WACC for Electric Power Transmission System Operators: The Case of Colombia

Abstract

In emerging countries, energy service users generally pay high rates of return to transmission system operators (TSOs). One of the causes of this situation is the application of the CAPM with the comparable beta method when estimating the cost of equity in the WACC. The purpose of this article is to present a new methodology for calculating the cost of equity of TSOs in Colombia. To achieve this objective, a multifactor model has been built to explain the variation in returns on the electric utilities portfolio in Colombia between April 2008 and March 2022 and then recalculate the WACC approved by the country’s regulatory commission. It was found that, in addition to the estimated market risk in the CAPM, there is a risk due to the regulatory framework and changes in interest rates, which helps to explain 73% of the variations in the electric utilities portfolio, resulting in a lower cost of equity, and therefore a lower WACC of 5.28% compared to the WACC estimated by the regulator of 11.79% in 2019. These results can support regulatory commissions in emerging countries in establishing a more accurate rate of return for users.

1. Introduction

The electric power supply chain is essentially composed of generation, transmission, distribution, and commercialization activities. In order to remunerate the investments made by energy transmission system operators (TSOs), each country’s regulatory commissions must guarantee investment recovery and return on investment. Return on investment is calculated by multiplying the regulatory asset base (RAB) by the discount rate, which is fundamental for the valuation of investments in the energy sector because it represents the minimum expected rate of return on an investment with a specified risk [1]. To determine the discount rate, many commissions around the world use the weighted average cost of capital (WACC) methodology, which seeks to recognize both the cost of financing and the cost of equity for RAB investments. According to each country’s regulator and conditions, the WACC can be used in its basic form (plain vanilla), where the effect of taxes is not taken into account, as in the case of England; it can also be used before taxes (pre-tax), as in the case of Colombia, or after taxes (post-tax), as in the case of Brazil. Additionally, the WACC can be expressed in nominal or real terms, where the effect of inflation is discounted.

Table 1. Real pre-tax WACC for TSOs in 2019.

Country	Regulator	Real Pre-Tax WACC
Colombia	CREG	11.79%
Albania *	ERE	2.40%
Austria *	E-Control	2.70%
Hungary *	MEKH	4.70%
North Macedonia *	-ERC	5.20%
Poland *	URE	3.00%
Turkey *	EMRA	13.30%
Kosovo *	ERO	8.30%
Nigeria *	NERC	11.00%
Oman *	APSR	5.10%
Italy	ARERA	6.30%
Netherlands	ACM	4.30%
Sweden	Ei	5.85%

Note: The WACC for Colombia was taken from the 2018 CREG-011 Document [3]; the WACC for countries marked with an asterisk (*) was taken from the ERRA organization [4]; the WACC for Italy was taken from the study conducted by The Australian Energy Regulator [5]; and the WACC for the Netherlands and Sweden was taken from the CEER organization [6].

shows some countries where regulators have adopted the real pre-tax WACC methodology to calculate the discount rate of TSOs, taking 2019 rates into account. We have chosen this year in particular because we found comparable information that exemplifies the problem. Table 1 shows that in Colombia and other emerging countries that use the real pre-tax WACC methodology, the discount rates are very high compared to the discount rates of developed countries. As Dobbs [2] mentions, very high discount rates can lead to financial inefficiency and increased user fees. However, very low discount rates discourage investment, which has negative effects on service quality, which is why the discount rate calculation should be as accurate as possible.

