Transcript 9.2 The Dividend-Discount Model

PowerPoint
to accompany
Chapter 9
Valuing Shares
9.1 Share Basics

Ordinary share: a share of ownership in the
corporation, which gives its owner rights to vote on
the election of directors, mergers or other major
events.


As an ownership claim, ordinary shares carry the
right to share in the profits of the corporation through
dividend payments.
Dividends: periodic payments, usually in the form
of cash, that are made to shareholders as a partial
return on their investment in the corporation.

Shareholders are paid dividends in proportion to the
amount of shares they own.
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9.2 The Dividend-Discount Model

A one-year investor

Two potential sources of cash flows from shares:
1. The firm might pay out cash to its shareholders in
the form of a dividend.
2. The investor might generate cash by selling the
shares at some future date.
 Future dividend payments and share price are
unknown.
 Investors will be willing to pay a price up to that
point that the investment has a zero NPV—at which
the current share price equals the PV of the
expected future dividend and sale price.
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9.2 The Dividend-Discount Model

A one-year investor (cont’d)

As the expected cash flows are risky, we cannot
discount them with the risk-free interest rate, but
need to use the cost of capital for the firm’s equity.

Equity cost of capital rE: the expected return of
other investments available in the market with
equivalent risk to the firm’s share.

P0: the price of the share at the beginning of the
period

P1: the price of the share at the end of the period

Div1: the expected dividend during the period
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9.2 The Dividend-Discount Model

A one-year investor (cont’d)

Share Price = PV(future cash flows)

Share Price = PV(Dividends + Capital Gains)
Po = (Dividends + P1 – Po )
(1+rE)
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9.2 The Dividend-Discount Model

The expected total return of a share should equal
its equity cost of capital—it should equal the
expected return of other investments available in
the market with equivalent risk.
Total return:
FORMULA!
(Eq. 9.2)
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9.2 The Dividend-Discount Model

Dividend yield: the expected annual dividend of
the share divided by its current price.

Capital gain: the amount the investor will earn on
the share - difference between the expected sale
price and the original purchase price for an asset.

Total return: the sum of the dividend yield and the
capital gain rate - the expected return the investor
will earn for a one-year investment in the share.
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Example 9.1
Share Prices and Returns (pp.267-8)
Problem:

Suppose you expect Coca Cola to pay an annual
dividend of $0.56 per share in the coming year
and to trade $45.50 per share at the end of the
year.

If investments with equivalent risk to Coca Cola
shares have an expected return of 6.80%, what is
the most you would pay today for Coca Cola
shares?

What dividend yield and capital gain rate would
you expect at this price?
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Example 9.1
Share Prices and Returns (pp.267-8)
Solution:
Plan:

We can use Eq. 9.1 to solve for the beginning
price we would pay now (P0) given our
expectations about dividends (Div1=0.56) and
future price (P1=$45.50) and the return we need to
expect to earn to be willing to invest (rE=6.8%).
FORMULA!

(Eq. 9.1)
We can then use Eq. 9.2 to calculate the dividend
yield and capital gain.
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Example 9.1
Share Prices and Returns (pp.267-8)
Execute:
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Example 9.1
Share Prices and Returns (pp.267-8)
Evaluate:

At a price of
is
cost of capital.
, Coca Cola expected total return
which is equal to its equity

This amount is the most we would be willing to pay
for the share. If we paid more, our expected return
would be less than 6.8% and we would rather invest
elsewhere.

If current share prices are less than this amount, it
would be a positive NPV investment.

If current share price exceeds this amount, selling it
would produce a positive NPV and the share price
would quickly fall.
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9.2 The Dividend-Discount Model

A multi-year investor

We now extend the intuition we developed for the
1-year investor’s return to a multi-year investor.

Eq. 9.1 depends upon the expected share price
in one year, P1

But suppose we planned to hold the shares for
two years. Then, we would receive dividends in
both year 1 and year 2 before selling the shares,
as shown in the following timeline:
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9.2 The Dividend-Discount Model

Setting the share price equal to the present value of
the future cash flows:
(Eq. 9.3)

As a two-year investor, we care about the dividend
and share price in year 2.
FORMULA!
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9.2 The Dividend-Discount Model

Dividend-discount model

This equation applies to a N-year investor.
The share price is equal to the present value of all
of the expected future dividends it will pay.

Dividend–discount model:
(Eq. 9.4)
(Eq. 9.5)
FORMULA!
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9.3 Estimating Dividends in the
Dividend-Discount Model

Constant dividend growth model

A constantly used approximation is to assume that
dividends will grow at a constant rate, g, forever.
Constant dividend growth model:
(Eq. 9.6)

The value of the firm depends on the dividend level
of next year, divided by the equity cost of capital
adjusted by the growth rate.
FORMULA!
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Example 9.2 Valuing a Firm with
Constant Dividend Growth (p.270)
Problem:

Greta’s Garbos is a waste collection company.

