‫أسباب االختالف في تقييمات الشركات‬
‫أ‪.‬د‪ .‬أسامة الخزعلي‬
‫‪kazali@aus.edu‬‬
‫الجامعة االمريكية فى الشارقة‬
‫مقدمة الى‬
‫هـيـئ ـة األوراق الـمال ـيـة والسـلع‬
‫‪1‬‬
Disclaimer
• The information reported and discussed in
this presentation do not represent the views
or the opinions of the Securities and
Commodities Authority (SCA) nor the
American University of Sharjah (AUS. They
represent my own views based on
information that are publically available in
books or newspapers. SCA or AUS are not
responsible for the content of this seminar.
2
Seminar's Outline
1. Introduction:
2. What Purpose Does a Valuation Serve?
3. Main Valuation Methods
4. The Most Common Errors in Valuation
3
Introduction
What is The Goal of the Financial
Management?
To Maximize the current value per share of the
existing stock (maximizing the value of the firm)
4
Introduction
How can we maximize the value of the firm?
By
1. Finding the right investment
2. Finding the right source of Financing
3. Minimizing risk
5
Introduction
Some important questions that need to be
answered by you
– What long-term investments should the firm
take on?
– Where will we get the long-term financing to
pay for the investment?
– How will we manage the everyday financial
activities of the firm?
6
Introduction
What is Valuation
• Valuation is the process of estimating the potential
market value of a financial asset or liability. Valuations
can be done on assets (for example, investments in
marketable securities such as stocks, options, business
enterprises, or intangible assets such as patents and
trademarks) or on liabilities (e.g., Bonds issued by a
company). Valuations are required in many contexts
including investment analysis, capital budgeting, merger
and acquisition transactions, financial reporting, taxable
events to determine the proper tax liability, and in
litigation.
7
Introduction
Steps of Valuation
1. Historic and strategic analysis of the company and
the industry
2. Projections of future cash flows
3. Determination of the cost (required return) of
capital
4. Net present value of future flows
5. Interpretation of the results
8
The Purpose of Valuation
WHY?
9
1.
In company buying and selling operations:
 For the buyer, the valuation will tell him
the highest price he should pay.
 For the seller, the valuation will tell him the
lowest price at which he should be
prepared to sell.
10
2.
Valuations for listed companies:
 The valuation is used to compare the value obtained
with the share’s price on the stock market and to
decide whether to sell, buy or hold shares.
 The valuation of several companies is used to decide
the security that the portfolio should concentrate
on: those that seem to it to be undervalues by the
market.
 The valuation of several companies is also used to
make comparisons between companies.
11
3. Public offerings:
 The valuation is used to justify the price at
which the shares are offered to the public
4. Inheritances and wills:
 The valuation is used to compare the shares’
value with that of other assets.
12
5.
Compensation schemes based on
value creation:
 The valuation of a company or business unit is
fundamental for quantifying the value creation
attributable to the executives being assessed.
6. Identification of value drivers:
 The valuation of a company or business unit is
fundamental for identifying and stratifying the
main value drivers.
13
7.
Strategic decisions on the company’s
continued existence:
 The valuation of a company or a business unit is a prior step
in the decision to continue in the business, sell, merge, milk,
grow or buy other companies.
8. Strategic planning:
 The valuation of the company and the different business
units is fundamental for deciding what products/business
lines/countries/customers… to maintain, grow or abandon.
 The valuation provides a means for measuring the impact of
the company’s possible policies and strategies on value
creation and destruction.
14
Main Valuation Methods
Discounted
Cash Flow
Income
Statement
Balance
Sheet
Mixed
(Goodwill)
Value
Creation
Options
Free Cash
flow
PER
Book value
Classic
EVA
Black and
Scholes
Equity cash
flow
P/Sales
Adjusted
book value
Indirect
Method
Economic
profit
Investment
options
Dividends
P/EBIT
Liquidation
value
Direct
Method
Expand the
project
Capital cash
flow
P/EBITDA
Substantial
value
Annual
Profit
Purchase
Method
Delay the
investment
APV
Other
multiples
15
Discounted Cash flow
Value of asset =
CF1
CF2
CF3
CF4
CFn



.....

(1 + r)1 (1 + r) 2 (1 + r) 3 (1 + r) 4
(1 + r) n
where CFt is the expected cash flow in period t, r is the
discount rate appropriate given the riskiness of the cash
 flow and n is the life of the asset.
Proposition 1: For an asset to have value, the expected cash
flows have to be positive some time over the life of the
asset.
Proposition 2: Assets that generate cash flows early in their
life will be worth more than assets that generate cash
flows later; the latter may however have greater growth
and higher cash flows to compensate.
16
Discounted Cash flow
• Inputs needed for DCF
1. Expected Cash flows
2. Discount Rate
3. Terminal Value
17
Generic DCF Valuation Model
DISCOUNTED CASHFLOW VALUATION
Expected Growth
Firm: Growth in
Operating Earnings
Equity: Growth in
Net Income/EPS
Cash flows
Firm: Pre-debt cash
flow
Equity: After debt
cash flows
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value
Value
Firm: Value of Firm
CF1
CF2
CF3
CF4
CF5
CFn
.........
Forever
Equity: Value of Equity
Length of Period of High Growth
Discount Rate
Firm:Cost of Capital
Equity: Cost of Equity
18
VALUING A FIRM
Cashflow to Firm
EBIT (1-t)
- (Cap Ex - Depr)
- Change in WC
= FCFF
Value of Operating Assets
+ Cash & Non-op Assets
= Value of Firm
- Value of Debt
= Value of Equity
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value= FCFF n+1 /(r-gn)
FCFF1
FCFF2
FCFF3
FCFF4
FCFF5
FCFFn
.........
