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In this chapter, we look at how to value a firm and its equity, given what we now
know about investment, financing and dividend decisions. We will consider two
approaches to valuation. The first and most fundamental approach to valuing a firm is
discounted cash flow valuation, which extends the present value principles that we
developed to analyze projects to value a firm. The value of any firm is determined by
four factors “ its capacity to generate cash flows from assets in place, the expected
growth rate of these cash flows, the length of time it will take for the firm to reach stable
growth, and the cost of capital. Consequently, to increase the value of a firm, we have to
change one or more of these variables.
The second way of valuing a firm or its equity is to based the value on how the
market is valuing similar or comparable firms; this approach is called relative valuation.
This approach can yield values that are different from a discounted cashflow valuation
and we will look at some of the reasons why these differences may occur.
In a departure from the previous chapters, we will take the perspective of
investors in financial markets in estimating value. Investors assess the value of a firm™s
stock in order to decide whether to buy the stock or, if they already own it, whether to
continue to it.

Discounted Cash Flow Valuation
In discounted cash flow valuation, we estimate the value of any asset by
discounting the expected cash flows on that asset at a rate that reflects their riskiness. In a
sense, we measure the intrinsic value of an asset. The value of any asset is a function of
the cash flows generated by that asset, the life of the asset, the expected growth in the
cash flows and the riskiness associated with them. In other words, it is the present value
of the expected cash flows on that asset.
t =N
E(Cash Flow t )
Value of Asset =
(1+ r) t
t =1

where the asset has a life of N years and r is the discount rate that reflects both the
riskiness of the cash flows and financing mix used to acquire the asset. If we view a firm


as a portfolio of assets, this equation can be extended to value a firm, using cash flows to
the firm over its life and a discount rate that reflects the collective risk of the firm™s
This process is complicated by the fact that while some of the assets of a firm have
already been created, and thus are assets-in-place, a significant component of firm value
reflects expectations about future investments. Thus, we not only need to measure the
cash flows from current investments, but we also must estimate the expected value from
future investments. In the sections that follow, we will introduce the discounted cash flow
model in steps. We begin by discussing two different ways of approaching valuation “
equity and firm valuation “ and then move on to consider how best to estimate the inputs
into valuation models, and then consider how to go from the value of a firm to the value
of equity per share.

Equity Valuation versus Firm Valuation
There are two paths to discounted cash flow valuation -- the first is to value just
the equity stake in the business; the Value of Equity: This is the value of the equity
second is to value the entire firm, stake in a business; in the context of a publicly
traded firm, it is the value of the common stock in
including equity and any other
the firm.
claimholders in the firm (bondholders,
preferred stockholders, etc.). While both approaches discount expected cash flows, the
relevant cash flows and discount rates are different for each.
The value of equity is obtained by discounting expected cash flows to equity ““
i.e., the residual cash flows after meeting all expenses, tax obligations, and interest and
principal payments ““ at the cost of equity ““ i.e., the rate of return required by equity
investors in the firm.

t =n
CF to Equity t
Value of Equity =
(1+ k e )t
t =1

CF to Equityt = Expected Cash flow to Equity in period t
ke = Cost of Equity


The dividend discount model is a specialized case of equity valuation, where the value of
a stock is the present value of expected future dividends.
The value of the firm is obtained by discounting expected cash flows to the firm,
i.e., residual cash flows after meeting all
Value of Firm: The value of the firm is the value of all
operating expenses and taxes, but prior
investors who have claims on the firm; thus, it includes
to debt payments ““ at the weighted
lenders and debt-holders, who have fixed claims and
average cost of capital ““ i.e., the cost equity investors, who have residual claims.
of the different components of financing
used by the firm, weighted by their market value proportions.
CF to Firm
! (1+ WACC)tt
Value of Firm =
t =1

CF to Firmt = Expected Cash flow to Firm in period t
WACC = Weighted Average Cost of Capital
While the two approaches use different definitions of cash flow and discount rates, they
will yield consistent estimates of value as long as the same set of assumptions is applied
for both. It is important to avoid mismatching cash flows and discount rates, since
discounting cash flows to equity at the weighted average cost of capital will lead to an
upwardly biased estimate of the value of equity, while discounting cash flows to the firm
at the cost of equity will yield a downward biased estimate of the value of the firm.

12.1. ˜: Firm Valuation and Leverage
It is often argued that equity valuation requires more assumptions than firm valuation,
because cash flows to equity require explicit assumptions about changes in leverage
whereas cash flows to the firm are pre-debt cash flows and do not require assumptions
about leverage. Is this true?
a. Yes
b. No


