Valuing firms within the utilities sector using regression analysis:

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INOM

EXAMENSARBETE TEKNIK,

GRUNDNIVÅ, 15 HP ,

STOCKHOLM SVERIGE 2020

Valuing firms within the utilities

sector using regression analysis:

An empirical study of the US and European

market

LUDVIG HARTING

NILS ÅKESSON

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Valuing firms within the utilities

sector using regression analysis:

An empirical study of the US and

European market

Ludvig Harting

Nils Åkesson

ROYAL

Degree Projects in Applied Mathematics and Industrial Economics (15 hp) Degree Programme in Industrial Engineering and Management (300 hp) KTH Royal Institute of Technology year 2020

Supervisor at KTH: Mykola Shykula Examiner at KTH: Sigrid Källblad Nordin

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TRITA-SCI-GRU 2020:115 MAT-K 2020:016

Royal Institute of Technology

School of Engineering Sciences

KTH SCI

SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

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Abstract

Valuing a company is an important task in finance, especially before a potential merger or acquisition of a company. It is then of great importance for both parties in a deal to make an accurate estimate of the value of the company. The goal of this paper is to investigate how well regression analysis can be applied in this matter and if it can perform at par or better than more frequently used methods in the industry today. The study was conducted within the utilities sector in the US and Europe, with data collected from historic public transactions dating back to 2009. The study concludes that a regression model as a valuation tool can generate several advantages as it identifies key value drivers and is based on core mathematical concepts. However, the model created in this thesis underperforms compared to the prominent methods in place today. For further research this thesis may provide useful insight into different areas to consider when creating a valuation model.

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Abstract

Att värdera ett företag är en viktig uppgift inom finanssektorn, särskilt innan en po-tentiell sammanslagning eller förvärv av ett företag. Det är d˚a av stor vikt för b˚ada parter i en affär att göra en exakt uppskattning av företagets värde. M˚alet med denna studie är att undersöka hur väl regressionsanalys kan tillämpas i denna fr˚aga och om den kan generera samma eller bättre resultat än mer använda värderingsmetoder inom branschen idag. Studien genomfördes inom el-, gas- och vattensektorn i USA och Eu-ropa, med data som samlats in fr˚an historiska offentliga transaktioner som g˚ar tillbaka till 2009. Studien drar slutsatsen att en regressionsmodell som ett värderingsverktyg kan generera flera fördelar eftersom den identifierar viktiga faktorer som driver en värdering och baseras p˚a grundläggande matematiska begrepp. Modellen som skap-ats i denna avhandling underpresterar dock jämfört med de framst˚aende metoderna som finns idag. För ytterligare forskning kan denna studie ge användbar insikt i olika omr˚aden att beakta när man skapar en värderingsmodell.

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1 Introduction

1.1 Background

Valuing a company is often described as more of an art than a science. How could one pos-sibly estimate the value of a large, dynamic corporation with a great amount of intangible and tangible assets accurately? Add to the task an ever changing market where the com-petition and consumer preferences changes by the day. Furthermore, predicting the future cash flows is an art itself since they heavily depend on immeasurable factors such as the staff’s skill set, the company culture, the brand recognition, technological advancements, etc. The common notion is that accurately valuing a company is in most cases impossible. However, there are several techniques and methods which yield a range of values in which one predicts the true value of the business to lie.

Notwithstanding the fact that the process is complex and arduous, valuing a company is a very important part of finance. A common and important use is in the investment banking profession when advising a client through a company transaction such as a merger or acquisition. During this task, it is of great importance for the acquirer, target com-pany, and underwriter to estimate the value of the target company accurately. Thus, the investment bank often charges a fee for providing expertise through this process, as well as additional equity earned through the deal. Apart from the valuation, the investment bank may also consult in the strategy of the acquisition.

An important distinction is the difference between a strategic and financial acquisition. A strategic acquisition is an acquisition of a company that is active in the same industry, which often is a supplier or customer to the company. The Purpose of such acquisitions is often to gain synergy effects, e.g. economies of scale. This added value for the buyer then also tends to increase the transaction value financial acquisitions, and thus generate a premium. Financial acquisitions are characterized by actors acquiring the company with the belief that the value of the company will increase in the future and generate a return on investment with or without active management involvement. The actor then sells the company or the stake that it has acquired in order to make a profit. Generally, this is done by institutional buyers with the most common being private equity firms, venture capitalists, and holding companies[11].

Naturally, there exist several different valuation methods, two of which will be discussed in this paper include the discounted cash flow analysis (DCF) and comparable companies valuation (CCV). The idea of this research is to extend on the existing CCV method in order to improve its applicability and precision. Corporate executives often reason for sim-plicity using a single multiple, which is ill advised among corporate finance professionals due to the uncertainty of relying on a single metric[2]. The use of several regressors may

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solve this issue in a simple manner. 1.2 Research Question

The research questions that will be covered in this paper are

• Is it possible for an regression analysis model to estimate utility companies’ enterprise value within North America more accurate than the existing comparable companies valuation approach?

• How well does this type of valuation method fit the need of investors today? 1.3 Limitations & Feasibility

The research has been limited to utility companies in the United States and Europe during the years 2009-2020. The utilities industry is particularly interesting from a regression analysis perspective, as the sector is characterized by large material assets and stable cash flows. Firms within the sector are likely not to be regarded as growth companies, which makes comparable company analysis more reliable and financial measurements such as EBITDA a relevant multiple factor. Furthermore, the stable cash flows enables the DCF method to achieve greater precision. [10]

The sector is particularly interesting from a valuation standpoint as the current busi-ness climate allows for great synergy effects. Economies of scale, push towards growth opportunities and a consolidation within renewable energy as an effect of decreasing oil reserves and prices generates a great market for mergers and acquisitions. [9]

The study will limit data collection to the year of 2009-2020, as a longer time frame characterized by large disruptive events will undermine the reliability of the results by skewing the data.

1.4 Purpose & aim

The aim of this paper is to create a valuation model for US and European utilities com-panies based on regression analysis and examine if it provides a more accurate result than comparative companies valuation (CCV).[4] In order to accomplish this, one must distin-guish explanatory covariates of a company within the given sector and region’s enterprise value. The significance level of the covariates’ explanatory value has been set at 5%. The purpose of the thesis is to analyse the potential applicability of a regression model as a valuation tool for financial institutions such as investment banks, and discuss its advantages and disadvantages compared to the currently more widely used methods of comparable companies valuation (CCV) and discounted cash flow analysis (DCF).

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2 Financial & Economical Theory

2.1 Enterprise Value

When valuing a company one must first formally define the measurement used for said evaluation. One simple measure is a company’s market capitalisation, otherwise known as Equity Value. This is the total value held by shareholders, and thus the theoretical price one must pay to acquire the company’s total outstanding shares. [10]

Another valuation measurement that is often regarded as more realistic is enterprise value (EV), also called asset value or firm value. Unlike equity value, enterprise value captures the company’s total value to all stakeholders, not only equity owners [10]. The formal definition of enterprise value is the following:

EV = (share price × number of shares) + total debt - cash

Thus, enterprise value encompasses the total value of the assets of the company excluding cash held by equity owners as well as debt owners [1]. Enterprise value is thus the theoretical price one would have to pay to acquire the whole company, i.e. its equity as well as its debt and cash. [10]

2.2 Valuation multiples

An effective way of valuing a company is the relative approach, using multiples of previous transactions of a similar company. The valuation theory is based on the assumption that similar assets should be priced similarly, and thus that one can extract valuation multiples for comparable companies with regards to a specific financial metric.