Forever
Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))
Cost of Equity
Riskfree Rate :
- No default risk
- No reinvestment risk
- In same currency and
in same terms (real or
nominal as cash flows
Expected Growth
Reinvestment Rate
* Return on Capital
+
Cost of Debt
(Riskfree Rate
+ Default Spread) (1-t)
Beta
- Measures market risk
Type of
Business
Operating
Leverage
X
Weights
Based on Market Value
Risk Premium
- Premium for average
risk investment
Financial
Leverage
Base Equity
Premium
Country Risk
Premium
19
EQUITY VALUATION WITH FCFE
Financing Weights
Debt Ratio = DR
Cashflow to Equity
Net Income
- (Cap Ex - Depr) (1- DR)
- Change in WC (!-DR)
= FCFE
Value of Equity
FCFE1
Expected Growth
Retention Ratio *
Return on Equity
FCFE2
FCFE3
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value= FCFE n+1 /(ke-gn)
FCFE5
FCFEn
.........
Forever
FCFE4
Discount at Cost of Equity
Cost of Equity
Riskfree Rate :
- No default risk
- No reinvestment risk
- In same currency and
in same terms (real or
nominal as cash flows
+
Beta
- Measures market risk
Type of
Business
Operating
Leverage
X
Risk Premium
- Premium for average
risk investment
Financial
Leverage
Base Equity
Premium
Country Risk
Premium
20
EQUITY VALUATION WITH DIVIDENDS
Dividends
Net Income
* Payout Ratio
= Dividends
Value of Equity
Dividend 1
Expected Growth
Retention Ratio *
Return on Equity
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value= Dividend n+1 /(ke-gn)
Dividend 5 Dividend n
.........
Forever
Dividend 2 Dividend 3 Dividend 4
Discount at Cost of Equity
Cost of Equity
Riskfree Rate :
- No default risk
- No reinvestment risk
- In same currency and
in same terms (real or
nominal as cash flows
+
Beta
- Measures market risk
Type of
Business
Operating
Leverage
X
Risk Premium
- Premium for average
risk investment
Financial
Leverage
Base Equity
Premium
Country Risk
Premium
21
First Principle of Valuation
• Never mix and match cash flows and discount
rates.
• The key error to avoid is mismatching cashflows
and discount rates, since discounting cashflows to
equity at the weighted average cost of capital will
lead to an upwardly biased estimate of the value
of equity, while discounting cashflows to the firm
at the cost of equity will yield a downward biased
estimate of the value of the firm.
22
Cash Flows and Discount Rates
• Assume that you are analyzing a company with the following
cashflows for the next five years.
Year
CF to Equity Interest Exp (1-tax rate)
CF to Firm
1
$ 50
$ 40
$ 90
2
$ 60
$ 40
$ 100
3
$ 68
$ 40
$ 108
4
$ 76.2
$ 40
$ 116.2
5
$ 83.49
$ 40
$ 123.49
Terminal Value$ 1603.0
$ 2363.008
• Assume also that the cost of equity is 13.625% and the firm can
borrow long term at 10%. (The tax rate for the firm is 50%.)
• The current market value of equity is $1,073 and the value of debt
outstanding is $800.
23
Equity versus Firm Valuation
Method 1: Discount CF to Equity at Cost of Equity to get value of
equity
– Cost of Equity = 13.625%
– Value of Equity = 50/1.13625 + 60/1.136252 + 68/1.136253 +
76.2/1.136254 + (83.49+1603)/1.136255 = $1073
Method 2: Discount CF to Firm at Cost of Capital to get value of firm
Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5%
WACC
= 13.625% (1073/1873) + 5% (800/1873) = 9.94%
PV of Firm = 90/1.0994 + 100/1.09942 + 108/1.09943 +
116.2/1.09944 + (123.49+2363)/1.09945 = $1873
Value of Equity = Value of Firm - Market Value of Debt
= $ 1873 - $ 800 = $1073
24
The Effects of Mismatching Cash
Flows and Discount Rates
Error 1: Discount CF to Equity at Cost of Capital to get equity
value
PV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 +
76.2/1.09944 + (83.49+1603)/1.09945 = $1248
Value of equity is overstated by $175.
Error 2: Discount CF to Firm at Cost of Equity to get firm value
PV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 +
116.2/1.136254 + (123.49+2363)/1.136255 = $1613
PV of Equity = $1612.86 - $800 = $813
Value of Equity is understated by $ 260.
Error 3: Discount CF to Firm at Cost of Equity, forget to
subtract out debt, and get too high a value for equity
Value of Equity = $ 1613
Value of Equity is overstated by $ 540
25
Discounted Cash Flow Valuation: The
Steps
• Estimate the discount rate or rates to use in the valuation
– Discount rate can be either a cost of equity (if doing equity valuation) or a
cost of capital (if valuing the firm)
– Discount rate can be in nominal terms or real terms, depending upon
whether the cash flows are nominal or real
– Discount rate can vary across time.
• Estimate the current earnings and cash flows on the asset, to either
equity investors (CF to Equity) or to all claimholders (CF to Firm)
• Estimate the future earnings and cash flows on the firm being valued,
generally by estimating an expected growth rate in earnings.
• Estimate when the firm will reach “stable growth” and what
characteristics (risk & cash flow) it will have when it does.
• Choose the right DCF model for this asset and value it.
26
Discounted Cash Flow Valuation:
The Inputs
27
Estimating Inputs: Discount Rates
• Critical ingredient in discounted cashflow valuation. Errors in
estimating the discount rate or mismatching cashflows and
discount rates can lead to serious errors in valuation.
