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Equity
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LM01 Equity Valuation: Applications and Processes

Intrinsic value and sources of perceived mispricing

Intrinsic value is the true or real value given a hypothetically complete understanding of
the asset’s investment characteristics. Intrinsic value might be different from the current
(market) price of an asset.
Perceived mispricing is the difference between the estimated intrinsic value and the
market price of an asset. It can be expressed as:
VE – P = (V – P) + (VE – V)
Interpretation:
• The first component (V-P) is the true mispricing or market error. It is the difference
between the unobservable intrinsic value V, and the observed market price P. An
analyst exploits the mispricing if it arises from the first term as it contributes to the
abnormal return.
• The second component (VE – V) is the error in the estimate of the intrinsic value or
analyst error. It is the difference between the valuation estimate and the
unobservable intrinsic value. The smaller the second term, the better it is for the
analyst.
For active investing to be successful, an analyst’s estimates must be different from the
consensus estimate and must be correct.

Going-concern value and liquidation value

A going-concern assumption is the assumption that the company will continue its business
activities into the foreseeable future, i.e., it will continue to produce and sell its products
and services. The value of a company based on this assumption is called the going-concern
value.
On the other hand, liquidation value is the value of a company if it were dissolved and its
assets sold individually.

Fair market value and investment value

Fair market value is the price at which an asset (or liability) would change hands between
a willing buyer and a willing seller when the former is not under any compulsion to buy
and the latter is not under any compulsion to sell.
Fair value is the price of an asset used for financial reporting, for example, impairment
testing.
Investment value is the value to a specific buyer based on potential synergies and the
investor’s requirements and expectations.

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Instructor’s Note: Of the many definitions of value, the definition most relevant to public
company valuation is intrinsic value calculated using the going-concern assumption.

Applications of equity valuation

Analysts use valuation concepts and models in the following practical scenarios:
• Selecting stocks
• Inferring market expectations
• Evaluating corporate events
• Rendering fairness opinion
• Evaluating business strategies
• Appraising private businesses

Industry and competitive analysis

The five steps in the valuation process are:

1. Understanding the business
2. Forecasting company performance
3. Selecting the appropriate valuation model
4. Converting forecasts to a valuation
5. Applying the valuation conclusions
The questions that should be addressed in conducting an industry and competitive analysis
include:
• Evaluate industry prospects: How attractive are the industries in which the
company operates, in terms of offering prospects for sustained profitability? Use
Porter’s five forces framework to understand industry structure.
• Perform a competitive analysis: What is the company’s relative competitive position
within its industry, and what is its competitive strategy - cost leadership or
differentiation?
• Evaluate execution of the strategy: How well has the company executed its strategy
and what are its prospects for future execution? Analyze the past and current
financial reports to assess how successful is the strategy.

Absolute and relative valuation models

An absolute valuation model estimates an asset’s intrinsic value that can be compared to
the asset’s market price. The two types of absolute valuation models are:
• Present value model: The value of an asset is the present value of its expected future
cash flows.
• Asset-based valuation: Value of a company is equal to the market value of the assets
or resources it controls.

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A relative valuation model estimates an asset’s value relative to that of another asset. The
underlying notion is that similar assets should sell at similar prices. Commonly used
multiples include:
• Price multiples: Ratio of a stock’s price to a fundamental such as earnings, book
value or cash flow per share.
• Enterprise multiples: Ratio of the total value of a firm to a fundamental such as
EBITDA.

Sum-of-the-parts valuation and conglomerate discounts

A valuation that sums the estimated values of each of the company’s businesses as if each
business were an independent going concern is known as a sum-of-the-parts valuation.
A conglomerate discount is a discount applied to the stock of a company operating in
multiple, unrelated businesses compared to the stock of companies with narrower focuses.
It is sometimes applied to value companies that require a sum-of-the-parts valuation.

Choosing a valuation approach

The criteria for choosing an appropriate approach for valuing a given company implies that
the model is:
• consistent with the characteristics of the company
• appropriate given the availability and quality of data
• consistent with the purpose of valuation or analyst’s perspective
Two important aspects of converting forecasts to valuation are:
• Sensitivity analysis that determines how changes to an input variable changes the
value of equity.
• Situation adjustments such as control premium, lack of marketability discount,
illiquidity discount, blockage factor, etc.

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Equity 2024 Level II High Yield Notes

LM02 Discounted Dividend Valuation

Streams of expected cash flows

Discounted cash flow models are based on the idea that value of a security today is equal to
the present value of its future cash flows.
The three most widely used definitions of cash flows are: dividends, free cash flow (FCFF
and FCFE), and residual income.
The suitability of each of these models is summarized in the table below:
Dividend discount model Free cash flow model Residual income model
The company has a history Company pays no Company pays no
of dividend payments. dividends. Or the dividends dividends.
significantly exceed or fall
short of free cash flow to
equity.
The investor takes a non- The investor takes a control
control perspective. perspective.
The board of directors has The company’s free cash The company’s expected
established a dividend flows align with the free cash flows are negative
policy that bears an company’s profitability within the analyst’s
understandable and within a forecast horizon comfortable forecast
consistent relationship to with which the analyst is horizon.
the company’s profitability. comfortable.
Applicable to mature, The firm has accounting
profitable firms disclosures of high quality.

Dividend discount model (DDM)

The value of a stock using DDM for a single-holding period is:

D1 P1 D1 + P1
V0 = + =
(1 + r)1 (1 + r)1 (1 + r)1

The value of a stock using DDM for multiple finite holding periods is:
n
Dt Pn
V0 = ∑ t
+
(1 + r) (1 + r)n
t=1

The value of a stock for infinite holding periods is:

𝛼
Dt
V0 = ∑
(1 + r)t
t=1

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There are two approaches to forecast dividends.