For example, consider the multiple EV/EBITDA. According to theory, two companies in the same sector and with other similarities should trade at the same multiple. Enter-prise value multiples and equity value multiples are most common, with a distinguishable difference in that equity value multiples unlike EV multiples can be affected by the firm’s capital structure but are more easily computed as market capitalization quicker to extract. The most common multiples are: EV/EBITDA, EV/EBIT, EV/Sales, Price/Earnings, Price/Earnings to growth.

2.3 Comparable Companies Valuation

Comparable companies valuation (CCV), or comparable company analysis is a very com-mon valuation method acom-mong particularly investment banks. The technique builds on the theoretical foundation presented above, where similar companies should trade at similar valuation multiples such as EV/EBITDA, EV/Sales and Price/Earnings.

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An important part of CCV is establishing a ”peer group” according to a set of criteria, often business industry classification, region, size, growth rate, and profitability. Establish-ing an efficient peer group can be difficult as it is very subjective and requires experience. A peer group with several companies that closely resembles the target company will allow the comparable valuation method to be precise, and thus this step is highly important. [10] As the peer group has established, a table of financial information for each company such as market capitalization, net debt, EV, Sales, and EBITDA is set up. Subsequently, multiples for each comparable company within the peer group is calculated and analysed, data from which the target company valuation can be calculated. Most often, one takes the median or mean of the multiples of the peer group and apply them to the target company with a certain interval. [10]

CCV is widely used in the financial industry because of its simplicity, where data is easily extractable and the results easily explained in a pitch to the target company’s owners. Another positive aspect of CCV is that it reflects the current market sentiment and is not sensitive to assumptions like the DCF method. CCV provides a highly realistic valuation method if the companies in the peer group are very similar, but as no two companies are exactly alike there will always exist discrepancies that CCV may not capture but will ultimately affect the real valuation. Furthermore, comparables are highly sensitive to tem-porary market conditions and non fundamental factors which can alter the extracted value disproportionally in the short term and leave an over- or undervaluation of the whole industry unnoticed. [5]

2.4 Discounted Cash Flow analysis

While CCV is based on relative measurements, discounted cash flow analysis is an intrin-sic valuation method where the net present value of future cash flows is estimated. This valuation is the most theoretically correct method of estimating the enterprise value of a firm, as it computes the present value of future free cash flows to all both equity- and debt holders [1].

The formula for discounted cash flows is DCF = t=n X t=1 CFt (1 + r)t

where CFt is free cash flow at time t and r is the used discount rate. The discount rate is also called WACC (Weighted Average Cost of Capital, and is defined as the average rate of return investors expects for a given year [1]. The expected cash flows are usually estimated for a period of 5 years into the future, and is complemented with a terminal value. The

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terminal value is calculated either through an exit multiple, where the business is assumed to be acquired, or perpetual growth at a fixed rate. The exit multiple is usually extracted from a CCV analysis, for example extracting the mean EV/EBITDA multiple of similar companies, whereas the perpetual growth rate is a realistic but conservative growth rate of 2-4%. [10]

The DCF analysis provides the advantage of estimating the intrinsic value of a firm based on its fundamentals, not by comparing to other companies. The method thus serves as the foundation on which other valuation methods are built by capturing the underlying drivers of value, and comes closest to the real intrinsic value of a company. Unlike the CCV method, DCF is not blind to sector under- and overvaluations.

The greatest disadvantage of the DCF method is that it is very sensitive to assumptions regarding WACC and perpetual growth rate. Small changes in these assumptions will cause great fluctuations in the estimated value, and thus an effective valuation requires precise assumptions that are very hard to make without a high degree of confidence. This is not very likely, as perpetual growth rate is almost impossible to estimate accurately.

3 Mathematical background

Regression analysis is a powerful and widely used technique to examine the influence of a selected set of prediction variables on a response variable. The research will be based on a linear regression model, which general form can be described by

yi= β0+ x1,iβ1+ ... + xn,iβn+ i

where y is the response variable, βj are the regression coefficients, xiare the observed values and i is the error term. The model can conveniently be described in vector notation as

y = Xβ + where y =      y1 y2 .. . yn      X =      1 x11 x12 · · · x1p 1 x21 x22 · · · x2p .. . ... . .. 1 xn1 xn2 · · · xnp      β =      β0 β1 .. . βn      ; =      1 2 .. . n     

The model is fitted by the ordinary least squares approach on a data set containing n observations of the response variable and the corresponding p prediction variables. That

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is, find the parameter β which minimizes the squared sum of the residuals, ei. The residu-als are the distances from the observed values y and the model’s predicted values ˆy. Thus, the parameter ˆβ that minimizes the squared sum is calculated by

ˆ

β = arg min

β (y − Xβ)

0_{(y − Xβ)}

where ˆβ is the estimate of the true regression coefficient β. ˆ

y = ˆβ0+ ˆβ1x1+ ˆβ2x2+ ... + ˆβpxp 3.1 Assumptions

In regression analysis there a a few underlying assumptions regarded the fit of the model that deserve great care in the analysis, since a violation of these may make the model misleading or erroneous. The assumptions are:

1. There is a linear, or at least approximately linear, relationship between the response y and the regressors.

2. The error term has zero mean.

3. The error term has constant variance σ2. 4. The errors are uncorrelated.

5. The errors have a normal distribution.

It is important to conduct analyses to examine the validity of these assumptions as gross violations can lead to an unstable and unreliable model. The methods of diagnosing the basic regression assumptions are primarily based on studying the model’s residuals and different residual plots. This form of model adequacy checking must be done for every model that is under consideration to be used in practice. If a violation is detected, one must alter the model in order for the assumptions to be true, which is often done by data transformation.

3.2 Transformations

Plots of the residuals are a very powerful tool for detecting violations of the basic regres-sion assumptions. When a violation is present one must perform a transform in order to correct for this model inadequacy. It it not unusual that the regressors are expressed in the incorrect scale of measurement or metric causing inequality of variance. Ideally, the choice of metric should be made by an analyst with knowledge of the subject that is examined. However in many cases the this information is not available and a data transform may then be chosen by a trial and error approach or by some analytical procedure.

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Furthermore, one may may realize that there is not a linear relationship between the response variable and the regressors which is a critical assumption for the model. It is then appropriate to linearize the model by a suitable transformation, when this is possible the model is said to be intrinsically linear. An example of an intrinsically linear model is the exponential function, where a logarithmic transformation yields a straight line.

3.3 Diagnostics and handling of outliers, leverage and influential obser-vations

An observation with an unusual x and y value may have a great influence over the model’s fit. This situation is undesirable because the model is supposed to be representative of the all the observations and not be overly influenced by a few extreme cases. It is therefore important to detect and handle these odd observations.

