CHAPTER 8
THE DIVIDEND DISCOUNT AND
FLOWS TO EQUITY MODELS
LEARNING OBJECTIVES
1.
2.
3.
4.
5.
6.
The dividend discount model.
The assumptions of the dividend discount model.
The concept of a just barely sustainable dividend stream and its importance to the dividend discount
model.
The limitations of the dividend discount model.
How the flows to equity model works.
Why the flows to equity and dividend discount models are equivalent.
TRUE/FALSE QUESTIONS
1.
There are two items of cash flows equityholders expect to receive from a stock investment.
(moderate, L.O. 1, Section 1, true)
2.
The dividend discount model discounts only dividends and as such does not consider net cash flows into
the firm.
(moderate, L.O. 2, Section 2, false)
3.
The reasonableness of the dividend discount model lies in its ability to measure the present value of
discounted cash flows from dividends, not from the assumptions used in the model itself.
(moderate, L.O. 2, Section 2, false)
4.
A small spread between the cost of equity and the growth rate causes the sensitivity to vary in the dividend
growth rate.
(difficult, L.O. 2, Section 2, true)
5.
A modest error in the value of g will cause a modest valuation error.
(moderate, L.O. 2, Section 2, false)
6.
To properly value a firm using the dividend discount model, we must value the firm using some other
method first.
(moderate, L.O. 3, Section 2, true)
7.
Selecting a “reasonable” dividend growth rate when using the dividend discount model is sufficient for
most analyses.
(difficult, L.O. 4, Section 2, false)
8.
When working with a multiple-stream dividend discount model, it is important to remember that the just
barely sustainable divided rate is not as critical as it is with a single-stream dividend discount model.
(moderate, L.O. 4, Section 3, false)
9.
The two-stage dividend discount model is very sensitive to assumed dividend growth rates.
(moderate, L.O. 4, Section 4, true)
10.
Although the dividend discount model is not practical to apply, it is still important to understand how it
functions since it is the basis for other cash flow models.
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(moderate, L.O. 4, Section 4, true)
11.
Using the long-term inflation rate assumption may appear to be a reasonable estimate in a dividend
discount valuation model, but there is no way to test if such an assumption is the just barely sustainable
rate for the firm.
(moderate, L.O. 4, Section 4, true)
12.
The higher the supernormal growth rate, the higher the normal growth rate.
(moderate, L.O. 4, Section 4, false)
13.
When a firm does not pay dividends, investors make an assumption that there will be a payout at some
time in the future when a firm is sold or liquidated.
(moderate, L.O. 4, Section 5, true)
14.
In the flows to equity model, the assumption is made that the present value of the dividend stream is
discounted at the rate of return demanded by the holders of the security.
(moderate, L.O. 4, Section 5, false)
15.
In the flows to equity model, the present value of the cash flows to equity do not necessarily equal the
present value of the dividend stream.
(moderate, L.O. 4, Section 5, false)
MULTIPLE CHOICE QUESTIONS
16.
The dividend discount model is based on the idea that the value of any security is the present value of the
security’s expected future cash flows as discounted at a rate of return demanded by the holders of that
security. Therefore, the value of common equity in the dividend discount model is equal to the present
value of the:
a. expected common dividend stream during the holding period
b. expected common dividend stream during the holding period plus the present value of the future stock
price
c. expected common dividend stream during the holding period plus the future value of the current stock
price
d. discounted cost of equity for the security
(moderate, L.O. 1, Section 1, b)
17.
Which statement below is incorrect regarding the dividend discount model?
a. Forecasting the dividend stream correctly in the model is complicated.
b. The value of the equity is the present value of all the expected future returns.
c. The value of the firm’s equity is dependent on the investor’s investment horizon.
d. The holder of a share of stock will receive dividends over the holding period, plus the value of the
stock when he or she sells it.
(moderate, L.O. 1, Section 1, c)
18.
