CofC in a Priv-Held Bus Environment

8/9/2019 CofC in a Priv-Held Bus Environment

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Cost of Capital Calculation in a

Small, Privately-Held Business Environment

Phil Murray

December 10, 2006

Presented to:

Dr. D. Anthony Plath

The Belk College of Business Administration

The University of North Carolina at Charlotte

MBAD 6890


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Abstract

Modern financial theory does not properly address the many behavioral and financial issuessurrounding the operation of a typical small, privately-held business. Cost of capital calculation, animportant topic in finance, is difficult to accomplish appropriately using traditional models which rely on

publicly available information and adherence of the particular firm and investor to a certain set ofrestrictive assumptions. Of particular concern is the cost of equity component of the cost of capitalcalculation.

The cost of capital is first explained and defined, and its purpose inside and outside of a firm identified.A review of traditional cost of capital models is undertaken, and then an expansive analysis of smalland large business differences is performed. After looking at a variety of adjusted models that havebeen recently proposed which attempt to deal with these differences, a new model (Firm OrientationCost of Capital Model FOCCM) is introduced and applied to a case study company which bettertakes into account behavioral and financial considerations in the small, privately-held businessenvironment. The model provides what is believed to provide highly accurate "internal" cost of capitalfigure for managers within a small firm to utilize in evaluating project investment.

Article Outline

INTRODUCTION

PART I: Definition and Traditional Calculation of the Cost of Capital

1. The Cost of Capital Defined2. Purpose of and Uses of the Cost of Capital3. Review of Traditional Models

PART II: Cost of Capital in the Small Business World

1. Examining the Small Business World: Differences between Large and Small Businesses2. Adjusted Models that Account for Small Business Differences3. Problems with the Traditional and Adjusted Models for Small Business

PART III: The Firm Orientation Cost of Capital Model (FOCCM)

1. Small Business Profiles in FOCCM2. Objectives and Implications of FOCCM3. Cost of Capital Calculation with FOCCM

PART IV: Application of Models to a Case Company

1. Introduction to the Case Company2. Application of traditional and adjusted models3. Application of FOCCM

CONCLUSION


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Introduction

Modern financial theory's fit to reality grows distant the further you move away from analysis of

and application to large, publicly-traded companies. This fact is certainly no truer than for a highly

empirical concept such as the cost of capital for a firm. The models designed to calculate the cost ofcapital which currently exist make assumptions that simply do not hold for smaller or privately-held

firms.

The traditional cost of capital models break down when they are utilized in a small business

environment, where those models' assumptions fail. The purpose of this paper is to evaluate the

appropriateness of applying the existing cost of capital models to small privately-held

businesses, and then to put forth an improved model (for use within a small firm) which takes

into account both the motivational (behavioral) differences and financial differences present in

these types of firms. The primary purpose of this model will be to enable proper internal

decision-making about the use of funds within small businesses.

After defining cost of capital and explaining its purpose at the beginning of Part I, context for

the study will be provided by contrasting differences between large, publicly-traded companies and

small, privately-held ones. In Part II, existing models for cost of capital calculation will be analyzed.

Newer "adjusted" models will be evaluated, and problems with both the traditional and adjusted

models will be unearthed to close out the section.

The Firm Orientation Cost of Capital Model (FOCCM) will be proposed in Part III. TheFOCCM addresses the problem of cost of capital calculation in a small business environment but

makes use of a new approach. It first examines the orientation (profile) of the small business owner.

After an accurate business ownership profile is identified, it makes use of a corresponding formula to

develop a much more accurate estimate of the small business' true cost of capital than would have

been possible with the traditional and adjusted models that have been developed over the last few

decades. The traditional, adjusted, and FOCCM models will be applied to an actual case study

business, and the results compared and contrasted. Finally, the paper will be concluded with a

discussion of the means of usefulness of this information to the small business community.

PART I: Traditional Definition and Calculation of the Cost of Capital

The Cost of Capital Defined


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The cost of capital can be defined simply as the rate of return required to compensate

providers of those funds (Palliam 335). This definition, although expressed from the point of view of

the investor, has strong implications for the firm. It says that firms must generate returns on an

ongoing basis that meet or exceed the funds providers' expected return, or the providers (investors)

will divert funds away to what they believe to be better uses of those funds.

Roger Ibbotson of the well-known Ibbotson and Associates further clarifies the concept as

follows: "The cost of capital is a function of the investment, not the investor." (#6 on pg 8 of Pratt) In

other words, the cost of capital should represent investors' expectations about a particularinvestment.

These expectations include an assumption that they will receive at the very least a rate of return

reasonable for allowing the use of their funds in a riskless environment, and that they will receive

additional return to compensate for the risk they are taking on for that particular investment. If an

investor does not achieve a return equal to or greater than the investment's cost of capital, the investorwill divert funds away from that investment to one that generates a rate of return equal to or higher

than their required return. On the matter of risk just mentioned, it should be acknowledged that few

environments or investments are anywhere close to being considered "riskless", of course, and so

stockholders have expectations that several different types of risks will be accounted for in the

expected rate of return.

Shannon Pratt summarizes the main types of risk well (35). He first mentions maturity risk,

which is related to the change in interest rates (inflation/deflation) in the economy. Maturity riskis

greater the longer the length or term of the investment. Systematic risk, also referred to as marketrisk, reflects the opportunity cost of investment due to the fact that the committed funds cannot be

invested by other means to receive at least a certain market or index-based acceptable return.

Unsystematic riskis the risk level unrelated to the market as a whole in other words, the specific risk

attributable to the firm in question, or the firm's industry. Many scholars, including Brigham and

Ehrhardt, state that this type of risk only exists in a portfolio that is notdiversified and term this type of

risk instead as "diversifiable risk" (219).

This is a heavily empirical topic which is more intuitive than it is calculable. It is easily

understood that those who provide funds to others, outside of philanthropy and charitable purposes,will require a certain payment or compensation in return for the provision of those funds. Above, we

laid out clear reasons why that compensation is important and for what it provides. It is not always

clear, however, exactly howthat level of compensation should be calculated. It is not as simple as just

asking an owner or investor what level of return they require. Investment decisions, particularly in


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small businesses, are typically made for the long run and involve a variety of motives and

uncertainties.

In the simplest example, consider a banker who gives funds to an individual for some purpose

to buy a vehicle, for example. He will not provide those funds nowjust to be repaid the same

amount in total over a timeframe that might extend over several years. He obviously needs to

generate profit to compensate him for the risk that the funds will not be repaid. This profit (or return)

must also compensate for the fact that the funds he has loaned out are tied up for a certain period of

time in other words, the liquidity of those funds has decreased when the funds were converted from

cash into an automobile. These factors are readily understood and accepted and yet it must be

admitted that the calculationof the rate of return this banker requires becomes complex and uncertain

the more factors that are introduced. In addition, he needs to be compensated for other realities the

lost opportunity cost of potentially higher interest rate loans, economic inflation which will make his

profits less valuable, among other issues.

Herein we find an irony in the calculation of the cost of capital: although it involves

significant considerations for risk and uncertainty, it is itself a somewhat imprecise and

uncertain calculation. And, as mentioned in the introduction, this uncertainly multiplies when

models which make big-firm, market-based assumptions are applied to small, privately held

firms those small firms typically operate under much different circumstances. But why is this

calculation so important? Thatis the question that will be addressed in the next section.

Purpose of and Uses of the Cost of Capital Inside of the Firm

The cost of capital is important for businesses to understand for several reasons. First of all, it

provides a starting point for considering the baseline minimum level of return required to which they

can compare various investment opportunities such as various corporate infrastructure projects,

expansion plans, or potential acquisitions. Secondly, it provides a discount rate for valuing the

business which allows for easier consideration of corporate suitors' offers, valuation for buy/sell

insurance, or in the case of privately held businesses it allows valuation for the purpose of considering

an IPO at different points in time. I will explore each of these two primary uses of the cost of capitalmeasure further below.

