Risk Analysis in Brand Valuation

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Risk Analysis in Brand Valuation

F. Beccacece1, E. Borgonovo1 and F. Reggiani2

1IMQ, Bocconi University,

20135 Viale Isonzo 25, Milano2IAFC, Bocconi University,

20135 Piazza Sra¤a 11, Milano

Abstract

After an empirical start, brand valuation has attracted the interest of bothaccounting practitioners and academicians. Several methods for the assessmentof brand value have been developed. However, a major critique shared by thesemodels has been the lack of objectivity. In view of such criticism, the JapaneseMinistry of Economy, Trade and Labour created a dedicated Committee withthe twofold task of rigorously de…ning brand and of developing a methodologyfor brand valuation based on publicly available balance sheet data. The resultgoes under the name of the Hirose methodology. The methodology, however,while achieving the above two mentioned key-merits, does not allow a …nancialinterpretation of the valuation results. We propose a brand valuation model whichmerges objectivity with robust underlying quantitative structure thus sharing a

direct …nancial interpretation and providing risk analysis insights. An empiricalanalysis allows us to compare both numerical results and …nancial insights derivedby analysts from the utilization of the Hirose Methodology, the Royalty Methodand the proposed model.

Keywords: Brand Valuation, Hirose Methodology, Risk Analysis, Brand De- fault Probability.

Acknowledgments: We would like to thank Mauro Bini for precious suggestionsand support throughout the development of this work. We would also like to thankFrancesco Momenté and Emanuel Bagna for useful comments and discussion.

1 IntroductionThe recent development of brand value assessment for accounting purposes has an em-pirical start. It can be seen to originate in Britain in the late 1980s. In those years,Guinness, Reckitt and Colman, Grand Metropolitan and United Biscuits reported thebrand values of …rms acquired in take-over activities in their balance sheets. In 1988,Ranks Hovis McDougall took this innovative …nancial accounting practice one step fur-ther by capitalizing internally-developed as well as externally-acquired brands. In 1995,

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the Accounting Standards Committee published Exposure Draft 50, Intangible Assets,(see [11]), allowing balance sheet inclusion of intangible …xed assets under the condi-tions: i) the historical cost is ascertainable, ii) assets are distinguishable from goodwill,and iii) the cost is measurable independently of goodwill, other assets and earnings.

Indeed, points i)-iii) have been “strongly criticized on grounds that very few assetswould be able to qualify for recognition with such restrictive requirements [Canibaeno etal (1999)].”. In the meantime, the academia was urging a deeper understanding of the…nancial value of brands. A growing body of empirical literature (see for example Barthet al (1998) [1] and Seethamraju (2003)[17]) was indeed supporting the hypothesis thatbrand assets are value relevant, i.e. associated with market values.

In 2004, the Accounting Standard Board published IFRS 3 Business Combinations(see [14]). In accordance with IFRS 3 Business Combinations, if a brand is acquired ina business combination, the cost of that brand is its fair value at the acquisition date.This reporting standard has therefore formally introduced in accounting practices thediscipline of brand valuation.

Several methods, in fact, had been developed by …nancial analysts and practitionersto assess brand value.1 The methods can be classi…ed broadly into cost, market and in-come approaches. The cost approach utilizes the cost spent in developing the brand as ameasure of brand value (Reilly and Schweis (1999) [16], Ch. 8, pp. 118-145.) Reilly andSchweis (1999) [16] distinguish the “historical cost approach,” which values the brandbased on the sunk costs associated with brand maintenance and management, from the“replacement cost approach,” which values the brand based on the expected total costrequired to recreate the brand. Shortcomings in the cost approach are highlighted inReilly and Schweis (1999) [16], which mention that the relationship between spent costsand brand value is not always clear, as in the cases in which high costs did not result in

a success brand. The market approach, also referred as “sales comparison approach”,values brand by making reference to the actual price of similar brands traded in themarket [Reilly and Schweis (1999) [16], Ch. 9, pp. 146-158.] Reilly and Schweis (1999)[16] note that it may not be appropriate to assume that similar brands will be pricedalike, since brands are by nature somewhat unique. Perrier (1997) [15], Ch. 4, andReilly and Schweis (1999) [16], Ch. 10, discuss the income approach. This approach,which may also be called “economic value approach,” values brands based on the netpresent value (NPV) of the excess pro…t or future cash ‡ows generated by the brand.The three most common variations of this approach are the Royalty Rate Analyses 2

[see Reilly and Schweis (1999) [16], pp. 194], the Premium Pricing Technique [Perrier(1997) [15], pp.21-22] and the Pro…t Split Analyses [see Reilly and Schweis (1999) [16],

pp. 193]. In formulae, all the methodologies share the view that:

V =N Xi=1

E [X i]

(1 + r)i(1)

1 Stobart (1991) [20] and Keller (2002) [9] provide a through overview of brand valuation techniques.2 We shall refer to this method as “Royalty Method.”