The dividend discount model requires a forecast for an infinite number of years. Since this assumption is
not reasonable or practical to calculate, the Gordon Growth Model is used, which assumes that:
a. the initial dividend used in the formula is the expected dividend in the first year of the future dividend
stream
b. a reasonable cost of equity can be determined using an asset pricing model such as CAPM
c. the dividend growth rate for the firm is the rate just barely sustainable over the long run for which the
firm would have sufficient resources to pay a specified dividend but would not build up any excess
cash
d. All of the answers above are correct.
50
(difficult, L.O. 2, Section 2, d)
19.
The following information is available for a firm: the current dividend paid to equityholders is $3; the
firm’s cost of equity is 12% and it is expected that it will increase dividends by 4% each year in the
foreseeable future. Using the Gordon Growth Model, the firm’s common equity is:
a. $66.00 per share
b. $75.00 per share
c. $25.00 per share
d. $37.50 per share
(moderate, L.O. 2, Section 2, d)
20.
The following information is available for a firm: the current dividend paid to equityholders is $2; the
firm’s cost of equity is 16%; and the firm’s common equity per share is $15.39. Using the Gordon Growth
Model, the value of g for the firm is:
a. g has a value of zero
b. 84%
c. 3%
d. 13%
(moderate, L.O. 2, Section 2, c)
21.
One of the assumptions used in the Gordon Growth Model is that of the dividend growth rate. What is the
relationship between g and g* in this model?
a. g represents a constant rate of growth whereas g* represents a constant rate of growth for time period
*.
b. g represents the initial expected dividend for the first year whereas g* represents the growth in the
dividend rate over a multiple-year reporting period.
c. g represents a constant rate of growth whereas g* represents the just barely sustainable growth rate.
d. There is no relationship between g and g* since g will never be equal to g*.
(moderate, L.O. 3, Section 2, c)
22.
When using the dividend discount model, the firm is properly valued only when g = g*, where g* is the
just barely sustainable growth rate. To be accurate and correct using the dividend discount model, the
analyst must:
a. value the firm without analyzing the just barely sustainable dividend growth rate
b. value the firm using some other method before using the dividend discount model
c. pick a dividend growth rate that approximates growth in the economy
d. solve for g first, then solve for g*, making the dividend discount model of value to the analyst
(moderate, L.O. 3 & 4, Section 2, b)
23.
An analyst working with the dividend discount model uses a growth rate that is greater than g*. The result
of using this particular growth rate is that the firm would:
a. eventually have to borrow money to make its dividend payments
b. build up an infinite amount of cash, which would never be paid out in dividends
c. never have to borrow money to pay dividends to equityholders
d. be able to use excess accumulated cash for investment purposes, thus increasing the value of its equity
(moderate, L.O. 3, Section 2, a)
24.
For an analyst to use the dividend discount model as a reliable method of valuation, the estimates of g must
be very close to g*. In this situation g* represents:
a. the dividend growth rate that approximates the growth in the economy over the long run
b. the dividend growth rate that makes excess cash tend toward zero over the long run for the firm
c. a variable that is greater than g over the long run for the firm
d. a variable that is less than g over the long run for the firm
(moderate, L.O. 3 & 4, Section 2, b)
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25.
To accurately estimate g*, an analyst is likely to use an approach such as:
a. the historical dividend growth rate for the firm
b. the expected growth rate in the economy or industry
c. the expected inflation over the long run for the firm
d. None of the above choices are correct.
(difficult, L.O. 2, Section 4, d)
26.
The dividend discount model can be modified to work with more complex patterns of dividend rates.
When a two-stage model is used, the first stage is generally considered a _______________ while the
second stage is generally considered a ______________.
a. supernormal dividend rate; normal dividend rate
b. just barely sustainable dividend rate; residual dividend rate
c. normal dividend rate; supernormal dividend rate
d. reasonable dividend rate; just barely sustainable dividend rate
(moderate, L.O. 4, Section 3, a)
27.
