Risk Analysis In Brand Valuation

Risk Analysis in Brand Valuation F. Beccacece1 , E. Borgonovo1 and F. Reggiani2 1 IMQ, Bocconi University, 20135 Viale Isonzo 25, Milano 2 IAFC, Bocconi University, 20135 Piazza Sra¤a 11, Milano

Abstract After an empirical start, brand valuation has attracted the interest of both accounting practitioners and academicians. Several methods for the assessment of brand value have been developed. However, a major critique shared by these models has been the lack of objectivity. In view of such criticism, the Japanese Ministry of Economy, Trade and Labour created a dedicated Committee with the twofold task of rigorously de…ning brand and of developing a methodology for brand valuation based on publicly available balance sheet data. The result goes under the name of the Hirose methodology. The methodology, however, while achieving the above two mentioned key-merits, does not allow a …nancial interpretation of the valuation results. We propose a brand valuation model which merges objectivity with robust underlying quantitative structure thus sharing a direct …nancial interpretation and providing risk analysis insights. An empirical analysis allows us to compare both numerical results and …nancial insights derived by analysts from the utilization of the Hirose Methodology, the Royalty Method and the proposed model. Keywords: Brand Valuation, Hirose Methodology, Risk Analysis, Brand Default Probability.

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

1

Introduction

The recent development of brand value assessment for accounting purposes has an empirical 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 the brand 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 further by capitalizing internally-developed as well as externally-acquired brands. In 1995, 1

the Accounting Standards Committee published Exposure Draft 50, Intangible Assets, (see [11]), allowing balance sheet inclusion of intangible …xed assets under the conditions: 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 assets would be able to qualify for recognition with such restrictive requirements [Canibae no et al (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 Barth et al (1998) [1] and Seethamraju (2003)[17]) was indeed supporting the hypothesis that brand 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 in a 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 the discipline of brand valuation. Several methods, in fact, had been developed by …nancial analysts and practitioners to assess brand value.1 The methods can be classi…ed broadly into cost, market and income approaches. The cost approach utilizes the cost spent in developing the brand as a measure of brand value (Reilly and Schweis (1999) [16], Ch. 8, pp. 118-145.) Reilly and Schweis (1999) [16] distinguish the “historical cost approach,” which values the brand based on the sunk costs associated with brand maintenance and management, from the “replacement cost approach,”which values the brand based on the expected total cost required to recreate the brand. Shortcomings in the cost approach are highlighted in Reilly and Schweis (1999) [16], which mention that the relationship between spent costs and 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 the market [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 priced alike, since brands are by nature somewhat unique. Perrier (1997) [15], Ch. 4, and Reilly 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 net present 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 Analyses2 [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: N X E[Xi ] V = (1 + r)i i=1 1 2

(1)

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

2

where V is the brand value, Xi 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[Xi ] is estimated. 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 clearest example 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 (or cash ‡ow) by the present and future price premium of branded products compared with products without brand. One considerable application of this technique is described in Section 2. Instead, the Royalty Method estimates the brand generated cash ‡ow as follows: E[Xi ] = E[Si ] R where Si 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 (VR ) equals: VR =

N X E[Si ]

(1 +

i=1

R i r)

(2)

In principle, R is found from a market analysis looking at the fees (expressed as percentage of sales) that a …rm required to licence its brand. The determination of the appropriate 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 to explore how to determine the appropriate royalty percentage, in the empirical analysis presented in Section 5 we have used the values published annually in “Licensing royalty rates”[Battersby and Grimes (2005) [5]]3 . The most delicate issue in the use of these methods is the arbitrarity in the identi…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…able data in measuring the value of brands, leading to results which relied on …nancial analysts’ 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 Ministry of Economy, Trade and Labor …nanced a project aimed at de…ning a brand valuation model solely based on public data [Hirose et al (2002) [6]]. Starting point of the report is 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 in ten 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 under the category “corporate”.

