CHAPTER 7 Valuation Models: Stocks

1
CHAPTER 7Valuation Models Stocks

• Features of common stock
• Determining common stock values
• Security market equilibrium
• Efficient markets
• Preferred stock

S05
2
Facts about Common Stock?

• Represents ownership?
• Ownership implies control?
• Agency problem
• Stockholders elect directors?
• Directors elect management?
• Managements goal Maximize stock price.

3
Whats 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.

4
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.

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.
• Prior to an IPO, shares are typically owned by
  the firms managers, key employees, and, in many
  situations, venture capital providers.

6
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.

7
ANALYZING STOCKS
8
Different Approaches for Valuing Common Stock

• Dividend growth model
• Using the multiples of comparable firms
• Free cash flow method (covered in Chapter 12)

9
DIVIDEND GROWTH MODEL
10
Stock value PV of dividends
D1 (1 r)
D2 (1 r)2
D? (1 r)?

P0 . . .
.
ABSOLUTELY FUNDAMENTAL!
11
Future Dividend Stream
D1 D0(1 g1) D2 D1(1 g2)
. . .
12
WHAT IS A CONSTANT GROWTH STOCK? HOW ARE
CONSTANT GROWTH STOCKS VALUED?

• A stock whose dividends grow at a constant rate.
• In application, doesnt 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.

13
WHAT IS A CONSTANT GROWTH STOCK? HOW ARE
CONSTANT GROWTH STOCKS VALUED?

• D1 D0(1g)
• D2 D1(1g)D0(1g)2
• .
• .
• .
• Dn D0(1g)n

14
If growth of dividends g is constant, then
D1 rs - g
D0 (1 g) rs - g

P0 .

• Model requires
• rs gt g (otherwise results in negative price).
• g constant forever.

15

0.25
0
Years (t)
16
What happens if g gt rs?

• If rslt g, get negative stock price, which is
  nonsense.
• We cant 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.

17
PROOF OF GORDON MODEL
18
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.
19
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.
20
Whats the stocks market value? D0 2.00, rs
13, g 6.
Constant growth model
2.12
2.12
30.29.
0.13 - 0.06
0.07
21
What is Bon Temps value one year from now?

22
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.

23
P0 D1/(rs - g) P1 D2/(rs - g) BUT, D2
D1( 1g)So, P1 D1( 1g) (rs -
g)OR P1 P0( 1g)
24
Find the expected dividend yield, capital gains
yield, and total return during the 1st, 2nd and
3rd years.
25
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.

26
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.

27
So, in CGR models, Dividend and Price both grow
at a rate g consequently the dividend yield
is

• ?

28
So, in CGR models, Dividend and Price both grow
at a rate g consequently the dividend yield
is

• CONSTANT!

29
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
30
Total yield Div. yield Cap. gains yield
7 6 13 rs.
31
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.

32
Rearrange model to rate of return form

Then, rs 2.12/30.29 0.06 0.07 0.06
13.
33
Points to Remember

• If a stock is in equilibrium, then
• Price Value.
• (P0 P0)
• Required return Expected return.
• (rs rs)

34

• For any stock, the expected total return in any
  year equals dividend yield capital gains yield.

35

• 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 (1g) - 1 g.
• Stock price grows at constant rate g.

36
DIGRESSION PRICE-EARNINGS RATIO

• Po D1/(rs - g)
• D1 E1( 1-b)
• Where b retention ratio, and (1-b) payout
  ratio.

37
PRICE-EARNINGS RATIO

• Po E1(1-b)/(rs - g)
• Po (1-b)
• E1 (rs - g)
• A greater g implies a larger P/E.