Although an observation may have an unusual x-value, its corresponding y-value may fall near the regression line. This is called a leverage point. It will not affect the fit of the regression, but will affect the model summary statistics such as the R2 and the standard errors of the regression coefficients. An influence point on the other hand will also have an unusual y-value, causing it to alter the regression line in its direction. The amount of leverage depends on its location in x space and can be determined from the hat matrix, H = X(X0X)−1X0. The elements hij can be interpreted as the leverage exerted by the ith observation yi on the jth fitted value ˆyj. The further away the observation is in regards of the centroid, the greater the leverage that point has. A point is remote enough to be considered a leverage point if the hat diagonal exceeds 2p/n, given that 2p/n > |1|. An often used method for measuring the observations’ influence and the model’s fit is Cook’s distance which will be further explained in this section.

3.3.1 Cook’s distance

As described above it is important to take both the location of the point in x space and its response variable into account when determining the observation’s influence. Cook suggested a way of dealing with this by a measure between the least square fitted coefficients

ˆ

β and the least square fitted coefficients with the ith observation deleted, ˆβ_(i). This measure can be calculated by Di = r_i2 p V ar(ˆyi) V ar(ei) = r 2 i p hii 1 − hii

Generally, a good criteria for determining influential points as outliers is the threshold D(i) > 4/n.

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3.4 Treatment of influential observations

Diagnostics of the observations leverage and influence is an important tool in order to identify important observation that deserve more attention. It can be difficult to decide whether or not to discard these observation and it is important to make that decision with care since they have a large influence on the model. Generally, if there was an error while collecting the data if the data point is not a part of the population that was intended to be sampled, the observation may be invalid and can be discarded. However, if the data collected can not be proven invalid there is no justification for having it removed, even if it has a large influence on the model.

3.5 Multicollinearity

In a perfect model, there exists no linear relationship between the prediction variables, and they are then said to be orthogonal. On the contrary, if the prediction variables are perfectly linear combinations of each other, problems arise when trying to solve for ˆβ in the OLS equation and one quickly realizes that there exists no solution.

The problem of multicollinearity is said to exist if there is near linear relationships be-tween regressors in the model. The presence of multicollinearity may lead to misleading or inaccurate inferences, which if the regressors were orthogonal would easily be avoided. Such inferences include:

1. Identifying e relative effects of the regressor variables 2. Prediction and/or estimation

3. Selection of an appropriate set of variables for the model The multiple regression model is described in section 2 as

Xβ +

where y is an n x 1 vector of the response variables, X is an n x p matrix of the regressor variables, and is a n x 1 vector of the normally distributed randos. Let Xj be the jth column of the X matrix. The vectors of Xj are said to linearly dependent if there is a set of constants kj, not all zero, such that

p X

j=1

kjXj = 0

If the equation above holds exactly for a subset of X, the rank of X’X is less than p, and its inverse does not exist. However, if the equation holds approximately, multicollinearity is said to exist.

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In order to adjust for multicollinearity and analyze the data correctly, it’s important to identify and understand its sources. There are three primary sources of multicollinearity: 1. The data collection method

2. Constraints on the model or population 3. Model specification

3.5.1 Variance inflation factor (VIF)

One method of detecting multicollinearity is by analyzing the Variance inflation factor (VIF). The diagonal elements of the matrix C = (X0X)−1 can be written as Cjj = (1 − R2_j)−1, where R2_j is the coefficient of determination obtained when xj is regressed on remaining the p − 1 regressors. Thus, as xj goes towards orthogonality to the remaining p−1 regressors, R2_j goes towards zero and consequently Cjj to unity. If xj is almost linearly dependent on some subset of the remaining regressors, R2_j is closer to unity and Cjj very large. The variance inflation factor (VIF) is thus defined as

V IFj = Cjj = (1 − Rj2)−1

If one or more larger VIFs are identified, it indicates multicollinearity within the model. Usually, a VIF that exceeds 5 or 10 indicate that associated regressor coefficients may be poorly estimated, while smaller VIFs indicate smaller multicollionearity.

3.5.2 Variable selection

Among the most common corrective techniques for multicollinearity is variable selection, yet it does not guarantee full elimination as there are cases where several regressors are related but some subset of them still belongs in the model. Selecting the ”best” regression model is the process of compromising the trade-off between having as many regressors as possible and thus having more information affecting the predicted variable y, and having as few regressors as possible and thus minimizing the variance of the prediction value y.

4 Methods

The method used for this research was largely based on the framework for regression model building presented by D. Montgomery et al in Introduction to Linear Regression[8]. After having collected the relevant data, the basic approach is first to fit the full model with all covariates and then perform a thorough analysis of the model, including residual analysis, investigating possible multicollinearity and handling outliers. If one then detects violations of the basic assumptions, a transformation would be needed to correct for the model inadequacies. Then, one needs to test the significance of the covariates and select

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the optimal subset with regards to a given criteria. Lastly, the final model needs to be thoroughly analyzed in order to determine its adequacy and performance.

4.1 Data collection

Finding relevant data is a difficult task, especially when dealing with financial data as many firms rarely report more than the are obliged to. Thus, the supply of financial data within the utilities sector in the US and Europe is limited. The data collected for this project was downloaded from Merger Markets, which is a financial database containing a record of historic MA transactions and some financial information of the target companies. Although the financial data is quite limited from this source, it is believed to still be suffi-cient for this thesis.

In addition to the data collected from Merger Markets, the Dow Jones Utility Average (DJUA) of the time of transaction was added to as it can reflect the macro economic envi-ronment during the time of transaction. The daily close of the index was downloaded from yahoo finance, dating back to 2009.

In total, 249 observations with disclosed financial information were obtained from transac-tions between 2009 and 2020, with six covariates that were relevant for the model.

4.1.1 Response variable Enterprise value

The response variable, i.e the variable which is to be estimated by the regression model, is enterprise value (EV). This metric is often used to valuate a company for a potential acquisition. EV measures the total value of the company and is often used as a more comprehensive alternative to market capitalization.

4.1.2 Covariates Revenue

Revenue, or sales, is the total income of a company generated by its business operations. Since revenue include the income from all business activities, it is a good indicator of the size of the company.

A frequent reason for using sales as a value driver is that earnings and cash flows may be negatives and in these cases the revenue multiple will convey more information than the negative earnings [7]. Although revenue has its advantages in these situations, it may often be an inconsistent value driver as the value of a company is heavily dependent on

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future cash flows which can vary greatly among firms that have similar incomes. EBITDA

Earnings Before Interest, Taxes, Depreciation and Amortization, or EBITDA, is a measure of a company’s overall financial performance and profitability. EBITDA is a widely used metric for valuation as it is a precise measure of corporate performance since it shows the company’s earnings before being influenced by accounting and financial deductions. How-ever, one has to keep in mind that in some occasions it may be misleading as it does not include the cost associated with capital investments such as property, plant and equipment. EBIT

Earnings before interest and taxes (EBIT) is, as one’s intuition would suggest, simply calculated by the revenue subtracted with expenses excluding interest and tax. EBIT is often also referred to as operating earnings or operating profit.

