CHAPTER 15 FIRM VALUATION: COST OF CAPITAL AND APV APPROACHES

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CHAPTER 15
FIRM VALUATION: COST OF CAPITAL AND APV APPROACHES
In the last two chapters, we examined two approaches to valuing the equity in the
firm -- the dividend discount model and the FCFE valuation model. This chapter develops
another approach to valuation where the entire firm is valued, by either discounting the
cumulated cashflows to all claim holders in the firm by the weighted average cost of
capital (the cost of capital approach) or by adding the marginal impact of debt on value
to the unlevered firm value (adjusted present value approach).
In the process of looking at firm valuation, we also look at how leverage may or
may not affect firm value. We note that in the presence of default risk, taxes and agency
costs, increasing leverage can sometimes increase firm value and sometimes decrease it. In
fact, we argue that the optimal financing mix for a firm is the one that maximizes firm
value.
The Free Cashflow to the Firm
The free cashflow to the firm is the sum of the cashflows to all claim holders in
the firm, including stockholders, bondholders and preferred stockholders. There are two
ways of measuring the free cashflow to the firm (FCFF).
One is to add up the cashflows to the claim holders, which would include cash
flows to equity (defined either as free cash flow to equity or dividends), cashflows to
lenders (which would include principal payments, interest expenses and new debt issues)
and cash flows to preferred stockholders (usually preferred dividends).
FCFF = Free Cashflow to Equity
+ Interest Expense (1 - tax rate) + Principal Repayments - New Debt Issues
+ Preferred Dividends
Note, however, that we are reversing the process that we used to get to free cash flow to
equity, where we subtracted out payments to lenders and preferred stockholders to
estimate the cash flow left for stockholders. A simpler way of getting to free cash flow to
the firm is to estimate the cash flows prior to any of these claims. Thus, we could begin

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with the earnings before interest and taxes, net out taxes and reinvestment needs and
arrive at an estimate of the free cash flow to the firm.
FCFF = EBIT (1 - tax rate) + Depreciation - Capital Expenditure - ∆ Working Capital
Since this cash flow is prior to debt payments, it is often referred to as an unlevered cash
flow. Note that this free cash flow to the firm does not incorporate any of the tax benefits
due to interest payments. This is by design, because the use of the after-tax cost of debt
in the cost of capital already considers this benefit and including it in the cash flows
would double count it.
FCFF and other cashflow measures
The differences between FCFF and FCFE arise primarily from cashflows
associated with debt -- interest payments, principal repayments, new debt issues and
other non-equity claims such as preferred dividends. For firms at their desired debt level,
which finance their capital expenditures and working capital needs with this mix of debt
and equity. As for the use of debt issues to finance principal repayments, the free
cashflow to the firm will exceed the free cashflow to equity.
One measure that is widely used in valuation is the earnings before interest, taxes,
depreciation and amortization (EBITDA). The free cashflow to the firm is a closely
related concept but it takes into account the potential tax liability from the earnings as
well as capital expenditures and working capital requirements.
Three measures of earnings are also often used to derive cash flows. The earnings
before interest and taxes (EBIT) or operating income comes directly from a firm’s income
statements. Adjustments to EBIT yield the net operating profit or loss after taxes
(NOPLAT) or the net operating income (NOI). The net operating income is defined to be
the income from operations, prior to taxes and non-operating expenses.
Each of these measures is used in valuation models and each can be related to the
free cashflow to the firm. Each, however, makes some assumptions about the relationship
between depreciation and capital expenditures that are made explicit in the Table 15.1.
Table 15.1: Free Cash Flows to the Firm: Comparison to other measures
Cashflow used
Definition
Use in valuation

