equivalent results, is to estimate the cash flows to the firm prior to debt payments, but
after reinvestment needs have been met:
Earnings before interest and taxes (1 - tax rate)
ÔÇ“ (Capital Expenditures - Depreciation)
ÔÇ“ Change in Non-cash Working Capital
= Free Cash Flow to the Firm
The difference between capital expenditures and depreciation (net capital expenditures)
and the increase in non-cash working capital represent the reinvestment made by the firm
to generate future growth. Another way of presenting the same equation is to add the net
capital expenditures and the change in working capital, and state that value as a
percentage of the after-tax operating income. This ratio of reinvestment to after-tax
operating income is called the reinvestment rate, and the free cash flow to the firm can
be written as:
(Capital Expenditures - Depreciation + " Working Capital) )
Reinvestment Rate =
EBIT (1- tax rate)
Free Cash Flow to the Firm = EBIT (1-t) (1 ÔÇ“ Reinvestment Rate)
Note that the reinvestment rate can exceed 100%17, if the firm has substantial
reinvestment needs. If that occurs, the free cash flow to a firm will be negative even
though after-tax operating income is positive. The cash flow to the firm is often termed
an unlevered cash flow, because it is unaffected by debt payments or the tax benefits18
flowing from these payments.
As with the dividends and the FCFE, the value of the operating assets of a firm
can be written as the present value of the expected cashflows during the high growth
period and a terminal value at the end of the period:
E(FCFF) t Terminal Value n E(FCFF) n +1
" (1 + r)t
Value 0 = + where Terminal Value n =
(1 + r) n (rn - g n )
where r is the cost of capital and gn is the expected growth rate in perpetuity.
17 In practical terms, this firm will need external financing, either from debt or equity or both, to cover the
18 If you are wondering where the tax benefits from interest payments, which are real cash benefits, show
up, it is in the discount rate, when we compute the after-tax cost of debt. If we add this tax benefit as a cash
flow to the free cash flow to the firm, we will double count the tax benefit.
Estimating Model Inputs
As with the dividend discount and the FCFE discount models, there are four basic
components that go into the value of the operating assets of the firm ÔÇ“ a period of high
growth, the free cashflows to the firm during that period, the cost of capital to use as a
discount rate and the terminal value for the operating assets of the firm. We have
additional steps we need to take to get to the value of equity per share. In particular, we
have to incorporate the value of non-operating assets, subtract out debt and then consider
the effect of options outstanding on the equity of the firm.
a. Estimating FCFF during High Growth Period
We base our estimate of a firmÔÇ™s value on expected future cash flows, not current
cash flows. It is the forecasts of earnings, net capital expenditures and working capital
that will yield these expected cash flows. One of the most significant inputs into any
valuation is the expected growth rate in operating income. As with the growth rates we
estimated for dividends and net income, the variables that determine expected growth are
simple. The expected growth in operating income is a product of a firm's reinvestment
rate, i.e., the proportion of the after-tax operating income that is invested in net capital
expenditures and non-cash working capital, and the quality of these reinvestments,
measured as the after-tax return on the capital invested.
Expected GrowthEBIT = Reinvestment Rate * Return on Capital
Capital Expenditure - Depreciation + ! Non - cash WC
Reinvestment Rate =
EBIT (1 - tax rate)
Return on Capital = EBIT (1-t) / (Book value of Debt + Book value of equity)
Both measures should be forward looking, and the return on capital should represent the
expected return on capital on future investments. In the rest of this section, we will
consider how best to estimate the reinvestment rate and the return on capital.
The reinvestment rate is often measured using a firmÔÇ™s past history on reinvestment.
