The Power of Multiples


The Power of Multiples Project  Valuation Multiples g Solution
Valuation Models The Valuation Project Background

The Power of Multiples Project

The Power of Multiples Project explores the use of Enterprise and Equity valuation multiples as comparative, predictive, and interpretive tools for analysts, investors, and financiers.  This project seeks to shed light on the use of valuation multiples and their ability to inform market inferred rates of growth for each of the subject firms and changes in these rates between 2015 and 2016.  Led by Richard Haskell, PhD1 and Bryce Nieberger2, the project includes an analysis of those firms in the DOW Industrials (30) and S&P 100 as of year-end 2015 and 2016 performed by student researchers at Westminster College’s Bill and Vieve Gore School of Business in May 2017.

With the resources of Westminster College’s Center for Financial Analysis (CFA), researchers assembled into data gathering teams to collect primary input data for the subject firms and years, synthesize market based Enterprise Values, and derive the required inputs to motivate both valuation multiples and valuation models.  Using FactSet3, Bloomberg4, ValueLine5, Market Line6, and eStatement Studies7  data repositories, researchers gathered and compared data sufficient to motivate each of six enterprise multiples and four equity multiples in an effort to understand market inferred rates of growth for each of the subject firms, changes in these rates between 2015 and 2016.

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Valuation Multiples: a multi-purpose analytical and predictive tool

Many analysts and investors seeking guidance with respect to appropriate firm valuations often rely on complex valuation models and metrics, while others may turn to simple, but reliable ratios often referred to as valuation multiples.  These ratios, most often a quotient including some notion of the firm’s value interacted with an income based variable, offer a comparative metric useful for many reasons, not the least being a sense of the firm’s relative position among a group of peers.  While on the surface this may appear to be more about a comparative metric, what underlies the ratio, or multiple, is a complex series of calculations and outcomes informing knowledgeable investors and analysts of the firm’s value.

To illustrate the power of a valuation multiple let’s consider a single-stage Enterprise Value/EBIT multiple (EV/EBIT) as an example.  Enterprise value (EV), the sum of the value of the firm’s equity and debt capital reduced by its available cash and cash equivalents, is an observable value for any firm as of a particular point in time.  Whether assessed from a purely market based perspective or from the more traditional, albeit less useful, market/book perspective, the firm’s enterprise value informs us of what it might take to own the rights to a firm’s future cash flows.  Similarly, EBIT – earnings before interest and taxes – is an observable value and is simply an accounting identity.  However, assessing the firm through an observed multiple is somewhat impotent without having some understanding or expectation of what the multiple value ought to be.

Many will turn to Public Comparables or Precedent Transactions to inform them of the value of the EV/EBIT multiple for other firms in the same market or industry at the same point in time, while others may consider the range of the firm’s EV/EBIT multiple over time.  Such an effort may result in determining a Target Multiple which, when interacted with the firm’s EBIT, suggests a potential EV for the firm were it to attain such a multiple value. Since EV/EBIT results in a multiple, we can rearrange the equation to solve for EV and in so doing have turned the multiple into a simplified valuation model.


If a target multiple is assigned, we can form an aspirational value of EV supposing the firm’s value may change to the aspirational value over time.


Or if we’ve forecasted a future EBIT for the firm we can solve for a future EV.


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g Solution

Though EV/EBIT is a metric with an observable value and can be rearranged into a simplified valuation models, it also has significant additional potential.  Like most multiples it can be expressed algebraically using additional firm level inputs for Return on Invested Capital (ROIC), Weighted Average Cost of Capital (WACC), expected growth (g) and average tax rate on EBIT (T).   When these inputs include time signatures in which t = 0 is the point of observation and t > 0 is some future point in time, the EV/EBIT equation can be rewritten as follows:


The right hand side of this equation may be used to shed some light on how the markets perceive the growth prospects of the firm.  Given that a market-based EV is informed by exchange transactions we can infer the market’s consensus of g by using observed values for EV, EBIT, ROIC, WACC and T and solving for this market inferred g:

