International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. IX Issue – 5 May, 2018 www.irjaf.com

Case Study Series
A Case Study on Equity Valuation for High Growth Firms
Judson W. Russell

Abstract
Brooks Hamilton recently completed his third year in college and has just started a summer
internship at a prestigious Wall Street investment firm. The investment firm is very selective
in hiring interns, but even more selective in extending full-time employment offers to
students upon completion of their last year of studies. Brooks is eager to make a good
impression at work and wants to be one of the few selected to join the firm after his last year
in college. The Program Manager for the interns gives each a time-sensitive assignment to
value a fast-growing company’s stock. Each intern is given one day to complete the
assignment. Brooks decides to use a three-stage dividend discount model to provide for fast
growth, transition, and a slower terminal growth period.
Keywords: Three-Stage Model, H Model, Dividend Discount Model, Valuing Growth
JEL Code: G11, G32, G35

Introduction
Brooks Hamilton is a college student who has just begun a summer investment banking
internship with a prestigious Wall Street firm. He is one of 50 students who were fortunate to
land an internship to work with the firm during the summer before their last year in college.
The firm is highly selective and accepted these 50 interns from over 700 applicants. Brooks
is excited about the work he’ll do during the summer and he knows that the top ten interns
will likely receive full-time job offers to join the firm upon the completion of their last year
in college. He wants to learn a lot during the summer and plans to make his best effort to
secure a full-time job offer by the end of summer. The firm’s program manager has just
presented each intern with a challenge. She assigns each intern a company and states that
each must value the company’s equity and expects to see their valuation and supporting
model the next morning. Brooks has been assigned a company called Rising Tide, Inc. He is
starting with a blank spreadsheet. It’s time to get busy.

The Company
Rising Tide Inc. has been in business for the past 20 years as a builder of fine fishing boats.
The company began as a collaboration between a top boat designer and a legendary fishing
guide. Rising Tide has modified its designs over the past two decades with an emphasis on
continuous improvement and has recently launched an exciting new shallow water boat that
is predicted to become the industry leader.

The shallow water boat industry has many manufacturers. Most of the large boat builders
have a range of boats that they manufacture from freshwater to saltwater, deep sea to shallow,
sports boats to pleasure craft. Rising Tide decided to focus solely on shallow water sports
fishing boats for saltwater fish species and has worked with professional guides, who depend
on boat performance and reliability for their livelihood, to create a new boat. The launch has
been well-received and customers have willingly paid the premium price of $62,500 that
Rising Tide charges for this boat.

Industry and Economic Analysis

Brooks gathers financial information on Rising Tide and begins reading about the sports
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fishing boat manufacturing industry. He discovers that, as with many industries, new design
launches provide a nice initial increase in sales, but slowly the competition catches up with
International Research Journal of Applied Finance ISSN 2229 – 6891
Vol. IX Issue – 5 May, 2018 www.irjaf.com
Case Study Series
their own designs to capture market share. It is estimated that the time advantage for new
design launches is approximately five years. During this period sales growth can be very
strong and it is not uncommon to see sales and earnings growth rates of 30-40% per year or
more. In order to sustain its design advantage, firms tend to reinvest heavily in new product
research and development and therefore pay only a modest dividend to shareholders. This is
also the period of time when firms tend to have the most business risk since the company is
so dependent on this specialized product which has limited customers.

Brooks notices that Rising Tide follows economic cycles, reporting strong financial results
during economic expansions and suffering disappointing results during economic downturns.
Although the number of people who participate in sports fishing has increased over the years,
the high cost to charter a boat and guide for a day of fishing creates a relatively limited
clientele1. Given current economic forecasts for continued expansion and the success of the
newest design by Rising Tide, Brooks decides to use a model which can accommodate fast
growth in the upcoming years that will gradually decline as competition gains market share.
He recalls such a model from his investments class at university and starts gathering the
necessary inputs.

