Chapter 9 Valuing Stocks
9.1 The Dividend Discount Model
A One-Year Investor
Potential Cash Flows
Dividend
Sale of Stock
Timeline for One-Year Investor
 Div1  P1 
P0  

 1  rE 
What is the discount rate?
What discount rate should we use?
Equity cost of capital
Dividend Yields, Capital Gains, and Total Returns
rE 
Div1  P1
 1 
P0
Div1
P0

Dividend Yield
P1  P0
P0
Capital Gain Rate
How do you make money investing in stocks?
The Dividend-Discount Model Equation
What is the price if we plan on holding the stock for N years?
P0 
Div1
Div2


1  rE
(1  rE ) 2

DivN
PN

N
(1  rE )
(1  rE ) N
This is known as the Dividend Discount Model.
What variables do we need?
The theoretical life span of the stock is infinity.
What is the PV of $10,000,000,
Future Value (FV)
Present Value (PV)
Annual Interest Rate (I/Y)
Time in Years (N)
P0 
$10,000,000.00
4.00%
500.00
500 years from now at 4%?
Solve for PV
-$0.03
Solve for FV
FV (Continuous Compounding)
Div3
Div1
Div2



2
1  rE
(1  rE )
(1  rE )3



n 1
$0.00
Divn
(1  rE ) n
9.2 Applying the Discount-Dividend Model
Constant Dividend Growth Model
P0 
Div0 1  g
Div1

rE  g
rE  g
rE 
Div1
 g
P0
Break-down the model
.
Constant Growth
The Sunrise Corp recently paid a $2.54 dividend. Dividends are expected to grow at
the historic growth rate of 5.6%. The required return for the company’s equity is
10%. What is the value of the stock?
If the stock traded at $58, what would you do?
Dividends Versus Investment and Growth
A Simple Model of Growth
What is the Dividend Payout Ratio?
What can a firm do to increase its dividend per share?
Profitable Growth
If a firm wants to increase its share price, should it cut its dividend and invest more, or should
it cut investment and increase its dividend?
The answer will depend on the profitability of the firm’s investments.
Cutting the firm’s dividend to increase investment will raise the stock price if,
and only if, the new investments have a positive NPV.
If and only if, there is information describing why they want to do this.
In class activity (find this data)
Variables for Dividend Discount model
Yahoo Finance
RF
Km
Beta
Div Yield
ROE
Div Payout Ratio
Historical DIV
D-1
D-2
D-3
D-4
D-5
Differential Growth (Variable)
Due to an innovative production process, the company will be able to pay dividends at an above
normal rate of 20% for the next 6years. After that, the growth will return to the industry standard
of 11%. The most recent dividend was $2.95. The required return for the company’s equity is
Super-normal Valuation
15%. What is the value?
What are the limitations of the dividend growth model?
9.3 Total Payout and Free Cash Flow Valuation Models
Share Repurchases and the Total Payout Model
The more cash the firm uses to repurchase shares, the less it has available to
pay dividends.
By repurchasing, the firm decreases the number of shares outstanding, which
increases its EPS and DPS.
Share Repurchases and the Total Payout Model
Total Payout Model
PV0 
PV (Future Total Dividends and Repurchases)
Shares Outstanding 0
Values all of the firm’s equity, rather than a single share.
You discount total dividends and share repurchases.
Use the growth rate of earnings (rather than earnings per share) when
forecasting the growth of the firm’s total payouts.
Go to thatswacc.com to find cost of capital (Total payout model)
Yahoo Finance
Shares repurchased
Number of shares
Dividends paid
Thatswacc.com
WACC
The Discounted Free Cash Flow Model
Discounted Free Cash Flow Model
Determines the value of the firm to all investors, including both equity and debt holders
Enterprise Value  Market Value of Equity  Debt  Cash
The enterprise value can be interpreted as the net cost of acquiring the firm’s equity,
taking its cash, paying off all debt, and owning the unlevered business.
Implementing the Model
V0 
FCF1
FCF2


1  rwacc
(1  rwacc ) 2

FCFN
VN

N
(1  rwacc )
(1  rwacc ) N
Often, the terminal value is estimated by assuming a constant long-run growth rate gFCF
for free cash flows beyond year N, so that:
VN 
 1  g FCF 
FCFN  1
 
  FCFN
rwacc  g FCF
 (rwacc  g FCF ) 
The free cash flow valuation model estimates the value of the entire company and uses the cost of
capital as the discount rate.
VF  Vs  VD  cash
to estimate the value of equity:
Vs  VF  VD  cash
Free Cash Flow Model
The firm has estimated the growth of FCF to be 10% over the foreseeable future. The most recent
FCF was $1,000,000. The firms WACC = 15%. What is the firms value?
VF 
1,000,000 * 1  .10  1,100,000