• At an intuitive level, the discount rate used should be consistent
with both the riskiness and the type of cashflow being discounted.
– Equity versus Firm: If the cash flows being discounted are cash flows
to equity, the appropriate discount rate is a cost of equity. If the cash
flows are cash flows to the firm, the appropriate discount rate is the
cost of capital.
– Currency: The currency in which the cash flows are estimated should
also be the currency in which the discount rate is estimated.
– Nominal versus Real: If the cash flows being discounted are nominal
cash flows (i.e., reflect expected inflation), the discount rate should
be nominal
28
The Cost of Equity: Competing Models
Model
CAPM
Expected Return
E(R) = Rf +  (Rm- Rf)
Inputs Needed
Riskfree Rate
Beta relative to market portfolio
Market Risk Premium
APM
E(R) = Rf + j=1j (Rj- Rf)
Riskfree Rate; # of Factors;
Betas relative to each factor
Factor risk premiums
Multi
factor
E(R) = Rf + j=1,,Nj (Rj- Rf)
Riskfree Rate; Macro factors
Betas relative to macro factors
Macro economic risk premiums
29
The CAPM: Cost of Equity
• Consider the standard approach to estimating cost of
equity:
Cost of Equity = Rf + Equity Beta * (E(Rm) - Rf)
where,
Rf = Riskfree rate
E(Rm) = Expected Return on the Market Index
(Diversified Portfolio)
• In practice,
– Short term government security rates are used as risk
free rates
– Historical risk premiums are used for the risk premium
– Betas are estimated by regressing stock returns against
market returns
30
Short term Governments are not
riskfree in valuation….
• On a riskfree asset, the actual return is equal to the
expected return. Therefore, there is no variance
around the expected return.
• For an investment to be riskfree, then, it has to have
– No default risk
– No reinvestment risk
• In valuation, the time horizon is generally infinite,
leading to the conclusion that a long-term riskfree
rate will always be preferable to a short term rate, if
you have to pick one.
31
Everyone uses historical premiums,
but..
• The historical premium is the premium that
stocks have historically earned over riskless
securities.
• Practitioners never seem to agree on the
premium; it is sensitive to
– How far back you go in history…
– Whether you use T.bill rates or T.Bond rates
– Whether you use geometric or arithmetic
averages.
32
If you choose to use historical
premiums….
• Go back as far as you can. A risk premium
comes with a standard error.
• Be consistent in your use of the riskfree rate.
Since we argued for long term bond rates, the
premium should be the one over T.Bonds
• Use the geometric risk premium. It is closer to
how investors think about risk premiums over
long periods.
33
Two Ways of Estimating Country Equity
Risk Premiums for other markets
• Default spread on Country Bond: In this approach, the country
equity risk premium is set equal to the default spread of the bond
issued by the country
• Relative Equity Market approach: The country equity risk premium
is based upon the volatility of the market in question relative to U.S
market.
Total equity risk premium = Risk PremiumUS* Country Equity / US Equity
• Country ratings measure default risk.
Country Equity risk premium = Default spread on country bond*
34
Country Equity / Country Bond
Implied Equity Premiums
• If we assume that stocks are correctly priced in the
aggregate and we can estimate the expected
cashflows from buying stocks, we can estimate the
expected rate of return on stocks by computing an
internal rate of return. Subtracting out the riskfree
rate should yield an implied equity risk premium.
• This implied equity premium is a forward looking
number and can be updated as often as you want
(every minute of every day, if you are so inclined).
35
Implied Equity Premiums
•
We can use the information in stock prices to back out how risk averse the market is and how
much of a risk premium it is demanding.
In 2004, dividends & stock
buybacks were 2.90% of
the index, generating 35.15
in cashflows
Analysts expect earnings to grow 8.5% a year for the next 5 years .
38.13
41.37
44.89
48.71
After year 5, we will assume that
earnings on the index will grow at
4.22%, the same rate as the entire
economy
52.85
January 1, 2005
S&P 500 is at 1211.92
•
If you pay the current level of the index, you can expect to make a return of 7.87% on stocks
(which is obtained by solving for r in the following equation)
38.13 41.37
44.89
48.71
52.85
52.85(1.0422 )
1211 .92 





(1 r) (1 r) 2 (1 r) 3 (1 r) 4 (1 r) 5 (r  .0422 )(1 r) 5
•
Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 7.87% 4.22% = 3.65%

36
Estimating Beta
• The standard procedure for estimating betas is to regress stock
returns (Rj) against market returns (Rm) –
Rj = a +  R m
– where a is the intercept and  is the slope of the
regression.
• The slope of the regression corresponds to the beta of
the stock, and measures the riskiness of the stock.
Beta is sensitive to:
• Data interval (monthly, weekly, daily)
• Study period
• Index
37
Beta Estimation: The Noise Problem
38
Beta Estimation: The Index Effect
39
Solutions to the Regression Beta Problem
• Modify the regression beta by
– changing the index used to estimate the beta
– adjusting the regression beta estimate, by bringing in information about
the fundamentals of the company
• Estimate the beta for the firm using
– the standard deviation in stock prices instead of a regression against an
index
– accounting earnings or revenues, which are less noisy than market
prices.
• Estimate the beta for the firm from the bottom up without
employing the regression technique. This will require
– understanding the business mix of the firm
– estimating the financial leverage of the firm
• Use an alternative measure of market risk not based upon a
regression.
40
In a perfect world… we would estimate
the beta of a firm by doing the following
Start with the beta of the business that the firm is in
Adjust the business beta for the operating leverage of the firm to arrive at the
unlevered beta for the firm.
