Growth is the key input in every valuation.
Three ways of estimating growth rates:
– Historical. While past growth is not always a good indicator
of future growth, it does convey information that can be
valuable while making estimates for the future.
• Arithmetic average - simple average of past growth rates
• Geometric average – takes into account the compounding that
occurs from period to period.
– The two estimates can be very different, especially for firms with volatile
earnings. The geometric average is a much more accurate measure of true
growth in past earnings, especially when year-to-year growth has been erratic.
• Linear and log-linear regression models
1
– Analyst estimates of growth. Analysts, in addition to using
historical data can avail themselves of five other types of
information that may be useful in predicting future
growth:
• Firm-specific information that has been made public since the last
earnings report
• Macroeconomic information that may impact future growth
• Information revealed by competitors on future prospects
• Private information about the firm
• Public information other than earnings
Analyst forecasts have been shown to be superior to historical
growth rates in forecasting the next quarter forecast. However,
in valuation, the focus is more on long-term growth rates.
There is little evidence to suggest that analysts provide
superior forecasts of earnings when the forecasts are over
three-five years.
2
– Fundamental growth rates. The third and soundest way of
estimating growth is to base it on a firm’s fundamentals.
Let’s first classify growth patterns into three categories:
• Firms that are in stable growth already
• Firms that expect to maintain a constant high growth rate for a
period and then drop abruptly to stable growth
• Firms that will have high growth for a specified period and then
grow through a transition phase to reach stable growth at some
point in the future
It is important that as the growth rate changes, the firm’s risk and
cash flow characteristics change as well. In general, as expected
growth declines toward stable growth, firms should see their risk
approach the average, and their reinvestment needs decline.
3
Length of high growth period
Three factors to look at when considering how long a firm will be
able to maintain high growth:
– Size of the firm in relation to the market.
•
•
Smaller firms usually have more room to grow than larger firms.
When looking at the size of the firm, we should look not only at its current market
share but also the potential growth in the total market for its products or services.
– Existing growth rate and excess returns.
•
For example, a firm earning excess returns on its current investments is far more
likely to have large positive excess returns on its marginal investments, and a long
growth period, than a firm currently earning excess returns of 2%.
– Magnitude and sustainability of competitive advantages.
•
•
This is perhaps the most critical determinant of the length of the high growth
period. If there are significant barriers to entry and sustainable competitive
advantages, firms can maintain high growth for longer periods.
The quality of existing management also influences our choices on growth.
4
Calculating growth rates
We will focus on growth rates that we use with the dividend
discount model (DDM), the free cash flows to equity model (FCFE),
and the free cash flows to the firm (FCFF) model.
– For the DDM:
Expected growth rate = Retention ratio * ROE
where
RetentionRatio  1  PayoutRatio
Dividends
 1
NetIncome
5
• For the FCFE:
Expected growth in net income = Equity reinvestment rate * ROE
where
EquityReinvestmentRate
CapitalExpenditures  Depreciation  WorkingCapital 1  DebtRatio 


NetIncome
• For the FCFF:
Expected growth in EBIT = Reinvestment rate * Return on capital (ROC)
where
ReinvestmentRate

CapitalExpenditures  Depreciation  WorkingCapital 
EBIT 1  t 
6
Stable growth
 As a firm grows, it becomes more difficult for it to maintain high
growth and it will eventually grow at a rate less than or equal to the
growth rate of the economy in which it operates. This growth rate,
called stable growth, can be sustained in perpetuity, allowing us to
estimate the value of all cash flows beyond that point as a terminal
value for a going concern.
 Since no firm can grow forever at a rate higher than the growth rate of
the economy in which it operates, the constant growth rate cannot be
greater than the overall growth rate of the economy.
 The stable growth rate can be lower than the overall growth of the
economy. There is nothing that prevents us from assuming that mature
firms will become a smaller part of the economy. This may, in fact, be
the more reasonable assumption to make since the overall growth rate
of the economy reflects the contributions of young, high growth firms,
and mature stable growth firms. If the former grow at a faster rate
than the economy, then the latter have to grow at a lower rate.
7
In making a judgment of what stable growth for a company should be,
we have to consider the following questions:
 Is the company constrained to operate as a domestic company, or does
it operate (or have the capacity to operate) multinationally?
 Companies operating domestically are constrained by the growth rate of the
domestic economy.
 Multinational companies are constrained by the growth rate of the global economy,
or at least those parts of the globe that the firm operates in.
 Is the valuation being done in nominal or real terms?
 If the valuation is a nominal valuation, the stable growth rate should also be a
nominal growth rate. (note: we are doing nominal valuations in class)
 What currency is being used to estimate cash flows and discount rates
in the valuation?
 If a high-inflation currency is used to estimate cash flows and discount rates, the
stable growth rate will be much higher, since the expected inflation rate is added on
to real growth.
8
Betas, Reinvestment and Retention ratios
 As firms become more mature, they tend to approach the
riskiness of the market portfolio, i.e., their betas tend to get
closer to one, and the cost of equity has to be recalculated to
reflect the changing beta of the firm.
 Stable growth firms tend to reinvest less than high-growth
firms, and it is critical that we capture the effects of lower
growth on reinvestment and that we ensure that the firm
reinvests enough to sustain its stable growth rate in the
terminal phase.
9
 For the DDM, this is calculated as
Retention ratio = Expected growth rate/ROE
 For the FCFE model, this is calculated as
Equity reinvestment rate = Expected growth rate/ROE
 For the FCFE model, this is calculated as
Reinvestment rate = Expected growth rate/ROC
10
Putting it all together
 The first decision we have to make is figuring out what the high
growth rate is, and how long the high growth period is going to be.
 The next step is to decide what the stable growth rate is, and calculate
the implied reinvestment rate from this.
 And, finally, we have to think about how the firm will make the
transition from high growth to stable growth. In general, you can think
of the following scenarios:
 Two-stage model: the firm will be in high growth for some time and transition to
stable growth abruptly. This model is more appropriate for firms with moderate
growth rates where the shift will not be too dramatic.
 Three-stage model: the firm will be in high growth, followed by a transition phase
where the growth rate slowly decreases to reach the stable growth rate. This is
more appropriate for firms with very high growth rates where the transition phase
allows for a more gradual adjustment to stable growth.
 N-stage model: the firm’s characteristics, and therefore growth rate, can change
from year to year, until it reaches the stable growth period. This is more
appropriate for young firms or for firms with negative earnings.
 Or, it is also possible that your firm is already in stable growth.
11
• Sources:
– Damodaran, Investment Valuation, 2nd ed.
– McKinsey & Company, Koller, Goedhardt, and Wessels, Valuation:
Measuring and managing the value of companies, 5th ed.
12