• One is to assume that they follow a stylized growth pattern (constant growth, two-
stages of growth, or three stages of growth).
• The other alternative is to forecast dividends for a finite period, then forecast the
remaining dividends based on a pattern or by calculating the terminal stock price.

Gordon growth model

The Gordon growth model assumes that:

• Dividends grow at a constant growth rate g.
• Discount rate r is constant and is greater than g.
• Dividends bear and understandable and consistent relationship with profits.
The value of a stock using the Gordon growth model is:
D1
V0 =
r − g
If prices are efficient (price equals value), the price is expected to grow at a rate of g,
known as the rate of price appreciation. In this case, the stock’s expected rate of return is:
D1
r= +g
P0
If an estimate of the next-period dividend and the stock’s required rate of return are given,
then the Gordon growth model can be used to estimate the dividend growth rate implied by
the current market price.
D1
g= r−
P0

Present value of growth opportunities (PVGO)

The present value of growth opportunities (PVGO), also known as the value of growth, is
the present value of opportunities to profitably reinvest future earnings.
A stock’s value comprises of two parts:
• present value of the company with no growth component and
• present value of growth opportunities.
E1
V0 = + PVGO
r
E1
If price = value, then PVGO = P0 − r

Justified leading and trailing P/E ratios

The Gordon growth model can also be used to estimate justified leading and trailing P/E
ratios based on the fundamentals of the firm.

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The leading P/E ratio is:

D1
P0 E 1−b
= 1 =
E1 r − g r − g

The trailing P/E ratio is:

D1 D0
(1
P0 E0 E0 + g) (1 − b)(1 + g)
= = =
E0 r − g r−g r−g

Value of a perpetual preferred stock

The value of a non-callable, fixed-rate, perpetual preferred stock is:

D
V0 =
r
Strengths and limitations of the Gordon growth model

The strengths of the Gordon growth model are:

• It is the simplest practical implementation of the dividend discount model.
• Broad equity market indices of developed markets frequently satisfy the conditions
of the model fairly well. It is used to judge whether the equity market is fairly valued
or not.
• It is applicable to stable, mature, dividend-paying firms that have a constant growth
in dividends. It can also be applied to firms that repurchase stock.
• g can be estimated using macroeconomic data; nominal GDP = real GDP + long-term
inflation.
• It is most suitable for a single stage DDM or can be used to model the last stable
stage in a multi-stage DDM.
The limitations of the Gordon growth model are:
• The model cannot be used if growth rate g is not constant. Since most firms have
non-constant growth in dividends, the model is not reliable. A multi-stage growth
model is more appropriate.
• The model cannot be used to value non-dividend paying firms. Dividends must also
be related to the level of earnings.
• Any small changes to (r – g) estimates can have a significant impact on stock value.

Multistage dividend discount models

Companies with varying growth prospects must be valued using multistage DCF models
such as the two-stage DDM, H-model, three-stage DDM or spreadsheet modeling. The
assumptions of these models are:

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• Two-stage DDM: This model assumes different growth rates in stage 1 and stage 2.
A supernormal growth in stage 1 is followed by a lower, sustainable growth rate in
second stage.
• H-model: The dividend growth rate declines linearly from a high supernormal rate
to the normal growth rate in stage 1, and becomes constant and normal in stage 2.
• Three-stage DDM: There are two variations of this model.
o In one version, the growth in the middle stage is constant.
o In the second version, the middle stage is similar to the first stage in the H-
model. Dividends grow at a constant high rate in the second stage, and
declines linearly to a sustainable, mature growth rate in the third stage. The
second and third stages can be valued as an H-model.
The value of a stock using two-stage DDM is:
N
D0 (1 + g s )t D0 (1 + g s )n (1 + g L )
V0 = ∑ +
(1 + r)t (1 + r)n (r − g L )
t=1

where:
gs = short-term high growth rate
gL = long-term sustainable growth rate
n = number of years of high growth rate

The value of a stock using the H-model is:

D0 (1 + g L ) + D0 ∗ H ∗ (g s − g L )
V0 =
r − gL
where:
H = half-life in years of the high-growth period; high-growth period = 2H years
gS = initial short-term dividend growth rate
gL = normal long-term dividend growth rate after year 2H

The strength of multistage models is that they are flexible to pattern different growth
patterns in dividends.
However, multistage models have several limitations:
• Often, the present value of the terminal stage represents more than three-quarters
of the total value of shares.
• Terminal value can be very sensitive to the growth and required return
assumptions.
• Technological innovation can make the lifecycle model a crude representation.

Phases of growth

Most companies experience varying phases of growth. The growth of most publicly traded

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companies can be classified into the following three categories of growth:

• Growth phase: Companies in a growth phase enjoy
o Rapidly expanding markets
o High profit margins
o Abnormally high growth rate in earnings per share
On the flip side, they have:
o Negative free cash flows to equity
o Low dividend payouts
o Earnings growth rates may decline eventually as they attract new
competitors
• Transition phase: For companies in transition phase:
o Earnings are still rising, but at a slower pace as there is pressure on prices
and profit margins. The earnings growth rate is above average but is moving
towards the nominal growth rate of the economy.
o There is a decline in capital requirements, which leads to positive free cash
flow.
o Increasing dividend payout ratios.
• Mature phase: For companies in mature phase:
o Return on equity equals required return on equity
o Earnings growth, dividend payout ratio, and return on equity stabilize at the
mature growth rate
o Can be valued using the Gordon growth model

Determining terminal value

The terminal value of a stock can be found using two methods:

• the Gordon growth model or
• multiplying the forecasted multiple such as P/E by forecasted EPS as of the terminal
date.

