capital Gains Yield
= (P1 – P0) / P0
= ($ $30.29) / $30.29 = 6.0%
Total Return (rs)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%

15. Expected price today if g = 0
Dividend stream would be a perpetuity.
2.00 1 2 3
rs = 13%
...

16. Supernormal growth: What if 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.

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

18. 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 non-constant 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%.

19. Nonconstant growth: g = 0% for 3 years THEN long-term growth of 6%1 2 3 4
D0 =
...
2.12
rs = 13%
g = 0%
g = 6%
1.77
1.57
1.39
20.99
= P0 ^
0.06 $
$30.29 P 3
2.12
0.13 = -

20. Dividend yield (first year) Capital gains yield (first year)
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%.

21. If the stock was expected to have negative growth (g = -6%), would anyone buy the stock, and what is its value?
Firm still has earnings and pays dividends, even though they may be declining, they still have value.

22. Find expected annual dividend and capital gains yields.
Dividend yield
= 13.00% - (-6.00%) = 19.00%
Since 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.

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

24. Applying the corporate value model
Find the Market Value (MV) of the firm, by finding the PV of the firm’s future Free Cash Flows [FCFs].
Subtract MV of firm’s debt and preferred stock to get MV of common stock.
Divide MV of common stock by the number of shares outstanding to get intrinsic stock price (value).

25. Issues regarding the corporate value model
Preferred to the dividend growth model,
Firms that don’t pay dividends
When dividends 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.

26. Given long-run gFCF = 6%, and WACC of 10%, use corporate value model to find firm’s intrinsic value.
[ WACC: Weighted Average Cost Capital ]
21.20 1 2 3 4
...
g = 6%
r = 10%
-4.545
8.264
15.026
21.20
530 = = TV3
0.10
0.06 -

27. If firm has $40 million in debt and has 10 million shares of stock, what is the firm’s intrinsic value per share?
MV of equity = MV of firm – MV of debt
= $ $40
= $ million
Value per share = MV of equity / # of shares
= $ / 10
= $37.69

28. iii Firm multiples method
Analysts often use following multiples to value stocks.
P / E -- Price Earnings Ratio
P / CF -- Price Cash Flow Ratio
P / Sales -- Price Sales Ratio
EXAMPLE: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to estimate stock price.

29. 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, two conditions hold:
The current market stock price equals its intrinsic value (P0 = P0).
Expected returns must equal required returns. ^

30. (Capital Asset Pricing Model)
Market equilibrium
Expected returns determined by:
estimating dividends
and expected capital gains.
Required returns are determined by estimating risk and applying the CAPM
(Capital Asset Pricing Model)

31. How is market equilibrium established?
If price is below intrinsic value …
The current price (P0) is “too low” and offers a bargain.
Buy orders will be greater than sell orders.
P0 will be bid up until expected return equals required return.

32. How equilibrium values determined?
Are equilibrium intrinsic value and expected return estimated
Managers
Something else?
Equilibrium levels are based on the market’s estimate of intrinsic value and the market’s required rate of return -- dependent upon the attitudes of the marginal investor.

33. 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.

34. Preferred stock with annual dividend of $5 sells for $50, what is preferred stock’s expected return?
Vp = D / rp
$50 = $5 / rp
rp = $5 / $50
= 0.10 = 10%
( no growth dividend ) ^