Start by dividing both sides of the equation by the denominators and substituting T’ for (1-T):


Expand each side of the equation:


Rearrange to include all g terms on the right


Factor out g and ROIC0

 g\, \big[(T')(EBIT_{0})\,\,-\,\,(EV_{0})(ROIC_{0})\big]\,\,=\,\,ROIC_{0}\,\big[(T')(EBIT_{0})\,\,-\,\,(EV_{0})(WACC_{0})\big]

Divide both sides by   to arrive at g solution

 g\,\,=\,\,\frac{ROIC_{0}\,\big[(T')(EBIT_{0})\,\,-\,\,(EV_{0})(WACC_{0})\big]}{ (T')(EBIT_{0})\,\,-\,\,(EV_{0})(ROIC_{0})}

Knowing the growth (g) the market projects for the firm allows us to make a more informed investment decision: if g is greater than might be reasonably expected then, the firm might warrant a sell recommendation; if g is less then perhaps a buying opportunity is being presented.

Also, if we forecast future changes in ROIC and WACC we can return to the consideration of the EV/EBIT multiple as a valuation model using the market inferred g by substituting expected values for EBIT, ROIC and WACC into the equation and solving for some future value of EV:

So, a valuation multiple is much more than simply a quotient or comparative ratio.  In the hands of a creative and informed analyst it becomes a multipurpose tool capable of informing expected values for a firm, inferring a consensus rate of growth for the subject firm, or even predicting and confirming an appropriate level for a target valuation multiple.

When the growth rate of a firm’s cash flow variable is expected to remain constant over time, a relatively unrealistic expectation, a single-stage valuation multiple similar to the EV/EBIT multiple form noted.  However, when forecast values of a firm’s cash flow variable are not expected to be constant a two-stage multiple construction may be useful; a form capable of assessing a period during which the growth rate of the cash flow is non-constant followed by a continuation period during which the rate is held constant.  Given that accurately forecasted cash flows become increasingly unlikely as the forecast period becomes lengthy, two-stage multiples are commonly applied, as are two stage valuation models in which a single stage valuation multiple is used to form the firm’s continuation value (terminal value).

The dynamics of valuation multiples are such that they may be readily observed, as noted, formed as a target multiple, or abstractly conceptualized as a multiple with some theoretical value.  The multipurpose valuation multiples includes each.

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Valuation Models

Valuation models based on varying forms of the discounted present value of a firm’s future cash flows are commonly used by analysts and investors seeking to determine a theoretical or target valuation for equity participation in publically traded firms.   These models range from relatively simple present value of discounted cash flow models to complex and sophisticated economic profit and adjusted cash flow models introducing estimated changes in a firm’s value based on opportunity costs and changes in the firm’s capital structure.  Most model forms share at least one common theme: the value of a firm, or any asset, is a function of claims firm stakeholders have on the firm’s future cash flows and their interaction with the firm’s expected growth rate (g), return on invested capital (ROIC), and weighted average cost of capital (WACC), more generally thought of as a discount rate (r).

Today we’re fortunate to have easily accessible data with respect to the market value of firms’ equity and debt positions, as well as detailed accounting and market data resulting from firm’s efforts.  As such, we can motivate the various valuation models, estimate a theoretical value for any particular firm, and then compare that value to the value observed in the open market reflective of the thinking of buyers and sellers the world over.  Assuming these buyers and sellers share symmetric information flows such that all agents in a transaction perfectly share and have access to the same data we might suppose potential buyers and sellers each estimate the same values for firms’ rates of growth, return on invested capital, and costs of capital.

Were this the case, why do buyers and sellers assign different values to firms such that a bargaining process is undertaken before a transaction price is agreed upon, if one is agreed upon at all?    Additionally, how is it that firm’s may ascribe a value to their operation different from that which the market sets?  We might argue this is simply a function of asymmetric or imperfect information between buyers and sellers, and it is, but we would certainly be left to also argue that a firm’s opportunity cost of capital may be different than an investor’s expected return or their opportunity cost of capital.  Other key considerations in this exploration include identifying expected growth rates for subject firms and how these rates effect the firm’s overall value.  If at firm’s ROIC < WACC, then growth adds value to the firm, while growth in the presence of ROIC < WACC results in growth destroying the firm’s overall value.