Determining a required return

A required return can be calculated if all the inputs to a DDM and price are given. For a
Gordon growth model, the return can be calculated using the formula:
D1
r= +g
P0

Formula for calculating expected return for the H-model:

D0
r = ( ) [(1 + g L ) + H(g S − g L )] + g L
P0

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For multistage models and spreadsheet models, required return is calculated through trial
and error by equating the present value of cash flows to the current stock price.

Spreadsheet modeling

• The DDM models, such as the Gordon growth model or the H-model, assume
patterns of growth. Spreadsheet modeling makes it easier to model any growth
pattern.
• It allows the analyst to build complicated models that would be very cumbersome to
describe using Algebra, or where an iterative process is necessary.
• Built-in spreadsheet functions (such as those for finding rates of return) use
algorithms to get a numerical answer when a mathematical solution would be
impossible or extremely challenging.
• Several analysts can work together or exchange information by sharing their
spreadsheet models.

Sustainable growth rate of a company

The sustainable growth rate is the dividend/earnings growth rate that can be sustained for
a given level of return on equity, assuming that the capital structure stays constant through
time and the firm issues no new stock.
The formula for calculating the sustainable growth rate is: g = b ∗ ROE
The sustainable growth rate using the DuPont analysis is:
Net Income − Dividends Net Income Sales Total Assets
g= ∗ ∗ ∗
Net Income Sales Total Assets Shareholder ′ s Equity
An easy way to remember this formula is:
g=P*R*A*T
where, P = profit margin; R = retention rate; A = asset turnover; T = financial leverage

Valuing a stock using DDM

• If the DDM estimate of a stock’s value is more than its current price, then the stock is
undervalued.
• If the DDM estimate of a stock’s value is less than its current price, then the stock is
overvalued.
• If the DDM estimate of a stock’s value is equal to its current price, then the stock is
fairly valued.

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Equity 2024 Level II High Yield Notes

LM03 Free Cash Flow Valuation

FCFF and FCFE approaches to valuation

Free cash flow to the firm (FCFF) is the cash flow available to the company’s suppliers of
capital after all operating expenses (including taxes) have been paid and necessary
investments in working capital and fixed capital have been made. A firm’s suppliers of
capital include common shareholders, bondholders, and preferred shareholders.
Free cash flow to equity (FCFE) is the cash flow available to the company’s common
shareholders after all operating expenses, interest, and principal payments have been paid
and necessary investments in working and fixed capital have been made.
The two methods to value equity using free cash flows are:
• Discount FCFF at the weighted average cost of capital (WACC) because FCFF is an
after-tax cash flow. Then, estimate the value of equity by subtracting the value of
debt from the estimated value of the firm.
• Discount FCFE at the required return of equity.
FCFF is preferred over FCFE for
• a levered company with negative FCFE, or
• for a company with changing capital structure.
In free cash valuation, the focus is on the value of assets needed to generate operating cash
flows. Analysts often exclude non-operating assets such as cash and marketable securities.
However, if the non-operating assets are significant and were excluded, then they must be
added to the value of operating assets.
Value of firm = Value of operating assets + Values of non-operating assets

Ownership perspective implicit in the FCFE approach

Analysts prefer to use the FCFF or FCFE approaches if one of the following conditions exist:
• The company does not pay dividends.
• The company pays dividends but the dividends do not reflect the company’s
capacity to pay dividends.
• The investor takes a control perspective.
Free cash flow approaches reflect a control (ownership) perspective, whereas DDM
approaches reflect a non-control perspective. An ownership perspective implies that the
acquirer can take control of the company and change the dividends substantially.
Therefore, free cash flow approaches make more sense than DDM approaches.

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Calculating FCFF and FCFE

FCFF
FCFF from NI: FCFF = NI + NCC + Int (1 − tax rate) − FCInv − WCInv
FCFF from EBIT: FCFF = EBIT (1 – Tax rate) + Dep – FCInv – WCInv
FCFF from EBITDA: FCFF = EBITDA (1 – Tax rate) + Dep (Tax rate) – FCInv – WCInv
FCFF from CFO: FCFF = CFO + Int (1 – Tax rate) - FCInv

FCFE
FCFE from FCFF: FCFE = FCFF – Int (1 – Tax rate) + Net Borrowing
FCFE from NI: FCFE = NI + NCC – FCInv – WCInv + Net borrowing
FCFE from CFO: FCFE = CFO – FCInv + Net borrowing
To determine the WCInv, we ignore cash and short-term debt. For example, if we are given
the following information about a company:
Y1 Y2
Cash 10 12
AR 20 22
Inv 30 33

AP 10 10
Short-term debt 14 17
WCInv = (22 + 33 – 10) – (20 + 30 – 10) = 5

Forecasting FCFF and FCFE

There are two approaches to forecast FCFF and FCFE:

• Constant growth: One approach is to assume that the free cash flows (FCFF and
FCFE) grow at a constant rate. The simplest assumption is to use the historical
growth rate if the relationships between free cash flow and the fundamental factors
are expected to continue.
• Forecast individual components: The second approach is to forecast the
individual components of free cash flow, such as EBIT, net noncash charges,
investment in fixed capital, and investment in working capital.
The equation for FCFE assuming the Debt ratio (DR) is maintained is:
FCFE = NI - (1 – DR) (FCinv – Dep) – (1 – DR) (WCInv)

FCFE model versus dividend discount models

Analysts prefer the FCFE model over dividend discount model for the following reasons:

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• Some companies pay no or low dividends.

