Valuation
Techniques
What is (financial) Value?
Different Views on Value
“Value” refers both to general moral values and financial value.
Shareholder Value in Finance assumes that shareholders are
primarily interested in financial value. However, there are also
major shareholders who prioritize other values like
- ethical investors (environment, human rights)
-  family owners (passing on family fortune to future generations)
-  governments (employment, national sovereignty)
-  religious institutions (religious principles)
Accounting view:
Value = Anchoring accounting value + Speculative value
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Different Concepts of Value
Market Value = Current price in the market place (e.g. stock price)
Fair value = “The price that would be received to sell an asset or
paid to transfer a liability in an orderly transaction between market
participants at the measurement date.”(IFRS 13: Appendix A)
Intrinsic value = The value of the asset given a hypothetically
complete understanding of the asset’s investment characteristics.
(Equity Valuation) It is also frequently called Fundamental value
(Wikipedia). Valuation estimates Intrinsic Value.
Company (Firm) Value, V = Market Value of total company, D + E
Enterprise Value = Market Value – (Excess) Cash
V = Operating Assets, Voper + Investment Assets, VInv
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Overview of Valuation Techniques
1. Absolute Valuation Models
Estimates asset’s intrinsic value from asset fundamentals
Dividend Discount Models (DDM)
Discounted Cash Flow Models (DCF)
Free Cash Flow to the Firm
Free Cash Flow to Equity
Abnormal Earnings (Residual Income, Economic Profit)
Adjusted Present Value
Asset-based Valuation
Venture Capital method
2. Relative Valuation Models
Comparables (Multiples)
P/E, P/B, EV/S, EV/EBITDA
3. Real Options Models
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Absolute Valuation
Models
DDM
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Apple stock price and dividends
Dividends: 0.48 (1994), 0.48 (1995), 0.12 (1996), 0 (1997-2011)
5.30 (2012), 14.80 (2013)
Source: Yahoo Finance, Nasdaq
Discounted Dividend Model (DDM)
Powerful insight: Value of company for shareholders is the
present value of all expected future dividends, discounted at
the cost of equity.
D1
D2
Dn
V0 =
+
+...
+
+...
2
n
(1+ r) (1+ r)
(1+ r)
∞
Di
i
i=1 (1+ r)
=∑
where
V0 = Equity value at time 0 (present moment)
Di = Dividend at time i
r = cost of equity (required rate of return for this stock)
Note: Mathematically the series might not converge!
Economically r (Beta and D/E) should remain constant!
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Operationalizing DDM
Use patterns of dividend growth
- constant growth rate (Gordon’s model)
- 2 or 3 growth stages (generalization)
- first T years detailed forecasts, then steady growth (cf. FCF)
Gordon’s constant growth rate (g) model (-1 < g < r)
Dt = D0(1+g)t
V0 = D0(1+g)/(1+r) + D0(1+g)2/(1+r)2 + … + D0(1+g)n/(1+r)n + …
V0 = D0(1+g)/(r-g) = D1/(r-g)
Note: This is a geometric series a = D0(1+g)/(1+r), q = (1+g)/(1+r)
If -1 < q < 1 then the series converges to a/(1-q)
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Dividend Discount Model (DDM) and Growth Rate
Gordon's Model, D0(1+g)/(r-g)
D0 = 100, r = 0.1, -1 < g < 0.1
12000.00
Value of Company V0
10000.00
8000.00
6000.00
4000.00
2000.00
0.00
Growth Rate g
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1-Period DDM and Holding Period Return
Assuming value V0 = market price P0 we get the equation
P0 =
D1 + P1
(1+ r)
From which we obtain Holding Period Return
r = dividend yield + capital appreciation
D1 (P1 − P0 )
+
=
P0
P0
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“Spreadsheet” DDM model
Note: g > r is not possible for ever, Value becomes infinite, and
the Gordon series does not converge!
Value = PV(Detailed Dividend Forecast + Terminal Value)
V0 =
D1
D2
Dn
Pn
+
+...
+
+
(1+ r) (1+ r)2
(1+ r)n (1+r)n
where Pn = Price at n (directly or Gordon’s formula)
Using Gordon’s formula we get
Dn (1+ g)
Pn = Terminal Value =
r−g
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Where do the growth rates come from?
Finance : terminal dividend growth rate < cost of equity
to go beyond sustainable growth requires strategy change
Economics : company growth cannot exceed Industry growth for ever
Near term dividends: detailed analysis of company strategy
Long term dividends: Industry analysis, sustainable growth rate
Sustainable growth rate applies also to dividend growth
g = (1-Dividend Payout) x ROE
= Retention Ratio x
(Net Income/Sales) x (Sales/Assets) x (Assets/Equity)
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DDM Examples
Preferred Stock: Perpetual Dividend 3€, cost of equity 5%,
Value of Preferred = 3/0.05 = 60€
The Growth Rate implied by stock price: Stock Price is 200€,
Cost of equity from CAPM is 7%, Current dividend yield is 5%.