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where V is the brand value, X i is the expected brand generated excess pro…t or cash‡ow at year i and r is the proper discount rate.

The main conceptual di¤erences among the methods lie in the way E [X i] is esti-mated. For example, the pro…t split method starts with the company forecasted pro…ts

and derives the pro…t fraction which can be attributed to a certain brand. The clearestexample of this type analysis is the yearly publication of brand values in Business Week(see [10]). The price premium technique measures the brand generated excess pro…t (orcash ‡ow) by the present and future price premium of branded products compared withproducts without brand. One considerable application of this technique is describedin Section 2. Instead, the Royalty Method estimates the brand generated cash ‡ow asfollows:

E [X i] = E [S i] R

where S i are the sales of the company at year i, and R is the appropriate royalty rate.There follows that the brand value determined by the Royalty Method (V R) equals:

V R =N Xi=1

E [S i] R

(1 + r)i(2)

In principle, R is found from a market analysis looking at the fees (expressed aspercentage of sales) that a …rm required to licence its brand. The determination of theappropriate rate is not always straightforward, especially for …rms that do not licence(or have not licensed yet) their brand. Since it is beyond the scope of this paper toexplore how to determine the appropriate royalty percentage, in the empirical analysispresented in Section 5 we have used the values published annually in “Licensing royaltyrates” [Battersby and Grimes (2005) [5]]3.

The most delicate issue in the use of these methods is the arbitrarity in the iden-ti…cation of which part of a …rms’ pro…ts (or cash ‡ows) is attributable to the brand.Thus, many valuation approaches made use of qualitative statements and not veri…abledata in measuring the value of brands, leading to results which relied on …nancial an-alysts’ subjective interpretation. In so doing, the methods failed in satisfying two of the principles required by fair value estimates: objectivity and no-arbitrarity (Treynor(1999) [21].) Let us quote directly from Treynor (1999) [21]: “the data should be veri…-able, at least in principle. When data are veri…able, ‘objectivity’ ceases to be an issue ”and (Treynor (1999) [21], p. 27) “the data should not depend on arbitrary decision by anybody (Treynor (1999) [21], p. 27).”

To overcome the shortcomings of many valuation approaches, the Japanese Ministryof Economy, Trade and Labor …nanced a project aimed at de…ning a brand valuationmodel solely based on public data [Hirose et al (2002) [6]]. Starting point of the reportis a rigorous de…nition of brand, and output of the Japanese study is a valuation model

3 The volume is a reference tool that provides detailed royalty rates for 1,500 products and services inten di¤erent licensed product categories: art; celebrity; character/entertainment collegiate; corporate;designer; event; music; nonpro…t; and sports. The royalty rates generated by brand names are underthe category “corporate”.

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(known as the Hirose methodology) based only on publicly available …nancial datadirectly extracted from the …rm Annual Reports. This makes the valuation resultsvery well grounded “empirically”, and capable of meeting the objectivity requirementmentioned above. However, while having solved the problem of “objectivity,” the model

is exposed to criticism as far as the …nancial interpretation of the results is concerned,which we illustrate.

We then advance an alternative model that merges the objectivity of the Hirosemethodology with a robust underlying quantitative structure that o¤ers a clear …nancialinterpretation of the results. The model also enables one to perform risk analysisof brand generated cash ‡ows, allowing to estimate brand default probabilities frombalance sheet data.

The above general discussion is followed by an empirical analysis in which we applythe new model, the Hirose methodology and the Royalty Method to estimate the brandvalue of a sample of 10 companies operating in di¤erent sectors. Results of the analysiswill enable us to compare not only the numbers, but also the information that an analyst

can derive from the use of the various models. We shall show that discrepancies in theRoyalty Method and the Hirose methodology results are attributable to the di¤erentcash ‡ows which are inputs of the two methods. We shall also show that applyingthe newly proposed method in conjunction with the other methods, an analyst derivesinsights not only on the brand value, but also on the riskiness of its cash ‡ows.

The remainder of the paper is organized as follows. Section 2 is devoted to a reviewof the Hirose methodology, highlighting its merits and discussing its (lack of) …nancialinterpretation. Section 3 introduces an alternative brand valuation model. Section 4presents the empirical analysis results. Conclusions are o¤ered in Section 5.

2 The Hirose methodology for Brand Valuation: the Japanese

Model

The brand valuation model we discuss in this Section, is the one developed by theCommittee on Brand Valuation (Chairman: Dr. Yoshikuni Hirose, Professor at WasedaUniversity), a consultative body organized under the Japanese Ministry of Economy,Trade and Industry. It is contained in the corresponding report, released on June 2002entitled, “The Report of the Committee on Brand Valuation (Hirose et al (2002) [6]).”The Report is considerable for two main reasons:

it has developed an objective brand valuation model using public …nancial data

extracted from the Annual Report; the methodology it provides is quite general and might be easily extended to the

valuation of intangibles other than brands.