Suppose Greta’s Garbos plans to pay $2.30 per
share in dividends in the coming year.

If its equity cost of capital is 7% and dividends
are expected to grow by 2% per year in the
future, estimate the value of Greta’s Garbos’
shares.
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Example 9.2 Valuing a Firm with
Constant Dividend Growth (p.270)
Plan:

Because the dividends are expected to grow
perpetually at a constant rate, we can use Eq. 9.6
to value Greta’s Garbos.

The next dividend (Div1) is expected to be $2.30,
the growth rate (g) is 2% and the equity cost of
capital (rE) is 7%.
Execute:
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Example 9.2 Valuing a Firm with
Constant Dividend Growth (p.270)
Evaluate:

You would be willing to pay 20 times this year’s
dividend of $2.30 to own Greta’s Garbos shares
because you are buying a claim to this year’s
dividend and to an infinite growing series of
future dividends.
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9.3 Estimating Dividends in the
Dividend-Discount Model

Dividend versus investment and growth

Often firms face a trade-off—increasing growth may
require investment, and money spent on investment
cannot be used to pay dividends.

What determines the rate of growth of a firm’s
dividend?

We can define a firm’s dividend payout rate as the
fraction of earnings that the firm pays as dividends
each year:
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9.3 Estimating Dividends in the
Dividend-Discount Model

Dividend payout rate

The firm’s dividend each year is equal to the firm’s
earnings per share (EPS) multiplied by its dividend
payout rate.
FORMULA!

(Eq. 9.8)
The firm can, increase its dividend in three ways:
1. It can increase its earnings (net income).
2. It can increase its dividend payout rate.
3. It can decrease its number of shares
outstanding.
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9.3 Estimating Dividends in the
Dividend-Discount Model

Retention rate

New investment equals the firm’s earnings
multiplied by its retention rate, or the fraction of
current earnings that the firm retains:
Retention Rate = 1 – Dividend Payout Rate
FORMULA!
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9.3 Estimating Dividends in the
Dividend-Discount Model

A simple model of growth

A firm can do two things with its earnings—it can
pay them out to investors, or it can retain and invest
them.

If all increases in future earnings result exclusively
from new investment made with retained earnings,
then:
Change in earnings =
New
investment
x
Return on new
investment
(Eq. 9.9)
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9.3 Estimating Dividends in the
Dividend-Discount Model
Change in earnings =
New investment =
Earnings growth rate =
(g)
FORMULA!

New
x
investment
Earnings
Return on new
investment
x
Retention rate
Change in earnings
Earnings
g =
Return on new
investment
x
Retention
Rate
The equation shows that a firm can increase its
growth by retaining more of its earnings, but will
have to reduce its dividends.
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Example 9.3 Cutting Dividends for
Profitable Growth (pp.272-3)
Problem:



Crane Sporting Goods expects to have earnings
per share of $6 in the coming year.
Rather than reinvest these earnings and grow,
the firm plans to pay out all of its earnings as a
dividend.
With these expectations of no growth, Crane’s
current share price is $60.
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Example 9.3 Cutting Dividends for
Profitable Growth (pp.272-3)
Problem (cont'd):

Suppose Crane could cut its dividend payout rate
to 75% for the foreseeable future and use the
retained earnings to open new stores.

The return on investment in these stores is
expected to be 12%.

If we assume that the risk of these new
investments is the same as the risk of its existing
investments, then the firm’s equity cost of capital
is unchanged.

What effect would this new policy have on
Crane’s share price?
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Example 9.3 Cutting Dividends for
Profitable Growth (pp.272-3)
Solution:
Plan:

We need to calculate Crane’s equity cost of capital and
determine its dividend and growth rate under the new
policy.

Because we know that Crane currently has a growth rate
of 0 (g = 0), a dividend of $6 and a price of $60, we can
use Eq. 9.6 to estimate rE.

Next, the new dividend will simply be 75% of the old
dividend of $6.

Finally, given a retention rate of 25% and a return on
new investment of 12%, we can calculate the new
growth rate (g) and calculate the price of Crane’s shares
if it institutes the new policy.
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Example 9.3 Cutting Dividends for
Profitable Growth (pp.272-3)
Execute:
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Example 9.3 Cutting Dividends for
Profitable Growth (pp.272-3)
Execute (cont’d):

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Example 9.3 Cutting Dividends for
Profitable Growth (pp.272-3)
Evaluate:

Crane’s share price should rise from $60 to
$64.29 if the company cuts its dividend in order
to increase its investment and growth, implying
that the investment has positive NPV.