3

(known as the Hirose methodology) based only on publicly available …nancial data directly extracted from the …rm Annual Reports. This makes the valuation results very well grounded “empirically”, and capable of meeting the objectivity requirement mentioned 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 Hirose methodology with a robust underlying quantitative structure that o¤ers a clear …nancial interpretation of the results. The model also enables one to perform risk analysis of brand generated cash ‡ows, allowing to estimate brand default probabilities from balance sheet data. The above general discussion is followed by an empirical analysis in which we apply the new model, the Hirose methodology and the Royalty Method to estimate the brand value of a sample of 10 companies operating in di¤erent sectors. Results of the analysis will 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 the Royalty Method and the Hirose methodology results are attributable to the di¤erent cash ‡ows which are inputs of the two methods. We shall also show that applying the newly proposed method in conjunction with the other methods, an analyst derives insights 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 review of the Hirose methodology, highlighting its merits and discussing its (lack of) …nancial interpretation. Section 3 introduces an alternative brand valuation model. Section 4 presents 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 the Committee on Brand Valuation (Chairman: Dr. Yoshikuni Hirose, Professor at Waseda University), a consultative body organized under the Japanese Ministry of Economy, Trade and Industry. It is contained in the corresponding report, released on June 2002 entitled, “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 4

now on the “Japanese model”) using the income approach, a valuation approach based on pro…tability. The Japanese model can be summarized as follows. The brand value (V ), is assumed to be function of several factors: V = f (P D; 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 to the price advantage of the brand. The proportion of advertising expense, or brand management cost, to total operation cost is used as the attribution rate. Formally, P D is given by: 0 Si Si Ai 1X C0 (3) PD = 5 i= 4 Ci Ci OEi

where : S = Sales C = Cost of sales S = Sales of a Benchmark Company C = Cost of sales of a Benchmark Company A = Advertising and promotion cost OE = Operating cost LD 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 is represented by the stability of the cost of sales. It is calculated by the formula: c

c

LD =

(4)

c

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 similar or di¤erent industries as well to overseas, expanding market geographically. ED is explained by an average of the growth rate of overseas sales and growth rate of sales

5

from non-main businesses. The formula to calculate ED has been stated as follows: " # 0 0 1 1 X SOi SOi 1 1 X SXi SXi 1 ED = +1 + +1 (5) 2 2 i= 1 SOi 1 2 i= 1 SXi 1 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 function f , given by: P D LD ED (6) V = r 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 numerator 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 or the Japanese model. Although the Japanese model shares the advantage of objectiveness and data accessibility, it does not o¤er a clear interpretation of the …nancial aspects of the brand value, as we are to discuss. 1. Discounting at the risk-free rate: brand cash ‡ows are risky. The Report underlines how, in accordance with the IAS 36, Appendix A [12], the uncertainty (and consequently the riskiness) of the cash ‡ow generated by the brand, must be handed by using one of the two methodologies: a. adjusting the interest rate with a risk premium and using the cash ‡ow we can estimate by considering a single scenario (the most likely one); b. considering the expected cash ‡ow and maintaining the risk-free rate for discounting the future cash ‡ows and it follows the latter methodology, determining the expected cash ‡ow as the average 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 provides the present value of the expected cash ‡ow, with no adjustment for the risk, in contrast 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 remark that 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.

6

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 that LD is not a correction term entailing the cash ‡ow riskiness. Let us consider the CEQ expression for the present value of a single cash ‡ow Ct that will be received at time t. It is: (Ct ;rm )

Ct

P Vt =

Ct

RPm

m

1+r

(7)

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

is the standard deviation of the cash ‡ow;

is the correlation coe¢ cient; RPm 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 on what we have discussed till now, if LD has to be interpreted as a risk correction factor, it must hold that P D = Ct (for the sake of simplicity, the factor ED is omitted). Hence, equating eq. (6) and (7), one obtains the condition: Ct (1

c c

)

r

=

(Ct ;rm )

Ct

m

Ct

RPm

r

(8)

After a …rst algebraic manipulation, one gets: c

Ct =

(Ct ; rm )

Ct

RPm

(9)

m

c

This condition has in itself no direct …nancial interpretation. However, let us try and 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 c c practical point of view, one can assume ' t . Inserting in eq. (9), one gets: c

Ct

=

(Ct ; rm )

Ct ct

RPm

(10)

m

ct

Now, since

ct

= 1 by de…nition, one is left with: 1=

(Ct ; rm ) m

7

RPm

(11)

Finally utilizing the often empirically veri…ed fact that equivalent to requiring : 1 (Ct ; rm ) =

RPm 2 m

= 1, condition (9) is (12)

m

Eq. (12) suggests that, in order LD to be a risk correction coe¢ cient, the correlation coe¢ cient between the brand generated cash ‡ow and the market should always equal the inverse of m . This is a strong condition that is not going to be veri…ed in the practice. Hence, one cannot but infer that the CEQ interpretation of the Japanese model, via Capital Asset Pricing Model, leads to an unacceptable conclusion. 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 the value drivers as factors which are strictly linked with the brand value, from the other 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 possible inconsistence between the structural form of the brand value function and the correlations among the factors. In fact, the product of the factors proposed in the model as brand value function, even if it shows the advantage of a very simple 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 the model for determining di¤erent value drivers are correlated. For example, it is evident 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 value drivers by the means of a benchmark company. In our opinion, the use of a benchmark is justi…ed in the model, since brand value is essentially determined by the advantage that the brand guarantees over competitors. On the other hand, this makes crucial the choice of the benchmark company, which, in the most cases can be interpreted as the worst 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 methodology, i.e. brand cash ‡ow estimation from public data. On the other hand, we aim at overcoming the di¢ culties in the …nancial interpretation of the Hirose methodology5 , 5

See the end of Section 2.

