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CHAPTER 7
Stocks, Stock Valuation, and Stock Market Equilibrium
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Topics in Chapter
Features of common stock Valuing common stock Preferred stock Stock market equilibrium Efficient markets hypothesis Implications of market efficiency
for financial decisions
EQUITIESWhy?
Key to understanding valuations
What is investment worth today?
Value of: Enterprise Entity Company/Firm
Business Application For Investor:
Determine value of asset/business/company
For Firm: Determine cost of
attracting investors & raising equity capital
Selling ownership stake to raise $
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Equities
Valuing companies that don’t pay dividends
Alternative valuation methods
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ValueStock = + + +D1 D2 D∞
(1 + rs )1 (1 + rs)∞(1 + rs)2
Dividends (Dt)
Dividends (Dt)
Market interest rates
Firm’s business riskMarket risk aversion
Firm’s debt/equity mixCost of
equity (rs)
Cost of
equity (rs)
Free cash flow(FCF)
The Big Picture:The Intrinsic Value of Common
Stock
...
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Common Stock: Owners, Directors, and Managers
Represents ownership. Ownership implies control. Stockholders elect directors. Directors hire management. Preemptive right. Since managers are “agents” of
shareholders, their goal should be: Maximize stock price.
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 firm’s managers, key employees, and, in many situations, venture capital providers
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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.
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Classified Stock
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.
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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.
Bonds vs. Stocks
Issuer Cost (company) int. paid out (i)
Bond value or price today
Discount the CFs by (i) (reqr’d return)
Cfs = Int pmts; principal PV, PMT,FV,N,i
Cost(dividends pd out
Cap gains
Stock value or price today
Discount the CFs by (R) (reqr’d return)
Cfs = Dividends
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Bonds vs. Stocks
Bond’s Value or Price Today
= sum of the PVs of the future CFs;
That is – discount CFs (int Pmts (PMT) & Principal (FV)) by i% over some period (N) to get PV
PMT,FV,N,I known; solve for PV
Stock’s Value
or Price Today
= sum of the PVs of the future CFs;
Discount CFs (divids) by (R) (reqr’d return) to get Po (PV)
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Different Approaches for Valuing Common Stock
Dividend growth model Constant growth stocks Nonconstant growth stocks
Free cash flow method Using the multiples of comparable
firms
Why Invest in Stock?
For Growth in Value From Dividends & Cap Gains
Generating Total Return = R
Stock Price = Growth = g Dividend Return or Yield = Annual divid / Price of stock= D1
/ Po
Return on Stock = Return on Divid + Growth (cap gains) R = D1 /Po + g (but want price
today)
R – g = D1 /Po Finally: Po = D1 / R - g 14
Constant Growth Approach to Equity Valuations
Po = D1 / R – g Discounting the Divids (or CFs) by R-g (return
adjusted for constant growth) Constant growth model: works when g is
constant rate (%) & R > g If g > R, then have supernormal or non-constant
growth If so, then look at PVs of CFs generated the stock to
determine its price today If we need R (req’d return) to use as disct factor, we
can use SML relationship from CAPM SML: Ri = rRF + (RM - rRF)bi .
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Stock Value = PV of Dividends
What is a constant growth stock?
One whose dividends are expected to grow forever at a constant rate, g.
P0 =^
(1 + rs)1 (1 + rs)2 (1 + rs)3 (1 + rs)∞
D1 D2 D3 D∞+ + + …
+
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For a constant growth stock:
D1 = D0(1 + g)1
D2 = D0(1 + g)2
Dt = D0(1 + g)t
If g is constant and less than rs, then:
P0 = ^ D0(1 + g)
rs – g=
D1
rs – g
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Dividend Growth and PV of Dividends: P0 = ∑(PV of Dt)
$
0.25
Years (t)
Dt = D0(1 + g)t
PV of Dt =
Dt
(1 + r)t
If g > r, P0 = ∞ !
