Developing and Selecting CAPM Betas –A New Cost of Capital Navigator Module
24 May 2023
Presented by: Carla S. Nunes, Kevin Madden, and Aaron Russo

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Carla S. Nunes, CFA, ABVManaging Director

Kevin Madden

Carla S. Nunes, CFA, ABV is a Kroll Institute Fellow and a Managing Director in the Office ofProfessional Practice of Kroll. She has over 25 years of experience. In that role, Carla provides
firm-wide technical guidance on a variety of valuation, financial reporting and tax issues. She
also co-authors Kroll’s U.S. and European Goodwill Impairment Studies. In addition, Carla is
the Global Leader of Kroll’s Valuation Digital Solutions group, which produces cost of capitalthought leadership content and data housed in the Cost of Capital Navigator.

Kevin Madden is a Director in the Valuation Digital Solutions group, based in the Chicago
office. Kevin has more than 10 years of experience in financial services, specializing in projectand product management and financial analysis. He is a lead contributor to the content anddata housed in the Cost of Capital Navigator platform.

Director

Aaron Russo is a Vice President in the Valuation Digital Solutions group. Aaron specializes indata management, automation, and product development management for the content anddata housed in the Cost of Capital Navigator platform.
Aaron Russo
Vice President

6

1. Beta Estimation Basics
2. Different Beta Types

Agenda

3. Beta Best Practices
4. Company-level Levered Beta Resources
5. Adjusting for Financial Risk (Unlevering and Relevering)
6. Case Study
7. Demo7

Beta Estimation Basics

8

What is Beta?
Beta is a measure of systematic (i.e., “market”) risk of a stock; the tendency of a stock’s
price to correlate with changes in a specific market index. Beta does not measureunsystematic risk.
Beta (β) is the CAPM measure of risk:

E(Ri)

Rf

β

ERP

RPs

9

What is an Industry Risk Premium (IRP)?

E(Ri)

RPi

Rf

ERP

RPi

RPs

ERP

10

Beta Estimation Basics – Five Considerations
There are choices you will have to make when calculating a beta using historical data*
1. The market benchmark
2. Amount of history (1 year, 3 years, 5 years, etc.)
3. Stability over time
4. Frequency (daily, weekly, monthly, etc.)
5. Statistical quality*There may be other things of course, but these are the “biggies”.
11Beta Estimation Basics – The Market Benchmark• In the U.S., the S&P 500 Index
is typically selected as themarket benchmark. The MSCIWorld Index used to be thechoice for global betas. Morerecently, the MSCI All Country
World Index (ACWI) is
considered an even betterproxy for a global benchmark.
• Because some market
benchmarks are so highly
correlated, betas calculatedusing each of them are also
very similar. Not true if an
undiversified index is chosen.
12Beta Estimation Basics – Frequency and Amount of History• Benchmark index and company returns can be computed based on:o Price Returns: often used, but without much thought
o Total Returns: considers both price and dividend-adjusted returns, which is theoretically morecorrecto Excess Returns: subtracts the risk-free rate from index and company returns• Frequency of returns can be computed :
o
o
o
o
o

Intra-day (mostly traders)
Daily
WeeklyMonthly
Annual• For valuation purposes, most common or “standard” historical period used to measure
returns is 5 years of monthly of returns. Another period often used is 2 years (andsometimes 3 years) of weekly returns.

13

Beta Estimation Basics – Stability Over Time
Is Bank ABC’s “pre-crisis”
beta or its “post-crisis” beta
more representative of risk
going forward?

14

Beta Estimation Basics – Statistical Quality

R-Squared
Commonly referred to as“Goodness of fit”.
R-Squares on beta regressions
are often less than 20% to30%, indicating that othercompany or industry factors
explain realized returns on asecurity

15

Beta Estimation Basics – Statistical Quality
Standard Error of Estimate

Measures likelihood that true beta iscaptured by the estimate of beta derived
through the regression equation16

Beta Estimation Basics – Statistical Quality
T-stat, 60-month betas

T-statIndicates if beta coefficient isdifferent from zero.
t-stat = Beta / (Standard Error of
the Beta Coefficient)
If the t-stat > Critical Value thenthe beta is “statistically different
from zero”. t-stat Critical Values
vary by sample size and different
confidence levels (e.g., 95%)

17

Beta Estimation Basics – Top down or bottom up?
Top-Down Betas• Calculated Directly (e.g., OLS, Sum Beta)• Individual company (historical) OLS betas are often too “noisy” from a statisticalstandpoint
Bottom-Up Betas• Also called a “proxy” beta
• Requires:o Identifying the businesses in which the subject business operateso Identifying guideline public companies and estimating their levered betas,
which will be used as proxy• Can be particularly useful for a division, reporting unit, or closely-held business18

Levered (Equity) vs. Unlevered (Asset) Beta
• “Levered” betas incorporate two risk factors that bear on systematic risk:(i) business operating risk and(ii) financial (or capital structure) risk.
Levered betas are sometimes referred to as “equity” betas.
• “Unlevered” betas control for (remove the effect of) a company’s financing
decisions. In other words, the unlevered beta is the beta that would be
expected if the company were financed 100% with equity capital (no debt).
These types of betas are sometimes referred to as “asset” betas.

19

Different Beta Types

20

What is an OLS Beta?
•

Ordinary Least Squares (OLS) is also referred
to as ‘least squares’ regression, or simply, a
regression. A regression is the analysis
between one variable (the dependent variable)
and one or more variables (the independent
variables), assuming a linear relationship.