8

by introducing an approach that enables to extract information on brand risk directly from balance sheet cash ‡ow estimation. We then consider the brand generated cash ‡ow composed of a risk-free component and a risky component. The rationale below this choice is the following. As we mentioned in our critique to the Hirose methodology in Section 2, since the brand generated cash ‡ow is, in its entirety, an uncertain/risky quantity, not all the cash ‡ow can be discounted at the risk-free rate. However, we consider that the brand is capable of assuring a minimum cash ‡ow equal to x0 2 R, which is risk-free and therefore represents the 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 generate a risky cash ‡ow. We model the additional cash ‡ow as ranging from 0 to its highest value, denoted by q. More formally, the risky cash ‡ow is a …nite support random variable X 2 [0; q] ; X FX , where FX is the cumulative distribution function for X. Hence we have that the cash ‡ow generated by the brand is the random variable: Y = x0 + X

(13)

In the current model, we still want to maintain input data on the same basis as in the Hirose methodology, since it is the main advantage of the Japanese model to enable brand evaluation based on accessible book data. Nonetheless, keeping the economically signi…cant time span of 5 years used in the Hirose methodology, one can get from 5 to 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 as end-year statements for valuing brands associated to products with a high seasonality in sales). Such a sample size is unfortunately not enough to guarantee a statistically accurate …tting of the distribution FX . We then utilize an alternative approach. In order to characterize the risk associated with the brand, we consider that the …rm can be 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 event a “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 “partial default probability.” We now introduce an auxiliary variable (T ) that shall enable us to characterize the default probability p utilizing the same database as in the Hirose methodology. To do 0 so, we de…ne T = , with the discrete probability mass function q 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) 9

Let us then compute the value of the bene…t generated by the brand utilizing the auxiliary random variable T . We now show that the introduction of T enables the computation 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 E[X] + r 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, then the 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 expected Net Present Value (NPV) of T at period 1 is: E[T1 ] =

(1 p)q p 0 + (1 p)q = 1+r 1+r

(18)

The presence of r at the denominator is due to the fact that we assume that all risks associated with q are contained in p. The brand is able to generate the bene…t in the second period only if it has not default in period 1. This means that P (T2 = q jT1 = 0) = 0. Given that the brand has not defaulted in period 1, then if the brand does not default in period 2, the brand shall be capable of generating again the bene…t. Then, the probability of getting the bene…t q at the end of the second period is: P (T2 = q) = P (T2 = q jT1 = q )P (T1 = q) + P (T2 = q jT1 = 0)P (T1 = 0) = = P (T2 = q jT1 = q )P (T1 = q) = (1 The presence of (1 Hence:

p)2 q

(19) (20)

p)2 is justi…ed by the assumption of independent shock arrivals. E[T2 ] =

(1 p)2 q (1 + r)2

(21)

Following the same logic, one can show that E[Tn ] =

(1 p)n q (1 + r)n

(22)

The expected present value of the cash ‡ow generated by the brand at year n is, then: E[Yn ] =

x0 (1 p)n q n + (1 + r) (1 + r)n 10

(23)

As a consequence, the total NPV equals: V =

1 X

E[Yn ] =

n=1

1 X n=1

X (1 p)n q x0 + (1 + r)n n=1 (1 + r)n 1

(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 EF [X]: These two quantities can be computed from the cash ‡ows generated by the brand over n past periods, where n is an appropriate time span for the analysis. For example n = 5 years in the Hirose methodology [eq.(3)]). The default probability p can be 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 value can 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 transparent interpretation in terms of brand risk w.r.t. the Hirose methodology. In the next Section the quantitative comparison of the results of the three models is proposed.