• Dividends are substantially lower or more than their free cash flow.
• Free cash flow to equity is the amount available for distribution without impairing a
company’s value.
• FCFE is an appropriate cash flow measure when a company is a target for a
takeover.

Impact of dividends, share repurchases, share issues, and changes in leverage on

FCFF and FCFE

Dividends, share repurchases, and share issues do not affect FCFE and FCFF.
Increase in leverage increases the tax savings for FCFF.
Leverage affects FCFE in two ways:
• When new debt is issued, FCFE increases by the amount of debt issued.
• Later, FCFE decreases as interest expense increases.

Using net income and EBITDA as proxies for FCFE and FCFF

EBITDA is a poor proxy for cash flow because it does not account for depreciation,
investments in fixed capital and working capital, and cash outflow due to taxes.
FCFF = EBITDA (1 – Tax rate) + Dep (Tax rate) – FCInv – WCInv
Similarly, net income is a poor proxy for FCFE because it does not account for fixed capital,
working capital investment and net borrowings.
FCFE = NI + NCC – FCInv – WcInv + Net borrowing

Estimating company value using cash flow models

Single-stage (constant-growth) FCFF and FCFE models:

FCFF1
Firm value =
WACC − g
FCFE1
Equity value =
r − g

Multi-stage FCFF and FCFE models

There are several versions of the multi-stage model. In one version, we estimate the free
cash flows up to a certain number of years and assume that the free cash flows will grow at
a constant rate from there on. The formulas for this version are:
n
FCFFt FCFFn+1 1
Firm value = ∑ t
+ ∗
(1 + WACC) WACC − g (1 + WACC)n
t=1

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n
FCFEt FCFEn+1 1
Equity value = ∑ + ∗
(1 + r)t r−g (1 + r)n
t=1

Another version assumes declining growth in Stage 1 followed by a long-run sustainable

growth rate in Stage 2. We can use the H-model formula (discussed in DDM) for this
version.
Three-stage growth models are appropriate for companies that have three distinct stages
of growth – growth phase, transition phase and mature phase.

Sensitivity analysis in FCFF and FCFE valuations

The value of a firm or equity depends on estimates for future growth rates, duration of
growth, and base-year values for FCFF and FCFE. Growth rate and duration of growth
depend on the growth phase of the company and the profitability of the industry.
Valuation models are sensitive to these inputs as the values can have a large impact on the
value of equity or firm. Analysts perform a sensitivity analysis to examine how valuation
changes with each of these inputs.

Calculating the terminal value in a multistage valuation model

The terminal value is calculated using two ways as seen in DDM:

• a single-stage model which assumes constant growth in the cash flows forever.
• a multiples approach which uses a valuation multiple such as the P/E ratio.

Valuing a stock using free cash flow valuation model

• If the model’s estimate of a stock’s value is more than its current price, then the
stock is undervalued.
• If the model’s estimate of a stock’s value is less than its current price, then the stock
is overvalued.
• If the model’s estimate of a stock’s value is equal to its current price, then the stock
is fairly valued.

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LM04 Market-Based Valuation: Price and Enterprise Value Multiples

Price multiples in valuation

Price multiples are ratios of a stock’s market price to some measure of fundamental value
per share, for example – price to earnings (P/E) ratio. There are two methods to use price
multiples: method of comparables and method based on forecasted fundamentals.
• The method of comparables compares the price multiple of an asset with
comparable or similar assets. The price multiple of an asset is compared to that of a
benchmark value of the multiple to evaluate if it is overvalued, undervalued, or
fairly valued. The benchmark value of the multiple may be the mean or median
value of a peer group of companies, an industry or sector, an equity index, or the
historical price multiple of the stock. The economic rationale for the method of
comparables is the law of one price: identical assets should sell at the same price.
• The method based on forecasted fundamentals compares the actual value of a
firm or its equity with one based on its forecasted fundamentals. The economic
rationale behind this method is that fundamentals drive future cash flows, and
multiples can be related to fundamentals through its DCF value.
The justified price multiple is an estimate of the fair value of a multiple using either the
method of comparables or the method of forecasted fundamentals. It represents what the
price multiple should be if the stock is fairly valued.

Commonly used price multiples

Price to earnings (P/E): Ratio of a stock’s market price to its earnings per share.
There are two variations of P/E: the trailing P/E and the forward P/E.
• Trailing P/E is a stock’s current market price divided by the most recent four
quarters’ EPS.
• The forward P/E or leading P/E, is a stock’s current price divided by next year’s
expected earnings.
Rationales for using P/E include:
• Earnings are the key driver of value.
• P/E ratio is widely recognized and used by investors.
• Differences in P/Es may be related to differences in long-run average returns.
Drawbacks of using P/E include:
• Earnings can be negative which will make the ratio meaningless.
• Earnings often contain volatile, transient components.
• Management’s choice of accounting policies may taint EPS’s value.

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Price to book value (P/B): Price divided by book value per share.
Book value per share represents, on a per-share basis, the investment that common
shareholders have made in the company. Book value will generally need to be adjusted.
When comparing, we often use tangible book value.
Rationales for using P/B include:
• Can be used when EPS is negative
• BVPS is more stable than EPS (especially when EPS is volatile)
• More useful for valuing companies with liquid assets (banks, etc.)
• Can be used when company is not a going concern
• Differences in P/B may relate to differences in long-run returns
Drawbacks of using P/B include:
• Some assets creating value (e.g. human capital) are not on the balance sheet
• Can be misleading when companies have different level of assets
• Accounting effects (e.g. R&D) can compromise BV
• BV is generally not reflective of market value
Price to sales (P/S): Ratio of market price per share to sales per share.
Rationale for using P/S include:
• Sales are less subject to accounting manipulation than EPS or BVPS
• Sales are positive even when EPS is negative
• Sales are more stable than EPS
• More useful in valuing mature, cyclical and zero income companies
• Differences in P/S may relate to differences in long-run returns
Drawbacks of using P/S include:
• A company may show sales growth despite low earnings and cash flow from
operations.
• P/S does not capture differences in cost structures.
• P/S does not capture different capital structures.
• Room for manipulating revenues remains.
Price to cash flow (P/CF): Ratio of market price to cash flow per share.
Rationales for using P/CF:
• Cash flow is less prone to manipulation than earnings.
• More stable than EPS
• Addresses the issue of accounting differences
• Differences in P/CF may relate to differences in long-run returns

