and equity, and free cash ¬‚ow to equity will all remain constant at the year 2003 level.3

Under this scenario, it is simple to estimate the terminal value, by dividing the 2003

level of each of the variables by the appropriate discount rate. Again assuming a cost of

equity of 12 percent and a WACC of 9.2 percent, the estimated terminal values at the be-

ginning of 2004 are shown in Table 12-7. As one should expect, terminal values in Table

12-7 are higher than those reported in Table 12-6. This is entirely due to the fact that we

are now assuming that the ¬rm can retain its superior performance on its existing base

of sales inde¬nitely.

Table 12-7 Sigma™s Terminal Values with Abnormal Earnings on Existing Sales Only

Present value of ¬‚ows

beyond 2003 (at the

Present value of ¬‚ows beginning of 1999),

beyond 2003 (at the or

Valuation attribute beginning of 2004) Terminal value

.............................................................................................................................................

[0.016 X (1.1) 4 — 1.0] / 0.092 0.25/(1.092)5

Abnormal operating ROA

= 0.25 = 0.161

[0.026 X (1.1) 4 — 1.0] / 0.12 0.319/ (1.12)5

Abnormal ROE

= 0.319 = 0.181

178.3 / (1.092)5 = $ 114.8

Abnormal NOPAT (millions) 16.4/0.092 = $ 178.3

137/ (1.12)5 = $78

Abnormal earnings (millions) 16.4/0.12 = $137

1228 / ( 1.092)5 = $ 791

Free cash ¬‚ow to debt and equity 113/0.092 = $ 1,228

(millions)

767 / (1.12)5 = $ 435

Free cash ¬‚ow to equity (millions) 92/0.12 = $767

.............................................................................................................................................

Terminal Value with Persistent Abnormal Performance and Growth

The approaches described above each appeal in some way to the “competitive equilibri-

um assumption.” However, there are circumstances where the analyst is willing to as-

sume that the ¬rm may defy competitive forces and earn abnormal rates of return on new

projects for many years. If the analyst believes supernormal pro¬tability can be extended

to larger markets for many years, one possibility is to project earnings and cash ¬‚ows

over a longer horizon, until the competitive equilibrium assumption can reasonably be

invoked.

Another possibility is to project growth in abnormal earnings or cash ¬‚ows at some

constant rate. Consider the following. By treating Sigma as if its competitive advantage

can be maintained only on the nominal sales level achieved in the year 2003, we were

470 Prospective Analysis: Valuation Implementation

12-10

Prospective Analysis: Valuation Implementation

previously assuming that in real terms, its competitive advantage will shrink. Let™s say

that the analyst expects Sigma to maintain its advantage (through supplies of new and

more advanced products to a similar customer base) on a sales base that remains con-

stant in real terms”that grows beyond the year 2003 at the expected long-run in¬‚ation

rate of 3.5 percent. The computations implied by these assumptions are described below.

The approach is more aggressive than the one described earlier, but it may be more re-

alistic. After all, there is no obvious reason why the real size of the investment base on

which Sigma earns abnormal returns should depend on in¬‚ation rates.

The approach just described still relies to some extent on the competitive equilibrium

assumption. The assumption is now invoked to suggest that supernormal pro¬tability

can be extended only to an investment base that remains constant in real terms. However,

there is nothing about the valuation method that requires any reliance on the competitive

equilibrium assumption. The calculations described below could be used with any rate

of growth in sales. The question is not whether the arithmetic is available to handle such

an approach, but rather how realistic it is.

Let™s stay with the approach that assumes Sigma will extend its supernormal margins

to sales that grow beyond 2003 at the rate of in¬‚ation. How would abnormal earnings

and free cash ¬‚ows beyond 2003 behave?

Table 12-8 projects performance for the years 2003 through 2006, assuming that sales

increase by 3.5 percent, NOPAT margin is 7 percent in 2004 and beyond, and that all

other performance assumptions remain the same as in Table 12-2. The balance sheet for

the beginning of 2004 shown in Table 12-7 differs from that in table 12-2 because the

latter re¬‚ects the assumption that sales will grow at 3.5 percent in 2004, whereas the

Table 12-8 Forecast of Sigma™s Free Cash Flows Beyond 2000,

with 3.5 Percent Sales Growth and Abnormal Profit Margins

2003 2004 2005 2006

.........................................................................................................................