One of the causes for these high rates in emerging countries is the recursive WACC application in countries with underdeveloped stock markets, such as Colombia. The general WACC methodology applied in Colombia can be found in CREG Resolution 95 of 2015 [7], while the detail on the variables and how they are calculated can be seen in CREG Document 011 of 2018 [3]. Equation (1) shows how to calculate the pre-tax WACC, and Equation (2) shows how to calculate the real pre-tax WACC:

$$WAC{C}_{cop,t}=W_d\ast R{d}_{cop,t}+\frac{W_e\ast R{e}_{cop,t}}{\left(1-Tx\right)}$$

(1)

$$real WAC{C}_{cop,t}=\frac{WAC{C}_{cop,t}-{\Pi }_{cop}}{\left(1+{\Pi }_{cop}\right)}$$

(2)

where $WAC{C}_{cop,t}$ is the nominal weighted average cost of capital in Colombian pesos (cop) before taxes for transmission and distribution activities; $W_d$ is the weighted cost of debt, equal to 40%; $W_e$ is the weighted cost of equity and is equal to 60%; $R{d}_{cop,t}$ is the cost of debt in pesos at time t and is equal to 9.62%; $R{e}_{cop,t}$ is the cost of equity in cop, equal to the cost of equity in dollars at time t (the value estimated by CREG was 12.83%); and $Tx$ is the tax rate in force in Colombia on the calculation date, which is 33% for the purposes of this article and traceability of the provisions of CREG Document 011 of 2018 [3]. The resulting $WAC{C}_{cop,t}$ in nominal pesos is 15.33%. However, as the applicable value in Colombia is determined in real pesos, an adjustment is made with the inflation expectation ${\Pi }_{cop}$ determined at 3.17%, leading to a $real WAC{C}_{cop,t}$ of 11.79% using Equation (2).

The weighted cost of debt and cost of equity used by CREG are very close to those used by most regulators, who generally assign a higher weight to the cost of equity. The cost of debt is calculated as the weighted average of commercial loan placement rates; therefore, the value assigned to the cost of debt is readily observable in the market and does not need to be discussed. On the contrary, the cost of equity cannot be observed in the market and is estimated based on the CAPM model, which has been widely discussed for its assumptions and the way it is applied to the calculation of regulated tariffs in emerging Latin American countries, since regulators do not use local variables, but rather U.S. market variables, which results in a less accurate measurement of the cost of capital since the market risk measured by the CAPM is different for each country and industry [8] and depends on the market index taken as a reference.

Based on the above, the objective of this article is to present the estimation of the cost of equity for TSOs in Colombia according to firms’ returns and the country’s local variables, defining an accurate discount rate that balances final user and TSO interests. To achieve this objective, we estimate the cost of equity through the CAPM and our proposed four-factor model, TD-4. As a target variable in both models, we use the returns of companies in the Colombian stock exchange (BVC) that operate as TSOs, and as determinants of these returns, we use the COLCAP index and Colombian economic variables. Finally, we sensitized the WACC calculation by changing the cost of equity value calculated by CREG with the values found through the two evaluated models.

For this analysis, in Section 2 of this article, we explain how the cost of equity is currently estimated in Colombia and why it should be changed. In Section 3, we present a state-of-the-art of asset pricing model and then present the models proposed for the cost of equity estimation. In Section 4, we present the proposed methods, and in Section 5, we show the results of the models used to estimate the cost of equity and its effect on the WACC calculation.

2. Cost of Equity for TSOs in Colombia

Like most regulators in the world, CREG uses the CAPM model to estimate the cost of equity by adding a variable called country risk, as shown in Equation (3):

$$R{e}_{usd,t}=R_{f,t}+{\beta }_{Rm,t}{R}_{m,t}+R_{p,t}$$

(3)

where $R_{f,t}$ is the average risk-free rate at time t, estimated as the average 10-year U.S. bond yield rate; $R_{m,t}$ is the leveraged beta at time t; ${\beta }_{Rm,t}$ is the average market premium at time t and corresponds to the arithmetic average of the premium between the Standard and Poor’s 500 (S&P 500) index yield and the 10-year U.S. bond yield; and $R_{p,t}$ is the average country risk premium at time t and is determined as the difference between the average of the Colombian 10-year CDS and the average of the U.S. 10-year CDS.

