metadata: authors: 0: author: de Castro,Luciano
1: author: Frischtak,Claudio R.
2: author: Rodrigues,Arthur
count: World
docna: 0: docna: How to Deal with Exchange Rate Risk in
            Infrastructure and Other Long-Lived Projects
docty: Policy Research Working Paper
abstracts: cdata!: Most developing economies rely on
            foreign capital to finance their infrastructure needs. These
            projects are usually structured as long-term
            (25&#x2013;35 years) franchises that pay in local
            currency. If investors evaluate their returns in terms of
            foreign currency, exchange rate volatility introduces risk
            that may reduce the level of investment below what would be
            socially optimal. This paper proposes a mechanism with very
            general features that hedges exchange rate fluctuation by
            adjusting the concession period. Such mechanism does not
            imply additional costs to the government and could be
            offered as a zero-cost option to lenders and investors
            exposed to currency fluctuations. This general mechanism is
            illustrated with three alternative specifications and data
            from a 25-year highway franchise is used to simulate how
            they would play out in eight different countries that
            exhibit diverse exchange rate trajectories.
display_title: How to Deal with Exchange Rate Risk
            in Infrastructure and Other Long-Lived Projects
listing_relative_url: /research/2023/09/34164630/deal-exchange-rate-risk-infrastructure-other-long-lived-projects
topicv3: Legal and Regulatory Framework m1326307 845,Exchange Rate Policy m1327143 1124,Infrastructure Funds m1327219 342,Public Procurement Concessions and PPP
            m1327711 1890
publishtoextweb_dt: 2023-09-19T00:00:00Z
dois: 10.1596/1813-9450-10568
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: NA
1: author_key: 434056
2: author_key: NA
model_extractions: Policy Research Working Paper 10568 How to Deal with Exchange Rate Risk in Infrastructure and Other Long-Lived Projects _Luciano de Castro Claudio Frischtak Arthur Rodrigues_ International Finance Corporation September 2023
Policy Research Working Paper 10568

# **Abstract**

Most developing economies rely on foreign capital to finance their infrastructure needs. These projects are usually structured as long-term (25–35 years) franchises that pay in local currency. If investors evaluate their returns in terms of foreign currency, exchange rate volatility introduces risk that may reduce the level of investment below what would be socially optimal. This paper proposes a mechanism with very general features that hedges exchange rate fluctuation by adjusting the concession period. Such mechanism does not imply additional costs to the government and could be offered as a zero-cost option to lenders and investors exposed to currency fluctuations. This general mechanism is illustrated with three alternative specifications and data from a 25-year highway franchise is used to simulate how they would play out in eight different countries that exhibit diverse exchange rate trajectories.

This paper is a product of the Economic Policy Research Department, International Finance Corporation. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank. org/prwp. The authors may be contacted at Luciano-decastro@uiowa.edu, claudio.frischtak@interb.com.br, and arthur.mauriciorodrigues@gmail.com.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# How to deal with exchange rate risk in infrastructure and other long-lived projects<sup>∗</sup>

Luciano de Castro<sup>†</sup> Claudio Frischtak<sup>‡</sup> Arthur Rodrigues<sup>§</sup>

**Keywords:** Exchange rate risk, infrastructure projects, Government protection, insurance for exchange rate risk, bidding for public projects, investors risk aversion, concession periods.

**JEL codes:** H4, F3, H8.

> ∗We are grateful to Eduardo Engel, Victor Tito, Cesaire Assah Meh and seminar participants at BNDES for helpful comments.

> †Department of Economics, Tippie College of Business, University of Iowa. E-mail: luciano-decastro@uiowa.edu Luciano acknowledges financial support by CNPq.

> ‡International Growth Centre (IGC). E-mail: claudio.frischtak@interb.com.br

> §Department of Economics, Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio). E-mail: arthur.mauriciorodrigues@gmail.com
# **Executive Summary**

Currency risk remains a significant deterrent to foreign investment flows to developing and emerging economies, particularly for long-duration infrastructure investments. Given the nature of such long-term investments, that take place in non-tradable sectors for which natural hedge is unlikely, hedging instruments are frequently costly, if at all available. Thus, either government assumes the implicit foreign exposure liability by providing guarantees, or contents itself with a smaller inflow of foreign capital. Countries that are most in need of to build or modernize their infrastructure and attract foreign investment typically face balance of payment problems and a high opportunity cost of foreign exchange. For those countries, finding alternative hedging mechanisms is a policy priority.