•

In the context of CAPM, the historical beta isestimated via an OLS regression (hence theterm, OLS beta).

•

The textbook CAPM OLS beta is the slope ofthe regression line, where the returns of asecurity are regressed against the returns on
the market portfolio.

•

Bloomberg calls this a “Raw Beta”.

21What is a Sum Beta?
• A Sum Beta is obtained through amultiple regression of a stock's current
month's excess returns (over the 30-day
T-Bill rate) on:*• The market's current month's excess
returns; and• The market's previous month's excess
returns.

The Sum Beta is computed bysumming up the resulting betacoefficients (current and lagged).

• Sum Betas have been shown to be better

predictors of smaller companies’
expected returns within the context of the
CAPM.

* If using monthly data. Sum Betas can also be
used for other return frequencies.

22

OLS Betas vs. Sum Betas in the Cost of Capital Navigator•••

CRSP Deciles Size Study: Uses OLS betas to calculate the size premia
Risk Premium Report Study: Uses Sum Betas in all calculations
European Size Study: Uses Sum Betas in all calculations

Cost of Capital Navigator – U.S. Cost of Capital Module

23

A Forward-looking Beta is What We Really Want
Three Common Adjustments for Making a Beta More “Forward-looking”• Like the cost of capital itself (and all of its inputs), beta is a forward-looking concept. We aretrying to estimate “future” beta.

• In practice, however, beta is often estimated using historical return data. In this sense, beta isforward looking……but only to the degree that the past is expected to repeat itself.

• Can a beta calculated using historical data be made more “forward-looking”? There are a few
common adjustments to do this:1) The Blume Adjustment (adjusts to the “market” beta)
2) The Vasicek Adjustment (adjusts to the “industry” beta)
3) The Portfolio (Peer Group) Beta (adjusts to “peers”/”industry”)
24Bloomberg’s Adjusted Beta is based on the Blume Adjustment

Adjusted Beta = (0.33 x 1.0) + [0.67 x historical (Raw) beta]
0.854 = (0.33) + (0.67 x 0.781)
25

Why Use 0.33 in the Blume Adjustment?

Prospective Beta = (0.33) + (0.67 x historical beta)• The adjustment is a simplification (1/3 vs. 2/3) and not an exact replication of Blume’s original
analysis in his 1971 paper.

• The original Blume adjustment was (based on an average of several periods from 1926 through1968 using 7-year monthly betas):

Prospective Beta = (0.371) + (0.635 x historical beta)• This simple adjustment of 0.33 makes the Blume adjustment a “one size fits all” adjustment.

Source: The original paper, “On the Assessment of Risk”, The Journal of Finance, Vol. 26, No. 1, (Mar 1971), pp. 1-10
26

A Few Thoughts on the Blume Adjustment…
Blume said in his 1971 paper that:•

The coefficients themselves will change over time (i.e., the ratio at which a beta
moves to the market beta of 1.0)

The use of a historical regression to correct for the future ratio:• Will not perfectly adjust betas• May overcorrect by introducing larger errors than in the unadjusted beta

Caution✓ If your project may end up in litigation, be aware of these limitations✓ You may not be able to defend the adjustment in court [See: Delaware Court ofChancery case “GT LP and Global GT LTD v. Golden Telecom, Inc.”]27

The Vasicek Adjustment• Betas with higher standard error (i.e., lower statistical quality) are the least reliable estimates, andtherefore are adjusted toward the market/peer group/industry average more than are betas withhigher statistical quality.

• Also known as a “shrinkage” or “smoothing” technique.
The Vasicek Adjustment is not “one size fits all”.

28Portfolio Beta

• The beta of a portfolio is the weighted average of the betas of the securities in theportfolio, using market-cap weights.

• Portfolio beta is the measure of an entire portfolio’s sensitivity to overall market
changes, whereas an individual company beta is based on an individual stock’s
sensitivity to the market.

• Portfolio betas are calculated in the Company-level Beta Module as the market-valueof-equity (market cap) weighted average of the OLS betas of the comparable
companies selected.

29

Beta Best Practices

30

Best Practices by Beta Type•OLS Beta– Best to only use betas that are “statistically significant”. A short-cut is to look at t-stats > 2.0– Be careful if a company underwent a significant transaction (e.g., acquisition, divestiture, etc.),
as the underlying business risk may have changed materially.
– Look at trailing betas over time (e.g., over the last 10 years) to analyze beta stability.

•

Sum Beta– Preferably, use only for small or thinly-traded comparable companies.
– Sum betas have been shown to be better predictors of smaller companies’ expected returns
within the context of the CAPM.

•

Vasicek Adjusted– Can be used for any project.
– Particularly important when standard errors of individual betas are large (look at the size ofthe standard error relative to the beta estimate).
31

Best Practices for Market Index– McKinsey & Company, “Valuation”, 7th Edition
Quote 1

“Most well-diversified indexes, such as the S&P 500 and MSCI World Index, are highly correlated(the two indexes had a 97 percent correlation between 2000 and 2018). Thus, the choice of index
will have only a small effect on beta. Do not, however, use a local market index, which somedata services provide. Most countries are heavily weighted in only a few industries, and in somecases, a few companies. Consequently, when measuring beta versus a local index, you are notmeasuring market-wide systematic risk, but often a company’s sensitivity to a particular set ofindustries.” [Emphasis Added]

Quote 2

“We recommend using a local CAPM for investors and companies facing restrictions to investing
abroad.” [Emphasis Added]