Use the financial leverage of the firm to estimate the equity beta for the firm
Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (Debt/Equity))
41
Adjusting for operating leverage…
Unlevered beta = Pure business beta * (1
+ (Fixed costs/ Variable costs))
42
Equity Betas and Leverage
• Conventional approach: If we assume that debt carries
no market risk (has a beta of zero), the beta of equity
alone can be written as a function of the unlevered
beta and the debt-equity ratio
L = u (1+ ((1-t)D/E))
In some versions, the tax effect is ignored and there is no (1t) in the equation.
• Debt Adjusted Approach: If beta carries market risk
and you can estimate the beta of debt, you can
estimate the levered beta as follows:
L = u (1+ ((1-t)D/E)) - debt (1-t) (D/E)
• While the latter is more realistic, estimating betas for
debt can be difficult to do.
43
Bottom-up Betas
Step 1: Find the business or businesses that your firm operates in.
Possible Refinements
Step 2: Find publicly traded firms in each of these businesses and
obtain their regression betas. Compute the simple average across
these regression betas to arrive at an average beta for these publicly
traded firms. Unlever this average beta using the average debt to
equity ratio across the publicly traded firms in the sample.
Unlevered beta for business = Average beta across publicly traded
firms/ (1 + (1- t) (Average D/E ratio across firms))
Step 3: Estimate how much value your firm derives from each of
the different businesses it is in.
Step 4: Compute a weighted average of the unlevered betas of the
different businesses (from step 2) using the weights from step 3.
Bottom-up Unlevered beta for your firm = Weighted average of the
unlevered betas of the individual business
Step 5: Compute a levered beta (equity beta) for your firm, using
the market debt to equity ratio for your firm.
Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity))
If you can, adjust this beta for differences
between your firm and the comparable
firms on operating leverage and product
characteristics.
While revenues or operating income
are often used as weights, it is better
to try to estimate the value of each
business.
If you expect the business mix of your
firm to change over time, you can
change the weights on a year-to-year
basis.
If you expect your debt to equity ratio to
change over time, the levered beta will
change over time.
44
Why bottom-up betas?
• The standard error in a bottom-up beta will be
significantly lower than the standard error in a single
regression beta. Roughly speaking, the standard error of a
bottom-up beta estimate can be written as follows:
Std error of bottom-up beta =Average Std Error across Betas
Number of firms in sample
• The bottom-up beta can be adjusted to reflect changes in

the firm’s business mix
and financial leverage. Regression
betas reflect the past.
• You can estimate bottom-up betas even when you do not
have historical stock prices. This is the case with initial
45
public offerings, private businesses or divisions of
The Cost of Equity: A Recap
Preferably, a bottom-up beta,
based upon other firms in the
business, and firm’s own financial
leverage
Cost of Equity =
Riskfree Rate
Has to be in the same
currency as cash flows,
and defined in same terms
(real or nominal) as the
cash flows
+
Beta *
(Risk Premium)
Historical Premium
1. Mature Equity Market Premium:
Average premium earned by
stocks over T.Bonds in U.S.
2. Country risk premium =
Country Default Spread* ( Equity /Country bond )
or
Implied Premium
Based on how equity
market is priced today
and a simple valuation
model
46
Estimating the Cost of Debt
• The cost of debt is the rate at which you can borrow
at currently, It will reflect not only your default risk
but also the level of interest rates in the market.
• The two most widely used approaches to estimating
cost of debt are:
– Looking up the yield to maturity on a straight bond
outstanding from the firm. The limitation of this approach
is that very few firms have long term straight bonds that
are liquid and widely traded
– Looking up the rating for the firm and estimating a default
spread based upon the rating. While this approach is
more robust, different bonds from the same firm can have
different ratings. You have to use a median rating for the
firm
47
Weights for the Cost of Capital
Computation
• The weights used to compute the cost of capital should
be the market value weights for debt and equity.
• As a general rule, the debt that you should subtract
from firm value to arrive at the value of equity should
be the same debt that you used to compute the cost of
capital.
48
Recapping the Cost of Capital
Cost of borrowing should be based upon
(1) synthetic or actual bond rating
(2) default spread
Cost of Borrowing = Riskfree rate + Default spread
Cost of Capital =
Cost of Equity (Equity/(Debt + Equity))
Cost of equity
based upon bottom-up
beta
+
Cost of Borrowing
(1-t)
Marginal tax rate, reflecting
tax benefits of debt
(Debt/(Debt + Equity))
Weights should be market value weights
49
The Cost of Capital (WACC)
The Weighted Average Cost of Capital is given by:
rWACC =
Equity
Debt
× rEquity +
× rDebt ×(1 – TC)
Equity + Debt
Equity + Debt
E
B
rWACC =
× re +
× rB ×(1 – TC)
E+ B
E+B
• Because interest expense is tax-deductible, we
multiply the last term by (1 – TC).
50
II. Estimating Cash Flows
DCF Valuation
51
Measuring Cash Flow to the Firm
EBIT ( 1 - tax rate)
- (Capital Expenditures - Depreciation)
- Change in Working Capital
= Cash flow to the firm
52
II. Correcting Accounting Earnings
• Make sure that there are no financial expenses mixed in
with operating expenses
– Example: Operating Leases: they are really financial expenses
and need to be reclassified as such. This has no effect on equity
earnings but does change the operating earnings
• Make sure that there are no capital expenses mixed in
with the operating expenses
– R & D Adjustment: Since R&D is a capital expenditure (rather
than an operating expense), the operating income has to be
adjusted to reflect its treatment.
