Stocks and Their Valuation
Facts about Common Stock
– Claim on income after interest and dividend payments to the creditors
and preferred stock holders
– Represents ownership and Ownership implies control
– Shareholders get cash flow rights and control rights
– Limited liability
Advantages of Financing with Stock
– No required fixed payments
– No maturity
– No default, no repayment to investors
Disadvantages of Financing with Stock
– Controlling shareholders may lose some control (Dilution of ownership)
– Future earnings shared with new stockholders.
=>Possible EPS Dilution
– Higher flotation costs vs. debt
– Higher component cost of capital
– Too little debt may encourage a takeover bid
Intrinsic Value and Stock Price
Outside investors, corporate insiders, and analysts use a
variety of approaches to estimate a stock’s intrinsic value
(P0).
In equilibrium we assume that a stock price equals its
intrinsic value.
o Outsiders estimate intrinsic value to help determine
which stocks are attractive to buy and/or sell.
o Stocks with a price below (above) its intrinsic value are
undervalued (overvalued) by the market.
Different approaches for estimating the intrinsic
value of a common stock
Dividend growth model
Corporate value model
Using the multiples of comparable firms
Stock Valuation
Stock value = PV of Dividends
D1 D2 D3 D
Pˆ0 ........
(1 ks )1 (1 ks )2 (1 ks )3 (1 ks )
For Valuation: we will assume stocks fall into one of the following
dividend growth patterns.
– Constant growth rate in dividends
– Zero growth rate in dividends
– “Supernormal” (non-constant) growth rate in dividends
Constant Growth Stock Valuation Model
D1 D0(1 g )1
D2 D0(1 g )2
Dt D0(1 g )t
If g is constant, then
D (1 g ) D1
Pˆ0 0
ks g ks g
,where
D0 = today’s (or current) dividend
D1 = expected dividend at the end of this year (year1)
Ks = stocks’ required rate of return
g = the constant growth rate in dividends
Example
ABC Inc. currently pays a dividend of $3 per share, and this dividend is
expected to grow at a constant annual rate of 8% forever. ABC’s stock
has a beta of 1.6, the risk-free rate is 5%, and the market risk premium is
9%. What is the most a well-diversified investor would be willing to pay
for a share of ABC Inc.?
Example – cont’d…
Solution
D0 = $3, g = 8% or 0.08, D1 = $3(1.08) = $3.24, need ks
Can find required return from
P̂0
Expected Return of Constant Growth Stocks
Expected rate of return = Expected dividend yield + Expected
Capital Gains Yield
D1/P0 = Expected Dividend Yield
g = Expected Capital Gains Yield
From our example, D1 = $3.24, P0 = $28.42, g = 8%
k̂ s
Expected Return of Constant Growth Stocks -cont’d..
What happens if g > ks ?
We can’t use model unless (1) ks > g and (2) g is expected to be
constant forever.
Zero Growth Stock Valuation
Just a special case of constant growth valuation, g = 0
P = D/ks, and ks = D/P
“Supernormal” Growth Stock Valuation
Framework: Assume Stock has period of non-constant growth in
dividends and earnings and then eventually settles into a normal
constant growth pattern (gn)
0 g1 1 g2 2 g3 3 gn 4 gn 5 gn
….
D1 D2 D3
“Supernormal” Growth Stock Valuation – cont’d…
Supernormal Growth Valuation Process ( 3 Step Process )
Step 1: Estimate dividends during “supernormal” growth period
Step 2: Estimate price, which is the PV of the constant growth
dividends, at the end of “supernormal” growth period which is also
the beginning of the constant growth period.
Step 3: Find the PV of “supernormal” dividends and constant
growth price. The total of these PVs = Today’s estimated stock
value.
Example
Webscape Software currently pays no dividends. Webscape plans
to pay a $1 per share dividend a year from today. Analysts predict
that Webscape’s dividends and earnings per share will grow by 30%
in year 2, and 50% in year 3. After year three, analysts predict that
Webscape’s dividends and earnings will grow at a constant 10%
annual rate forever. What is the value of Webscape’s stock if the
stock’s required return is 20%?
Solution
D1 = $1, g2 = 30% or 0.3, g3 = 50% or 0.5, gn = 10% or 0.1, ks =
20% or 0.2
Example – cont’d…
Find “Supernormal” Dividends:
D1 =
D2 =
D3 =
Need to find P3 : Recall gn = 10%, ks = 20%
P3 =
Now, we need to find the PV of the supernormal dividends and PV
of P3 at the required rate of return.
The sum of these PVs will be the today’s value of the stock.
Preferred Stock Characteristics
– Unlike common stock, no ownership interest
– Second to debt holders on claim on company’s assets in the
event of bankruptcy
– Like bonds, preferred stockholders receive a fixed dividend that must
be paid before dividends are paid to common stockholders.
– Annual dividend yield as a percentage of par value
– Preferred dividends must be paid before common dividends
Preferred Stock Valuation
– Promises to pay the same dividend year after year
forever, never matures.
– A perpetuity
– Vps = D/kps
Preferred Stock Valuation – cont’d…
Example: GM preferred stock has a $25 par value with a 8%
dividend yield. What price would you pay if your required return is
9%?
D=
Vps =
Expected Return on Preferred Stock
Just adjust the valuation model:
D
k ps
P0
Example:
If we know the preferred stock price is $40, and the preferred
dividend is $4.125, the expected return is:
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
o FCF = NOPAT – Net capital investment
Applying the corporate value model
Find the value of the firm, by finding the PV of the firm’s
future FCFs.
Subtract the value of firm’s debt and preferred stock to get
the value of common stock.
Divide the value of common stock by the number of shares
outstanding to get intrinsic stock price.
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.
Given the long-run gFCF = 6%, and r= 10%, use the
corporate value model to find the firm’s intrinsic value.
0 r = 10% 1 2 3 4
...
g = 6%
-5 10 20 21.20
-4.545
8.264
15.026 21.20
398.197 530 = = TV3
0.10 - 0.06
416.942
If the firm has $40 million in debt and has 10 million shares
of stock, what is the firm’s intrinsic value per share?
Value of equity= value of firm – value of debt
= $416.94 - $40
= $376.94 million
Value per share=value of equity / # of shares
= $376.94 / 10
= $37.69
Firm multiples method
Analysts often use the following multiples to value
stocks.
o P / E
o P / CF
o P / Sales
EXAMPLE: Based on comparable firms, estimate the
appropriate P/E. Multiply this by expected earnings to
back out an estimate of the stock price.
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:
o The current market stock price equals its intrinsic
value (P0 = P0).
o Expected returns must equal required returns.
^ D1
rs g r^s rRF (rM rRF )b
P0
Market equilibrium
Expected returns are determined by estimating dividends
and expected capital gains.
Required returns are determined by estimating risk and
applying the CAPM.
How is market equilibrium established?
If price is below intrinsic value …
o The current price (P0) is “too low” and offers a bargain.
o Buy orders will be greater than sell orders.
o P0 will be bid up until expected return equals required
return.