Quote 3

“Nevertheless, we don’t recommend the local CAPM approach for integrated markets. […] [W]ith alocal CAPM, you cannot make a straightforward estimate of a company’s beta based on the
average of the estimated betas for a sample of industry peers. [….] The reason is that if the peers
are in different countries, their local betas are not directly comparable.” [Emphasis Added]
32

Best Practices for Market Index• By definition, the market portfolio in CAPM consists of all assets in all markets, where each asset isweighted by its market capitalization.
– In theory, this include all types of assets that are held as an investment (e.g., artwork, realestate, human capital, etc.)– In practice, such market portfolio is unobservable and is substituted by a broad-based stock
market index, which is comprised of a diversified portfolio of common stocks.
•

Choice of Index: Should I use a Local Market Index or a Regional/Global Index?

– Fully Integrated Market: Use a diversified regional or global index. Note: U.S. stock market isfully integrated–

Completely Segmented Market: Use a diversified local index–

Not Fully Integrated/Segmented: Consider looking it a both at diversified local and global
indices33

Best Practices for Market Index
Kroll Company-level Beta Module• All indices are in the MSCI index family, so there is no inconsistency between index providers’methodologies.
•

Country-level indices are not available for every comparable company’s local stock market.
• Country-level indices with a small number of constituents and indices dominated by a single
industry sector are not included.
• All country-level indices available for selection in this module had at least 25 constituents asof December 31, 2022, with the exception of MSCI Mexico and MSCI Italy, which had 23 each.

•

The following academic paper is an example of the empirical evidence on why it is important to use
diversified market indices for beta estimation:
Lally, Marty, Steve Swidler (2008), “Betas, market weights and the cost of capital: The example of Nokia and small cap stocks
on the Helsinki Stock Exchange”, International Review of Financial Analysis.
https://www.sciencedirect.com/science/article/abs/pii/S1057521907000610

34

Best Practices for Currency• Currency of comparable companies should match the currency of the market index used
when regressing betas.

35

Best Practices for Return Frequency and Lookback Period•

Most common or “standard” historical period used to measure returns = 5 years of monthly returns(i.e., 60 months). Another period often used = 2 or 3 years of weekly returns (i.e., 104 or 156
weeks).

•

If company characteristics change significantly (e.g., major divestiture or acquisition, significant
deregulation), it may be more appropriate to use a shorter period (e.g., weekly returns).

•

The shorter the time period, the more “noise” is introduced, reducing the statistical quality of theregression.

•

Care should be taken such that the sample size is not too small. For example, a beta based on lessthan 30 monthly observations may not be reliable (i.e., not statistically significant). Likewise, a beta
based on less than 104 weeks may be unreliable.

•

Be careful with companies that went through an IPO within the last year, as those betas are often
unreliable and not a good proxy for their future risk.
36

Best Practices for Capital Structure
Cost of Capital Input

Post Coronavirus Considerations(Asset) Beta –Unlevered•

Significant equity market declines can lead to greater debt % in the capital
structure (particularly, if using book value).

•

May significantly distort the calculated unlevered betas. Hamada unleveringformula may exacerbate the issue.

•

Consider using other unlevering methods (e.g., Harris-Pringle) in times ofheightened market volatility or when leverage is high.

Capital Structure• Corporate finance theory tells us to use market value weights for debt
component• Don’t automatically assume debt book value = market value• Review Fair Value footnotes in annual & interim financials• Consider long-term averages instead of point-in-time capital structure37Company-level
Levered Beta Resources38

Sources Of Levered Company-level Betas• Kroll Company-level Beta Module1• S&P Capital IQ• Bloomberg

1) Available through the Cost of Capital Navigator. Industry-level betas (levered and unlevered) can be found in the (i) U.S. Industry Benchmarking
Module and (ii) the International Industry Benchmarking Module39•

Sources of Levered Betas – Kroll Company-level Beta Module(New)

Coverage:••

Benchmark Index:•••

30+ market indices in the MSCI universe.
Guidance on index selection: multiple pre-selected indices offered based on subject company location. If a
country index is too small to capture the risk of a given company, the user will not be able to select it for beta
computation purposes.

Currency:•••

35,000+ companies located in 110+ countries that can be searched by several criteria (e.g., company name,industry, size, country).

100+ currencies to choose from.
Betas are computed consistently in thesame currency (an issue often ignored
inadvertently by practitioners).

Frequency and Period of Returns:•

Users may select weekly and monthly
returns for different look-back periods(1-,2-,3-,4-, and 5-years).

Kroll.com/costofcapitalnavigator

40

Sources of Levered Betas – Kroll Company-level Beta Module (New)•Beta Types:
•
•
•

•

Excel Download:••

Users can download various results into Excel without running into data provider limitations (e.g., Bloomberg)

Statistical Quality of Betas:••

There are five different methodologies to estimate betas.
The methodologies are transparent and easy to explain to auditors and other stakeholders.
Competing products only offer betas calculated using the slope of a regression (i.e., the ordinary least squared beta)

We provide users with multiple
indicators to assess the statisticalsignificance of a beta

Source of Data:•

Company-level returns are sourced
from S&P Global Market Intelligence,
Compustat database. Market Index
returns are sourced from MSCI Inc.