38
WHAT WOULD THE STOCK PRICE OF BON TEMPS BE IF
DIVIDENDS HAVE ZERO GROWTH?
39
What would P0 be if g 0?
The dividend stream would be a perpetuity.
0
1
2
3
rs13
2.00
2.00
2.00
PMT
2.00

P0 15.38.
r
0.13
40
What is Subnormal or Supernormal Growth
41
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

42
If we have supernormal growth of 30 for 3 years,
then a long-run constant g 6, what is P0?

0 rs16 1 2 3 4
g 30 g 30 g 30 g
6
D0 2.00
43
Nonconstant growth followed by constant growth
0
1
2
3
4
rs13
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)
44
What is the expected dividend and capital gains
yields at t 0? At t 4?
45
What is the expected dividend yield and capital
gains yield at t 0? At t 4?
At t 0
2.60
D1
Dividend yield 4.81.
54.11
P0
CG Yield 13.0 - 4.8 8.19.
(More)
46
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
47

• 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.

48
At Year 4, stock is constant growth, so CG
yield4 6 g. Div. yield4 7.
49
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

50
If most of a stocks 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.

51
Suppose g 0 for t 1 to 3, and then g is a
constant 6. What is P0?

0
1
2
3
4
rs13
...
g 0
g 0
g 0
g 6
2.00 2.00 2.00 2.12
1.7699
1.5663
2.12
1.3861
?
?
?
P
30.2857
20.9895
3
.
0
07
25.7118
52
What is dividend yield and capital gains yield at
t 0 and at t 3?
D1
2.00
?
?
7.8.

t 0
P0
25.72
CGY 13.0 - 7.8 5.2.
t 3 Now have constant growth with g capital
gains yield 6 and dividend yield 7.
53
If g -6, no one buy the stock? Right?
54
If g -6, would anyone buy the stock? If so,
at what price?
Firm still has earnings and still pays dividends,
so P0 gt 0

2.00(0.94)
1.88
9.89.
0.13 - (-0.06)
0.19
55
What are the annual dividendand capital gains
yield?
Capital gains yield g -6.0. Dividend
yield 13.0 - (-6.0) 19.0. Both yields
are constant over time, with the high dividend
yield (19) offsetting the negative capital gains
yield.
56
Using Free Cash Flows
We will cover this later in Chapter 12.
57
Suppose this firm decides to expand

• Finance expansion by borrowing 40 million and
  halting dividends.
• How do we value a firm with no dividends?

58

• Projected free cash flows (FCF)
• Year 1 FCF -5 million
• Year 2 FCF 10 million
• Year 3 FCF 20 million
• FCF grows at constant rate of 6 after year 3.

59

• The corporate cost of capital, kc, is 10.
• The company has 10 million shares of stock.

60
Free Cash Flows

• Recall the definition of free cash flows
• FCFNOPAT - Net Capital Investment
• where
• Net Capital Investment Net operating working
  capital non-interest bearing CA - CL -
  operating capital

61
Find the value of operations by discounting the
free cash flows atthe cost of capital.
0
1
2
3
4
g 6
rc10
FCF -5.00 10.00 20.00 21.2
-4.545
8.264
15.026
21.2
Vop at 3
530.
?
?
398.197
.
.
10
0
06
?
0
416.942 Vop
62
Find the price per share ofcommon stock.

• Value of equity Value of operations
• - Value of debt
• 416.94 - 40
• 376.94 million.
• Price per share 376.94/10 37.69.

63
In equilibrium, expected returns must equal
required returns

rs D1/P0 g rs rRF (rM - rRF)b.
64
Using multiples of comparable firms
65
Second Method Using the Multiples of Comparable
Firms to Estimate Stock Price (Price Multiples)

• Analysts often use the following multiples to
  value stocks
• P/E
• P/CF or P/EBITDA
• P/Sales
• P/margin
• P/Customer
• .

66
Using the Stock Price Multiples to Estimate Stock
Price

• Analysts often use the P/E multiple (the price
  per share divided by the earnings per share) or
  the P/CF multiple (price per share divided by
  cash flow per share, which is the earnings per
  share plus the dividends per share) to value
  stocks (or other multiples).
• Example
• Estimate the average P/E ratio of comparable
  firms. This is the P/E multiple.
• Multiply this average P/E ratio by the expected
  earnings of the company to estimate its stock
  price.

