Valuation Methods for
Corporate Restructuring Transactions
Robert M. Dammon
Tepper School of Business
Carnegie Mellon University
This material is copyright protected and may not be copied, reproduced, or distributed
without the written consent from the author.
©2010 Robert M. Dammon
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Agenda
 Overview of valuation
 Discounted cash flow (DCF) valuation
 Alternative DCF valuation methods
 Estimating residual values
 Estimating the cost of capital (discount rate)
 Multiples valuation
 Trading multiples
 Transaction multiples
 Premiums paid analysis
©2010 Robert M. Dammon
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Overview of Corporate Valuation
©2010 Robert M. Dammon
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Overview of Valuation
 Purpose of valuation:
 Valuing alternative corporate strategies
 Valuing an acquisition target
 Valuing a division as a potential divestiture
 Valuing a change in financial (capital) structure
 In theory, asset values depend upon the present value of
expected future free cash flows.
Value of firm’s assets = PV of expected future FCF
©2010 Robert M. Dammon
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Overview of Valuation
 Securities issued by the firm (primarily debt and equity)
represent claims to the firm’s future free cash flows.
 Hence, the current market prices of these securities should
reflect the market’s estimate of what the firm’s future free cash
flows are worth today.
Value of firm’s assets = PV of expected future FCF
= Value of debt + Value of equity
©2010 Robert M. Dammon
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Overview of Valuation
 In many control contests, outside buyers (acquirers) believe that
they can run the firm’s assets more efficiently, or under a new
strategy, to create higher future cash flows.
 Hence, an outside buyer may be willing to pay a control
premium for the firm’s securities in order to enhance the value
of the firm’s assets.
 Since equityholders own the control rights of the firm,
determining the price that can be paid for the firm’s equity is
generally the objective of most valuation exercises.
©2010 Robert M. Dammon
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Overview of Valuation
 In valuing an acquisition candidate, it is important to determine
the following:
 Stand-alone value of the target company: What is the target
company currently worth on its own? This sets the minimum price
that the seller will consider.
 Synergy value: The value of the revenue enhancements and cost
savings that the acquirer can generate from the acquisition.
 Maximum purchase price: The maximum purchase price is the
sum of the stand-alone value and the synergy value. Any price
above this will destroy value for the acquirer’s shareholders.
 The final purchase price will be determined by the relative
negotiating positions (and skills) of the two companies.
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Overview of Valuation
 The value created for the target firm’s shareholders is equal to
the takeover premium:
Value created for = Purchase - Stand-alone value
target shareholders
price
of target
= Takeover premium
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Overview
 The value created for the acquiring firm’s shareholders is
equal to the value of the synergies less the takeover premium:
Value created for
= Stand-alone value + Value of - Purchase
acquirer shareholders
of target
synergies
price
=
©2010 Robert M. Dammon
Value of - Takeover
synergies
premium
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Illustration
Assumptions:
Stand-alone value of aquirer
Stand-alone value of target
Value of synergies
Purchase price
$10,000
$5,000
$2,000
$6,250
Target firm:
Purchase price
- Stand-alone value of target
Value created for target shareholders
Pct. Gain for target shareholders
$6,250
($5,000)
$1,250
25.00%
Acquiring firm:
Value of synergies
- Takeover premium
Value created for acquiring shareholders
Pct. Gain for acquiring shareholders
$2,000
($1,250)
$750
7.50%
©2010 Robert M. Dammon
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Valuation Methods
 There are three common valuation methods used in valuing an
acquisition candidate:
 Discounted cash flow (DCF)
 Trading Multiples
 Transaction Multiples (and Premiums Paid Analysis)
 Each method has its advantages and disadvantages.
 Multiples valuation is easiest to implement, but also requires a set
of truly “comparable” companies to use in the valuation.
 DCF is the most difficult to implement, but is the most
fundamentally sound approach.
©2010 Robert M. Dammon
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Triangulation
DCF Valuation
Triangulation
provides a range of
values that more
accurately reflects the
actual value of the
company.
Trading
Multiples
Valuation
©2010 Robert M. Dammon
Transaction
Multiples
Valuation
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Valuation Range
1,000
2,000
Trading Multiples
1,200
2,500
Transaction Multiples
600
1,600
Discounted Cash Flow
1,200
1,600
Range of Overlap
©2010 Robert M. Dammon
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Discounted Cash Flow Valuation
©2010 Robert M. Dammon
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Alternative DCF Valuation Methods
 WACC Approach
 Appropriate when the firm’s target debt ratio is fixed over time.
 Value of interest tax shields captured in the discount rate.
 Adjusted Present Value (APV) Approach
 Appropriate when the firm’s target debt ratio is changing over time.
 Value of interest tax shields calculated separately.
 Capital Cash Flow (CCF) Approach
 Appropriate when the firm’s target debt ratio is fixed over time.
 Interest tax shields included in the capital cash flows.
 Cash Flow to Equity (CFE) Approach
 Appropriate when the firm’s target debt ratio is fixed over time.
 Interest tax shields included in the equity cash flows.
 Most appropriate for valuing financial institutions.
©2010 Robert M. Dammon
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NOPAT
1.
Capital CF Approach
2.
WACC Approach
3.
APV Approach
4.
CF to Equity Approach
Plus: Depr. and other
non-cash charges
Less: CapX and
changes in WC
Capital Cash Flows
1
Discount at
unlevered COC
Levered firm value
Plus: Interest tax
shields
2
Operating FCF
Less: A.T. interest
and principal pmts.
3
Discount at
WACC
Levered firm value
©2010 Robert M. Dammon
Equity Cash Flows
4
Discount at
unlevered COC
Discount at levered
cost of equity
Unlevered firm value
Value of equity
Plus: PV of ITS
Plus: Total debt
Levered firm value
Levered firm value
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WACC Approach
©2010 Robert M. Dammon
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WACC Valuation
 The WACC approach to valuation is the most common
approach used in practice.
 The WACC approach involves the following steps:
 Estimate the future free cash flows for a period of 5 to 10 years
(forecast period).
 Estimate a residual (or terminal) value at the end of the forecast
period. The residual value captures the value of all free cash flows
beyond the forecast period.
 Estimate the WACC that is appropriate for the risk of the cash
flows.
 Discount the free cash flows and residual value at the WACC.
©2010 Robert M. Dammon
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WACC Valuation
 Mathematically, the value of the firm using the WACC approach
is:
T
V
t
FCFt
t
(1
W)
1
RVT
(1 W) T
 FCFt = Free cash flow in period t
 RVT = Residual value at the end of period T
 W = Weighted average cost of capital
 V = Total value of the firm (debt plus equity)
©2010 Robert M. Dammon
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WACC Valuation
0
1
2
3
4
5
…
FCF1 FCF2 FCF3 FCF4 FCF5 …
T
FCFT
Present value of FCF over forecast period.
T
t
FCFt
t
1 (1 W)
RVT
(1 W) T
RVT
Present value of residual value at the end
of the forecast period.
©2010 Robert M. Dammon
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Operating FCF
 The calculation of Operating FCF includes the following:
 Operating FCF ignores any and all financing costs (e.g., interest
payments, principal payments, dividends, etc.). It is the FCF
available to pay all capital providers (debt and equity).
 Operating FCF ignores any income or expenses generated by nonoperating assets and liabilities (e.g., excess cash, marketable
securities, or other financial assets).
 Taxes are calculated on operating income directly. The taxes on
operating income do not include the effects of interest tax shields or
the taxes on non-operating income.
 All non-cash charges (e.g., depreciation, amortization, non-cash
compensation expenses, etc.) need to be added back to NOPAT in
calculating Operating FCF.
©2010 Robert M. Dammon
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Operating FCF
 Capital expenditures represent investment in fixed assets that the
company needs to support its future operations.
 Replacement CapX: Capital expenditures needed to replace worn out
plant and equipment.
 Discretionary CapX: Capital expenditures needed to support the
company’s future growth in sales.
 Working capital investments are needed to support the company’s
future growth in sales.
 Typically, working capital is assumed to be a constant percentage of
sales revenues.
 Unlike the accountant’s definition, working capital should exclude any
interest-bearing debt (e.g., short-term debt and current portion of longterm debt), excess cash, and marketable securities.
©2010 Robert M. Dammon
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WACC
WACC Valuation
9.8%
0
1
Forecasts of FCF:
Sales Revenues
- CGS (excluding depreciation)
- Depreciation
- SGA
Operating Profits
- Taxes on Operating Profits
NOPAT
+ Depreciation
Operating Cash Flows
- Additions to WC
- Capital Expenditures
Free Cash Flows
+ Residual Value (levered)1
Present Value (WACC)
Value of Operations
+ Non-operating assets
Enterprise value
- Existing Debt
Equity Value
$0
$0
------------$0
2
$1,000
($640)
($40)
($120)
------------$200
($70)
------------$130
$40
------------$170
($12)
($112)
------------$46
$0
$42
3
$1,120
($717)
($45)
($134)
------------$224
($78)
------------$146
$45
------------$190
($11)
($112)
------------$67
$56
4
$1,232
($788)
($49)
($148)
------------$246
($86)
------------$160
$49
------------$209
($10)
($108)
------------$91
$69
5
$1,331
($852)
($53)
($160)
------------$266
($93)
------------$173
$53
------------$226
($8)
($101)
------------$117
$81
6
$1,410
($903)
($56)
($169)
------------$282
($99)
------------$183
$56
------------$240
($7)
($99)
------------$134
$84
7
$1,481
($948)
($59)
($178)
------------$296
($104)
------------$193
$59
------------$252
($6)
($95)
------------$151
$86
$1,540
($986)
($62)
($185)
------------$308
($108)
------------$200
$62
------------$262
($7)
($115)
------------$140
$2,761
$1,507
$1,924
$0 (e.g., excess cash, marketable securities, unconsolidated subsidiaries)
------------$1,924
($350) (e.g. short-term borrowing, long-term debt, and other interest-bearing liabilities)
------------$1,574 (includes the value of preferred stock and any employee stock options)
©2010 Robert M. Dammon
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Enterprise Value
 Before we can calculate the total enterprise value we need to
add the value of non-operating assets to the value of operations.