Evaluating a Firm's Investment and Project Opportunities


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Within firms, this issue of deciding how to invest a company's funds in useful projects is a daily

challenge to managers. Various investment options are presented continually. Managers have a

variety of tools at their disposal with which they can properly evaluate an opportunity. Per McKinsey &

Company, however, the "enterprise DCF model is a favorite of academics and practitioners alike

because it relies solely on how cash flows in and out of the company" (116). The potential for

complexity is replaced with a simple question: did cash change hands, and if so then in what direction

did the cash move in or out of the firm?1 But this analysis is not possible without a cost of capital to

use as a discount rate.

If managers lack a discount rate with which to use in an analysis of cash flows, decisions will

instead be made via judgment and intuition, experience, and other ego-related factors such as a

desire to grow the dominance of a business. Undoubtedly some of these tools (such as a manager's

extensive experience in his field) are indeed valuable and should be an integral part of the decision.

But a strong empirical analysis supporting the decision, even if not the tool used to initially come to thedecision, will still lend significant creditability to the proposal and will aid in the persuasion of others

involved in the making of the decision. If possible, even more subjective factors such as a manager's

judgment should be translated into quantitative figures i.e. projected sales revenue or cost for the

first few years of the investment and so those figures could then be plugged into your DCF

spreadsheet, with the confidence that a quality discount rate exists to apply to the analysis.

Firm Valuation

Firm valuation is a common task that depends heavily on the use of the cost of capital

measure. From the classic standpoint of an investor, this valuation may be done for the purposes of

discovering a company whose value is not fully reflected in their stock price (and thus represents an

opportunity for excess return potential). But within a company, firm valuation is practiced often during

the process of considering an acquisition or merger, and there is a need to properly value the

projected cash flows of one or both of the firms.

Certainly many other methods of firm valuation exist, including determining liquidation value or

examining a host of multiples, including price-to-earnings, EBITDA multiples, price-to-sales multiples,etc. In fact, multiples valuation methods could be most helpful as "a useful check of your DCF

forecasts" (McKinsey 380). And yet, in order to perform a thorough valuation analysis of a target firm

1 The "DCF", or Discounted Cash Flow, model mentioned here makes use of future cash flowprojections for a certain timeframe, and then discounts each period's cash flow back to a present valueaccording to a certain cost of capital.


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using a discounted cash flow (DCF) approach, it is mandatory that the cost of capital figure is known

and is accurate.

Differences and Similarities with Cost of Capital for Investment Opportunities vs. Valuation

An overall company cost of capital is most appropriately utilized in the valuation of that

business, or in the assessment of an investment opportunity considered to be of "typical" or "average"

risk for the company. Problems arise, however, when the overall cost of capital used to value a firm is

also applied to projects with very specific risks and circumstances.

Ross points out that companies often refer to the firm's cost of capital as a "corporate discount

rate" or "hurdle rate" (330). By doing so, those companies imply and even encourage the use of the

firms' overall cost of capital in the analysis of various projects and investments. Ross is in agreementwith virtually all other authors when he says that a project/venture should be assigned a an adjusted

discount rate that is commensurate with the risk level of that specific project, but he refers to this

adjustment as "necessarily ad hoc" (331). Ehrhardt is in agreement with the need for differing project-

specific discount rates and points out that the "academic literature is virtually unanimous in

recommending adjustments when evaluating projects with different levels of risk" (102). He then cites

the Brigham study (1975) which found that about one-half of 33 large companies surveyed did make

project-specific adjustments either directly to the cash flows or adjustments to the specific cost of

capital used.

Although significant differences exist between cost of capital for valuation purposes and cost

of capital calculation for project/investment evaluation, there is still value in the overall cost of capital

measure. Higgins reinforces the point made above while also demonstrating the link between the

overall cost of capital and a specific project's cost of capital:

We conclude that the cost of capital is an appropriate acceptance criterion only when the risk

of the new investment equals that of existing assets. For other investments, the cost of capital

is inappropriate; but even when inappropriate itself, the cost of capital frequently serves as an

important, practical keystone about which further adjustments are made. (288, emphasis

added)This implies that for a typical company, the overall cost of capital should be knownand used

throughout the organization, but should be viewed primarilyas a starting point of adjustments and

analysis.


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The most important link between these two uses of cost of capital for our purposes,

however, is that the approach to valuation of and cost of capital calculation for a small

business is much more like that of a typical capital project! Authors mention this frequently,

including Palliam, who says a small business can be "thought of more as a capital project" (336).

Ehrhardt shares this opinion and lumps cost of capital calculation for a small privately-held company

into the same category as cost of capital calculation for a project within a larger firm (101). Pratt

makes a very similar comparison, relating small company cost of capital to divisionalcost of capital in

a larger company (13). Another argument for the similarity of small business and capital project

assessment is that capital project approaches consider the investments within their common context of

very specific risk that cannot necessarily be diversified away, which is the very situation in which small

firms often find themselves. In addition, due to the common existence of behavioralmotivations with

small business owners, a firm valuation approach using typical, market-contrast risk premiums, would

only be appropriate for certain potential acquirers to take in valuing the company. The small business

owner himself, however, cannot be so easily explained, as we will later see in Part II.

Review of Traditional Models

A few formulas have been developed to aid in the calculation of a firm's cost of capital. The

weighted average cost of capital (WACC) calculation provides an interest rate that takes into account

a company's cost of debt and cost of equity, or put another way, the rate of return required by the

firm's creditors and the rate of return required by the firm's stockholders. This formula is relatively

straightforward and standard. It is shown and described as follows (Brigham and Ehrhardt, 435):

Equation 1-1: Weighted Average Cost of Capital

WACC = wdkd(1-T) + wpskps + wcekce

Where:

wd :Weight of market-value debt financing in the company's capital structure

wps : Weight of market-value preferred stock in the company's capital structure

wce : Weight of common equity in the company's capital structure

kd : Weighted average cost of company debtkps :Component cost of preferred stock2

kce :Cost of common equity

2 The component cost of preferred stock is calculated as Dps / Pn where Dps is the annual preferredshare dividend and where Pn is the "net issuing price" (preferred share price discounted by flotationcosts incurred for the stock listing) (Brigham and Ehrhardt, 424).


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T : Effective corporate tax rate

This formula is widely accepted and utilized, and can be found in any MBA-level corporate

finance textbook. Its calculation reduces even further in a firm making no use of preferred stock

then, the calculation would boil down to the after-tax cost of debt combined with the cost of equity

(weighted, in both cases).

Fortunately, the cost of debt is typically calculated fairly easily. Within a firm, this rate can be

determined very quickly by examining a debt schedule and weighing the interest rates according to the

values of the various balances. Even parties external to a firm can determine this by examining the

interest expense and long-term debt balances off the firm's financial statements in order to come up

with a figure. Alternatively, one could also look up the company's bond rating and then compare it to

typical bond rates of similarly rated bonds to develop a close approximation of the company's cost of

debt. In the cases of privately held businesses where financial information is not known by outsiders,one could still estimate a fairly accurate cost of debt simply by examining public interest rate indices

such as LIBOR (London Inter-Bank Offer Rate) or Prime (an indicator used in consumer and small

business lending), and then surveying a commercial banker as to what a small firm of a given revenue

size in average financial condition could expect in terms of a rate, relative to one of those indices. Due

to banks' significant aversion to risk and the generally consistent lending guidelines existing from one

bank to another, it can be expected that such an approach would actually yield results with acceptable

accuracy.

The cost of equity(kce), however, is where most of the "heavy lifting" involved in cost ofcapital calculation occurs. The two most widely referenced methods are the Discounted Cash Flow

(DCF) approach to cost of equity calculation, and an approach making use of the Capital Asset Pricing

Model (CAPM).

