Forever
When
valuing an ongoing business with a discounted
cash flow model, the bulk of the value usually
comes from the terminal value. While there
are numerous approaches used to estimate terminal
value, the one that is most consistent with
an intrinsic or discounted cash flow view
of the world is a stable growth model, where
the terminal value in year n is estimated
as follows:
There
are two key principles that govern this estimation
that have to be followed to keep it within
bounds. The first is the expected growth rate
in perpetuity, which cannot exceed the growth
rate of the economy in which the firm operates.
The second is that the growth is never free;
to grow, companies have to reinvest. Applying
this principle to valuing a business, we can
derive the terminal value:
The
reinvestment rate itself is a function of
the return on capital that the firm will earn
in the long term:
Thus,
a firm with an expected growth rate of 4%
and a return on capital of 10% will have to
reinvest 40% of its after-tax operating income
in perpetuity to maintain this growth. With
this framework, the key input that determines
the terminal value for a firm becomes the
return on capital that we assume for the firm
in perpetuity. As the return on capital increases,
the terminal value will also increase for
any given growth rate. If the return on
capital is equal to the cost of capital, increasing
the stable growth rate will have no effect
on value. This can be proved quite easily.
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:
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