This paper proposes an alternative approach to address currency risk in infrastructure and long-term investments. The main idea is to adjust the length of the concession in such a way that a guarantee defined ex ante as a “target function” is achieved. In this mechanism, an unfavorable (to the foreign investor) exchange rate would cause an extension of the concession period, while an appreciation of the local currency leads to a shortened length of the concession. We show that a risk-neutral government would be indifferent to the purely financial implications of providing the mechanism, even if it were not to charge for access. Moreover, considering the likely increase in foreign investors’ willingness to bid for the countries’ projects, the mechanism would in fact lead to gains on a social welfare function independent on how the government values consumer (user) surplus and efficiency of firms providing the service. This finding is intuitive to the extent that by providing hedge to suppliers of foreign capital, governments would attract a larger number of competitors willing to offer a lower tariff to consumers and/or greater revenues to government.

We initially present the government guarantee mechanism in its most general form, with a non-specific “target function” for each partner in the concession. The paper then discusses in greater detail three specific mechanisms: ensuring an exchange rate level, with the government guaranteeing a specific inflation-adjusted exchange rate; a guarantee of the net present value at the beginning of the franchise; and a guarantee of equal returns among (national and non-national) partners, while not committing to a specific return. Note that in all three instances, the mechanism is presented as an option, in principle at zero cost: at the contractual outset of the concession, the investor decides whether she wants protection or not, and what share of the project is to be insured. The mechanism is also adaptable to countries with limited regulatory resources, insofar as the tests to establish if the partner supplying capital in foreign currency should enjoy additional concession time (the “test function”) can be conducted in notional (or proxy) values, thereby reducing information requirements from the concession to the government, and thereby minimizing the probability of (bilateral) opportunistic behavior, while eventually facilitating court decisions.

Finally, empirical tests use data from a real world 25-year highway concession and exchange rates from 8 countries – Mexico, Peru, Chile, Brazil, South Africa, Mozambique, Indonesia and the Philippines – to show that the variations in concession length resulting from a hypothetical guarantee are relatively small under alternative functions. Given the baseline of 25 years, it is striking that the adjustment is less than 4 years (that is, 16% of the project’s length) for all countries. It is equally noteworthy that in six of the sixteen simulations per2
formed, the government would receive back excess value at the end of the concession period. The results are similar and consistent across countries at different levels of development and exchange rate trajectories, with countries sharing only a relatively free-floating exchange rate regime.

The mechanism proposed would be a valuable addition to the toolkit of emerging and developing countries which aim to attract larger volumes of long-term investment for economic and social infrastructure projects. By removing what is generally regarded as a binding entry barrier for investors – currency risk – the guarantee mechanism enables a greater participation of private capital in such projects. And it does so with positive social welfare gains under general assumptions. Firm and government preferences suggest low (or even negative) opportunity cost to providing guarantees against long-term exchange rate movements as illustrated by relatively small variations in concession length.

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# **Contents**

|**Exe**|**cutive Summary**|**2**|
|---|---|---|
|**1**<br>**Intr**|**oduction**|**5**|
|**2**<br>**Lite**|**rature Review**|**9**|
|**3**<br>**Mod**|**el**|**12**|
|3.1|Time periods and discount factor . . . . . . . . . . . . . . . . . . . . . . . . . . . .|14|
|3.2|Investments, prices, costs and demand for each period . . . . . . . . . . . . . . .|14|
|3.3|Present value of the project<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|15|
|3.4|Partners from diferent countries . . . . . . . . . . . . . . . . . . . . . . . . . . . .|15|
|3.5|Firms’ preference<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|16|
|3.6|The competition of diferent consortia for the project . . . . . . . . . . . . . . . . .|17|
|3.7|Government’s preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|17|
|**4**<br>**The **|**general guarantee mechanism**|**18**|
|4.1|The defnition of the concession period . . . . . . . . . . . . . . . . . . . . . . . . .|19|
|4.2|Transfer to the government in case of excess value. . . . . . . . . . . . . . . . . .|21|
|4.3|Foreign partners and their values . . . . . . . . . . . . . . . . . . . . . . . . . . . .|22|
|4.4|Impact of the mechanism on the bidding process. . . . . . . . . . . . . . . . . . .|24|
|4.5|Impact of the mechanism on the government’s objective<br>. . . . . . . . . . . . . .|25|
|**5**<br>**Spe**|**cifc guarantee mechanisms: target functions**|**27**|
|5.1|Guaranteed exchange rate level . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|27|
|5.2|Guaranteed return<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|28|
|5.3|Guaranteed equal returns among partners<br>. . . . . . . . . . . . . . . . . . . . . .|29|
|**6**<br>**Spe**|**cifc guarantee mechanisms: test functions**|**30**|
|6.1|Notional costs and investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|31|
|6.2|Notional demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|32|
|6.3|Notional prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|32|
|6.4|Notional and real values<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|32|
|6.5|Information requirements under diferent target functions and alternative test<br>functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|33|
|**7**<br>**Sim**<br>|**ulating alternative guarantee mechanisms in a real life highway concession**<br>|**34**|
|7.1|Guaranteed return<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|36|
|7.2|Guaranteed equal returns among partners<br>. . . . . . . . . . . . . . . . . . . . . .|38|
|**8**<br>**Con**|**clusion**|**39**|
|**A Pro**|**ofs**|**40**|
|A.1|Proof of of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|40|
|A.2|Other proofs<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .|42|
|**B Sim**|**ulations’ data**|**46**|