The Report de…nes “brands” as “emblems including names, logos, marks, symbols,

package designs and etc. Used by companies to identify and di¤erentiate their products

and services from those of competitors ” and presents a brand valuation model (from

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now on the “Japanese model”) using the income approach, a valuation approach basedon pro…tability.

The Japanese model can be summarized as follows. The brand value (V ), is assumedto be function of several factors:

V = f (PD;LD;ED;r)

The implied factors are:P D: “Prestige Driver” (Price advantage of the brand)LD: “Loyalty Driver” (Stability of the brand)ED: “Expansion Driver” (Brand expansion capability)r : risk-free interest rate.We now examine the …rst three factors in details.P D is a factor of brand value that focuses on the price advantage created by the

power of the brand that enables the company to sell its products constantly at higher

prices than those of its competitors. P D is represented by cash ‡ows attributable tothe price advantage of the brand. The proportion of advertising expense, or brandmanagement cost, to total operation cost is used as the attribution rate. Formally, P D

is given by:

P D =1

5

0Xi=4

S i

C i

S iC i

Ai

OE i

C 0 (3)

where :S = SalesC = Cost of salesS = Sales of a Benchmark Company

C = Cost of sales of a Benchmark CompanyA = Advertising and promotion costOE = Operating costLD is a factor that focuses on the capability of the brand to maintain stable sales

for a long period based on the stable customers or repeaters with high loyalty. LD isrepresented by the stability of the cost of sales. It is calculated by the formula:

LD =c c

c

(4)

where:

c = 5-term average of cost of sales;c = 5-term standard deviation of cost of sales.ED focuses on the fact that a brand with high status is widely recognized, and

therefore, is capable of expanding from its traditional industry and markets to similaror di¤erent industries as well to overseas, expanding market geographically. ED isexplained by an average of the growth rate of overseas sales and growth rate of sales

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from non-main businesses. The formula to calculate ED has been stated as follows:

ED =1

2

"1

2

0

Xi=1

SOi SOi1

SOi1+ 1

+

1

2

0

Xi=1

SX i SX i1

SX i1+ 1

#(5)

where :SO = Overseas sales;SX = Sales from non-main businesses.The brand value V can be easily interpreted as a non decreasing function f of the

factors. In particular, the Japanese model provides a very simple form for the functionf , given by:

V =P D LD ED

r(6)

We note that from a practical point of view the brand value is estimated as follows:one gathers the past 5 years balance sheet data, estimates the three terms in the numer-

ator of eq. (6) and discounts them at the risk free rate. From a …nancial point of view,eq. (6) measures brand value as a perpetuity with cash ‡ow given by (P D LD ED).In the remainder of the work we refer to eq. (6) as either the Hirose methodology orthe Japanese model.

Although the Japanese model shares the advantage of objectiveness and data ac-cessibility, it does not o¤er a clear interpretation of the …nancial aspects of the brandvalue, as we are to discuss.

1. Discounting at the risk-free rate: brand cash ‡ows are risky . The Report un-derlines how, in accordance with the IAS 36, Appendix A [12], the uncertainty(and consequently the riskiness) of the cash ‡ow generated by the brand, mustbe handed by using one of the two methodologies:

a. adjusting the interest rate with a risk premium and using the cash ‡ow we canestimate by considering a single scenario (the most likely one);

b. considering the expected cash ‡ow and maintaining the risk-free rate for dis-counting the future cash ‡ows

and it follows the latter methodology, determining the expected cash ‡ow as theaverage cash ‡ow of the last period (…ve years for P D and two years for ED).With respect to (w.r.t.) this point we move our …rst critique to the Japanese

model in that the followed approach is risk neutral4

since it simply providesthe present value of the expected cash ‡ow, with no adjustment for the risk, incontrast to standard principles in evaluation theory and practice (see Smith J.K. and Smith R.L. (2000) [19], Brealey and Myers (2000) [3].) One could remarkthat the factor LD may be interpreted as the correction of the present value of the expected cash ‡ow, in accordance with the certainty equivalent form (CEQ )

4 On the concept of risk neutral valuation, please see Hull (1998), p. 237.

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of the Capital Asset Pricing Model [see Smith J. K. and Smith R.L. (2000) [19].]Our second critique is just devoted to show that this is not true.

2. LD cannot be interpreted as a correction term in accordance with CEQ . We show

now thatLD

is not a correction term entailing the cash ‡ow riskiness. Let usconsider the CEQ expression for the present value of a single cash ‡ow C t thatwill be received at time t. It is:

P V t =C t

(C t;rm)C tm

RP m

1 + r(7)

where:

rm and m are the expectation and the standard deviation of the market return,respectively;

C t is the standard deviation of the cash ‡ow;

is the correlation coe¢cient;

RP m is the risk premium of the market.