53
Dealing with Operating Lease
Expenses
Adjusted Operating Earnings = Operating Earnings + Operating
Lease Expenses - Depreciation on Leased Asset
As an approximation, this works:
Adjusted Operating Earnings = Operating Earnings + Pre-tax cost
of Debt * PV of Operating Leases.
54
Net Capital Expenditures
• Net capital expenditures represent the difference
between capital expenditures and depreciation.
Depreciation is a cash inflow that pays for some or a lot
(or sometimes all of) the capital expenditures.
• In general, the net capital expenditures will be a
function of how fast a firm is growing or expecting to
grow. High growth firms will have much higher net
capital expenditures than low growth firms.
• Assumptions about net capital expenditures can
therefore never be made independently of assumptions
about growth in the future.
55
Capital expenditures should include
• Research and development expenses, once they have
been re-categorized as capital expenses. The adjusted
net cap ex will be
Adjusted Net Capital Expenditures = Net Capital
Expenditures + Current year’s R&D expenses Amortization of Research Asset
• Acquisitions of other firms, since these are like capital
expenditures. The adjusted net cap ex will be
Adjusted Net Cap Ex = Net Capital Expenditures +
Acquisitions of other firms - Amortization of such
acquisitions
56
Working Capital Investments
• In accounting terms, the working capital is the difference between
current assets (inventory, cash and accounts receivable) and current
liabilities (accounts payables, short term debt and debt due within
the next year)
• A cleaner definition of working capital from a cash flow perspective
is the difference between non-cash current assets (inventory and
accounts receivable) and non-debt current liabilities (accounts
payable)
• Any investment in this measure of working capital ties up cash.
Therefore, any increases (decreases) in working capital will reduce
(increase) cash flows in that period.
• When forecasting future growth, it is important to forecast the
effects of such growth on working capital needs, and building these
effects into the cash flows.
57
Estimating FCFE
• Cash flows to Equity for a Levered Firm
Net Income
- (Capital Expenditures - Depreciation)
- Changes in non-cash Working Capital
- (Principal Repayments - New Debt Issues)
= Free Cash flow to Equity
– I have ignored preferred dividends. If preferred stock
exist, preferred dividends will also need to be netted
out
58
Estimating FCFE when Leverage is Stable
Net Income
- (1- ) (Capital Expenditures - Depreciation)
- (1- ) Working Capital Needs
= Free Cash flow to Equity
 = Debt/Capital Ratio
For this firm,
– Proceeds from new debt issues = Principal Repayments + 
(Capital Expenditures - Depreciation + Working Capital Needs)
• In computing FCFE, the book value debt to capital ratio
should be used when looking back in time but can be
replaced with the market value debt to capital ratio,
looking forward.
59
Estimating FCFE
•
•
•
•
•
•
Net Income=
$ 1533 Million
Capital spending =
$ 1,746 Million
Depreciation per Share = $ 1,134 Million
Increase in non-cash working capital = $ 477 Million
Debt to Capital Ratio = 23.83%
Estimating FCFE
Net Income
$1,533 Mil
- (Cap. Exp - Depr)*(1-DR) $465.90
[(1746-1134)(1-.2383)]
Chg. Working Capital*(1-DR) $363.33
[477(1-.2383)]
= Free CF to Equity
$ 704 Million
Dividends Paid
$ 345 Million
60
III. Estimating Growth
DCF Valuation
61
Ways of Estimating Growth in
Earnings
• Look at the past
– The historical growth in earnings per share is usually a good
starting point for growth estimation
• Look at what others are estimating
– Analysts estimate growth in earnings per share for many firms. It
is useful to know what their estimates are.
• Look at fundamentals
– Ultimately, all growth in earnings can be traced to two
fundamentals - how much the firm is investing in new projects,
and what returns these projects are making for the firm.
62
I. Historical Growth in EPS
• Historical growth rates can be estimated in a number of
different ways
– Arithmetic versus Geometric Averages
– Simple versus Regression Models
• Historical growth rates can be sensitive to
– the period used in the estimation
63
I. Expected Long Term Growth in
EPS
• When looking at growth in earnings per share, these inputs can be
cast as follows:
Reinvestment Rate = Retained Earnings/ Current Earnings = Retention Ratio
Return on Investment = ROE = Net Income/Book Value of Equity
• In the special case where the current ROE is expected to remain
unchanged
gEPS = Retained Earningst-1/ NIt-1 * ROE
= Retention Ratio * ROE
= b * ROE
• Proposition 1: The expected growth rate in earnings for a company
cannot exceed its return on equity in the long term.
64
Changes in ROE and Expected Growth
• When the ROE is expected to change,
gEPS= b *ROEt+1 +(ROEt+1– ROEt)/ ROEt
• Proposition 2: Small changes in ROE translate into large
changes in the expected growth rate.
• Proposition 3: No firm can, in the long term, sustain
growth in earnings per share from improvement in ROE.
65
ROE and Leverage
• ROE = ROC + D/E (ROC - i (1-t))
where,
ROC = EBITt (1 - tax rate) / Book value of
Capitalt-1
D/E = BV of Debt/ BV of Equity
i = After-tax Cost of Debt / BV of Debt
t = Tax rate on ordinary income
• Note that Book value of capital = Book Value
of Debt + Book value of Equity.
66
67
Getting Closure in Valuation
• A publicly traded firm potentially has an infinite life.
The value is therefore the present value of cash flows
t =  CF
t
forever.