4

Quantitative Investigation and Results

This Section details the application of the three models to the valuation of the brands of 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 by application of the Hirose methodology [eq. (6)] and the Royalty Method [eq. (2)]. The yellow horizontal bar of Figure 1 (…rst bar in each group) reports the corresponding value as published in Business Week’s traditional annual review of the top one-hundred brands6 [see ref. nr. [10]]. Figure 1 evidences that some disagreement among the brand values assigned by the three methods. We investigate the results …rst examining the degree of agreement/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 towards agreement/disagreement. The correlation coe¢ cients for our sample of 10 …rms are reported in Figure 2. Figure 2 shows that the highest agreement is found between the values of the Hirose methodology 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).

11

McDonald's Kodak Gillette Disney Colgate Budweiser Business Week Royalty

Nike

Hirose

Tiffany Pepsi CocaCola 0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

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

Hirose Hirose 1 Royalty 52.8% Interbrand 84.9%

Royalty 1 43.2%

Interbrand

1

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

12

Company CocaCola Pepsi Tiffany Nike Budweiser Colgate Disney Gillette Kodak McDonald's

Our Model 21,407 13,147 2,693 376 5,591 8,928 7,935 6,751 3,477 9,683

Hirose 22,846 13,739 3,376 477 6,017 9,334 11,015 7,479 4,064 12,320

p 53% 51% 42% 59% 50% 54% 66% 59% 49% 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 Methodology cash ‡ows.

and the Hirose methodology is intermediate (52:8%), while the lowest agreement is registered 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 ‡ow basis of the methodologies. Figure 3 shows the brand values that one obtains by eq. (17) when one utilizes as input 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 term P Di =

Si Ci

Si Ci

Ai OEi

C0

(27)

is one of the summands in eq. (3), and represents the cash ‡ow generated by the brand price 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). S Figure 4 shows CSii and Ci for the …rm. i The …ve years cash ‡ows obtained from book values are reported in Figure 5. From this Figure it is also possible to see that the minimum cash ‡ow generated by brand equals 1047M U SD. Choosing this value as x0 , then the expected additional risky cash ‡ow is E[X] = 270M U SD, and the maximum cash ‡ow equals max xi = x0 + q = 1617M U SD i

(28)

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

13

S/C and S/C* 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00

CocaCola Benchmark

1999

2000

2001

2002

2003

Year

Figure 4:

Si Ci

and

Si Ci

for Coca Cola from 1999-2003

xi for Coca Cola 1700 1600 1500 1400

xi

1300

E[xi]

1200 1100 1000 1999

2000

2001

x0=1047 p=0.53 q=570

2002

2003

V=21407MUSD

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

14

Company CocaCola Pepsi Tiffany Nike Budweiser Colgate Disney Gillette Kodak McDonald's

Our Model 27,457 29,015 2,960 12,375 17,733 14,626 47,130 13,629 23,218 26,804

Royalty 23,604 27,960 2,952 11,697 16,928 12,723 43,146 11,852 19,694 26,345

p 58% 46% 58% 59% 50% 62% 50% 50% 47% 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 0 sum of the sure part xr = 20940 and the risky portion E[X] = 467. r+p 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 our model and the Hirose methodology shows the following (Figure 3.) The correlation coe¢ cients on the values is 0:999, meaning that there is a systematic relationship between the results of the two methods. The high correlation is the consequence of the choice of the cash ‡ows basis, which is the same for the two evaluations. The resulting values of p shown in the third column of Figure 3 are the partial default probabilities (see Section 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 CocaCola with the Royalty Method …rst. The cash ‡ows are reported in Figure 7. They are found by multiplying the sales times the royalty rate extracted from the annual publication “Licensing royalty rates” [Battersby and Grimes (2005) [5]] (7% in this case.) Capitalizing the average cash ‡ows at 6% 7 one …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.: VR =

R E[S]

r

with r = 8% and g = 2%.

15

g

1,500,000 1,480,000 1,460,000 1,440,000 1,420,000 1,400,000 1,380,000 1,360,000 1,340,000 1,320,000 1,300,000