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What happens if g > rs?
P0 =^
(1 + rs)1 (1 + rs)2 (1 + rs)∞
D0(1 + g)1 D0(1 + g)2 D0(1 + rs)∞ + + … +
(1 + g)t
(1 + rs)t
P0 = ∞^> 1, and
So g must be less than rs for the constant growth model to be applicable!!
If g > rs, then
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Required rate of return: beta = 1.2, rRF = 7%, and RPM = 5%.
rs = rRF + (RPM)bFirm
= 7% + (5%)(1.2)= 13%.
Use the SML to calculate rs:
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Projected Dividends
D0 = $2 and constant g = 6%
D1 = D0(1 + g) = $2(1.06) = $2.12 D2 = D1(1 + g) = $2.12(1.06) =
$2.2472 D3 = D2(1 + g) = $2.2472(1.06) =
$2.3820
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Expected Dividends and PVs (rs = 13%, D0 = $2, g = 6%)
0 1
2.2472
2
2.3820
3g = 6%
1.87611.75991.6508
13%
2.12
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Intrinsic Stock Value: D0 = $2.00, rs = 13%, g = 6%
Constant growth model:
= = = $30.29.0.13 – 0.06
$2.12 $2.12
0.07
P0 = ^ D0(1 + g)
rs – g=
D1
rs – g
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Expected value one year from now:
P1 = ^ D2
rs – g=
$2.2472
0.07= $32.10
D1 will have been paid, so expected dividends are D2, D3, D4 and so on.
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Return = Dividend Yield + Capital Gains Yield
Dividend yield = D1
P0
CG Yield = =P1 – P0^
P0
New - Old
Old
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Expected Dividend Yield and Capital Gains Yield (Year 1)
Dividend yield = = = 7.0%.
$2.12$30.29
D1
P0
CG Yield = =P1 – P0^
P0
$32.10 – $30.29$30.2
9= 6.0%.
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Total Year 1 Return
Total return = Div yield + Cap gains yield.
Total return = 7% + 6% = 13%. Total return = 13% = rs. For constant growth stock:
Capital gains yield = 6% = g.
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Rearrange model to rate of return form:
Then, rs = $2.12/$30.29 + 0.06= 0.07 + 0.06 = 13%.
^
P0 = ^ D1
rs – gto
D1
P0
rs^ = + g.
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If g = 0, the dividend stream is a perpetuity.
2.00 2.002.00
0 1 2 3rs = 13%
P0 = = = $15.38.PMT
r$2.000.13
^
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Supernormal Growth Stock I
Supernormal growth of 30% for first three years, then 6% constant g thereafter. Just paid dividend of $2.00 /sh, & required return for investments of this risk is 13%. What’s the price today (Po)?
Can no longer use constant growth model. However, growth becomes constant after
3 years.
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Nonconstant growth followed by constant growth
0
?
?
?
?
1 2 3 4rs = ? %
?? = P0
g = ? % g = ? % g = ? % g = ? %
Do=?(1+g) D1=? D2=? D3=? D4=?
^
P3 = ^ D4
R - g
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Nonconstant growth followed by constant growth (D0 = $2):
0
2.30
2.65
3.05
46.11
1 2 3 4rs = 13%
54.11 = P0
g = 30% g = 30% g = 30% g = 6%
Do=2.00(1+g) D1=2.60 D2=3.38 D3=4.39 D4=4.66
^
P3 = ^ $4.66
0.13 – 0.06
= $66.54
Using Cfs
After Determining:
CFo = Do
CF1 = D1
CF2 = D2
CF3 = D3 + P3
i = R % Po = NPV = ?
Future Divs & gk terminal value (price)
CFo = 0 CF1 = 2.60 CF2 = 3.38 CF3 = 4.39 + 66.54
=70.93 i = 13 % Po = NPV = ? = $54.11
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Expected Dividend Yield and Capital Gains Yield (t = 0)
CG Yield = 13.0% – 4.81% = 8.19%.