Which statement below is correct regarding a multiple-stage dividend discount model?
a. The two-stage dividend discount model is less sensitive to assumed growth rates than the singledividend growth rate model.
b. The three-stage dividend discount model is less sensitive to assumed growth rates than the two-stage
dividend growth rate model.
c. The Gordon Growth Model is better suited to a multiple-stage dividend discount model than a singledividend growth rate model.
d. To accurately determine a combination of growth rates that are just barely sustainable requires the
analyst to estimate the value of the firm using some other method.
(difficult, L.O. 4, Section 3, d)
28.
When a two-stage dividend discount model is used, the analyst must make assumptions about:
a. the normal growth rate
b. the supernormal growth rate
c. the number of years of the firm’s supernormal growth rate
d. All of the answers are correct.
(easy, L.O. 4, Section 4, d)
29.
Under the dividend discount model, the value of equity:
a. will be zero when no dividends are paid by a firm
b. is the present value of future dividends forever
c. is the future value of the initial first-year dividends of a firm
d. is easier to determine when no dividends are paid by a firm since g will equal the just barely
sustainable dividend rate by default
(moderate, L.O. 4, Section 4, b)
30.
In a two-stage dividend discount model, what is the relationship between the first and second stage growth
rates?
a. Generally, the first stage is the supernormal growth rate and the second is the normal growth rate,
which is assumed to be sustainable indefinitely.
b. Generally, the first stage is the normal growth rate and the second is the supernormal growth rate,
which mirrors the firm’s growth and maturity as a competitor in the marketplace.
c. The valuation formula requires that the stage one growth rate is always higher than the stage two
growth rate.
d. The valuation formula requires that the stage one growth rate is always lower than the stage two
growth rate.
(moderate, L.O. 4, Section 4, a)
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31.
How is the just barely sustainable dividend stream used in a two- or three-stage dividend discount model?
a. It is not necessary to use the just barely sustainable dividend stream in two-stage models.
b. No matter how dividend streams are presented in the model, it is necessary to use a dividend stream
that the firm’s net cash inflows can support, but just barely.
c. In a two- or three-stage model, it is not necessary to use the just barely sustainable dividend stream for
the stage considered to be the normal dividend growth rate.
d. It is necessary to use the just barely sustainable dividend stream in a two-stage model, but its use is
optional in a three-stage model.
(moderate, L.O. 4, Section 4, b)
32.
In the flows to equity model:
a. the just barely sustainable dividend growth rate is disregarded
b. the dividend stream will not be the same as the flows to equity
c. the dividend stream must match the flows to equity in each year
d. the present value of the dividend stream must be equal to the present value of the net cash flows
coming into the firm
(easy, L.O. 5, Section 5, d)
33.
In the flows to equity formula used to solve for common equity, cash flows to equity equal the free cash
flows:
a. from core operations plus nonoperating cash flows
b. from core operations minus nonoperating cash flows minus debt service and flows to other capital
providers
c. plus nonoperating cash flow minus debt service and flows to other capital providers
d. minus nonoperating cash flow plus debt service and flows to other capital providers
(difficult, L.O. 5, Section 5, c)
34.
The valuation model that relies on the idea that the value of any security is the present value of the cash
flows the security is expected to generate, which amount is identical to the cash flows into the firm’s equity
component, is known as:
a. dividend discount model
b. free cash flow model
c. flows to equity model
d. None of the answers above are correct.
(easy, L.O. 6, Section 5, c)
35.
One key difference between the dividend discount and flows to equity models is:
a. the flows to equity model looks at the cash flows that would be available to fund the dividend stream
b. the dividend discount model looks at the cash flows that would be available to fund the dividend
stream
c. the flows to equity model looks at the dividend stream itself
d. the dividend discount model discounts the free cash inflow into the equity component of the firm
(moderate, L.O. 6, Section 5, a)
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ESSAYS
36.
Explain the problems associated with the dividend growth rate used in the Gordon Growth Model.