To find the beta value of Equation (3), CREG uses the comparable beta method where CREG search for a set of U.S.-listed TSOs and calculates their covariance with the S&P 500. The resulting beta is then deleveraged based on Hamada’s equation [9] and then leveraged again with Colombia’s financial structure. After finding the beta and multiplying it by the market premium, the average of the so-called country risk premium is added as a constant, which causes the rate to increase. Finally, to find an equivalent rate in Colombian pesos, CREG uses the Fisher equation. As shown, this procedure ignores the risk-return relationship of the TSOs listed in the Colombian Stock Exchange (BVC). This is because, for a long time, it has been assumed that there are few instruments and little information available in the Colombian market, which has led to the implementation of alternative procedures for calculating the cost of equity. However, to date, we have information from the last 14 years of the COLCAP index, which is the most representative index in Colombia, as well as information on electric utilities representative of Colombia and other macroeconomic variables that allow other cost of equity estimation models to be explored, which would produce alternative WACC calculations. The use of electric power infrastructure firms and local variables for the cost of equity estimation has recently been incorporated in emerging market papers [10,11,12], where the need to find a new calculation methodology was also identified.

3. Literature Review and the Four-Factor Model

Despite advances in asset pricing models, regulators continue to use traditional models such as the CAPM to estimate the cost of equity [13]. This model assumes that the idiosyncratic risks of an industry can be canceled out by efficient diversification, meaning only the market risk exists, which is common to all investments and cannot be diversified [14,15,16]. This model has received two relevant criticisms in the financial literature. The first criticism is that of Roll [17], who argued that it is not possible to efficiently measure market risk because there is no instrument that includes all investment classes. The second criticism is this model’s poor empirical results [18]. The CAPM model has also been questioned for remunerating investments in electric power systems since the market risk factor is reduced because these investments are used to provide an essential service, where there is a natural monopoly and regulations that protect these investments to varying degrees in the face of changes in market price. This can be summarized as follows: for electric power infrastructure operators, market risk is low and individual risks are high [19,20,21], which is contrary to the fundamental assumptions of the CAPM.

A different approach is presented by Chen et al. [22], stating that investment returns can be explained by macroeconomic factor movement, as mentioned by Franc-Dabrowska et al. [8]. A similar approach is popularized by Fama and French [23,24,25,26], who have shown that investment returns can be explained by multiple factors or characteristics. The most relevant criticism of these multifactor approaches is the difficulty in recognizing the risk factors that impact a given investment. For example, Harvey et al. [27] found that at least 316 determinants had been identified in the financial literature, which is why this approach has been referred to as the “zoo of factors” [28]. However, despite the difficulty in finding the determinant risk factors of an industry, in our literature review for the utilities industry (including TSOs), we found that in different articles published in the last 25 years [29,30,31,32,33], interest rates have been identified as a determinant risk factor for explaining utility returns, since they are seen as a conservative investment that competes with fixed income instruments—when interest rates on these instruments increase, utility returns are negatively impacted. Thus, in addition to the market risk premium, we determined two macroeconomic factors that involve interest rates to explain the returns on Colombia’s electric utilities. The first is called INT and corresponds to the risk premium between the rates of the 360-day and 90-day fixed-term certificates of deposit (CDTs) in Colombia. The second, called DEF, corresponds to the spread between the interest rates of Colombian government treasury securities (TES) and U.S. Treasury bonds.

The other risk factor for the public utilities industry that we identified in the literature is regulatory risk, which has been discussed theoretically and empirically in different studies [34,35,36,37]. Since public utilities, including electric utilities, are natural monopolies, they are subject to different regulatory schemes such as cost-plus pricing, price cap, or revenue cap regulations that introduce different levels of risk in these companies’ performance. In cost-plus pricing regulation, there are few associated risks since all the firms’ operating costs are remunerated. In the revenue cap regulation, there is an approved revenue cap for operators that encourages them to be more cost-efficient to increase their profit margins. One aspect to take into account in this scheme is that, since there is a guaranteed revenue cap, network operators do not depend on increases in service demand, i.e., there is no demand risk. This is contrary to the price cap scheme, where the price for the service has a limit that cannot be exceeded. Therefore, the profit margins of firms under the revenue cap scheme depend on operating cost efficiency and service demand, i.e., there is a demand risk. Accordingly, a risk factor we propose is the risk premium between revenue cap and price cap regulation schemes.