Dividend yield = = = 4.81%
$2.60$54.11
D1
P0
Today (@ t =0):
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Expected Divd & Cap Gains Yield (after t = 3)
During nonconstant growth, dividend yield and capital gains yield are not constant.
If current growth is greater than gk, current capital gains yield is greater than g.
After year 3 (t = 3), gk = constant = 6%, so CGY = 6%.
Because rs = 13%, after yr 3 div yld = 13% – 6% = 7%.
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Is stock price based onshort-term growth?
The current stock price is $54.11.The PV of dividends beyond Year 3 is:=̂terminal or horizon value in year 3 (P3)
discounted to present by req’d Return (R=13%) = $46.11
= 85.2%.$46.11$54.11
% of stock price due to “long-term” dividends is:
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Intrinsic Stock Value vs. Quarterly Earnings
If most of a stock’s value is due to long-term cash flows, why do so many managers focus on quarterly earnings?
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Intrinsic Stock Value vs. Quarterly Earnings
Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This affects current stock price (Po).
Sometimes managers have bonuses tied to quarterly earnings.
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Supernormal Growth Stock II Supernormal growth of 30% for
Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, and then long-run constant g = 6%.
Can no longer use constant growth model.
However, growth becomes constant after 3 years.
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Nonconstant growth followed by constant growth (D0 = $2):
0
2.3009
2.5452
2.5903
39.2246
1 2 3 4rs = 13%
46.6610 = P0
g = 30% g = 25% g = 15% g = 6%
2.6000 3.2500 3.7375 3.9618
^
P3 = ^ $3.9618
0.13 – 0.06
= $56.5971
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Expected Dividend Yield and Capital Gains Yield (t = 0)
CG Yield = 13.0% – 5.6% = 7.4%.
Dividend yield = = = 5.6%
$2.60$46.66
D1
P0
At t = 0:
(More…)
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Expected Dividend Yield and Capital Gains Yield (after t = 3)
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 capital gains yield = 6%.
Because rs = 13%, after t = 3 dividend yield = 13% – 6% = 7%.
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Is the stock price based onshort-term growth?
The current stock price is $46.66.The PV of dividends beyond Year 3 is:
^P3 / (1+rs)3 = $39.22
= 84.1%.$39.22$46.66
The percentage of stock price due to “long-term” dividends is:
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Suppose g = 0 for t = 1 to 3, and then g is a constant 6%.
0
1.76991.56631.3861
20.9895
1 2 3 4rs = 13%
25.7118
g = 0% g = 0% g = 0% g = 6%2.00 2.00 2.00 2.12
2.12P3 0.07 30.2857= =^
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Dividend Yield and Capital Gains Yield (t = 0)
Dividend Yield = D1/P0
Dividend Yield = $2.00/$25.72 Dividend Yield = 7.8%
CGY = 13.0% – 7.8% = 5.2%.
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Dividend Yield and Capital Gains Yield (after t = 3)
Now have constant growth, so: Capital gains yield = g = 6% Dividend yield = rs – g Dividend yield = 13% – 6% = 7%
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Suppose negative growth:If g = -6%, would anyone buy stock? If so, at what price?
Firm still has earnings and still pays
dividends, so P0 > 0:^
= = = $9.89.
$2.00(1-.06)0.13 – (-0.06)
$1.880.19
P0 = ^ D0(1 + g)rs – g
=D1
rs – g
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Annual Dividend and Capital Gains Yields
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.
What if company pays no dividends?