Three-Stage Dividend Discount Model

Brooks believes that the three-stage dividend discount model is ideal for this company. This
model allows for varying growth rates and can accommodate adjustments to dividend payout
and discount factors from changing business risk. The flexibility of the model allows it to be
used to value a variety of firm types and it is ideally suited to value firms that are currently
experiencing abnormally fast growth rates but will eventually lose this current competitive
advantage. He gathers financial information for his main value drivers. He believes the
drivers for Rising Tide share value are earnings growth, dividend payout, and the discount
rate. The value of Rising Tide’s equity is determined by taking the present value of the
dividends. There are three stages to consider for this valuation exercise; the fast growth
period in years 1-5, the transition phase in years 6-10, and the constant growth phase for
years 11 to infinity. Brooks has his plan in place and starts building his model.

Earnings Growth
He believes that earnings will grow with sales over the next five years at very high rates then
gradually decline and ultimately reach a lower constant growth rate as Rising Tide loses its
competitive advantage. Figure 1 illustrates the view that Brooks has for earnings growth at
Rising Tide. Over the next five years the firm will enjoy limited competition and will
experience substantial earnings growth. After viewing past successful product launches in
the industry, Brooks believes that Rising Tide can generate earnings growth of 30% per year
over each of the next five years. In the most recent financial year, Rising Tide reported
earnings per share of $2.50. Brooks sees that figure compounding to $9.28 per share by the
end of the five year period2.

With the entrance of new designs from competitors, Brooks believes that sales and earnings
growth will decline. He expects to see a gradual reduction of earnings growth over years six

1
The U.S. Department of Interior reports that the most recent five-year survey by the U.S. Fish and Wildlife
Service showed that 101.6 million Americans, 40 percent of the U.S. population 16 years old and older,
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participated in wildlife-related activities in 2016. Almost 36 million engaged in fishing and overall expenditures
increased by 8% from the prior survey. Source: U.S. Department of Interior.
2
Earnings compound at 30% per year for five years, therefore $2.50(1.30)5 = $9.28 after five years.
International Research Journal of Applied Finance ISSN 2229 – 6891
Vol. IX Issue – 5 May, 2018 www.irjaf.com
Case Study Series
through ten until Rising Tide reaches a constant growth rate of three percent, which follows
the expected long-term growth rate for this industry.

Figures

Figure 1. Earnings Growth for Rising Tide, Inc.

Earnings Growth
High Growth in Years 1-5, Transition in Years 6-10, Infinite Growth Phase
35.00%
High Growth = 30%
30.00%

25.00%

20.00%

15.00%

10.00%

5.00% Infinite Growth = 3%

0.00%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Source: Author

He plans to use 30% earnings growth for each of the next five years and then allow this to
linearly decline to 3% over the subsequent five years in a straight line reduction. The
formula he uses for the linear transition periods is:

Valuet = Valuet-1 + [(target value – high growth value)/n] (1)

where:
Valuet = the value at t
Valuet-1 = the value at time t-1
target value = the long-term value we expect after the transition
high growth value = the value during the high growth phase
n = number of transition periods

For instance, if you observe a company with earnings growth at 30% and you want to see it
transition to 3% over a five-year period then you would calculate each of the transition
periods using (1) above. For Period 6, the result would be:

Value6 = Value5 + [(3% – 30%)/5]

With the value at time 5 of 30%, the value at time 6 becomes 30% - 5.4% or 24.6%. For time
period 7 you simply subtract 5.4% from 24.6% and so on. This terminates at time period 10
when you reach the target value of 3% earnings growth in the infinite growth period.