Cost of Equity Discounted Cash Flow (DCF) approach

The Discounted Cash Flow method makes use of current market data as well as analysts'

growth expectations to produce a cost of equity figure. The subject company's cash flows are

examined, either by observing the current dividends paid to investors or by looking at cash flow

generated by the company's operations. Then, an estimated growth rate is combined with the

company's current value (stock price) and the company-generated cash flow or dividend payments to


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determine the company's cost of equity. The Discounted Cash Flow cost of capital formula can be

stated as follows (Brigham and Ehrhardt, 431)3:

Equation 1-2: DCF Cost of Equity using Dividends

k = D0 (1+g) / PWhere:

k : cost of capital

D0 : dividend per share paid in period 0 (the period immediately preceding the

current period)

g : expected long-term dividend growth rate4

P : firm's current stock price

A firm with a current share price of $20, a recent dividend of $3.00 per share, and a growth rate of4.0% as predicted by analysts, would accordingly have a cost of capital of 15.6% 5. Using this

approach, several assumptions are made, including that:

the firm will continue to grow at the rate used in the formula no faster or slower

the firm's shares price properly values the firm and its expected cash flows as part of a

relatively efficient market

the firm's dividend payout ratio is reflective of the company's earnings, and that the dividend

will continued unchanged into the future6

This approach may be helpful in the case where those assumptions hold it certainly makes foran easy calculation. But what about firms who pay no dividends, or who pay dividends inconsistently

in frequency? Other firms may pay a "token" amount to appease stockholders. Indeed, as Shannon

Pratt points out, in these situations "theoretically, the growth component, g, will be larger than that of

an otherwise similar company that pays higher dividends" (112). In other words, stockholders are not

benefiting as directly and immediately as investors in other similar firms are benefiting. Any long-term

gains as a result of a firm's ability to grow faster from retaining cash would be theoretically realized at

a later time.

3 This formula is an algebraic re-writing of what is commonly known in the financial world as theGordon Growth model, which is used to determine the theoretical value of a firm's stock when the costof capital (as well as the dividend level, and growth rate is known. The Gordon Growth Model in itsoriginal form is as follows: P = D0(1+g) / k-g4 This is typically the growth rate as projected by company and/or industry analysts; often it will bedesirable to take an average of several analysts' growth rate projections for use in this model5 [ 3 (1+.04) / 20 = 15.6% ]6 The dividend payout ratiois defined as the percentage of a period's after-tax profits distributed by afirm in the form of dividend payments to its stockholders.


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A common way to avoid this issue with dividend payments is to look at the total cash flow to equity

generated by the firm, regardless of the level of dividends actually paid out of this cash flow. This

approach takes a broader look at the cash flow situation of the firm and should fare better in firm-to-

firm comparisons. First, what is referred to as "Free Cash Flow" (FCF) for the firm is calculated. FCF

is typically calculated as follows (Pratt, 16):

Equation 1-3: FCF Calculation

Net Income After Tax

+ Non-cash charges (depreciation & amortization, deferred revenue/taxes)

- Capital Expenditures (necessary to support projected operations)

+ Increase in working capital from operations

- Decrease in long-term debt

-----------------------------------------------------------------------------------------------------

= Free Cash Flow to equity (FCF)

Next, the DCF equation presented earlier (Equation 1-2) is modified slightly to reflect Free Cash Flow

instead of dividend payments, and the value of the firm as a whole instead of looking at just a single

share price. With this modification, a better comparison can be made between similar firms with

differing dividend payment policies.

Equation 1-4: DCF Cost of Equity using FCF

k = FCF0 (1+g) / PMV

Where:

k : cost of capital

FCF0 : Free Cash Flow to equity in period 0 (the period immediately preceding the current

period) see Equation 1-3

g : expected long-term dividend growth rate

PMV : present market value of the firm7

Now, the resulting cost of capital reflects all of the firm's cash flows to equity. In theory at some point

a firm should distribute most or all of its earnings to shareholders. Typically this point in time wouldroughly coincide with a period of firm maturation and slower growth. This is, in fact, the ideal situation

7 This is commonly referred to as "total market capitalization". This can be calculated by multiplyingthe current share price by the total number of shares outstanding. Alternatively, the Free Cash Flowfigure can be divided by the total number of shares outstanding to determine the FCF per share. Thisfigure could then be used (in place of FCF0) in conjunction with the individual share price (in place ofPMV) to complete the calculation.


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in which this model would be applied. However, there are many situations in which a firm's growth is

predictably high in the short-term, but slower growth is just as equally predictable in the long-term. In

such cases a two or three stage Discounted Cash Flow calculation, with varying business stages and

growth rates, may be warranted8. Regardless of whether a single-stage or multiple-stage model is

used, the output of the Discounted Cash Flow approach remains the same: the cost of capital is

determined by looking at company cash flow combined with growth rate projections.

Cost of Equity the Capital Asset Pricing Model (CAPM) approach

Possibly the most common way of calculating a company's cost of equity is through use of the

Capital Asset Pricing Model, referred to commonly as "CAPM". The Capital Asset Pricing Model was

developed by William Sharpe in the early 1960's and although the model is not perfectly accepted by

all, it is by far the most broadly accepted in the academic and financial community in terms of cost ofequity calculation.

There are several assumptions that must apply in order to make use of CAPM in a given situation.

As Brigham and Ehrhardt state, the "primary conclusion of the CAPM is this: the relevant risk of an

individual stock is its contribution to the risk of a well-diversified portfolio". Embedded in their

statement is the assumption of minority ownership: that is, the assumption that a given investor is

piling money into a company's stock simply as one part of a well diversified portfolio. As a result, the

model makes no allowances for unsystematic risk, which was defined earlier as the risk level unrelated

to the market as a whole the specific risk attributable to the firm in question or the firm's industry. Inaddition to the significant assumption of ownership by minority investors with diversified portfolios, the

model also makes the following assumptions (Tesfatsion, 1):

The company's stock is traded in a competitive, efficient market with no taxes or transactions

costs.

There exists a risk-free return rate at which investors can freely borrow and lend

Investors have a common time horizon for portfolio choiceWith these assumptions now in place, the CAPM model is presented below (Brigham and

Ehrhardt, 230):

8 A multiple-stage DCF model allows one to calculate cost of capital for a company with several stagesof different rates of growth. For example, a firm may expect 20% growth for years 1-3, 10% growth foryears 4-5, and then 3% annual growth thereafter. This calculation is extremely complex when donemanually, but may be performed more practically may done through an iterative process usingMicrosoft Excel or other spreadsheet/financial calculator. See Pratt (113-114) or Brigham & Ehrhardt(433) for more information.


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Equation 1-5: CAPM (traditional)

kce = krf + (RPm) B

Where:

kce : cost of equity for the firm

krf : risk-free rate9

RPm : equity risk premium of the market as a whole10

B : Beta coefficient for the company in question (see Equation 1-6)

Mechanically, the CAPM is doing several things. First, it identifies a "risk free rate" as a base marker

to start from. Secondly, it adds a premium that includes investors' expectation of what the market

would generate on average over that risk free rate. Finally, it takes into account the specific volatility

of the company in question relative to the comparison market through the Beta coefficient.

For illustrative purposes, consider the following example: A given firm is operating in an

environment where U.S. Treasury bonds are yielding 4.5% and where the market as a whole has

returned an average of 10.0% over the same time period (leading to an equity risk premiumof 5.5%,

or the difference between the two values). The Beta for the firm has been calculated by regressing the

company's stock returns against the S&P 500 and has been determined to be 1.10. The cost of equity

for this firm would be 10.55%11. The CAPM modifications that will be presented below are all

calculated in essentially with the same manner, except for some changes in the specific equation

terms included.