Kroll.com/costofcapitalnavigator

41

Sources of Levered Betas – Kroll Company-level Beta Module (New)•

Features and Functionality Coming Soon
•
•
•
•
•
•
•

The ability to save estimates
Option to include/exclude operating leases from Total Debt
Option to include/exclude cash from Total Debt (i.e., Net Debt)
Harris Pringle Unlevering
Company tearsheet view
Beta and other metric trends over time
Dataset added to Navigator Excel Add-in

Kroll.com/costofcapitalnavigator

42

Sources of Levered Betas – S&P Capital IQ
S&P Capital IQ’s (“CIQ”) levered historical betas, also known as raw levered betas, are derived from an ordinary leastsquares regression analysis using individual stock and benchmark index returns based on a monthly or weekly
frequency and over a given period of time.
•Three off-the-shelf betas are available through CIQ:o 1-year (“IQ_BETA_1YR”) – 52-week OLS betao 2-year (“IQ_BETA_2YR”) – 104-week OLS betao 5-year (“IQ_BETA_5YR”) – 60-month OLS beta•

The benchmarks for these off-the-shelf betas are the S&P 500 for all U.S. stocks, the S&P/TSX Composite for all
Canadian stocks, the MSCI EAFE for all developed market stocks in Europe, Australasia, and the Far East, and the
MSCI Emerging Markets for all other international stocks.

•

CIQ also offers a custom beta function (“IQ_CUSTOM_BETA”) where you define the market benchmark, date range(i.e., lookback period), monthly or weekly return frequency, and currency.

https://www.capitaliq.com/

43

Sources of Levered Betas – S&P Capital IQ
Notes:
When using the three CIQ “off-the-shelf” betas:•

If your comp set includes U.S. and International stocks, betas will be regressed against different local indices•U.S. stocks: companies and market index are denominated in USD•

Canadian stocks: companies and market index are denominated in CAD•

Developed market stocks in EAFE: companies denominated in local currency, market index denominated in USD•

Emerging market stocks: companies denominated in local currency, market index denominated in USD

Scenarios
U.S. Stock
Canadian StockIntl - Developed
Intl - Developed
Intl - Developed
Intl - Emerging
Intl - Emerging

TickerCompany
NasdaqGS:MSFT Microsoft Corporation
TSX:RYRoyal Bank of Canada
ENXTPA:MC
LVMH Moët Hennessy - Louis Vuitton, Société Européenne
TSE:7203
Toyota Motor Corporation
SWX:NESN
Nestlé S.A.
KOSE:A005930 Samsung Electronics Co., Ltd.
NSEI:TCS
Tata Consultancy Services Limited

https://www.capitaliq.com/

Currency of Company Currency of Index Index
USD
USD
S&P 500
CAD
CAD
S&P/TSX Composite
EUR
USD
MSCI EAFE
JPY
USD
MSCI EAFE
CHF
USD
MSCI EAFE
KRW
USDMSCI Emerging Markets
INR
USD
MSCI Emerging Markets

44Sources of Levered Betas – S&P Capital IQ
Notes:•

CIQ “off-the-shelf” and “custom” betas define the number of observations based on price not return.
– Sometimes there is a difference in the value pulled using IQ_BETA (1 year, 2 year, and 5 year) and
IQ_CUSTOM_BETA for the same time period due to the way the price is picked for calculation– Depending on your valuation date, a 5-year off-the-shelf (“IQ_BETA_5YR”) may be based on 60 prices andregressed against 59 returns (i.e., 59 observations)– Depending on your valuation date, a “custom” beta using 60 months before the end date, the beta may be based on
60 prices and regressed against 59 returns•

When using the “Custom” beta function and changing currency:– Make sure to change the market index to be denominated in the currency you’ve selected. For example, the S&P 500(CIQ identifier = ^SPX) is denominated in USD. If you want to regress betas against EUR, you will need to update
the S&P 500 index to be denominated in EUR by changing to the appropriate CIQ identifier

https://www.capitaliq.com/

45

Sources of Levered Betas – Bloomberg
Type the ticker symbol, hit <EQUITY>, type BETA and hitGO•
Can only access at Bloomberg Terminal, unless using
Bloomberg Anywhere•
View one security at a time•
Betas calculated include Raw (i.e., OLS) and Adjusted (i.e.,
simplified version of the Blume adjustment)•
Lots of features and functionality:– Select between monthly, weekly, and daily returns– Select start and end date for regression– Select different market indices– Select different currencies
Note:•
If you select a different currency for the equity, you will
also need to change the currency of the market index (itsnot automatic)•
Be mindful of data download limits at Bloomberg
Terminals•
US equity default index is S&P 500 in USD•
International equity default index is local country index inlocal currency•

46

Bloomberg Default: 59 Months of Returns for 5-yr Monthly Betas

47

Bloomberg Default: 59 Months of Returns for 5-yr Monthly Betas
Results can differ using 60 months of returns!

Difference = 0.781 – 0.793 = -0.012 => In this case, not very material, but it can be at times
48

Bloomberg Defaults to Currency of Country Where Share Trades
Currency of Market Index returns may be different from the currency in which the share trades

Index

MSCI ACWICurrency

LCL (KRW)

49

Bloomberg Defaults to Currency of Country Where Share Trades
Changing index currency can affect results!