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Drawbacks of using P/CF

• When cash flow is defined as earnings plus noncash charges, items such as noncash
revenue and net changes in working capital are ignored.
• FCFE is viewed as more appropriate than cash flow. But, FCFE can be more volatile
or negative for certain businesses.

Dividend yield: Ratio of dividend rate to market price per share.

The formulas for trailing and leading dividend yield are given below:
Dividend rate
Trailing dividend yield = Market price per share
where dividend rate = annualized amount of the most recent dividend
If the dividend is paid quarterly, then dividend rate = 4 * the most recent quarterly per-
share dividend.
Forecasted dividends per share over the next year
Leading dividend yield = Current market price per share

Rationales for using dividend yield:

• Dividend yield is a component of total return.
• Dividends are less risky than capital appreciation in total return.
Drawbacks of using dividend yield:
• Since dividend yield is only a part of total return, not using all the parts make this
valuation approach suboptimal.
• Dividend displacement of earnings is when investors choose to receive dividends
now over future earnings growth.
• The assumption that dividends are less risky than the capital appreciation
component implies that market prices are biased in the assessment of relative risk
of the two components.

Normalized EPS

Analysts address the issue of cyclicality in business by using normalized EPS. Normalized
EPS for cyclical companies are earnings expected under mid-cyclical conditions. Two main
methods for calculating normalized EPS are:
• Historical average method: Normalized EPS is calculated as the average EPS over
the most recent full cycle.
• Average ROE method: Normalized EPS = average full cycle ROE * current BV per
share
The ROE method is preferred because the historic average method does not account for
change in a business’s size.

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Earnings yield (E/P)

Earnings yield (E/P) is the reciprocal of the P/E. A high E/P indicates an undervalued
security, whereas a low E/P indicates an overvalued security.
When stocks have zero or negative EPS, a ranking by earnings yield is meaningful, whereas
a ranking by P/E is not.

Justified multiples based on forecasted fundamentals

An analyst can compute ratios based on company fundamentals and compare with ratios
based on actual market price.
If the ratio based on actual market price is low then the stock is undervalued.
D1
P0 E 1−b
Forward P/E: = 1 =
E1 r − g r − g
P0 (1 − b)(1 + g)
Trailing P/E: =
E0 r−g
P0 ROE − g
Price to book value: =
B0 r−g
E0
P0 ( S0 ) (1 − b)( 1 + g)
Price to sales: =
S0 r−g
D0 r − g
Dividend yield: =
P0 1 + g
(1 + g)FCFE0
Value based on cash flow: V0 =
r−g
We can make the following inferences from the above formulas:
• P/E is directly related to expected earnings growth and inversely related to the
required rate of return.
• P/B is directly related to ROE. The larger the difference between ROE and r, the
higher the P/B.
• P/S is directly related to profit margin and growth, and inversely related to the
required rate of return.
• Dividend yield is directly related to the required rate of return and negatively
related to the expected rate of growth in dividends.

Predicted P/E based on cross-sectional regression

A predicted P/E can be estimated from a cross-sectional regression of P/E on the

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fundamentals believed to drive security valuation. We can take several similar companies
and run a regression with the predicted P/E as the dependent variable and fundamental
characteristics such as the dividend payout ratio, beta, earnings growth rate, etc. as the
independent variables.
Example: Predicted P/E = 12.12 + (2.25 x DPR) – (0.20 X Beta) + (14.43 x EGR)
Predicted P/E is calculated by substituting the values of the variables in the estimated
regression equation. If the predicted P/E is less than the actual P/E, then the stock is
overvalued.
This method has three limitations:
• The model captures valuation relationships only for the specific stock over a
particular time period.
• Regression coefficients and explanatory power of regression tend to change
substantially over time.
• The method is prone to multicollinearity, or correlation within linear combinations
of the independent variables.

Valuation based on comparables

In the method of comparables, the analyst compares the price multiple of a stock with the
mean or media price multiple of comparable stocks. The method of comparables to
estimate the value of a company’s stock involves the following four steps:
1. Select and calculate the price multiple that will be used in the comparison.
2. Select the comparison asset or assets and calculate the value of the multiple for the
comparison assets. For a group of comparison asset, calculate the median or mean
value of the multiple for the assets. This multiple of the comparison asset(s) is called
the benchmark value of the multiple.
3. Adjust for differences in the fundamentals of stock and comparison stocks. Use the
benchmark value of the multiple to estimate the value of a company’s stock. Or,
compare the stock’s actual multiple with the benchmark value.
4. Fundamentals play an important role in the method of comparables as analysts can
use fundamentals to explain the differences between the estimated value of a
company’s stock and the current price of the company’s stock.

P/E – to – growth ratio (PEG)

PEG is calculated as the stock’s P/E divided by the expected earnings growth rate in
percent. Stocks with lower PEGs are more attractive than stocks with higher PEGs, all else
being equal. Some consider that a PEG ratio less than 1 is an indicator of an attractive value
level.

