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Valuation: Principles and
Practice
06/02/08
Ch. 12
Valuation techniques
 Relative valuation
 the value of an asset is derived from the pricing of
'comparable' assets, standardized using a common
variable such as earnings, book value or revenues.
 Discounted cash flow valuation
 The value of an asset is the discounted expected cash
flows on that asset at a rate that reflects its riskiness.
 Residual Income valuation
 The value of an asset is based on the discounted
expected difference between net income and its
associated cost of equity.
Relative valuation
 The value of the firm is determined as:
Comparable multiple * Firm-specific denominator value
where the denominator value can be earnings, book value, sales,
etc.
 A firm is considered over-valued (under-valued) if the calculated
price (or multiple) is greater (less) than the current market price
(comparable firm multiple)
 Assumptions:


Comparable firms, on average, are fairly valued
Comparable firms have similar fundamental characteristics
to the firm being valued.
Relative valuation
 Examples of relative valuation multiples

Price/Earnings (P/E)


Earnings calculations should exclude all transitory
components
Price/Book (P/BV)

Book value of equity is total shareholders equity – preferred
stock

Price/Sales (P/S)

Enterprise Value/EBITDA


Enterprise Value = Mkt Cap + Debt – Cash
EBITDA = Earnings before Interest Taxes Depreciation and
Amortization
Advantages and drawbacks of P/E
 Advantages:
Earnings power is the chief driver of investment value
 Main focus of security analysts
 The P/E is widely recognized and used by investors
 Drawbacks
 If earnings are negative, P/E does not make economic sense
 Reported P/Es may include earnings that are transitory
 Earnings can be distorted by management
 Assumption:
 Required rate of return, retention ratio (with DDM) and
growth rates are similar among comparable firms

Advantages and drawbacks of P/BV
 Advantages



Since book value is a cumulative balance sheet amount, it is
generally positive
BV is more stable than EPS, therefore P/BV may be more
meaningful when EPS is abnormally low or high
P/BV is particularly appropriate for companies with
primarily liquid assets (financial institutions)
 Disadvantages

Differences in asset age among companies may make
comparing companies difficult
 Assumption:

Required rate of return, return on equity, retention ratio (with
DDM) and growth rates are similar among comparable firms
Advantages and drawbacks of P/S
 Advantages



Sales are generally less subject to distortion or manipulation
Sales are positive even when EPS is negative
Sales are more stable than EPS, therefore P/S may be more
meaningful when EPS is abnormally low or high
 Disadvantages


High growth in sales may not translate to operating
profitability
P/S does not reflect differences in cost structure
 Assumption:

Required rate of return, profit margin, retention ratio (and
DDM) and growth rates are similar among comparable firms
Advantages and drawbacks of
EV/EBITDA
 Advantages
 This represents a valuation indicator for the overall company and
not just equity.
 It is more appropriate for comparing companies that have different
capital structures since EBITDA is a pre-interest measure of
earnings.
 Appropriate for valuing companies with large debt burden: while
earnings might be negative, EBITDA is likely to be positive.
 Disadvantages
 Differences in capital investment is not considered.
 Assumption:
 Required rate of return, growth rates, working capital needs, capital
expenditures and depreciation are similar among comparable firms
Benchmarks for comparison
 Peer companies
 Constituent companies are typically similar in their
business mix
 Industry or sector
 Usually provides a larger group of comparables
therefore estimates are not as effected by outliers
 Own historical
 This benchmark assumes that the firm will regress to
historical average levels
 Considerations: market efficiency, historical trends,
comparable assumptions
Leading and trailing P/E
 Trailing (or current) P/Es is calculated using
the firm’s current market price and the four
most recent quarters’ EPS.
 Leading P/Es is calculated using the firm’s
current market price and next year’s expected
earnings.
PEG Ratio
 “I don’t buy stocks with P/E’s over 30. To our Foolish ear, that
sounds identical to: I don't buy hydrogenated milk; I am born in
May.” Motley Fool
 When comparable firm P/Es are used to calculate the value of a
firm, the assumption is that the firm has characteristics that are
similar to that of the average comparable firm.
 However, differences may exist. For example, a higher P/E for a
particular firm may be justified because the firm has higher
growth.
PEG Ratio
 The Price/Earnings-to-Growth (PEG) accounts for
differences in the growth in earnings between
companies.
 PEG is calculated as:
P/E divided by expected earnings growth (%).
 "The P/E ratio of any company that's fairly priced will
equal its growth rate." Peter Lynch
Discounted Cashflow Valuation:
Basis for Approach
The intrinsic value of a firm is the present value
of all of the firm’s cash flows.
t = n CF
t
Value = 
t
(1+
r)
t =1
where,
 n = Life of the asset
 CFt = Cashflow in period t
 r = Discount rate reflecting the riskiness of
the estimated cashflows
What cash flow do we use?
Cash Flows
To Equity
The Strict View
Dividends +
Stock Buybacks
To Firm
The Broader View (FCFE)
Net Income
- Net Cap Ex (1-Debt Ratio)
- Chg WC (1 - Debt Ratio)
= Free Cashflow to Equity
EBIT (1-t)
- ( Cap Ex - Depreciation)
- Change in Working Capital
= Free Cashflow to Firm (FCFF)
What cash flow do we use?
 Dividends (discount rate = cost of equity):