By using its earnings to invest in projects that
offer a rate of return (12%) greater than its equity
cost of capital (10%), Crane has created value
for its shareholders.
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9.3 Estimating Dividends in the
Dividend-Discount Model

Changing growth rates

Successful young firms have very high initial growth
rates and often retain 100% of their earnings to
exploit investment opportunities.
As they mature, growth slows, earnings exceed
their investment needs and they begin to pay
dividends.
We cannot use the constant dividend model to
value such a firm for two reasons:


1. These firms often pay no dividends when they are young.
2. Their growth rate continues to change over time until
they mature.
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9.3 Estimating Dividends in the
Dividend-Discount Model

Limitations of the DDM

Uncertainty is associated with forecasting a firm’s future
dividends.
Let’s consider an example, where a firm pays annual
dividends of $0.72.
With an equity cost of capital of 11% and expected
dividend growth of 8%, the DDM implies a share price of:



With a 10% growth rate, however, this estimate would
rise to $72 per share; with a 5% growth rate it would fall
to $12 per share (Figure 9.2).
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Figure 9.2 Share Prices for Different
Expected Growth Rates
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9.4 Total Payout and Free Cash
Flow Valuation Models

Discounted free cash flow model

The discounted free cash flow model determines the
total value of the firm to all investors - equity holders
and debt holders.

The enterprise value is equivalent to owning the
unlevered business. It can be interpreted as the net
cost of acquiring the firm’s equity, taking its cash and
paying off all debt.
Enterprise value(V0)= Market value of equity + Debt – Cash
(Eq. 9.16)
FORMULA!
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9.4 Total Payout and Free Cash
Flow Valuation Models

Discounted free cash flow model (cont’d)

Measures the cash generated by the firm before any
payments to debt and equity holders are considered
Enterprise Value (V0)= PV (Future free cash flow of firm)
(Eq. 9.18)

Given the enterprise value, V0, we can estimate the
share price by using Eq. 9.16 to solve for the value
of equity and then divide by the total number of
shares outstanding.
Market Value of Equity = V0 – Debt0 + Cash0
P0 =
FORMULA!
V0 – Debt0+ Cash0
Shares outstanding0
(Eq. 9.19)
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9.4 Total Payout and Free Cash
Flow Valuation Models

Implementing the model

A key difference between the discounted free cash
flow model and the dividend discount model is the
discount rate.

Previously, we used the firm’s equity cost of capital,
rE, because we were discounting the cash flow to
equity holders.

Here, we are discounting the free cash flow that will
be paid to both debt and equity holders, thus, we use
the firm’s weighted average cost of capital
(WACC)—it is the cost of capital that reflects the
overall risk of the business, rWACC, and is the
expected return that a firm needs to pay to investors.
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9.4 Total Payout and Free Cash
Flow Valuation Models

Free cash flow (FCF) measures the cash generated by
the firm before any payments to debt or equity holders
are considered
FCF= EBIT * (1 - tax rate) + Depreciation – Capital Expenditure –
Increases in net working capital
(Eq. 9.17)

We can forecast the firm’s free cash flow up to some
horizon and add a terminal (continuation) value of the
enterprise
(Eq. 9.20)

Often we estimate the terminal value(Vn) by assuming a
constant long-run growth rate g FCF for free cash flows
beyond year n
(Eq. 9.21)
FORMULA!
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Example 9.8 Valuation Using free cash
flow (pp.281)
Problem:

JBH’s free cash flows over the next 5 years are estimated
as follows
Year
2010
2011
2012
2013
2014
2015
FCF ($ million)
128.5
155.2
173
181.7
189
196.6

After then, the free cash flows are expected to grow at the
industry average of 4% per year.

The weighted average cost of capital of JBH is 10%, while
JBH has $30 million in cash and $90 million in debt and
107.25 million shares outstanding

Estimate the value of JBH shares in 2009 using the free
cash flow method.
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Example 9.8 Valuation Using free cash
flow (pp.281)
Plan:




In order to calculate the enterprise value of JBH we
need the terminal value for JBH at the end of the
given projections.
Given an expected constant growth rate (4%) for
JBH after 2015, we can use eq 9.21 to calculate a
terminal enterprise value.
The present value of the free cash flows during
years 2010-2015 and the terminal value will be the
total enterprise value for JBH.
Using that value, we can subtract the debt, add the
cash and divide by the number of shares
outstanding to calculate the price per share.
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Example 9.8 Valuation Using free cash
flow (pp.281)
Execute:
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Example 9.8 Valuation Using free cash
flow (pp.281)
Evaluate:

The valuation principal tells us that the present
value of all future cash flows generated by JBH
plus the value of the cash held by the firm
today must equal the total value today of all the
claims, both debt and equity, on those cash
flows and cash.

