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Cost 01 Caplll
Applications and Examples
Fifth Edition
SHANNON P. PRATT
ROGER J. GRABOWSKI
Langsdale Library
University of Baltimore
1420 Maryland Avenue
Baltimore, MD 21201
WILEY
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10987654321
Cost 01 Capital lor a
Smaller-Sized Company1
Case Background
Valuation Procedures
Cost of Equity Capital
Build-up Method (Using Morningstar Data)
Build-up Method (Using Duff & Phelps Data)
Modified CAPM (Using Morningstar Data)
Modified CAPM (Using Duff & Phelps Data)
Reconci liation
Conclusion
Appendix 43A: Report for Cost of Capital for a Smaller-Sized Company
CASE BACKGROUND
This example is a valuation of a 100% controlling ownership interest in a packaging
supply company for buy/sell purposes. The valuation date was as of December 31,
2011. The standard of value was fair market value.
Packaging Supply, Inc., was based in New York City with branches in Springfield,
New Jersey, and Yonkers, New York. While free of the regulatory constrictions facing
ABC OpCo as described in Chapter 42, relocating Packaging Supply, Inc., was similarly
limited since the company’s customers were concentrated within a 100-mile radius of
New York City. The company faced significant competition in the region, but had
strong, experienced management, a diversified supply chain, and a history of leveraging
its assets to successfully compete in the marketplace. Packaging Supply, Inc., was
organized as a C corporation and had a long history of profitable operations.
In this chapter, we will detail key valuation concepts and demonstrate the cost of
equity and cost of equity premium computations using Morningstar and Duff &
Phelps data.
lOur thanks to Kimberly Linebarger and Paul Anthony of Shannon Pratt Valuations for
assembling the material.
11&2
Cost of
for a Smaller-Sized (‘”n,n”‘>I’
1183
VALUATION PROCEDURES
We first employed the discounted cash flow (DCF) to equity method, a form of the
income approach, to value Packaging Supply, Inc. In the DCF method, projected
economic income is converted into present value using an appropriate required rate of
return or discount rate. The terminal value under the DCF method is equivalent to the
formula utilized for the capitalized economic income method. Management forecasts
provided the basis for the DCF analysis, we employed the DCF to equity method, and
normalization adjustments were made as appropriate.
The discount and the capitalization rate used should match the economic income
being converted into present value. We therefore used the company’s cost of equity
of 18.5% when discounting cash flows to equity (for an explanation of the
calculation of cost of equity, see the following the next section, “Cost of Equity
Capital” section). For the terminal value, we used the company’s cost of equity of
18.5% minus its assumed growth rate of 3.5% to arrive at a terminal capitalization
rate of 15.0%.
The guideline publicly traded company method, a method under the market
based approach, was also used in the valuation of Packaging Supply, Inc. This
approach provides an indication of value based on the prices investors were paying
for interests in comparable guideline publicly traded companies at the time of the
valuation date. Adjustments are required for the differences in size, growth prospects,
geographic diversification, profitability, asset management, and return on investment
between the guideline publicly traded companies and the subject company.
We computed market multiples based on the market value of invested capital
(MVIC) over revenue, gross profit, EBITDA, and EBIT, then adjusted the median
multiples in each category using data published in Duff & Phelps Risk Premium
Report to reflect the differences in size, then for differences in growth prospects,
geographic diversification, profitability, asset management, and return on investment
between the subject company and the guideline publicly traded companies.
The guideline publicly traded company method, applying the valuation multiples,
subtracting long-term debt, and adding in cash and equivalents to Packaging Supply,
Inc., which indicated an equity value of $7,460,188. Results were comparable to the
$7.03 million indicated enterprise value from the income approach. As applied the
guideline publicly traded method arrived at a controlling level of value.
The guideline transaction method, another market-based approach, was also used
to value Packaging Supply, Inc. This approach provides an indication of value based
on the direct comparison of the subject company’s equity and total invested capital to
the equity and total invested capital of similar companies involved in the same or
similar lines of business. The economic theory underlying the market approach is the
principle of substitution; that is, one would not pay more than one would have to pay
for an equally desirable alternative.
Using information on the company provided by management, general industry
research, and SIC codes as filters, we reviewed information available through Pratt’s
Stats, BIZCOMPS, S&P Capital IQ, and the web portal of the Securities and
Exchange Commission (www.sec.gov) to determine a list of guideline transactions.
