Principles of Private Firm Valuation

Valuation Models and Metrics 59

requirements exceed after-tax cash flows, then the firm needs outside

funding in the form of new equity and/or debt. When competitive pressure

results in a rate of return that equals the cost of capital, gwill be zero

because the retention will be zero. Put differently, reinvesting firm capi-

tal when the ROA equals kresults in no additional value created by

the investments made. When the long-run value of gis greater than zero,

the firm has a sustainable competitive advantage, allowing it to earn rates

of return that exceed the cost of capital in perpetuity.^6 Imposing competi-

tive market conditions in Equation 4.8 implies that gˆ 1 >gˆ 2 >gˆ 3 <...>gˆn,

gˆn=0 whenk=ROA, and RRn=0. Thus, Equation 4.8 can be written as

Equation 4.9.

V 0 =CFˆ 1 /(1 +k)^1 +CFˆ 2 /(1 +k)^2

+...+[CFˆn − 1 ×(1 +gˆn)](k −gˆn)/(1 +k)n (4.9)

gˆn=0 ifk =ROA

Based on this discussion, one might ask: Is there an optimal value for g?

While there is no optimal value per se, there is a plausible range. To start,

the U.S. economy has a long-term growth rate of about 5 percent (3 percent

real growth and 2 percent inflation). The long-term growth in firm cash

flows should not be expected to grow significantly faster than the long-term

growth potential of the U.S. economy. If this were assumed, it would imply

that the firm would represent an increasing share of the total economy over

time, and at some point in the future the firm would be equal in size to the

total economy. This implication, of course, makes no sense, and hence the

long-term value of gshould reflect both the long-term competitive condi-

tions facing the firm and the long-term growth potential of the total econ-

omy. This suggests that long-term growth rates in excess of the long-term

growth of the economy are not sensible.

Valuing Tentex Using the Discounted Free

Cash Flow Model

In this section we use the nonconstant growth model to value Tentex. The

version of the model used combines Tentex’s expected cash flow with its

expected capital requirements to generate what is termed free cash flow.

More precisely, free cash flow is defined as NOPAT less the change in work-

ing capital and net capital expenditures. Table 4.4 shows the inputs used in

the Tentex valuation. Table 4.5 shows the Tentex valuation and the various

components that make it up.

Note that Tentex revenue is expected to grow at 7 percent a year for

each of the next four years and then to slow as expansion opportunities

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