Value =

t
t = 1 (1 + r)
t = N CFt
Terminal Value
Value = 

t
(1 + r)N
t = 1 (1 + r)
• Since we cannot estimate cash flows forever, we
estimate cash flows for a “growth period” and then
estimate a terminal value, to capture the value at the
end of the period:
68
Ways of Estimating Terminal Value
69
Stable Growth and Terminal Value
• When a firm’s cash flows grow at a “constant” rate forever, the present value of
those cash flows can be written as:
Value = Expected Cash Flow Next Period / (r - g)
where,
r = Discount rate (Cost of Equity or Cost of Capital)
g = Expected growth rate
• This “constant” growth rate is called a stable growth rate and cannot be higher
than the growth rate of the economy in which the firm operates.
• While companies can maintain high growth rates for extended periods, they will
all approach “stable growth” at some point in time.
• When they do approach stable growth, the valuation formula above can be used
to estimate the “terminal value” of all cash flows beyond.
70
Summarizing the Inputs
• In summary, at this stage in the process, we should have an
estimate of the
– the current cash flows on the investment, either to equity
investors (dividends or free cash flows to equity) or to the firm
(cash flow to the firm)
– the current cost of equity and/or capital on the investment
– the expected growth rate in earnings, based upon historical
growth, analysts forecasts and/or fundamentals
• The next step in the process is deciding
– which cash flow to discount, which should indicate
– which discount rate needs to be estimated and
– what pattern we will assume growth to follow
71
Which cash flow should I discount?
• Use Equity Valuation
(a) for firms which have stable leverage, whether high or not, and
(b) if equity (stock) is being valued
• Use Firm Valuation
(a) for firms which have leverage which is too high or too low, and
expect to change the leverage over time, because debt payments
and issues do not have to be factored in the cash flows and the
discount rate (cost of capital) does not change dramatically over
time.
(b) for firms for which you have partial information on leverage
(eg: interest expenses are missing..)
(c) in all other cases, where you are more interested in valuing the
firm than the equity. (Value Consulting?)
72
Given cash flows to equity, should
I discount dividends or FCFE?
• Use the Dividend Discount Model
– (a) For firms which pay dividends (and repurchase stock) which are close to
the Free Cash Flow to Equity (over a extended period)
– (b)For firms where FCFE are difficult to estimate (Example: Banks and
Financial Service companies)
• Use the FCFE Model
– (a) For firms which pay dividends which are significantly higher or lower
than the Free Cash Flow to Equity. (What is significant? ... As a rule of
thumb, if dividends are less than 80% of FCFE or dividends are greater than
110% of FCFE over a 5-year period, use the FCFE model)
– (b) For firms where dividends are not available (Example: Private
Companies, IPOs)
73
What discount rate should I use?
• Cost of Equity versus Cost of Capital
– If discounting cash flows to equity -> Cost of Equity
– If discounting cash flows to the firm -> Cost of Capital
• What currency should the discount rate (risk free rate) be in?
– Match the currency in which you estimate the risk free rate to
the currency of your cash flows
• Should I use real or nominal cash flows?
– If discounting real cash flows
-> real cost of capital
– If nominal cash flows
-> nominal cost of capital
– If inflation is low (<10%), stick with nominal cash flows since
taxes are based upon nominal income
– If inflation is high (>10%) switch to real cash flows
74
Which Growth Pattern Should I use?
• If your firm is
– large and growing at a rate close to or less than growth rate of the economy,
or
– constrained by regulation from growing at rate faster than the economy
– has the characteristics of a stable firm (average risk & reinvestment rates)
Use a Stable Growth Model
• If your firm
– is large & growing at a moderate rate (≤ Overall growth rate + 10%) or
– has a single product & barriers to entry with a finite life (e.g. patents)
Use a 2-Stage Growth Model
• If your firm
– is small and growing at a very high rate (> Overall growth rate + 10%) or
– has significant barriers to entry into the business
– has firm characteristics that are very different from the norm
75
Use a 3-Stage or n-stage Model
The Building Blocks of Valuation
Choose a
Cash Flow
Dividends
Expected Dividends to
Stockholders
Cashflows to Equity
Cashflows to Firm
Net Income
EBIT (1- tax rate)
- (Capital Exp. - Deprec’n)
- (1- ) (Capital Exp. - Deprec’n)
- Change in Work. Capital
- (1- ) Change in Work. Capital
= Free Cash flow to Equity (FCFE) = Free Cash flow to Firm (FCFF)
[ = Debt Ratio]
& A Discount Rate
Cost of Equity
Cost of Capital
WACC = ke ( E/ (D+E))
 Basis: The riskier the investment, the greater is the cost of equity.
 Models:
+ kd ( D/(D+E))
CAPM: Riskfree Rate + Beta (Risk Premium)
kd = Current Borrowing Rate (1-t)
E,D: Mkt Val of Equity and Debt
APM: Riskfree Rate + Betaj (Risk Premiumj): n factors
& a growth pattern
Stable Growth
Two-Stage Growth
g
g
Three-Stage Growth
g
|
t
High Growth
|
Stable
High Growth
Transition
Stable
76
Income Statement-Based Method
1. Value of Earnings: PER
Equity Value = PER X earnings
2. Value of the Dividends:
Equity value = DPS/Ke
Equity value = DPS1/(Ke- g)
77
Income Statement-Based Method
3. Sales Multiples:
Price/Sale =
(Price/earnings)x(earnings/sales)
78
Income Statement-Based Method
• Other Multiples:
Value of the company/EBIT
Value of the company/EBITDA
Value of the company/book value
Value of the company/operating cash flow
79
Balance Sheet-Based Methods
1. Book Value (the value of the shareholders’
equity stated in the balance sheet, TA-TL)
2. Adjusted Book Value
3. Liquidation Value (the value of the company
if it is liquidated, that is, its assets are sold
and its debts are paid off)
80
Balance Sheet-Based Methods
4. Substantial Value (the investment that must be made to
form a company having identical conditions as those of
the company being valued); assets replacement value.
a) Gross substantial value (the assets’ value at market
price)
b) Net substantial value or corrected net assets (the gross
substantial value less liabilities or adjusted net worth)
c) Reduce gross substantial value (gross substantial value
reduced only by the value of the cost-free debt)
81
Goodwill-Based Methods
Goodwill is the value that a company has above
its book value or above the adjusted book value.