From Gordon’s equation (0.05x200)(1+g)/(0.07-g) = 200 we get
(10+10g)=0.07x200-200g and 210g= 14-10, finally g = 1.9%
Growth rate from long-term ROE: ROE = 10%, Dividend Payout
= 30%, growth rate g = (1-0.3)10% = 7%
Required rate of return: Current Dividend 2€, growth rate 5%,
Stock Price 20€ , from 20 = 2x1.05/(r-0.05) we get
20r-1=2.1 and r = 5.5%
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Features of DDM
•  Conceptually convincing
•  Computationally easy
• 
• 
• 
• 
• 
Dividend policy is irrelevant in perfect markets, not value driver
Problematic with young, growing companies with no dividends
Dividends are decision - not performance – variables
Actual current dividends may differ from sustainable dividends
Need very long forecasting periods, not easy to forecast
•  Basis for other more pragmatic approaches
•  Connected to P/E multiples
•  Works well if stable payout ratio
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Illustration of irrelevance of dividends
Under some conditions dividend policy does not matter at all.
Here is one stylized situation. More discussion later on.
Assume that an all-equity company can produce a return at
cost of equity 10% for all its capital. Let capital C(0) = 100
D(1) = dividends at time 1, D(2) = terminal dividends at time 2.
C(1) = 100*1.1; C(2) = [100*1.1 – D(1)]*1.1 = D(2), then
V = D(1)/1.1 + D(2)/1.1^2
= D(1)/1.1 + [100*1.1 – D(1)]*1.1/1.1^2
= D(1)/1.1 + 100 – D(1)/1.1
= 100 (DOES NOT DEPEND ON TIMING OF DIVIDENDS)
Note: This company provides expected return, no extra value
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Effect of dividend announcements
12.5
1 700 000
12
11.5
1 200 000
11
700 000
10.5
200 000
6
1400000
5.75
1200000
5.5
1000000
800000
5.25
600000
5
400000
4.75
200000
16.75
1 000 000
16.5
800 000
16.25
16
600 000
15.75
400 000
15.5
200 000
Starbucks Corp: Dividend from 0 $ to 0,1$*
13
Volume (shares)
Price (EUR)
YIT Oyj: Dividend from 0,38 € to 0,18 €
1 200 000
Volume (shares)
2 200 000
17
12.75
40000000
35000000
30000000
12.5
25000000
12.25
20000000
12
11.75
Announcement: YIT implements the Torkinmäki public-private
partnership project in Kokkola, Finland in co-operation with
Caverion
15000000
Volume (shares)
13
Price (EUR)
2 700 000
Price (USD)
13.5
Elisa Oyj: Dividend from 0,40 € to 1,30 €
Volume (shares)
Price (EUR)
Elisa Oyj: Dividend from 1,80 € to 0,60 €
10000000
5000000
*Quarterly
Price and volume data source: Google Finance
Effect of dividend announcements
Elisa Oyj: Dividend from 1,80 € to 0,60 €
Elisa Oyj: Dividend from 0,40 € to 1,30 €
•  Elisa is known as a stable dividend
payer
•  Revenues and profit decreased
•  19 % EPS decrease -> 67 %
decrease in dividend
•  Revenues and profit increased
•  33 % EPS increase -> 225 %
increase in dividend
YIT Oyj: Dividend from 0,38 € to 0,18 €
Starbucks Corp: Dividend from 0 $ to
0,1$*
•  Started paying dividend and
announced new dividend policy
•  Implication: no longer a growth
stock
•  Resulted in a short-term price drop
•  Revenue and profit decreased
•  Record housing sales in Russia
and Baltic countries
•  40 % EPS decrease -> 53 %
decrease in dividend
*Quarterly
Price and volume data source: Google Finance
Discounted Cash Flow
Models
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Starbucks Corporation and FCFF
FCFF -$13.2M (1996), -$109.5M (1997), -$67.0M (1998), -$77.2M (1999), -$49.6 (2000)
source: Yahoo Finance, Penman:Financial Statement Analysis and Security Valuation
Free Cash Flow to Firm (FCFF) Model
Mathematically, FCFF uses the same (DCF) formula than DDM. The
interpretation of the variables is different. FCFF uses Free Cash
Flows (to debt and equity) and the discount rate is Weighted
Average Cost of Capital and the result is Corporate Value.