EV = Value of Operations + Non-operating assets
 Non-operating assets include:
 Excess cash and marketable securities
 Long-term financial assets
 The value of unconsolidated subsidiaries
©2010 Robert M. Dammon
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Equity Value
 To calculate equity value, we need to subtract total debt (longterm plus short-term), preferred stock, and any other contingent
liabilities from enterprise value (EV).
Equity Value = EV – Debt – Preferred – Other Liabilities
 Other contingent liabilities include:
 Unfunded pension and post-retirement liabilities.
 Capitalized value of operating leases.
 Employee stock options and deferred compensation
 Minority interest
 Off-balance sheet contingent liabilities (e.g., lawsuits).
©2010 Robert M. Dammon
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Estimating Residual Values
©2010 Robert M. Dammon
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WACC
WACC Valuation
9.8%
0
1
Forecasts of FCF:
Sales Revenues
- CGS (excluding depreciation)
- Depreciation
- SGA
Operating Profits
- Taxes on Operating Profits
NOPAT
+ Depreciation
Operating Cash Flows
- Additions to WC
- Capital Expenditures
Free Cash Flows
+ Residual Value (levered)1
Present Value (WACC)
Value of Operations
+ Non-operating assets
Enterprise value
- Existing Debt
Equity Value
$0
$0
------------$0
2
$1,000
($640)
($40)
($120)
------------$200
($70)
------------$130
$40
------------$170
($12)
($112)
------------$46
$0
$42
3
$1,120
($717)
($45)
($134)
------------$224
($78)
------------$146
$45
------------$190
($11)
($112)
------------$67
$56
4
$1,232
($788)
($49)
($148)
------------$246
($86)
------------$160
$49
------------$209
($10)
($108)
------------$91
$69
5
$1,331
($852)
($53)
($160)
------------$266
($93)
------------$173
$53
------------$226
($8)
($101)
------------$117
$81
6
$1,410
($903)
($56)
($169)
------------$282
($99)
------------$183
$56
------------$240
($7)
($99)
------------$134
$84
7
$1,481
($948)
($59)
($178)
------------$296
($104)
------------$193
$59
------------$252
($6)
($95)
------------$151
$86
$1,540
($986)
($62)
($185)
------------$308
($108)
------------$200
$62
------------$262
($7)
($115)
------------$140
$2,761
$1,507
$1,924
$0 (e.g., excess cash, marketable securities, unconsolidated subsidiaries)
------------$1,924
($350) (e.g. short-term borrowing, long-term debt, and other interest-bearing liabilities)
------------$1,574 (includes the value of preferred stock and any employee stock options)
©2010 Robert M. Dammon
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Estimating Residual Value
 The residual (terminal) value captures the remaining value of
the firm at the end of the forecast period.
 Residual values can be estimated in a number of different ways:
 After-tax liquidation value of the assets.
 Multiple of earnings or cash flows in the terminal period.
 Perpetuity growth formula.
 We will focus on using the perpetuity growth formula for
estimating residual values.
©2010 Robert M. Dammon
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Estimating Residual Value
 The standard formula for the present value of a perpetuity that
grows at a constant rate, G, is:
RVT
FCFT 1
W-G
FCFT (1 G)
W-G
where
RVT = residual value of the firm at the end of period T
G = long-run nominal growth rate
W = the nominal weighted average cost of capital (WACC).
©2010 Robert M. Dammon
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Estimating Residual Value
 Recall the definition for free cash flow (FCF):
FCF = NOPAT + Depreciation – CapX – WC
 Now define Net New Investment (NNI) as follows:
NNI = CapX – Depreciation + WC
 This allows us to write FCF as follows:
FCF = NOPAT – NNI
©2010 Robert M. Dammon
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Estimating Residual Values
 Now we make the simplifying assumption that during the
perpetuity period (after date T) the company reinvests a constant
fraction of earnings.
 Define the constant plowback rate, k, as follows:
k
NNI t
,
NOPATt
for all t T
 This allows us to write the FCF for period T as follows:
FCFT = NOPATT(1 – k)
©2010 Robert M. Dammon
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Estimating Residual Value
 Substituting for FCFT in our residual value formula gives us:
RVT
NOPATT (1 - k)(1 G)
W-G
 The next step is to examine the drivers of the company’s longrun nominal growth rate, G. This will allow us to fine tune our
estimate of G and the residual value, RVT.
©2010 Robert M. Dammon
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Long-Run Growth Rate
 Let R denote the long-run marginal Return on Invested Capital
(ROIC).
 This allows us to write the long-run growth rate, G, as follows:
G
NOPATt
NOPATt
1
NNI t x R
NOPATt
kR
 NNIt = [k x NOPATt] is the Net New Investment made by the
company at date t. This marginal investment earns a nominal
return of R per period.
©2010 Robert M. Dammon
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Long-Run Growth Rate
G = kR
 Long-run nominal growth, G, depends upon two things:
 Plowback Rate (k): Fraction of earnings that are reinvested back
into net new investments in the long-run.
 Return on Invested Capital (R): The marginal rate of return the
company earns on investment in the long-run.
©2010 Robert M. Dammon
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Value Driver Formula
 The expression for long-run growth allows us to use the Value
Driver Formula in estimating the residual value, RVT.
RVT
NOPATT (1 G)(1- G/R)
W-G
NOPATT (1 kR)(1 - k)
W - kR
 Notice that you have the flexibility to choose only two of the three
variables: R, k, and G.
©2010 Robert M. Dammon
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Estimating Residual Value
 Estimates of k, G, and R for the perpetuity period are not always
easy to come by. They depend upon many factors, including:
 The long-run growth prospects for the industry.
 Barriers to entry in the industry.
 The firm’s long-run sustainable competitive advantage.
 Economies of scale and scope in the industry.
 The durability of physical capital.
 The rate of technological innovation and obsolescence.
 As mentioned earlier, k, G, and R are interrelated. One need
only estimate two of the three parameters to determine the third.
©2010 Robert M. Dammon
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Empirical Evidence on ROIC and Growth
 Estimating ROIC and growth for the residual value formula
should reflect the company’s long-run prospects.
 To understand the sustainability of ROIC and growth over the
long-run, it is worth spending some time discussing the
empirical evidence.
 The empirical evidence shown on the following pages comes
from Chapter 6 of Valuation: Measuring and Managing the
Value of Companies, T. Koller, M. Goedhart, and D. Wessels.
©2010 Robert M. Dammon
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ROIC Distribution for Non-Financial Companies
Source: Valuation: Measuring and Managing the Value of Companies, T. Koller, M. Goedhart, and D.
Wessels, Wiley, 4th edition, pg.147.
©2010 Robert M. Dammon
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ROIC By Industry Group
Source: Valuation: Measuring and Managing the Value of Companies, T. Koller, M. Goedhart, and D.
Wessels, Wiley, 4th edition, pg.148.
©2010 Robert M. Dammon
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ROIC Decay Analysis: Non-Financial Companies
Source: Valuation: Measuring and Managing the Value of Companies, T. Koller, M. Goedhart, and D.
Wessels, Wiley, 4th edition, pg.150.
©2010 Robert M. Dammon
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ROIC Transition Probability, 1994-2003
Source: Valuation: Measuring and Managing the Value of Companies, T. Koller, M. Goedhart, and D.
Wessels, Wiley, 4th edition, pg.152.
©2010 Robert M. Dammon
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Revenue Growth By Industry
Source: Valuation: Measuring and Managing the Value of Companies, T. Koller, M. Goedhart, and D.
Wessels, Wiley, 4th edition, pg.154.
©2010 Robert M. Dammon
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Revenue Growth Decay Analysis
Source: Valuation: Measuring and Managing the Value of Companies, T. Koller, M. Goedhart, and D.
Wessels, Wiley, 4th edition, pg.158.
©2010 Robert M. Dammon
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Revenue Growth Transition Probability,
1994-2003
Source: Valuation: Measuring and Managing the Value of Companies, T. Koller, M. Goedhart, and D.
Wessels, Wiley, 4th edition, pg.159.
©2010 Robert M. Dammon
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Implications for Residual Values
 The empirical evidence on the sustainability of ROIC and growth
has important implications for estimating residual values.
 Companies with barriers to entry and sustainable competitive
advantage, such as patents and brands, tend to earn high ROICs.
 Companies in competitive industries with few barriers to entry tend
to earn relatively low ROICs.
 High ROICs tend to decline over time, but are still somewhat
persistent.
 High growth rates are unsustainable and decay quickly.
 Companies growing faster than 20% per year (in real terms)
typically grow at only 8% within 5 years and 5% within 10 years.
 In the long-run, no company can grow faster than the overall
economy.