Choosing the Right Valuation Model
All discounted cash flow models ultimately boil down to estimating four inputs -
current cashflows, an expected growth rate in these cashflows, a point in time when the
firm will be growing a rate it can sustain forever and a discount rate to use in discounting
these cashflows. In this section, we will examine the choices available in terms of each of
these inputs.
In terms of cashflows, there are three choices - dividends or free cashflows to
equity for equity valuation models, and free cashflows to the firm for firm valuation
models. Discounting dividends usually provides the most conservative estimate of value
for the equity in any firm, since most firms pay less in dividends than they can afford to.
In the dividend policy section, we noted that the free cash flow to equity, i.e., the cash
flow left over after meeting all investment needs and making debt payments, is the
amount that a firm can pay in dividends. The value of equity, based upon the free cash
flow to equity, will therefore yield a more realistic estimate of value for equity, especially
in the context of a takeover. Even if a firm is not the target of a takeover, it can be argued
that the value of equity has to reflect the possibility of a takeover, and hence the expected
free cash flows to equity. The choice between free cash flows to equity and free cash
flows to the firm is really a choice between equity and firm valuation. Done consistently,
both approaches should yield the same values for the equity in a business. As a practical
concern, however, cash flows to equity are after net debt issues or payments and become
much more difficult to estimate when financial leverage is changing over time, whereas
cashflows to the firm are pre-debt cash flows and are unaffected by changes in the
leverage. Ease of use dictates that firm valuation will be more straightforward under this
While we can estimate any of these cashflows from the most recent financial
statements, the challenge in valuation is in estimating these cashflows in future years. In
most valuations, this takes the form of an expected growth rate in earnings that is then
used to forecast earnings and cash flows in future periods. The growth rates estimated
should be consistent with our definition of cashflows. When forecasting cashflows to
equity, we will generally forecast growth in net income or earnings per share that are


measures of equity earnings. When forecasting cashflows to the firm, the growth rate that
matters is the growth rate in operating earnings. 1
The choice of discount rates will be dictated by the choice in cash flows. If the
cash flow that is being discounted is dividends or free cash flows to equity, the
appropriate discount rate is the cost of equity. If the cash flow being discounted is the
cash flow to the firm, the discount rate has to be the cost of capital.
The final choice that all discounted cash flow models have to make relates to
expected growth patterns. Since firms have infinite lives, the way in which we apply
closure is to estimate a terminal value at a point in time and dispense with estimating cash
flows beyond that point. To do this in the context of discounted cash flow valuation, we
have to assume that the growth rate in cash flows beyond this point in time are constant
forever, an assumption that we refer to as “stable” growth. If we do this, the present value
of these cash flows can be estimated as the present value of a growing perpetuity. There
are three questions that every valuation then has to answer:
1. How long in the future will a company be able to grow at a rate higher than the stable
growth rate?
2. How high will the growth rate be during the high growth period and what pattern will
it follow?
3. What will happen to the firm™s fundamentals (risk, cash flow patterns etc.) as the
expected growth rate changes?
At the risk of being simplistic, we can broadly classify growth patterns into three
categories - firms which are in stable growth already, firms which expect to maintain a
˜constant” high growth rate for a period and then drop abruptly to stable growth and firms
which will have high growth for a specified period and then grow through a transition
phase to reach stable growth at a point in time in the future. As a practical point, it is
important that as the growth rate changes, the firm™s risk and cash flow characteristics
change as well. In general, as expected growth declines towards stable growth, firms
should see their risk approach the “average” and reinvestment needs decline. These

1 We should generally become much more conservative in our growth estimates as we move up the income
statements. Generally, growth in earnings per share will be lower than the growth in net income, and
growth in net income will be lower than the growth in operating income.


choices are summarized in Figure 12.1. We will now examine each of these valuation
models in more detail in the next section.
Figure 12.1: The Ingredients in a Valuation
Cashflows can be
Growth rate can be
a. After debt payments to equity
a. In Equity Earnings
- Dividends
- Net Income
- Free Cashflow to Equity Firm is in stable growth
- Earnings per share
b. Before debt payments to firm which it can sustain
b. In Operating Earnings
- Free Cashflolw to Firm forever

Expected Cashflows during extraordinary growth phase Terminal Value

Discount the cashflows and terminal value to the present
Present value is
a. Value of equity, if cashflows to
equity discounted at cost of Discount Rate can be
equity a. Cost of equity, if cashflows are equity cashflows
b. Value of operating assets of b. Cost of capital, if cashflows are to the firm
the firm, if cshflows to firm
discounted at the cost of capital

model.xls: This spreadsheet allows you to pick the right discounted cash flow
valuation model for your needs, given the characteristics of the business that you are

In Practice: What Is A Stable Growth Rate?
Determining when your firm will be in stable growth is difficult to do without
first defining what we mean by a stable growth rate. There are two insights to keep in
mind when estimating a “stable” growth rate. First, since the growth rate in the firm's
cashflows is expected to last forever, the firm's other measures of performance (including
revenues, earnings and reinvestment) can be expected to grow at the same rate. Consider
the long-term consequences of a firm whose earnings grow 6% a year forever, while its
dividends grow at 8%. Over time, the dividends will exceed earnings. Similarly, if a
firm's earnings grow at a faster rate than its dividends in the long term, the payout ratio
will converge towards zero, which is also not a steady state. The second issue relates to
what growth rate is reasonable as a 'stable' growth rate. Again, the assumption that this
growth rate will last forever establishes rigorous constraints on “reasonableness”. A firm
cannot in the long term grow at a rate significantly greater than the growth rate in the
economy in which it operates. Thus, a firm that grows at 8% forever in an economy


growing at 4% will eventually become larger than the economy. In practical terms, the
stable growth rate cannot be larger than the nominal (real) growth rate in the economy in
which the firm operates, if the valuation is done in nominal (real) terms.
Can a stable growth rate be much lower than the growth rate in the economy?

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