Goodwill seeks to represent the value of the
company’s intangible assets, which often do
not appear on the balance sheet but which,
contribute an advantage with respect to other
companies operating in the industry (quality of
the customer portfolio, industry leadership,
brands, strategic alliances, etc.).
82
Goodwill-Based Methods
1. The “Classic” Valuation Method:
Value = value of net assets + value goodwill
 Goodwill is valued as n times the company’s net
income, or as a certain percentage of the
turnover.
V = A + (n x B), or
V = A + (z x F)
A = net asset value, n = coefficients between 1.5
and 3; B = net income; z = % of sales revenue;
and F = turnover.
83
Goodwill-Based Methods
2. Abbreviated Goodwill income
V = A + PVA (B- iA)
A = corrected net assets or net substantial value
PVA = present value of annuities factor with n between
5 and 8 years.
B = net income
I = rate on long term government bond
84
Goodwill-Based Methods
3. Indirect Method
V = (A + B/i)/2, or V = A + (B – iA)/2i)
85
Goodwill-Based Methods
4. Anglo-Saxon or Direct Method:
V = A + (B + iA)/K
where, K is rate on fixed income securities
multiply by a coefficient between 1.25 and
1.5 to adjust for the risk
86
Goodwill-Based Methods
5. Annual Profit Purchase Method:
V = A + m(B-iA)
m: number of years for super profits period,
ranges between 3 and 5.
87
Value Creation Method
1. Economic Value Added (EVA)
EVA = NOPAT- (WACC)(Capital)
NOPAT = EBIT (1-t)
WACC is weighted average cost of capital
88
Value Creation Method
2. Market Value Added (MVA)
• MVA = Market Value of the Firm - Book Value
of the Firm
• Market Value = (# shares of stock)(price per
share) + Value of debt
• Book Value = Total common equity + Value of
debt
(More…)
89
Value Creation Method
• If the market value of debt is close to the
book value of debt, then MVA is:
• MVA = Market value of equity – book value
of equity
90
MVA for a Constant Growth Firm
MVAt =
┌
│
└
┐
┐┌
CR
Sales (1 + g)
OP – WACC (
│
│
│
)
(1+g)
WACC - g
┘
┘└
t
91
MVA and the Four Value Drivers
• MVA is determined by four drivers:
– Sales growth
– Operating profitability (OP=NOPAT/Sales)
– Capital requirements (CR=Operating capital
/ Sales)
– Weighted average cost of capital
92
MVA in Terms of Expected ROIC
MVAt =
Capitalt (EROICt – WACC)
WACC - g
If the spread between the expected return, EROICt,
and the required return, WACC, is positive, then MVA
is positive and growth makes MVA larger. The
opposite is true if the spread is negative.
93
Expected Return on Invested Capital
(EROIC)
• The expected return on invested capital is
the NOPAT expected next period divided by
the amount of capital that is currently
invested:
EROICt =
NOPATt + 1
Capitalt
94
Options Method
95
What are some types of
real options?
• Investment timing options
• Growth options
– Expansion of existing product line
– New products
– New geographic markets
96
Types of real options (Continued)
• Abandonment options
– Contraction
– Temporary suspension
• Flexibility options
97
Five Procedures for
Valuing Real Options
1.DCF analysis of expected cash flows, ignoring the
option.
2.Qualitative assessment of the real option’s value.
3.Decision tree analysis.
4.Standard model for a corresponding financial
option.
5.Financial engineering techniques.
98
The Most Common Errors in Valuation
99
1. Errors in the discount rate
calculation and concerning the
company’s riskiness
100
A. Wrong risk-free rate used for the
valuation
1. Using the historical average of the risk-free
rate.
2. Using the short-term Government rate.
3. Wrong calculation of the real risk-free rate.
101
B. Wrong beta used for the valuation
1. Using the historical industry beta, or the average of the
betas of similar companies, when the result goes against
common sense.
2. Using the historical beta of the company when the result
goes against common sense.
3. Assuming that the beta calculated from historical data
captures the country risk.
4. Using the wrong formula for levering and unlevering the
beta.
5. Arguing that the best estimation of the beta of a
company from an emerging market is the beta of the
company with respect to the S&P 500.
6. When valuing an acquisition, use the beta of the
acquiring company.
102
B. Wrong market risk premium used for
the valuation
1. The required market risk premium is equal to the
historical equity premium.
2. The required market risk premium is equal to
zero.
3. Assume that the required market risk premium is
the expected risk premium.
103
D. Wrong calculation of WACC
1. Wrong definition of WACC.
2. The debt to equity ratio used to calculate the
WACC is different from the debt to equity ratio
resulting from the valuation.
3. Using discount rates lower than the risk-free
rate.
4. Using the statutory tax rate, instead of the
effective tax rate of the levered company.
5. Valuing all the different businesses of a
diversified company using the same WACC
(same leverage and same Ke).
104
D. Wrong calculation of WACC
6. Considering that WACC/(1-T) is a reasonable
return for the company’s stakeholders.
7. Using the wrong formula for the WACC when the
value of debt is not equal to its book value.
8. Calculating the WACC assuming a certain capital
structure and deducting the outstanding debt
from the enterprise value.