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# **1 Introduction**

In most developing and emerging economies there is excess demand for infrastructure investment. Meanwhile, the stock of “public capital” (defined as the stock of assets in water, power, transportation and eventually telecoms) is significantly below what is required to provide universal services, which is estimated to be at 60% of GDP.<sup>1</sup> Moreover, in order to expand infrastructure investment, the government of these countries often face significant fiscal restrictions in addition to limited execution capability. Such constraints tend to be even more critical in poorer economies, with less developed capital markets, weaker institutions and stronger dependency on external flows, both public and private. Nonetheless, foreign capital – for both equity and debt — is also quite relevant for larger and more sophisticated economies. Modernization of the physical infrastructure is not only capital (and technology) intensive, but dependent on investors willing to commit for relatively long periods (anywhere from 10 to over 30 years), and therefore the ability to attract “patient” (institutional and long-term oriented) capital.

Investing in infrastructure involves constraints and risks which sometimes distort capital allocation away from areas with highest social rates of return and where investment is most needed.<sup>2</sup> Investors are driven away by poor governance – the absence of a stable legal and regulatory framework, a planning process which provides visibility for investors, and transparency in project identification, tender and monitoring. They are also deterred by macroeconomic instability, demand-related risks and the specific operational and technical risks. Nonetheless, to the extent that governments attempt to improve the governance of infrastructure investment, reduce macroeconomic policy volatility, while ensuring a well understood PPP model and auction design, they contribute to present investors a more attractive — or less uncertain — environment.

In recent years, governments and multilateral institutions have been engaged in attempts to reduce perceived and actual risks facing infrastructure investors. However, some risks are exogenous to both the private investor and the contracting (government) party, while the costs to minimize them are not known ex-ante by either party. Among the main risks, project (construction cost), demand and exchange rate stand out. Countries deal with these risks through contractual and other means (Table 1).

> 1 Frischtak and Mourão (2017a) and Frischtak and Mourão (2017b) estimate both the current level of capital stock and that which would bring about universal coverage of services in power, telecom, transportation, and water in Brazil, with the later calculated as 60.4% of GDP. Meanwhile, Kamps (2006) reports that the average level of net capital stock among 22 OECD countries decreased from 57.8% (20.6) of GDP in 1980 to 51.4% (17.1) of GDP in 2000 (with standard deviation in parentheses). In view of increased private sector participation in infrastructure investment since 1980, some of this slack was probably taken up by the private sector.

> 2See An (2017) on the nature of the risks associated with infrastructure projects and instruments for risk mitigation, either through contractual arrangements or through instruments (for credit enhancement, co-financing, among others). See also Verdouw et al. (2015).