©2010 Robert M. Dammon
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Residual Value Calculation
 The residual value included in the WACC valuation shown
earlier was based upon the following assumptions:
Perpetuity Assumptions:
Nominal ROI (R )
Nominal growth rate (G)
15.0%
4.5%
Perpetuity Calculations:
Plowback rate (k)
Residual Value (levered)
30.0%
$2,761
©2010 Robert M. Dammon
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Residual Value Calculation
 Substituting the values of R, G, and k into the Value Driver
Formula yields the following residual value:
RVT
NOPATT (1 G)(1 G/R)
W-R
$200(1.045)(1 .045/.15)
$2,761
.098 - .045
©2010 Robert M. Dammon
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Using Multiples to Estimate Residual Values
 Sometimes I-Bankers will use a multiple of NOPAT (or other
income item such as Sales, EBIT, or EBITDA) to estimate
residual values.
RVT
Multiple x NOPATT
 Using the Value Driver formula, an explicit expression can be
derived for the I-Bankers’ NOPAT multiple:
Multiple
©2010 Robert M. Dammon
(1 G)(1 - k)
W-G
48
Common Mistakes
 There are two common mistakes in estimating residual values
that can have a major impact on the valuation analysis:
 Underestimating the amount of capital investment needed to
support long-run growth.
 Using a multiple to calculate the residual value that implies an
unrealistically high long-run growth rate, G, or long-run ROIC.
 To illustrate, consider the following changes to the forecasts in
the terminal year of our earlier WACC valuation (FCF forecasts
for years 1-6 remain unchanged):
 Capital expenditures = Depreciation
 Residual Value = 18 x NOPAT
 What do these assumptions imply about long-run growth, G, and
long-run ROIC? Do they seem reasonable?
©2010 Robert M. Dammon
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WACC
9.8%
0
7
Fore ca sts of FCF:
Sales Revenues
- CGS (excluding depreciation)
- Depreciation
- SGA
Operating Profits
- Taxes on Operating Profits
NOPAT
+ Depreciation
Operating Cash Flows
- Additions to WC
- Capital Expenditures
Free Cash Flows
+ Residual Value (levered)1
Present Value (WACC)
Value of Operations
+ Non-operating assets
Enterprise value
- Existing Debt
Equity Value
©2010 Robert M. Dammon
$0
$0
------------$0
$0
$2,390
$0
------------$2,390
($350)
------------$2,040
$1,540
($986)
($62)
($185)
------------$308
($108)
------------$200
$62
------------$262
($7)
($62)
------------$193
$3,604
$1,973
CapX = Dep.
RV = 18 x NOPAT
Equity value increase
of $466 or 29.6%
50
Common Mistakes
 We can use the perpetuity formula to back out from the residual
value the long-run growth rate, G, that is implied by the NOPAT
multiple of 18x.
RVT
$3,604
FCFT (1 G)
W -G
$193(1 G)
.098 - G
G 4.22%
 The implied long-run growth rate is actually lower than we had
assumed initially (4.5%), despite the fact that the residual value
itself is now higher than before ($2,761).
©2010 Robert M. Dammon
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Common Mistakes: An Illustration
 The problem is that the residual value is based on an
unreasonably low plowback rate, k:
NNI T
NOPATT
k
$7
3.5%
$200
 With a terminal growth rate of G = 4.22% and a plowback rate of k
= 3.5%, the implied long-run marginal ROIC is unreasonably high:
R
©2010 Robert M. Dammon
G
k
4.22%
120.6%
3.5%
52
Common Mistakes: An Illustration
 This example illustrates the importance of making forecasts of
FCF and residual values that are consistent with the
fundamental relationship:
G=kR
 The table on the next page shows the plowback rates, k, and
NOPAT multiples that are internally consistent with various
combinations of long-run growth, G, and long-run ROIC.
©2010 Robert M. Dammon
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Common Mistakes: An Illustration
WACC
ROIC
10.0%
12.5%
15.0%
17.5%
20.0%
ROIC
10.0%
12.5%
15.0%
17.5%
20.0%
9.8%
0.00%
0.0%
0.0%
0.0%
0.0%
0.0%
0.00%
10.2
10.2
10.2
10.2
10.2
1.50%
15.0%
12.0%
10.0%
8.6%
7.5%
Required Plowback Rates, k
Long-Run Growth Rate, G
3.00%
4.50%
6.00%
7.50%
30.0%
45.0%
60.0%
75.0%
24.0%
36.0%
48.0%
60.0%
20.0%
30.0%
40.0%
50.0%
17.1%
25.7%
34.3%
42.9%
15.0%
22.5%
30.0%
37.5%
9.00%
90.0%
72.0%
60.0%
51.4%
45.0%
1.50%
10.4
10.8
11.0
11.2
11.3
Implied NOPAT Multiple
Long-Run Growth Rate, G
3.00%
4.50%
6.00%
7.50%
10.6
10.8
11.2
11.7
11.5
12.6
14.5
18.7
12.1
13.8
16.7
23.4
12.6
14.6
18.3
26.7
12.9
15.3
19.5
29.2
9.00%
13.6
38.2
54.5
66.2
74.9
©2010 Robert M. Dammon
54
Estimating the Cost of Capital
©2010 Robert M. Dammon
55
Estimating the WACC
 The textbook formula for the nominal WACC is:
W R D (1- t c )
D
V
RE
E
V
where
RD = cost of debt
RE = cost of equity
tc = corporate tax rate
D/V = debt-to-value ratio (based upon market values)
E/V = equity-to-value ratio (based upon market values)
©2010 Robert M. Dammon
56
Estimating the WACC
 The WACC should reflect the risk and debt capacity of the
cash flows that are being valued.
 The WACC that is used to value a target company should reflect
the risk and debt capacity of the target.
 This means that the cost of capital for the acquiring company is
irrelevant for valuing the cash flows of the target company.
 What matters to your shareholders is that they receive a return on
the investment that compensates them for the risk of the
investment being made.
 The cost of capital must always reflect the risk of the marginal
investment, not the risk of the company’s existing assets.
©2010 Robert M. Dammon
57
Cost of Capital
 To illustrate, suppose Company A is considering an acquisition of
Company T.
 Company A is in a low-risk business and has a WACC = 8%.
 Company T is in a high-risk business and has a WACC = 15%.
 Company A plans to finance the acquisition with cash that is currently
invested in Treasury bills that earn an after-tax return of 2%.
 What is the most appropriate cost of capital to use to evaluate an
investment in Company T?
 What rate of return would Company A’s shareholders be able to
earn on a similar investment in the capital markets?
 If Company A acquires Company T, what will likely happen to
Company A’s WACC?
©2010 Robert M. Dammon
58
Cost of
Capital
Risk-adjusted
cost of capital
Company T’s
Cost of Capital
Company A’s
Cost of Capital
Rate of return
on T bills
Risk
Risk of Company
A’s business
©2010 Robert M. Dammon
Risk of Company
T’s business
59
Cost of Equity
 The cost of equity is the rate of return (dividends plus capital
appreciation) that investors expect to earn from holding the
company’s equity.
 The cost of equity is typically estimated using some equilibrium
asset pricing model such as the CAPM or multi-factor model.
 For example, the CAPM provides the following estimate of the
cost of equity:
RE
©2010 Robert M. Dammon
R F [R M - R F ]
E
60
Cost of Equity
 RF is the risk-free interest rate.
 Since equity is a long-term security, we typically use the YTM on
the 30-year government bond as an estimate of Rf.
 [RM – RF] is the market risk premium.
 The MRP measures the expected difference between the rate of
return on a well-diversified portfolio of stocks and the long-term
government bond rate.
 Historically, in the U.S., stocks have outperformed long-term
government bonds by about 6% per annum since 1928.
 In recent years, academics and practitioners have forecasted an
equity risk premium closer to the 4% to 6% range.
©2010 Robert M. Dammon
61
Historical Returns and Risk Premia
1928-2009
Arithmetic Average Annual Returns and Risk Premia, 1928-2009
Stocks
Treasury
Bills
Treasury
Bonds
Stocks Bills
Stocks Bonds
1928-2009
11.27%
3.74%
5.24%
7.53%
6.03%
1960-2009
10.81%
5.33%
7.03%
5.48%
3.78%
2000-2009
1.15%
2.74%
6.62%
-1.59%
-5.47%
©2010 Robert M. Dammon
62
Levered Equity Betas

E
is the levered equity beta. It reflects two things:
 The systematic business risk of the company as measured by the
asset (unlevered) beta, U
 The financial risk of the company as measured by the target debtto-equity ratio, D/E.
 Betas are not directly observable, but must be statistically
estimated from historical returns.
 Typically, betas are estimated using historical monthly returns over
the previous 5 year period.
 Estimates of beta can be found from a number of different sources
(e.g., Value Line Investment Survey, Yahoo!Finance, Google, etc.).
 Industry betas tend to be more stable and, therefore, more reliable
than company betas.
©2010 Robert M. Dammon
63
Asset Betas and Levered Equity Betas
 Miller and Modigliani argued that the total market value of the
firm’s debt and equity securities must be equal to the value of the
firm’s assets, including the interest tax shields on debt.
VL = VU + VITS = D + E
 Taking this a step further, the risk of a portfolio of the firm’s debt
and equity securities must be equal to the risk of the firm’s assets.
U
VU
VL
©2010 Robert M. Dammon
ITS
VITS
VL
D
D
VL
E
E
VL
64
Asset Betas and Levered Equity Betas
 The previous relationship can be rearranged to provide a general
expression for the asset (unlevered) beta:
U
D
D
VU
E
E
VU
VITS
VU
ITS
 Rearranging the above formula provides a general expression for
the levered equity beta:
E
©2010 Robert M. Dammon
U
VU
E
ITS
VITS
E
D
D
E
65
Special Cases
 The formulas on the previous page are not very practical without
some additional assumptions that will allow us to pin down ITS
and/or VITS.
