Valuing common stocks The plan of the lecture
Review what we have
accomplished in the last lecture
Application of the DCF approach
Some terms about stocks
TIP Valuing stocks using
If you do not understand
something, Dividend growth model
ask me! Corporate value model
the multiples of comparable firms
Some terms about stocks
What have we accomplished?
PV concepts Common Stock - Ownership shares in a
Discount rates publicly held corporation.
NPV rules for taking a project Book Value – Total common equity on the
The formula for calculating perpetuity balance sheet.
and annuity Market Value – Stock price per share * # of
Compounding interest rate shares outstanding.
Some terms about stocks Facts about common stock
Dividend - Periodic cash distribution from Represents ownership
the firm to the shareholders. Ownership implies control
P/E Ratio – Stock Price per share divided Stockholders elect directors
by earnings per share (EPS). Directors elect management
Dividend yield – Dividends per share Management’s goal: Maximize the stock
(DPS) over the stock price of per share price
Types of stock market Stock Market Reporting
transactions 52 WEEKS YLD VOL NET
HI LO STOCK SYM DIV % PE 100s HI LO CLOSE CHG
52.75 19.06 Gap Inc GPS 0.09 0.5 15 65172 20.50 19 19.25 -1.75
Initial public offering market (“going Gap pays a
dividend of 9 Gap ended trading
public”) (Company sells shares to the public Gap has
cents/share at $19.25, down
for the 1st times.) $1.75 from
high as Given the
Primary market (Company sells shares to $52.75 in current price,
the last the dividend
the public for the 2nd, 3rd,…times.)
year. yield is ½ %
Secondary market (stockholders sell shares Given the
to each other) current price, the 6,517,200 shares
been as low traded hands in the
as $19.06 in PE ratio is 15
times earnings last day’s trading
the last year.
Expected return Expected Return
Expected Return - The percentage return that an
The formula for the expected return can be
investor forecasts from a specific investment
over a set period of time.
broken into two parts:
At this stage, you do not need to distinguish
Expected return = Dividend Yield + Capital
between expected return and the discount rate. Appreciation Yield
Div1 + P1 − P0 Div1 P1 − P0
Expected Return = r = Expected Return = r = +
P0 P0 P0
If Fledgling Electronics is selling for $100 per share Jennifer has bought one IBM share in the
today and is expected to sell for $110 one year from
now, what is the expected return if the dividend one
beginning of this year and decides to hold
year from now is forecasted to be $5.00? this share until next year. The expected
dividend this year is $10 per share and the
stock is expected to sell at $110 per share
in the end of the year. If the discount rate
5 + 110 − 100 is 10%, what is the current stock price?
Expected Return = = . 15
Valuing Common Stocks using Valuing common stocks using
Stock value equals the present value of all Example
expected future dividends plus the selling Current forecasts for XYZ Company’s dividends are
price of the stock. $3, $3.24, and $3.50 over the next three years,
respectively. At the end of three years you anticipate
selling your stock at a market price of $94.48. What
Div1 Div2 Div H + PH is the price of the stock now given a 12% discount
P0 = + +...+ rate?
(1 + r ) (1 + r )
(1 + r ) H
H - Time horizon for your investment.
Valuing common stocks using
If we forecast no dividend growth, and plan to
3.00 3.24 3.50 + 94.48 hold out stock indefinitely, we will then value
P = + + the stock as the PV of a PERPETUITY.
(1 + .12) (1 + .12)
(1 + .12)3
P = $75.00 PV ( perpetuity ) = P = or
Assumes all earnings are
paid to shareholders.
Suppose that a stock is going to pay a (a) P0=3/0.1=$30
dividend of $3 every year forever. If the (b)P0=PV (annuity) + PV( the stock price at
discount rate is 10%, what is the current
= 3/1.1 + 3/1.12+(3/0.1)/1.12
stock price for the following cases:
(a) you invest and hold it forever?
(c) P0=PV (annuity of 20 years) +
(b) you invest and hold it for two years? PV (the stock price at the year of 20)
(c) you invest and hold it for 20 years? =$30
Conclusion Dividend growth model
The stock price does not depend on how Since the stock value does not depend on the investment
horizon, let’s assume the investor will hold onto it
long you intend to hold it! forever.
So, value of a stock is the present value of all future
dividends expected to be generated by the stock.
D1 D2 D3 D∞
P = + + + ... +
(1 + r )1 (1 + r )2 (1 + r )3 (1 + r )∞
Constant growth stock I: Dividend Growth Model
A stock whose dividends are expected to Under the assumption that dividends grow at a
grow forever at a constant rate, g. constant rate, stocks can be valued as a
D1 = D0 (1+g)1
perpetuity with a growth rate, (still remember
D2 …...D0 (1+g)2
= the PV of a growth perpetuity?) that is
Dt = D0 (1+g)t Div1
What happens if g > r? Example
If g > r, the constant growth formula leads Suppose that a stock is going to pay a
to a negative stock price, which does not dividend of $3 next year. Dividends grow
make sense. at a growth rate of 3%. If the discount rate
is 10%, what is the stock price?