There has been a plethora of articles and debates through the years concerning CAPM, but

this last item mentioned the Beta coefficient is undoubtedly the most controversial. The CAPM

makes no provision for unsystematic risk because it assumes that is can be diversified away from; the

Beta coefficient, however, is the measure of the specific company's systematicrisk. A Beta of 1.0

indicates perfect correlation with the comparison market; a Beta of 1.2 indicates a 20% greaterdegree

of movement than the market; a Beta of 0.80 indicates a 20% lesserdegree of movement than the

market. The standard formula for Beta is as follows (Brigham and Ehrhardt, 221):

9 The risk-free rate is indicated by the returns on U.S. Treasury bonds. Brigham & Ehrhardt's textmentions a ten or twenty year horizon (as does Pratt), Ehrhardt's Search for Valueadvocates onlyshort-term (90 day) rate usage, and Ross does not provide a strong opinion in his text other than tosuggest that the time periods for the risk-free rate and the equity risk premium should be similar.10 The market equity risk premium is often expanded inside of the CAPM formula. It expanded form isRPm = km - krf where km is the average return on the market over a given time period. Typically asimilar time period is used for km as the time period of the risk-free instrument referenced.11 [ 4.5% + (5.5%)(1.10) = 10.55% ]


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Equation 1-6: Market Beta calculation

B = ( StDevs/ StDevm ) Corrsm

Where:

B : Beta coefficient for a given firm, indicating systematic risk

StDevs : Standard Deviation of the firm's stock returns over the observation period

StDevm : Standard Deviation of stock market returns over the observation period

Corrsm : Correlation of the firm's stock performance with market performance during

observation period1213

The implications behind this calculation are numerous. First of all, as the standard deviation of the

individual stock's returns increases, the systematic risk of that stock increases. Second, the higher the

correlation between the returns of the individual stock and the market, the higher the risk level of the

individual stock. It also indicates that a stock with a Beta of 1.0 would not only have to perfectly matchthe market in the standard deviation of its returns, its returns would also have to correlateperfectly

with the market returns. This concept of Beta will be revisited later in the paper.

For a company whose stock is publicly traded, the CAPM may very well be a viable approach.

Whereas the DCF approach captures these multiple factors (risk, equity risk premium, etc.) into one

cost of equity number, the CAPM approach seeks to identify those components individually through

historical observation, and does not require the somewhat subjective growth projections demanded by

the DCF method. If the market within which the stock trades is stable and relatively predictable, then a

fairly accurate market risk premium can probably be determined with the CAPM approach. A stockprice history exists against which a market index may be regressed to determine a Beta. As we will

see later, however, the problems with the CAPM model arise when information is lacking (such as the

information deficiency that exists in a small firm environment), when the assumptions mentioned

earlier do not hold in the environment where it is being applied, and when returns do not correlate well

with a market index.

PART II: Cost of Capital in the Small Business World

12 The coefficient of correlation is calculated as follows: Cov(s,m) / [StDev(s) * StDev(m)] , whereCov(s,m) is the covariance of the individual stock and market returns, StDev is standard deviation ofthe stock (s) and market (m) returns.13 Covariance, a required factor for calculating the coefficient of correlation needed to find beta, iscalculated as follows: Cov(s, m) = 1/n * (si - save) * (mi - mave) where the terms s i and mi are actualvalues of the annual rates of return of an individual stock and the market respectively, taken overseveral periods, n is the total number of values of mi and si used, and mave and save are the averagevalues of si and mi


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differences. Collectively, these differences/distinctives in fact are the primary impetuses for this paper

and the FOCCM model that will be introduced later. For now, let us explore these differences in more

depth.

Equity Owner (Motivational) Differences

The manner in which businesses are operated and in which decisions within those firms are

made varies greatly depending on the ownership structure of the business. In virtually all publicly-

traded firms, all of the equity owners are minority owners, meaning that no single owner owns more

than 50% of the outstanding shares. As a result, no one shareholder is able to control the hiring and

firing of board members who in turn make major decisions on behalf of the shareholders. In a SPHB,

there is often a controlling member or a group of unified owners who make up an ownership

percentage large enough to control the business. As a result, the majority owner's very active,personal connection to the business will bias the decision-making of the firm in the direction of their

personal preferences, even to the possible detriment of other investors. And so the equity owner

difference is the reality of different motivatingfactors behind their ownership of the firm.

In the most common case of one or two individuals owning and operating a small company,

the reality of their owner-manager profile creates no conflict in the short run. In fact, any "selfish"

decisions made in the course of the running of the company (i.e. providing themselves perquisites

through the business, giving themselves a bonus, etc.) are in fact in the positive interest of the equity

holders they arethe equity holders and those benefits make up a portion of their expected return!The claim that owners' personal preferences drive decision-making is well supported in the literature.

The relevant question here is: what are these preferences of small firm owners? A review of journal

articles commenting on this topic reveals a wide range of opinions and findings. These findings about

SPHB preferences range from the importance of independence and flexibility, to income and "prestige"

considerations. Petty and Bygrave make the following comment in a discussion on traditional small

businesses:

The concept of wealth maximization has reduced meaning, since there are so many

exogenous considerations influencing the decisions, besides that of economics. Utility

maximization becomes the rule, rather than the conventional wisdom of wealth

maximization. The objective is not so much to create value, but to provide a

"preferred" life style within the community. Even for the "successful" lifestyle firms,

there is little in the way of value created beyond providing a living for the owner and

his or her family (93, emphasis added).


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A return to the classic idea of utility maximizationwould indeed appear to be the conceptual

solution to the broad base of desires and motivations that may drive a given business owner. In a

publicly traded company, it would be impossible for a company to generate returns in a customized

way that would meet each of its shareholders' needs securing a spot at a well-known retirement

home for one, giving another a vehicle, provide a sense of security and belonging to a stockholder,

provide children's educational needs to another, provide prestige within the community by virtue of

stock ownership, provide a sense of independence to a stockholder, etc. Becausethat is not possible,

the natural way of compensating each owner for their stake within the company is through the

payment of monetary dividends. The equity owners (stockholders) in turn can use the funds in

whatever way they see fit to accomplish their goals. But in a SPHB it is often feasible for such

"returns" to be provided directly by the company to its owner, or to its few owners. In fact, the very

ownership of the business may provide a "return" of community prestige that the owner may be unable

to achieve in anyother way.

It may be appropriate to break out returns to a small business owner in two categories: that of

pecuniary (monetary) returnsand non-pecuniary returns. This lines up with McMahon and Stanger's

suggestion:

The next step is to reconsider what is meant by 'utility' and 'consumption.' Basically,

utility arises from anything which yields an investor satisfaction. This mostly comes

from consumption of goods and services. However, consumption can be defined more

widely to include access to non-pecuniary (sometimes referred to as psychological or

psychic) benefits, which might provide satisfaction to a particular investor (28).

It is important to note, however, that at least some degree of pecuniary returns are required before anynon-pecuniary returns can be expected, as a company would cease to exist at some point if it failed to

generate pecuniary returns (profits) over the long run. Once the company ceases to exist, then

obviously neither pecuniary nor non-pecuniary benefits will continue. McMahon and Stanger weigh in

on this issue as well: "It is important to note that the investor can use the maximized pecuniary return

provided to acquire whatever non-pecuniary benefits he or she might desire. That is to say, pecuniary

returns are traded for non-pecuniary benefits afterthe pecuniary returns have been received (29)."

Boyer and Roth also remind us of that same fact: "It is offered that businessmen are sacrificing

opportunity return in exchange for behavioral satisfaction. There is, however, a limit to the size of the

behavioral return. The overall cost of capital in the long-run cannot fall below the weighted cost ofdebt, or the owner will soon experience financial difficulties by accepting projects that are debt

financed and on which he is unable to meet the interest payments." (9).

Barton Hamilton (2000) compares small businesses owners' pay and returns to what their

peers in industry are being paid. His study makes use of many variables in an attempt to identify a


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proper comparison pool in the workforce by examining many factors including work

experience/background, level of education, race, and marital status. Despite the appropriateness of

the use of many questionable variables, through the course of his research he did discover that

undeniably, significant factors beyond just financial returns contributed to the entrepreneurs' choice to

enter self-employment. In fact, a notable amount of research on a number of owner-manager

motivators has been performed and cannot all be conveyed here in detail. More empirical research

needs to be performed, however, to better understand the exact trade-offs that occur between these

non-pecuniary benefits and pecuniary benefits. The non-pecuniary benefits mentioned repeatedly in

the literature have been summarized in Figure 2-A below:

Figure 2-A: Non-Pecuniary Returns to Small Business Owner-Managers

as identified in recent literature

Type of Non-Pecuniary

Benefit

Relevant factors Authors

SECURE EMPLOYMENT /

FUTURE

Being secure in self-

employment, owning an

investment transferable to

others

Boyer and Roth, McMahon and

Stanger

CONTROLRetention of control; "Being

your own boss"

Borland, Boyer and Roth, Brigham

and Smith, Forsaith, Gallo, B.