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FCFF
Free Cashflow to firm
Discounting free cash flow
to the firm at the cost of
capital will yield the value
of the operating assets of
the firm. To this, you
would add on the value of
non-operating assets
to
arrive at firm value.
FCFF - Interest (1-t) – Principal Discounting free cash flows
FCFE
repaid + New Debt Issued – to equity at the cost of
Preferred Dividend
equity will yield the value
of equity in a business.
FCFF + EBIT(t) + Capital If you discount EBITDA at
EBITDA
Expenditures
+
Change
in the cost of capital to value
working capital
an asset, you are assuming
that there are no taxes and
that the firm will actively
disinvest over time. It
would be inconsistent to
assume a growth rate or an
infinite life for this firm.
EBIT (1-t)
FCFF + Capital Expenditures –
If you discount after-tax
Depreciation + Change in
operating income at the
(NOPLAT is a slightly working capital
cost of capital to value a
modified version of this
firm, you are assuming no
estimate and it removes
reinvestment.
The
any
non-operating
depreciation is reinvested
items that might affect
back into the firm to
the reported EBIT.)
maintain existing assets.
You can assume an infinite

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life but no growth.
Growth in FCFE versus Growth in FCFF
Will equity cashflows and firm cashflows grow at the same rate? Consider the
starting point for the two cash flows. Equity cash flows are based upon net income or
earnings per share – measures of equity income. Firm cash flows are based upon operating
income – i.e. income prior to debt payments. As a general rule, you would expect growth
in operating income to be lower than growth in net income, because financial leverage can
augment the latter. To see why, let us go back to the fundamental growth equations we
laid out in Chapter 11.
Expected growth in net income = Equity Reinvestment rate * Return on Equity
Expected growth in operating income = Reinvestment Rate * Return on Capital
We also defined the return on equity in terms of the return on capital:
Return
on
Equity
=
 Debt 
Capital
on
Return
+
(
After

-

capital
on
Return
-
of
cost
tax
debt

)




 Equtiy 
When a firm borrows money and invests in projects that earn more than the after-tax cost
of debt, the return on equity will be higher than the return on capital. This, in turn, will
translate into a higher growth rate in equity income at least in the short term.
In stable growth, though, the growth rates in equity income and operating income
have to converge. To see why, assume that you have a firm whose revenues and operating
income and growing at 5% a year forever. If you assume that the same firm’s net income
grows at 6% a year forever, the net income will catch up with operating income at some
point in time in the future and exceed revenues at a later point in time. In stable growth,
therefore, even if return on equity exceeds the return on capital, the expected growth will
be the same in all measures of income.1
Firm Valuation: The Cost of Capital Approach

1 The equity reinvestment rate and firm reinvestment rate will adjust to ensure that this happens. The equity
reinvestment rate will be a lower number than the firm reinvestment rate in stable growth for any levered
firm.

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The value of the firm is obtained by discounting the free cashflow to the firm at
the weighted average cost of capital. Embedded in this value are the tax benefits of debt
(in the use of the after-tax cost of debt in the cost of capital) and expected additional risk
associated with debt (in the form of higher costs of equity and debt at higher debt ratios).
Just as with the dividend discount model and the FCFE model, the version of the model
used will depend upon assumptions made about future growth.
Stable Growth Firm
As with the dividend discount and FCFE models, a firm that is growing at a rate
that it can sustain in perpetuity – a stable growth rate – can be valued using a stable
growth model.
The Model
A firm with free cashflows to the firm growing at a stable growth rate can be
valued using the following equation:
FCFF
Value of firm =
1
g

-

WACC
n
where,
FCFF1 = Expected FCFF next year
WACC = Weighted average cost of capital
gn = Growth rate in the FCFF (forever)
The Caveats
There are two conditions that need to be met in using this model. First, the growth
rate used in the model has to be less than or equal to the growth rate in the economy –
nominal growth if the cost of capital is in nominal terms, or real growth if the cost of
capital is a real cost of capital. Second, the characteristics of the firm have to be consistent
with assumptions of stable growth. In particular, the reinvestment rate used to estimate
free cash flows to the firm should be consistent with the stable growth rate. The best way
of enforcing this consistency is to derive the reinvestment rate from the stable growth
rate.