According to this literature review, we propose estimating the cost of equity with the traditional CAPM [14,15,16] using local variables for the Colombian market (local CAPM), shown in Equation (4), as well as with a new proposed model with four risk factors (TD-4), shown in Equation (5):

$$R_{cop,t}-R_{F,t}=\alpha +{\beta }_{Rm}{R}_{m,t}+e_t$$

(4)

$$R_{cop,t}-R_{F,t}=\alpha +{\beta }_{Rm}{R}_{m,t}+{\beta }_{REG}RE{G}_t+{\beta }_{Int}IN{T}_t+{\beta }_{DEF}DE{F}_t+e_t$$

(5)

where $R_{cop,t}$ is the monthly return on the Colombian electric utilities portfolio at time t used to estimate the cost of equity; $R_{F,t}$ is the risk-free rate estimated as the monthly equivalent rate of the zero coupon rate of Colombian TES in pesos for a term of 1 year at time t; $R_{m,t}$ is the Colombian market risk premium at time t and is calculated as the premium between the yield of the Colombian Stock Exchange’s (BVC) COLCAP index and the risk-free rate; $RE{G}_t$ is the risk premium per regulation scheme estimated as the return of a regulated electric utilities portfolio under the price cap scheme and another regulated electric utilities portfolio under the revenue cap scheme; $IN{T}_t$ is the interest rate risk at time t and is calculated as the spread between the interest rate of the 360-day and 90-day fixed-term certificates of deposit (CDTs); $DE{F}_t$ is the default risk estimated as the spread between Colombian TES rates and U.S. Treasury bond rates at time t and is represented by the Emerging Markets Bond Indicator (EMBIG) for Colombia. The beta coefficients ${\beta }_{Rm}, {\beta }_{Reg}, {\beta }_{Int}, {\beta }_{Def}$ represent the sensitivity of the returns on the Colombian electric utilities portfolio to risk factors. The coefficient α is the regression intercept expected to be zero, and $e_t$ represents the residuals of the model at time t. The hypotheses proposed with this model are:

Hypothesis 1 (H1). 

There is a significant positive relationship between the Colombian market risk premium and the returns on the electric utilities portfolio in Colombia.

Rationale. Only the market risk premium is relevant when explaining the returns on financial assets since the other risks can be diversified. Therefore, asset movements are a function of market risk [14,15,38].

Hypothesis 2 (H2). 

There is a significant negative relationship between the regulatory risk premium and the returns on the electric utilities portfolio in Colombia.

Rationale. The returns of public utility firms regulated under a revenue cap scheme are lower than those of firms regulated under a price cap scheme because they are not exposed to the risk of service user demand [35,37].

Hypothesis 3 (H3). 

There is a significant negative relationship between the interest rate spread of 90-day and 360-day CDTs and the returns on the electric utilities portfolio in Colombia.

Rationale. Investments in electric utilities are considered conservative by investors and therefore compete with other low-risk investments, such as fixed-income instruments. Therefore, when interest rates on these fixed-income instruments increase, investors’ investment preferences change, and electric utilities’ returns are negatively impacted [29,30,32].

Hypothesis 4 (H4). 

There is a statistically significant positive relationship between the spread of Colombian TES and U.S. Treasury bond rates represented by the EMBIG and the returns on the electric utilities portfolio in Colombia.

Rationale. An increase in the EMBIG represents a higher risk of default in emerging countries due to economic and political factors [39,40]. This risk is offset by higher investment returns.