Using dividends models to estimate
Solution the discount rate or the growth rate
P=3/(0.1-0.03)=$42.86 Discount Rate can be estimated by:
Will the stock value change if you plan to
(a) buy and hold it forever?
(b) buy and hold it for two years? P =
(c) buy and hold it for 20 years? r−g
Some terms about dividend
Valuing Common Stocks
Example- continued If a firm elects to pay a lower dividend, and
A stock is selling for $100 in the stock market. Next reinvest the retained earnings, the stock price
may increase because future dividends may be
year’s dividend is $3. The discount rate for this stock
is 12%.what is the market estimate about the growth
Payout Ratio : Fraction of earnings paid out as
dividends=dividend per share/EPS
Plowback (Retention) Ratio : Fraction of earnings
$3.00 retained by the firm.
.12 − g Payout ratio=1-plowback ratio
g = .09
Deriving the dividend growth rate g Example
Growth can be derived from applying the Our company forecasts to pay a $5.00
return on equity to the percentage of dividend next year, which represents
earnings plowed back into operations. 100% of its earnings. The discount rate
is 12%. Instead of paying out all
ROE = Return on Equity earnings, we decide to plow back 40% of
EPS the earnings at the firm’s current return
= on equity of 20%. What is the value of
Book Equity Per Share
the stock before and after the plowback
g = return on equity X plowback ratio decision?
Solution Example (continued)
5 The difference between these two numbers (75.00-
P = = $41.67 41.67=33.33) is called the Present Value of Growth
g = 0.4* 0.2 = 0.08 Present Value of Growth Opportunities (PVGO) :
Net present value of a firm’s future investments.
P = = $75
0.12 − 0.08
The importance of growth II: Corporate value model (Free Cash
opportunity Flow model)
We often use earnings to value stocks as 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.
P = + PVGO
r A firm generates free cash flows for its stock
holders and debt holders, so:
Why do some hi-tech stocks have high Market value of a firm=Market value of stocks +
prices even though they have little or market value of debt
Issues regarding the corporate
Applying the corporate value model value model
Find the market value (MV) of the firm. Similar to dividend growth model, often
Find PV of firm’s future FCFs assumes at some point free cash flow will
Subtract MV of firm’s debt (and preferred stock, if grow at a constant rate.
any) to get MV of common stock.
MV of common stock = MV of firm– MV of debt
Terminal value (TVn) represents value of
firm at the point of time that growth
Divide MV of common stock by the number of becomes constant.
shares outstanding to get intrinsic stock price
P = MV of common stock / # of shares of common stock
Valuing common stocks using
FCF (free cash flows) FCF and PV
The value of a business is usually computed
as the discounted value of FCF out to a FCF1 FCF2 FCFH PVH
valuation horizon (H). PV = + + ... + +
(1 + r )1 (1 + r ) 2 (1 + r ) H (1 + r ) H
The value after H is sometimes called the
terminal value or horizon value. PV (free cash flows) PV (terminal value)
FCF1 FCF2 FCFH PVH
PV = + + ... + +
(1 + r )1 (1 + r ) 2 (1 + r ) H (1 + r ) H
Given the long-run gFCF = 6%, and firm discount rate of
If the firm has $40 million in debt and has 10
10%, use the corporate value model to find the firm’s
million shares of stock, what is the firm’s stock
value per share?
MV of equity = MV of firm – MV of debt
= $416.94m - $40m
0 r = 10% 1 2 3 4 = $376.94 million
g = 6% Value per share = MV of equity / # of shares
-5 10 20 21.20
= $376.94m / 10m
8.264 = $37.69
398.197 530 = = TV3
0.10 - 0.06
Usually it is more difficult to predict How to get free cash flows
dividend than free cash flows (FCF)?
The corporate value model is often preferred to Remember, free cash flow is the firm’s after-tax
operating income (NOPAT) less the net capital
the dividend growth model, especially when investment
considering firms that don’t pay dividends or FCF = NOPAT – Net capital investment
when dividends are hard to forecast.
NOPAT (net operating profit after tax)= EBIT* (1 –
Projecting free cash flows might give us more Tax rate)
accurate estimates of a firm’s value. FCF = NOPAT – Net capital investment
A lot of accounting information to predict free
cash flow (FCF).
How to get net capital investment then?
How to get net capital investment
then? (Not required) III: Firm multiples method
net capital investment =change in operating capital between adjacent
years. Analysts often use the following multiples to
net capital investment in year t =operating capital at the end of year t
- operating capital at the end of year t-1.
Operating capital = NOWC + Net Fixed Assets
NOWC = Current assets - Non-interest bearing current liability P/B
Examples of Non-interest bearing current liability: account payable, P / Sales
Example of interest bearing current liability: note payable EXAMPLE: Based on comparable firms,
estimate the appropriate P/E. Multiply this
If we ignore change in working capital, then net capital investment
=capital expenditure - depreciation by expected earnings per share to figure out
an estimate of the stock price.
Firm ABC has EPS=$2, a similar firm in
the same industry has a P/E ratio of 30.
What’s you estimate of ABC’s stock price?
Simple and useful.