 There are four cases in particular that we want to consider:

1.
Modigliani-Miller (1958): No corporate taxes (tc = 0).
2.
Modigliani-Miller (1963): Company maintains a constant dollar
amount of debt, D, in its capital structure for the indefinite future.
3.
Harris-Pringle (1985): Company continuously adjusts its capital
structure to maintain a constant D/V ratio.
4.
Miles-Ezzell (1980): Company adjusts its capital structure on an
annual basis back to its target D/V ratio.
The table on the next page summarizes the results. The
derivations can be found in the appendix.
©2010 Robert M. Dammon
66
Asset Betas and Levered Equity Betas Under
Different Capital Structure Policies.
Theories
Assumptions
Implications
Asset Beta
Levered Equity Beta
Modigliani
-Miller
(1958)
No corporate
taxes.
VITS = 0
BU = BD(D/V) + BE(E/V)
BE = BU + (BU –BD)(D/E)
Modigliani
-Miller
(1963)
Constant and
perpetual debt
level, D.
VITS = tCD
BITS = BD
BU = BD(1-tc)(D/V)
+ BE(E/V)
BE = BU + (BU –BD)(1tc)(D/E)
HarrisPringle
(1985)
Continuous
adjustment to
maintain a
constant D/V ratio.
VITS > 0
BITS = BU
BU = BD(D/V) + BE(E/V)
BE = BU + (BU –BD)(D/E)
MilesEzzell
(1980)
Annual adjustment
back to the target
D/V ratio.
VITS > 0
BD < BITS < BU
BU = BD(1-tcq)[D/(V-tCqD)]
+ BE[E/(V-tCqD)]
BE = BU + (BU –BD)(1tcq)(D/E)
1. In all formulas, D and E represent the market values of debt and equity, respectively, and V = D+E is
the value of the levered firm.
2. In the Miles-Ezzell (1980) formulas, q = RD/(1+RD).
©2010 Robert M. Dammon
67
Some Comments on Harris-Pringle (1985)
 Notice that the Harris-Pringle (1985) beta formulas are the same
as those without corporate taxes!
 Without corporate taxes the value of the interest tax shields is zero,
VITS = 0.
 When the firm continuously adjusts its capital structure to maintain a
constant D/V ratio the risk of the interest tax shields is the same as
the risk of the assets themselves, ITS = U (see appendix).
 Both sets of assumptions result in an asset beta, U, that is a
weighted average of the debt beta, D, and equity beta, E.
 Both sets of assumptions will also produce the same unlevered cost
of capital, RU, and the levered cost of equity, RE.
 However, because interest is tax deductible, the WACC will be lower
in the presence of corporate taxes.
©2010 Robert M. Dammon
68
Which Model Should Be Used in Practice?
 It is preferable to use either the Miles-Ezzell (1980) or the HarrisPringle (1985) formulas for levering and unlevering betas:
 Although firms do not adjust their capital structures continuously, or
even annually, they do tend to make adjustments over time toward a
target debt ratio.
 The assumptions underlying the MM (1963) formulas are too
restrictive and, therefore, are less appropriate for use in practice.
 Because the estimates provided by the Miles-Ezzell (1980) and
Harris-Pringle (1985) formulas are very similar, it is much easier to
use the Harris-Pringle (1985) formulas.
©2010 Robert M. Dammon
69
Illustration
 Let’s examine the procedure for estimating the WACC in our
earlier example.
 Assume that the company in that example operates in the
Household Products industry.
 The tables on the following several pages provide levered and
unlevered betas for various industries.
 The average levered equity beta for firms in the Household
Products industry is E = 1.15.
 The average industry D/V = 18.3%.
 The unlevered (asset) beta for the Household Products industry is
U = 0.98 (assuming D = 0.2).
©2010 Robert M. Dammon
70
Industry Betas
Industry
Advertising
Aerospace/Defense
Air Transport
Apparel
Auto & Truck
Auto Parts
Bank
Beverage
Biotechnology
Building Materials
Cable TV
Chemical (Basic)
Chemical (Diversified)
Chemical (Specialty)
Coal
Computer Software/Svcs
Computers/Peripherals
Diversified Co.
Drug
E-Commerce
Educational Services
Electric Util. (Central)
Electric Utility (East)
Electric Utility (West)
Average
Equity Beta
1.60
1.19
1.06
1.30
1.72
1.75
0.75
1.04
1.10
1.45
1.69
1.27
1.37
1.29
1.67
1.02
1.29
1.20
1.11
1.18
0.75
0.79
0.73
0.75
Market
D/E
72.8%
22.9%
70.7%
23.6%
154.5%
51.2%
198.2%
16.9%
14.8%
83.8%
85.2%
20.4%
19.9%
29.0%
23.7%
5.6%
10.9%
138.8%
12.6%
8.7%
7.2%
102.9%
75.7%
90.0%
Market
D/V
42.1%
18.7%
41.4%
19.1%
60.7%
33.9%
66.5%
14.5%
12.9%
45.6%
46.0%
16.9%
16.6%
22.5%
19.1%
5.3%
9.9%
58.1%
11.2%
8.0%
6.7%
50.7%
43.1%
47.4%
Unlevered Beta
(Debt beta = 0)
0.93
0.97
0.62
1.05
0.68
1.16
0.25
0.89
0.96
0.79
0.91
1.06
1.14
1.00
1.35
0.97
1.16
0.50
0.99
1.09
0.70
0.39
0.42
0.39
Unlevered Beta
(Debt beta = 0.2)
1.01
1.01
0.70
1.09
0.80
1.22
0.38
0.92
0.98
0.88
1.00
1.09
1.18
1.04
1.39
0.98
1.18
0.62
1.01
1.10
0.71
0.49
0.50
0.49
Note: The unlevered (asset) beta is calculated using the formula: BU = BE(E/V) + BD(D/V). Two
cases are considered: (1) BD = 0 and (2) BD = 0.2. Equity betas and D/E ratios are taken from
http://pages.stern.nyu.edu/~adamodar/
©2010 Robert M. Dammon
71
Industry Betas
Industry
Electrical Equipment
Electronics
Entertainment
Entertainment Tech
Environmental
Financial Svcs. (Div.)
Food Processing
Foreign Electronics
Funeral Services
Furn/Home Furnishings
Healthcare Information
Heavy Construction
Homebuilding
Hotel/Gaming
Household Products
Human Resources
Industrial Services
Information Services
Insurance (Life)
Insurance (Prop/Cas.)
Internet
Investment Co.
Machinery
Manuf. Housing/RV
Average
Equity Beta
1.41
1.16
1.81
1.32
0.97
1.39
0.86
1.13
1.19
1.52
0.97
1.42
1.45
1.74
1.15
1.38
1.07
1.28
1.38
0.92
1.04
0.76
1.32
1.21
Market
D/E
16.9%
26.4%
56.8%
11.7%
49.4%
305.0%
29.3%
29.1%
56.5%
38.5%
13.6%
7.6%
102.3%
85.9%
22.4%
13.2%
34.0%
23.7%
36.8%
24.0%
2.3%
59.3%
46.8%
4.0%
Market
D/V
14.5%
20.9%
36.2%
10.5%
33.1%
75.3%
22.7%
22.6%
36.1%
27.8%
11.9%
7.0%
50.6%
46.2%
18.3%
11.6%
25.4%
19.1%
26.9%
19.4%
2.2%
37.2%
31.9%
3.8%
Unlevered Beta
(Debt beta = 0)
1.21
0.92
1.15
1.18
0.65
0.34
0.67
0.88
0.76
1.10
0.85
1.32
0.72
0.94
0.94
1.22
0.80
1.03
1.01
0.74
1.02
0.48
0.90
1.16
Unlevered Beta
(Debt beta = 0.2)
1.23
0.96
1.23
1.20
0.72
0.49
0.71
0.92
0.83
1.15
0.88
1.33
0.82
1.03
0.98
1.24
0.85
1.07
1.06
0.78
1.02
0.55
0.96
1.17
Note: The unlevered (asset) beta is calculated using the formula: BU = BE(E/V) + BD(D/V). Two
cases are considered: (1) BD = 0 and (2) BD = 0.2. Equity betas and D/E ratios are taken from
http://pages.stern.nyu.edu/~adamodar/
©2010 Robert M. Dammon
72
Industry Betas
Industry
Maritime
Medical Services
Medical Supplies
Metal Fabricating
Metals & Mining (Div.)
Natural Gas (Div.)
Natural Gas Utility
Newspaper
Office Equip/Supplies
Oil/Gas Distribution
Oilfield Svcs/Equip.
Packaging & Container
Paper/Forest Products
Petroleum (Integrated)
Petroleum (Producing)
Pharmacy Services
Power
Precious Metals
Precision Instrument
Property Management
Public/Private Equity
Publishing
R.E.I.T.