In order to …t the Japanese model [eq. (6)] in the CEQ framework, one needs…rst to identify the cash ‡ow and adjust it for the correction term. Based onwhat we have discussed till now, if LD has to be interpreted as a risk correctionfactor, it must hold that P D = C t (for the sake of simplicity, the factor ED isomitted). Hence, equating eq. (6) and (7), one obtains the condition:

C t(1 cc

)

r

=C t

(C t;rm)C tm

RP m

r

(8)

After a …rst algebraic manipulation, one gets:

c

c

C t = (C t; rm) C t

m

RP m (9)

This condition has in itself no direct …nancial interpretation. However, let us tryand dig in the meaning of eq. (9) by utilizing some conditions on the elements of eq. (9) that …nd usual ground in the practice. The …rst condition is that, from a

practical point of view, one can assumec

c

'ct

ct

. Inserting in eq. (9), one gets:

C t

ct

= (C t; rm)

m

RP m (10)

Now, since C tct

= 1 by de…nition, one is left with:

1 = (C t; rm)

m

RP m (11)

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Finally utilizing the often empirically veri…ed fact that RP m2m

= 1, condition (9) isequivalent to requiring :

(C t; rm) =1

m

(12)

Eq. (12) suggests that, in order LD to be a risk correction coe¢cient, the corre-lation coe¢cient between the brand generated cash ‡ow and the market shouldalways equal the inverse of m. This is a strong condition that is not going to beveri…ed in the practice. Hence, one cannot but infer that the CEQ interpretationof the Japanese model, via Capital Asset Pricing Model, leads to an unacceptableconclusion.

3. Relationship between value drivers and parameters used to compute them. If,from one hand, it can be fully shared the role attributed in the model to thevalue drivers as factors which are strictly linked with the brand value, from theother one, the suitability of the parameters used in order to compute them is not

immediate.

4. Analytic form of the brand value function and correlations among the factors

used for explaining it. The last weakness of the Japanese model is the possibleinconsistence between the structural form of the brand value function and thecorrelations among the factors. In fact, the product of the factors proposed inthe model as brand value function, even if it shows the advantage of a verysimple analytic form, is valid when the factors are thought of as uncorrelated.Unfortunately, this is not the case, since the some of the parameters used in themodel for determining di¤erent value drivers are correlated. For example, it isevident that sales and cost of sales, which are present in both P D and LD, cannot

be thought of as completely uncorrelated.

A …nal note. After analyzing the main advantages and some of the limitations of the model, we would like to draw some remarks on the approach of measuring the valuedrivers by the means of a benchmark company. In our opinion, the use of a benchmarkis justi…ed in the model, since brand value is essentially determined by the advantagethat the brand guarantees over competitors. On the other hand, this makes crucial thechoice of the benchmark company, which, in the most cases can be interpreted as theworst of the sector.

3 An Alternative Model

This Section introduces an alternative brand valuation model. Our purpose is twofold.On the one hand, the model is aimed at preserving the key merits of the Hirose method-ology, i.e. brand cash ‡ow estimation from public data. On the other hand, we aim atovercoming the di¢culties in the …nancial interpretation of the Hirose methodology 5,

5 See the end of Section 2.

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by introducing an approach that enables to extract information on brand risk directlyfrom balance sheet cash ‡ow estimation.

We then consider the brand generated cash ‡ow composed of a risk-free componentand a risky component. The rationale below this choice is the following. As we men-

tioned in our critique to the Hirose methodology in Section 2, since the brand generatedcash ‡ow is, in its entirety, an uncertain/risky quantity, not all the cash ‡ow can bediscounted at the risk-free rate. However, we consider that the brand is capable of as-suring a minimum cash ‡ow equal to x0 2 R, which is risk-free and therefore representsthe portion of the cash ‡ow that can be discounted at the risk-free rate as in eq. (6).In addition to the sure cash ‡ow, we consider the capability of the brand to generatea risky cash ‡ow. We model the additional cash ‡ow as ranging from 0 to its highestvalue, denoted by q . More formally, the risky cash ‡ow is a …nite support randomvariable X 2 [0; q ] ; X F X , where F X is the cumulative distribution function for X .Hence we have that the cash ‡ow generated by the brand is the random variable:

Y = x

0

+ X (13)In the current model, we still want to maintain input data on the same basis as in theHirose methodology, since it is the main advantage of the Japanese model to enablebrand evaluation based on accessible book data. Nonetheless, keeping the economicallysigni…cant time span of 5 years used in the Hirose methodology, one can get from 5to 10 data per …rm (10 data would be gotten if one considered mid-year and end-year…nancial statements. However, mid-year …nancial statements are not as reliable asend-year statements for valuing brands associated to products with a high seasonalityin sales). Such a sample size is unfortunately not enough to guarantee a statisticallyaccurate …tting of the distribution F X . We then utilize an alternative approach. Inorder to characterize the risk associated with the brand, we consider that the …rm canbe hit during each time period by a shock. Due to this external or an internal event,the brand looses the capability to generate the additional bene…t X (we call this eventa “partial default”) with probability p. We note that if one …xes x0 at zero, then p

is the brand (total) default probability, while when x0 > 0, p is denoted as “partialdefault probability.”