Earnings

Earnings, or net income, is the bottom line on the income statement and is the final profit after having paid all expenses, including interest and tax. Earnings is the most reli-able indicator of a company’s success and therefore an important covariate for this analysis. Dow Jones Utility Average

Dow Jones Utility Average (DJUA) is a stock index that aims to represent the perfor-mance of large utility companies in the US by keeping track of 15 prominent firms. Adding DJUA to the model is believed to adjust the valuation according to the overall market conditions at the time of transaction.

4.2 Data Processing

The data set is processed in R which is a free software environment for statistical computing. It is widely used among statisticians for developing statistical software and analysis. It was chosen for this project as it implements a wide variety of statistical techniques for linear modeling.

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4.2.1 Initial model

A multi linear regression model was initially fitted with all regressors under consideration. The linear model is on the form

Y = β0+ β1X1+ β2X2... + β5X5+ The variables are presented in table 1 below.

Y Enterprise Value X1 Revenue

X2 EBITDA

X3 EBIT

X4 Earnings

X5 Dow Jones Utility Average Table 1: Variables for initial model

5 Results

5.1 Initial model

Estimate Std. Error t value Pr(>|t|) (Intercept) -3947.1311 1271.9292 -3.10 0.002141 Revenue -0.1090 0.0618 -1.76 0.079155 EBITDA 11.8079 0.9430 12.52 <2e-16 EBIT -7.2290 1.7189 -4.21 3.67e-05 Earnings 8.2292 1.8881 4.36 1.93e-05 DJUA close 8.8664 2.2482 3.94 0.000105

Table 2: Summary of initial model

R2 0.74 R2_adj. 0.7347 Table 3: Initial model

A brief summary of the initial model is presented in table 2. One can clearly see that all regressors except for revenue have a significant explanatory value of the enterprise value of a utility company. The R2 of the initial model was computed to 0.7519 meaning that these regressors can explain 75% of the variance of the response variable. Although these initial results are promising, a major flaw is the negative signs of the revenue- and

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EBIT-coefficients, which imply a reverse relationship between enterprise value and the two covariates. A common reason for a coefficient having the wrong sign is that the model suffers from multicollinearity which will be further analysed later in this section.

5.1.1 Analysis of initial model

Presented below is an analysis of the initial model in accordance with the theories pre-sented in section 3.

Fitted Values

Figure 1: Initial model - fitted values

As can be seen from the plot above, the model generates negative company valuation in several cases. A negative enterprise value is not necessarily a problem, and can be the case when the company has little debt and the market value is below the value of its cash equivalent. This happens especially in bear markets. As data was imported in descending order based on date, it can be seen that most negative valuations are on transactions be-tween 2009-2010 from the extracted data. This brings potential explanation, as the years following the financial crisis of 2008 were characterised by a bear market, but the relatively high number of negative valuations still poses a problem as it should be rather unusual for the market to value a company with low debt below its cash equivalents. Thus, this will be corrected in subsequent models.

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Figure 2: Initial model - Normal QQ plot

Shown in the Q-Q-plot above is a distribution with considerably lighter tails than a normal distribution. This poses a problem as an assumption of Ordinary Least Squares is for the standardized residuals to follow a normal distribution.

Multicollinearity

Ind. variable VIF Revenue 2.738671 EBITDA 6.812031 EBIT 10.516609 DJUA 1.108537 Region 1.097706 Table 4: VIF for independent variables

The general rule is that a VIF factor above 10 indicates multicollinearity. As can be seen, the model is not characterized by high multicollinearity, except for EBIT. This is perhaps rather surprising, as Revenue, EBITDA, and EBIT are derived from a unified and correlated financial statement.

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Figure 3: Initial model - Cook’s distance

The plot above shows the Cook’s distance for the extracted data points according to the description in 3.3.1. As can be seen, there are several outliers, but observation #46 stands out with a value above 30. Thus, there are several influential points which can skew the model and need to be dealt with.

After investigating each influential observation a common theme was that several of these observation had negative earnings and some even negative EBIT. Consequently, since the model acts similar to a multiple valuation the results of having negative metrics will have cause negative valuations on the companies. The issue was solved by limiting the data set to only include observations with positive margins. In effect, the model will only be applicable for companies meeting this criteria.

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Figure 4: Initial model - Residuals vs fitted values

As presented in under 3.1, one of the assumptions of Ordinary Least Squares is that the error term has constant variance. The plot above of the residuals vs fitted values shows that the said assumption probably is not the case. One can distinguish a fairly clear ”outwards cone”, which suggests the residual variance is linearly correlated with the magnitude of the fitted values. For the assumption to hold, this must be corrected in a subsequent model. 5.1.2 Improvement of initial model

As has been analysed, several improvements need to be made to the model, in part to fulfill the assumptions of OLS, and in part to provide a better performing model. Firstly, one need to adjust the model to fulfill the assumption of normally distributed residuals. This is done by performing a square root transformation of the dependent variable, which also hypothetically would stabilize the variance. Secondly, all data points with negative covariate values, most often EBIT, are removed as the model performs poorly in these instances and is heavily influenced by these points. Lastly, a no-intercept restrictions is imposed as it is assumed that a company with a value of zero for all covariates also will be valued at zero. This adjustment is viable as the intercept of the initial model is fairly close to zero. Furthermore, Region is removed from the model as it is deemed unrealistic to add a value to all US companies regardless of size. Lastly, the Dow Jones Utility Index is weighted in the model to provide a more dynamic and realistic affect of the macro environment on individual companies, rather than just a set mark-up or mark-down for all entities regardless of size.

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5.2 Second model

In the second model, a square root transformation was performed, zero-intercept restriction imposed, and reduction of data set to positive only covariates set. These adjustments were made in order to achieve greater normality among the standardized residuals, correct for negative enterprise values, stabilize the variance, and correct for heavily influential points. Furthermore, Region was removed from the model and the dependent variable divided by the absolute value of the DJUA index to provide a weighted affect on the companies.

Estimate Std. Error t value Pr(>|t|) Revenue -0.0012 0.0006 -1.97 0.050411 EBITDA 0.0799 0.0104 7.67 7.17e-13 EBIT -0.0637 0.0189 -3.38 0.000869 Earnings 0.0444 0.0115 3.87 0.000147 DJUA close 0.0487 0.0035 13.81 < 2e-16

R2 0.8942 R2_adj. 0.8916 Table 5: Second model 5.2.1 Analysis of second model

Fitted Values

Figure 5: Second model - Fitted values

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yield a better performing model for those companies with positive covariates. Normality

Figure 6: Second model - Normal QQ plot

The square root transformation of the dependent variable improved the fit of the residuals to the normal distribution curve significantly, which can be seen in the Q-Q plot above. This fulfills the OLS assumption and allows for further analysis of the model.

Multicollinearity

Ind. variable VIF Revenue 3.705776 EBITDA 39.154518 EBIT 46.589236 Earnings 6.182972 DJUA 1.305640

The adjustments in the model increased the VIF of EBITDA and EBIT significantly. This is not surprising, as they both are highly correlated and originate from the income statement of the company. Apart from inflating the estimates and variances, the presence of high multicollinearity also tends to cause the confidence interval for the regression estimates to become very wide and the statistics very small. Thus, it becomes difficult to reject the null hypothesis of any study where multicollinearity is present in the data under study. It can be seen in table 6 that the confidence interval of the EBIT coefficient estimate is indeed very wide. This multicollinearity and poor estimate is handled in the third model.