Hamilton, R. Hamilton and Fox

(1998), McMahon & Stanger,

Pandey and Tewary, Perry,Shapero, Timmons, Van Auken

LIFESTYLEPreferred Lifestyle /

Independence

Berger and Udell, Boyer and Roth,

Brigham and Smith, Forsaith, R.

Hamilton and Fox (1987),

Hutchinson, McMahon and Stanger

COMMUNITY

Contributing to the wider

community, community

prestige, benevolence to

employees, philanthropy

Boyer and Roth, McMahon and

Stanger

Determining the level of non-pecuniary returns required as compared to the pecuniary returns

desired is one of the objectives of the FOCCM model that will be presented later in this paper. It is

interesting, however, that the degree of real trade-off that occurs between the pecuniary and non-


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pecuniary benefits received is difficult to measure. Indeed, Forsaith demonstrates there may indeed

be some dissonance between the benefits that owner-managers claim to desire and the benefits that

in judging by their actions are actually the most important to them:

The owner-managers' willingness to trade off financial return for the reduction of unsystematic

risk factors is significantly less than would be expected from the owners' reports of the

importance they place on these factors. That is, the owners report that these factors are

important to them but they appear to be unwilling to give up much return to mitigate these

risks. The findings provide evidence that the owner-managers studied derive utility from a

wide range of inter-related sources and that their objective functions include a consideration of

the exposure to unsystematic sources of risk and the pursuit of non-financial returns. Within

the limitations of the study, the findings give some support to the proposition that small

enterprise financial management is not underpinned by wealth-maximizing assumptions alone.

(Forsaith, 11-12)

A piece of information in Boyer and Roth's data (who created a model we will investigate later) revealssome similar evidence: one of the supposed behavioral (non-pecuniary) rewards cited as highly

important by the interviewed executives was described as "I control my income by my actions" a

statement you could say implies a high degree of pecuniary reward! Nonetheless, it must be admitted

that considerable more non-pecuniary benefits seem exist in the SPHB environment (as they are

hugely motivating factors for SPHB owners) and therefore must affect decision-making to some

degree.

Size Differences

By definition, SPHB's are smaller in size than large publicly-traded companies. However,

exactly what this means for managers, owners, and investors is not completely clear. There is much

debate as to the relationship between firm size and expected returns, between firm size and cost of

capital, and between firm size and capital structure. In the case of expected returns and cost of

capital, there is little disagreement that a negative correlation exists (that is, the smaller the firm, the

higher the expected return and the higher that firm's cost of capital). There are significant differences

of opinion concerning capital structure specifics, however, with some authors claiming that debt in a

small firm composes a smaller percentage of the capital structure, and other authors claiming that itmakes up a higher percentage. But for all three issues, the biggest point under debate is the

explanation of whyand howthese differences exist.

All three issues are closely related, of course, as both the expected returnof equity holders

and the capital structure weights(percentage debt and equity funding the business) are both inputs


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into the cost of capital calculation. Recall that we put forth the WACC equation which accounts for

those weights earlier in Equation 1-1. We will examine the debate surrounding small business capital

structure decisions shortly, but for now let us look at some of the issues surrounding this debate on the

relationship between size and expected returns.

Ibbotson (2001) reports beta and return information for decile portfolios from the major U.S.

stock exchanges. I have reported the information from three of the deciles below in Figure 2-B.

Figure 2-B: Partial listing of return information for selected U.S. major stock exchange decile portfolios

(Adapted from SSBI 2001)

DecilePortfolio

BetaArithmetic

MeanReturn

RealizedReturn inExcess of

Riskless Rate

EstimatedReturn inExcess of

Riskless Rate

Size Premium(Return inExcess of

CAPM)1 (Large Caps) 0.91 12.06% 6.84% 7.03% -0.20%

5 (Mid Caps) 1.16 15.18% 9.95% 9.03% 0.93%

10 (Smallest) 1.42 20.90% 15.67% 11.05% 4.63%

It should be noted that the Beta (a measure of volatility/risk) increases as firm size decreases,

and that the return of smaller company stocks also increases as firm size decreases. In Ibbotson's

Yearbook a complete table of information with information for all ten deciles is shown, and the

movement in the entire data set is consistent with the trend shown here. Rather than exploring thefundamental differences underlying these figures, most of the research has focused instead on how to

take this information and use it to determine an expected return on an investment of similar size. The

problem with this approach is the assumption that is made that a generic size premium can be used in

a cost of capital calculation for another firm of the same size. Standard & Poor's reports comparative

operating margins for twenty five portfolios, the first made up of the largest companies all the way

down to a portfolio of the smallest companies, and the information is presented nicely in Pratt's book

(102). They calculated a standard deviation of returns between the firms in the largest company

portfolio of 17.53%. The same statistic for the smallest portfolio (out of twenty five) is 28.86%, with the

figures in between trending consistently higher as the portfolio size examined became smaller. Thestandard deviation of the small companies' operating margins was over 50% higher than that of large

companies, despite the smallest portfolio being made up of twice as many firms as the largest (169 in

the small company portfolio compared to 84 in the large company portfolio). With such volatility even

within the group of small firms, it would be difficult to make any blanket assumptions about any

particular small firm's returns based only on the group performance compared to large company

performance. In addition, the 169 firms in the Standard & Poor's study, and the data of the hundreds


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of stocks making up the lowest decile of Ibbotson statistics, were spread across dozens of industries,

each with different demand, business cycles, levels of risk, and market characteristics. To take an

approach as Heaton (1998) does, with a simple small company risk premium over treasury bill returns

based on historical evidence, is insulting to the realities of the challenges of running a small business.

Such a flippant approach produces an equally flippant result actual returns for a given small

company may fall in the general ballpark of the prediction in a very expansive portfolio, but from a

standpoint of cost of capital calculation for a specific firm, this approach is simply inadequate. "Ex

post" returns for a portfolio of small company stocks with extremely diverse financial and industry

structure are not good predictors of future returns of a specific company's stock.

Alberts and Archer (1973) also discovered some negative correlation between company size

and cost of equity, but mentioned reasons for this difference being due to industry specifics and lack of

owner diversification.

Brigham and Smith's 1967 work, performed early on when evidence of any correlation

(positive or negative) between company size and cost of equity/return measures was scarce,

confirmed evidence of a negative correlation. And yet, in his conclusion, even he alludes to behavioral

factors as the realities behind the numbers. Other models have been developed that attempt to

address some of the particularities related to firm size, and will be discussed later.

Business Culture Differences

Small businesses are not as homogeneous as larger ones are in terms of their culture. There

are certain things about business processes and expectations that are relatively standard in larger

enterprises. This standardization can manifest itself in a large company's approach to planning,

budgeting, training, pay levels, facilities, financial management, marketing image, and in many other

ways. It could be argued that this fact is largely driven by the reality that large companies employee

most of the employees in the U.S. and consequently are typically competing with other large

companies for employees. Expectations that employees and customers have of the enterprise are

high. Also, the company's very size indicates a certain degree of strength and maturity in its industry,

which most likely allows for more spending in areas that small firms may not find necessary orpossible.

A significant way that culture differences manifest themselves is in the approach to financial

management and decision-making. Gallo (2004) has done a fair amount of research on family-owned

small businesses, and demonstrates that those businesses are more labor intensive (as family equity


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holders removed from the daily operations of the business tend to be skeptical about capital

investments that might reduce variable costs) than non-family owned businesses, even though the

comparison businesses may also be relatively small. Gallo extensively discusses the tension between

family control and profits and says that often those goals are at odds with one another (resulting from

capital structure decisions relating to capital investments more capital structure issues will be

discussed below). In addition, he highlights the problem of the lesser prospects of future

competitiveness of the family-owned firm as result of their "peculiar" financial management resulting

from control concerns.