67
Using the Stock Price Multiples to Estimate Stock
Price

• Example BOH
• Estimate the average P/E ratio of comparable
  firms. This is the P/E multiple.
• The P/E multiple for Pacific Banks is 19.06.
• Multiply this average P/E ratio by the expected
  earnings of the company to estimate its stock
  price.
• The EPS(ttm) is 3.22
• Consequently, the Implied price is 61.37
• This is 16 greater than the current 52.81 price.

68
Using Entity Multiples

• The entity value (V) of the comparable firm is
• the market value of equity ( shares of stock
  multiplied by the price per share)
• plus the value of debt.
• Pick a measure, such as EBITDA, Sales, Customers,
  Eyeballs, etc.
• Calculate the average entity ratio for a sample
  of comparable firms. For example,
• V/EBITDA
• V/Customers

69
Using Entity Multiples (Continued)

• Find the entity value of the firm in question.
  For example,
• Multiply the firms sales by the V/Sales
  multiple.
• Multiply the firms of customers by the
  V/Customers ratio
• The result is the total value of the firm.
• Subtract the firms debt to get the total value
  of equity.
• Divide by the number of shares to get the price
  per share.

70
Problems with Market Multiple Methods

• It is often hard to find comparable firms.
• The average ratio for the sample of comparable
  firms often has a wide range.
• For example, the average P/E ratio might be 20,
  but the range could be from 10 to 50. How do you
  know whether your firm should be compared to the
  low, average, or high performers?
• What factors account for the difference in P/E
  ratios?

71
Why are stock prices volatile?

• rs rRF (RPM)ßi could change.
• Inflation expectations
• Risk aversion
• Company risk
• g could change.

72
Stock value vs. changes in rs and g
D1 2, rs 10, and g 5 P0 D1 / (rs-g)
2 / (0.10 - 0.05) 40. What if rs or g
change? g g g rs 4 5 6 9 40.00 50.00
66.67 10 33.33 40.00 50.00 11 28.57 33.33 40
.00
73
Are volatile stock prices consistent with
rational pricing?

• Small changes in expected g and rs cause large
  changes in stock prices.
• As new information arrives, investors continually
  update their estimates of g and rs.
• If stock prices arent volatile, then this means
  there isnt a good flow of information.

74
What is market equilibrium?
75
What is market equilibrium?
In equilibrium, stock prices are stable. There
is no general tendency for people to buy versus
sell. In equilibrium, expected returns
must equal required returns

r D1/P0 g r rRF (rM - rRF)ß.
76
How is equilibrium established?

77
How is equilibrium established?
D1 P0

If r g gt r, then P0 is too low, a
bargain. Buy orders gt sell orders P0 bid up
D1/P0 falls until D1/P0 g r r.

78
Why do stock prices change?

• ri rRF (rM - rRF )ßi could change.
• Inflation expectations
• Risk aversion
• Company risk
• g could change.

79
Whats the Efficient Market Hypothesis?
80
Whats the Efficient Market Hypothesis?
EMH Securities are normally in equilibrium and
are fairly priced. One cannot beat the
market except through good luck or inside
information.
81
What are the three forms of the EMH?
82
1. Weak-form EMH
Cant profit by looking at past trends. A recent
decline is no reason to think stocks will go up
(or down) in the future. Seems empirically true,
but technical analysis is still used.
83
2. Semistrong-form EMH
All publicly available information is reflected
in stock prices, so doesnt pay to pore over
annual reports looking for undervalued stocks.
Largely true, but superior analysts can still
profit by finding and using new information
especially on smaller stocks.
84
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 thats illegal.
85
Markets are generally efficient because
1. 100,000 or so trained analysts--MBAs, CFAs,
and PhDs--work for firms like Fidelity, Merrill,
Morgan, and Schwab. 2. These analysts have
similar access to data and megabucks to
invest. 3. Thus, news is reflected in P0 almost
instantaneously.
86
Preferred Stock

• Hybrid security.
• Similar to bonds in that preferred stockholders
  receive a fixed dividend which must be paid
  before dividends can be paid on common stock.
• However, unlike bonds, preferred stock dividends
  can be omitted without fear of pushing the firm
  into bankruptcy.

87
Whats the expected return on preferred stock
with Vps 50 and annual dividend 5?
88
END!