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2.5 % 97.5 % Revenue -8.942938e-05 1.011914e-05 EBITDA 2.358830e-03 4.129233e-03 EBIT -4.045037e-03 -8.408365e-04 Earnings 1.128717e-03 3.077828e-03

Table 6: Confidence intervals of the regression coefficients

Influential Points

Figure 7: Second model - Cook’s distance

It can be seen that the most influential points of the initial were those that provided a negative fitted value. When removed, there are still several influential points, but to a much lesser degree which can be seen as an improvement of the model. Variance

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Figure 8: Second model - Residuals vs fitted values

As can be seen from the plot above, the residuals follow a pattern that resembles that of a constant variance much more than the initial model. The square root transformation of the dependent variable thus succeeds to fulfill another assumption necessary for OLS. 5.2.2 Improvement of second model

The second model presented high multicollinearity in EBITDA and EBIT. In order to combat this, EBIT will be removed from the model with the hypothesis that it will not greatly affect R2_adj..

5.3 Third model

In the third and last model, EBIT was removed as covariate in order to reduce the multi-collinearity within the model.

Estimate Std. Error t value Pr(>|t|) Revenue -0.0001 0.0000 -2.02 0.04436 EBITDA 0.0021 0.0002 9.37 < 2e-16 Earnings 0.0015 0.0005 3.20 0.00157 DJUA close 0.0019 0.0002 12.38 < 2e-16

R2 0.8894 R2_adj. 0.8873 Table 7: Third model

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The third and final model include Revenue, EBITDA, Earnings and the closing price of the Dow Jones Utility Average Index on the day of the announcement of the transaction. The R2_adj. was reduced marginally when removing EBIT, and is still 0.8873 which is deemed fairly high in relation to the high variance of enterprise values in the data set. Furthermore, all independent variables contribute to the model with a significance level less than .05. Multicollinearity

Ind. variable VIF Revenue 3.616314 EBITDA 9.021762 Earnings 4.992659 DJUA 1.303615

As can be seen in the table above, removing EBIT from the model reduced the VIF of EBITDA to below the threshold of 10. This is not surprising, as EBITDA and EBIT both stem from the income statement of the entity with the difference being depreciation and amortization, and thus are highly correlated. With all VIF factors being less than the general threshold level of 10, the model is not considered to suffer from excessive multi-collinearity.

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5.3.1 Summary of the third model

Neither the distribution of the standardized residuals, the variance of the residuals, and fitted values are altered significantly with the third model. The Cook’s Distance increased somewhat for a number of observations, as the removal of EBIT might have caused some observations that drove the EBIT regressor to become more influential. Still, no value exceeds 1 and the model is thus not considered to contain highly influential outliers. In conclusion, the third model fulfills the assumptions of OLS as the standardized residuals follows the normal distribution curve with marginal errors, and presents what can be inferred as a constant residual variance. Furthermore, the fitted values provides a fairly realistic view of the span in which the observed entities might fall within Enterprise value.

6 Analysis

In order to test the predictability of the model, a new data set from Merger Markets was retrieved on which the model estimated the enterprise values of 25 different companies. The results are found in table 7. Noted is a fairly large deviance from the true enterprise values and the mean absolute error is roughly 36%.

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Target Company Enterprise Value (Millionse) EV-estimate (Millionse) ∆ |∆| Energy Transfer Partners, L.P. 51605.2082 86155.0887 67% 0.669503752 Williams Partners L.P. 46954.3028 36873.01802 -21% 0.214704174 MPLX LP 27782.8918 11786.98906 -58% 0.575746501 Spectra Energy Partners, LP 23758.6453 10704.8076 -55% 0.54943527 Spectra Energy Partners, LP 21812.6808 9253.555069 -58% 0.575771765 Calpine Corporation 14495.2486 15057.80474 4% 0.038809692 Andeavor Logistics LP 12564.9829 19715.49793 57% 0.56908275 Andeavor Logistics LP 11843.3546 19715.49793 66% 0.664688645 Western Midstream Operating, LP 10616.7703 14695.59193 38% 0.384186671 EnLink Midstream Partners LP 9111.0438 9709.571395 7% 0.065692538 Enbridge Energy Partners LP 8965.6369 15050.1884 68% 0.678652456 EQGP Holdings, LP 8383.238 8558.102358 2% 0.020858809 Energen Corporation 8009.5238 8872.949376 11% 0.107799864 RSP Permian, Inc. 7665.9708 7545.603234 -2% 0.015701542 Great Plains Energy Inc 7229.2192 11895.83314 65% 0.645521157 Antero Midstream Partners LP 6330.18 8918.37652 41% 0.408866181 WGL Holdings Inc. 6227.4827 7402.434725 19% 0.188672066 Cheniere Energy Partners LP Holdings, LLC 6184.5572 4745.941718 -23% 0.232614144 Antero Midstream Partners LP 6171.337 8918.37652 45% 0.445128749 Pattern Energy Group Inc. 5469.3804 4918.582976 -10% 0.100705635 Tallgrass Energy Partners, LP 4418.6613 5481.23412 24% 0.240473924 Dominion Energy Midstream Partners 4400.0974 5430.596152 23% 0.234199077 Peoples Natural Gas Company, LLC 3728.0893 4491.20503 20% 0.204693522 Anadarko Petroleum Corporation 3518.2264 5586.801701 59% 0.587959689 KLX Inc. 3471.1622 5813.267229 67% 0.674732235

Average 0.363768032

Table 8: Performance of final model

There has been extensive research of the accuracy of different valuations methods. Peter Harbula conducted a research for multiple valuation and evaluated the accuracy of different multiples and concluded that the EV/EBITDA-multiple shows the most consistent results. Within the energy sector, Harbula estimated the mean absolute error of the EV/EBITDA-mulitple at 21% [2]. Although it may be difficult to determine an absolute value for the accuracy of CCV as it is heavily dependent on the occasion, the number presented above may still be used as an indication of how well one would expect a CCV to perform. Addi-tionally, the more extensive approach, DCF analysis, have also been thoroughly analyzed. The use of a DCF analysis in valuation purposes provide even better accuracy. Shahed et al estimated the mean absolute error of an DCF valuation at 16.88%[3], by conduct-ing a comprehensive content analysis of equity research reports for most of the firms on the components list of the Dow Jones EuroStoxx 50 Index. Comparing the results of the regression model with the prior research of CCV and DCF, it is clear that the regression model in this case performs poorly in comparison.

Also noted from the results of the regression model is that it performs poorly among smaller firms as it has a large relative deviation from the true enterprise value. The simple reason for this lies within the fundamental assumptions of the regression model - That the error term has constant variance. Thus, the errors are of the same magnitude in absolute terms among the larger and smaller firms, which causes the relative deviation to be inflated among the smaller companies. In order to mitigate for this problem, a limited interval of the company size would have been appropriate. However, the limited data available for this project made just that unfeasible since it would cause more problems with the reliability of the model.