Average
Equity Beta
1.38
0.97
1.04
1.54
1.23
1.29
0.68
1.94
1.19
0.89
1.45
1.20
1.63
1.24
1.16
0.88
1.23
1.18
1.24
1.63
2.40
1.43
1.60
Market
D/E
159.6%
43.1%
11.4%
18.8%
14.8%
47.8%
80.5%
55.7%
56.8%
61.5%
26.0%
61.3%
86.5%
14.4%
27.0%
20.1%
103.6%
8.5%
15.0%
191.9%
169.7%
70.3%
67.5%
Market
D/V
61.5%
30.1%
10.2%
15.8%
12.9%
32.4%
44.6%
35.8%
36.2%
38.1%
20.6%
38.0%
46.4%
12.6%
21.3%
16.7%
50.9%
7.8%
13.1%
65.7%
62.9%
41.3%
40.3%
Unlevered Beta
(Debt beta = 0)
0.53
0.68
0.93
1.30
1.07
0.87
0.38
1.25
0.76
0.55
1.15
0.74
0.87
1.08
0.91
0.73
0.60
1.09
1.08
0.56
0.89
0.84
0.96
Unlevered Beta
(Debt beta = 0.2)
0.65
0.74
0.95
1.33
1.10
0.94
0.47
1.32
0.83
0.63
1.19
0.82
0.97
1.11
0.96
0.77
0.71
1.10
1.10
0.69
1.02
0.92
1.04
Note: The unlevered (asset) beta is calculated using the formula: BU = BE(E/V) + BD(D/V). Two
cases are considered: (1) BD = 0 and (2) BD = 0.2. Equity betas and D/E ratios are taken from
http://pages.stern.nyu.edu/~adamodar/
©2010 Robert M. Dammon
73
Industry Betas
Industry
Railroad
Recreation
Reinsurance
Restaurant
Retail (Special Lines)
Retail Automotive
Retail Building Supply
Retail Store
Retail/Wholesale Food
Securities Brokerage
Semiconductor
Semiconductor Equip
Shoe
Steel (General)
Steel (Integrated)
Telecom. Equipment
Telecom. Services
Thrift
Tobacco
Toiletries/Cosmetics
Trucking
Utility (Foreign)
Water Utility
Wireless Networking
Average
Equity Beta
1.29
1.43
1.07
1.34
1.43
1.46
0.95
1.35
0.73
1.18
1.56
1.93
1.34
1.61
1.85
1.15
1.10
0.73
0.78
1.23
1.30
1.07
0.82
1.50
Market
D/E
33.0%
49.8%
17.7%
22.5%
16.1%
44.6%
19.1%
27.0%
26.2%
281.1%
8.1%
7.3%
3.6%
30.8%
39.3%
10.9%
47.0%
21.7%
22.9%
26.3%
85.3%
101.3%
88.0%
19.8%
Market
D/V
24.8%
33.2%
15.0%
18.4%
13.9%
30.8%
16.1%
21.2%
20.7%
73.8%
7.5%
6.8%
3.4%
23.6%
28.2%
9.8%
32.0%
17.9%
18.7%
20.8%
46.0%
50.3%
46.8%
16.5%
Unlevered Beta
(Debt beta = 0)
0.97
0.95
0.91
1.09
1.23
1.01
0.80
1.06
0.58
0.31
1.44
1.80
1.29
1.23
1.33
1.04
0.75
0.60
0.63
0.97
0.70
0.53
0.44
1.25
Unlevered Beta
(Debt beta = 0.2)
1.02
1.02
0.94
1.13
1.26
1.07
0.83
1.11
0.62
0.46
1.46
1.81
1.30
1.28
1.38
1.06
0.81
0.64
0.67
1.02
0.79
0.63
0.53
1.28
Note: The unlevered (asset) beta is calculated using the formula: BU = BE(E/V) + BD(D/V). Two
cases are considered: (1) BD = 0 and (2) BD = 0.2. Equity betas and D/E ratios are taken from
http://pages.stern.nyu.edu/~adamodar/
©2010 Robert M. Dammon
74
Illustration
 The company for which we want to estimate the WACC has the
following capital structure policy:
 Target debt ratio of D/V = 25%.
 Cost of debt is 130 bps over long-term Treasuries.
 Tax rate of 35%.
 You have also collected the following capital market information:
 The long-term Treasury bond rate is Rf = 5.5%.
 The expected market risk premium is 5.0%.
 What is the cost of debt, the cost of equity, and the WACC for
this company?
©2010 Robert M. Dammon
75
Illustration
 The cost of debt, RD, for the company is:
RD
Treasury Rate Credit Risk Premium
5.5% 1.3% 6.8%
 The debt beta can be calculated using the CAPM relationship:
D
©2010 Robert M. Dammon
RD - RF
RM - RF
1.3%
0.26
5.0%
76
Illustration
 We can now use the asset beta for the industry, along with the
debt beta and target debt ratio for the company, to estimate the
levered equity beta for the company.
E
U
[
U
D
- D]
E
0.98 [0.98 - .26]
©2010 Robert M. Dammon
.25
.75
1.22
77
Illustration
 The cost of equity capital can now be estimated using the CAPM:
RE = 5.5% + (5.0%)(1.22) = 11.6%
 The company’s WACC is:
D
W R D (1 - t c )
V
RE
E
V
6.8%(1- .35)(.25) 11.6%(.75) 9.8%
©2010 Robert M. Dammon
78
Illustration
Cost of Capital Assumptions:
Unlevered (Asset) Beta
L.T. Govt. Bond Rate
Market Risk Premium
Cost of Debt
Tax Rate
Target D/V Ratio
0.98
5.5%
5.0%
6.8%
35.0%
25.0%
Cost of Capital Calculations:
Unlevered COC
Debt Beta
Levered Equity Beta
Cost of Equity
WACC
10.40%
0.26
1.22
11.60%
9.8%
Note: The levered cost of equity is calculated using the
Harris-Pringle (1985) formulas, which assume a
constant D/V ratio.
©2010 Robert M. Dammon
79
Illustration
 The table below summarizes the beta and cost of capital
calculations using the four different approaches discussed
earlier.
Theories
Levered
Equity Beta
Cost of
Equity
WACC
Modigliani-Miller
(1958)
1.22
11.6%
10.4%
Modigliani-Miller
(1963)
1.14
11.2%
9.5%
Harris-Pringle
(1985)
1.22
11.6%
9.8%
Miles-Ezzell
(1980)
1.21
11.6%
9.8%
Note: All calculations assume an unlevered (asset) beta of 0.98, a cost of debt
of 6.8%, a debt beta of 0.26, a debt ratio of D/V = 0.25, and a tax rate of 35%.
©2010 Robert M. Dammon
80
APV Approach
©2010 Robert M. Dammon
81
The APV Approach
 In some cases (e.g., an LBO situation) the debt ratio is changing
over time. This makes the WACC approach to valuation difficult
to implement.
 In these cases, it is easier to rely on the Adjusted Present
Value (APV) approach to valuation:
V = VU + VITS
where
VU = unlevered value
VITS = value of interest tax shields on debt
©2010 Robert M. Dammon
82
The APV Approach
 The unlevered value is calculated by discounting the future
FCFs and unlevered residual value, RVU,T, at the unlevered cost
of capital, RU:
T
VU
t 1
FCFt
(1 R U ) t
RVU,T
(1 R U ) T
 The unlevered cost of capital, RU, can be estimated using the
CAPM:
RU
©2010 Robert M. Dammon
Rf
[R m - R f ]
U
83
Unlevered Residual Value
 The calculation of the unlevered residual value, RVU,T, is based
upon the same Value Driver Formula that we used earlier in the
WACC approach.
 The only difference in calculating the unlevered residual value is
that we will use the unlevered cost of capital, RU, instead of the
WACC.
RVU,T
NOPATT (1 G)(1- G/R)
RU -G
NOPATT (1 kR)(1 - k)
R U - kR
©2010 Robert M. Dammon
84
Discounting Interest Tax Shields
 The appropriate discount rate for the interest tax shields should
reflect the risk of the interest tax shields.
 The risk of the interest tax shields depends upon the firm’s
capital structure policy:
Theories
Assumptions
Implications
Discount Rate for ITS
Modified
ModiglianiMiller (1963)
Constant (or predetermined) future debt
levels, D.
ITS have the same risk as
the debt, BD.
Discount all future ITS at
the pre-tax cost of debt, RD
Harris-Pringle
(1985)
Continuous adjustment
to maintain a constant
D/V ratio.
ITS have the same risk as
the firm’s assets, BU.
Discount all future ITS at
the unlevered cost of
capital, RU.
Miles-Ezzell
(1980)
Annual adjustment back
to the target D/V ratio.
Risk of the ITS is a weighted
average of BD and BU.
Discount the ITS at date t
by (1+RD)(1+RU)t-1
©2010 Robert M. Dammon
85
Illustration: APV Approach
 Let’s use the APV approach to value operations, using the
forecasts provided earlier in the WACC approach.
 The FCF forecasts and calculation of the unlevered value, VU,
are shown on the following page.
 The FCFs used in the APV approach are the same as those used
in the WACC approach.
 The unlevered beta is
RU = 10.4%.
U
= 0.98 and the unlevered cost of capital is
 The company’s tax rate is tc = 35%.
 The long-run ROIC is assumed to be R = 15% and the long-run
growth rate is assumed to be G = 4.5%. This produces a long-run
plowback rate of k = 30%.