Suggested solution:
The Gordon Growth Model, as part of the dividend discount valuation model, operates with three
assumptions: the initial dividend paid by the firm; the firm’s cost of equity; and the growth rate of the
firm’s dividends. The initial dividend paid by the firm is easy to determine, and it may be based on
historical information. The firm’s cost of equity can be reasonably estimated using a model such as the
capital asset pricing model (CAPM). The harder assumption to work with is the growth rate of the firm’s
dividends (represented by the letter g in the formula).
The dividend growth rate (or g) in the Gordon Growth Model is the rate at which dividends will grow for
an indefinite period of time. If an analyst uses a rate of 5%, the assumption is made that dividends will
grow 5% for each succeeding period for the firm. The major problem with this assumption is that it is not
reasonable or practical to expect a firm to increase its dividends each succeeding period by a rate of 5%.
The issue, then, is what rate can be used that is accurate and sustainable by the firm in the long term.
The best way to estimate the dividend growth rate in the Gordon Growth Model is to use the dividend rate
that is just barely sustainable by the firm in the long term (denoted as g*). The just barely sustainable
dividend growth rate is the rate at which the firm would have sufficient resources to pay the specified
dividend but would not build up any excess cash. If the firm’s growth rate for dividends is higher than g*,
at some point it would not have sufficient funds to pay its dividends. If the firm’s growth rate for dividends
is less than g*, it would begin to generate an infinite amount of excess cash that would eventually build up
and never be paid to equityholders. Either scenario would cause distortions in the model, since the
objective of the model is to use the just barely sustainable rate where g = g*.
Basing g* on some estimate such as historical information, the long-term inflation rate, or the long-term
growth rate of the economy may be a reasonable approach, but it will still fall short of accuracy and
precision required to find the firm’s correct g* rate. The only way to properly determine g* is to “step
outside” of the dividend discount model and use some other valuation model, considering the first year
dividend paid by the firm. This becomes the most accurate method to use in finding the rate where g = g*.
(moderate, L.O. 2, Section 2)
37.
How does a two-stage dividend discount model work?
Suggested solution:
A two-stage dividend discount model assumes that there will be two distinct dividend growth rates for the
firm. Usually this model assumes that the first stage of growth will be greater than the second stage of
growth (although this is not a requirement of the model itself). The first stage of dividend rate growth is
termed the supernormal rate, because it is a greater and more accelerated rate than the second stage. The
second stage, usually assumed to be a lower rate than the first, is called the normal growth rate.
Irrespective of the rates used for stage one or stage two, the rates should reflect the just barely sustainable
growth rate for the firm. Deviations from the just barely sustainable rate will lead to distortions in the
model, either with the firm being unable to fund the rate of dividend growth, or the firm building an
infinite amount of cash that would never be paid to equityholders.
The solution to the dilemma of finding the just barely sustainable dividend growth rate is to use some other
valuation method to arrive at the rate. This makes the two-stage model impractical, since the analyst is
required to “step outside” of the model to find the correct value to use in the model. The model, although
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impractical, is worth understanding as the idea of finding the present value of discounted dividends is key
in valuation analysis.
(moderate, L.O. 3, Section 3)
38.
Discuss how the dividend discount model is applied to a firm that does not pay dividends.
Suggested solution:
A firm may not pay dividends to its equityholders for any number of reasons. A firm in a growth stage of
development may elect to forgo dividends to achieve growth and expand its operations. A company may
make it a matter of policy to not pay dividends (such as Berkshire Hathaway).
Irrespective of a firm’s reasons for not paying dividends, an analyst will assume that in some way
equityholders will receive a payout from the firm at some time in the future. The fact that a firm does not
pay dividends today does not mean it will never will in the future. The payout may come at the time a firm
is either sold or is liquidated.
In such a situation the dividend discount model would not be used to value the firm. The analyst may
choose to use another valuation method that indirectly values the dividend stream by valuing the cash
flows coming into the firm, rather than cash flows going out of the firm in the form of dividends.
(moderate, L.O. 4, Section 4)
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