Sales growth 10% 3.5% 3.5% 3.5%

Sales (millions) $1,611 $1,667 $1,725 $1,786

NOPAT (millions) $113 $117 $121 $125

Net income (millions) $92 $95 $98 $102

Net assets (millions) $1,047 $1,083 $1,121 $1,161

Equity (millions) $628 $650 $673 $696

Abnormal operating ROA 1.6% 1.6% 1.6% 1.6%

Abnormal ROE 2.6% 2.6% 2.6% 2.6%

Abnormal NOPAT (millions) $16.4 $17.0 $17.6 $18.2

Abnormal earnings (millions) $16.4 $17.0 $17.6 $18.2

Free cash ¬‚ow to debt and equity

(millions) $76.1 $78.8 $81.5 $84.4

Free cash ¬‚ow to equity (millions) $69.8 $72.3 $74.8 $77.4

.........................................................................................................................

471

Prospective Analysis: Valuation Implementation

12-11 Part 2 Business Analysis and Valuation Tools

former assumes that the growth rate is 0 percent. So the free cash ¬‚ows shown in Table

12-7 for 2003 are different from those shown in Table 12-2.

Beyond 2003, which is our terminal year, as the sales growth rate remains constant

at 3.5 percent, abnormal earnings, free cash ¬‚ows, and book values of assets and equity

also grow at a constant rate of 3.5 percent. This is simply because we held all other per-

formance ratios constant in this period. As a result, abnormal operating ROA and abnor-

mal ROE remain constant at the same rate as in the terminal year.

The above exercise shows that, when we assume that the abnormal performance per-

sists at the same level as in the terminal year, projecting abnormal earnings and free cash

¬‚ows is a simple matter of growing them at the assumed sales growth rate. Since the rate

of abnormal earnings and cash ¬‚ows growth is constant beginning in 2004, it is also

straightforward to discount those ¬‚ows. For a given discount rate r, any ¬‚ow stream

growing at the constant rate g can be discounted by dividing the ¬‚ows in the ¬rst year

by the amount (r “ g). The resulting terminal value calculations are shown in Table 12“9.

Table 12-9 Sigma™s Terminal Values with Persistent Abnormal Earnings and Sales Growth

Present value of ¬‚ows

beyond 2003 (at the

Present value of ¬‚ows beginning of 1999),

beyond 2003 (at the or

Valuation attribute beginning of 2004) Terminal Value

............................................................................................................................................................

[0.016 X (1.1) 4 — 1.035] / (0.092 “ 0.035) 0.417/(1.092)5

Abnormal operating ROA

= 0.417 = 0.269

[0.026 X (1.1) 4 — 1.035] / (0.12 “ 0.035) 0.466/(1.12)5

Abnormal ROE

= 0.466 = 0.265

298.2/(1.092)5 = $192.0

Abnormal NOPAT (millions) 17/(0.092 “ 0.035) = $298.2

200/(1.12)5 = $113.5

Abnormal earnings (millions) 17/(0.12 “ 0.035) = $200

Free cash ¬‚ow to debt and equity

1382.5/(1.092)5 = $890.3

(millions) 78.8/(0.092 “ 0.035) = $1,382.5

850.6/(1.12)5 = $482.6

Free cash ¬‚ow to equity (millions) 72.3/(0.12 “ 0.025) = $850.6

............................................................................................................................................................

Terminal Value Based on a Price Multiple

A popular approach to terminal value calculation is to apply a multiple to abnormal earn-

ings, cash ¬‚ows, or book values of the terminal period. The approach is not as ad hoc as

it might at ¬rst appear. Note that under the assumption of no sales growth, abnormal

earnings or cash ¬‚ows beyond 2003 remain constant. Capitalizing these ¬‚ows in perpe-

tuity by dividing by the cost of capital, as shown in Table 12-7, is equivalent to multiply-

ing them by the inverse of the cost of capital. For example, capitalizing free cash ¬‚ows

to equity at 12 percent is equivalent to assuming a terminal cash ¬‚ow multiple of 8.3.

Thus, applying a multiple in this range is similar to discounting all free cash ¬‚ows be-

472 Prospective Analysis: Valuation Implementation

12-12

Prospective Analysis: Valuation Implementation

yond 2003, while invoking the competitive equilibrium assumption on incremental sales.

The mistake to avoid here is to capitalize the future abnormal earnings or cash ¬‚ows

using a multiple that is too high. The earnings or cash ¬‚ow multiples might be high cur-

rently because the market anticipates abnormally pro¬table growth. However, once that

growth is realized, the PE multiple should fall to a normal level. It is that normal PE, ap-

plicable to a stable ¬rm, or one that can grow only through zero net present value

projects, that should be used in the terminal value calculation. Thus, multiples in the

range of 7 to 11”close to the reciprocal of cost of equity and WACC”should be used

here. Higher multiples are justi¬able only when the terminal year is closer and there are

still abnormally pro¬table growth opportunities beyond that point.