McMahon and Stanger (1990) reference a study that looked at small petroleum distributors,

tried to look at those owners' objectives, and then made assumptions about all small biz owners'

objectives. However, the author of thispaper you have before you previously worked in the petroleum

distribution industry and from experience knows that the industry is dominated by many, small, family-

owned firms. Typically, these firms have few growth opportunities and may be owned by a second orthird generation family member. McMahon and Stanger report that net income was the important

objective of these owners, as would come to no surprise in a "sleepy" industry such as oil and

petroleum distribution. The point to be made here is this: the financial behavior and motivations of

individual SPHB's or even industries dominated by SPHB's isaffected by the culture of the firm, which

is largely driven by the desired outcomes of the owner(s) of the business in question.

Capital Structure Differences

Because a business' cost of capital is large determined by its capital structure, it is important

to develop an understanding about the capital structures of SPHB's. This topic has been examined

extensively in the literature, with a wide range of findings resulting. Two contradictory views pervade

the literature: one set of researchers claim that small businesses in general carry a higher debt load

than large businesses; another group says that small businesses carry lessdebt in their capital

structure than do large businesses. Both groups reference use of internal funds as a strongly

preferred funding source.

Hamilton and Fox (1998) also find themselves among those who cite data showing that smallfirms carrying higher debt levels, and they say this is due to those small businesses' non-equity

financing preferences. They reject any notion of a "supply problem" of finance for small businesses

existing in the market, but rather say that the demand is very high. Both the Forsaith and the Walker

and Petty's article show that small businesses use high levels of short-term debt financing (such as

operating credit lines), although Walker and Petty claim that they carry lower levels of debt in general.


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R.W. Hutchinson speaks extensively about owner debt and equity preferences, and provides an in-

depth explanation as to why in virtually every situation, a small business owner will do whatever is

necessary to avoid additional equity issuance in order to avoid putting his control of the business in

jeopardy. This often means adding increasing debt to the business in order to fund growth without

adding to the ownership structure. Hutchinson does point out, however, that internal funds can still be

used to grow the business but does so with a disclaimer: "Here, however, [internal] equity capital still

has an opportunity cost. The owner-manager will only be willing to pursue this route in line with his

own attitude to risk, which if risk averse will result in a combination of investment and debt policy which

produces relatively low risk and hence a low return on equity" (235). In other words, if a small

businessman avoids equity issuance in order to avoid loss of control, his remaining option is to use

internal funds, or if internal funds are limited then he may fund the business through debt. If he does

not wish to add risk to the business, however, he will not issue debt and so as a result the growth of

his business and the profits it can generate may very well be limited.

Some authors in fact, such as Carpenter and Peterson and Lopez-Gracia, focus heavily on the

use of internal funds by small businesses. Carpenter and Peterson claim that internal funds are the

constraining factor to such firms although they provide no behavioral explanation for his claim. Their

empirical data all came from a 1982-1990 sample data set of manufacturing firms, and their conclusion

may have been appropriate for old cash-cow firms in a non-service industry (such as manufacturing),

but like the McMahon and Stanger article referenced earlier, created a "straw man" fallacy by throwing

up a very limited, restrictive sample and then applying his conclusion to the \world of small business as

a whole. Hutchinson's and Carpenter's views are in direct contradiction Hutchinson says that

conservatism on the part of small business owners will lead them to issue debt, whereas Carpenterclaims that same attitude of conservatism will lead them to avoid debt! The source of this

contradiction can be explained by the sample used by Carpenter and Peterson already explained, in

combination with the fact that Hutchinson looked at small business owner behavior more holistically.

Hutchinson highlights the needfor debt in small businesses depending on their life stage: "For most

owner-managed small firms, there is an additional emphasis on the need to finance expansion through

debt capital provided by banks because the use of equity in the early stages of development is limited

to an individual and/or his family's contributions" (233).

Berger and Udell (1998) show that small businesses within their sample were, on average,financed by approximately 50% debt and 50% equity. In addition, they said that changes in capital

structure were due largely to accumulations in retained earnings, and not necessarily new equity

partners. Berger and Udell also demonstrate heavier use of debt in firms as "adolescent"businesses.


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Otherauthors put forth opposingfindings. McConnell and Pettit (1984) say that small firms

have, in general, less debt as a percentage of their capital structure than do large firms. They look

through the lens of traditional financial theory to come to this conclusion, and claim this should be true

because:

1. small firms typically have lower marginal tax rates than larger firms, resulting in less of a

tax deduction benefit

2. small firms may have higher bankruptcy costs than large firms, increasing the risk of debt

3. small firms have difficulty "signaling" their health to creditors which in turns raises the

firm's cost of debt

Barton and Matthews (1989), on the other hand, question the application of such stoic financial theory

to the small business environment (as does Van Auken, 2005), and say that prior literature does not

sufficiently account for the strategic decisions in the operation of a small business that directly affect

the capital structure. They propose a variety of strategic choices that affect the small firm's capital

structure, including management goals, risk propensity of the owner-manager (including the realities ofpersonal debt guarantees on the part of the owners), and the preference for internal funds over

external funds with which to finance the business16. Chaganti, Decarolis, and Deeds conclude that

"craftsmen entrepreneurs" (as they refer to trade-based businessmen with few managerial skills) will

make use of new equity before debt, but "managerial entrepreneurs" will prefer debt before equity.

Their "findings" fly directly in the face with the other research because they fail to consider control

issues in the small business environment.

In summary, however, it can be said that small and large firms have distinctly different

approaches to capital structure decisions. Small firm behavior in terms of debt and capital structureseems to primarily be a function of the priorities and objectives of the owner(s).

Informational Differences

Little support should be needed for the assertion that financial and operational information

about SPHB's is very difficult to collect. Anyone who has ever attempted to gather such information

would agree readily. The difference in this matter when comparing large, publicly held businesses to

small, privately held ones is as dramatic as any mentioned here. The relationship between this SPHBattribute difference and the other differences examined in this section is interesting, because it acts as

both a causal factor andresult of the other differences. This can be well summarized in chart form:

16 Norton (1990) provides a good literature survey on this topic of small business capital structuredifferences, and through use of a small business survey methodology also concludes thatmanagement has the biggest influence on capital structure. He does not, however, provide anexplanation as to what drives these managers' decision-making.


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Figure 2-C: Relationship between Informational Differences and other

identified small / large business differences

Informational Differencescompared to which

attribute?

Informational DifferencesRelationship

Motivation

Equity Owner

Motivational Differences

Equity Owner Differences

RESULTin Informational

Differences

In a SPHB you have one individual or

small group of equity holders; no incentive

to disclose information; no SEC regulation

Size Differences RESULT

in Informational Differences

The smaller the SPHB, the fewer the

people (internally and externally) who

have their hands on the numbers

Size DifferencesInformational Differences

may CAUSESize

Differences

Put differently, a SPHB may find it difficult

to grow and attract capital as a result of a

desire to keep information close to thevest

Business Culture

Differences

Business Culture

Differences RESULTin


A tightly controlled, owner-managed small

business will likely be less open with

employees about financial condition of the

firm, etc. The firm's finances are closely

linked to the owner's finances.

Capital Structure

Differences

Capital StructureDifferences RESULTin


When no public stock or public debt

(SEC-regulated bonds, for example) has

been issued, then information reportingrequirements are limited to only private

financing relationships (bank, other

primary creditors, the owner or small

group of owners, etc.)

Parties external to a SPHB will have significant difficulty accessing information about a firm,

particularly financial information, for the reasons shown above in Figure 2-C. One of the few sources

of information is Dun & Bradstreet, which even then just reports the information that is provided tothem by small businesses. It should be noted, however, that these informational differences will only

affect cost of capital from an internal perspective to the extent that a company's cost of debtincreases

as a result of lack of complete and/or comparable information provided to outsiders. Externalparties'

attempts to calculate a company's cost of capital will be greatlyaffected by a lack of information.