Index

MSCI ACWICurrency

USD

Difference = 1.280 – 1.044 = 0.236 => In this case, very material difference50Sources of Levered Betas – Comparison of all Beta Databases
Company-level Beta
ModuleS&P Capital IQ

Bloomberg

AccessOnline Platform

Online Platform

Bloomberg Terminal or Bloomberg
Anywhere

Excel Add/Plug-in

On Roadmap

Yes

Yes (only at a Terminal/Anywhere)# of Beta Types

5

1

2

Return Frequency

Monthly & WeeklyMonthly & WeeklyMonthly, Weekly, and Daily

Return Type

Total (Excess) ReturnDefault setting: Price ReturnDefault setting: Price Return

Lookback Periods

1-, 2-, 3-, 4-, and 5-year

1-, 2-, and 5-year, and custom
range

6M, YTD, 1-, 2-, 5-year, and custom range

Off-the-shelf 2-year Beta # of
Observations

2-year weekly = 104
2-year monthly = 24

2-year weekly = 103/104(inconsistent)

Default setting:
2-year weekly = 103

Off-the-shelf 5-year Beta # of
Observations

5-year weekly = 260
5-year monthly = 60

5-year monthly = 59/60(inconsistent)

Default setting:
5-year monthly = 59

Market Indices

Minimum of 2 options basedon subject company location

Off-the-shelf betas = 4 depending
on if U.S. or int’l stock
Custom = multiple

Multiple, U.S. equity default = S&P 500
Intl equities default = based on location

Currency

150

Off-the-shelf betas = multiple,
mostly with a currency mismatch
Custom = multiple

Multiple, U.S. equity default = USD
Intl equities default = based on local
currency

51

Sources of Levered Betas – Advantages and Disadvantages
Advantages

Disadvantages

Companylevel Beta
Module• Access anywhere through online Cost of Capital Navigator• Five different methods to estimate betas, with methodologies
being transparent and easy to explain to auditors and otherstakeholders• Betas are computed consistently in the same currency• Select weekly and monthly returns for different look-backperiods• Pre-selected and screened market indices (that consider
diversification)• View multiple comps at the same time
• Statistical quality of betas provided• Download results to Excel• No Excel Add-in (on our Roadmap)• Still needs to gain recognition with stakeholders (e.g., auditors)

S&P Capital
IQ• Access through Excel plug-in or platform• Select weekly and monthly returns for different look-backperiods• Easy to update for recurring engagements• View multiple comps at the same time (only with Excel plugin)• Well recognized by stakeholders (e.g., auditors, clients)• Betas may not be computed consistently in the same currency unlessadjustments are made (biggest issue with off-the-shelf betas)• For custom betas, users have to select their own market index and
identify the ticker for the correct currency• At times, the computation doesn’t pick up the correct number of returnobservations (e.g., 59 vs 60)

Bloomberg• Select daily, weekly and monthly returns for different lookback periods• Both Raw (OLS) and Adjusted (based on Blume) Betas areprovided• Statistical quality of betas provided• Well recognized by stakeholders (e.g., auditors, clients)• Can only access at Bloomberg Terminal, unless using Bloomberg
Anywhere• Betas may not be computed consistently in the same currency, unlessadjustments are made• Can only view one comp at a time
• Bloomberg (Blume) Adjusted Beta has been rejected in Delaware Court
52

What Types of Betas are Available by Database?

Company-level
Beta Module

S&P Capital IQ

Bloomberg

OLS

X

X

X

Sum

X

Blume-Adjusted

X

Vasicek-Adjusted

X

Portfolio

X

Levered Beta TypeX

53

Adjusting for Financial Risk
(Unlevering andRelevering)54

There are Various Formulas for Unlevering and Relevering
Betas• These alternative formulas vary depending on the likelihood that tax
deductions on interest will be realized.

• We will focus on 3 of these formulas:
IMPORTANT!
Because of interest deductibility limitations
introduced by the 2017 U.S. Tax Reform,
you may need to adjust your tax rate
assumptions in your unlevering/levering
calculations.

HamadaMilesEzzell

HarrisPringle

55

Hamada Beta Unlevering/ Relevering
Formulas• Is the most commonly used formula.
• Is applicable in situations where the absoluteamount of debt is fixed.

• Consistent with theory that there is no risk
surrounding the ability to get full tax
deductions

HamadaMilesEzzell

HarrisPringle

56Miles Ezzell Beta Unlevering/Relevering Formulas•

Assumes that the risk of realizing the tax deductions is greaterthan is assumed in the Hamada formulas.
• Year 1: The discount rate used to calculate the value ofthe tax shield equals the cost of debt capital during thefirst year (i.e., the tax shield has the same risk as debt).
• Years 2 and beyond: The discount rate used to calculate
the value of the tax shield in years 2 and beyond equals
the cost of equity calculated using the asset beta of thefirm (i.e., the risk of the tax shield after the first year iscomparable to the risk of the operating cash flows).

•

HamadaMilesEzzell

HarrisPringle

Market value of debt capital remains at a constant percentageof equity capital, which is equivalent to saying that debt
increases in proportion to increases in the net cash flow of thefirm (net cash flow to invested capital) in every period.
57

Harris Pringle Beta Unlevering/ Relevering Formulas• Assumes the tax shield is even riskier.
• Consistent with theory that tax deductions are as risky as
operating cash flows and the discount rate on thosedeductions equals cost of equity

HamadaMilesEzzell• Assumes the market value of debt capital remains at aconstant percentage of equity capital, which is equivalent
to saying that debt increases in proportion to the net cash
flow of the firm (net cash flow to invested capital) in every
period.