©2010 Robert M. Dammon
86
Unlevered COC
10.40%
APV Approach
0
1
NOPAT
4
5
6
7
$146
$160
$173
$183
$193
$200
$0
$0
-------------
$40
------------$170
($12)
($112)
-------------
$45
------------$190
($11)
($112)
-------------
$49
------------$209
($10)
($108)
-------------
$53
------------$226
($8)
($101)
-------------
$56
------------$240
($7)
($99)
-------------
$59
------------$252
($6)
($95)
-------------
$62
------------$262
($7)
($115)
-------------
$0
$46
$67
$91
$117
$134
$151
$140
$83
$2,482
$1,312
Free Cash Flows
+ Residual Value (unlevered)1
Present Value (unlevered COC)
Unlevered Firm Value
3
$130
+ Depreciation
Operating Cash Flows
- Additions to WC
- Capital Expenditures
2
$0
$42
$55
$68
$79
$82
$1,721
Note: The FCFs in the APV approach are identical to those used in the WACC approach.
©2010 Robert M. Dammon
87
Illustration: APV Approach
 The unlevered residual value in the APV approach is calculated
as follows:
RVU
NOPAT(1 G)(1- G/R)
W -G
$200(1.045)(1- (.045/.15))
.104 - .045
$2,482
©2010 Robert M. Dammon
88
Illustration: Value of ITS
 The next step is to calculate the value of interest tax shields on
debt. We will break this down into two parts:
 The value of ITS over the forecast period (years 1 – 7).
 The value of ITS beyond the forecast period (after year 7).
 We want to illustrate that the WACC approach and the APV
approach provide the same valuation if used properly.
 Since the WACC approach assumes a constant D/V ratio, for
consistency we will need to discount the future ITS at the
unlevered cost of capital, RU.
 The interest rate on the debt is RD = 6.8% and the target debt
ratio is D/V = 25%.
 The following page shows the calculations of the interest tax
shields.
©2010 Robert M. Dammon
89
Illustration: Value of ITS
Expected Levered Firm Value1
Interest rate on debt
Discount factor for ITS 2
Interest payments
Interest tax shields
PV of ITS (years 1-7)
PV of ITS (beyond year 7)
0
$1,924
1
$2,067
2
$2,203
3
$2,327
4
$2,438
5
$2,544
6
$2,642
7
$2,761
0.9058
$32.7
$11.5
$10.4
0.8205
$35.1
$12.3
$10.1
0.7432
$37.4
$13.1
$9.7
0.6732
$39.6
$13.8
$9.3
0.6098
$41.5
$14.5
$8.8
0.5523
$43.2
$15.1
$8.4
0.5003
$44.9
$15.7
$7.9
6.8%
$65
$139
Beginning Debt
Scheduled principal payments
Add. principal payments (issuances)3
Ending Debt
$350
$0
$481
$0
$517
$0
$551
$0
$582
$50
$610
$50
$636
$50
$660
$200
($131)
$481
($36)
$517
($34)
$551
($31)
$582
($78)
$610
($76)
$636
($75)
$660
($230)
$690
Debt / Value
25.0%
25.0%
25.0%
25.0%
25.0%
25.0%
25.0%
25.0%
©2010 Robert M. Dammon
90
Illustration: Value of ITS
 At the end of the forecast period (T=7), the value of the interest
tax shields going forward is simply the difference in the levered
and unlevered residual values:
VITS,T
RVL,T - RVU,T
$2,761- $2,482 $279
 Discounting this back to t = 0 using the unlevered cost of capital
yields:
PV ITS (beyond year 7)
©2010 Robert M. Dammon
$279
(1.104)7
$139
91
Illustration: Value of ITS
 The ITS over the forecast period (years 1 – 7) are calculated
using the following procedure:
 At the end of each year, use the WACC approach to calculate the
levered firm value, VL,t .
 Calculate the amount of debt needed to maintain a constant debt
ratio: Dt = VL,t(D/V).
 The interest tax shield at date t is: ITSt = RDtcDt-1.
 The present value of these interest tax shields is calculated by
discounting at the unlevered cost of capital, RU.
7
PV ITS (years 1 - 7)
t 1
©2010 Robert M. Dammon
ITS t
(1 R U ) t
$65
92
Illustration: APV Approach
Unlevered Firm Value
+ PV ITS (forecast period)
+ PV ITS (perpetuity period)
Value of Operations
+ Non-operating assets
Enterprise Value
- Existing debt
Equity value 2
$1,721
$65
$139
------------$1,924
$0
------------$1,924
($350)
------------$1,574
 The value of operations and the value of equity are identical to
those we derived earlier using the WACC approach.
 The APV approach is more difficult to use than the WACC
approach when the firm maintains a constant debt ratio, but will
be easier to use than the WACC approach when the debt ratio is
changing over time (e.g., LBO situations).
©2010 Robert M. Dammon
93
Capital Cash Flow Approach
©2010 Robert M. Dammon
94
Capital Cash Flow Approach
 Capital Cash Flow (CCF) is the sum of the FCF and the ITS:
CCF FCF ITS
 The Capital Cash Flow approach to valuation discounts the
future CCFs at the unlevered cost of capital, RU.
T
VL
t 1
©2010 Robert M. Dammon
CCFt
(1 R U ) t
RVT
(1 R U ) T
95
CCF Residual Value
 The CCF residual value, RVT, can be calculated using the
perpetuity formula used earlier in either the WACC or the APV
approach.
 The only differences are that the residual value will rely on CCFT
and the unlevered cost of capital, RU.
RVT
CCFT (1 G)
RU -G
FCFT (1 G)
RU - G
NOPATT (1 G)(1- G/R)
RU - G
©2010 Robert M. Dammon
ITS T (1 G)
RU - G
ITS T (1 G)
RU - G
96
Capital Cash Flow Approach
 The CCF residual value is composed of the unlevered residual
value, RVU,T, plus the residual value of ITS, VITS,T.
 The CCF residual value is identical to the residual value
calculated under the WACC approach.
 Since the CCF approach discounts ITS at the unlevered cost of
capital, it is technically correct only when the firm maintains a
constant debt ratio.
 The CCF approach does not alleviate the need to estimate the
future debt levels and the associated interest tax shields in the
calculation of the CCF.
 Therefore, it is still easier to use the WACC approach when the firm
maintains a constant debt ratio.
 If the debt ratio is expected to vary over time, the CCF approach is
not valid and you are better off using the APV approach.
©2010 Robert M. Dammon
97
Unlevered COC
10.40%
Capital Cash Flow Approach
0
NOPAT
+ Depreciation2
Operating Cash Flows
- Additions to WC3
- Capital Expenditures2
Free Cash Flows
Interest tax shields
Capital Cash Flows1
1
2
3
4
5
6
7
$130
$146
$160
$173
$183
$193
$200
$40
$45
$49
$53
$56
$59
$62
------------- ------------- ------------- ------------- ------------- ------------- ------------$170
$190
$209
$226
$240
$252
$262
$0
($12)
($11)
($10)
($8)
($7)
($6)
($7)
$0
($112)
($112)
($108)
($101)
($99)
($95)
($115)
-------------------------- ------------- ------------- ------------- ------------- ------------- ------------$0
$46
$67
$91
$117
$134
$151
$140
$0
$11
$12
$13
$14
$15
$15
$16
------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------$0
$57
$79
$104
$131
$148
$166
$156
2
+ Residual Value (levered)
Present Value (unlevered COC)$0
Value of Operations
+ Non-operating assets
Enterprise Value
- Existing Debt
3
Equity value
$52
$65
$77
$88
$91
$92
$2,761
$1,459
$1,924
$0 (e.g., excess cash, marketable securities, unconsolidated subsidiaries)
------------$1,924
($350) (e.g. short-term borrowing, long-term debt, and other interest-bearing liabilities)
------------$1,574
(includes the value of preferred stock and any employee stock options)
©2010 Robert M. Dammon
98
Equity Cash Flow Approach
©2010 Robert M. Dammon
99
The Equity Cash Flow Approach
 In some cases, it can be easier to calculate the value of the
company’s equity directly by discounting the cash flows to equity
(CFE) by the levered cost of equity, RE.
T
VE
t 1
CFE t
(1 R E ) t
RVE T
(1 R E ) T
where RVET is the residual value of equity at date T.
 The cash flow to equity approach is commonly used in valuing
banks and other financial institutions, where interest expense is
treated as an operating cost and not a financial cost.
©2010 Robert M. Dammon
100
Equity Cash Flows
 The Cash Flows to Equity (CFE) can be calculated in the
following ways:
CFE = FCF – A.T. Interest – Net Principal Payments
CFE = NI – NNI – Net Principal Payments
CFE = NI – Net New Equity
CFE = Dividends + Net Share Repurchases
©2010 Robert M. Dammon
101
Equity Cash Flows
 The definitions of CFE involve the following:
 Net Principal Payments = Principal Payments – New Debt Issuance
 NI = Net Income
 NNI = Net New Investment
 Net New Equity = Retained Earnings + New Equity Issuances
 Retained Earnings = NI – Dividends – Share Repurchases
 Net Share Repurchases = Share Repurchases – New Equity Issuances
 Because CFE is net of after-tax interest payments, the benefits of
interest tax shields are included in CFE.
 Because the CFE are cash flows to equity holders, we must
discount them at the levered cost of equity, RE.
©2010 Robert M. Dammon
102
Residual Value of Equity
 The residual value of equity, RVET, can be calculated using a
perpetuity formula similar to those used previously.
RVE T
CFE T (1 G)
RE - G
[NI T - NNE T ](1 G)
RE - G
where NI = Net Income and NNE = Net New Equity.
 Next, define the constant equity plowback rate, kE, as follows:
kE
©2010 Robert M. Dammon
NNE
NI
103
Residual Value of Equity
 This allows us to write the residual value of equity as follows:
RVE T
NI T (1- k E )(1 G)
RE - G
 The long-run growth rate, G, can now be calculated as follows:
G
NI
NI
NI NNE
x
NNE
NI
ROE x k E
where ROE is the marginal Return on Equity (book value) and kE
is the equity plowback rate.
