5.2.3 Applying DCF Formulas 
As we have seen, the
capitalization of earnings method using
the DCF formulas is simplicity itself  if you
know the cash flows and their discount rates.
Estimating these inputs (and it is always an estimate)
involves significant judgment calls.
Cash flows. You must measure
earnings and estimate cash flows. You must
decide which particular accounting figures reflect
investor returns and adjust
book earnings. You must decide whether past
trends will continue and what projections
are reasonable.
Discount rate. You must estimate
a discount rate or capitalization rate to apply
to the cash flows. To
estimate the discount (capitalization) rate
you can use the discount rates of comparable
companies, by employing multiples based on their
priceearnings ratio and other ratios. You can
also use the Capital Asset Pricing
Model (CAPM) to estimate the stock's expected
rate of return (discount rate) based on historic
price volatility compared to the market. To
reflect the company's capital structure, you
should weight the average cost
of capital.
Adjustments. Even if your
cash flow and capitalization rates are solid,
you must also consider whether there are extraneous
risks not captured by the capitalization of
earnings. For example, publiclytraded shares
often trade at a discount reflecting their lack
of control, and minority shares in a closelyheld
business often include an illiquidity (lack
of marketability) discount. On the other hand,
a majority block in a closelyheld business
carries a control premium, since its owner not
only sells an investment instrument but the
power to control the investment. A business
may have special risks, warranting further adjustments.
For example, valuators often discount the value
of a business that relies on one key person,
that has unusually heavy contingent liabilities
(such as a manufacturer of dangerous chemicals),
or that is being investigated for securities
violations.


Cases Applying Income Valuation Method
In Re Pullman Construction
Industries Inc., 107 B.R. 909 (1989)
(valuation business to determine whether Chapter
11 reorganization plan should be confirmed)
Neal v. Alabama ByProducts Corp.,
1990 Del. Ch. LEXIS 127 (judicial appraisal of
minority shareholder interest)
Laurel Gonsalves v. Straight Arrow Publishers,
Inc., 2002 Del. Ch. LEXIS 105. (judicial
appraisal of minority shareholder interest)
Cede & Co. v. Technicolor, Inc.,
1990 Del. Ch. LEXIS 259 (judicial appraisal of
minority shareholder interest)

Estimating
cash flows / earnings
Sometimes we can predict a business's cash flows
with confidence. For example, the rental income
from a shopping center can be computed if there
are longterm leases with fixed payment obligations.
But the future is rarely this simple. Often shopping
center rentals are based on gross receipts, which
can rise or fall. Generally, business returns
are erratic and uncertain.
Most valuations rely on company income statements,
which describe revenues, expenses and income for
prior accounting periods. This accounting information
presents two difficulties.
 These numbers are based on accounting conventions
that vary between companies (public and private)
and countries (US and elsewhere). Thus, these
numbers may not accurately reflect the returns
that investors may obtain in the future. Often
valuators adjust accounting income (or earnings)
figures to identify the free cash flow
that is available for distribution to investors.
 Accounting information is historic. It does
not purport to provide estimates of future results.
Trends must be identified, often using information
not available on the company's income statements.
Many valuations also rely on projections by company
managers. But these projections, sometimes prepared
to entice a lender to provide credit to the business
or to comfort an anxious board of directors, must
be taken with a grain of salt. 
Adjustments
of book earnings
Company financial statements reflect information
about financial transactions, but not necessarily
the company's ability to generate cash flow or
income. For example, many small ownermanaged
businesses show earnings that the ownermanager
actually views as personal income for her services.
If the owner were asked to work for the business,
or if new owners had to hire an outside manager,
the company's earnings would be much lower.
Likewise, ownermanagers of closelyheld businesses
often choose to lend money to the business, rather
than invest permanent capital. (There are some
advantages to this structure: interest on owner
loans is taxdeductible by the corporation, while
dividends are not; lending may protect the owner
from a complete loss in case of bankruptcy; lending
can allow different levels of financial participation
without affecting voting allocations). This means
that sometimes deductible interest payments really
reflect payments to investors.
Often professional valuators will adjust book
earnings to get a better picture of a company's
capacity to present cash flow. Consider the information
available from a typical income statement:
ALBEGA
CORPORATION
Income Statement
Year ended December 31, 20xx 
Net sales 

$500,000 
Cost of goods sold 

$304,000 
Gross margin 

$196,000 
Other expenses 

$115,000 
Depreciation 
$ 15,000 

Selling and administrative expenses 
$100,000 

Operating income 

$81,000 
Other income 

$ 0 
1 Total income 

$81,000 
Dividends and interest 

$13,000 
Interest on longterm notes 
$ 13,000 

2 Income before income taxes 

$68,000 
Income taxes 

$18,000 
3 Net profit 

$50,000 
Extraordinary items 

$12,000 
Net income 

$38,000 
Net income per share
(1,000 shares outstanding) 

$ 38.00 
The object of the game is to figure out what
cash flow the business is generating
for investors  which requires making adjustments
to items in the income statement. To see how important
cash flow is, see DeathWatch.

