Journal of Advanced Transportation

Volume 2018 (2018), Article ID 2153536, 9 pages

https://doi.org/10.1155/2018/2153536

## Cost of Capital Estimation for Highway Concessionaires in Chile

Department of Industrial Engineering, University of Santiago, Chile, Santiago, Chile

Correspondence should be addressed to Juan Pedro Sepúlveda-Rojas; lc.hcasu@adevlupes.ordepnauj

Received 29 August 2017; Revised 7 December 2017; Accepted 4 January 2018; Published 13 February 2018

Academic Editor: Zhi-Chun Li

Copyright © 2018 Cristian Vergara-Novoa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this paper, we present the cost of capital estimation for highway concessionaires in Chile. We estimated the cost of equity and the cost of debt and determined the capital structure for each one of twenty-four concessionaires that operate highways. We based our estimations on the developments of Sharpe (1964), Modigliani and Miller (1958), and Maquieira (2009), which were also compared with the Brusov et al. (2015) developments. We collected stock prices for different highway concessionaires around the world from Google Finance and Reuters’ websites in order to determine the Beta of equity using a representative company. After that, we estimated the cost of equity considering Hamada (1969) and a Capital Asset Pricing Model. Then, we estimated the cost of capital using the cost of debt and the capital structure of Chile’s highway concessionaires. With all above, we were able to determine the Weighted Average Cost of Capital (WACC) for highway concessions which ranges from 5.49 to 6.62%.

#### 1. Introduction

Highway concessions have been the main field where the Public Private Partnership (PPP) model has been applied in Chile. Eighty-four percent of the total investment in concessions since 1993 correspond to highways. This year, the Melón Tunnel was tendered through a public bid which raised an investment around 70 million dollars. After that, more than twenty years of concessions with an accumulated investment around 19.2 billion dollars have been demonstrated to be a good way of improving the road infrastructure of Chile. As Engel et al. [1] have mentioned, infrastructure provided by private participation has the advantage of ensuring funds for the future maintenance of the road and preserving standard and consistent services overtime. This has even been empirically proven in Chile.

As we mentioned above PPP has had success, not only from the private perspective but also from that of the State. In fact, the promulgation of the Chilean Concessions Law and its modifications have allowed the Government to regulate this market as well as make it a more friendly environment for investors. Nevertheless, this market faces some information asymmetries, specifically those associated with the costs incurred by concessionaires [2].

Considering this, we think it would be necessary to estimate the cost of capital. This represents the minimum return of investment that concessionaires would be willing to accept for a business or, in other words, the opportunity cost of their money. Thus, we might perform a better assessment of highway concession projects fitted to the real concessionaires’ costs, and in this way, we could reduce fares paid by users and improve the people welfare caused by the use of roads well maintained and with good level of services.

However, the estimation of the cost of capital is not an easy task, specifically when the analyzed companies do not trade in stock exchanges, as is the case with Chilean concessionaires. For this reason, we had to collect stock prices from foreign highway concessionaires using information provided by websites like Google Finance and Reuters in order to estimate the Beta of equity used to calculate the cost of equity by means of the Capital Asset Pricing Model (CAPM) developed by Sharpe [3].

The aforementioned and the cost of debt calculation, along with the data related to capital structure of Chilean concessionaires, both gathered from Assets and Insurances Authority website [4], allowed us to determine the Weighted Average Cost of Capital (WACC). We used WACC [5] in our calculations, although we could have used a more general and modern theory, that is, the developments of Brusov et al. [6] (BFO theory) who dismiss the perpetuity considered by Modigliani and Miller [5] and take the finite lifetime of companies to estimate their market values. However, most of the highway concessions in Chile have been tendered using the Present Value of Revenues (PVR) method. In this case, the company that bid the minimum PVR gets the concession. After that, the lifetime of concession is calculated every year. If the company’s revenue has reached the PVR it finishes its operation; on the contrary it follows operative. Given that, we could not use this clever approach because it is difficult to know when the concession will expire.

This article is organized as follows. Section 2 presents a review of the literature related to determining the cost of capital. Section 3 shows our developments and the way we estimated the cost of equity, the cost of debt and the cost of capital for highway concessionaires in Chile. Finally, Section 4, presents some comments and the main conclusions.