HarrisPringle

58

U.S. Debt Betas (by credit grade) Over Time
December 2006 – December 2022
2008 Financial Crisis
1.0

COVID-19
Non-investment Grade (Average of Ba - Caa)
Investment Grade (Average of Aaa - Baa)

0.5

0.0

-0.5

59

Source: Cost of Capital NavigatorPractical Issues• The beta of a portfolio is always the market-value weighted average of the betas of theindividual investments in that portfolio. For example, the beta of a mutual fund is theweighted average of the betas of the stocks and other investments in that portfolio.

• The beta of a company after a merger is the market-value weighted average of the betasof the companies involved in the merger.
• The beta of an overall company is the market-value weighted average of the businesses(i.e., divisions and/or projects) comprising the overall company.

60

Recommendations• Use public comparable (or guideline) companies as proxies when valuing a private company.
Even for companies that are traded, it’s better to also look at comparable companies.
• Consider differences between subject company and public comparables.
• Use betas from consistent source.
• Be cautious of data from small firms without an active market: true betas tend to beunderestimated. Therefore, consider avoiding betas from thinly-traded companies or use Sum
Betas.

• Be careful with betas of highly levered companies: Harris-Pringle unlevering methodologies
should be used in such cases.
• Consider avoiding unlevered (asset) beta that is 0.10 or lower. Such estimate is likely notstatistically different from zero.
• Consider impact of unusual effective tax rates on unlevering Beta (e.g., negative tax rate).
• May want to adjust betas of companies with large cash balances (objective is to estimate
underlying (asset) beta of operations).
61

Case Study
Calculating and Selecting Betas for Valuation Date = 31 December 2022

62

Our Example Subject Company“Kroll’s Clothing Store” is a company that operates in the U.S. and sells branded apparel.
The company operates out of approximately 1,000 stores, based entirely in the UnitedStates. The company generates ~$5 billion a year in sales.
Our industry is GICS 25504010 – Apparel Retail.
Our valuation date is 31 December 2022.

What steps do we follow to estimate beta for our subject company?

63

Decisions to Estimate Beta
1. What is the currency of your WACC and where is your subject company located?
2. The length of the time period over which the historical returns are measured (i.e., the length ofthe look-back period)

3. The periodicity (frequency) of return measurement within that time period (e.g., weekly, monthly,etc.)

4. The choice of which index to use as a market proxy64

Decisions to Estimate Beta
1. What is the currency of your WACC and where is your subject company located?
USD, located in the United States

2. The length of the time period over which the historical returns are measured (i.e., the length ofthe look-back period)

3. The periodicity (frequency) of return measurement within that time period (e.g., weekly, monthly,etc.)

4. The choice of which index to use as a market proxy65

Decisions to Estimate Beta
1. What is the currency of your WACC and where is your subject company located?
USD, located in the United States

2. The length of the time period over which the historical returns are measured (i.e., the length ofthe look-back period)

5 years

3. The periodicity (frequency) of return measurement within that time period (e.g., weekly, monthly,etc.)

4. The choice of which index to use as a market proxy66

Decisions to Estimate Beta
1. What is the currency of your WACC and where is your subject company located?
USD, located in the United States

2. The length of the time period over which the historical returns are measured (i.e., the length ofthe look-back period)

5 years

3. The periodicity (frequency) of return measurement within that time period (e.g., weekly, monthly,etc.)Monthly (60 months)

4. The choice of which index to use as a market proxy67

Decisions to Estimate Beta
1. What is the currency of your WACC and where is your subject company located?
USD, located in the United States

2. The length of the time period over which the historical returns are measured (i.e., the length ofthe look-back period)

5 years

3. The periodicity (frequency) of return measurement within that time period (e.g., weekly, monthly,etc.)Monthly (60 months)

4. The choice of which index to use as a market proxy
MSCI USA Index

68

Decisions to Estimate Beta
The choice of which index to use as a market
proxy: MSCI USA Index• MSCI country-level indices (e.g., MSCI

USA, MSCI Brazil, MSCI China, etc.), aredesigned to measure the performance ofthe large and mid cap segments of thatparticular country and cover approximately
85% or more of the country’s free floatadjusted market capitalization.

• As such, the MSCI country-level indicestend to be highly correlated with the major
local stock market indices of a particularcountry. For example, the MSCI USA index
has a 99.9% correlation with the S&P 500.

69

Company-level Beta Module

70Selecting Comparable Companies
GICS 25504010 – Retail Apparel•

When selecting comparable companies, it is useful
begin by looking at companies that operate in the same
industry as your subject company•••

The Company-level Beta module in the Kroll Costof Capital Navigator provides lists of companies
by industry.
A user can also search by financial statement
metrics such as Market Cap, Total Assets,
EBITDA, and Sales, as well as by Country of
Headquarters and Country of Incorporation.

There are various additional factors that that can beconsidered when narrowing down your list ofcomparable companies. For example:•

Industry-specific measures•

Geographic segments•

Product sales mix•

Company size
71Company Search Tool in Company-level Beta Module

72

Company Search Tool in Company-level Beta Module

73

Company Search Tool in Capital IQ

74

Urban Outfitters – Industry Specific Measures

Source: Capital IQ

75

Urban Outfitters – Industry Specific Measures

Source: Capital IQ

Not a very large footprint and not majorly
distressed!
76

Urban Outfitters – Geographic Segments

Source: Capital IQ

77

Urban Outfitters – Geographic Segments

Source: Capital IQ

Good proportion of sales in the United States(% of Sales in U.S. in Jan 2023 - 86.7%)
78

Urban Outfitters – Business Segments (Product Mix)

Source: Capital IQ

79

Urban Outfitters – Business Segments (Product Mix)

Source: Capital IQ

Retail apparel is the focus of thebusiness(% of Retail Sales = 92%)80

Comparable Subject Companies – Size Metrics

Companies

Market Cap ($)

Sales ($)

Total Assets ($)

Abercrombie & Fitch Co.