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Some factors analysts must be aware of when using PEG are:

• PEG assumes a linear relationship between P/E and growth. But, the Gordon growth
model to derive a justified P/E shows the relationship is not linear.
• PEG does not account for differences in risk.
• PEG does not account for differences in the duration of growth. For instance, if the
denominator is the growth rate for a four-year period, it would not show differences
for longer term growth prospects.

Using P/Es to obtain terminal values in DDM

Terminal price multiple based on fundamentals: Divide both sides of the Gordon
growth model equation by the EPS. This gives the justified trailing terminal price multiple.
Terminal price multiple based on comparables: Determine the benchmark value, which
is the median industry P/E, the average industry P/E, or an average of its own historical
P/Es. The benchmark value is used to estimate the terminal P/E multiple using the formula
below:
P
Terminal value at time n: Vn = Benchmark value of trailing terminal E ∗ En
P
Terminal value at time n: Vn = Benchmark value of forward terminal E ∗ E(n+1)

Cash flows used in price and enterprise value multiples

The major cash flow measures used in calculating multiples are

• earnings plus noncash charges (CF),
• cash flow from operations (CFO),
• free cash flow to equity (FCFE), and
• earnings before interest, taxes, depreciation and amortization (EBITDA).
Important points to note:
• CF and EBITDA are not cash flow numbers because they do not account for noncash
revenue and net changes in working capital.
• In case of CFO, adjustments must be made for different accounting standards.
• FCFE is more closely linked to valuation theory. The disadvantage of FCFE is it is
more volatile than the CFO.

EV multiples

Enterprise value is measured as:

Enterprise value = Market value of common equity + Market value of preferred stock +
Market value of debt - Cash and investments
EV/EBITDA is one of the most widely used enterprise value multiples. It is the ratio of the

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total company value to EBITDA. The rationales for using EV/EBITDA are as follows:
• For companies with different financial leverage, EV/EBITDA is a better choice than
P/E as it is a pre-interest figure.
• It increases the comparability across businesses as the age of the assets (and hence,
depreciation and amortization) may vary.
• EBITDA is often positive, whereas EPS can be negative.
The drawbacks for using EV/EBITDA are as follows:
• EBITDA overestimates cash flow from operations if working capital is growing.
• FCFF is more appropriate in valuation than EBITDA because it takes into account
capital expenditures. EBITDA will reflect capital expenditures only if depreciation
expenses match capital expenditures.
Other income measures used instead of EBITDA includes EBIT, EBITA, and FCFF.
EV/EBITDA is positively related to the expected growth rate in FCFF, profitability and
negatively related to the firm’s weighted average cost of capital.

Cross- border valuation comparisons

It is challenging to compare companies across countries because of differences in:

• accounting standards
• macroeconomic factors
• ability of companies to pass on the increase in costs to consumers
• cultural factors
• risk and growth opportunities

Momentum valuation indicators

Momentum indicators are valuation indicators that relate price to a fundamental such as
earnings to its own past values, or expected value. Three momentum indicators widely
used include:
• Earnings surprise: Earnings surprise (also called unexpected earnings) is the
difference between reported earnings and expected earnings.
• Standardized unexpected earnings (SUE): SUE is unexpected earnings divided by
the standard deviation in past unexpected earnings.
• Relative strength: Relative-strength indicators compare a stock’s performance
during a given period with its own past performance or with the performance of
some group of stocks.

Averaging P/E multiples

Using arithmetic means to calculate the P/E of a portfolio/index is inappropriate, because

the arithmetic mean is heavily influenced by outliers. The most appropriate measure to

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calculate the average P/E is to use a weighted harmonic mean.

The expression for the weighted harmonic mean is:
1
XWH = wi
∑N
i=1 X
i
where: wi = portfolio value weights summing to 1 and Xi > 0 for i = 1, 2, ……, n

Valuing a stock based on comparison of multiples

• If the price multiple of a stock is less than the benchmark value of the multiple, then the
stock is undervalued.
• If the price multiple of a stock is greater than the benchmark value of the multiple, then
the stock is overvalued.
• If the price multiple of a stock is equal to the benchmark value of the multiple, then the
stock is fairly valued.

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LM05 Residual Income Valuation

Residual income, economic value added (EVA), and market value added (MVA)

Residual income is defined as the earnings for a given period minus the opportunity cost of
equity holders. It can be calculated in two ways:
Residual income = net income – (equity capital x cost of equity)
Residual income = EBIT (1 – tax rate) – (total capital x WACC)

EVA is a commercial implementation of the residual income concept.

EVA = NOPAT – (C% * TC)
where,
NOPAT = company’s net profit after taxes
C% = cost of capital
TC = total capital.
MVA is based on the idea that a company must generate economic profit for its market
value to increase.
MVA = Market value of the company – Accounting book value of total capital

Uses of residual income models

The residual income model is used to:

• value equity
• test goodwill impairment
• measure internal corporate performance
• determine executive compensation

Residual income model

According to the residual income model, the intrinsic value of equity is a sum of two
components:
• The current book value of equity
• The present value of expected future residual income
There are three ways to express the value of a stock under this model:
∞
RIt
V0 = B0 + ∑
(1 + r)t
t=1
∞
(Et − rBt−1 )
V0 = B0 + ∑
(1 + r)t
t=1

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∞
(ROEt − r)Bt−1
V0 = B0 + ∑
(1 + r)t
t=1

As compared to the DDM and FCFE/FCFF models, residual income models are less sensitive
to terminal value estimates. This is because RI models include the company’s current book
value which usually represents a large portion of the estimated intrinsic value.