Some Terminology
1  Total income 
This is a misleading measure of cash flow.
It does not take into account taxes, nor does
it reflect that depreciation is an accounting
convention that does not actually diminish
cash produced by a business. 
2  Pretax profits
(or "Income Before Income Taxes") 
This reflects income after payment of interest
and dividends, but is also misleading. Often
in a closely held business, investors receive
interest payments instead of dividends since
interest is deductible, but dividends are
not. In such a case, cash flow should be seen
as including interest and dividends. 
3 Net profits after taxes 
This reflects the effect of income taxes.
[Taxes are not inevitable  and sometimes
this creates a misimpression about the cash
flow available to a purchaser of the business.] 
Earnings before interest and taxes
(EBIT) 
This is a common adjustment in a closelyheld
business where interest payments to owners
may actually represent an investment return
to the owners. (Remember interest is deductible
and reduces the business's tax liability.)
By looking at earnings before interest and
taxes are deducted, we are assuming that interest
is really an element of return to the owners
and its deduction reduces taxes. 
Earnings before interest, taxes,
depreciation and amortization (EBITDA) 
These adjustments reflect the effect of
taxes on cash flows, the cost of replacing
aging assets [and so on.] This adjustment
adds back depreciation and amortization [links].
The assumption is that these items did not
actually diminish cash flow. There should,
nonetheless, be a recognition in calculating
earnings that aging assets eventually will
have to be replaced. 
Gross cash flow 
This is net income, plus depreciation, amortization
and other noncash charges. [more here] 
Free cash flow 
This is the valuator's holy grail  cash
flow after taking account of cash drains.
It reflects the actual returns of the investment.


Future projections
Once a valuator has identified (and adjusted)
those earnings items that reflect investor returns,
the next step is to project these cash flows into
the future. This is tricky. Will current earning
levels continue indefinitely? Will earnings rise
with inflation? Will the rise more than inflation?
These questions must be answered in projecting
cash flows.
Generally, the projections for the first several
years will be critical. Given the time value of
money  particularly when the discount rate is
relatively high  cash flows that occur after
five years will carry relatively less valuation
weight. Often valuators will focus on the first
57 years and then project a stable cash stream
afterward to compute a "terminal value."
(Why? Because they really can't be sure what cash
flows will be that far into the future, so they
just make a broadbrush guess.) Summing the present
value of the first 57 years of income and the
present value of the terminal value yields an
estimate of firm value. 
Example
Consider two companies, whose average earnings
are identical, but the record of past earnings
is remarkably different. How should earnings be
projected into the future?
Year 
Company A 
Company B 
1 (actual) 
$100,000 
$140,000 
2 (actual) 
$120,000 
$180,000 
3 (actual) 
$150,000 
$100,000 
4 (actual) 
$170,000 
$90,000 
5 (actual) 
$200,000 
$230,000 
Average 
$148,000 
$148,000 
Average rate
of growth 
19.00% 
32.42% 
Period growth
rate 
14.87% 
10.44% 
This leads to a host of questions. For Company
B were the two off years (Years 3 and 4) aberrational,
or was Year 5 an aberration? Is the steady growth
for Company A likely to continue or has it topped
off? Is Company B on the verge of explosive growth,
or does its period growth rate (from Year 1 to
Year 5) tell the story?
Answer: We get dramatically
different results depending on how we answer these
questions about the companies' growth prospects.
For example, consider the valuation of the two
companies if we assume that Company A's earnings
of $200,000 will continue to grow at a 15% rate
for the next five years and then level off, and
that Company B's earnings will be $148,000, but
will grow at a 33% rate for the next five years
before leveling off. Assume a discount rate of
20%  to reflect the riskiness of both companies.
Year 
Company A 
Company B 
6 (estimate) 
$230,000 
$196,840 
7 (estimate) 
$264,500 
$261,797 
8 (estimate) 
$304,175 
$348,190 
9 (estimate) 
$349,801 
$463,093 
10 (estimate) 
$402,271 
$615,914 
11on (estimate) 
$462,612 
$819,165 
PV of Years 610

$881,731 
$1,018.186 
PV of Years11on
perpetuity 
$905,398 
$1,603,224 
TOTAL 
$1,787,130 
$2,621,410 
This example is similar to that of Wilson
v. Great American [earnings for first five
years].

Estimating the discount (capitalization)
rate
While earnings projections can be grounded in
accounting data on past performance, the expected
riskiness of those earnings floats in the air.
Determining the discount rate (or capitalization
rate) often turns on a comparative analysis of
multipliers that have been used in valuing similar
businesses. Ultimately, the question is how an
investor would discount (or capitalize) an investment
with similar earnings potential?
A capitalization rate allows a valuator to calculate
the value of an earnings stream. The market determines
capitalization rates, like discount rates, based
on the duration and risk of the investment. They
vary with time and incorporate, longterm inflationary
expectations.
Capitalization rates based on market comparisons
do not, however, tell us the discount rate. Why
is this? A marketbased capitalization rate does
not tell us what growth rate is built into the market's
pricing assumptions. That is, the capitalization
rate is really the denominator in the Gordon model