9. Calculating the WACC using book values of debt
and equity.
10. Calculating the WACC using strange formula.
105
E. Wrong calculation of the value
of tax shields
1. Discounting the tax shield using the cost of
debt or the required return to unlevered
equity.
2. Odd or ad-hoc formula.
106
F. Wrong treatment of country risk
1. Not considering the country risk, arguing that it is
diversifiable.
2. Assuming that a disaster in an emerging market will
increase the beta of the country’s companies
calculated with respect to the S&P 500.
3. Assuming that an agreement with a government
agency eliminates country risk.
4. Assuming that the beta provided by Market Guide
with the Bloomberg adjustment incorporates the
illiquidity risk and the small cap premium.
5. Odd calculations of the country risk premium.
107
G. Including an illiquidity, small-cap, or specific
premium when it is not appropriate
1. Including an odd small-cap premium.
2. Including an odd illiquidity premium.
3. Including a small-cap premium equal for all
companies.
108
2. Errors while calculating or
forecasting the expected cash
flows
109
A. Wrong definition of the cash flows
1. Forgetting the increase in Working Capital
Requirements when calculating cash flows.
2. Considering the increase in the company’s cash position
or financial investments as an equity cash flow.
3. Errors in the calculation of the taxes that affect the FCF.
4. Expected Equity Cash Flows are not equal to expected
dividends plus other payments to shareholders (share
repurchases…).
5. Considering net income as a cash flow.
6. Considering net income plus depreciation as a cash flow.
110
B. Errors when valuing seasonal
companies
1. Wrong treatment of seasonal working
capital requirements.
2. Wrong treatment of stocks that are cash
equivalent.
3. Wrong treatment of seasonal debt.
111
C. Errors due to not projecting the
balance sheets
1. Forgetting balance sheet accounts that
affect the cash flows.
2. Considering an asset revaluation as a cash
flow.
3. Interest expenses not equal to D Kd.
112
D. Exaggerated optimism when
forecasting cash flows
113
3. Errors in the calculation of the
residual value
A. Inconsistent cash flow used to calculate perpetuity.
B. The debt to equity ratio used to calculate the WACC to
discount the perpetuity is different from the debt to
equity ratio resulting from the valuation.
C. Using ad hoc formulas that have no economic meaning.
D. Using arithmetic averages instead of geometric averages
to assess growth.
E. Calculating the residual value using the wrong formula.
F. Assume that a perpetuity starts a year before it really
starts.
114
4. Inconsistencies and
conceptual errors
115
A. Conceptual errors about the free cash
flow and the equity cash flow
1. Considering the cash in the company as an equity cash
flow when the company has no plans to distribute it.
2. Using real cash flows and nominal discount rates, or
vice-versa.
3. The free cash flow and the equity cash flow do not
satisfy:
ECF=FCF + D – Int(1- T)
116
B. Errors when using multiples
1. Using the average of multiples extracted from
transactions executed over a very long period of
time.
2. Using the average of transactions multiples that
have a wide scatter.
3. Using multiples in a way that is different to their
definition.
4. Using a multiple from an extraordinary
transaction.
5. Using ad hoc valuation multiples that conflict
with common sense.
6. Using multiples without using common sense.
117
C. Time Inconsistencies
1. Assuming that the equity value will be
constant for the next five years.
2. The equity value or the enterprise value
does not satisfy the time consistency
formula.
118
D. Other conceptual errors
1. Not considering cash flows resulting from future
investments.
2. Considering that a change in economic conditions
invalidates signed contracts.
3. Considering that the value of debt is equal to its book
value when they are different.
4. Not using the correct formula when the value of debt is
not equal to its book value.
5. Including the value of real options that have no
economic meaning.
6. Forgetting to include the value of non-operating assets.
7. Inconsistencies between discount rates and expected
inflation.
119
D. Other conceptual errors
8. Valuing a holding company assuming permanent losses (without
tax savings) in some companies and permanent profits in others.
9. Wrong concept of the optimal capital structure.
10. In mature companies, assuming projected cash flows that are
much higher than historical cash flows without any good reason.
11. Assumptions about future sales, margins, etc. that are
inconsistent with the economic environment, the industry
outlook, or competitive analysis.
12. Considering that the ROE is the return to the shareholders.
13. Considering that the ROA is the return of the debt and equity
holders.
120
D. Other conceptual errors
14. Using different and inconsistent discount rates for cash flows of
different years or for different components of the free cash flow.
15. Using past market returns as a proxy for required return to equity.
16. Adding the liquidation value and the present value of cash flows.
17. Using ad hoc formulas to value intangibles.
18. Arguing that different discounted cash flow methods provide
different valuations.
19. Wrong notion of the meaning of the efficient markets.
20. Applying a discount when valuing diversified companies.
21. Wrong arbitrage arguments.
22. Adding a control premium when it is not appropriate.
121
5.
Errors when interpreting the
valuation
A.
B.
C.
D.
E.
F.
Confusing value with price.
Asserting that “the valuation is a scientific fact, not an opinion”.
A valuation is valid for everybody.
A company has the same value for all buyers.
Confusing strategic value for a buyer with fair market value.
Considering that the goodwill includes the brand value and the
intellectual capital.
G. Forgetting that a valuation is contingent on a set of expectation
about cash flows that will generated and about their riskiness.
H. Affirming that “a valuation is the starting point of a negotiation”.
I. Affirming that “a valuation is 50% art and 50% science”.
122
6. Organizational errors
A. Making a valuation without checking the
forecasts made by the client.
B. Commissioning a valuation from an investment
bank without having any involvement in it.
C. Involving only the finance department in valuing
a target company.
123