Basic Free Cash Flow to Firm (FCFF) model of corporate value
∞
Corporate Value = NPV(Free Cash Flows) =
FCFi
∑ (1+ WACC)
i
i=1
where FCF(i) = Free Cash Flow in period i
WACC = weighted average cost of capital
Equity Value = Corporate Value – Market Value of Debt
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Operational FCFF model
Detailed Forecast plus Terminal Value
T
V0
FCFi
TVT
+
= ∑
i
T
(1+
WACC)
(1+
WACC)
i=1
where
TVT
=
FCFT +1
WACC − g
!
$
!
$
Debt
Equity
WACC = # Debt + Equity & rd (1− TaxRate) + # Debt + Equity & re
"
%
"
%
Note: Debt and Equity at Market Value
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What is a Free Cash Flow ?
FCFF = How much Cash “Business Operations” produce for
suppliers of capital after tax and after all needed investments in
working capital and non-current capital have been made.
Starting from EBIT (CFA), Popular estimate for valuation forecasts
FCFF = Earnings Before Interest and Taxes(EBIT) x (1 – Tax Rate)
+ Depreciation
- Investments in Fixed Capital
- Investment in Working Capital
Note: Actually paid cash taxes may deviate annually from taxes
calculated with tax rate
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Working Capital for FCF Valuation Purposes
Investments in Working Capital to estimate Cash Flows
available to capital providers do not include Cash & Marketable
Securities or Current Debt as these are not operating items.
Working Capital FOR FCF VALUATION (CFA)
= OPERATING Working Capital (Palepu)
= (Current Assets – Cash and Marketable Securities)
- (Current Liabilities – Current Debt and Current Portion of
Non-Current Debt)
Note: In Financial Statement Analysis the definition is
Working Capital = Current Assets – Current Liabilities
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Variations for estimating FCFF
Starting from Operative Cash Flows (CFA)
FCFF = Cash Flow from Operations
+ Interest Expense* x (1 – Tax Rate)
- Investments in Fixed Capital
Starting from Net Income (CFA), Complicated Accruals
FCFF = Net Income available to common shareholders
+ Net Noncash Charges
+ Interest Expense x (1 – Tax Rate)
- Investments in Fixed Capital
- Investments in Working Capital
* Assuming Interest Expense has been deducted in CFO
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Typical Non-Cash Charges
(starting from Net Income)
Depreciation of tangible assets or long-term bond discounts
Amortization of intangible assets
Depletion of natural resources
Restructuring charges
Losses/Gains on sale of non-operating assets
Write-downs of assets
(Change in Deferred taxes (depends))
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Detailed work on FCFF
Actual, realized FCFF can be measured by standardized Cash
Flow Statement (Palepu).
For valuation forecasting purposes it makes sense to leave out
non-recurring, one-time or extraordinary items for future years.
Also it makes sense to assume nominal or average tax rates
even if starting year taxes had been exceptional.
The purpose is to estimate the cash generating power of
company Operations. For this reason Interest Expense After
Tax have to be added back if they were deducted in CFO.
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Free Cash Flow to Equity (FCFE) Model
Value of Equity is estimated by discounting future Free Cash
Flows to Equity (FCFE) with cost of equity (DCF formula). If there
are not share issues/repurchases, FCFE tells what amount could
be paid out as dividends from annual cash flow.
T
V0 =
FCFEi
∑ (1+ r )
i
i=1
e
+
TVT
(1+ re )T
TVT = FCFET +1
re − g
Various ways to calculate FCFE (CFA)
FCFE = FCFF – Int(1 – Tax Rate) + Net Borrowing
FCFE = NI + NCC – FCInv – WCInv + Net Borrowing
FCFE = CFO –FCInv + Net Borrowing
FCFE from Standardized Cash Flow Statement (Palepu)
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What is WACC?
WACC measures the average cost of capital for the company.
Weights are market weights of Debt and Equity.
!
$
!
$
Debt
Equity
WACC = #" Debt + Equity &% rd (1− TaxRate) + #" Debt + Equity &% re
Tax Rate = Estimate of long-term tax rate, often nominal
rd = Cost of Debt (e.g. from similarly rated companies)
re = Cost of Equity
Cost of Equity from analysts or from two popular models:
re = Risk-free Rate + Beta x Market Equity Premium (CAPM)
re = rf + Beta (Rm – rf) + b Size + c Book-to-Market (Fama&French)
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What are Debt and Equity in WACC?
Both Debt and Equity should be measured in market values.
Normally Debt can be estimated by using book values. Debt is total
interest-bearing liabilities.
Equity = Corporate Value – Debt
Note: Equity is circular in the FCF formula. Two ways out.
Use Target ratios for the weights D/(D+E), E/(D+E)
Solve E from Value, plug it in as E, repeat until converges
Note: To use constant WACC, D/E ratio has to remain constant.