1,123

3,713

2,939

American Eagle Outfitters Inc.

2,616

5,011

3,787

Burlington Stores, Inc.

13,218

9,322

7,090

The Children’s Place

459

1,915

1,037

The Gap, Inc.

4,117

16,67012,761

Guess?, Inc.

1,126

2,495

2,556

Ross Stores, Inc.

40,022

18,916

13,640The TJX Companies, Inc.

92,03948,55028,461

Urban Outfitters, Inc.

2,198

4,549

3,791

*Denominated in USD in millions. Sales and Total Assets as of the latest annual period.
81Comparable Subject Companies – Size Metrics

Companies

Market Cap ($)

Sales ($)

Total Assets ($)

Abercrombie & Fitch Co.

1,123

3,713

2,939

American Eagle Outfitters Inc.

2,616

5,011

3,787

Burlington Stores, Inc.

13,218

9,322

7,090

The Children’s Place

459

1,915

1,037

The Gap, Inc.

4,117

16,67012,761

Guess?, Inc.

1,126

2,495

2,556

Ross Stores, Inc.

40,022

18,916

13,640The TJX Companies, Inc.

92,03948,55028,461

Urban Outfitters, Inc.

2,198

4,549

3,791

*Denominated in USD in millions. Sales and Total Assets as of the latest annual period.
82Comparable Subject Companies – Statistical
Quality
OLS Levered
BetaStandard Errorof Estimate

T-statR2

Is Beta significant?
(95%)

Abercrombie & Fitch Co.

1.39

0.35

3.96

20%

Yes

American Eagle Outfitters Inc.

1.41

0.27

5.29

31%

Yes

Burlington Stores, Inc.

1.02

0.23

4.36

23%

Yes

The Children’s Place

1.92

0.44

4.35

23%

Yes

The Gap, Inc.

1.85

0.30

6.23

39%

Yes

Guess?, Inc.

1.86

0.29

6.38

40%

Yes

Urban Outfitters, Inc.

1.39

0.25

5.66

34%

Yes

Companies

83Comparable Subject Companies – Four Beta Types
Companies OLS Levered Beta

Sum Beta

Blume Adjusted
Beta*

Vasicek Adjusted
Beta

Abercrombie & Fitch Co.

1.39

1.95

1.25

1.47

American Eagle Outfitters Inc.

1.41

2.54

1.27

1.46

Burlington Stores, Inc.

1.02

1.71

1.02

1.20

The Children’s Place

1.92

2.54

1.59

1.69

The Gap, Inc.

1.85

2.31

1.54

1.72

Guess?, Inc.

1.86

2.40

1.55

1.73

Urban Outfitters, Inc.

1.39

1.43

1.26

1.45

*Using the original version from Blume’s 1971 paper

84Comparable Subject Companies – Beta Stability over Time
10-year trailing 60-month OLS and Sum Betas regressed against MSCI USA

85

Comparable Subject Companies – Beta Stability over Time
10-year trailing 60-month OLS and Sum Betas regressed against MSCI USA

86

Comparing Navigator Results to Alternate Sources of Beta
Levered OLS Betas

Company-level
Beta Module

CapIQ
5yr Beta

CapIQ
Custom Beta 1

CapIQ Custom
Beta 2

Abercrombie & Fitch Co.

1.39

1.39

1.39

1.38

American Eagle Outfitters Inc.

1.41

1.43

1.43

1.43

Burlington Stores, Inc.

1.02

1.05

1.05

1.04

The Children’s Place

1.92

1.94

1.94

1.94

The Gap, Inc.

1.85

1.89

1.89

1.86

Guess?, Inc.

1.86

1.90

1.90

1.89

Urban Outfitters, Inc.

1.39

1.44

1.44

1.42

Index

MSCI USA

S&P 500

S&P 500

MSCI USA

Return Type

Total

Price

Price

Price

# of Returns

60

59

59

59

Companies

87Unlevering Assumptions
D/TC
Companies Including Op.
Leases 1

D/TC
Excluding Op.
Leases 1

Tax Rate 2

Credit Rating 3

Abercrombie & Fitch Co.

52%

21%

25.81%BB

American Eagle Outfitters Inc.

41%

13%

25.81%BBB

Burlington Stores, Inc.

25%

10%

25.81%BB

The Children’s Place

50%

38%

25.81%BB

The Gap, Inc.

60%

31%

25.81%

BB

Guess?, Inc.

51%

30%

25.81%BB

Urban Outfitters, Inc.

35%

0%

25.81%BBBMedianAverage

D/TC = Debt / Total Capitalization

50%

21%

45%

21%

Concluded Market
Participant Credit
Rating: BB

1 Debt/Total Capital and Leases as of the latest annual period.
2 Tax rate of home (headquarter) country of each comparable company. Use of a U.S blended Federal and State corporate tax rate is a simplifying

assumption. A different rate may be appropriate for companies with foreign operations.
3 Source: S&P Credit Analytics Credit Model Score

88Unlevering via Hamada

D/TC Including and Excluding Operating Leases
OLS Unlevered Beta
Companies Including Operating
LeasesOLS Unlevered Beta
Excluding Operating
LeasesAbercrombie & Fitch Co.