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Growth rate
Reinvestment rate in stable growth =
capital
on
Return
If reinvestment is estimated from net capital expenditures and change in working capital,
the net capital expenditures should be similar to those other firms in the industry
(perhaps by setting the ratio of capital expenditures to depreciation at industry averages)
and the change in working capital should generally not be negative. A negative change in
working capital creates a cash inflow and while this may, in fact, be viable for a firm in the
short term, it is dangerous to assume it in perpetuity.2 The cost of capital should also be
reflective of a stable growth firm. In particular, the beta should be close to one – the rule
of thumb presented in the earlier chapters that the beta should be between 0.8 and 1.2 still
holds. While stable growth firms tend to use more debt, this is not a pre-requisite for the
model, since debt policy is subject to managerial discretion.
Limitations
Like all stable growth models, this one is sensitive to assumptions about the
expected growth rate. This is accentuated, however, by the fact that the discount rate
used in valuation is the WACC, which is significantly lower than the cost of equity for
most firms. Furthermore, the model is sensitive to assumptions made about capital
expenditures relative to depreciation. If the inputs for reinvestment are not a function of
expected growth, the free cashflow to the firm can be inflated (deflated) by reducing
(increasing) capital expenditures relative to depreciation. If the reinvestment rate is
estimated from the return on capital, changes in the return on capital can have significant
effects on firm value.
Illustration 15.1: Valuing a firm with a stable growth FCFF Model: Tube Investments of
India (TI)
Tube Investments of India is a diversified manufacturing firm, with its
headquarters in South India. In 1999, the firm reported operating income of Rs. 632.2
million and paid faced a tax rate of 30% on income. The firm had a book value of equity of

2 Carried to its logical extreme, this will push net working capital to a very large (potentially infinite)
negative number.

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Rs 3432.1 million rupees and book value of debt of Rs. 1377.2 million at the end of 1998.
The firm’s return on capital can be estimated as follows:
EBIT(1- t)
=
of

Book value
debt

+
of

Book value
Equity

Return on capital
632.2(1 − 0.30)
=
= 9.20%
3432.1 + 1377.2
The firm is in stable businesses and expects to grow only 5% a year.3 Assuming that it
maintains its current return on capital, the reinvestment rate for the firm will be:
g
5%
Reinvestment rate =
=
= 54.34%
ROC
9.20%
The firm’s expected free cash flow to the firm next year can be estimated as follows:
Expected EBIT (1-t) next year = 632.2 (1-0.30) (1.05)
=
464.7
- Expected Reinvestment next year
= EBIT(1-t) (Reinvestment rate)
= 464.7 (0.5435)
=
252.5
Expected Free Cash flow to the firm
=
212.2
To estimate the cost of capital, we use a bottom-up beta (adjusted to 1.17 to reflect TI’s
additional leverage), a nominal rupee riskfree rate of 10.50% and a risk premium of 9.23%
(4% for the mature market premium and 5.23% for country risk in India). The cost of
equity can then be estimated as follows:
Cost of Equity = 10.5% + 1.17 (9.23%) = 21.30%
The cost of debt for Tube Investments is 12%, which in conjunction with their market
debt to capital ratio of 44.19% - the market value of equity at the time of the valuation
was Rs.2282 million and the market value of debt was Rs. 1807.3 million - yields a cost
of capital of 15.60%:
= (




of
Cost
) E
Equity


 + (After -
of
Cost
tax
) D
Debt



Cost of capital
 D + E 
 D + E 
= (21.30%)(
)
0.5581 + (12%)(1- 0.3)(0.4419)= 15.60%
With the perpetual growth of 5%, the expected free cash flow to the firm shown above
(Rs 212.2 million) and the cost of capital of 15.60%, we obtain a value for the firm of:

3 Note that while this resembles growth rates we have used for other firms, it is a low growth rate given
that this valuation is in Indian rupees. As a simple check, note that the riskfree rate that we use is 10.50%.

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212.2
Value of the operating assets of firm =
=
million