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© 2013 Elroy Dimson, Paul Marsh and Mike Stanton
From: Credit Suisse Global Investment Returns Yearbook 2013
31
Eero Kasanen Interaction Part 4
© 2013 Elroy Dimson, Paul Marsh and Mike Stanton
From: Credit Suisse Global Investment Returns Yearbook 2013
Eero Kasanen Interaction Part 4
32
WACC when capital structure changes
If company wants to change its capital structure (D/(D+E)),
WACC has to be recalculated. Not only do the weights D/(D+E) and
E/(D+E) change but also cost of debt rD and cost of equity rE.
New capital structure is a target figure.
New cost of debt have to be estimated from financial institutions.
New cost of equity can be estimated with CAPM and WACC
Capital structure can change for example in
-  Acquisition situation which is financed by new debt or equity issue
-  New equity for major expansion
-  Change of financial strategy
-  In LBO company will be highly leveraged
-  Company purchases its own shares
Eero Kasanen Interaction Part 4
33
Unlevering Beta, D constant
Unlevered (=Asset) betas can be used for two tasks:
-  Eliminating capital structure effect in company beta comparisons.
-  Calculating new cost of equity when target capital structure changes
Starting from equation V = D + E = Vu + TD,
where Vu = Value of unlevered company, TD = Value of Tax Shield
we get Vu = (1-T)D + E. Using the result that Beta of a portfolio is weighted
sum of the Betas of the assets in the portfolio, we have
BU =
(1− T )D
E
BD +
BE
(1− T )D + E
(1− T )D + E
Often it is assumed that BD = 0. Then dividing by E we have
BU =
1
"D%
1+ (1− T ) $ '
#E&
BE
(Hamada formula, see Palepu p. 334)
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Unlevering Beta, D/E constant
To keep WACC constant in TV growth, D/E has to be constant.
Then the following formula should be used for unlevering
(
D"
TrD % +
* BL + $1−
' BD E
1+
r
#
)
,
D&
BU =
D"
TrD %
1+ $1−
'
E # 1+ rD &
And for relevering, same thing solved for BL
( D"
TrD %+
D"
TrD %
BL = *1+ $1−
'- BU − $1−
' BD
E
1+
r
E
1+
r
#
#
)
D &,
D&
See: Titman & Martin: Valuation, p.334
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Unlevering and relevering Beta
(here assuming D constant, BD=0, and using Hamada formula)
BetaUnlevered = BetaLevered / (1 + (1-T)(D/E)old)
where BetaUnlevered = BetaAsset = Beta of all-equity version of company
BetaLevered = Beta of company with existing D/E ratio
T = corporate tax rate
(D/E)old = existing debt-to-equity ratio in market values
Relevered beta is the beta with new capital structure.
BetaRelevered = BetaUnlevered(1 + (1-T)(D/E)new)
where (D/E)new = new target debt-to-equity ratio in market values
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Calculating new WACC
using Hamada formula
Old WACC
D=40, E=60, D/E = 0.667, rd = 3.5%, rf = 3%, MRP = 3%, Beta = 1.1,
T = 25%, from these it follows
re = 3% + 1.1x3% = 6.3%
WACC = 3.5%(40/(40+60))(1-25%) + 6.3%(60/(40+60)) = 4.83%
New WACC
New D/E = 60/40 = 1.5
Unlevered Beta = 1.1/(1+(1-25%)0.667) = 0.733
Relevered Beta = 0.733(1+(1-25%)1.5) = 1.558
New re = 3% + 1.558x3% = 7.68%
New price of debt (from bank) rd = 3.6%
New WACC = 3.6%(60/(60+40))(1-25%) + 7.68%(40/(60+40)) = 4.69%
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Excess Cash in FCF
If there is substantial excess cash (or other non-operating assets)
not needed in operations, it can be taken out by treating it
separately(CFA). Two “companies”: Operations and Cash.
VC = Value of the company = Value of Operations + Excess Cash
BC =
VO
Cash
BO +
BCash
VO +Cash
VO +Cash
and setting Bcash = 0 we have
BetaOperations = BetaCompany x ( Value of the Company / Excess Cash)
Alternatively BetaOperations can be estimated from comparables.
Cost of Equity re = rf + BetaOperations (Rm – rf) will change.
Note: Excess Cash have to be backed out from Assets and Equity.
Interest Income from Excess Cash has to be deducted.
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Preferred Stock in FCF
Preferred Stock is another source of capital:
WACC =
D
E
P
rD (1− T ) +
rE +
rP
D+E+P
D+E+P
D+E+P
FCFF = calculated from EBIT the same way
(Common) Equity = Company Value – Debt – Value of Preferred
Value of Preferred Stock from Gordon’s formula = PrefDiv/rP
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Minority Interests and several classes
of shares in FCF
FCF produces an estimate of Equity Value for all equity holders.
