The Stable Growth Rate

Of
all the inputs into a discounted cash flow valuation model, none can affect the
value more than the stable growth rate. Part of the reason for it is that small
changes in the stable growth rate can change the terminal value significantly
and the effect gets larger as the growth rate approaches the discount rate used
in the estimation. Not surprisingly, analysts often use it to alter the
valuation to reflect their biases.

The
fact that a stable growth rate is constant forever, however, puts strong
constraints on how high it can be. 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. In
making a judgment on what the limits on stable growth rate are, 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 multi-nationally?*If a firm is a purely domestic company, either because of internal constraints (such as those imposed by management) or external (such as those imposed by a government), the growth rate in the domestic economy will be the limiting value. If the company is a multi-national or has aspirations to be one, the growth rate in the global economy (or at least those parts of the globe that the firm operates in) will be the limiting value. Note that the difference will be small for a U.S. firm, since the U.S economy still represents a large portion of the world economy. It may, however, mean that you could use a stable growth rate that is slightly higher (say 1/2 to 1%) for a Coca Cola than a Consolidated Edison.*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, i.e. include an expected inflation component. If the valuation is a real valuation, the stable growth rate will be constrained to be lower. Again, using Coca Cola as an example, the stable growth rate can be as high as 5.5% if the valuation is done in nominal U.S. dollars but only 3% if the valuation is done in real dollars.*What currency is being used to estimate cash flows and discount rates in the valuation?*The limits on stable growth will vary depending upon what currency is used in the valuation. If a high-inflation currency is used to estimate cash flows and discount rates, the limits on stable growth will be much higher, since the expected inflation rate is added on to real growth. If a low-inflation currency is used to estimate cash flows, the limits on stable growth will be much lower. For instance, the stable growth rate that would be used to value Titan Cements, the Greek cement company, will be much higher if the valuation is done in drachmas than in euros.

While
the stable growth rate cannot exceed the growth rate of the economy in which a
firm operates, it can be lower. There is nothing that prevents us from assuming
that mature firms will become a smaller part of the economy and it may, in
fact, be the more reasonable assumption to make. Note that the growth rate of
an economy reflects the contributions of both young, higher-growth firms and
mature, stable growth firms. If the former grow at a rate much higher than the
growth rate of the economy, the latter have to grow at a rate that is lower.

Setting
the stable growth rate to be less than or equal to the growth rate of the
economy is not only the consistent thing to do but it also ensures that the
growth rate will be less than the discount rate. This is because of the
relationship between the riskless rate that goes into the discount rate and the
growth rate of the economy. Note that the riskless rate can be written as:

Nominal
riskless rate = Real riskless rate + Expected inflation rate

In
the long term, the real riskless rate will converge on the real growth rate of
the economy and the nominal riskless rate will approach the nominal growth rate
of the economy. In fact, a simple rule of thumb on the stable growth rate is
that it should not exceed the riskless rate used in the valuation.

Can the stable growth rate be negative?
There is no reason why not since the terminal value can still be estimated. For
instance, a firm with $100 million in after-tax cash flows growing at Ð5% a
year forever and a cost of capital of 10% has a value of:

Value
of firm =

Intuitively,
though, what does a negative growth rate imply? It essentially allows a firm to
partially liquidate itself each year until it just about disappears. Thus, it
is an intermediate choice between complete liquidation and the going concern
that gets larger each year forever.

This
may be the right choice to make when valuing firms in industries that are being
phased out because of technological advances (such as the manufacturers of
typewriters with the advent of the personal computer) or where an external and
critical customer is scaling back purchases for the long term (as was the case
with defense contractors after the end of the cold war).

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