growth rates much lower than the growth rate in the economy will become smaller in
proportion to the economy over time. Since there is no economic basis for arguing that
this cannot happen, there is no reason to prevent analysts from using a stable growth rate
much lower than the nominal growth rate in the economy. In fact, the stable growth rate
can be a negative number. Using a negative stable growth rate will ensure that your firm
peaks in your last year of high growth and becomes smaller each year after that.
There is one rule of thumb that works well in setting a cap on the stable growth
rate. The stable growth rate should generally not exceed the riskfree rate used in a
valuation. Why should the two be related? The riskfree rate can be decomposed into an
expected inflation rate and an expected real interest rate. If we assume that the real
growth rate of an economy will be equal to the real interest rate in the long term, the
riskfree rate becomes a proxy for the nominal growth rate in the economy.
12.2 â˜ž: Cyclical firms and Constant Growth Rates
Models that are built on the assumption of an expected constant growth rate over time
cannot be used for cyclical firms, whose earnings growth is likely to be very volatile over
time - high during economic booms, and very low or negative during recessions.
Estimation in DCF Models
While all discounted cashflow models require the same four ingredients â€“
cashflows, a discount rate, a period of high growth and a growth rate during the period,
there are different estimation challenges we face with each model. In this section, we will
begin by estimating these inputs to the simplest of the three models, the dividend
discount model, and then extend the discussion to cashflow to equity and firm valuation
I. Dividend Discount Models
When an investor buys stock, he generally expects to get two types of cash flows -
dividends during the holding period and an expected price at the end of the holding
period. Since this expected price is itself determined by future dividends, the value of a
stock is the present value of just expected dividends. The dividend discount model is
therefore the most direct and the most conservative way of valuing a stock since it counts
only those cashflows that are actually paid out.
Setting up the Model
In itâ€™s most general form, the value of a stock in the dividend discount model is
the present value of the expected dividends on the stock in perpetuity.
Expected Dividends in period t
Value per share of stock =
(1 + Cost of Equity) t
Since we cannot estimate dividends in perpetuity, we
Terminal Value: This is the
generally allow for a period where dividends can grow at expected price of a stock (or
extraordinary rates but we allow for closure in the model equity) at the end of a
specified holding period.
by assuming that the growth rate will decline to a stable
rate that can be sustained forever at some point in time in
the future. By assuming stable growth at some point in time in the future, we can stop
estimating dividends and estimate what we think the stock will be worth at the end of the
extraordinary growth period.
E(Dividends) t Terminal Value n E(Dividends)n +1
Value 0 = + where Terminal Value n =
(1 + r) t (1 + r) n (rn - g n )
where r is the cost of equity and gn is the expected growth rate in dividends in perpetuity
after year n.2 Note that it is possible for a firm to already be in stable growth, in which
case this model collapses into itls simplest form:
Value of a stock in stable growth = Expected Dividends next year/ (Cost of equity â€“ gn)
This model is called the Gordon Growth model and is a special case of the dividend
discount model. It can be used only for firms that are already in stable growth.3
Estimating Model Inputs
Breaking down the general version of the dividend discount model, there are four
basic components. The first is the length of the high growth period, during which the firm
can sustain extraordinary growth. The second is the expected dividends each year during
the high growth period. The third is the cost of equity that stockholders will demand for
holding the stock, based upon their assessments of risk. The final input is the expected
price at the end of the high growth period â€“ the terminal value. In this section, we will
consider the challenges associated with estimating each of these components.
a. Length of High-Growth Period
The question of how long a firm will be able to sustain high growth is perhaps the
most difficult of all to answer in a
High Growth Period: This is a period during which
valuation, but two points are worth a companyâ€™s earnings or cash flows are expected to
keeping in mind. One is that it is not a grow at a rate much higher than the overall growth
rate of the economy.
question of whether but when; all firms
will ultimately be stable growth firms, because high growth makes firms larger, and the
firmâ€™s size will eventually become a barrier to further high growth. The second is that
high growth in valuation, at least high growth that creates value, comes from firms
earning high returns on their marginal investments. Using the terminology that we have
used before in investment analysis, it comes from firms having a return on equity
(capital) that is well in excess of the cost of equity (capital). Thus, when we assume that a
2 The cost of equity can be different for the high growth and stable growth periods. Hence, rn is the cost of
equity for the stable growth period.
3 When the Gordon Growth model is used to value high growth companies, it is entirely possible that g>r
and the model will yield a negative value. The problem is not with the model but in its msapplication to a
high growth firm.
firm will experience high growth for the next 5 or 10 years, we are also implicitly
assuming that it will earn excess returns (over and above the cost of equity or capital)
during that period. In a competitive market, these excess returns will eventually draw in
new competitors, and the excess returns will disappear.
We should look at three factors when considering how long a firm will be able to
maintain high growth.
1. Size of the firm: Smaller firms are much more likely to earn excess returns and
maintain these excess returns than otherwise similar larger firms. This is so because
they have more room to grow and a larger potential market. When looking at the size
of the firm, we should look not only at its current market share, but also at the
potential growth in the total market for its products or services. Thus, Microsoft may
have a large market share of the computer software market, but it may be able to
grow in spite of it because the entire software market is growing. On the other hand,
Boeing dominates the market for commercial airliners, but we do not expect the
overall market for airliners to increase substantially. Boeing, therefore, is far more
constrained in terms of future growth.