©2010 Robert M. Dammon
104
Residual Value of Equity
 Substituting the definition for long-run growth, G, into the formula
for the residual value of equity yields:
G
(1 G)
ROE
RE - G
NI T 1 RVE T
RVE T
©2010 Robert M. Dammon
NI T (1 - k E )(1 (k E x ROE))
RE - G
105
Cost of Equity
11.60%
0
NOPAT
+ Depreciation2
Operating Cash Flows
- Additions to WC
- Capital Expenditures
Free Cash Flows
- After-Tax Interest Expense
+ Debt Issuance (repayments)2
Equity Cash Flows
+ Residual Value of Equity1
Present Value (cost of equity)3
PV of Equity CF
+ Non-operating assets
Equity Value4
$0
$0
------------$0
$131
------------$131
$131
Cash Flow to Equity Approach
1
$130
$40
------------$170
($12)
($112)
------------$46
($21)
$36
------------$60
$54
2
$146
$45
------------$190
($11)
($112)
------------$67
($23)
$34
------------$78
$63
3
$160
$49
------------$209
($10)
($108)
------------$91
($24)
$31
------------$98
$71
4
$173
$53
------------$226
($8)
($101)
------------$117
($26)
$28
------------$119
$77
5
$183
$56
------------$240
($7)
($99)
------------$134
($27)
$26
------------$133
$77
6
$193
$59
------------$252
($6)
($95)
------------$151
($28)
$25
------------$148
7
$200
$62
------------$262
($7)
($115)
------------$140
($29)
$30
------------$141
$76
$2,071
$1,026
$1,574
$0 (e.g. short-term borrowing, long-term debt, and other interest-bearing liabilities)
------------$1,574 (includes the value of preferred stock and any employee stock options)
©2010 Robert M. Dammon
106
CFE Residual Value
 The residual value in the Cash Flow to Equity approach can be
calculated as follows:
RVE T
CFE T (1 G)
RE - G
$141(1.045)
$2,071
.116 .045
 This residual value is also equal to the following formulation:
RVE T
©2010 Robert M. Dammon
NI T (1 G)(1- G/ROE)
RE - G
$2,071
107
CFE Residual Value
 Net income in year T is equal to NOPAT less after-tax interest
expense. That is,
NI T
NOPATT - R D D T -1 (1 - t C )
$200 - .068($660.5)(1- .35)
$170.8
 Substituting the appropriate values into the residual value
formula gives us:
RVE T
$170.8(1.045)(1- .045/ROE)
.116 - .045
©2010 Robert M. Dammon
$2,071
108
CFE Residual Value
 Solving this equation for ROE gives us the long-run ROE of
25.5%.
 This implies the following reinvestment (plowback) rate for
equity:
kE = G/ROE = .045/.255 = 17.6%
or a payout ratio (dividends plus repurchases) equal to 82.4% of
net income.
 The reason that kE < k is because the market value of equity is
greater than the book value of equity when the firm is investing
in positive NPV projects (ROIC > WACC).
©2010 Robert M. Dammon
109
Multiples Valuation
©2010 Robert M. Dammon
110
Multiples Valuation
 The multiples valuation approach is popular among
investment bankers and practitioners because of its relative
simplicity.
 The multiples valuation approach uses a set of valuation
multiples for comparable companies to provide an estimate of
value for the acquisition target.
 There are two basic types of multiples that are commonly used:
 Trading multiples – Multiples based upon the traded market prices
of the comparable companies.
 Transaction multiples – Multiples based upon the transaction
prices paid in recently completed acquisitions.
©2010 Robert M. Dammon
111
Types of Multiples
Enterprise value1 divided by:
Market value of equity divided by:
Revenues
Earnings before taxes
EBITDA
Net income
EBIT
Net cash flow
Operating CF
Book value of equity
Book value of assets
1.
Enterprise value = Market value of equity + Total debt. Enterprise value may need to be
adjusted to account for any non-operating (financial) assets that are held.
©2010 Robert M. Dammon
112
Steps in Multiples Valuation
 Select a set of comparable companies
 Select a set of comparable companies with similar business
characteristics to the firm you are attempting to value.
 Determine the relevant business characteristics in advance of your
search for comparables to avoid selection bias.
 Compute the multiples for the comparable companies.
 Select the set of multiples that provide the most reliable estimates
of value for the industry.
 Adjust the operating metrics for differences in accounting methods,
unusual items, and non-operating assets.
 Compute the multiples for each of the comparable firms.
 Calculate the mean, median, minimum, and maximum for each
multiple.
©2010 Robert M. Dammon
113
Steps in Multiples Valuation
 Apply the multiples for the comparables to value the target
company.
 Adjust the operating metrics for the target company for any
differences in accounting methods.
 Multiply the multiples for the comparable companies by the target
company’s operating metrics to estimate the value of the target
company.
 Adjust the estimate of enterprise value (or equity value) for excess
cash, marketable securities, or other non-operating assets or
liabilities of the target company.
 The multiples will typically provide a range of values for the target.
Judgment may be needed to determine a final estimate of value.
©2010 Robert M. Dammon
114
Common Adjustments to Operating Metrics
 To ensure comparability, the operating metrics for the
comparable companies may need to be adjusted for the following:
 Inventory accounting (LIFO vs. FIFO)
 Extraordinary items (e.g., litigation settlements)
 Non-recurring items (e.g., sale of assets, discontinued operations)
 Non-operating assets (e.g., excess cash, marketable securities)
 NOL carryforwards or other special tax items
 Lease payments (e.g., operating and capital leases)
©2010 Robert M. Dammon
115
Basic Financial Information
Target
Company A
Company B
Company C
Company D
Income statements:
Sales revenues
- Cost of goods
- Depreciatiion
- SG&A
+ Non-recurring income
Operating income
+ Interest income
- Interest expense
Taxable income
- Taxes
Net income
14,000
(9,520)
(700)
(1,680)
(500)
1,600
250
(444)
1,406
(492)
914
10,000
(7,000)
(500)
(1,500)
0
1,000
0
(150)
850
(298)
553
20,000
(13,600)
(800)
(2,400)
(200)
3,000
150
(325)
2,825
(989)
1,836
15,000
(10,350)
(675)
(1,950)
400
2,425
25
(210)
2,240
(784)
1,456
18,000
(12,600)
(990)
(2,520)
250
2,140
50
(576)
1,614
(565)
1,049
Balance sheet:
Working capital
Net PP&E
Goodwill
Investments
Total Net Assets
2,100
7,000
900
5,000
15,000
1,000
5,000
0
0
6,000
3,000
8,000
0
3,000
14,000
1,800
6,750
450
500
9,500
3,240
9,900
1,860
1,000
16,000
Total debt
Shareholders' equity
Total capital
6,000
9,000
15,000
2,000
4,000
6,000
5,000
9,000
14,000
3,000
6,500
9,500
8,000
8,000
16,000
©2010 Robert M. Dammon
116
Adjustments to Basic Financial Information
 The non-recurring income (expenses) must be removed from the
income statement to provide comparable data.
Sales revenues
Adjusted OI
Adjusted EBITDA
Adjusted NI
Total capital
- Investments
Invested capital
- Goodwill
Tangible IC
ROIC
Target
14,000
2,100
2,800
1,239
Company A
10,000
1,000
1,500
553
Company B
20,000
3,200
4,000
1,966
Company C
15,000
2,025
2,700
1,196
Company D
18,000
1,890
2,880
887
15,000
(5,000)
10,000
(900)
9,100
6,000
0
6,000
0
6,000
14,000
(3,000)
11,000
0
11,000
9,500
(500)
9,000
(450)
8,550
16,000
(1,000)
15,000
(1,860)
13,140
13.7%
10.8%
18.9%
14.6%
8.2%
1.
OI and EBITDA are adjusted by the pre-tax non-recurring income (expenses). NI is adjusted by the after-tax
non-recurring income (expenses).
2.
ROIC is equal to the after-tax operating income (NOPAT) divided by the amount of invested capital.