If there is a sizable Minority Interest in Total Equity then the
Value of Equity for Shareholders of the company can be roughly
estimated from initial Balance Sheet.
Equity for Shareholders = Equity(FCF) x ( 1 -
Minority Interest
)
Total Equity
Similarly, If there are several classes of shares, the Value of a
share class can be roughly estimated from initial market values.
Equity Class n = Equity(FCF) x
Market Value of Class n
Market Value of All Classes of Shares
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Estimating Terminal Value
Empirically, in FCF most of the value is in Terminal Value.
Terminal Value is driven by the choice of growth rate g.
Growth g cannot exceed cost of equity or sustainable ROE.
Negative Terminal Value FCF is not realistic. Why?
Terminal Value Free Cash Flow, FCFT+1 (especially Investments)
has to match supposed growth rate g (not the same as growth
rate from 1 to T !).
For example, In “No-Growth” scenario (g = 0)
WCInv = 0, FCInv = Depr, TVT = FCFT+1/WACC
In practice Terminal Value is also estimated by multiples
TVT = (EV/EBITDA)*EBITDAT
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Popular Valuation Version
(more advanced version for re)
Free Cash Flow to Firm, calculated from EBIT
Weighted Average Cost of Capital, after tax (nominal rate)
Gross Debt in WACC
Target (Market) Weights in WACC
Risk-Free Rate from Long-term Government Bonds
Equity Risk Premium from historical country averages
Beta from published estimates
Cost of Equity from CAPM (Fama&French formula)
Beta re-leverage with Hamada correction (D/E constant formula)
Cost of Debt from actual company rates
(Terminal Value from EV/EBITDA multiples)
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Strengths and challenges of FCFF
Strengths
strong link to finance theory and NPV
not dependent on accounting rules or choices
popular among investment bankers
cash flows are easy to understand and “real”
Challenges
FCFF can be negative for extended period of time
Requires long forecasting periods
Most of the value often in uncertain Terminal Value
Easy to make unrealistic forecasts (check Balance Sheet)
Lots of moving parts (FCFF, BetaE, BetaD, D/E, g)
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Accruals Based
Valuation Models
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Discounted
Abnormal Earnings
Model
Abnormal Earnings Model (Palepu)
Residual Income Model (CFA)
Both FCFE and Abnormal Earnings estimate Dividends. Both
models are based on DDM Model.
BVE = Book Value of Equity. Starting from Accounting Equation
we get Dividends
BVEt+1 = BVEt + Net Profitt – Dividendst
Dividendst = Net Profitt – (BVEt+1 – BVEt)
Using DDM we obtain the formula
Net Profit1 − re BVE0 Net Profit 2 − re BVE1
+
+...
V0 = BVE0 +
2
(1+ re )
(1+ re )
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Interpreting Abnormal Earnings Model
To hold strictly it requires “clean surplus” accounting, meaning all
income goes through Net Income. If Comprehensive Income items
are big and do not seem to reverse to zero then Net Income has to be
adjusted. Typical items in Comprehensive Income
- foreign currency translation
- pension fund adjustments
- fair-value changes of financial instruments
Abnormal Earnings Model (Palepu) is also called Residual Income
Model (CFA). Economic Profit Model (McKinsey) or Economic Value
Added Model (Stern Stewart) are similar but use Capital Charge on
Total Capital.
Abnormal Earnings is Profit over and above the required rate of
return for company equity re times Beginning Equity (Equity Charge).
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Operational Abnormal Earnings Model
As Net Profitt = ROEt x BVEt-1 Abnormal Earnings Model becomes
∞
(ROEt − re )Bt−1
(1+ re )t
t=1
V0 = B0 + ∑
If company is growing at sustainable growth rate g (=bROE) then
Bt = B0(1+g)t and by geometric series we get
(ROE-re ) ∞ B0 (1+ g)t−1
(ROE − re )B0
V0 = B0 +
=
B
+
∑
0
(1+ re ) t=1 (1+ r)t−1
re − g
Note: If ROE = re then V0 = B0 (no additional value in the future)
Here sales growth g (<ROE) does not matter. (why?)
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Terminal values in AEM
In AEM Terminal Value is of different kind as in FCF. Terminal
Value in
T
(ROEt − re )Bt−1
TVT
+
V0 = B0 + ∑
t
T
t=1
(1+ re )
(1+ re )
is driven by competitive assumptions on long-term ROE:
1)  If competitive advantage disappears after T, then ROE = re,
Abnormal Earnings (Residual Income) and TVT = 0.
