Estimating Terminal Value

Since you cannot estimate cash flows
forever, you generally impose closure in discounted cash flow valuation by
stopping your estimation of cash flows sometime in the future and then
computing a terminal value that reflects the value of the firm at that point.

Value of a Firm =

You can find the terminal value in one of
three ways. One is to assume a liquidation of the firmÕs assets in the terminal
year and estimate what others would pay for the assets that the firm has
accumulated at that point. The other two approaches value the firm as a going
concern at the time of the terminal value estimation. One applies a multiple to
earnings, revenues or book value to estimate the value in the terminal year.
The other assumes that the cash flows of the firm will grow at a constant rate
forever Š a stable growth rate. With stable growth, the terminal value can be
estimated using a perpetual growth model.

In
some valuations, we can assume that the firm will cease operations at a point
in time in the future and sell the assets it has accumulated to the highest
bidders. The estimate that emerges is called a liquidation value. There are two
ways in which the liquidation value can be estimated. One is to base it on the
book value of the assets, adjusted for any inflation during the period. Thus,
if the book value of assets ten years from now is expected to be $2 billion,
the average age of the assets at that point is 5 years and the expected
inflation rate is 3%, the expected liquidation value can be estimated.

Expected
Liquidation value = Book Value of Assets_{Term yr} (1+ inflation rate)^{Average
life of assets}

^{ } =
$ 2 billion (1.03)^{5} = $2.319 billion

The
limitation of this approach is that it is based upon accounting book value and
does not reflect the earning power of the assets.

The
alternative approach is to estimate the value based upon the earning power of
the assets. To make this estimate, we would first have to estimate the expected
cash flows from the assets and then discount these cash flows back to the
present, using an appropriate discount rate. In the example above, for
instance, if we assumed that the assets in question could be expected to
generate $400 million in after-tax cash flows for 15 years (after the terminal
year) and the cost of capital was 10%, your estimate of the expected
liquidation value would be:

Expected
Liquidation value =

When
valuing equity, there is one additional step that needs to be taken. The
estimated value of debt outstanding in the terminal year has to be subtracted
from the liquidation value to arrive at the liquidation proceeds for equity
investors.

In
this approach, the value of a firm in a future year is estimated by applying a
multiple to the firmÕs earnings or revenues in that year. For instance, a firm
with expected revenues of $6 billion ten years from now will have an estimated
terminal value in that year of $12 billion if a value to sales multiple of 2 is
used. If valuing equity, we use equity multiples such as price earnings ratios
to arrive at the terminal value.

While this approach has the virtue of
simplicity, the multiple has a huge effect on the final value and where it is
obtained can be critical. If, as is common, the multiple is estimated by
looking at how comparable firms in the business today are priced by the market.
The valuation becomes a relative valuation rather than a discounted cash flow
valuation. If the multiple is estimated using fundamentals, it converges on the
stable growth model that will be described in the next section.

All
in all, using multiples to estimate terminal value, when those multiples are
estimated from comparable firms, results in a dangerous mix of relative and
discounted cash flow valuation. While there are advantages to relative
valuation, and we will consider these in a later chapter, a discounted cash
flow valuation should provide you with an estimate of intrinsic value, not
relative value. Consequently, the only consistent way of estimating terminal
value in a discounted cash flow model is to use either a liquidation value or a
stable growth model.

In the liquidation value approach, we are
assuming that your firm has a finite life and that it will be liquidated at the
end of that life. Firms, however, can reinvest some of their cash flows back
into new assets and extend their lives. If we assume that cash flows, beyond
the terminal year, will grow at a constant rate forever, the terminal value can
be estimated as.

Terminal Value_{t} =

where
the cash flow and the discount rate used will depend upon whether you are
valuing the firm or valuing the equity. If we are valuing the equity, the
terminal value of equity can be written as:

Terminal
value of Equity_{n} =

The
cashflow to equity can be defined strictly as dividends (in the dividend
discount model) or as free cashflow to equity. If valuing a firm, the terminal
value can be written as:

Terminal value_{n} =

where
the cost of capital and the growth rate in the model are sustainable forever.

In
this section, we will begin by considering how high a stable growth rate can
be, how to best estimate when your firm will be a stable growth firm and what
inputs need to be adjusted as a firm approaches stable growth.