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Furthermore, the data consists of transactions from both the US and Europe. The reason for having data on two different markets was simply due to the fact that there was not enough data available for a single market. A problem arising with this is that the different market conditions in which the companies operate within will potentially have an effect on the valuation of the companies. A market characterized by stability and prosperity will probably have a positive effect on the value of the companies in that market. There are also different rules and regulations among different countries which will affect its actors differently. For example the corporate tax rate varies notably among countries which will have a direct affect on the companies financial. The regression model does not take these geographical factors into account, unlike the traditional CCV valuation where it is crucial to only compare companies which operate under the same market conditions.

The greater weaknesses from multiples valuation are inevitable inherited into the regression model. The underlying assumption of the model that two companies can be compared in an absolute manner is incorrect. Every company is unique and has its own competitive advantages and disadvantages. The fact that the regression model is a generalized model of an entire industry inflates this issue. Additionally, Marc Goedhart et al argues in ”The right role for multiples in valuation” to only use peers with similar prospects for ROIC and growth [5]. Finding the right companies is challenging and usually starts with an ex-tensive examination of the industry. Although being very time consuming it is important for the accuracy of the valuation. This critical component of valuing a company precisely with multiples is disregarded when creating a regression model across an entire industry, naturally this follows with poor performance of the model. Lastly, the data from which the model was based does not specify if it is a strategic- or a financial acquisition. This adds another level of discrepancy as strategic acquisition are often accepted at i higher premium due to the synergy benefits achieved.

7 Discussion

7.1 Data

As of writing this report, the market has experienced a tumble amid the Covid-19 crisis. Most companies have decreased in implied value by the market, and the situation is in many aspects unique. The data on the transactions was collected from the fiscal year of 2009 to end of march 2020. Thus, the data set incorporates many macro economic fluctu-ations, but might fail to encompass the wide uncertainty and new reality that individuals and companies face in in the midst and post Covid-19. Subsequently, the results may be skewed and the model not perform as well as hopes in the near future. However, it should adapt somewhat as the the DJUA covariate reflects the current general market sentiment, and thus adjusts the value accordingly even for companies that manage to endure this crisis

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with a relatively intact income statement.

When deciding to extract data from a longer time period, the risk of developing a model that could not perform due to the highly changing global environment during that time was discussed. On the other hand, it was observed that the greater number in data points that the longer period provided lead to a more precise model with lower significance level for all covariates. The larger sample size allowed for better estimations in the regression model, and thus the longer time frame was with the inclusion of the Dow Jones Utility Average index as a covariate in order to identify the current general utility market sen-timent. This should theoretically mean that the model is not static but rather dynamic, and thus provide useful results not only during the given time period but afterwards as well. In the initial model, the standardized residuals did not follow a normal distribution. In order to solve for this, two solutions were proposed: gather a larger samples size or trans-form the dependent variable. The first was not possible, as only 173 transactions disclosed the full financial information needed for the model. Thus, a square root transformation was made which also solved for the constant variance of the residuals.

7.2 Covariates

The final model included the covariates Revenue, EBITDA, Earnings, and Dow Jones Util-ity Average index. All covariates except for DJUA are derived from the income statement, which implies that there is large correlation between the covariates as they are derived from each other. However, the most important tools in order to value a company are the financial statements, from which one can calculate the firms cash flow and project future cash flows from which the fundamental value of a company is derived. Thus, the covariates from the income statement are very important in order to determine the entity’s enterprise value, and indeed belong in the model.

EBIT was removed from the model as it drove the multicollinearity to unacceptable lev-els which would make the results unreliable and skewed. When removed, the model lost very little in R2_adj. which was expected as EBIT and EBITDA contain mostly the same information. Region was removed as a dummy variable as it was deemed unrealistic that a company, regardless of size, would have a set premium added if it originated from a specific continent. It is not the value-add per se that was a problem, but that the same addition was made on all companies, which especially would make the model overvalue certain smaller companies greatly.

Lastly, it would have been very interesting to include more covariates in the model such as Total Assets and Leverage. Unfortunately, it was not possible to gain that kind of data efficiently enough through given sources, and it was ruled out. However, if future revision

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of the model is made, Total Assets and Leverage in particular would two very interest-ing variables to investigate. Utility companies often have large material assets on their books and the stable cash flows allow for high leverage. Thus, including these variables as covariates can hypothetically make the model better performing.

7.3 Methodology

The resulting regression model and its performance is a direct determinant of the method-ology used to achieve it. In this project, a set of hypothetical covariates was determined beforehand and data gathered from Merger Market to form an initial model. Subsequently, updated versions of the model were iterated, were covariates were removed based on VIF-tests and assumptions fulfilled through transformations on the dependent variable. The iterative process might have yielded a slightly different model if exclusion tests such as BIC or AIC were applied, but it was deemed enough to recognize a high VIF value and con-clude that the R2_adj.was left practically unchanged when, for example, EBIT was removed. Thus, EBIT contributed little to the model but drove multicollinearity as it was heavily correlated with EBITDA.

It became evident that the initial set of covariates were not enough, and that data on for example total assets and leverage would hypothetically have provided a better model with more explanatory value and nuance. The final model in this thesis was very similar to a simple comparative company analysis, and a larger set of covariates may have allowed for performance that would capture some of the aspects of a valuation that CCV misses. However, there is always a trade off between having many covariates and thus a large ex-planatory value with the risk of suffering from large multicollinearity.

Lastly, a shortcoming is the wide range of companies that was used in this model. The util-ities sector is very varied with many distinct sub-sectors with completely different business models and thus foundations for valuation. A solar panel producer with private consumers as clientele might depend heavily on a strong brand entity and marketing, while an old oil refinery instead create value through supply chain efficiency and client relationships. Furthermore, there was no limit of company size when extracting data, which proved to limit the result of the model as the deviation from the true enterprise value was very large relatively for small companies while small for larger companies. The model might have been more effective if the scope of companies in relation to size was more limited, which would have reduced the relative deviation even if the total squared residual was the same. However, a specialization in a specific sub-segment of the utilities sector as well as the size of the companies would have reduced the amount of data available and made the model less statistically significant.

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7.4 Practical usage

The purpose and aim of this thesis was to evaluate if a regression model could provide a valuation method that outperformed CCV and furthermore to be used by professionals in the financial industry. In particularly the investment banking industry, which involves in investing and advisory on transactions, such a model could be of great use.

It is important to remember that valuing a company is more than a strict science, and requires vast experience to be done efficiently. Included in the valuation methodology is much more than information on the income statement and the current macroeconomic envi-ronment, which this model tries to encompass. An interview with an unnamed investment banker at Morgan Stanley confirms this and states that oftentimes the most difficult part of a valuation is valuing a company’s intangibles such as a strong brand identity, in-house technology systems, loyal clientele, a thriving company culture etc. These are highly rele-vant factors for an entity’s future success and thus its value, but is hard to account for in a mathematical model such as the regression model this thesis proposes and CCV. In prac-tice, if a company is identified to have a higher value than what is captured in a model based on the financial statement, a premium is applied which might stem from raw valuation of the intangibles, but most often by comparing it to the highest performers of the peer group. The interviewee noted that the regression model might be more suitable for industries not characterized by high intangibles, and that this makes the utilities sector especially interesting. Companies withing the utilities sector are not as dependent on brand entity and other intangible asset such as for example the technology and media industry. The sector in general is characterized by high tangible assets and low intangible assets, which might make it well suited for a regression model. However, an old and very large oil and gas refinery differ greatly from a startup reinventing hydroelectric power generation but still in the RD state. Thus, the industry provides a wide spectrum of different business models, why the regression model might fail to perform consistently on its own without individual tampering on a stand-alone basis.

