Chapter 4 The Value of Common Stocks 95
bre44380_ch04_076-104.indd 95 09/30/15 12:46 PM
Valuation Format
The value of a business is usually computed as the discounted value of free cash flows out
to a valuation horizon (H), plus the forecasted value of the business at the horizon, also dis-
counted back to present value. That is,
PV =FCF 1
_____
1 + r+FCF 2
_______
(1 + r)^2+ ⋅ ⋅ ⋅ +FCFH
_______
(1 + r)H+PVH
_______
(1 + r)H(^) PV(free cash flow) PV(horizon value)
Of course, the concatenator business will continue after the horizon, but it’s not practical to
forecast free cash flow year by year to infinity. PVH stands in for free cash flow in periods
H + 1, H + 2, etc.
Valuation horizons are often chosen arbitrarily. Sometimes the boss tells everybody to use
10 years because that’s a round number. We will try year 6, because growth of the concatena-
tor business seems to settle down to a long-run trend after year 7.
Estimating Horizon Value
There are several common formulas or rules of thumb for estimating horizon value. First, let
us try the constant-growth DCF formula. This requires free cash flow for year 7, which we
have from Table 4.7; a long-run growth rate, which appears to be 6%; and a discount rate,
which some high-priced consultant has told us is 10%. Therefore,
Horizon value (PV looking forward from period 6) = PVH = ____1.09
.10 − .06
= $27.3 million
Horizon value (discounted back to PV in period 0) = _2 7. 3
(1.1)^6
= $15.4 million
The PV of the near-term free cash flows is $.9 million. Thus the present value of the concat-
enator division is
PV(business) = PV(free cash flow) + PV(horizon value)
= .9 + 15.4
= $16.3 million
Now, are we done? Well, the mechanics of this calculation are perfect. But doesn’t it make
you just a little nervous to find that 94% of the value of the business rests on the horizon
value? Moreover, a little checking shows that the horizon value can change dramatically in
response to apparently minor changes in assumptions. For example, if the long-run growth
rate is 7% rather than 6%, the value of the business increases from $16.3 to $19.2 million.^14
In other words, it’s easy for a discounted-cash-flow business valuation to be mechani-
cally perfect and practically wrong. Smart financial managers try to check their results by
calculating horizon value in different ways. Let’s try valuation by comparables, using P/E and
market–book ratios.
BEYOND THE PAGE
mhhe.com/brealey12e
Try It! Table 4.7:
Valuing the
concatenator
division
(^14) If long-run growth is 7% instead of 6%, an extra 1% of asset value will have to be plowed back into the concatenator business, reduc-
ing free cash flow from $1.09 million to $.97 million. The PV of cash flows from dates 1 to 6 stays at $.9 million.
Horizon value (discounted back to PV at date 0) = ^1
(1.1)^6
× __.97
.10 − .07
= $18.3 million
PV(business) = 0.9 + 18.3 = $19.2 million