We now introduce an auxiliary variable (T ) that shall enable us to characterize thedefault probability p utilizing the same database as in the Hirose methodology. To do

so, we de…ne T =

0q

, with the discrete probability mass function

T P (T = 0) = p

P (T = q ) = 1 p (14)

and we impose the condition that

E [T ] = E [X ] (15)

This condition preserves the expected value of the brand generated cash ‡ow. In fact,it holds

E [x0 + T ] = x0 + E [T ] = x0 + E [X ] = E [Y ] (16)

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Let us then compute the value of the bene…t generated by the brand utilizing theauxiliary random variable T . We now show that the introduction of T enables thecomputation of the brand value (V ) through the following expression.

Proposition 1 Considering an in…nite time horizon, the risk-free cash ‡ow x0

and the additional risky cash ‡ow X , the brand value V equals:

V =x0

r+

E [X ]

r + p(17)

where r is the risk-free rate and p the partial default probability after a shock [eq.(14)].

Proof. Let us study what can happen at period 1. The expected number of shocks,as we mentioned, is 1. If the shock at period 1 does not result in brand default, thenthe brand shall generate the bene…t q at the end of the period. Let us now de…ne the

periods such that the revenues and costs are scheduled at the period end. The expectedNet Present Value (NPV) of T at period 1 is:

E [T 1] =p 0 + (1 p)q

1 + r=

(1 p)q

1 + r(18)

The presence of r at the denominator is due to the fact that we assume that all risksassociated with q are contained in p.

The brand is able to generate the bene…t in the second period only if it has notdefault in period 1. This means that P (T 2 = q jT 1 = 0) = 0. Given that the brandhas not defaulted in period 1, then if the brand does not default in period 2, the brandshall be capable of generating again the bene…t. Then, the probability of getting thebene…t q at the end of the second period is:

P (T 2 = q ) = P (T 2 = q jT 1 = q )P (T 1 = q ) + P (T 2 = q jT 1 = 0)P (T 1 = 0) = (19)

= P (T 2 = q jT 1 = q )P (T 1 = q ) = (1 p)2q (20)

The presence of (1 p)2 is justi…ed by the assumption of independent shock arrivals.Hence:

E [T 2] =(1 p)2q

(1 + r)2(21)

Following the same logic, one can show that

E [T n] =(1 p)nq

(1 + r)n(22)

The expected present value of the cash ‡ow generated by the brand at year n is, then:

E [Y n] =x0

(1 + r)n+

(1 p)nq

(1 + r)n(23)

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As a consequence, the total NPV equals:

V =1

Xn=1

E [Y n] =1

Xn=1

x0

(1 + r)n+

1

Xn=1

(1 p)nq

(1 + r)n(24)

which equals eq. (17), thanks to the properties of the geometric series.Eq. (17) requires as inputs the minimum (x0) and the average of the cash ‡ows

E F [X ]: These two quantities can be computed from the cash ‡ows generated by thebrand over n past periods, where n is an appropriate time span for the analysis. Forexample n = 5 years in the Hirose methodology [eq.(3)]). The default probability p canbe either inserted by the analyst, or inferred from historical data. In fact:

E [T ] = E [X ] =) (1 p)q = E [X ] =) p = 1 E [X ]

q (25)

In eq. (25), E [X ] is found from the average of the past N years brand generated cash‡ow, and q is the highest cash ‡ow that the brand can generate. Hence, brand valuecan be directly quanti…ed by means of available balance sheet data through eqs. (17)and (25) as in the Hirose methodology. However, eq. (17) shares a more transparentinterpretation in terms of brand risk w.r.t. the Hirose methodology.

In the next Section the quantitative comparison of the results of the three modelsis proposed.

4 Quantitative Investigation and Results

This Section details the application of the three models to the valuation of the brandsof a sample of 10 …rms listed in Figure 1. The study is based on publicly available…nancial statements data.

Figure 1 displays the results of the computation of the brand values produced byapplication of the Hirose methodology [eq. (6)] and the Royalty Method [eq. (2)]. Theyellow horizontal bar of Figure 1 (…rst bar in each group) reports the correspondingvalue as published in Business Week’s traditional annual review of the top one-hundredbrands6 [see ref. nr. [10]].