4. Methods

To validate the two proposed models with the hypotheses associated with their risk factors, a time series regression was run for both the local CAPM model and the TD-4 model. The t-statistic was used to determine whether the coefficients of the risk factors were statistically significant, and the directionality of the dependence of the electric utilities’ portfolio returns on the risk factors was validated through the sign obtained from the regression coefficients. We evaluated the overall performance of the models with the R-squared statistic (R²) and the root-mean-square error (RMSE) within the sample. Finally, with the values found for the coefficients, we estimated the cost of equity capital with each model to then calculate the actual pre-tax WACC and compare it with the value established in CREG Document 011 of 2018 [3].

4.1. Data for Risk Factors and Cost of Equity

To calculate the risk factor betas of the local CAPM and TD-4 models, a time series regression was performed using the ordinary least squares (OLS) method with Newey and West’s adjustment [41] to overcome heteroscedasticity and correlation issues. Monthly data were used for each of the variables. A 14-year estimation window was used from April 2008 to March 2022 for a total of 168 monthly observations. CREG uses a 5-year window to calculate the market beta for U.S. companies. Kayo et al. [11] found that the stability of the market beta is obtained with an 11-year window using local companies. We used a 14-year window because the COLCAP index was constituted in 2008, enabling a market premium estimation for Colombia with all available data. Free databases were used to construct all the variables so that any person or entity could construct and debate the results of this study and have access to and become involved in its discussion.

4.2. Portfolio of Colombian Electric Utilities and Risk Factors

4.2.1. Portfolio of Colombian Electric Utilities $\left(R_{cop}\right)$

The Colombian electric utilities portfolio was constructed using returns on the shares of firms operating as TSOs and listed in the BVC. In Colombia, TSOs are companies that operate transmission assets with voltages between 220 and 500 kilovolts (kV). Figure 1 shows the firms whose systems meet these criteria, which are Interconnection Electric SA ESP (ISA), the main TSO managing 71% of the transmission assets, followed by Grupo Energía de Bogota SA ESP (GEB), managing 10%, and then by Celsia SA ESP (CELSIA), which manages 2% (the remaining 17% of the transmission assets are managed by other firms that are not listed in the BVC). We built the electric utilities portfolio with ISA, GEB, and CELSIA, which together manage 83% of the transmission assets between 220 and 500 kV. The stock returns of each of these firms have an equal weight in the portfolio. Monthly returns were taken from the investing database, which can be accessed free of charge.

4.2.2. Market Risk Premium $\left(R_m\right)$

As a proxy for the Colombian market, we use the monthly return of the COLCAP index, which reflects the price variations of the most liquid stocks on the Colombian Stock Exchange (BVC). Monthly index returns were taken from the investing database, which can be accessed free of charge. As Colombia’s risk-free rate, we took the 1-year TES rate, which is extracted from the zero-coupon curve of public debt securities in Colombian pesos. Finally, we took the monthly TES rate from the statistics database of Colombia’s Central Bank, which can be accessed free of charge.

4.2.3. Risk Premium by Regulatory Scheme $\left(REG\right)$

To estimate the risk premium by the regulation scheme, we first constructed an equal-weighted portfolio with the returns on the electric utilities that are TSOs in Colombia and are currently regulated under the revenue cap scheme. We then constructed an equal-weighted portfolio with the returns of the electric utility firms operating as TSOs in Brazil that are currently regulated under the price cap scheme. The risk premium at each time t corresponds to the return on the price cap portfolio minus the return on the revenue cap portfolio.

Table 2. Electric utility portfolios.

Portfolio	Country	Ticker	Electric Utility
Revenue Cap	Colombia	CELSIA	Celsia SA ESP
		GEB	Grupo Energia Bogota SA ESP
		ISA	Interconnection Electric SA ESP
Price Cap	Brazil	AESBM&F	Aes Brasil Energia SA
		ALUP11	Alupar Investimento SA
		CMIG4	Companhia Energetica de Minas Gerais CEMIG
		COCE5	Companhia Energetica do Ceara
		CPFE3	CPFL Energia SA
		CPLE6	Companhia Paranaense de Energia
		ELET6	Centrais Eletricas Brasileiras SA
		ENBR3	EDP Energias do Brasil SA
		ENGI11	Energisa SA
		EQTL3	Equatorial Energia SA
		LIGT3	Light SA
		NEOE3	Neoenergia SA
		TAEE11	Transmissora Alianca de Energia Eletrica SA
		TRPL4	CTEEP

shows the electric utilities included in each portfolio. The monthly returns on each electric utility were taken from the investing database, which can be accessed free of charge.