Terminal values can also be based on book value multiples. The computations for ab-

normal operating ROA and ROE in Table 12-7 suggest that the value of Sigma™s assets

and equity at the end of 2003 will be in the range of 1.2 to 1.3 times their book value.

These multiples will be higher if one assumes abnormal pro¬tability on future growth

also, as shown in Table 12-8.

Selecting the Terminal Year

A question begged by the above discussion is how long to make the detailed forecast ho-

rizon. When the competitive equilibrium assumption is used, the answer is whatever

time is required for the ¬rm™s returns on incremental investment projects to reach that

equilibrium”an issue that turns on the sustainability of the ¬rm™s competitive advan-

tage. As indicated in Chapter 10, historical evidence indicates that most ¬rms in the U.S.

should expect ROEs to revert to normal levels within ¬ve to ten years. But for the typical

¬rm, we can justify ending the forecast horizon even earlier”note that the return on in-

cremental investment can be normal even while the return on total investment (and

therefore ROE) remains abnormal. Thus, a ¬ve- to ten-year forecast horizon should be

more than suf¬cient for most ¬rms. Exceptions would include ¬rms so well insulated

from competition (perhaps due to the power of a brand name) that they can extend their

investment base to new markets for many years and still expect to generate supernormal

returns. In 1999 the Wrigley Company, producer of chewing gum, is still extending its

brand name to untapped markets in other nations, and appears to be such a ¬rm.

In the case of Sigma, the terminal year used is ¬ve years beyond the current one. Table

12-2 shows that the return on capital (in this case, ROE) is forecast to decline only grad-

ually over these ¬ve years, from the unusually high 25 percent in 1999 to a level that holds

steady at 14.6 percent by 2003. If NOPAT margins could be maintained at the projected 7

percent on ever-increasing sales, this high ROE could be achieved even on new investment

in 2004 and beyond. However, even a slight decline in the NOPAT margin to about 6 per-

cent would, in the face of continued 10 percent sales growth, be enough to render the re-

turn on the incremental investment to be no higher than the cost of capital. Thus, the

performance we have already projected for the terminal year 2003 is not far removed

from a competitive equilibrium, and extending the forecast horizon by a few more years

473

Prospective Analysis: Valuation Implementation

12-13 Part 2 Business Analysis and Valuation Tools

would have little impact on the calculated value. Even if we project continuation of the 7

percent NOPAT margin through 2009 with 10 percent annual sales increases (and with the

competitive equilibrium assumption invoked thereafter), the ¬nal estimated ¬rm value

would increase only marginally. Large changes in the value estimate would arise only if

the analyst is willing to assume abnormal rates of return on investments well into the

twenty-¬rst century. In light of historical patterns for corporate performance, such an as-

sumption would have to be based on a strong belief in Sigma™s continued competitive ad-

vantage. The upshot is that an analyst could argue that the terminal year used for Sigma

should be extended from the ¬fth year to, say, the tenth year or even a few years beyond

that point, depending on the perceived sustainability of its competitive advantage. How-

ever, because Sigma is already assumed to be close to a competitive equilibrium in 2003,

the ¬nal value estimate would not be particularly sensitive to this change.

COMPUTING A DISCOUNT RATE

Thus far, the discount rates used have been offered without explanation. How would they

be estimated by the analyst?

To value a company™s assets, the analyst discounts the cash ¬‚ows available to both

debt and equity holders. The proper discount rate to use is therefore the weighted aver-

age cost of capital (WACC). The WACC is calculated by weighting the costs of debt and

equity capital according to their respective market values:

Vd Ve

----------------------- rd ( 1 “ T ) + ----------------------- re

WACC =

Vd + Ve Vd + Ve

where Vd = the market value of debt and Ve = the market value of equity

rd = the cost of debt capital

re = the cost of equity capital

T = the tax rate re¬‚ecting the marginal tax bene¬t of interest

Weighting the Costs of Debt and Equity

The weights assigned to debt and equity represent their respective fractions of total cap-

ital provided, measured in terms of market values. Computing a market value for debt

should not be dif¬cult. It is reasonable to use book values if interest rates have not

changed signi¬cantly since the time the debt was issued. Otherwise, the value of the debt

can be estimated by discounting the future payouts at current market rates of interest ap-

plicable to the ¬rm.

What is included in debt? Should short-term as well as long-term debt be included?

Should payables and accruals be included? The answer is revealed by considering how

we calculated free cash ¬‚ows. Those free cash ¬‚ows are the returns to the providers of

the capital to which the WACC applies. The cash ¬‚ows are those available before servic-