Dividend Payout
Brooks sees that Rising Tide is currently paying a dividend of $0.10 per share on earnings of
$2.50 per share. The dividend payout ratio is shown in (2) below:
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International Research Journal of Applied Finance ISSN 2229 – 6891
Vol. IX Issue – 5 May, 2018 www.irjaf.com
Case Study Series
Dividend payout = dividends per share / earnings per share (2)

Therefore, Rising Tide currently has a dividend payout of $0.10/$2.50 or 4%. Brooks thinks
that is a very low figure, but then sees that the firm is putting a lot of money back into the
firm to keep up with production demands for the new boat. This is typical for a firm with
large working capital or fixed asset needs. Brooks recalls a sustainable growth formula that
his professor mentioned that related retained earnings and the return on earnings to growth.
He grabbed his notes and found the sustainable growth formula shown in (3) below:

g = b x ROE (3)

where:
g = growth rate in earnings
b = earnings retention ratio, (1-dividend payout rate)
ROE = return on equity, Net Income / Equity

In order to sustain a growth rate of 30%, Rising Tide must retain most of its earnings. In this
case 96%, (1-$0.10/$2.50). That equates to an approximate return on equity of 31.25%.
Currently Rising Tide is a fast growing company, but what about the competition. Surely this
type of return on equity will attract competition and before long earnings slow. The gradual
reduction in sales and earnings growth places less capital reinvestment demands on the
company. At that point the company may wish to return more money to shareholders in the
form of increased dividends. Brooks notices that the long-term return on equity for many
firms in this industry is very low, approximately 4-5%. He also knows that reinvestment is
important to survive through continual research and development. He estimates that the long-
term dividend payout ratio should be 30% and checks that using equation (3) above with a
long-term growth rate of 3% and ROE of 4%.

3% = b x 4%
b = 75%

A retention rate of 75% implies a dividend payout of 25%. He feels like 30% is justified for
the long-term and that his assumptions are reasonable and defensible when he presents his
model to the Program Manager the next day. As before he needs to transition the dividend
payout rate from the low rate now of 4% to the high rate later at 30%. Figure 2 shows the
illustration.

Returning to equation (1) we see the dividend payout in period 6 is 4% + (30%-4%)/5 =

9.2%. The dividend payout for 7 builds on this by adding to the 9.2%. This continues
through year 10 when the firm attains a dividend payout rate of 30%. Brooks builds his
model now with earnings growth slowing through the transition period and with dividend
payout increasing through this time. This results in a much higher dividend due to the large
increase in payout. Equation (2) is used to determine the dividend per share by multiplying
earnings per share by the dividend payout rate. Earnings are growing at a slowing pace, but a
larger portion of earnings are being returned to shareholders. These dividends form his cash
flows for equity valuation. He now sets about calculating the discount factor for these cash
flows to arrive at the firm’s equity value.
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International Research Journal of Applied Finance ISSN 2229 – 6891
Vol. IX Issue – 5 May, 2018 www.irjaf.com
Case Study Series
Figure 2. Dividend Payout for Rising Tide, Inc.

Dividend Payout
Low Payout in Years 1-5, Transition in Years 6-10, Higher Payout Phase
35.00%
High Payout = 30%
30.00%

25.00%

20.00%

15.00%

10.00%
Low Payout = 4%
5.00%

0.00%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Source: Author

Discount Factor
The intrinsic value of any asset is the present value of its future cash flows. In the case of
Rising Tide, Brooks is assuming that dividends are the source of cash flows to investors. He
calculates an equity discount factor (ke) for Rising Tide using the Capital Asset Pricing
Model with key inputs of the risk-free rate, market risk premium and beta of Rising Tide with
the market shown in Equation (4). Brooks uses a 4.0% historical Treasury rate for the risk-
free rate and 6.0% as the historical market risk premium3.

ke = Risk-free rate + beta (Market Risk Premium) (4)