4.2.4. Interest Risk Factor $\left(INT\right)$

To determine the risk for interest rate changes, we took the spread between the monthly reports of interest rates for 90-day and 360-day fixed-term certificates of deposit (CDTs). CDT rates are calculated as the weighted average of the deposit rates of financial institutions for the given terms. We use these rates since CDTs are the most popular fixed-income instruments in Colombia. The interest rates for the 90-day and 360-day CDTs were taken from the statistics database of Colombia’s Central Bank, which can be accessed free of charge.

4.2.5. Default Risk $\left(DEF\right)$

The default risk is taken as the spread between Colombian TES interest rates and U.S. Treasury bond rates. To represent this spread, we used the Emerging Markets Bond Indicator (EMBIG) for Colombia. The monthly EMBIG for Colombia was taken from the statistics database of Peru’s Central Reserve Bank, which can be accessed free of charge.

4.3. Real Pre-Tax WACC

Once the betas were found, we estimated the annual average of each of the risk premiums and calculated the annual cost of equity ($R_e$) with the local CAPM and TD-4 models. Finally, we calculated the WACC according to Equation (1) (shown in the introduction) and compared the results with those established by CREG. It is important to highlight that in the WACC formula, only the value of variable $R_e$ was modified. The other values were kept constant in order to specifically determine the impact of this variable’s calculation methodology, which we consider to be the most critical.

5. Results and Discussion

5.1. Summary Statistics

Table 3. Variable statistics.

	Excess Returns	Risk Factors
Statistic	${\mathit{R}}_{\mathit{c}\mathit{o}\mathit{p}}-{\mathit{R}}_{\mathit{F}}$	${\mathit{R}}_{\mathit{m}}$	$\mathit{R}\mathit{E}\mathit{G}$	$\mathit{I}\mathit{N}\mathit{T}$	$\mathit{D}\mathit{E}\mathit{F}$
Mean	0.49	0.08	0.47	0.82	2.22
Median	0.31	0.26	0.85	0.76	1.98
Maximum	17.57	14.13	27.79	2.67	5.50
Minimum	−14.20	−27.83	−16.39	−0.56	1.11
Std. Dev.	4.93	5.17	6.50	0.42	0.83

shows the summary statistics of the variables of the models presented with each of the values expressed as a percentage. The Colombian electric utilities portfolio showed an average monthly return higher than the risk-free rate of 0.49%, while the excess return of the COLCAP index was 0.08%. This shows that, during the period analyzed, the returns on the Colombian electric utilities portfolio were higher than the Colombian market returns. A monthly premium of 0.82% could also be observed, resulting from differences between the price cap and revenue cap regulation schemes and based mainly on the market risk assumed in the price cap scheme. The premiums or spreads related to $INT$ and $DEF$ factor interest rates were the highest, with values of 0.82% and 2.22%, respectively. However, they are the variables with the lowest standard deviation.

Table 4. Risk factor correlation matrix.

Factor	${\mathit{R}}_{\mathit{m}}$	$\mathit{R}\mathit{E}\mathit{G}$	$\mathit{I}\mathit{N}\mathit{T}$	$\mathit{D}\mathit{E}\mathit{F}$
$R_m$	1.00	−0.22	0.15	−0.01
$REG$	−0.22	1.00	0.07	−0.06
$INT$	0.15	0.07	1.00	0.27
$DEF$	−0.01	−0.06	0.27	1.00

shows the correlation matrix of the proposed risk factors. We used Pearson’s correlation coefficient to identify the existence of any dependency relationship between the risk factors used as explanatory variables that would limit the use of the OLS method. No significant correlations are evident, leading us to conclude that the factors are statistically independent.