2. Existing growth rate and excess returns: Although the returns we would like to
estimate are the marginal returns on new investments, there is a high correlation
between the returns on current investments and these marginal returns. Thus, a firm
earning excess returns of 20% on its current investments is far more likely to have
large positive excess returns and a long growth period than a firm currently earning
excess returns of 2%. There are cases where this rule will not work, such as in new
industries going through major restructuring.
3. 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. If, on the other hand, there are no or minor barriers to
entry, or if the firmâ€™s existing competitive advantages are fading, we should be far
more conservative about allowing for long growth periods. The quality of existing
management also influences growth. Some top managers4 have the capacity to make
the strategic choices that increase competitive advantages and create new ones.
Again, the sensitivity of value to changes in the length of the high growth period can
always be estimated. While some analysts use growth periods greater than 10 years, the
combination of high growth rates and long growth periods creates a potent mix in terms
of increasing the size of the firm, in many cases well beyond the realm of what is
reasonable. Looking back, there are very few firms that have been able to grow at high
rates for more than 10 years.
Illustration 12.1: Length of High Growth Period
To assess how long high growth will last at Disney, Aracruz and Deutsche Bank,
we assessed their standings on each of the above characteristics in Table 12.1:
Table 12.1: Assessment of Length of High Growth Period
Disney Aracruz Deutsche Bank
Firm Size/Market Size Firm is one of the Firm has a small market Firm has a significant
largest players in the share of the paper/pulp market share of a mature
entertainment and theme business, but the business.
park businesses but the business is mature.
Current Excess Returns Firm is earning less than Returns on capital are Firm has a return on
its cost of capital, and largely a function of equity that has lagged its
has done so for last few paper/pulp prices but, on cost of equity in recent
years average, have been less years.
than the cost of capital.
Competitive Advantages Has some of the most Cost advantages because Has an edge in the
recognized brand names of access to Brazilian commercial banking
in the world. Knows rainforests. Has invested business in Germany but
more about operating in newer, updated plants this advantage is
theme parks than any and has skilled dissipating in the EU.
other firm in the world. workforce.
Has skilled animation
Length of High Growth 10 years, entirely 5 years, largely due to 5 years, mostly to allow
period because of its strong access to cheap raw firms to recover to pre-
competitive advantages material. downturn levels.
(which have been
wasted over the last few
years) but the excess
returns are likely to be
4 Jack Welch at GE and Robert Goizueta at Coca Cola are good examples of CEOs who made a profound
difference in the growth of their firms.
What about Bookscape? The single biggest competitive advantage possessed by the firm
is its long-term lease, at favorable terms, in a superb location in New York City. It is
unlikely that the firm will be able to replicate this advantage elsewhere. Adding to this
the fact that this is a private firm leads us to conclude that there will be no high growth
12.3. â˜ž: Length of High Growth Period and Barriers to Entry
Assume that you are analyzing two firms, both of which are enjoying high growth. The
first firm is Earthlink Network, an internet service provider, which operates in an
environment with few barriers to entry and extraordinary competition. The second firm is
Biogen, a biotechnology firm which is enjoying growth from two drugs to which it owns
patents for the next decade. Assuming that both firms are well managed, which of the two
firms would you expect to have a longer high growth period?
a. Earthlink Network
c. Both are well managed and should have the same high growth period
b. Expected Dividends during High Growth Period
The first step in estimating expected dividends during the high growth period is to
estimate the expected earnings for each year. This can be done in one of two ways â€“ you
can apply an expected growth rate to current Historical Growth Rate (in Earnings): This is
the growth rate over the past few periods in
earnings or you can begin by estimating future
earnings - it can be calculated either by
revenues first and then estimate net profit
averaging the year-specific growth rates
margins in each year. The first approach is
(arithmetic average) or by estimating at the
easier but the second approach provides for compounded growth rate over the whole
more flexibility since margins can change over
time. The resulting expected earnings are
paired with estimated dividend payout ratios in each period, which may change over the
high growth period. This may seem like an awkward procedure, since expected dividends
could well be estimated using the current dividends and applying a dividend growth rate,
but it is used for two reasons. First, most analyst projections for growth are stated in
terms of revenues and earnings rather than dividends. Second, separating earnings
forecasts from dividend payout provides more flexibility in terms of changing dividend
payout ratios as earnings growth rates change. In particular, it allows us to raise dividend
payout ratios as earnings growth rates decline.
The growth rate in earnings can be estimated using one of three approaches. The
first is to look at the past and measuring the historical growth rate in earnings over
previous years. In measuring earnings growth, we will have to consider both how far
back to go in time and whether to use arithmetic average or geometric average growth
rates. In general, geometric growth rates yield more meaningful values than arithmetic
average growth rates. The second is to look at estimates made by others following the
same stock. In fact, growth estimates made by equity research analysts following a stock