2002

Rs
0.156 - 0.05
Adding back cash and marketable securities with a value of Rs 1365.3 million and
subtracting out the debt outstanding of Rs 1807.3 million yields a value for the equity of
Rs 1560 million and a value per share of Rs. 63.36 (based upon the 24.62 million shares
outstanding). The stock was trading at Rs 92.70 at the time of this valuation.
An interesting aspect of this valuation is that the return on capital used to
compute the reinvestment rate is significantly lower than the cost of capital. In other
words, we are locking in this firm into investing in negative excess return projects forever.
If we assume that the firm will find a way to earn its cost of capital of 15.6% on
investments, the reinvestment rate would be much lower.
g
0.05
Reinvestment rate
=
=
ROC=Cost of capital =
32.05%
ROC
0.156
 1- 0.3205 
Value of operating assets =(464.7)
 = Rs. 2979 million
 0.1560 - 0.05 
+ Value of cash and marketable securities
= Rs 1365 million
- Debt
= Rs 1807 million
Value of equity
= Rs 2537 million
2537
Value per share =
= Rs 103.04 per share
24.62
Market Value Weights, Cost of Capital and Circular Reasoning
To value a firm, you first need to estimate a cost of capital. Every textbook is
categorical that the weights in the cost of capital calculation be market value weights. The
problem, however, is that the cost of capital is then used to estimate new values for debt
and equity that might not match the values used in the original calculation. One defense
that can be offered for this inconsistency is that if you went out and bought all of the debt
and equity in a publicly traded firm, you would pay current market value and not your
estimated value and your cost of capital reflects this.
To those who are bothered by this inconsistency, there is a way out. You could
do a conventional valuation using market value weights for debt and equity, but then use
the estimated values of debt and equity from the valuation to re-estimate the cost of

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capital. This, of course, will change the values again, but you could feed the new values
back and estimate cost of capital again. Each time you do this, the differences between the
values you use for the weights and the values you estimate will narrow, and the values
will converge sooner rather than later.
How much of a difference will it make in your ultimate value? The greater the
difference between market value and your estimates of value, the greater the difference
this iterative process will make. In the valuation of Tube Investments above, we began
with a market price of Rs 92.70 per share and estimated a value of Rs 63.36. If we
substituted back this estimated value and iterated to a solution, we would arrive at an
estimate of value of Rs 70.66 per share.4
The General Version of the FCFF Model
Rather than break the free cash flow model into two-stage and three-stage models
and risk repeating what was said in the last chapter, we present the general version of the
model in this section. We follow up by examining a range of companies – a traditional
manufacturing firm, a firm with operating leases and a firm with substantial R&D
investments – to illustrate the differences and similarities between this approach and the
FCFE approach.
The Model
The value of the firm, in the most general case, can be written as the present value
of expected free cashflows to the firm.
t =∞
FCFF
Value of Firm =
t
∑(1+WACC)t
t =1
where,
FCFFt = Free Cashflow to firm in year t
WACC = Weighted average cost of capital

4 In Microsoft Excel, it is easy to set this process up. You should first go into calculation options and put
a check in iteration box. You can then make the cost of capital a function of your estimated values for debt
and equity.

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If the firm reaches steady state after n years and starts growing at a stable growth rate gn
after that, the value of the firm can be written as:
t = n
FCFF
Value of Firm =
t
∑
+ [FCFFn+1 / (WACC − gn)]
(1+ WACC)t
(1+ WACC)n
t =1
Best suited for:
Firms that have very high leverage or are in the process of changing their leverage
are best valued using the FCFF approach. The calculation of FCFE is much more difficult
in these cases because of the volatility induced by debt payments (or new issues) and the
value of equity, which is a small slice of the total value of the firm, is more sensitive to
assumptions about growth and risk. It is worth noting, though, that in theory, the two
approaches should yield the same value for the equity. Getting them to agree in practice is
an entirely different challenge and we will return to examine it later in this chapter.
Best suited for:
There are three problems that we see with the free cash flow to the firm model.
The first is that the free cash flows to equity are a much more intuitive measure of cash
flows than cash flows to the firm. When asked to estimate cash flows, most of us look at
cash flows after debt payments (free cash flows to equity), because we tend to think like
business owners and consider interest payments and the repayment of debt as cash
outflows. Furthermore, the free cash flow to equity is a real cash flow that can be traced
and analyzed in a firm. The free cash flow to the firm is the answer to a hypothetical
question: What would this firm’s cash flow be, if it had no debt (and associated
payments)?
The second is that its focus on pre-debt cash flows can sometimes blind us to real
problems with survival. To illustrate, assume that a firm has free cash flows to the firm of
$100 million but because of its large debt load makes the free cash flows to equity equal
to -$50 million. This firm will have to raise $50 million in new equity to survive and, if it
cannot, all cash flows beyond this point are put in jeopardy. Using free cash flows to
equity would have alerted you to this problem, but free cash flows to the firm are
unlikely to reflect this.

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