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Also, remember that informational differences affect small firms in their relationship to other

small firms, as well. A firm will notbe limited by the fact that it holds its financial results "close to the

vest" when attempting to calculate its cost of capital. But if for that process or for any other purpose

the firm wishes to examine industry competitors, it will encounter difficulty. Informational issues about

small firms is not just a problem outside of a firm, it is also a problem inside of an industrydominated

by small firms.

Adjusted Models for Small Business Differences

Finance scholars often struggle to explain market and "real-world" aberrations that do not hold

up against the theories inside their academic box. After all, much time and thought and analysis goes

into the formation of their models. Follow-up scholarly journal articles are written well into the future

either supporting or attempting to disprove the validity of any substantial idea put forth, and so theacademics pride themselves of the level of rigor in their analysis and subsequent critique.

Consequently, when a widely-accepted model such as the CAPM fails to hold true in certain

circumstances, there is often disbelief, or simple adjustments are created in order to fit a new problem

into an old mold. The problems with the traditional cost of equity models presented earlier when

applied to the small business environment are many, however, and those problems have not been lost

on allacademics. A variety of models have been put forth in various attempts to capture the

differences between the large firm environments for which the traditional models have been designed,

and the small firm environment in which there are many more variables to be considered in a

calculation such as the cost of capital.

Variations of CAPM

As mentioned earlier, many finance researchers have examined historical data and

determined there needs to be a "size premium" taken into affect for small firms. But it was pointed out

that although a generally higher return level exists for small firms, this fact alone gives little guidance

to those trying to determine cost of capital for a small firm in an undiversified portfolio, as a small

business owner may hold. Heaton's "equity risk premium" mentioned earlier, which he applied tosmall firms, is only one of dozens of similar suggestions that try to gross up large company returns by

adding a "small firm risk premium" to a point where the returns end up in the expected range for

smaller companies. But they do not take into account specific differences in the small business

environment and differences in the ownership structure. McMahon comments on the outstanding


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questions of the CAPM for large enterprises, not to mention small enterprises with numerous special

considerations:

Because there is by no means universal agreement on the validity of the CAPM for large

business enterprises, let alone for small enterprises, it might be considered that such an ad

hoc extension to the CAPM as is described above [referring to a "small enterprise premium"

advocated by some] is not an appropriate means for making explicit the proposed liquidity,

diversification, transferability, flexibility, control, and accountability considerations in the

financial objective function of small enterprises. (McMahon 1995, 32).

And in his finance text published two years earlier, he drove home the point about the SPHB owner

diversification problem:

It is difficult to disregard the mounting evidence that as far as small enterprises are concerned,

the CAPM seems to be missing some vital explanatory factors which would account for the

relationship between return and risk in such concerns. The existence of the small firm effect

lends support for the possibility that these might include information, marketability andtransaction cost considerations. However, it does not shed light on the other important

deficiency of the CAPM in the context of small enterprise financial managementthat contrary

to the underlying assumptions of the CAPM the typical small enterprise owner manager does

not hold a diversified wealth portfolio. (McMahon 1993, 115, emphasis added).

Consider the comments of a tax court judge, knowledgeable of CAPM, who made the following

comments as part of a business valuation case where a discount rate had been provided by an expert

witness based on the CAPM:

[The witness] followed the principles of CAPM and did not make any provision for [the subject

company's] unsystematic risk, based on the assumption that such risk was diversifiable[R]espondent and [the witness] have overlooked the difficulties in diversifying an investment in

a block of stock they argued is worth approximately $8.94 million. Construction of a diversified

portfolio that will eliminate most unsystematic risk requires from 10 to 20 securities of similar

value. See Brealey & Myers, supra at 137-139. Thus proper diversification of an investment

in the [the subject company] shares owned by petitioner, as valued by respondent, would

require a total capital investment of $89 million. We do not think the hypothetical buyer should

be limited only to a person or entity that has the means to invest $89 million in [subject

company] and a portfolio of nine other securities (Pratt, 196, quoting from Estate of

Hendrickson v. Commissioner, T.C. Memo 1999-278, 78 T.C.M. (CCH) 322 (U.S. Tax Ct.1999) (Oct 1999 J&L) (Oct 1999 BVU). ).

Although proven earlier in our discussion relating to size differences that a "small firm effect"

or "size premium" does indeed exist, hopefully it is clear that no single explanation exists for the

difference, and as such, a simple modification to the existing CAPM model based on differences


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calculated on a large scale (hundreds of companies) will notprove to be an accurate predictor of

returns for a particularcompany. In addition, it has been demonstrated that the diversified portfolio

which the traditional CAPM demands is not always realistic or attainable by the small business owner.

One of the strengths of the CAPM, however, is its simplicity of use and its consideration of

numerous factors individually. Levy (1990) produced a significant work which both identified the

reason for the small firm effect (he says it existence is due to market segmentation related to the lack

of optimal investor portfolios, and the existence of transaction costs) and provided a modified version

of CAPM that takes into account this market segmentation reality. This Generalized Capital Asset

Pricing Model, or GCAPM, can be written as follows:

Equation 2-1: GCAPM

kce-pq = krf + (RPm) Bpq

Where:kce : cost of equity for firm p in market segment q

krf : risk-free rate

RPmq : equity risk premium of market segment q

Bpq : Beta coefficient for firm p in market segment q

Levy's GCAPM model takes the same form as the traditional CAPM but restricts risk and return

information to a certain market segment, or industry. As unremarkable as this may seem at first

glance, it actually handles many of the issues present in a small business environment that are leftunaddressed in the traditional CAPM. McMahon's analysis of Levy's model, in fact, is quite good:

Unlike the CAPM, the GCAPM can address and accommodate the immobility of financial and

human capital invested in a typical small enterprise. The GCAPM would acknowledge that the

owner-manager of an unprofitable small enterprise may not be easily able to escape from it

and enter another pursuit due to the transaction costs involved, such as sale of the enterprise

at a distress price, brokering and legal fees, and relocation expenses. The GCAPM would also

recognize the possible existence and influence of incomplete information such as not knowing

the whereabouts of a buyer, not being aware of other opportunities available, and not having

the expertise required to become established in another field. (McMahon, 1993, 34).

The diversification problem pointed out by many authors (and tax court judges!) begins to be

addressed in Levy's model. Still, however, company-specificcharacteristics have no way of being

captured in Levy's GCAPM, but rather the model assumes that a company's unsystematic risk is


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represented accurately by the unsystematic risk inherent to the broader industry within which the firm

operates.

Merger and acquisition valuation expert Frank Evans tackles this problem by proposing what

he terms a "Modified Capital Asset Pricing Model" (MCAPM), which adds a term to account for the

"small firm effect" mentioned earlier, and then an additional term to account for unsystematic risk

specificto the firmin question (Evans, 125):

Equation 2-2: MCAPM

kce = krf + (RPm) B + SCP + SCRP

Where:



RPm : equity risk premium of the market as a whole

B : Beta coefficient for the company in question

SCP : "Small company" premium

SCRP : "Specific company" risk premium

And so although the model does address specific company (unsystematic) risk unlike many of the

other traditional and newer adjusted models, Evans advocates a fairly subjective approach to

determining the specific company risk premium in which various aspects of company structure (such

as marketing capacity, breadth of products and services, purchasing power, vendor relations, etc.) are

identified and a percentage attributed to each.

The problems inherent in this approach are readily apparent, however. First of all, there are

no standards by which to compare each of these issues, and no empirical data to suggest what size

adjustment should be made for each. Secondly, Evans' model makes use of a "small company

premium" which we identified earlier as questionable17. One on hand Evans is using a heavily

empirical measure with no explanation (SCP), and then on the other hand is he utilizing a very

subjective measure with no empirical support (SCRP). These two inputs confuse the issue and could

lead to a calculated result with little empirical support and few company or benchmark comparisons.