Using that principal we calculate the total value
of all of JBH’s claims and then subtract the
debt portion to value the equity.
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9.5 Valuation Based on Comparable
Firms






Method of comparables: estimates 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 multiples: ratio of the value to some
measure of the firm’s scale.
Trailing earnings: earnings over the prior 12 months.
Forward earnings: expected earnings over the
coming 12 months.
Trailing P/E: the resulting ratio from trailing earnings.
Forward P/E: the resulting ratio from forward
earnings.
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Example 9.9 Valuation Using the Price–
Earnings Ratio (pp.284-5)
Problem:

Suppose electronics retailer Great Spark has
earnings per share of $1.38.

If the average P/E of comparable retail shares is
21.3, estimate a value for Great Spark’s shares
using the P/E as a valuation multiple.

What are the assumptions underlying this
estimate?
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Example 9.9 Valuation Using the Price–
Earnings Ratio (pp.284-5)
Solution:
Plan:

We estimate a share price for Great Spark by
multiplying its EPS by the P/E of comparable
firms.
Execute:

P0 = $1.38 x 21.3 = $29.39
This estimate assumes that Great Spark will have
similar future risk, payout rates and growth rates
to comparable firms in the industry.
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Example 9.9 Valuation Using the Price–
Earnings Ratio (pp.284-5)
Evaluate:

Although valuation multiples are simple to use,
they rely on some very strong assumptions about
the similarity of the comparable firms to the firm
you are valuing.

It is important to consider these assumptions are
likely to be reasonable—and thus to hold—in
each case.
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9.5 Valuation Based on Comparable
Firms

Limitations of multiples

Firms are not identical, so usefulness of a valuation
multiple will depend on the nature of the differences.
Furthermore, multiples only provide information
about value of the firm relative to other firms in the
comparison set.
Table 9.1 lists several valuation multiples for
selected firms in the retail industry as of October
2009.
Data shows that the retail industry has a lot of
dispersion for all of the multiples, which most likely
reflects differences in expected growth rates and
risks (therefore, cost of capital).



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Table 9.1 Share Prices and Multiples for
Selected Firms in the Retail Sector
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9.5 Valuation Based on Comparable
Firms

Share valuation techniques—the final
word

No single technique provides a final answer
regarding a share’s true value.

Practitioners use a combination of these
approaches.

Confidence comes from consistent results from a
variety of these methods.
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9.6 Information, Competition and
Share Prices

Information in share prices

Investors trade until they reach a consensus
regarding the value of the shares, which aggregate
the information and views of many different
investors.

A valuation model is best applied to tell us
something about the firm’s future cash flows or
cost of capital, based on its current share price.

Only if we have some superior information that
other investors lack regarding the firm’s cash flows
and cost of capital would it make sense to secondguess the stock price.
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Figure 9.5 The Valuation Triad
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Example 9.10 Using the Information in
Share Prices (p.289)
Problem:

Suppose Tecnor Industries will pay a dividend this
year of $5 per share.

Its equity cost of capital is 10%, and you expect its
dividend to grow at a rate of approximately 4% per
year, though you are somewhat unsure of the
precise growth rate.

If shares are currently trading at $76.92, how
would you update your beliefs about its dividend
growth rate?
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Example 9.10 Using the Information in
Share Prices (p.289)
Solution:
Plan:



If we apply the constant dividend growth model
based on a 4% growth rate, we can estimate a
share price.
If the market price is higher than our estimate, it
implies that the market expects higher growth in
dividends than 4%.
Conversely, if the market price is lower, it expects
dividend growth to be less than 4%.
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Example 9.10 Using the Information in
Share Prices (p.289)
Execute:
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52
Example 9.10 Using the Information in
Share Prices (p.289)
Evaluate:

Given the $76.92 market price for the share, we
would lower our expectations for the dividend
growth rate from 4%, unless we have very strong
reasons to trust our own estimate.
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9.7 Information, Competition and
Stock Prices

Competition and efficient markets

Efficient markets hypothesis: the idea that
competition among investors works to eliminate all
positive NPV trading opportunities.

It implies that securities will be fairly priced, based
on their future cash flows, given all information that
is available to investors.

Underlying rational is the presence of competition.
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9.7 Information, Competition and
Stock Prices

Competition and efficient markets

Public, easily available information: information
available to all investors includes information in
news reports, financial statements, corporate press
releases or other public data sources.

If effects of this information on the firm’s future
cash flows can be readily ascertained, then all
investors determine how this information changes
the firm’s value.

We expect share prices to react instantaneously to
such news.
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9.7 Information, Competition and
Stock Prices

Competition and efficient markets

Private or difficult-to-interpret information: some
expert information is not publicly available or might
be difficult to interpret.

While fundamental information may be public, the
interpretation of that information will affect the firm’s
future cash flows.

When private information is only in the hands of a
relatively small number of investors, these investors
may be able to profit by trading on their information.

As these traders begin to trade, their actions will
tend to move prices, so over time prices will reflect
their information as well.
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