2)  Nominal level of competitive advantage in terms of
Abnormal Earnings will remain constant after T, then
TVT =
(ROE − re )BT
re
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Terminal Values in AEM
3) Competitive advantage is so strong that the company grows
at sustainable growth rate g, with ROE > re > g from time T, then
Abnormal Earnings grow at rate g and
TVT =
(ROE − re )BT
re − g
4) Terminal Value may be estimated as company having a
premium over book value, PT – BT , then
TVT = PT – BT
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DISCOUNTED ABNORMAL EARNINGS EXAMPLE
• 
Down Under Company:
Krishna G. Palepu, Paul M. Healy and Erik Peek, Business Analysis and Valuation: 3rd IFRS Edition
© Copyright Cengage Learning EMEA 2013
Strengths and challenges of AEM(RI)
Strengths:
•  In AEM Terminal Values are typically small
•  (Standardized) Accounting info can be used
•  Connection to competitiveness and ROE
•  Can be applied if DIV = 0, or FCF hard to predict or negative
Challenges:
•  Clean Surplus condition has to hold or adjustments needed
•  Accounting data may need adjustments
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Economic Profit
Valuation Models
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Enterprise Value using Economic Profit
Abnormal Earnings (Residual Income for equity) above were
used to directly value equity. Economic Profit (Residual Income
for firm) can also be used to estimate Enterprise Value.
Economic Profit = Net Operating Profit After Taxest (NOPATt)
- WACC x Book Value of Assetst-1 (BVAt-1)
McKinsey uses this approach and defines analogously
Economic Profit = Net Operating Profit Less Adjusted Taxes
(NOPLAT) – WACC x Invested Capital
= (ROIC – WACC) x Invested Capital.
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Economic Profit Valuation Model
Similarly as Abnormal Earnings model for Equity, Economic
Profit model becomes
V0 = BVA0 +
∞
NOPATt − WACC x BVA t−1
∑
t
(1+
WACC)
t=1
In McKinsey
V0 = Invested Capital0 +
∞
NOPLATt − WACC x Invested Capitalt−1
∑
(1+ WACC)t
t=1
∞
= IC0 +
(ROICt - WACC) x ICt
(1+ WACC)t
t=1
∑
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Adjusted Present
Value (APV)
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Adjusted Present Value (APV)
useful with changing capital structure*
Standard DCF assumes constant capital structure and uses
constant WACC. In LBOs and reorganizations etc. (D/E) levels
change in the beginning and APV is a good choice. Basic idea
of APV is to calculate unlevered company value and tax shields
(and other possible financing side effects) separately:
VCompany = VUnlevered(FCF) + VInterest Tax Shield
Assume that Tax Shields follow fixed Debt schedule during first
T years and have the same discount rate as debt rD, and in
terminal growth as D/E is constant have the same discount rate
as unlevered equity rU. Then we get
*see Titman & Martin: Valuation
APV continues
T
V =∑
T
FCFt
t=1 (1+ rU )
+∑
t
TrD Dt−1
t=1 (1+ rD )
+
t
TVUnlevered
TVTax Shields
+
(1+ rU )T
(1+ rU )T
Terminal Value of Tax Shields TVTax Shields is the difference
between the Terminal Value of Levered Firm and the Unlevered
Firm TVTax Shields = TVLevered Firm – TVUnlevered Firm .
Plugging in the formula, TVUnlevered cancels out, and using
standard TVLevered formula with WACC, we get the final result
T
V =∑
T
FCFt
t=1 (1+ rU )
t
+∑
TrD Dt−1
t=1 (1+ rD )
t
FCFT (1+ g) " 1 %
+
$
'
(1+ WACC)T # (1+ rU )T &
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Numerical example of APV
FCF(1) = 100, FCF(2) = 120, FCF(3) = 140, rD = 5%, BD = 0.3, rUnlevered = 10%, g = 3%
BetaUnlevered = 1.5, T = 25%, D(0) = 900, D(1) = 800, D(2) = 600, rf = 2%, MP = 4%
V(1,T)U = 100/1.1 + 120/1.1^2 + 140/1.1^3 = 295.3
V(1,T)ITS = 0.25*0.05*900/1.05 + 0.25*0.05*800/1.05^2 + 0.25*0.05*600/1.05^3 = 26.3
Assuming target long-term D/E = 0.8 then WACC is obtained from
( D"
TrD %+
D"
TrD %
BL = *1+ $1−
B
−
1−
'- U
$
' BD = 2.45
E # 1+ rD &
) E # 1+ rD &,
re = 0.02 + 2.45*0.04 = 0.118
Expressing D/(D+E), E/(D+E) with (D/E) we have
WACC = (0.8/(1+0.8))*0.75*0.05 + (1/(1+0.8))0.118 = 0.082
TVLevered = 140*1.03/(0.082 – 0.03) = 2773
V = V(1,T)U + V(1,T)ITS + TVLevered /(1+0.082)3 = 2511
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Valuation using
Multiples
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Using Multiples in Valuation
Value multiples are collected from comparable companies
Multiple =
Market Price
Indicator
V0 = Multiple from comparables x Indicator of company
Typical Market Values: Share Price (P), Equity Value (M)
Enterprise Value (EV)
Typical Indicators: Earnings (E), EBITDA, Cash Flow (CF), Sales
(S), Book Value of Equity (B),
Typical Multiples: P/E, P/B, P/S, P/CF, ROE, PEG, EV/EBITDA
Operative Issues in Multiples
Selection of comparables: similarity criteria – industry, country,
accounting system, strategy, size,…
Finding “average” of comparables : median (or weighted
harmonic mean), simple average suffers from outliers
Adjustments: leaving out extraordinary items, standardizing
accounting practices
Choices: Trailing or Forward Multiples, Basic or Diluted
Earnings, Current or Smoothed Multiples
DCF and AEM models provide “justified” Multiple values
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Be Consistent
and check definitions
Several services and sources, including companies in Financial
Statements, publish multiples. But P/E, M/B, EV/EBITDA differ!