Furthermore, a big part of the investment banker’s job is to present the valuation and its foundation in an explainable manner for the client. The most positive aspect of CCV is its simplicity to explain to any company executive regardless of experience and education. A regression model might, as the interviewee put it, ”fly above the clients head”, which can potentially be a deal breaker. If the regression model is just marginally better than CCV, the latter might still be chosen because of its simplicity and the fact that the implied valuation often is presented in a range. However, it was noted that professionals might use the regression model internally where a greater complexity is accepted and will provide a sanity-check for other valuation methods.

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7.5 Further research

The regression model that was developed in this thesis can be used as a complementary valuation tool, if analysed by individuals with proper knowledge about regression analysis and statistics. However, if it were to be applied as a primary valuation tool, further re-search is required to investigate if the model could be improved and yield better results. Firstly, more covariates may be included in the model to increase its explanatory value. In order to limit the multicollinearity when introducing new covariates, one should avoid additional variables stemming from the income statement and focus on other endogenous variables. As brought up earlier in the discussion, the balance sheet can provide interesting variables such as total assets and leverage, but other covariates such as the crude oil price per barrel or the Household Energy Price Index may also be of value in the utilities sector. Furthermore, a larger sample size would perhaps be the most effective way of yielding bet-ter results. However, this would require a larger database, perhaps by merging data from Merger Markets, Pitchbook, and Orbis.

Another interesting point of further research is if the model performs better in specific sub-sections of an industry with a limit on company size. This restriction would make the sample size of the companies more similar to a peer group in CCV and thus reduce the application width of the model, but perhaps the credibility and precision of its results. One example would be to create a model specifically for oil and gas companies with an enter-prise value between 1 and 5 billion EUR. This would hypothetically increase the models precision as the companies should engage in more comparable value driven activities, but will reduce the sample size which may pose some issues regarding statistical significance. The interview with an investment banking professional concluded that the model may not be very useful in her daily tasks, as it proved hard to account for intangible assets on a company-specific basis but most importantly fails to be simple enough for clients to under-stand. However, the model may be of great use for in-house corporate finance departments or institutional investors such as hedge funds, mutual funds, endowments or private equity firms.

In this thesis, the regression model’s average deviation from the true enterprise value was compared to CCV, specifically with the EBITDA multiple as it is deemed the most reliable in the utilities sector. An interesting continuation of the research would be to compare the model to valuations through DCF and precedent transactions. These are heavily used valuation techniques and are thus relevant to include if one were to investigate the relative precision and feasibility of a regression model. However, DCF is generally a highly time consuming task and relies on a variety of assumptions regarding cost of capital and future cash flow. This would make the process very inefficient and dependent on these

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assump-tions.

Lastly, an interesting aspect to further study is the application of a regression model as a valuation tool in other industries. It was previously touched upon that the model would perform optimally in industries characterized by low intangible assets. The utilities falls into this category [6], with a low average net PPE (percentage of physical assets owned as compared to total assets known). Other interesting industries with the same charac-teristics include minerals, transportation, and industrial services. It might be of value to explore the models performance in such industries, but also in sectors with the opposite characteristics regarding intangible assets. Building a regression model in industries such as health technology, consumer durables, and commercial services might not provide a usable valuation tool, but serve as a great indicator of the importance of incorporating intangible assets in company valuations.

8 Conclusion

The research and analysis performed in this thesis does not confirm that regression analysis provides a more accurate valuation tool than comparable companies valuation. The final model generated a fairly high explanatory value of R_adj2 = 0.89 in general, but the relative deviation proved to be very large for smaller companies. However, the model performed quite well for larger companies and identified Revenue, EBITDA, Earnings as key drivers to company value, as well as the current market sentiment represented here as the Dow Jones Utility Average.

As mentioned, the model tend to underperform compared to CCV in specifically smaller companies, but yields a higher accuracy for larger companies. This provides an interesting base for further research with a more narrow spectrum of companies in regards of size. Furthermore, one may include more covariates such as total assets and leverage in further studies, the utilities industry generally is characterized by large material assets and stable cash flows which allows for a very leveraged capital structure.

The main drawback for using regression model in the investment banking industry is its complexity and difficulty to explain to a client without the relevant educational background. An important part of the investment banker’s task is to sell its advisory services during a merger or acquisition to such clients, which often is easier when pitching a company value that can be explained and easily motivated. Thus, regression analysis may not be suited for such tasks, but can serve as a sanity-check for internal use and as a primary valuation tool in buy-side firms not relying as heavily on client sales.

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valuation methods such as CCV, but may provide an efficient complementary tool for in-ternal use. Thus, firms will be able to triangle a value that may more accurately portray the true enterprise value of a firm.

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References

[1] Jonathan B. Berk and Peter DeMarzo. Corporate finance. Pearson, 2020.

[2] P´eter Harbula. “Valuation Multiples: Accuracy and Drivers Evidence from the Eu-ropean Stock Market”. In: Business Valuation Review 28.4 (2009), pp. 186–200. doi: 10.5791/0882-2875-28.4.186.

[3] Shahed Imam, Jacky Chan, and Syed Zulfiqar Ali Shah. “Equity valuation models and target price accuracy in Europe: Evidence from equity reports”. In: International Review of Financial Analysis 28 (2013), pp. 9–19. doi: 10.1016/j.irfa.2013.02. 008.

[4] Mimi James and Zane Williams. Not enough comps for valuation? Try statistical modeling. Aug. 2012. url: https://www.mckinsey.com/business- functions/ strategy and corporate finance / our insights / not enough comps for -valuation-try-statistical-modeling.

[5] Koller et al. The Right Role for Multiples in Valuation. Sept. 2005. url: https : //papers.ssrn.com/sol3/papers.cfm?abstract_id=805166.

[6] Barry Libert, Megan Beck, and Yoram. Investors Today Prefer Companies with Fewer Physical Assets. Oct. 2017. url: https://hbr.org/2016/09/investors-today-prefer-companies-with-fewer-physical-assets.

[7] Jing Liu, Doron Nissim, and Jacob Thomas. “Equity Valuation Using Multiples”. In: Journal of Accounting Research 40.1 (2002), pp. 135–172. doi: 10.1111/1475-679x.00042.

[8] Douglas C. Montgomery, Elizabeth A. Peck, and G. Geoffrey Vining. Introduction to linear regression analysis. Wiley-Blackwell, 2013.

[9] PricewaterhouseCoopers. North American power and utilities deals insights Year-end 2019. url: https://www.pwc.com/us/en/industries/power- utilities/ library/quarterly-deals-insights.html.

[10] Joshua Rosenbaum and Joshua Pearl. Investment Banking. Wiley, 2018.