Although this is a good place to start, it is not necessarily the best estimate of the future
reinvestment rate. A firmÔÇ™s reinvestment rate can ebb and flow, especially in firms that
invest in relatively few large projects or acquisitions. For these firms, looking at an
average reinvestment rate over time may be a better measure of the future. In addition, as
firms grow and mature, their reinvestment needs (and rates) tend to decrease. For firms
that have expanded significantly over the last few years, the historical reinvestment rate is
likely to be higher than the expected future reinvestment rate. For these firms, industry
averages for reinvestment rates may provide a better indication of the future than using
numbers from the past. Finally, it is important that we continue treating R&D expenses
and operating lease expenses consistently. The R&D expenses, in particular, need to be
categorized as part of capital expenditures for purposes of measuring the reinvestment
The return on capital is often based upon the firm's return on capital on existing
investments, where the book value of capital is assumed to measure the capital invested
in these investments. Implicitly, we assume that the current accounting return on capital
is a good measure of the true returns earned on existing investments, and that this return
is a good proxy for returns that will be made on future investments. This assumption, of
course, is open to question if the book value of capital is not a good measure of the
capital invested in existing projects and/or if the operating income is mis-measured or
volatile. Given these concerns, we should consider not only a firmÔÇ™s current return on
capital, but also any trends in this return as well as the industry average return on capital.
If the current return on capital for a firm is significantly higher than the industry average,
the forecasted return on capital should be set lower than the current return to reflect the
erosion that is likely to occur as competition responds.
Finally, any firm that earns a return on capital greater than its cost of capital is
earning an excess return. These excess returns are the result of a firmÔÇ™s competitive
advantages or barriers to entry into the industry. High excess returns locked in for very
long periods imply that this firm has a permanent competitive advantage.
In Practice: After-tax Operating Income
The income statement for a firm provides a measure of the operating income of the
firm in the form of the earnings before interest and taxes (EBIT) and a tax rate in the
form of an effective tax rate. Since the operating income we would like to estimate is
before capital and financing expenses, we have to make at least three adjustments to the
accounting operating income:
The first adjustment is for financing expenses that accountants treat as operating
expenses. The most significant example is operating leases. Since these lease
payments constitute firm commitments into the future, they are tax deductible, and
the failure to make lease payments can result in bankruptcy, we treat these expenses
as financial expenses. The adjustment, which we describe in detail in chapter 4,
results in an increase in both the operating income and the debt outstanding at the
The second adjustment is to correct for the incidence of one-time or irregular income
and expenses. Any expense (or income) that is truly a one-time expense (or income)
should be removed from the operating income and should not be used in forecasting
future operating income. While this would seem to indicate that all extraordinary
charges should be expunged from operating income, there are some extraordinary
charges that seem to occur at regular intervals ÔÇ“ say once every four or five years.
Such expenses should be viewed as ÔÇťirregularÔÇŁ rather than extraordinary expenses
and should be built into forecasts. The easiest way to do this is to annualize the
expense. Put simply, this would mean taking one-fifth of any expense that occurs
once every five years, and computing the income based on this apportioned expense.
As for the tax rate, the effective tax rates reported by most firms are much lower than the
marginal tax rates. As with the operating income, we should look at the reasons for the
difference and see if these firms can maintain their lower tax rates. If they cannot, it is
prudent to shift to marginal tax rates in computing future after-tax operating income.
Illustration 12.6: Estimating Growth Rate in Operating Income - Disney
We begin by estimating the reinvestment rate and return on capital for Disney in
2003, using the numbers from the latest financial statements. We did convert operating
leases into debt and adjusted the operating income and capital expenditure accordingly.19
Reinvestment Rate2003 = (Cap Ex ÔÇ“ Depreciation + Chg in non-cash WC)/ EBIT (1-t)
19The book value of debt is augmented by the $1,753 million in present value of operating lease
commitments. The unadjusted operating income for Disney was $2,713 million. The operating lease
adjustment adds the inputed interest expense on the PV of operating leases to the operating income (5.25%
of $1753 million= $92 million), the current yearÔÇ™s operating lease expense to capital expenditures ($556
million) and the depreciation on the leased asset to depreciation ($195 million).
= (1735 ÔÇ“ 1253 + 454)/(2805(1-.373)) = 53.18%
Return on capital2003 = EBIT (1-t)2003/ (BV of Debt2002 + BV of Equity2002)
= 2805 (1-.373)/ (15,883+23,879) = 4.42%
If Disney maintains its 2003 reinvestment rate and return on capital for the next few
years, its growth rate will be only 2.35%.