5.2. Regression Results

Table 5. Regression results.

Model	Variable	Coeff.	Std. Error	t-stat	P(t-stat)	R2
CAPM	$\alpha$	0.00	0.00	1.56	0.12	0.60
	${\beta }_{Rm}$	0.74	0.09	7.89	0.00
TD-4	$\alpha$	0.00	0.01	0.70	0.49	0.73
	${\beta }_{Rm}$	0.69	0.05	12.86	0.00
	${\beta }_{REG}$	−0.25	0.04	−6.25	0.00
	${\beta }_{INT}$	−1.29	0.44	−2.92	0.00
	${\beta }_{DEF}$	0.52	0.27	1.93	0.06

presents the results of the CAPM regression and the proposed TD-4 model. The CAPM validated the hypothesis of a positive relationship between variations in the Colombian market risk premium and variations in the returns on the Colombian electric utilities portfolio because the ${\beta }_{Rm}$ coefficient was positive and significant for 1%, 5%, and 10% significance levels, as shown in the P(t-stat) value. The value of the ${\beta }_{Rm}$ coefficient was 0.74, confirming that COLCAP index variations are greater than those of the constructed portfolio, a remarkable fact since the returns on the electric utility portfolio are less volatile and more profitable than the market returns. Finally, the intercept, $\alpha$, in the CAPM model was not statistically significant, indicating that the portfolio does not generate abnormal returns in the CAPM, meaning it could be used. This model was able to explain 60% of the variations in returns.

In the proposed TD-4 model, all the factor coefficients were statistically significant for 1%, 5%, and 10% significance levels, except for the ${\beta }_{DEF}$ coefficient, which was only significant for a level of 10%, as observed in the P(t-stat) value. Therefore, we can conclude that all the proposed hypotheses were validated. The hypothesis on the negative relationship between the variations of the regulatory risk premium and the variations of the portfolio returns was validated. The value of the ${\beta }_{REG}$ coefficient was −0.25, confirming a lower expected return when electric utilities are regulated under the revenue cap scheme. However, sensitivity to this factor is the lowest. The hypothesis on the negative relationship between the variations of the spread between CDT interest rates and portfolio returns was also validated. The value of the ${\beta }_{INT}$ coefficient was −1.29, showing that the returns on the electric utilities are highly sensitive to increases in interest rates, which is due to the fact that the returns for this type of firm are conservative due to their low volatility, competing with the returns on fixed income instruments when interest rates increase. Finally, we validated the positive relationship between the variations of the interest rate spread of Colombian TES and U.S. Treasury bonds, represented by the EMBIG, and the portfolio returns for a significance level of 10%. The ${\beta }_{DEF}$ coefficient value was 0.52, which shows the portfolio’s low sensitivity to the factor.

Finally, in the TD-4 model, the intercept, $\alpha$, was not statistically significant, validating that there are no significant abnormal yields in this four-factor model. The TD-4 model was able to explain 73% of the variations in the returns on the electric utilities portfolio, which is 13% more than the CAPM. This means that the TD-4 model is more accurate since it allows for reflection on other determining risk factors in the variations in the returns on the Colombian electric utilities portfolio. We believe that this model could be used to establish the cost of equity in future methodology changes.

5.3. Fitted Values of the Regression Models

The RMSE obtained with the adjustment made through the local CAPM model was 3.12%, while the RMSE obtained with the adjustment made through the TD-4 model was 2.56%. Figure 2 shows two graphs, (a) and (b), comparing the real values and the values adjusted by both models. Graph (a) shows errors of greater magnitude with the local CAPM model in periods with extreme values of TSO returns, such as in 2008–2009, 2014–2015, and during the COVID 2020–2021 years. In graph (b), it is observed that the errors are of lower magnitude as there is a smaller distance between the real values and those adjusted with the TD-4 model, especially in the periods where extreme values of returns were presented, thus confirming that the four factors included in this model allow to better explain the returns of the TSOs in Colombia, by presenting a lower RMSE and a higher R² as shown in the previous section.