Figure 1 evidences that some disagreement among the brand values assigned bythe three methods. We investigate the results …rst examining the degree of agree-ment/discrepancy, and then investigating the …nancial meaning of the results.

As a synthetic measure of agreement, we compute the correlation coe¢cients on

the values. In fact a correlation coe¢cient close to 1 would signal a trend towardsagreement/disagreement. The correlation coe¢cients for our sample of 10 …rms arereported in Figure 2.

Figure 2 shows that the highest agreement is found between the values of the Hirosemethodology and the Interbrand one (84:9%). The agreement between Royalty values

6 The values are Interbrand’s estimates, whose evaluation methodology belongs to the Pro…t Split Analyses (see Section 1).

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0 10,000 20,000 30,000 40,000 50,000 60,000 70,000

CocaCola

Pepsi

Tiffany

Nike

Budweiser

Colgate

Disney

Gillette

Kodak

McDonald's

Business Week

Royalty

Hirose

Figure 1: Brand Values estimated with the Hirose Methodology [eq. (6)], the RoyaltyMethod [eq. (2)] and by Interbrand as published on Business Week.

Hirose Royalty Interbrand

Hirose 1

Royalty 52.8% 1Interbrand 84.9% 43.2% 1

Figure 2: Correlations among the brand values estimated by the Hirose Methodology,the Royalty method and by Interbrand as published on Business Week.

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Company Our Model Hirose p

CocaCola 21,407 22,846 53%

Pepsi 13,147 13,739 51%

Tiffany 2,693 3,376 42%

Nike 376 477 59%

Budweiser 5,591 6,017 50%

Colgate 8,928 9,334 54%

Disney 7,935 11,015 66%

Gillette 6,751 7,479 59%

Kodak 3,477 4,064 49%

McDonald's 9,683 12,320 45%

Figure 3: Brand values utilizing our model [eq. (17)] and the Hirose Methodology.Column p contains the partial default probabilities intrinsic in the Hirose Methodologycash ‡ows.

and the Hirose methodology is intermediate (52:8%), while the lowest agreement isregistered between the Royalty Method and the Interbrand Method (43:2%).

As we are to show, the reason of the discrepancies lies in the di¤erent cash ‡owbasis of the methodologies.

Figure 3 shows the brand values that one obtains by eq. (17) when one utilizes asinput the cash ‡ows of the Hirose methodology.

More speci…cally the values in Column 2 of Figure 3 are obtained utilizing as cash‡ow in eq. (17) the values:

xi = P Di ED (26)

where the termP Di =

S i

C i

S iC i

Ai

OE i

C 0 (27)

is one of the summands in eq. (3), and represents the cash ‡ow generated by the brandprice advantage at year i; while ED is interpreted as a constant growth factor.

We detail the calculations of the brand value for the …rst …rm in the list (Coca-Cola).

Figure 4 shows S iC i

andS i

C i

for the …rm.

The …ve years cash ‡ows obtained from book values are reported in Figure 5. Fromthis Figure it is also possible to see that the minimum cash ‡ow generated by brandequals 1047MUSD. Choosing this value as x0, then the expected additional risky cash

‡ow is E [X ] = 270M U SD, and the maximum cash ‡ow equals

maxi

xi = x0 + q = 1617M U SD (28)

Figure 5 also shows the value of the partial default probability, p, computed as thecomplement to unity of the ratio between the average and the maximum cash ‡ow [eq.

13



S/C and S/C*

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

1999 2000 2001 2002 2003

Year

CocaCola

Benchmark

Figure 4: S iC i

andS i

C i

for Coca Cola from 1999-2003

xi for Coca Cola

1000

1100

1200

1300

1400

1500

1600

1700

1999 2000 2001 2002 2003

xi

E[xi]

x

0

=1047p=0.53q=570

V=21407MUSD

xi for Coca Cola

1000

1100

1200

1300

1400

1500

1600

1700

1999 2000 2001 2002 2003

xi

E[xi]

x

0

=1047p=0.53q=570

V=21407MUSD

Figure 5: Brand Valuation according to eq. (17).

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Company Our Model Royalty p

CocaCola 27,457 23,604 58%

Pepsi 29,015 27,960 46%

Tiffany 2,960 2,952 58%Nike 12,375 11,697 59%

Budweiser 17,733 16,928 50%

Colgate 14,626 12,723 62%

Disney 47,130 43,146 50%Gillette 13,629 11,852 50%

Kodak 23,218 19,694 47%

McDonald's 26,804 26,345 56%

Figure 6: Brand valuation results with our model [eq. (17)] and the Royalty method.p is the partial default probability intrinsic in the Royalty method cash ‡ows.