E[X]+xo xi

1999

2000

2001

x0=1370 p=0.58 q=103

2002

2003

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 displays the cash ‡ows and the values of x0 , E[X] and q. One has: x0 = 1370M U SD, q = 44 = 0:58. Substituting into eq. (17), one 103M U SD, E[X] = 44M U SD, and p = 1 104 …nds that the sure portion of the brand values would amount at 27350M U SD, while amounts at around 100. the extra amount, E[X] r+p Let us now discuss the overall ranking agreement. As one can compute from Figure 6, the correlation coe¢ cient among the brand values estimated with our model and with the Royalty Method equals 0:985. This result evidences the presence of a systematic relationship. Such relationship is again due to the fact that the two values share the same cash ‡ows basis. However, it is immediately apparent the discrepancy of the royalty cash ‡ows and the cash ‡ows derived by the Hirose methodology (reported in Figure 5.) As far as risk analysis is concerned, the partial default probabilities implied by the Royalty Method are reported in the third column of Figure 6. Let us now investigate whether the risk views implied by the Hirose methodology and the Royalty Method coincide. Figure 8 compares the partial default probabilities obtained with the two methods. It is immediate to note that Hirose methodology and the Royalty Method can lead to a di¤erent view on the brand partial default probability. The reason lies in the fact that in this analysis p is extracted out of the cash ‡ows, so it is the partial default probability “implied” by the valuation method. The fact that the cash ‡ow basis is di¤erent explains the di¤erence in the p’s. We now show that one can also derive the default (with no more “partial”) probability straightforwardly using eq. (25). It is enough to choose as minimum cash ‡ow 16

McDonald's Kodak Gillette Disney Colgate Budweiser Royalty

Nike

Hirose

Tiffany Pepsi CocaCola 0%

10%

20%

30%

40%

50%

60%

70%

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

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Company CocaCola Pepsi Tiffany Nike Budweiser Colgate Disney Gillette Kodak McDonald's

Hirose 19% 21% 17% 25% 9% 5% 43% 16% 18% 34%

Royalty 4% 11% 16% 11% 9% 5% 7% 7% 4% 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 more than 0, i.e. the brand default probability. Figure 9 shows the default probabilities implied 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 and the partial default probabilities of Figures 3 and 6, shows that the default probabilities are lower than the partial default probabilities. This is consistent with the fact that it is more likely that a brand generates more than 0, rather than it generates more than a minimum cash ‡ow x0 > 0. As far as the risk views implied by the Royalty Method and the Hirose methodology are concerned, Figure 9 shows that they are not linked by a systematic relationship. In fact, the default probabilities practically coincide for Budwiser and Colgate, while little agreement is found on the brand default probabilities of Disney, McDonalds’, Kodak and Nike. Hence, one ought to conclude that the Royalty and the Hirose methods not only lead to di¤erent brand values, but also give rise to a di¤erent underlying interpretations 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 say that 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 would range between 22000 — with eq. (17) and the Hirose cash ‡ows — and 67000. One can 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 as highlighting to the fact that brand market is not complete. We also recall that in the case of incomplete markets also the valuation of real options does not lead to a unique value, but to a range [Smith and Nau (1995)].

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then be summarized as follows. Probability of Coca-Cola not to generate more than the 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 its brand 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 seen that, after an empirical start, brand valuation has attracted international attention with the publication of the IFRS 3 Business Combinations. Such publication has lead to the development of several valuation methods that have been envisioned by …nancial analysts and practitioners. We have brie‡y reviewed such methods, highlighting that most 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, as a result of a research project aimed at de…ning brand value based on publicly available data. Such method, named the Hirose methodology, has the key-merit of solving the historical problem of objectivity and arbitrarity in brand valuation, since its cash ‡ow estimation scheme relies solely on publicly available …nancial reports. However, we have seen that the Japanese model presents some drawbacks. The …rst one is the di¢ culty in reconciling the model with traditional valuation results. This prevents one from assigning a meaningful …nancial interpretation to its terms and in particular 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 these limitations, we have then o¤ered an alternative model, with the purpose of providing a brand valuation tool supported by a more robust underlying quantitative structure and allowing a more direct …nancial interpretation of the results, while preserving the key merit of the Hirose methodology — i.e. to use publicly available information. The model allows to estimate a brand default probability from balance sheet data which re‡ects brand risk. Speci…cally, it allows to set a threshold, i.e. a minimum brand generated cash ‡ow, and to assess the capability of the brand of not generating more than such threshold. Since the minimum cash ‡ow can be greater than or equal to 0, the model 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 a sample of ten companies. First subject of investigation has been the agreement among the valuation results of the Royalty Method, the Hirose methodology and brand values published yearly on Business Week and estimated by Interbrand. We have seen that the correlation between the brand values is low, signalling the absence of a systematic relationship 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 ones of the Royalty Method. Consistent results have been obtained. Moreover, though the application of our approach, we have determined the brand partial and total default probabilities implied by the Royalty Method and the Hirose methodology. The estimated values of the probabilities demonstrate the di¤erent view on the brand risk implicit in the two models. Finally, we have discussed that the joint utilization of the methods allows analysts to determine valuation boundaries and to obtain …nancial and risk analysis insights.

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