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

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

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

6. 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:

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

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

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

10. 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

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

12. 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:

13. 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%

14. 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.

15. 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 ^

16. 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%.

17. 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 = -

18. 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%.

19. 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.

20. 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.
Remember, free cash flow is the firm’s after-tax operating income less the net capital investment
FCF = NOPAT – Net capital investment

21. Applying the corporate value model
Find the market value (MV) of the firm.
Find PV of firm’s future FCFs
Subtract MV of firm’s debt and preferred stock to get MV of common stock.
MV of = MV of – MV of debt and common stock firm preferred
Divide MV of common stock by the number of shares outstanding to get intrinsic stock price (value).
P0 = MV of common stock / # of shares

22. 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.

23. 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 -

24. If the 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
= $416.94m - $40m
= $ million
Value per share = MV of equity / # of shares
= $376.94m / 10m
= $37.69

25. 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.

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

27. How is market equilibrium established?
If expected return exceeds required return …
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

28. Factors that affect stock price
Required return (ks) could change
Changing inflation could cause kRF to change
Market risk premium or exposure to market risk (β) could change
Growth rate (g) could change
Due to economic (market) conditions
Due to firm conditions

29. 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

30. Weak-form efficiency
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.

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

32. Strong-form efficiency
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.