Expected Growth Rate from existing fundamentals = 53.18% * 4.42% = 2.35%
To make our estimates for the future, we look at DisneyÔÇ™s returns on capital and
reinvestment rates from 1995 to 2003 in Figure 12.5:
Note the dramatic drop in the return on capital after the Capital Cities acquisition from
more than 19% in 1997 to less than 10% in 1998.20 While this may sound optimistic, we
will assume that Disney will be able to earn a return on capital of 12% on its new
investments and that the reinvestment rate will be 60% for the immediate future.21 The
expected growth in operating income over this period will be 7.20%.
20 Part of this drop can be explained by accounting factors; the acquisition of Capital Cities increased the
book value of equity and debt substantially.
21 We are, however, leaving the return on capital on existing investments at 4.55% since improving those
returns will be much more difficult to do.
Expected Growth Rate in operating income = Return on capital * Reinvestment Rate
= 12% * .60 = 7.20%
fundgrEB.xls: There is a dataset on the web that summarizes reinvestment rates
and return on capital by industry group in the United States for the most recent quarter.
b. Estimating Cost of Capital
Unlike equity valuation models, where the cost of equity is used to discount
cashflows to equity, the cost of capital is used to discount cashflows to the firm. The cost
of capital is a composite cost of financing that includes the costs of both debt and equity
and their relative weights in the financing structure:
Cost of Capital = kequity (Equity/(Debt+Equity) + kdebt (Debt/(Debt + Equity)
where the cost of equity represents the rate of return required by equity investors in the
firm, and the cost of debt measures the current cost of borrowing, adjusted for the tax
benefits of borrowing. The weights on debt and equity have to be market value weights.
We discussed the cost of capital estimation extensively earlier in this book, in the context
of both investment analysis and capital structure. We will consider each of the inputs in
the model, in the context of valuing a firm.
The cost of equity, as we have defined it through this book, is a function of the non-
diversifiable risk in an investment, which, in turn, is measured by a beta (in the single
factor model) or betas (in the multiple factor models). We argued that the beta(s) are
better measured by looking at the average beta(s) of other firms in the business, i.e,
bottom-up estimates, and reflecting a firmÔÇ™s current business mix and leverage. This
argument is augmented, when we value companies, by the fact that a firmÔÇ™s expected
business mix and financial leverage can change over time, and its beta will change with
both. As the beta changes, the cost of equity will also change, from year to year.
Just as the cost of equity can change over time as a firmÔÇ™s exposure to market risk
changes, so too can the cost of debt, as its exposure to default risk changes. The default
risk of a firm can be expected to change for two reasons. One is that the firmÔÇ™s size will
change as we project earnings further into the future; the volatility in these earnings is
also likely to change over time. The second reason is that changes occur in financial
leverage. If we expect a firmÔÇ™s financial leverage to change over time, it will affect its
capacity to service debt and hence its cost of borrowing. The after-tax cost of debt can
also change as a consequence of expected changes in the tax rate over time.
As a firm changes its leverage, the weights attached to equity and debt in the cost
of capital computation will change. Should a firmÔÇ™s leverage be changed over the forecast
period? The answer to this depends upon two factors. The first is whether the firm is
initially under or over levered. If it is at its appropriate leverage, there is a far smaller
need to change leverage in the future. The second is the views of the firmÔÇ™s management
and the degree to which they are responsive to the firmÔÇ™s stockholders. Thus, if the
management of a firm is firmly entrenched and steadfast in its opposition to debt, an
under levered firm will stay under levered over time. In an environment where
stockholder have more power, there will eventually be pressure on this firm to increase
its leverage toward its optimal level.
Illustration 12.7: Cost of capital - Disney
Recapping the inputs we used to estimate the cost of capital in Disney, we will
make the following assumptions:
The beta for the first 5 years will be the bottom-up beta of 1.2456 that we
estimated in illustration 4.5. In conjunction with a riskfree rate of 4% and market
risk premium of 4.82%, this yields a cost of equity of 10%.
Cost of Equity = Riskfree Rate + Beta * Risk Premium = 4% + 1.2456(4.82%) = 10%
The cost of debt for Disney for the first 5 years, based upon its rating of BBB+, is
5.25%. Using DisneyÔÇ™s tax rate of 37.30% gives us an after-tax cost of debt of
After-tax cost of debt = 5.25% (1-.373) = 3.29%