Fundamental determinants of residual income

The fundamental determinants of residual income are:

• book value of equity, and
• return on equity
This can be seen from the following expression:
RIt = (ROEt − r)Bt−1

Relationship between ROE and P/B

The justified price is the stock’s intrinsic value (P0 = V0 ).

ROE − r
P0 = B0 + ∗ B0
r−g
• If ROE > r, then residual income is positive, intrinsic value > book value, and justified
P/B > 1.
• If ROE = r, then residual income is zero, intrinsic value = book value, and justified P/B =
1.
• If ROE < r, then residual income is negative, intrinsic value < book value, and justified
P/B < 1.

Residual income valuation

In a multistage residual income model, we assume different growth rates for the short term
and the long-term. We forecast the residual incomes over a short term horizon and
estimate a terminal value based on the assumption made about continuing residual income
over the long term.
Continuing residual income is residual income after the forecast horizon. Usually, one of
the following assumptions is made for continuing residual income:
• Residual income continues indefinitely at a positive level.
• Residual income is zero from the terminal year forward.
• Residual income declines to zero as ROE reverts to the cost of equity through time.
• Residual income declines to some mean level.
If residual income continues indefinitely at a positive level, then we can use the following

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formula (single stage model):

ROE − r
V0 = B0 + ∗ B0
r−g
If at the end of time horizon T, a certain premium over book value (PT – BT ) exists for the
company, then we can use the following formulas:
T
Et − rBt−1 PT − BT
V0 = B0 + ∑ +
(1 + r)t (1 + r)T
t=1
T
(ROE − r)Bt−1 PT − BT
V0 = B0 + ∑ +
(1 + r)t (1 + r)T
t=1

If residual income fades over time, we can use the following formula:
T−1
Et − rBt−1 ET − rBT−1
V0 = B0 + ∑ +
(1 + r)t (1 + r − ω)(1 + r)T−1
t=1
Where, ω = persistence factor between 0 and 1
1 → residual income will not fade
0 → residual income will not continue after the initial forecast horizon
The following exhibit reproduced from the curriculum indicates characteristics associated
with high and low levels of persistence:
Lower residual income persistence Higher residual income persistence
Extreme accounting rates of return (ROE) Low dividend payout
Extreme levels of special items (e.g., High historical persistence in the
nonrecurring items) industry
Extreme levels of accounting accruals

Implied growth rate

This equation can be used to calculate the implied growth rate in residual income given the
market P/B ratio and the required rate of return.
ROE − r
P0 = B0 + ∗ B0
r−g

Residual income models versus dividend discount and free cash flow models

The DDM and free cash flow to equity discount future cash flows, while the residual income
model starts with the book value of equity, and discounts the expected stream of residual
income available to equity shareholders.
As compared to the DDM and FCFE/FCFF models, residual income models are less sensitive

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to terminal value estimates. This is because, RI models include the company’s current book
value which usually represents a large portion of the estimated intrinsic value.

Strengths and weaknesses of residual income models

Strengths of the residual income model include:

• The model gives less weight to terminal value.
• RI models use readily available accounting data.
• It can be used to value non-dividend paying companies.
• It can be used to value companies with no positive expected near-term free cash
flows.
• It can be used when cash flows are unpredictable.
Weaknesses of the residual income model include:
• The model is based on accounting data that is prone to manipulation.
• The accounting data may need adjustments.
• The model assumes that the clean surplus relation holds true.
• The model assumes that the cost of debt is equal to the interest expense.
Residual income models are most appropriate when:
• A company does not pay dividends.
• A company’s expected free cash flows are negative.
• When there is uncertainty in forecasting terminal values.
Residual income models are not appropriate when:
• The clean surplus relationship does not hold.
• The determinants of residual income such as book value and ROE are not
predictable.

Accounting considerations

When using residual income models, analysts must take the following into account:
1. Violations of the clean surplus relationship: Bt = B(t–1) + Et − Dt
2. Balance sheet adjustments for fair value
3. Intangible assets
4. Nonrecurring items
5. Other aggressive accounting practices
6. Differences in accounting standards across countries

Stock valuation using the residual income model

• If the intrinsic value based on residual income model is lower than the market price,
then the stock is overvalued.

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• If the intrinsic value based on residual income model is equal to the market price, then
the stock is fairly valued.
• If the intrinsic value based on residual income model is greater than the market price,
then the stock is undervalued.

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Equity 2024 Level II High Yield Notes

LM06 Private Company Valuation

Private versus public company valuation

The differences between private and public companies can be categorized into company-
specific and stock-specific factors.
Company specific factors include:
• Stage in lifecycle – are generally in the early stages.
• Size – are generally smaller.
• Concentrated ownership – are often characterized by family ownership or other
forms of concentrated control.
• Limited disclosures – disclose limited financial information.
• Overlap of shareholders and management – have high managerial ownership.
Stock-specific factors include:
• Liquidity – Shares are less liquid.
• Concentration of control – Control may be limited to one or two investors and
controlling shareholders may benefit at the cost of minority shareholders.
• Sale restrictions - Agreements may limit the ability to sell shares.