Shannon Pratt, a respected valuation and cost of capital expert, presents virtually the identical

model as Evans, calling it instead the "Expanded CAPM Cost of Capital Formula". Pratt considers that

17 Evans references Ibbotson data for the appropriate portfolio decile to determine the "small companypremium.


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formula a modification of a "Build-Up Model" he pulls from SSBI (125), which is essentially the

MCAPM/Expanded CAPM withthe Beta coefficient excluded but with the addition of an industryrisk

premium (Pratt, 76):

Equation 2-3: Ibbotson/Pratt "Build-Up" Cost of Equity Model

kce = krf + RPm + RPs + RPi + RPu

Where:



RPm : equity risk premium of the market as a whole

RPs : size premium18

RPi : industry risk premium (or a negative figure would represent an industry risk

discount)19

RPu : company-specific risk premium (unsystematic risk)

In this model, Pratt clearly separates industry risk and company specific risk and describes company-

specific risk as that which is true unsystematic risk. This distinction is important, because in the same

way that one avoids risk in one industry by investing in others, another way to diversify from

investment in a stock is to simply invest in another firm, either in the same industry or a different

industry. Except in the case of oligopolies in small industries (where few companies would exist with

different risk levels than the broader market, but also are very similar to one another in size and

performance), it is unlikely that industry and company-specific risk will be identical from one firm to

another, or easily lumped together, as Levy attempts to do in his GCAPM. The Build-Up model

presented here does take such distinctions of industry-specific and company-specific risk into account,

although Pratt goes into no explanation whatsoever as to how RPu should or would be calculated,

simply deferring to valuation consultants' discretion.

Take note of what Pratt's says regarding one difference between the Build-Up and the

GCAPM/Expanded CAPM: "The value of the company-specific risk premium [used in the Expanded

CAPM], however, is likely to differ from that used in the build-up model, because some portion of the

company-specific risk may have been captured in beta." (76). His comment highlights the difficulty

18 Pratt also references Ibbotson data for the appropriate portfolio decile to determine the "smallcompany premium".19 No clear guidance is given as to how the industry risk premium should be calculated, although Prattexplains (126) that Ibbotson's Yearbookalready referenced in this paper since 2001 has providedindustry data down to the three-digit SIC (Standard Industrial Classification Code) level. Prattsuggests that through use of this data, the industry risk premium can be determined


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involved with calculating the risk of an investment as diverse in nature as a small business, when

systematic and unsystematic risk both exist with imprecise measures of each in play.

Proxies for Beta in CAPM

As we have seen above, some academics and practitioners have made modifications to the

CAPM in an attempt to account for small firm differences. Others have suggested alternative or

substitute ways of calculating Beta that could be used within the normal CAPM structure to calculate

cost of capital in a small firm environment. Two of the most common proxies (substitutes) for a market

Beta are the pure playtechnique and the accounting beta.

The "pure play" method involves identifying a similar publicly traded company, preferably a

competitor, and using its published Beta as a proxy for the small business. This may work to somedegree if the SPHB actually operates within an industry with publicy-traded firms or competitors.

Otherwise, this method will not be possible.

The "accounting beta" method requires a set of time series data consisting of both a measure

of a company's earning power (such as Return on Assets 20) and consisting of market index data for

that same time series. A regression analysis would be run against the data set to compute Beta

(replacing market returns in Equation 1-6 with these accounting returns). Accounting returns are a

somewhat decent predictor of company cash flow, and consequently, stock price. It should come as

no surprise then that there is widespread agreement on the association between accounting andmarket Betas, although there are differences of opinion as to the degree of association between the

different Betas (Palliam, 339).

However, as Ralph Palliam points out, "neither the 'pure play' nor the 'accounting beta'

technique considers the many non-systematic risk factors that should be included in estimating the

cost of capital for a small business." (Palliam, 339).

Methods that combine Behavioral and Financial Return

Boyer and Roth did some significant work in 1976 in which they asserted that the cost of

equity in a small owner-managed firm was a function of both monetary return and behavioral reward.

Small business owners were surveyed and interviewed to determine to what degree they were willing

20 Could be calculated as EBIT / Total Assets; EBIT represents earnings before interest and taxes.


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to sacrifice monetary reward in order to retain behavioral rewards (consisting of such things as shown

in Figure 2-A earlier). This was Boyer and Roth's conclusion:

The survey responses strongly indicate that the cost of equity capital for a small business is a

function not only of the required rate of return of a pecuniary nature, but also of returns

consisting only of psychological rewards or those behavioral in nature. The cost of equity is

dependent on factors which motivate the owners to forego opportunity return for behavioral

satisfaction. If an opportunity returnthe ability to earn more on an equally risky investment

outside the firmexists, which was the case in many instances, rational behavior would

suggest that behavioral rewards must constitute the difference (7).

Equation 2-4: Boyer's Cost of Equity formula, considering financial and non-financial benefits

kce = ROEo ROEb

Where:kce : cost of equity for the firm

ROEo : opportunity return on owner's investment

ROEb : return of a non-monetary or behavioral nature

Boyer and Roth explain that this cost of equity calculation could not be less than zero, since the

"overall cost of capital cannot fall below the weighted cost of debt" (7). Accordingly, then, there is a

limit on the degree of behavioral return an owner can achieve over the long run, otherwise the owner

at some point would fail to meet debt service payments. The value in this model is that it recognizesthat the desiring of behavioral returns may result in a reductionof opportunity return. The authors say

the exact level of reduction should be determined by surveying the business owners to determine

which behavioral factors they are willing to sacrifice return for, and how much for each factor they are

willing to sacrifice up to an overall cap. Rather than taking the questionable, difficult-to-measure

returns of non-monetary benefits as a challenge to the cost of capital issue and one that adds more

risk (and thus more cost), Boyer and Roth see it as an issue which reduces the demand on the

company to produce as high of a profit level as an owner with lesser non-monetary reward desires

may have demanded.

Ralph Palliam, mentioned earlier for his suggested alternate Beta calculation methods,

realizes the significant shortfalls inherent to the CAPM as it pertained to the small business

environment. He advocates use of an Analytical Hierarchical Process (AHP) model which has been

put forth in literature in the past focused specifically on complex decision-making in non-financial

arenas. Palliam is to be commended for his "out of the box" thinking with this approach, and

admittedly the model does allow for a calculation based on the many subjective and behavioral issues


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relating to business operations along with financial health considerations. Unfortunately, it requires

the user to first identify the cost for several "levels" of risk, and then requires one to identify the risk

level for each of the functional areas considered for the company, as well as the "intensity" or

importance of each area. The combination of these three very subjective measures (pre-defined risk

cost percentages, risk level of each area of the company's operations, and importance of each area of

the company's operations) could lead you to a calculation of a company's cost of equity (and

ultimately, cost of capital) that may have little or nothing to do with the actual hard return dollars

demanded or expected by the owner(s).

Problems with the Traditional and Adjusted Models

Despite the good intentions of the finance scholars who developed these models we have

examined, they still fail to fully consider the range of exceptions that arise in small business financialenvironment. Miller and Modigliani's model, although considered a breakthrough in the world of

finance, contained such restrictive assumptions as to entirely exclude small and/or privately held

businesses from consideration. Cheung, Forsaith, Boyer and Roth, and Palliam are among just a few

of the many authors that point out the failure of those traditional models in the small business

environment. And yet many of the adjusted models explained so far are built in some way on the

assumptions of the M&M model.

Behavioral/motivational issues along with unique issues specific to each small business have

been identified as the key factors preventing use of the traditional models. Several "adjusted" modelshave been examined that have attempted to move beyond traditional models by taking these

behavioral issues into account, but the bulk of them still advocate a building on to the CAPM. Few if

any authors have advocated anything other than a "one size fits" strategy, even thought their strategy

may be a unique one to them. In fact, throughout this paper criticism and shortfalls in several of the

models have been identified. Problems still remain with the adjusted models examined earlier,

however,

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CofC in a Priv-Held Bus Environment