Discount Free Cash Flows (CFs which can be returned to investors) instead of dividends
Where FCF = NOPAT – Net Capital Spending
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Uses of Free Cash Flows
Pay interest on debt Repay principal on debt Pay dividends to equityholders Repurchase stock from
equityholders Buy mrktbl securities or other non-
operating assets
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Equity Valuation using FCFs
A young firm just recorded a $<1.0> million FCF. It expects the FCF 1-yr from today to be $<5.0>million. In yrs 2 & 3, they are expected to become positive at $10 and $20 million. In the 4th yr, a constant growth in FCFs is expected to kick-in at 6%. The required return for investments of this risk is 10%. The firm has $40 million in debt, and 10 million shares outstanding. What’s the price per share today?
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Equity Valuation using FCFs
0
?
?
?
?
1 2 3 4rs = 10%
?? = P0
g = 6 %
FCFo=<1> FCF1=<5> FCF2=10 FCF3=20 *(1+g)
FCF4=?
^
P3 = ^ FCF4
R - g
Using Cfs for FCFs Equity Valuation
After Determining:
CFo = FCFo
CF1 = FCF1
CF2 = FCF2
CF3 = FCF3 + P3
i = R % Po = NPV =?= value of
firm
Future Divs & gk terminal value (price)
CFo = 0 CF1 = <5> CF2 = 10 CF3 = 20 + 530
=550.00 i = 10 % Po = NPV = ? =
$416.94
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Equity Valuation using FCFs
Value of firm = $416.94 - Debt 40.00 =Value of equity $376.94 / 10 mil
shrs
=price per share of $37.69
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Market Cap (Capitalization)
= Market Value of firm’s equity = (price/sh)*(#shs outstanding)
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Enterprise Value
= Value of firm’s underlying business, unencumbered by Debt, and separate from cash & marketable securities Enterprise Value= MV of equity + Debt -
cash Think:: Enterprise Value = Net cost of
acquiring a firm’s equity, taking its cash, and paying off debt. In essence, it’s equivalent to owning the unlevered (debt-free) business. 56
Market Cap & Enterprise Value I
H.J. Heinz has a share price of $46.78, its shares outstanding were 319.2 million. It has a market-to-book ratio of 8.00, a book debt-equity ratio of 2.62, and cash of $352 million. What’s Heinz’s market cap? What’s its enterprise value?
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Using Stock Price Multiples to Estimate Stock Price
Analysts often use the P/E multiple (the price per share divided by the earnings per share).
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.
Multiples Approach IAuto Industry
Industry P/E = 5
If Pinto trading on NYSE =
$9.00 If $4.00
Pinto Car Co Pinto EPS = $1.50/sh
Industry Pinto
5/1 = P/E = ?/$1.50 So Pinto relative price
per share (P) = $7.50
=overvalued (sell) =undervalued
(buy)59
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Using Entity Multiples The entity value (V) 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
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Using Entity Multiples (Continued)
Find the entity value of the firm in question. For example, Multiply the firm’s sales by the V/Sales multiple. Multiply the firm’s # of customers by the
V/Customers ratio The result is the firm’s total value. Subtract the firm’s debt to get the total
value of its equity. Divide by the number of shares to calculate
the price per share.
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Problems w/ Market Multiple Methods
It is often hard to find comparable firms. What are relevant multiples? New Co.’s often lack earnings Average ratio for sample of comparable firms
often has a wide range. I.E, ave P/E ratio might be 20, but range from 10 to
50. How do you know whether firm should be compared to low, average, or high performers?
Differences between firms in comparables pool i.e: growth rates, risk, cost of capital
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What if an equity’s dividend is fixed? No g !
P0 = ^ D1
rs – g
So, Po = D1 /rs
And return = D1 / Po
It’s a perpetuity
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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 firm into bankruptcy.
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Expected return =?, given Preferred stock share trading at $50 & pays annual dividend = $5
Vps = $50 =$5rps^
rps$5
$50^ = = 0.10 =
10.0%
A determinant of Growth
Relationship between ROE, Retention Rate, EPS growth, and Dividends
A firm has an ROE of 25% & Retention Rate of 80%. If the most recent EPS was $3.00, what’s the expected dividend at the end of the year?
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Why are stock prices volatile?