[11] Strategic vs. Financial Buyers: Maximizing MA Transaction Value. Oct. 2019. url: https://investmentbank.com/strategic-vs-financial-buyers/.

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9 Appendix

9.1 Collected data

Announced Date Currency Enterprise Value Revenue EBITDA EBIT Earnings Region DJUA close 1 2020-04-02 EUR 3252.29 3820.09 348.98 165.49 45.98 Europe 729.36 2 2020-04-02 EUR 3143.54 3820.09 348.98 165.49 45.98 Europe 729.36 3 2020-03-05 EUR 3674.29 2321.80 673.30 403.50 302.40 Europe 908.14 4 2020-01-16 EUR 41120.86 35434.00 2267.00 794.00 -42.00 Europe 900.42 5 2019-12-23 EUR 964.59 127.05 24.77 -5.36 -18.09 USA 870.15 6 2019-11-25 EUR 4383.00 4100.00 415.00 162.00 121.00 Europe 848.88 7 2019-10-08 EUR 12808.18 78176.00 1371.00 -161.00 -452.00 Europe 868.17 8 2019-09-26 EUR 637.05 65.75 2.13 -4.58 -13.12 USA 879.11 9 2019-06-03 EUR 3794.58 788.42 234.37 150.27 73.57 USA 791.77 10 2019-05-10 EUR 9070.16 3584.57 598.95 363.87 -51.51 USA 777.46 11 2019-04-02 EUR 5548.58 2435.70 472.04 311.77 164.38 USA 775.44 12 2019-03-29 EUR 8471.54 731.25 409.96 281.98 167.51 USA 778.72 13 2018-10-23 EUR 3728.09 670.91 229.14 164.38 49.08 USA 737.04 14 2018-10-11 EUR 42.32 9.03 1.83 1.18 0.69 Europe 723.37 15 2018-09-18 EUR 8965.64 2023.33 1240.83 872.50 166.67 USA 738.39 16 2018-09-03 EUR 564.98 42.72 28.02 21.24 5.87 Europe 726.41 17 2018-08-24 EUR 23758.65 1625.00 757.50 469.17 200.00 USA 731.08 18 2018-08-14 EUR 8009.52 800.87 523.76 120.95 255.69 USA 725.68 19 2018-06-19 EUR 84.31 25.06 8.17 5.87 5.19 Europe 687.96 20 2018-06-01 EUR 34.41 6.41 0.76 0.52 0.65 Europe 684.74 21 2018-05-17 EUR 46954.30 6675.00 2277.50 860.83 725.83 USA 668.56 22 2018-04-23 EUR 6609.83 2214.42 495.50 265.33 180.00 USA 691.34 23 2018-04-18 EUR 2607.41 1966.28 142.70 102.06 51.88 Europe 697.82 24 2018-04-04 EUR 3000.00 231.80 162.20 80.50 49.70 Europe 690.65 25 2018-03-17 EUR 2564.95 1035.21 241.23 148.80 92.13 Europe 691.82 26 2018-03-15 EUR 895.50 89.21 43.07 28.52 20.88 USA 684.23 27 2018-03-12 EUR 36520.31 43139.00 4331.00 2816.00 778.00 Europe 675.34 28 2018-03-07 EUR 43.95 2.52 2.02 1.65 1.25 Europe 664.80 29 2018-02-22 EUR 34247.10 23306.00 3760.00 2112.00 1237.00 Europe 668.20 30 2018-02-08 EUR 636.76 42.96 75.17 75.17 72.31 USA 647.90 31 2018-01-22 EUR 21812.68 1625.00 757.50 469.17 200.00 USA 684.86 32 2018-01-03 EUR 11844.14 3672.50 381.67 63.33 -99.17 USA 706.52 33 2017-12-20 EUR 46.40 41.22 9.01 5.27 5.21 Europe 728.98 34 2017-12-19 EUR 15.99 0.15 -1.88 -1.97 -1.93 Europe 733.84 35 2017-12-18 EUR 3056.58 10136.25 -21.26 -137.55 -227.62 Europe 745.84 36 2017-12-18 EUR 3056.58 10136.25 -21.26 -137.55 -227.62 USA 745.84 37 2017-12-15 EUR 11050.82 1575.29 785.13 418.28 -15.67 Europe 753.38 38 2017-12-13 EUR 3971.18 315.32 168.44 84.80 -15.37 Europe 750.50 39 2017-12-11 EUR 321.26 81.28 9.40 1.75 0.93 USA 762.59 40 2017-11-22 EUR 43.99 12.65 4.22 2.31 1.67 Europe 757.73 41 2017-11-08 EUR 810.45 1715.77 85.60 31.01 -4.18 USA 759.59 42 2017-11-01 EUR 537.52 520.81 62.03 -39.48 -90.12 USA 748.95 43 2017-10-23 EUR 431.42 230.33 179.98 141.24 -24.21 Europe 749.55 44 2017-10-13 EUR 263.00 373.44 20.23 11.33 6.67 Europe 737.25 45 2017-10-05 EUR 111.77 201.61 12.84 8.91 6.31 Europe 731.62 46 2017-09-26 EUR 9688.12 67788.00 2122.00 -3963.00 -3217.00 Europe 731.67 47 2017-08-31 EUR 58.91 28.71 3.67 1.83 1.29 USA 743.24 48 2017-08-18 EUR 14495.25 6589.79 1424.64 796.32 87.32 USA 738.38 49 2017-07-25 EUR 134.61 35.00 6.54 3.61 1.73 Europe 715.86 50 2017-07-21 EUR 82.89 177.09 11.82 5.13 3.53 Europe 725.48 51 2017-07-10 EUR 7229.22 2539.86 1013.48 587.41 259.59 USA 701.43 52 2017-05-02 EUR 1902.07 360.84 157.22 90.94 36.12 Europe 701.68 53 2017-04-28 EUR 11.68 16.43 1.17 0.79 0.51 Europe 704.35 54 2017-02-21 EUR 245.03 57.70 16.06 10.29 4.97 USA 679.80 55 2017-02-08 EUR 1467.99 269.25 150.39 93.89 58.36 Europe 669.99 56 2017-02-01 EUR 21634.76 8464.75 1617.97 1249.17 1012.50 USA 656.08 57 2017-01-25 EUR 6227.48 2095.80 386.14 267.86 150.21 USA 655.38 58 2017-01-10 EUR 49610.24 7109.91 2863.52 1231.02 409.07 USA 651.14 59 2017-01-09 EUR 50812.53 7109.91 2863.52 1231.02 409.07 USA 653.19 60 2016-12-30 EUR 31.13 55.52 4.00 3.09 1.90 Europe 659.61

Valuing firms within the utilities sector using regression analysis:

Valuing firms within the utilities

sector using regression analysis:

An empirical study of the US and European

market

LUDVIG HARTING

NILS ÅKESSON

Valuing firms within the utilities

sector using regression analysis:

An empirical study of the US and

European market

Ludvig Harting

Nils Åkesson

Contents

1

Introduction

2

Financial & Economical Theory

3

Mathematical background

4

Methods

5

Results

6

Analysis

7

Discussion

8

Conclusion

References

9

Appendix