Firm pays out more than 75% of its net income and;
Firm has stable leverage
 FCFF (discount rate = WACC):



Firm has changing leverage or;
Firm currently has negative FCFE.
With the FCFF, the intrinsic value of equity is determined by calculating
the firm’s total value and then subtracting the market value of debt and
adding back the firm’s current cash balance.
 FCFE is simpler to use than the FCFF.
 Regardless of the model used, the approach used to calculate intrinsic
value is similar.
 We will use the FCFE to calculate value in our discussions.
Discounted cash flow valuation with
FCFE
 The intrinsic value of equity is obtained by
discounting free cash flow 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 =
FCFEt
Value of Equity = 
t
(1
+
r
)
t =1
e
where,
re = cost of equity
Discounted cash flow valuation with
FCFE
 Since we cannot estimate cash flows forever, we may estimate
cash flows for a “high growth period” and then estimate a
terminal value, to capture the value at the end of the period
t=N
FCFEt TerminalVa lue

t
(1  re ) N
t =1 (1 + re )
Value of Equity = 
where terminal value is the present value at time N of cash flows
after period N.
 Note: If we do not expect the firm to have a
‘high growth period, the intrinsic equity value
is just the terminal value.
Valuation steps
 Estimate the discount rate
 Estimate the current free cash flow to equity
 Estimate growth rate(s) to estimate future cash flows
 Estimate a terminal value
 Compute the firm’s equity value and estimated stock
price
Discount rate
 The appropriate discount rate in valuing
equity is the cost of equity which can be
estimated using the CAPM.
Current FCFE
 We can use the estimated FCFE equation to
calculate CF to equity as this provides a better long
run estimate than the exact FCFE equation.
FCFE = Net Income- (1- )(Cap Exp - Depr&Amort + Δ in WC) – Pref. Div.
 When determining Cap Exp, Depreciation and
change in working capital, we can either:


take a historical average of these values if the firm
does not have smooth expenditure streams.
Or use the current value.
Estimating future FCFE
 Depending on the insight you have into the firm’s
operations, we can approach future FCFE estimation
in two ways:

We can start with the top line (revenues) and
individually estimate the components of FCFE
(expenses, cap. ex, etc.). We can use historical
averages or regression models to estimate this.

We can assume that the relationship between the top
line and FCFE remain stable into the future, in which
case we need to estimate a growth rate in FCFE.
Current growth in FCFE
 We can estimate the current growth in FCFE by first
calculating the equity reinvestment rate (ERR).
 The ERR represents the proportion of net income
that the firm will retain for reinvestment. Whatever
is left over can be paid out.
(Cap Exp. - Depr   in WC)(1 -  )
ERR 
Net Income - Interest Income
 Normalized values (historical averages) are
typically used to determine ERR.
Current growth in FCFE
 The current growth rate then can be estimated as:
g = ERR * non-cash ROE
where non-cash ROE is defined as:
(Net Income – Interest Income)t
(BV of equity – (Cash + Marketable securities))t-1
Estimating future growth
 A key assumption in all discounted cash flow models
is the period of high growth, and the pattern of growth
during that period. In general, we can make one of
two assumptions:


there is no high growth, in which case the firm is
already in stable growth
there will be high growth for a period, at the end of
which the growth rate will drop to the stable growth rate
(2-stage). Some advocate a smoother drop in growth
between the first and second stages.
 We need to determine the growth rates in each
period as well as the length of the different
periods if a 2-stage model is used.
Determinants of length of high
growth period
 Size of the firm
Success usually makes a firm larger. As firms
become larger, it becomes much more difficult for
them to maintain high growth rates
 Current growth rate
 While past growth is not always a reliable indicator
of future growth, there is a correlation between
current growth and future growth. Thus, a firm
growing at 30% currently probably has higher
growth and a longer expected growth period than
one growing 10% a year now.

Determinants of length of high
growth period
 Barriers to entry and differential advantages


Ultimately, high growth comes from high project
returns, which, in turn, comes from barriers to
entry and differential advantages.
The question of how long growth will last and how
high it will be can therefore be framed as a
question about what the barriers to entry are, how
long they will stay up and how strong they will
remain.
Determinants of length of high
growth period
 Questions to ask about firms:
 What drives revenue growth? Can that be
maintained?
 What kinds of capital expenditure will be required to
maintain free cash flow growth?
 Can firms maintain their operating and gross
margins?
 Standard 1st stage lengths used are 5 years and
10 years.
Firm characteristics as growth
changes
Variable
High Growth Firms
tend to
Risk
be above-average risk
Dividend Payout pay little or no dividends
Net Cap Ex
have high net cap ex
ROC
earn high ROC and ROE
Leverage
have little or no debt
Stable Growth
Firms tend to
be average risk
pay high dividends
have low net cap ex
(just covering depreciation)
earn ROC closer to WACC
or ROE closer to cost of
equity
higher leverage
Ways of Estimating Terminal Value
Estimating terminal value
 Estimating stable growth
 This is the growth rate that we assume the firm FCFE
will grow forever
 The stable growth rate cannot exceed the growth rate
of the economy (3-5%) but it can be set lower.