There are a variety of methods for calculating beta. Brooks could find beta by regressing five
years of weekly Rising Tide returns of the S&P 500. He could also use five years of monthly
returns or two years of weekly returns. Each of these is a valid sample period. One well-
known data source provides an “adjusted” beta which is determined by first calculating a
“raw” beta by regressing two years of weekly security returns on the market. This is then
adjusted by taking 2/3 of the raw beta plus 1/3 of one. This adjusts the beta to be closer to
one, since beta is not stationary and should naturally move towards one through time as a
firm expands. Brooks runs a regression of five years of stock returns for Rising Tide versus
the S&P 500 using monthly observations and gets a beta of 1.6. Using (4) above the discount
rate for Rising Tide is 4% + 1.6*6% or 13.6%. As mentioned earlier, Rising Tide is currently
in a relatively high business risk environment. Brooks assumes that as the new boat design
gains traction among fishermen and guides, the business risk will slow. He estimates that the
beta will be 1.0 in the long-term and plans to see it transition over the period same period as
earning growth and dividend payout. Figure 3 shows the expected change in discount rate
through time.
Using Equation 1, Brooks is able to show the declining discount rate. For instance, the year 6
discount rate should be 13.6% + (10%-13.6%)/5 or 12.88%. Years 7-10 follow as similar
method until reaching 10% in year 10, determined by 4% + 1.0(6%) as beta becomes 1.0.
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3
The risk-free rate is determined based on the geometric average of the long-term Treasury. The market risk
premium is calculated based on the difference between the geometric return on the Standard & Poor’s 500 index
and the long- term Treasury.
International Research Journal of Applied Finance ISSN 2229 – 6891
Vol. IX Issue – 5 May, 2018 www.irjaf.com
Case Study Series
Figure 3. Discount Factor for Rising Tide, Inc.

Discount Factor
High Business Risk in Years 1-5, Transition in Years 6-10, Low Risk Phase
16.00%
High Risk = 13.6%
14.00%
12.00%
Long-Term Risk = 10%
10.00%

8.00%

6.00%
4.00%

2.00%

0.00%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Source: Author

Valuation Process – Years 1-5

Now Brooks can begin the task of determining the present value of each of the dividends.
For instance in year 1. He starts with earnings of $2.50 and let’s these grow at a rate of 30%.
This results in an earnings per share figure for year 1 of $3.25. He then takes a dividend
payout of 4% to see dividends per share in year 1 of 4%*$3.25 or $0.13. Taking the present
value of the year 1 dividend results in $0.13/(1+0.136)1 or $0.1144. We see this illustrated in
the Figure 4 below.

Figure 4. Present Value of Year 1 Dividend for Rising Tide, Inc.

Description/Year 0 1
Earnings growth rate 30.00% 30.00%
Earnings per share (EPS) $ 2.50 $ 3.25
Dividend payout (DPS/EPS) 4.00% 4.00%
Dividends per share (DPS) $ 0.10 $ 0.13
Cost of equity (Ke) 13.60% 13.60%
Present value of cash flows $ 0.11

Source: Author

Brooks continues this process to get the present value of all dividends during the fast growth
years of 1-5 using a steady 30% growth rate of earnings, 4% dividend payout, and 13.6% cost
of equity as the discount factor. He now has the present value of the next five years of
dividends for Rising Tide.

Valuation Process – Years 6-10

At this point, the firm begins to transition to a new normal operating period with earnings
growth declining, dividend payout increasing, and discount factor declining. He recalls that
there is a different method for discounting during the transition period and stops to ensure he
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has his notes on that topic. He finds an example that illustrates the method for discounting
International Research Journal of Applied Finance ISSN 2229 – 6891
Vol. IX Issue – 5 May, 2018 www.irjaf.com
Case Study Series
cash flows when the discount rate changes over time. The example from his notes are shown
in Figure 5 below.

Figure 5. Example of Discounting with Varying Discount Rates

Time Period 1 2 3 4 5 6
Dividend $1.00 $1.20 $1.46 $1.68 $2.00 $2.25
Discount Rate 12% 12% 12% 12% 12% 10%
Present Value $0.89 $0.96 $1.04 $1.07 $1.13 $1.16

Time Period 0 1 2 3 4 5 6
Discount Rate 12% 12% 12% 12% 12% 10%

$1.16 $1.30 $1.46 $1.63 $1.83 $2.05 $2.25

Source: Author

Cash flows are discounted by the discount factor prevailing at each discount period. For
instance, as shown in Figure 5, the dividend in year 6 is discounted at each discount factor
over the six-year span. With a $2.25 dividend in year, it is discounted once at 10% and then
five times at 12% resulting in a present value of $1.16. This is shown mathematically, in
Equations (5) and (6) below.