SAME DEFINITIONS FOR COMPANY AND ITS PEERS
For example check: Gross vs Net Debt, CFO vs CF, Common vs
Total Equity, Unadjusted or Adjusted Financial Statements,
Undiluted or Diluted EPS, Nominal vs. Effective Tax Rates,…
Stockmann 2014, Equity Ratio = (Equity plus non-controlling interests)/
(Total Assets less Advance payments received)
Verkkokauppa 2014, Equity Ratio = (Equity plus depreciation reserve*(1 –
tax rate))/(Total sum of the balance sheet – advances received)
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Amazon stock price,
no dividends
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Amazon P/E ratio
compare Dell(2000) P/E = 88, price from $58 to $13.75 and exit(2013)
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Price to Earnings (P/E)
Consistency: Price of common stock and Earnings available to
Common Stock (after Minority Interest and after Preferred Stock).
P/E =
Price of Common Stock (P)
Earnings Per Share (EPS)
In EPS, the number of shares refers to outstanding common
shares (exluding any potential Treasury Stocks).
Adjustments:
Diluted EPS more comparable
Non-recurring components can be taken away
Differences in accounting practices can be corrected
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P/E Variations
Industries and companies can be cyclical, have negative
Earnings, or face transitions, then different versions can be better
in finding the “true” intrinsic value and comparability
trailing P/E Earnings:
previous 12 months, fiscal year, actual or corrected
trailing P/E averaged over several years
leading P/E Earnings forecast:
ongoing calendar year, ongoing fiscal year, next calendar
year, next fiscal year
PEG = (P/E)/Growth rate
popular practical investor metric
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“Justified”(Intrinsic) P/E
A detailed valuation model gives an estimate of intrinsic P (and
next year’s Earnings). The estimate can be communicated
through P/E.
Justified P/E =
Value of Common Equity from Model
(Trailing or Leading) Earnings
DDM and P/E connection can be expressed analytically
Leading P/E = P0/E1 = [D1/(re - g)]/E1 = (1 – b)/(re – g)
Trailing P/E = P0/E0 = [D0(1+g)/(re – g)]/E0 = (1 – b)(1 + g)/(re – g)
where b = retention rate
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Sony P/B ratio
(P/E = 20.45, FCF $7.2B, ROE = 4.7%)
Source ycharts.com
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Price to Book (P/B)
Consistency: Price of common stock is related to book value of
equity belonging to common shareholders (no Preferred Stock
or Minority Interest).
Market Capitalization (MV)
Price of Common Stock (P)
P/B =
= Book Value of Common Equity (BVE)
Book Value Per Share (BPS)
In BPS the number of shares is the number of outstanding
shares belonging to common shareholders (no Treasury Stock)
Note: One variant is to deduct Intangible Assets, especially
Goodwill, from the Book Value.
Note P/B = (P/E) x ROE
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P/B and fundamentals
Valuation results can be communicated as implied P/B.
DDM and AEM have analytical connection to P/B
Gordon’s formula and equations E1 = ROE x B0 , b = g/ROE
lead to
DIV1
B0 ROE(1- g/ROE) ROE − g
=
=
P0/B0 =
B0 (r − g)
B0 (r − g)
r−g
AEM (RI) formula produces the connection
∞
(ROEt − re )Bt−1
∑ (1+ r )t
e
P0/B0 = 1 + t=1
= 1 + Present Value of Abnormal Earnings
B0
B0
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Price to Sales (P/S)
P/S relates price to “Top Line” which is positive for most
companies.