Capitalization
rate = discount rate  growth rate
C = D  g

Capitalization rates assume the principle of
substitution, since they are based on the yields
available on alternative investments. There are
two of principal methods, both based on comparisons
to market, for determining a capitalization rate
or multiplier.
 Comparison of earnings and prices of comparable
business  establishing a priceearnings (or
P/E) ratio.
 Using the CAPM to determine an investment's
required rate of return based on the asset's
volatility, compared to market volatility.
Usually, valuators choose a single discount rate
for a particular investment or asset  taking
into account both the riskfree time value of
money and the particular risk of the investment
or asset. But sometimes valuators choose different
discount rates for different cash flows.
Note
on Terminology
The term capitalization rate is
often used in this context rather than discount
rate  though they are not quite the same.
The discount rate is the rate of return
investors would demand (required rate) for
a particular return, compared to other available
returns. But the discount rate does not
take into account a growing investment.
The capitalization rate does  it is the
rate that investors would demand for a particular
investment, which is expected to offer growing
returns. Thus, the capitalization rate of
an investment with growing returns is 
Capitalization rate = Discount
rate minus Growth rate
The term capitalization multiplier
is similarly the reciprocal of the capitalization
rate. As the earlier table showing various
capitalization rates and multipliers illustrated,
the higher the risk, the smaller the multiplier. 

Capitalization
Rates in Legal Contexts
Section 6 of Revenue
Ruling 5960:
"A determination of the proper capitalization
rate presents one of the most difficult problems
in valuation."
Smith
v. Smith, 111 N.C. App. 460, 433 S.E.2d 196
(1994):
"A critical element of the excess earnings
methodology is the capitalization rate used."
Barth H. Goldberg, Valuation
of Divorce Assets, §; 6.6 (1984):
"It is generally true that
the higher the risk of creating future earnings,
the higher will be the annual rate or return
which an investor will seek, and hence, the
higher the capitalization rate.
"Determination of the proper
percentage rate to use in the capitalization
of earnings of a particular business is somewhat
speculative.
2 John P. McCahey, Valuation
and Distribution of Marital Property, §
22.08(2), 22103104 (1993).
"The risk involved refers
to the degree of uncertainty that there will
be any return on the investment. The greater
uncertainty as to a return, the higher the risk."
"Thus, the capitalization
rate represents the rate of return a prudent
investor would expect annually on his investment
given current interest rates and the relative
risk involved in the type of business in question."
"In fact, criticism of the excess earnings
methodology has been based on the difficulty
in selection of an appropriate capitalization
rate."


Capital Asset Pricing
Model (CAPM)
Another shortcut for finding a capitalization
rate is to use the CAPM.
Valuators use CAPM as part of a "building
up" pricing model to estimate a small company's
discount rate.
 riskfree rate (which includes both a timevalueofmoney
real interest rate and an inflation factor)
 risk premium (derived using CAPM for comparable
large company common stock)
 additional risk premium (for small company
common stock)  a somewhat controversial matter
 specific company risk
Added together these risk rates provide a discount
rate for the company's equity stock. 
Example
If a publiclytraded company has a beta of 1.7
and the riskless rate for oneyear Treasury bills
is 4.5% and the expected return for the market
is 12.5%. What is the company's capitalization
rate?
Suppose the company has current earnings of $5.20
per share that have been growing at a rate of
6.5%. What should be the company's share price
using a capitalization of earnings approach?
Answer: Using the CAPM
straightline formula, the capitalization rate
(the required return an investor would
demand to invest in the company) is
4.8% + 1.7*(12.5%  4.5%) =
4.8% + 13.6% = 18.4%.
Applying the Gordon model, the price
should be
[$5.20*(1+.065] / (.184  .065) =
$5.54 / .119 = $46.54

Weighted average
cost of capital
Many appraisers derive the discount rate from
the weighted average cost of capital (WACC). This
methodology has its roots in sophisticated financial
management theory, but it is premised on basic,
easily understood assumptions.
A firm derives capital from debt investors (who
demand a fixed return) and equity investors (who
accept a variable return). Debt, up to a point,
is cheaper than equity—that is, the required
rate of return for debt is typically less than
for equity. To determine the value of a firm,
we must be sensitive to the firm's different costs
of capital.
For example, consider a company that has an overall
risk (discount rate) of 15.6%, but 40% of its
capital is supplied by debt which carries a 9.0%
interest rate. Notice that this means its equity
capital has a much higher required rate of return.

Proportion 
Rate
of return 
Weighted 
Debt 
40% 
.09 
.036 
Equity 
60% 
.20 
.120 
Weighted 
100% 

.156 
Debt cost is derived by comparing the subject
company’s debt with that of comparable issues
in the public market. For example, if a AAArated
company’s debt is currently selling at 6.5%,
and the subject company being valued would be
AAA rated, then the appraiser would use a 6.5%
cost for the debt component.
Deriving equity cost is more complicated.Often,
the appraiser starts with the riskfree rate (ordinarily,
the U.S. Treasury borrowing rate) and adds elements
that account for the risk characteristics of the
subject company—such as the volatility of
the business related to other firms (beta), the
economic outlook for the particular industry,
and other factors.