©2010 Robert M. Dammon
117
Valuation Multiples for the Comparable Companies
Company A
Market Valuations:
Market capitalization
Total debt
Enterprise value
- Non-operating assets
Value of operations
10,000
2,000
12,000
0
12,000
Company B
35,000
5,000
40,000
(3,000)
37,000
Company C
22,000
3,000
25,000
(500)
24,500
Company D
20,000
8,000
28,000
(1,000)
27,000
Company A
Company B
Company C
Company D
2.0
2.9
2.6
1.8
Value of Ops/IC
Value of Ops/Tangible IC
Value of Ops/Revenues
Value of Ops/OI
Value of Ops/EBITDA
2.0
2.0
1.2
12.0
8.0
3.4
3.4
1.9
11.6
9.3
2.7
2.9
1.6
12.1
9.1
1.8
2.1
1.5
14.3
9.4
Market Cap/NI
Market Cap/BV of Equity
18.1
2.5
17.8
3.9
18.4
3.4
22.6
2.5
Valuation Multiples:
EV/TC
©2010 Robert M. Dammon
118
Estimate of Enterprise Value of the Target Company
Valuation Multiples:
EV/TC
Min
Mean
1.8
2.3
Median
2.3
Max
Value of Ops/IC
Value of Ops/Tangible IC
Value of Ops/Revenues
Value of Ops/OI
Value of Ops/EBITDA
1.8
2.0
1.2
11.6
8.0
2.5
2.6
1.5
12.5
8.9
2.4
2.5
1.6
12.0
9.2
3.4
3.4
1.9
14.3
9.4
Market Cap/NI
Market Cap/BV of Equity
17.8
2.5
19.2
3.1
18.2
2.9
22.6
3.9
Estimates of Enterprise Value for the Target Company
Valuation Multiple
Inputs
Min
EV/TC
15,000
26,250
Mean
34,645
Median
34,737
Max
42,857
2.9
Value of Ops/IC
Value of Ops/Tangible IC
Value of Ops/Revenues
Value of Ops/OI
Value of Ops/EBITDA
10,000
9,100
14000
2,100
2,800
23,000
23,200
21,800
29,281
27,400
29,715
28,396
26,642
31,222
29,989
28,611
27,387
26,933
30,304
30,654
38,636
35,609
30,900
35,000
31,250
Market Cap/NI
Market Cap/BV of Equity
1,239
9,000
28,053
28,500
29,803
33,615
28,606
32,481
33,947
41,000
25,936
26,825
30,503
29,896
29,964
29,457
36,150
35,305
Average
Median
©2010 Robert M. Dammon
119
Calculations
 The values in the previous table are estimates of Enterprise
Value (EV) for the target company.
 To illustrate how these values are derived, we will do the explicit
calculations using the medians for three different multiples.
 EV/TC
 Value of Ops/EBITDA
 Market Cap/BV of Equity
 The other values in the table are calculated similarly.
 The value of the target company’s equity can be determined
simply by subtracting the target company’s total debt from the
enterprise values shown in the previous table.
©2010 Robert M. Dammon
120
Calculations
Calculations of EV and Equity Value for the Target
Target Total Capital
x Median EV/TC
Target EV
- Target Total Debt
Target Equity Value
15,000
2.3
34,737
(6,000)
28,737
Target EBITDA
x Median Value of Ops/EBITDA
Target Value of Ops
+ Target Non-Operating Assets
Target EV
- Target Total Debt
Target Equity Value
2,800
9.2
25,654
5,000
30,654
(6,000)
24,654
Target BV of Equity
x Median Market Cap/BV of Equity
Target Value of Equity
+ Target Total Debt
Target EV
9,000
2.9
26,481
6,000
32,481
©2010 Robert M. Dammon
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Multiples Valuation
 The advantage of the multiples approach is that it is simple and
intuitive.
 The methodology follows from the Efficient Markets Hypothesis
(EMH): Comparable assets should sell at comparable prices.
 There are some problems (difficulties) in using the multiples
approach:
 It can be difficult to identify truly comparable companies.
 Even if a comparable set of companies can be found, it is not always
obvious which multiple should be used in the valuation.
 Different multiples can provide widely different valuations, even for
similar firms in the same industry.
©2010 Robert M. Dammon
122
Multiples Valuation
 Listed below are some things to be cautious of when using the
multiples approach:
 Investors value cash flows, not accounting earnings.
 Multiples are applied to short-term accounting metrics, whereas
market valuations reflect the company’s long-run prospects.
 Firms may have different risk characteristics that affect their
valuations.
 Firms may have different capital structures that affect their
valuations.
 Firms may have different growth opportunities that affect their
valuations.
©2010 Robert M. Dammon
123
Premiums Paid Analysis
©2010 Robert M. Dammon
124
Premiums Paid Analysis
 Investment bankers will also use a premiums paid analysis to
analyze the fairness of a takeover bid.
 The premium (above the pre-announcement market price) being
offered is compared to the premiums paid in the most recently
completed transactions to determine “fairness”.
 The premiums paid analysis is intended to provide a measure of
the control premium that should be expected from an
acquisition.
 Premiums differ across hot and cold takeover markets.
 Premiums differ across industries.
©2010 Robert M. Dammon
125
Premiums Paid Analysis
 Although the premiums paid analysis can be useful, there are a
number of potential pitfalls:
 Premiums should reflect the value of the synergies that can be
created, or the inefficiencies that can be eliminated.
 Pre-announcement market prices may already be bid up by
investors if a takeover is anticipated.
 The premiums paid in completed transactions may be biased
upward:
 The most valuable acquisitions should be expected to take place first.
 “Winners curse” problem.
 Kaplan and Ruback have found that a combination of the
multiples approach and DCF approach works best for predicting
the premium paid in an acquisition.
©2010 Robert M. Dammon
126
References
1. Valuation: Measuring and Managing the Value of Companies, T. Koller, M.
Goedhart, and D. Wessels, Wiley, Fourth Edition.
2. “Are You Paying Too Much for That Acquisition?”, R. Eccles, K. Lanes, and T.
Wilson, Harvard Business Review, July-August 1999.
3. “Ten Ways to Create Shareholder Value,” A. Rappaport, Harvard Business
Review, September 2006.
4. “Corporate Valuation and Market Multiples,” T. Luehrman, Harvard Business
School, Case No. 9-206-039.
5. “The Right Role for Multiples in Valuation,” McKinsey Quarterly, Spring 2005.
©2010 Robert M. Dammon
127
Appendix: Derivations of the Asset Beta and
Levered Equity Beta
©2010 Robert M. Dammon
128
Asset Betas and Levered Equity Betas
 The general expression for the asset (unlevered) beta is:
U
D
VU
D
E
E
VU
ITS
VITS
VU
 Rearranging the above formula provides a general expression for
the levered equity beta:
E
©2010 Robert M. Dammon
U
VU
E
ITS
VITS
E
D
D
E
129
Case 1: No Corporate Taxes
 Modigliani-Miller (1958).
 Without corporate taxes VITS = 0 and VU = VL.
 Substituting these into the general beta formulas yields the
following:
Asset beta:
Equity beta:
©2010 Robert M. Dammon
U
E
D
U
D
VL
[
E
U -
D]
E
VL
D
E
130
Case 2: Constant and Perpetual Debt Level
 Modigliani-Miller (1963).
 When the amount of debt, D, is constant and perpetual VITS =
tcD and VL = VU + tcD
 Substituting these into the general beta formulas yields the
following:
Asset beta:
Equity beta:
U
E
©2010 Robert M. Dammon
D
D (1 - t C )
VL
U
[
U -
E
D ](1 - t C )
E
VL
D
E
131
Case 3: Continuous Adjustment to Maintain a
Constant D/V Ratio
 Harris-Pringle (1985).
 When the company continuously adjusts its capital structure to
maintain a constant D/V ratio:
 The company’s future debt levels and associated interest tax
shields will vary in direct proportion to any changes in the value of
the firm’s assets.
 This means that the risk of the future interest tax shields is the
same as the risk of the firm’s assets. That is, ITS = U.
 Substituting VL = VU + VITS and
formulas yields the following:
Asset beta:
©2010 Robert M. Dammon
U
D
D
VL
ITS
=
U
E
into the general beta
E
VL
132
Case 3: Continuous Adjustment to Maintain a
Constant D/V Ratio
Equity beta:
E
U
[
U -
D]
D
E
 Notice that the formulas for the asset beta and the levered
equity beta in this case are the same as those without corporate
taxes!
 Without corporate taxes, there is no tax adjustment needed since
VITS = 0.
 With corporate taxes, but with continuous adjustment in the
company’s debt levels to maintain a constant D/V ratio, VITS > 0 but
ITS = U.
 Both cases result is the same set of formulas for the asset beta and
levered equity beta.
©2010 Robert M. Dammon
133
Case 4: Adjustment Back to the Target D/V Ratio
on an Annual Basis
 Miles-Ezzell (1980).
 When the company adjusts its capital structure annually (as
opposed to continuously) back to its target debt ratio, then
 The level of debt, D, and the associated interest tax shields, tCRDD,
are fixed over the first year.
 Because the debt level is fixed over the first year, the risk of the
interest tax shields in the first year is the same as the debt itself.
That is, ITS = D.
 The level of debt and the associated interest tax shields beyond the
first year will vary in direct proportion to the value of the firm’s
assets. Therefore, beyond the first year, ITS = U.
©2010 Robert M. Dammon
134
Case 4: Adjustment Back to the Target D/V Ratio
on an Annual Basis
 The value of the interest tax shields, VITS, can be written as
follows:
VITS
t CR DD
1 RD
t CR DD
VITS 1 RD
 The first term is the value of the interest tax shield in the first
year. Notice that the interest tax shield, tCRDD, is discounted at
the cost of debt, RD.
 The second term is simply the present value of the interest tax
shields beyond the first year.
©2010 Robert M. Dammon
135
Case 4: Adjustment Back to the Target D/V Ratio
on an Annual Basis
 Using the previous expression, it should also be the case that
the risk of the left-hand side is equal to the risk of the right-hand
side.
 The beta for the first term on the right-hand side is
D.
 The beta for the second term on the right-hand side is
U.
 This produces a beta for the interest tax shields, ITS, that is a
weighted average of D and U (where q = RD/(1+RD)):
IT S
©2010 Robert M. Dammon
D t Cq
D
VIT S
U
1 - t Cq
D
VIT S
136
Case 4: Adjustment Back to the Target D/V Ratio
on an Annual Basis
 If we now substitute the above formula for ITS into the general
formulas for the asset beta and the levered equity beta we get:
Asset beta:
Equity beta:
©2010 Robert M. Dammon
U
E
D
D (1 - t C q)
VL
U
[
U -
E
D ](1 - t C q)
E
VL
D
E
137