#### 2. The Review of Related Literature

Many companies’ investment decisions are assessed using the cash flow method, which represents the sum of discounted future benefits. In this way, they can estimate the net present value associated with the stream of future flows of money due to, among other things, a project, the operational company result, or the asset performance. However, the cash flow estimation depends on the cost of the capital rate, which represents the money opportunity cost for companies. The money opportunity cost is what the return of its investment would be because of having put their money in an alternative asset or project. For this reason, the cost of capital estimation is a sensible topic for companies whose value might depends on not only the company’s operational behavior, but also its finance risk associated with the debt. As Modigliani and Miller [12] demonstrated, in a world where a company pays taxes , the cost of capital for a levered company depends on the cost of capital related to a company financed only with equity and the rate between debt and the company market value , as shown in the next equation. In this context, shareholders require a cost of capital lower than , which is when they finance the company completely with their equity. This is due to the fact that shareholders transfer some of the risk to financiers. Another way to express the cost of capital, usually used by the industry’s professionals, considers that it is a weighted sum between cost of equity and cost of debt , as follows: where and represent the ratio of equity and debt with respect to the company market value. These two fractions represent the capital structure of the company. Equations (2) and (1) are the Weighted Average Cost of Capital (WACC). Equation (2) is the trivial determination of WACC, while (1) is just perpetuity limit of WACC. Recent development of capital structure theory presents another way to calculate the WACC. In 2008, a modern capital structure theory (BFO theory) [13] was developed, Modigliani-Miller being a particular case of the BFO theory. The WACC in the BFO theory can be calculated from the following expression:which has been obtained having considered the present value of company’s cash flow without perpetuity. Here, is the finite lifetime of the company and is . The finite lifetime of the companies is one of the main differences with the Modigliani-Miller theory. However, in this work, we chose Modigliani-Miller theory because an estimation of is a difficult task. As we told early, highway concessions have tendered using the Present Value of Revenues (PVR) method, where companies bid the minimum PVR in order to get the concession. After that, the accumulated revenues are calculated every year and compared with the PVR bid by the company. If the PVR is reached, then the concession is finished; otherwise the company follows operating the highway. Additionally, the Government has allowed many concessionaires to extend their contracts, since they have built additional works improving their highways and bettering the experience of users (car drivers). The aforementioned do not allow us exactly to determine when a concession will expire.

If we use (2) to estimate the cost of capital, then we should calculate the cost of equity as well as the cost of debt and determine the company’s capital structure, which comes from its finance reports.

To determine the cost of debt is easier than the equity. In fact, there are some proxies to do that. For example, it is possible to use the average estimation of the interest debts rate at which companies borrow funds [14]. It is possible also to use the internal return rate of the debt if the companies’ debts have different periods or a Capital Assets Pricing Model (CAPM) can be used, as will be explained below.

On the other hand, to determine the cost of equity , according to the risk level of the company, we can use the Capital Assets Pricing Model (CAPM), proposed by Sharpe [3], as follows:where the return of the equity depends on , which is the risk free rate, that will always be fixed and will not depend on the market changes. In general, is associated with securities released by the State. Additionally, is the expected or average market return (associated with the stock exchange where the asset is traded). The difference between and represents the Expected Risk Premium (ERP) which is related to investment in an asset whose return will be different of risk free rate and it will depend on market change. Given this, Beta of equity measures the sensitivity of the company to the risk of investing in the market instead of a risk free asset [11].

Thus, Beta values greater than one mean that the return of the equity moves more than the market and it would be riskier than an asset whose Beta is less than one. Therefore, the estimation of Beta allows us to infer the risk of the equity, as well as, along with the above variables, to determine its expected return.

According to Brealey et al. [11], the Beta estimation can be performed doing a linear regression between the returns of the company’s stocks and their market index as, for example, with S&P 500, Nikkei 225, FTSE 100, or IPSA in Chile.

Figure 1 presents Amazon’s returns with respect to the market index returns between 2010 and 2014. The red line represents the tendency obtained by means of a linear regression analysis. The slope corresponds to Beta, which is greater than one and means that an Amazon’s stock returns more than the market where it is traded.