P0 = ^ D1
rs – g
rs = rRF + (RPM)bi could change. Inflation expectations Risk aversion Company risk
g could change.
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Consider the following situation.
D1 = $2, rs = 10%, and g = 5%:
P0 = D1/(rs – g) = $2/(0.10 – 0.05) = $40.
What happens if rs or g changes?
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Stock Prices vs. Changes in rs and 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
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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 aren’t volatile, then this means there isn’t a good flow of information.
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What is market equilibrium?
In equilibrium, the intrinisic price must equal the actual price.
If the actual price is lower than the fundamental value, then the stock is a “bargain.” Buy orders will exceed sell orders, the actual price will be bid up. The opposite occurs if the actual price is higher than the fundamental value.
(More…)
Stock’sIntrinsic Value
“True” Expected
Future Cash Flows
“Perceived”
Risk
“True”
Risk
“Perceived” Expected
Future Cash Flows
Stock’sMarket Price
Intrinsic Values and Market Stock Prices
Managerial Actions, the Economic
Environment, and the Political Climate
Market Equilibrium:
Intrinsic Value = Stock Price
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rs = D1/P0 + g = rs = rRF + (rM – rRF)b.^
In equilibrium, expected returns must equal required returns:
Expected Return vs. Required Return
16% >
10% <
15% reqr’d to invest :: undervalued
Stock priced too low so buy b/c bargain
As more people buy it, Price & return
:: then reach equilibrium level of return
:: overvalued -SELL
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How is equilibrium established?
If rs = + g > rs, then P0 is “too low.”
If the price is lower than the fundamental value, then the stock is a “bargain.” Buy orders will exceed sell orders, the price will be bid up until:
D1/P0 + g = rs = rs.
^D1
^
^P0
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What’s the Efficient MarketHypothesis (EMH)?
Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or inside information.
EMH does not assume all investors are rational.
EMH assumes that stock market prices track intrinsic values fairly closely.
(More…)
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EMH (continued)
If stock prices deviate from intrinsic values, investors will quickly take advantage of mispricing.
Prices will be driven to new equilibrium level based on new information.
It is possible to have irrational investors in a rational market.
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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.
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Semistrong-form EMH
All publicly available information is reflected in stock prices, so it doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true.
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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.
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Markets are generally efficient because:
100,000 or so trained analysts—MBAs, CFAs, and PhDs—work for firms like Fidelity, Morgan, and Prudential.
These analysts have similar access to data and megabucks to invest.
Thus, news is reflected in P0 almost instantaneously.
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Market Efficiency
For most stocks, for most of the time, it is generally safe to assume that the market is reasonably efficient.
However, periodically major shifts can and do occur, causing most stocks to move strongly up or down.
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Implications of Market Efficiency for Financial Decisions
Many investors have given up trying to beat the market. This helps explain the growing popularity of index funds, which try to match overall market returns by buying a basket of stocks that make up a particular index.
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Implications of Market Efficiency for Financial Decisions
Important implications for stock issues, repurchases, and tender offers.
If the market prices stocks fairly, managerial decisions based on over- and undervaluation might not make sense.
Managers have better information but they cannot use for their own advantage and cannot deliberately defraud investors.
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Rational Behavior vs. Animal Spirits, Herding, and Anchoring Bias
Stock market bubbles of 2000 and 2008 suggest that something other than pure rationality in investing is alive and well.
People anchor too closely on recent events when predicting future events. When market is performing better than
average, they tend to think it will continue to perform better than average.
Other investors emulate them, following like a herd of sheep.
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Conclusions Markets are rational to a large extent, but at
time they are also subject to irrational behavior. One must do careful, rational analyses using
the tools and techniques covered in the book. Recognize that actual prices can differ from
intrinsic values, sometimes by large amounts and for long periods.
Good news! Differences between actual prices and intrinsic values provide wonderful opportunities for those able to capitalize on them.