If you assume that the economy is composed of high
growth and stable growth firms, the growth rate of the
latter will probably be lower than the growth rate of the
economy.
The stable growth rate can be negative. The terminal
value will be lower and you are assuming that your firm
will disappear over time.
No net capital expenditures and
long-term growth
 You are looking at a valuation, where the terminal value is based
upon the assumption that operating income will grow 3% a year
forever, but there are no net cap ex or working capital
investments being made after the terminal year. When you
confront the analyst, he contends that this is still feasible
because the company is becoming more efficient with its
existing assets and can be expected to increase its return on
capital over time. Is this a reasonable explanation?
 Yes
 No
 Explain.
Calculating terminal value
 Terminal value (commencing in period N+1) is
calculated as:
terminal value 
FCFEN 1
re  g s
where g is the stable growth stage growth rate.
Calculating equity value
 Our estimate for the equity value of the firm is then calculated as
the present value of the individual future FCFEs during the 1st
stage plus the present value of the terminal value. (For a single
stage model, the equity value is simply the terminal value.)
 To this we should add back the current cash balance of the firm.
 Our estimated (intrinsic) value per share is:
(Estimated equity value + cash)
number of shares outstanding
DCF vs. relative valuation
 DCF valuation assumes that markets make
mistakes in estimating value (i.e., current
price is not an accurate reflection of the value
of the firm) and these mistakes tend to be
corrected over time and can occur over entire
sectors.
 Relative valuation assumes markets are
correct on average (i.e., comparables on
average are correctly priced)
Basis for Residual Income Valuation
 The appeal of the residual income (RI) model
is based on the fact that traditional
accounting does not include a “charge” for
equity capital.
 Specifically, a company may generate a
positive net income but may not be adding
value to its shareholders if it does not earn
more than the cost of equity.
Basis for RI valuation
 RI is sometimes referred to as the economic
profit earned by firms.
 One example of a residual income model is
referred to as the Economic Value Added
(EVA) model.
Strengths of the RI model
 Terminal value does not make up a large
portion of the total value
 The model can be used for companies that
do not pay dividends and/or firms that have
near-term negative free cash flows
 The model can be used when cash flows are
unpredictable or difficult to forecast. This can
be particularly true for financial institutions.
Weaknesses of the RI model
 The model relies on accounting data that can
be subject to manipulation
 When book value and ROE are
unpredictable, the resulting estimate is less
valid.
The RI valuation model
 The RI model analyzes the intrinsic value of
equity into two components:


The current book value of equity, plus
The present value of expected future residual
income
The RI valuation model
 The intrinsic value of common stock can be
expressed as:
t 
RI t
EPSt  re * BVt 1
V0  Value/shar e of Equity = BV0  
 BV0  
t
t
(
1
+r
)
(
1

r
)
t =1
t 1
e
e
t =
where
BV0 = current book value of equity per share
BVt = expected per-share book value at period t
EPSt = expected Earnings per share for period t
RIt = expected residual income per share for period t
The RI valuation model
 In the model book value each period is determined
by the following clean surplus relation:
BVt = BVt -1  EPS t - DPS t
 The model also assumes that the growth in book
value comes by the firm earning more than the
cost of equity (ROE > re). The numerator of the
second term can therefore be defined as:
EPS t - re * BVt -1 = (ROE - re ) * BVt -1
Single-stage RI valuation
 If we assume that the firm’s book value (and RI per
share) will grow at a constant rate, g, forever, we
can value a firm using a single-stage RI model:
ROE  re
V0  BV0 
* BV0
re  g
Multi-stage RI valuation
 If the assumption of constant growth is not appropriate, which
may be particularly true if the firm currently generates a high
ROE relative to the cost of equity, we can model the firm using
two stages.
 During the first stage we calculate present values of residual
incomes individually.
 In the second (terminal) stage we make one of the following
assumptions about continuing residual income:
 Residual income remains constant through perpetuity (and
ROE > re) from the terminal year forward
 Residual income is zero from the terminal year forward
(ROE = re)
Multi-stage RI valuation
 We can calculate the value today using a multi-
stage model using the following formula
T
V0  BV0  
t 1
( ROE t  re ) * BVt 1 Terminal Value

t
(1  re )
(1  re )T
 If RI is expected to be constant through perpetuity
from terminal year forward, terminal value = RIT / re
 If RI is expected to be zero from terminal year
forward, terminal value = 0