0.77

1.16

American Eagle Outfitters Inc.

0.93

1.26

Burlington Stores, Inc.

0.82

0.95

The Children’s Place

1.11

1.31

The Gap, Inc.

0.87

1.39

Guess?, Inc.

1.06

1.41

Urban Outfitters, Inc.

0.99

1.39

MedianAverage

0.93

1.31

0.94

1.27

89

Unlevering via Hamada
D/TC Including Operating Leases

Companies OLS Unlevered Beta

Blume Adjusted
Beta*

Vasicek Adjusted
Beta

Abercrombie & Fitch Co.

0.77

0.69

0.81

American Eagle Outfitters Inc.

0.93

0.84

0.97

Burlington Stores, Inc.

0.82

0.82

0.96

The Children’s Place

1.11

0.92

0.98

The Gap, Inc.

0.87

0.72

0.81

Guess?, Inc.

1.06

0.88

0.98

Urban Outfitters, Inc.

0.99

0.90

1.04

0.93

0.84

0.97

0.94

0.82

0.94

MedianAverage*Using the original version from Blume’s 1971 paper

90Harris Pringle Beta Unlevering/Relevering Formulas
Step 1𝛽𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 =𝑊𝛽𝑙𝑒𝑣𝑒𝑟𝑒𝑑 + 𝛽𝑑𝑒𝑏𝑡 × 𝑊 𝑑𝑒𝑏𝑡

𝑒𝑞𝑢𝑖𝑡𝑦𝑊
1 + 𝑑𝑒𝑏𝑡
𝑊𝐸𝑞𝑢𝑖𝑡𝑦

𝑊𝑑𝑒𝑏𝑡
𝛽𝐿𝑒𝑣𝑒𝑟𝑒𝑑 = 𝛽𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 + (𝛽𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 − 𝛽𝑑𝑒𝑏𝑡 ) ×
𝑊𝐸𝑞𝑢𝑖𝑡𝑦βunlevered=

unlevered beta

βlevered=levered beta

βdebt

=

beta of debt capital

Wdebt

=

percent of debt in the company's capital structure

Wequity=

percent of equity in the company's capital structure

Unlever Company’s
beta

Step 2
Relever Company’s
beta

91

Debt Betas Assumption
As of December 31, 2022

Source: Cost of Capital Navigator

Credit Rating

Debt Beta

AAA

0.19

AA

0.19

A

0.21

BBB

0.30

BB

0.39

B

0.40

CCC

0.47

CC

0.65

92

Unlevering via Harris-Pringle
D/TC Including Operating Leases

OLS
Unlevered Beta

Blume
Adjusted Beta

Vasicek
Adjusted Beta

*Guess?, Inc.

0.87
0.96
0.86
1.16
0.97
1.12

0.80
0.87
0.86
1.00
0.85
0.96

0.91
0.99
1.00
1.05
0.92
1.05

Urban Outfitters, Inc.

1.01

0.92

1.05

Median

0.97

0.87

1.00

Average

0.99

0.89

0.99

*Average excl.
Outliers

0.93

0.86

0.97

Companies
Abercrombie & Fitch Co.
American Eagle Outfitters Inc.
Burlington Stores, Inc.
*The Children’s PlaceThe Gap, Inc.

*Companies excluded are The Children’s Place, Inc. and Guess?, Inc.

93

Gap, Inc. Unlevered Betas

OLS

Vasicek
Adjusted

Hamada0.87

0.81

Harris-Pringle

0.97

0.92

D/TC
including
Op. Leases
=
60%

94

Comparable Companies – Selecting/Concluding on
Unlevered Harris-Pringle Beta(s)OLS
Vasicek Adjusted
Unlevered Beta Unlevered Beta
First Quartile
MedianAverage
Average excl. outliers*

Third Quartile

0.91
0.97
0.99
0.93
1.06

0.95
1.00
0.99
0.97
1.05
95

*Companies excluded are The Children’s Place, Inc. and Guess?, Inc.

Relevering Assumptions
We will assume a D/TC (including Op. Leases) ratio of40%

We will assume a credit rating of BB
We will assume a tax rate of 25.8%(U.S. 2022 Tax Rate)

96

Relevering with Harris-Pringle

First Quartile
MedianAverage
Average excl. outliers
Third Quartile

OLS
Unlevered Beta

Vasicek Adjusted
Unlevered Beta

0.91
0.97
0.99
0.93
1.06

0.95
1.00
0.99
0.97
1.05

βLevered

1.40

𝑊𝑑𝑒𝑏𝑡
𝛽𝐿𝑒𝑣𝑒𝑟𝑒𝑑 = 𝛽𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 + (𝛽𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 − 𝛽𝑑𝑒𝑏𝑡 ) ×
𝑊𝐸𝑞𝑢𝑖𝑡𝑦97

Relevering with HamadaFirst Quartile
MedianAverage
Average excl. outliers
Third Quartile

OLS
Unlevered Beta

Vasicek Adjusted
Unlevered Beta

0.85
0.93
0.94
0.88
1.03

0.89
0.97
0.94
0.92
0.98

βLevered

1.45

98

Key Takeaways

1. Start with comparable companies that closely reflect
your subject company’s underlying business risk

2. Use multiple methods to estimate your betas
3. Be critical about the methods you are using and theresults you obtain99

Cost of Capital Navigator

Company-Level Beta Module DEMO

100

Questions?
If you need general assistance with the Cost of Capital Navigator, please contact the
support team: CostofCapital.Support@kroll.com

101