It is these considerations of growth, cash flows, return on capital, cost of capital and the resulting valuations using discounted present value models that form the basis for The Valuation Project.

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The Valuation Project

The Valuation Project, a companion and predecessor project to The Power of Multiples explores the value of firms in the DOW Industrials and S&P 100 by assigning values to each firm based on each of five discounted present value models: income augmented dividend growth or discounted dividend model, key value driver model, free cash flow model, adjusted present value model, and economic profit model.  The cash flows used in these models, net operating profit less adjusted taxes (NOPLAT), free cash flow (FCF), tax shield (TS) and economic profit (Eπ), each share common inputs, but each measure somewhat different change effects for their respective firms.  Each model employs forms of firm growth rate, return on invested capital, and cost of capital or discount rate values, but also bring in other measurable variables from the firm’s income statement and balance sheet.

The Valuation Project seeks to isolate the firm’s core operating assets, explore expected rates of growth for the subject firm’s revenues and expenses, and estimate future returns and costs of capital in an effort to assign value to the firm.  The analysis compares these assigned values with actual market values, estimate hypothetical discount rate values reflected in these market values, and perform multi-linear regression analyses to estimate which model forms most consistently assign values aligned with adjusted market values.  Through the study hypotheses will be developed with respect to those motivating principles behind observed differences which hypotheses and theories will be available to investors, academics, and others through critically developed academic articles, the Valuation Project’s website and a series of Wikipedia pages devoted to the subject and process through which the analysis was performed.

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In the Western conceptualization of the role of firms in society we generally accept that a firm’s stakeholders, those with claims on the firm’s cash flows, include those who have financed the firm through equity and debt investments8.  Equity participants have claims on the firm’s cash flows including the profits, some of which are distributed in the form of dividends and the remainder of which are reinvested in the firm through its retained earnings, and accept the risk of firm pricing, production, and distribution decisions, varying dividend levels, and share valuations.  Debt holder claims supersede those of equity investors as debt investors enjoy claims on the firm’s cash flow as observed through its net margins from which interest payments and debt retirement funds, often referred to as sinking funds, arise.  Together, the market value of a firm’s equity and debt form the firm’s enterprise value, which value rises and falls based on firm performance, market forces, investor’s rational expectations, and what John Maynard Keynes referred to as “animal spirits”9 – the sometimes less than rational expectations of firm stakeholders arising from the vagaries of the human condition.

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1 Richard Haskell, PhD is an Associate Professor of Finance in Westminster College’s Bill and Vieve Gore School of Business, Salt Lake City, Utah, 2017.

2 Bryce Nieberger (2017), Student, Bill and Vieve Gore School of Business, Westminster College, Salt Lake City, Utah,

3 FactSet is a data repository delivering information to investment professionals and investors using publicly available analytics, service, content and technology; copyright FactSet Research Systems, Inc.;

4 Bloomberg connects investors, decision makers and investment professionals with real-time and historical information for a wide range of domestic and international firm; Bloomberg L.P.;

5 Value Line is publication of Value Line, Inc., 485 Lexington Avenue, 9th Floor, New York, NY 10017;

6 Market Line, a trading name of Progressive Digital Media Ltd. Registered Office John Carpenter House, John Carpenter Street , London EC4Y 0AN. Registered in England and Wales Number 01813905;

7 eStatement Studies is a publication of The Risk Management Association, 1801 Market Street Suite 300, Philadelphia, PA  19103, 800-677-7621;

8 The European conceptualization of firm stakeholders includes equity and debt investors, customers, workers, management, suppliers, governments, and the broader society in which the firm operates.

9 “Animal spirits” is a term emphasizing the importance of investor sentiment on the market value of a firm’s debt and equity components. J.M. Keynes, General Theory of Employment, Interest and Money, pp 161-162, McMillan, London, 1936