Publicly traded firms do not have
finite lives. Given that we cannot estimate cash flows forever, we generally
impose closure in valuation models by stopping our estimation of cash flows
sometime in the future and then computing a terminal value that reflects all
cash flows beyond that point. There are three approaches generally used to
estimate the terminal value. The most common approach, which is to apply a
multiple to earnings in the terminal year to arrive at the terminal value, is
inconsistent with intrinsic valuation. Since these multiples are usually
obtained by looking at what comparable firms are trading at in the market
today, this is a relative valuation, rather than a discounted cash flow
valuation. The two more legitimate ways of estimating terminal value are to
estimate a liquidation value for the assets of the firm, assuming that the
assets are sold in the terminal year, and the other is to estimate a going
concern or a terminal value.

If we assume that the business will
be ended in the terminal year and that its assets will be liquidated at that
time, we can estimate the proceeds from the liquidation. This liquidation value
still has to be estimated, using a combination of market-based numbers (for
assets that have ready markets) and cashflow-based estimates. For firms that
have finite lives and marketable assets (like real estate), this represents a
fairly conservative way of estimating terminal value. For other firms,
estimating liquidation value becomes more difficult to do, either because the
assets are not separable (brand name value in a consumer product company) or
because there is no market for the individual assets. One approach is to use
the estimated book value of the assets as a starting point, and to estimate the
liquidation value, based upon the book value.

If we treat the firm as a going concern
at the end of the estimation period, we can estimate the value of that concern
by assuming that cash flows will grow at a constant rate forever afterwards.
This perpetual growth model draws on a simple present value equation to arrive
at terminal value:

Our definitions of cash flow and growth rate have to be
consistent with whether we are valuing dividends, cash flows to equity or cash
flows to the firm; the discount rate will be the cost of equity for the first
two and the cost of capital for the last. The perpetual growth model is a
powerful one, but it can be easily misused. In fact, analysts often use it is
as a piggy bank that they go to whenever they feel that the value that they
have derived for an asset is too low or high. Small changes in the inputs can
alter the terminal value dramatically. Consequently, there are three key
constraints that should be imposed on its estimation:

a. __Cap the
growth rate__: 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. 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. So, what is the maximum stable
growth rate that you can use in a valuation? The answer will depend on whether
the valuation is being done in real or nominal terms, and if the latter, the
currency used to estimate cash flows. With the former, you would use the real
growth rate in the economy as your constraint, whereas with the latter, you
would add expected inflation in the currency to the real growth. 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.

__b. Use mature
company risk characteristics__:
As firms move from high growth to stable growth, we need to give them the
characteristics of stable growth firms. A firm in stable growth is different
from that same firm in high growth on a number of dimensions. In general, you
would expect stable growth firms to be less risky and use more debt. In
practice, we should move betas for even high risk
firms towards one in stable growth and give them debt ratios, more consistent
with larger, more stable cashflows.

__c. Reinvestment and Excess Return
Assumptions__: Stable
growth firms tend to reinvest less than high growth firms and it is critical
that we both 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. Given the relationship between growth, reinvestment rate and
returns that we established in the section on expected growth rates, we can
estimate the reinvestment rate that is consistent with expected growth :

In
the dividend discount model:

In the FCFE model:

In
the FCFF model: _{}

Linking
the reinvestment rate and retention ratio to the stable growth rate also makes
the valuation less sensitive to assumptions about stable growth. While
increasing the stable growth rate, holding all else constant, can dramatically
increase value, changing the reinvestment rate as the
growth rate changes will create an offsetting effect.

The gains from
increasing the growth rate will be partially or completely offset by the loss
in cash flows because of the higher reinvestment rate. Whether value increases
or decreases as the stable growth increases will entirely depend upon what you
assume about excess returns. If the return on capital is higher than the cost
of capital in the stable growth period, increasing the stable growth rate will
increase value. __If the return on capital is equal to the stable period cost
of capital, increasing the stable growth rate will have no effect on value__. Substituting in the stable growth
rate as a function of the reinvestment rate, from above, you get:

Setting the return on capital equal to the cost of capital,
you arrive at:

You could establish the same propositions
with equity income and cash flows and show that the terminal value of equity is
a function of the difference between the return on equity and cost of equity.

In
closing, the key assumption in the terminal value computation is not what
growth rate you use in the valuation, but what excess returns accompany that
growth rate. If you assume no excess returns, the growth rate becomes
irrelevant. There are some valuation experts who believe that this is the only
sustainable assumption, since no firm can maintain competitive advantages
forever. In practice, though, there may be some wiggle room, insofar as the
firm may become a stable growth firm before its excess returns go to zero. If
that is the case and the competitive advantages of the firm are strong and
sustainable (even if they do not last forever), we may be able to give the firm
some excess returns in perpetuity. As a simple rule of thumb again, these
excess returns forever should be modest (<4-5%) and will affect the terminal
value.