Six companies were found to be sufficiently comparable to Packaging Supply, Inc., to
provide an indicated range of estimated values. Each of the six companies identified
was closely held, operated in the same industry as Packaging Supply, Inc., and
1184
CASE STUDIES
operated in the Northeastern United States. Acquisition dates ranged from October
2005 to July 201l.
We weighed the indications of value based on analysis of the multiples, to arrive at
an overall indication of value.
Based on the guideline transaction method the aggregate value of the com
pany’s invested capital on a controlling basis was estimated to be $7,911,544 as of
the valuation date. We then subtract long-term debt of $861,180 to get the equity
value, so that the fair market value of equity indication for Packaging Supply, Inc.,
using the guideline transaction method was $7,050,364.
As applied the DCF method arrived at a controlling, non-marketable level of
value, a discount for lack of marketability was considered. As applied the guideline
publicly traded method arrived at a controlling level of value. As applied the
guideline merged and acquired company method arrived at controlling level of
value. The possible effect of synergies reflected in the acquisitions was taken into
consideration.
The asset approach was not used for Packaging Supply, Inc. The asset approach is
most often applied in the valuation of companies for which tangible assets comprise a
significant portion of the company’s value or when the company is being valued for
the purpose of liquidation. Given the nature of Packaging Supply, Inc.’s operations,
with few tangible assets in comparison to the company’s cash-flow-generating ability,
the asset approach was not appropriate.
COST OF EQUITY CAPITAL
The cost of equity was estimated using the build-up method and the modified capital
asset pricing model (CAPM). Each method was calculated using Morningstar data
and Duff & Phelps data. The average of the four resulting cost of equity estimates was
utilized for Packaging Supply, Inc.’s cost of equity.
Recall the cost of equity formula for the build-up method (repeating Formula
9.1):
where: E(R i ) = Expected (market required) rate of return on security i
R f = Rate of return available on a risk-free security as of the valuation
date
RP m General expected equity risk premium (ERP) for the market
RPs Risk premium for smaller size
RPc Risk premium attributable to the specific company or to the
industry
Also recall the cost of equity formula for the modified CAPM (repeating
Formula 10.6):
Cost of Capital for a Smaller-Sized Company
1185
5
where: E(Ri)
Expected rate of return on security i
Rf Rate of return available on a risk-free security as of the valuation
date
‘
B = Beta
RPm = Market ERP
RPs = Risk premium for small size
RPc Risk premium attributable to other company risk factors
The sources used were as follows:
Rf
Risk-free rate based on a normalized 20-year long-term U.S. government
bond yield as of December 31,2011, equal to 4%, in all methods
(explained in Chapter 7, “Risk-free Rate”).
(Rm – Rf ) = General equity risk premium (ERP). The supply-side expected equity
risk premium from the SBBl20l2 Valuation Yearbook was used in both
Morningstar calculations. The then recommended 6% ERP by Duff &
Phelps was used in the Duff & Phelps calculations.
B = Beta derived from publicly traded guideline companies. This was applied
in the modified CAPM and an industry premium based on indications of
the beta was used in the build-up method.
RPi = Risk premium for the industry. A beta derived from publicly traded
guideline companies was applied in the modified CAPM and an industry
premium based on indications of the beta was used in the build-up
method.
RP s = Risk premium for smaller size. The size premium for the 10th decile
from the SBBI Yearbook was used in the Morningstar calculations.
The indicated size premium over CAPM using the 25th portfolio of the
Duff & Phelps 2012 Risk Premium Report was used in the Duff &
Phelps modified CAPM model.
The risk premium in the build-up method for Duff & Phelps already
incorporates a size premium.
RPc = Company-specific risk premium, we estimated a premium of zero based
on the analysts’ experience and published data in all methods.
=
Build-up Method (Using Morningstar Data)
Using the formula and the appropriate Morningstar data, we calculated the first build
up method as follows:
For the ERP, we take the supply side historical equity risk premium from the SBBI
Yearbook (which was 6.14%).
For the industry risk premium, as the published Morningstar industry premia
were inconsistent and included companies too different from our subject company, we
do not rely on the Morningstar data. Instead, we estimate based on analysts’ research
and indications from beta (which lead us to use 1.5%),
For the size premium, we took the 10th decile of the S&P 500 Market Benchmark
in the SBBI Yearbook (6.10%).