PV of Div6 = Div6 / [(1+ke1)1 x (1+ke2)1 x (1+ke3)1 x (1+ke4)1 x (1+ke5)1 x (1+ke6)1] (5)

PV of Div6 = Div6 / [(1+ke1)5 x (1+ke6)1] (6)

Relating this to Rising Tide, Brooks takes his calculated dividend for year six and discounts
this as the product of the discount factors over periods one through five and the discount
factor for year six using Equation (6). He then continues with dividends seven through 10 in
a similar process adding an additional term in Equation (6) for each next discount factor and
ensuring that the sum of his exponents is equivalent to the cash flow period in question. He
now has the present value of the dividends in years 6-10 for Rising Tide.

Valuation Process – Terminal Value

His final task is to gather the terminal value for Rising Tide using a constant growth dividend
discount approach. At the conclusion of year 10 we note that Rising Tide will have a
constant earnings growth of 3%, a constant dividend payout of 30%, and a constant discount
factor of 10%. Brooks can now employ the constant growth formula shown in Equation (7)
to find the terminal value of Rising Tide over the period from year 10 through infinity. He’ll
next need to discount this terminal value to find the present value just as he did with the prior
dividends by using the discount factors for prevailing at each discount period. He recalls that
this discount factor for the terminal value should be the same as the discount factor used for
the dividend in year 10.

Value of Equity10 = EPS11 x (dividend payout11) / [ke11 – EPS growth11] (7)

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International Research Journal of Applied Finance ISSN 2229 – 6891
Vol. IX Issue – 5 May, 2018 www.irjaf.com
Case Study Series
He now has the present value of dividends one through five, six through 10, and 10 to infinity
which match his three time periods. He takes the sum of these three present values to provide
his estimate of the firm’s equity value. This methodology is illustrated in Figure 6.
Figure 6. Illustration of the Three-Stage Dividend Discount Model
Fast Growth Period Transition Period Terminal Period
Time Period 1 2 3 4 5 6 7 8 9 10 … ∞
Div 1 Div 2 Div 3 Div 4 Div 5 Div 6 Div 7 Div 8 Div 9 Div 10
PV Div 1
Present Value PV Div 2
of Fast PV Div 3
Growth Period PV Div 4
PV Div 5
+
PV Div 6
Present Value of PV Div 7
Transition Period PV Div 8
PV Div 9
PV Div 10
+
Present Value of V10 = D11/(ke - g)
Terminal Value PV of V10

Equity Value

Source: Author

Knowing the model is dependent on his assumptions, he double checks his work to ensure his
inputs are both reasonable and defensible and prepares a document to highlight his work for
the next day’s meeting with his Program Manager.

Specific Questions:
1. Using the information provided in the case and the template provided, what are your
earnings forecasts over the ten-year period which includes a fast growth period and a
transition period to constant growth?
2. What are the dividends over the ten-year period using the earnings from question 1
and your forecast of dividend payout?
3. What discount factors do you use for each of the discount periods?
4. What are the present values of each dividend over the first five years (Fast Growth
Period) and years six through 10 (Transition Period)?
5. What is the terminal value of Rising Tide, Inc. in year 10 using the constant growth
formula?
6. What is the present value of the terminal price?
7. Using the present values of dividends in years one through 10 and the present value of
terminal price, what is the value of Rising Tide, Inc. stock?
8. What words of advice would you give to Brooks as he prepares for the meeting with
his Program Manager the next day?

Author

Judson W. Russell, Ph.D., CFA

University of North Carolina Charlotte, Clinical Professor of Finance, University of North
Carolina Charlotte, Department of Finance, Charlotte, USA, jrussell@uncc.edu
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