 22,000,000
.15  .10
.05
The firm has 3,000,000 in cash and market value of debt at 12,500,000. The firm has
500,000 shares. What is the value of equity? Per share?
VS  VF - VD  cash
 22,000,000  12,500,000  3,000,000
 12,500,000
Free Cash Flow Valuation
WACC
FCF (last)
FCF (beg)
time
Market value of debt
Cash
# shares
Connection to Capital Budgeting
The firm’s free cash flow is equal to the sum of the free cash flows from the firm’s current and
future investments, so we can interpret the firm’s enterprise value as the total NPV that the
firm will earn from continuing its existing projects and initiating new ones.
The NPV of any individual project represents its contribution to the firm’s enterprise
value.
How can we maximize the value of the firm?
9.4 Valuation Based on Comparable Firms
Method of Comparables (Comps)
Estimate the value of the firm based on the value of other, comparable firms or
investments that we expect will generate very similar cash flows in the future.
Valuation Multiple
A ratio of firm’s value to some measure of the firm’s scale or cash flow
The Price-Earnings Ratio
P/E Ratio
Share price divided by earnings per share
Firms with high growth rates, and which generate cash well in excess of their investment
needs so that they can maintain high payout rates, should have high P/E multiples.
Textbook Example 9.9
Multiplier models
Enterprise Value Multiples
V0
FCF1 / EBITDA1

EBITDA1
rwacc  g FCF
This valuation multiple is higher for firms with high growth rates and low capital requirements
(so that free cash flow is high in proportion to EBITDA).
Textbook Example 9.10
Company data
Yahoo Finance
PE 1
EPS1
PE industry
EV multiplier
EBITDA
Cash
# shares
Price to sales
Rev 1
Debt
Growth Opportunities (not in text)
Growth opportunities are opportunities to invest in positive NPV projects.
The value of a firm can be conceptualized as the sum of the value of a firm that pays out
100% of its earnings as dividends plus the net present value of the growth opportunities.
Value as a cash cow
P
Value of investment opportunities
EPS
 NPVGO
R
The NPVGO Model: Example
Consider a firm that has EPS of $5 at the end of the first year, a dividend-payout ratio
of 30%, a discount rate of 16%, and a return on retained earnings of 20%.
The dividend at year one will be $5 × .30 = $1.50 per share.
The retention ratio is .70 ( = 1 -.30), implying a growth rate in dividends of 14% = .70
× 20%.
From the dividend growth model, the price of a share is:
P0 
Div1
$1.50

 $75
R  g .16  .14
First, we must calculate the value of the firm as a cash cow.
P0 
EPS $5

 $31.25
R
.16
Second, we must calculate the value of the growth opportunities.
(3.50 = 5.00 – 1.50) = retained earn per share.
g = retention calculation
3.50  .20 

 3.50 
$.875
.16 
P0 

 $43.75
Rg
.16  .14
P0  31.25  43.75  $75
What does a negative NPVGO value mean?
For a company add next years forecasted EPS to the stock valuation model.
Retention Rate and Firm Value
What would an increase in retention rate do to the company?
Comparison with Discounted Cash Flow Methods
Discounted cash flows methods have the advantage that they can incorporate specific
information about the firm’s cost of capital or future growth.
The discounted cash flow methods have the potential to be more accurate than
the use of a valuation multiple.
Stock Valuation Techniques: The Final Word
No single technique provides a final answer regarding a stock’s true value. All
approaches require assumptions or forecasts that are too uncertain to provide a definitive
assessment of the firm’s value.
Most real-world practitioners use a combination of these approaches and gain
confidence if the results are consistent across a variety of methods.
Information in Stock Prices
For a publicly traded firm, its current stock price should already provide very accurate
information, aggregated from a multitude of investors, regarding the true value of its shares.
Based on its current stock price, a valuation model will tell us something about the
firm’s future cash flows or cost of capital.
What things would you like to know about prices impacted by information?
Competition and Efficient Markets
Efficient Markets Hypothesis
Implies that securities will be fairly priced, based on their future cash flows, given all
information that is available to investors.
Public, Easily Interpretable Information
If the impact of information can be readily ascertained, then all investors can
determine the effect of this information on the firm’s value.
In this situation, we expect the stock price to react nearly instantaneously to such
news.
Private or Difficult-to-Interpret Information
Private information will be held by a relatively small number of investors. These
investors may be able to profit by trading on their information.
In this case, the efficient markets hypothesis will not hold in the strict sense.
However, as these informed traders begin to trade, they will tend to move prices,
so over time prices will begin to reflect their information as well.
If the profit opportunities from having private information are large, others will devote the
resources needed to acquire it.
In the long run, we should expect that the degree of “inefficiency” in the market
will be limited by the costs of obtaining the private information.
Lessons for Investors and Corporate Managers
Consequences for Investors
If stocks are fairly priced, then investors who buy stocks can expect to receive future cash
flows that fairly compensate them for the risk of their investment.
In such cases the average investor can invest with confidence, even if he is not fully
informed.
Implications for Corporate Managers
Focus on NPV and free cash flow
Avoid accounting illusions
Use financial transactions to support investment
5 points each
1) You are investigating a stock. The last dividend paid was 3.75. The dividend paid
12 years ago was 2.00. We are going to assume that the future growth of
dividends will be 4% greater than the historic average. The risk free rate of return
is currently 5% The average return for the market is 14%. This company has a beta
of 1.46.
What is the required return for the company’s stock?
2) What is the current value of this stock? If the stock is currently selling for $50.00,
what is the expected return? Should you buy the stock? Why or why not?
3)
We have a stock with a current dividend of 5.25. It is estimated that it will have a
growth rate of 15% for the next 4 years, at which time the growth will normalize to
around 8%. The required return on this stock is 14%.. What is the value of this
stock?