Private company valuation uses and areas of focus

The uses of private company valuation fall into three categories:

Transaction-related valuations are required when selling or financing the firm.
Transaction types include:
• Venture capital financing (early stage)
• Private equity financing (growth or buyout stage)
• Debt financing
• Initial public offering
• Acquisition
• Bankruptcy
• Share-based payment
Compliance-related valuations are required by law or regulation. Two primary focuses
are:
• Financial reporting
• Tax reporting
Litigation-related valuations are required to settle legal disputes such as:
• Shareholders disputes
• Damage claims

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• Lost profit claims

• Divorce claims/ settlements
Private company valuation areas of focus
Analysts using the free cash flow to the firm (FCFF) model to value a private company must
make three important adjustments: Cash flow and earnings adjustment, discount rate and
rate of return adjustments, and valuation discount or premium.
This is illustrated in Exhibit 3 below:

Earnings normalization and cash flow estimation issues

Private company valuations may require adjustments to the reported earnings to estimate
normalized earnings of the company.
Normalized earnings are earnings with specific adjustments for non-recurring, non-
economic items and other anomalies which prevent direct comparisons to publicly owned
companies. Examples of adjustments include:
• Goodwill impairment
• Market pricing and terms for sales between affiliates
• Related party compensation
• Real estate use
• Adjustments related to asset value
• Adjusted taxes
• Adjustments for distribution to private owner versus public company shareholders
In addition to earnings normalization, cash flow estimation is an important part of the
estimation process. Free cash flow to the firm (FCFF) represents cash flow at the enterprise

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level and is used to value the firm or, indirectly, the firm’s equity. Alternatively, free cash
flow to equity (FCFE) can be used to value equity directly.
The cash flow estimation issues relate to the nature of equity interest being appraised and
uncertainty regarding future cash flows resulting in several possible scenarios of growth
and profitability.

Private company discount rates and required rates of return

The following factors make estimating the discount rate for a private company challenging:
• Application of size premiums: Size premiums are added to reflect financial/operating
distress and risk of private companies. The smaller the firm size, the higher the risk.
Adding a size premium increases the discount rate.
• Relative debt availability and cost of debt: Since private companies have less access
to debt financing than public companies, they must use more equity financing, which
is expensive. Furthermore, the smaller size can also lead to greater operating risk
and higher cost of debt. Both these factors increase the WACC for private companies.
• Discount rates in an acquisition context: The cost of capital used to value an
acquisition should be based on the target company’s capital structure and the
riskiness of the target company’s cash flows. The buyer’s cost of capital is not
relevant.
• Discount rate adjustment for projection risk: Less financial information is available
for a private company relative to a comparable public company and the management
may be inexperienced in forecasting future cash flows. This uncertainty in projecting
future cash flows leads to a higher required rate of return.

Models used to estimate the required rate of return for private companies

To estimate the discount rate we start with the CAPM model.

CAPM: Required return = risk-free return +βi (equity risk premium)
However, CAPM is suitable for large public companies. For small private companies,
additional premiums for small size and company-specific risk have to be added. These
adjustments are shown by the expanded CAPM model.
Expanded CAPM: Required return = Risk-free rate + Equity risk premium adjusted for beta
+ Small stock premium + Company-specific risk adjustment
Analysts can also use the build-up model to estimate the discount rate. Like the expanded
CAPM, risk premiums are added. However, no beta is used because it is assumed to be 1.
Analysts must include an industry risk premium to reflect the industry risk factor.
Build-up method: Required return on equity = Risk-free rate + Equity risk premium +
Small stock premium + Industry risk premium + Company-specific risk adjustment

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Valuation discounts and premiums

Two factors that affect the valuation of private companies are issues related to control and
marketability.
Discounts for lack of control are used to convert a controlling interest value into a non-
controlling equity interest value. The formula for a discount for lack of control is given by:
1
DLOC = 1 − [ ]
1 + Control premium
A discount for lack of marketability (DLOM) is an amount or percentage deducted from
the value of an ownership interest to reflect the relative absence of marketability.
DLOC and DLOM are multiplicative and not additive.
Total discount = 1 – [(1 − DLOC)(1 − DLOM)]

Approaches to private company valuation

The three major private company valuation approaches are:

• Income approach: is based on the present value of expected future cash flows.
• Market approach: is based on the pricing multiples from the sale of similar
companies.
• Asset approach: is based on the value of net assets.
The selection of an appropriate valuation approach depends on the firm’s nature of
operations and its lifecycle stage.

Private company valuation: Income based approach

The three methods used in the income approach are: free cash flow, capitalized cash flow
and excess earnings method.
In the free cash flow method, value of the firm = PV of expected future cash flows + PV of
terminal value.
In the capitalized cash flow method, the value of the firm is calculated as:
FCFF1 FCFE1
Vf = or V𝑒 =
WACC−gf r−g

The steps to calculate the value of equity using the excess earnings method are:
1. Calculate the return on working capital.
2. Calculate the return on fixed assets.
3. Calculate residual income.
Residual income = Normalized earnings – return on working capital – return on
fixed assets
4. Calculate the value of intangible assets for a growing perpetuity.

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RI(1 + g)
Value of intangible assets =
r−g
5. Calculate the value of the business as:
Value of the firm = Value of intangible assets + Value of fixed assets + Value of
working capital

Private company valuation: Market based methods

The three methods used in a market approach are:

Guideline public company method (GPCM): Value based on multiples of comparable
public companies; multiples are adjusted to reflect differences in the relative risk and
growth prospects.
The advantage is the availability of a large number of guideline companies with financial
and trading information. The disadvantage is that risk and growth adjustments to the
pricing multiple are subjective.
Guideline transactions method (GTM): Value based on pricing multiples derived from
the acquisition of control of entire public or private companies that were acquired.
Whereas GPCM uses a multiple that could be associated with trades of any size, GTM uses a
multiple that specifically relates to sales of entire companies.
The advantage is that it uses data from the acquisition of entire public companies instead of
small blocks of stock. The disadvantage is that data may be unreliable if the transactions
are not subject to public disclosure.
Prior transaction method (PTM) considers actual transactions in the stock of the subject
private company.
The advantage is it is most relevant since it is based on actual transactions on the
company’s stock. The disadvantage is that it can be less reliable if the transactions are
infrequent.

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