5.4. WACC

Table 6. Real pre-tax WACC under current and proposed models.

Component	Variable	Current U.S. CAPM	Local CAPM	Local TD-4
Equity Parameters	$R_F$	2.33	5.11	5.11
	${\beta }_{Rm}$	0.69	0.74	0.69
	$R_m$	6.38	1.25	1.25
	$R_p$	1.86
	${\beta }_{REG}$			2.96
	$REG$			−0.25
	${\beta }_{INT}$			0.82
	$INT$			−1.29
	${\beta }_{DEF}$			2.22
	$DEF$			0.52
	$R{e}_{usd}$	8.58
	${\Pi }_{cop}$	3.17
	${\Pi }_{usd}$	1.87
Equity	$R{e}_{cop}$	12.83	6.03	5.32
	$W_e$	60.00	60.00	60.00
	$Tx$	33.00	33.00	33.00
Debt	$R{d}_{cop}$	9.62	9.62	9.62
	$W_d$	40.00	40.00	40.00
WACC	Nominal Pre-Tax WACC	15.33	9.25	8.61
	${\Pi }_{cop}$	3.17	3.17	3.17
	Real Pre-Tax WACC	11.79	5.89	5.28

shows all the variables used in calculating the real pre-tax WACC. The first column shows the different components of the WACC calculation. The second column shows all the variables used, and the third column shows the values of the variables established by CREG to calculate the WACC with the cost of equity estimated using the CAPM with the beta method compared with the U.S. market. Finally, the fourth and fifth columns show the WACC calculation using the local CAPM and local TD-4 models evaluated in this study. As mentioned in Section 4, only the cost of equity capital was changed in the WACC calculation. The other values remained constant, as defined in the CREG document.

At the bottom of Table 6, we can see that when using the local CAPM, the Pre-Tax Real WACC was 5.89%, approximately half of the present value. When using the TD-4 model to obtain a more accurate cost of equity, the real pre-tax WACC is 5.28%. These results confirm that the calculation of the cost of capital with the CAPM model using the beta criterion comparable to the U.S. market overstates the discount rate value, which increases the tariff established for users.

6. Conclusions

In this article, we showed that in Colombia and other emerging countries that use the real pre-tax WACC methodology to establish the discount rate for TSOs, the discount rates are higher compared to those of developed countries. One of the causes of this situation is the way in which the cost of equity is calculated using the CAPM model with the comparable beta method. This study proposed the calculation of the cost of equity using a local CAPM model and a model with four risk factors called TD-4, where electric utilities operating as TSOs in Colombia were used, and the risk factors were constructed with local variables.

We found that the two proposed models were robust and statistically significant in all the proposed factors. However, the TD-4 model was able to explain 73% of the variations in the electric utilities portfolio returns, while the CAPM model explained 60% of the variations. Finally, we calculated the real pre-tax WACC with the cost of equity calculated using the two proposed models and found that both resulting values were lower than what was estimated using the regulator’s methodology. A higher discount rate to remunerate investments in energy transmission may affect the 14 million census households in Colombia, considering that spending on housing, water, electricity, and other fuels represents 29.4% of total household expenditures, being the highest item of household expenditures, according to the National Administrative Department of Statistics (DANE) [43]. For example, for the year 2019, 19 energy transmission projects with an approximate investment of USD 291 million entered into operation [44], with the rate recognized in 2019 by the regulator of 11.79%, the return on investment is USD 34 million, however, with the rates estimated in this study of 5.89% and 5.28% the remuneration should be USD 17 million or USD 15 million.

The results presented in this article can help formulate a new methodology for calculating the discount rate for power transmission activities involving companies and risk factors specific to the Colombian market, thus establishing a better rate for both users and power transmission companies. Future research could use the TD-4 model with local variables from other emerging countries with similar problems to calculate the cost of equity and could also go more in-depth in establishing the weighted cost of equity and cost of debt where there is generally no support for the established values.