(25)]. In this case, p = 0:53. According to eq. (17), the brand value is given by the

sum of the sure part x0

r= 20940 and the risky portion E [X ]

r+ p = 467.Following the same method, the brand values for the other companies have been

obtained and are shown in Figure 3. The comparison of the values obtained with ourmodel and the Hirose methodology shows the following (Figure 3.) The correlation co-e¢cients on the values is 0:999, meaning that there is a systematic relationship betweenthe results of the two methods. The high correlation is the consequence of the choiceof the cash ‡ows basis, which is the same for the two evaluations. The resulting valuesof p shown in the third column of Figure 3 are the partial default probabilities (seeSection 3) implied by the cash ‡ows of the Hirose methodology.

If instead of utilizing the Hirose methodology, one made use of the Royalty Method,one would obtain the results of Figure 6.

In order to understand the results of Figure 6, let us illustrate the valuation of Coca-Cola with the Royalty Method …rst. The cash ‡ows are reported in Figure 7. Theyare found by multiplying the sales times the royalty rate extracted from the annualpublication “Licensing royalty rates” [Battersby and Grimes (2005) [5]] (7% in thiscase.) Capitalizing the average cash ‡ows at 6% 7one …nds the value of 23600M U SD

displayed in Figure 6.The same cash ‡ows can be utilized to compute brand value and the brand default

7 The formula utilized in this analysis is the perpetuity equivalent of eq. (2), i.e.:

V R =RE [S ]

r g

with r = 8% and g = 2%.

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1,300,000

1,320,000

1,340,000

1,360,000

1,380,000

1,400,0001,420,000

1,440,000

1,460,000

1,480,000

1,500,000

1999 2000 2001 2002 2003

E[X]+xo

xi

x0=1370p=0.58

q=103

V=27500MUSD

Figure 7: Cash ‡ows for Coca Cola employing the royalty method in MUSD.

probability according to the model introduced in this work [eq. (17)]. Figure 7 displaysthe cash ‡ows and the values of x0, E [X ] and q . One has: x0 = 1370M U SD, q =103MUSD, E [X ] = 44M U SD, and p = 1 44

104= 0:58. Substituting into eq. (17), one

…nds that the sure portion of the brand values would amount at 27350MUSD, whilethe extra amount, E [X ]

r+ pamounts at around 100.

Let us now discuss the overall ranking agreement. As one can compute from Figure6, the correlation coe¢cient among the brand values estimated with our model and withthe Royalty Method equals 0:985. This result evidences the presence of a systematicrelationship. Such relationship is again due to the fact that the two values share thesame cash ‡ows basis. However, it is immediately apparent the discrepancy of theroyalty cash ‡ows and the cash ‡ows derived by the Hirose methodology (reported inFigure 5.) As far as risk analysis is concerned, the partial default probabilities impliedby the Royalty Method are reported in the third column of Figure 6. Let us nowinvestigate whether the risk views implied by the Hirose methodology and the RoyaltyMethod coincide. Figure 8 compares the partial default probabilities obtained with thetwo methods.

It is immediate to note that Hirose methodology and the Royalty Method can leadto a di¤erent view on the brand partial default probability. The reason lies in the factthat in this analysis p is extracted out of the cash ‡ows, so it is the partial defaultprobability “implied” by the valuation method. The fact that the cash ‡ow basis isdi¤erent explains the di¤erence in the p’s.

We now show that one can also derive the default (with no more “partial”) prob-ability straightforwardly using eq. (25). It is enough to choose as minimum cash ‡ow

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0% 10% 20% 30% 40% 50% 60% 70%

CocaCola

Pepsi

Tiffany

Nike

Budweiser

Colgate

Disney

Gillette

Kodak

McDonald's

Royalty

Hirose

Figure 8: Comparison of partial default probabilities ( p) implicit in the Hirose Method-ology and the Royalty Method cash ‡ows.

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Company Hirose Royalty

CocaCola 19% 4%

Pepsi 21% 11%

Tiffany 17% 16%

Nike 25% 11%

Budweiser 9% 9%

Colgate 5% 5%

Disney 43% 7%

Gillette 16% 7%

Kodak 18% 4%

McDonald's 34% 13%

Figure 9: Brand (total) default probabilities implicit in the cash ‡ows of the Hirose and

the Royalty methodologies.

x0 = 0. In fact, if x0 = 0, p measures the probability of the brand not generating morethan 0, i.e. the brand default probability. Figure 9 shows the default probabilitiesimplied by the Royalty Method and the Hirose methodology cash ‡ows.

First of all, a comparison of the values of the default probabilities of Figure 9 andthe partial default probabilities of Figures 3 and 6, shows that the default probabilitiesare lower than the partial default probabilities. This is consistent with the fact that itis more likely that a brand generates more than 0, rather than it generates more thana minimum cash ‡ow x0 > 0.

