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Chapter One | Overview of Financial Statement Analysis 41

payoffs are specified. With equity, the investor has no claim on predetermined payoffs.
Instead, the equity investor looks for two main (uncertain) payoffs—dividend payments DECIMAL PRICING
and capital appreciation. Capital appreciation denotes change in equity value, which in Wall Street long counted
turn is determined by future dividends, so we can simplify this task to state that the money in the same units
that 17th century pirates
value of an equity security at time t, or V , equals the sum of the present values of all fu- used—pieces of eight. But
t
ture expected dividends: fractional pricing—pricing
stocks in eighths,
E(D t 1 ) E(D t 2 ) E(D t 3 ) sixteenths, and the
V t
(1 k) 1 (1 k) 2 (1 k) 3 occasional thirty-secondth
of a dollar—went the way
where D t n is the dividend in period t n, and k is the cost of capital. This model is of Spanish doubloons;
called the dividend discount model. This equity valuation formula is in terms of stock and options markets
now use decimal pricing.
expected dividends rather than actual dividends. We use expectations instead of actual
dividends because, unlike interest and principal repayments in the case of a bond, future
dividends are neither specified nor determinable with certainty. This means our analy-
sis must use forecasts of future dividends to get an estimate of value.
Alternatively, we might define value as the present value of future cash flows. This
definition is problematic for at least two reasons. First, the term cash flows is vague.
There are many different types of cash flows: operating cash flows, investing cash flows,
financing cash flows, and net cash flows (change in cash balance). Hence, which type of
cash flows should one use? Second, while we can rewrite the equity valuation formula
in terms of one type of cash flows, called free cash flows, it is incorrect to define value in
terms of cash flows. This is because dividends are the actual payoffs to equity investors
and, therefore, the only appropriate valuation attribute. Any other formula is merely
a derived form of this fundamental formula. While the free cash flow formula is
technically exact, it is simply one derived formula from among several. One can also de-
rive an exact valuation formula using accounting variables independent of cash flows.
Practical Considerations in Valuation. The dividend discount model faces practical
obstacles. One main problem is that of infinite horizon. Practical valuation techniques
must compute value using a finite forecast horizon. However, forecasting dividends is
difficult in a finite horizon. This is because dividend payments are discretionary, and dif-
ferent companies adopt different dividend payment policies. For example, some com-
panies prefer to pay out a large portion of earnings as dividends, while other companies
choose to reinvest earnings. This means actual dividend payouts are not indicative of
company value except in the very long run. The result is that valuation models often
replace dividends with earnings or cash flows. This section introduces two such valua-
tion models—the free cash flow model and the residual income model.
The free cash flow to equity model computes equity value at time t by replacing
expected dividends with expected free cash flows to equity:

E(FCFE t 1 ) E(FCFE t 2 ) E(FCFE t 3 )
V t
(1 k) 1 (1 k) 2 (1 k) 3
where FCFE t n is free cash flow to equity in period t n, and kis cost of capital. Free cash
flows to equity are defined as cash flows from operations less capital expenditures plus in-
creases (minus decreases) in debt. They are cash flows that are free to be paid to equity
investors and, therefore, are an appropriate measure of equity investors’ payoffs.
Free cash flows also can be defined for the entire firm. Specifically, free cash flows to
the firm (or simply free cash flows) equal operating cash flows (adjusted for interest expense
and revenue) less investments in operating assets. Then, the value of the entire firm equals