The sum of these gave us a cost of equity for the build-up method usmg
Morningstar data of 17.74% (see Exhibit 43AA in Appendix 43A).
1188
CASE STUDIES
Build-up Mathod (Using Dull. Phelps Dltl)
Using the formula and the appropriate Duff & Phelps data, we calculate the second
build-up method:
For the ERP and size premium, we took the median risk premium (ERP plus size
premium) from the Duff & Phelps data, which includes an adjustment for the
recommended ERP (which gave 14.06%).
For the industry risk premium, as the published Morningstar industry premia
were inconsistent and included companies too different from our subject company, we
do not rely on the Morningstar data. Instead, we estimate based on analysts’ research
and indications from beta (which lead us to use 1.5%).
The sum of these gave us a cost of equity for the build-up method using Duff &
Phelps data of 19.56% (see Exhibit 43A.S in Appendix 43A).
Medlned CAPM (Using MOl’nlnlstl1′ Dltl)
Using the formula and the appropriate data, we calculate the modified CAPM estimate
using Morningstar data:
For the ERP, we took the supply-side historical ERP from the SBBI Yearbook,
which was 6.14%.
For beta, we use a relevered adjusted beta (which is 1.27) (see Exhibit 43AA in
Appendix 43A).
For the size premium, we took the 10th decile of the S&P 500 Market Benchmark
in the SBBI Yearbook (6.10%).
Multiplying the ERP by beta gives us 7.79%, and adding this to the risk-free rate,
and the size premium gave a cost of equity for the modified CAPM using Morningstar
data of 17.89% (see Exhibit 43AA in Appendix 43A).
Modlnad CAPM (Uslnl Dull. Phllps Dltl)
Using the formula and the appropriate data, we calculate the second modified CAPM
using Duff & Phelps Data:
For the ERP, we took the recommended ERP from Duff & Phelps equal to 6.00%.
For beta, we used a relevered adjusted beta (which is 1.27) (see Exhibit 43A.S in
Appendix 43A).
For the size premium, we take the median size figure from the Duff & Phelps data
(which is 6.68%).
Multiplying the equity risk premium by beta gives us 7.61 %, and adding this to
the risk-free rate, and the size premium gave a cost of equity for the modified CAPM
using the Duff & Phelps data of 18.29% (see Exhibit 43A.S in Appendix 43A).
Reconclllition
Taking the four results of the different computations of cost of equity, we take the
average (see Exhibit 43A.3 in Appendix 43A):
Build-up method using Morningstar data
Build-up method using Duff & Phelps data
Modified CAPM using Morningstar data
Modified CAPM using Duff & Phelps data
Estimated cost of equity capital (rounded)
17.7%
19.6%
17.9%
18.3%
18.5%
Cost of Capital for a Smaller-Sized Company
1167
CONCLUSION
&
is
rs
A final issue in the valuation analysis of Packaging Supply, Inc., is the relative weight
an investor would place on the discounted cash flow of equity method versus the two
methods of the market-based approaches to valuation.
Revenue Ruling 59-60 suggests the primary weight in an analysis of operating
companies should be placed on measures that reflect the value of the earnings and the
cash-flow-generating capacity.
At the same time, Revenue Ruling 59-60 requires the analyst to consider in the
valuation of closely held company both the earnings capacity of the company and the
market price of stocks of corporations engaged in the same or similar line of business
having their stocks actively traded in a free and open market.
In addition to the fact that Revenue Ruling 59-60 requires consideration of both
earnings-based and market-based factors in the valuation, we also have to consider the
appropriateness of the methods to the subject company. We also consider the quality
and quantity of data available under each method. In this case, we believe the
discounted cash flow method is more reliable than each of the two market-based
approaches. This is because Packaging Supply, Inc., is a small, closely held company.
We accorded 60% weight to the income approach and 20% weight to each of the
market-based methods.
The weight in percentage terms and dollar terms awarded to each indication of
value was as follows. Sixty percent weight was given to the value derived by the
discounted cash flow method (or $7,032,619 x 60% $4,219,571). The weight given
to the guideline transaction method was 20% (or $7,050,464 x 20% = $1,410,073).
The weight given to the guideline public company method was 20% (or
$7,460,188 x 20% $1,492,038).
The sum of the three weighted values is our estimation of the fair market value
of the common equity in Packaging Supply, Inc., on a controlling interest basis:
$7,000,000 (rounded).
I
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