As far as the risk views implied by the Royalty Method and the Hirose methodologyare concerned, Figure 9 shows that they are not linked by a systematic relationship. Infact, the default probabilities practically coincide for Budwiser and Colgate, while littleagreement is found on the brand default probabilities of Disney, McDonalds’, Kodakand Nike. Hence, one ought to conclude that the Royalty and the Hirose methodsnot only lead to di¤erent brand values, but also give rise to a di¤erent underlyinginterpretations of brand risk.

Finally, let us see how an analyst can pro…t from the joint use of the di¤erent models.Suppose one is assigned the task of valuing, say, Coca-Cola’s brand. Then one can saythat the value of Coca-Cola is in a range between the minimum and the maximum

value estimated by the four methods8

. In the case of Coca-Cola, the brand value wouldrange between 22000 — with eq. (17) and the Hirose cash ‡ows — and 67000. Onecan also gain insights on the brand risk. The riskiness of the brand cash ‡ows can

8 On a more general line of thought, the reason for the discrepancy among the values can be seen ashighlighting to the fact that brand market is not complete. We also recall that in the case of incompletemarkets also the valuation of real options does not lead to a unique value, but to a range [Smith andNau (1995)].

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then be summarized as follows. Probability of Coca-Cola not to generate more thanthe sure portion (say of around 21000) is 53% according to the Hirose method and 58%according to the Royalty Method. The default probability, i.e. the probability that itsbrand looses any value varies between 4% (according to the Royalty Method) and 19%

according to the Hirose methodology.

5 Conclusions

In this paper, we have dealt with the problem of assigning brand value. We have seenthat, after an empirical start, brand valuation has attracted international attentionwith the publication of the IFRS 3 Business Combinations. Such publication has leadto the development of several valuation methods that have been envisioned by …nancialanalysts and practitioners. We have brie‡y reviewed such methods, highlighting thatmost of the criticism against them stems from their lack in objectivity and arbitrariness,as underlined in Treynor (1999) [21].

We have seen that, in order to counterbalance the criticism against current methods,a recent model has been developed by the Japanese Ministry of Economics and Labor, asa result of a research project aimed at de…ning brand value based on publicly availabledata. Such method, named the Hirose methodology, has the key-merit of solving thehistorical problem of objectivity and arbitrarity in brand valuation, since its cash ‡owestimation scheme relies solely on publicly available …nancial reports.

However, we have seen that the Japanese model presents some drawbacks. The …rstone is the di¢culty in reconciling the model with traditional valuation results. Thisprevents one from assigning a meaningful …nancial interpretation to its terms and inparticular to its loyalty driver portion. In addition, the model foresees discounting of brand cash ‡ows at the risk free rate, while, again due to the structural de…ciency, no

model term can be seen as an indicator of the cash ‡ow riskiness. To overcome theselimitations, we have then o¤ered an alternative model, with the purpose of providinga brand valuation tool supported by a more robust underlying quantitative structureand allowing a more direct …nancial interpretation of the results, while preserving thekey merit of the Hirose methodology — i.e. to use publicly available information. Themodel allows to estimate a brand default probability from balance sheet data whichre‡ects brand risk. Speci…cally, it allows to set a threshold, i.e. a minimum brandgenerated cash ‡ow, and to assess the capability of the brand of not generating morethan such threshold. Since the minimum cash ‡ow can be greater than or equal to 0, themodel then allows to estimate both a partial or a total default probability, respectively.

We have illustrated the above …ndings through an empirical analysis based on asample of ten companies. First subject of investigation has been the agreement amongthe valuation results of the Royalty Method, the Hirose methodology and brand valuespublished yearly on Business Week and estimated by Interbrand. We have seen thatthe correlation between the brand values is low, signalling the absence of a systematicrelationship among the valuation methods.

We have then estimated the brand values utilizing the alternative model proposed

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in Section 3, using …rst the cash ‡ows of the Hirose methodology, and then the onesof the Royalty Method. Consistent results have been obtained. Moreover, though theapplication of our approach, we have determined the brand partial and total defaultprobabilities implied by the Royalty Method and the Hirose methodology. The es-

timated values of the probabilities demonstrate the di¤erent view on the brand riskimplicit in the two models.

Finally, we have discussed that the joint utilization of the methods allows analyststo determine valuation boundaries and to obtain …nancial and risk analysis insights.

References

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[15] Perrier R. (edited by), 1997: "Brand Valuation", III edition, Premier Book,London UK , ISBN 1-900-617-00-5, 236 pages.

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[17] Sithamraju C., 2003: "The Value Relevance of Trademarks" in "IntangibleAssets", edited by Hand J. and Lev B., Oxford University Press, Oxford , ISBN0-19-925694-2, 537 pages.

[18] Smith J.E. and Nau R.F., 1995: “Valuing Risky Projects: Option PricingTheory and Decision Analysis,” Management Science , 41 (5), pp.795-816.

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Risk Analysis in Brand Valuation