P/S =
Share Price
Net Sales per share
Net Sales = Total Sales – Customer Discounts – Returns
P/S and fundamentals from Gordon’s formula and D0 = E0(1-b)
becomes
P0/S0 = (E 0 / S0 )(1− b)(1+ g)
r−g
Note: P/S = (P/E) x Profit Margin
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Price to Cash Flow (P/CF)
P/CF relates Price to Cash Flow which is not dependent on
accounting choices (compared to P/E).
P/CF =
Share Price
Cash Flow per Share
Where Cash Flow is (CFA):
CF = EPS + Noncash Charges (Depreciation, Amortization,
Depletion) per share [simple approximation]
Following definitions can also be used in practice (Check out)
Cash Flow = CFO (Cash Flow from Operations) per share
Cash Flow = FCFE per share
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P/FCFE and fundamentals
If Free Cash Flow to Equity (FCFE) model, with steady state
growth g from beginning, is used then
1+ g
P0/FCFE0 =
re − g
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Enterprise Value to EBITDA (EV/EBITDA)
Consistency: Enterprise Value (Net Debt plus Equity (Including
Preferred Stock) ) is related to Profit available for both debt and
equity (incl. Pref.Stock) holders. (Note: EBITDA is also an
approximation of Cash Flow from Operations)
EV/EBITDA =
Enterprise Value
Earnings Before Interest, Taxes, Depreciation and Amortization
where
Enterprise Value* (CFA) = Equity + Net Debt
= (Market Value of Common Equity + Market Value of Preferred
Stock + Minority Interest) + (Market Value of Debt – (Excess) Cash)
* If (Excess) Cash = 0 then Enterprise Value = Firm Value
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Multiples and key ratios
25,5
22,3
20,8
P/E
P/S
3,8
2,1
2,3
Company
Sales
growth
Gross
margin
Operatin
g margin
Debt to
equity
1%
61,70
%
24 %
1,47
-3,20 %
55,50
%
15 %
1,90
3,80 %
58,50
%
19 %
1,19
9,50 %
58,90
%
32 %
No debt
8,9
6,1
P/B
59,3
6,5
8,8
15,5
Source: Yahoo! Finance & Market Realist. June 23, 2015
Multiple
Strengths
Challenges
P/E
EPS actively followed and forecasted
Widely used
Direct link to DDM and ROE
EPS can be negative or zero making P/E
unusable
Hard to distinguish ”Recurring” and ”Nonrecurring” earnings
Hard to compare internationally
P/B
Can be used even if EPS < 0
Book value is stable
Connection to Fama&French, DDM, AEM
and P/E
Book values do not account for human
capital and brands
Book values may differ due to strategy
Share repurchases distort P/B
P/S
Can be used even if EPS < 0
More stable than P/E
Not consistent: sales refers to enterprise,
share price to equity
Profitability not taken into account
Revenue recognition practices may distort
comparisons
P/CF
CF less subject to manipulation than
earnings
Not affected by accounting policy
differences
CF more stable than earnings
EPS + Noncash charges is not right for
working capital
FCFE can be negative
EV/EBITDA
EBITDA is often positive when EPS is
negative
More consistent than P/E for varying
leverages
EBITDA is less dependent on accounting
policies than Net Profit
EBITDA is not treating working capital
properly
Different Fixed Capital may distort analysis
Venture Capital Method
Based on target return rVC for Venture Capitalist in exit at T.
1.  Project how much VC initial investment IVC(0) should be
worth at the end IVC(T). We get IVC(T) = IVC(0)(1 + rVC)T
2.  Project what is the EBITDA(T) and estimate Enterprise Value
EV(T) with multiples = (EV/EBITDA) EBITDA(T).
3.  Calculate Equity Value E(T) = EV(T) – Interest-Bearing Debt –
(Excess) Cash
4.  Calculate which part k Venture Capitalist has to own of
equity to get IVC(T). We have k = IVC(T)/E(T)
5.  Now we know E(0) = IVC(0)/k
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VC Terminology
Post-Money Value of Equity = E(0)
Pre-Money Value of Equity = E(0) – IVC(0)
Example. If IVC(0) = 100, EBITDA(T) = 500, EV/EBITDA = 5, T = 5,
Debt(T) = 300, Cash(T) = 20, rVC = 40% then
IVC(T) = 100(1 + 0.4)5 = 537.8
EV(T) = 5 x 500 = 2500
E(T) = 2500 - 300 – 20 = 2180
k = 537.8/2180 = 0.247
Post-Money Value of Equity = 100/0.247 = 404.9
Pre-Money Value of Equity = 404.9 – 100 = 304.9
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