5
Table 1: A sample of country approaches to mitigate risk

|||Risk to be mitigated||
|---|---|---|---|
||Construction|Demand|Exchange Rate|
|Mexico|Government<br>secures<br>right of way, provides<br>detailed<br>engineering<br>design and a construc-<br>tion<br>subsidy<br>(CAI)<br>in<br>one concession model|||
|Chile||Least Present Value bid<br>by concession winner**;|For<br>highway<br>conces-<br>sions in Chile, the gov-|
|||MIG<br>-<br>Minimum<br>In-<br>come (or trafc) Guar-<br>antee covers up to 70%<br>of costs,<br>adjusted for<br>excess trafc or IRR.|ernment<br>has<br>in<br>the<br>past<br>provided<br>an<br>ex-<br>change rate guarantee<br>for the hard currency-<br>denominated fnancing<br>component.|
|Peru*|RPI-CAO<br>mechanism:<br>government<br>payment<br>obligations<br>ensuring<br>the private party repay-<br>ment for construction<br>costs *||RPI-CAO<br>denominated<br>in hard currency; USD<br>indexed and infation-<br>adjusted rates|
|Brazil|||Lump-sum<br>payments<br>due to the government<br>during the concession<br>period may be used to<br>compensate<br>exchange<br>rate variations as they<br>afect debt principal re-<br>payment, for debt taken|
||||in the frst 5 years of<br>the concession.***|

Source: Own elaboration. (*) RPI-CAO mechanism: government payment obligations ensuring the private party repayment for construction costs, and O&M if falling below revenues. (***) It is a symmetric arrangement, and compensation may be due to the government.

For many countries, exchange rate risk is an effective deterrent, not only to greater external equity inflows, but also foreign-exchange denominated debt<sup>3</sup> . The problem is exacerbated by

> 3Exchange rate risk has been identified by the World Economic Forum (WEF) as one of the main concerns of infrastructure investors. See Forum (2016). See as well Verdouw et al. (2015), which starts by noting that “In PPPs, an optimal risk allocation generally means that a risk should be allocated to the party that is best positioned to manage or bear that risk, or more specifically, the party that can accept the risk at the lowest costs. However, regarding currency risk in these markets, this optimal risk allocation may not be so straightforward. A typical private sector developer has no influence over the exchange rate. Although the central bank has some control

6
the cost and unavailability of hedging instruments (such as derivative contracts).<sup>4</sup> Thus, either government assumes the implicit liability by providing guarantees (as in the case of Peru), and thereby increases their foreign exchange exposure or contents itself with a smaller inflow of foreign capital. A weak version of exchange rate volatility mitigation instrument (as the case in Brazil) appears to have a limited impact. The fact that countries which are most in need of infrastructure investment inflows typically face balance of payment problems and a high opportunity cost of foreign exchange makes this a non-trivial problem.

Is there a better way to address currency risk in infrastructure investments? In this paper we propose an alternative approach grounded on adjustments on the concession period. By concession period we mean the length of time during which the firm can explore the services that the infrastructure project provides. Obviously, this period impacts the returns of the project to the firm. Our main idea is that it would be more efficient for the government to provide a hedging or guarantee mechanism which adjusts the length of the concession through some publicized function defined ex-ante and dependent on the exchange rate (a "target function"). Depending whether the exchange rate is more or less favorable to the investor, the concession period may be shortened or extended. Moreover, we show that a riskneutral government would be indifferent to the purely financial implications of the mechanism. Taking into account the likely increase in foreign investors interest for the countries’ projects, the government might in fact benefit. In fact, we show an increase in social welfare under general conditions. These and other desired properties make the mechanism proposed in this paper potentially attractive to governments which are struggling to attract larger volumes of foreign capital to infrastructure.

We initially present the government guarantee mechanism in its most general form, with a non-specific “target function” for each partner in the concession. In addition, there is a “test function”, that is a proxy for the actual profits that the project generate.<sup>5</sup> The main idea is to adjust the concession period in order that the test function achieves the level specified by the target function. In other words, a satisfactory concession period is reached when the "test function" is at least as high as the "target function". Either there is no excess value at the end of the satisfactory concession period and the adjustment is purely among partners, or there is excess value that can be returned to the government. Both target and test functions may be regarded as “black boxes” in their degree of generality.

over the exchange rate through its monetary policies, the government’s effective control of the exchange rate may be limited. As a result of the above, unhedged currency risk is largely unmanageable for the private sector and may be beyond the control of the government agency in charge of infrastructure development, which means that it may not be easily acceptable for either party. Given the inherent uncertainties in exchange rate risk and the lack of a predetermined logical risk allocation to either the government or the private sector, currency risk can be a difficult and sensitive topic in negotiations between the private sector developer and the government” (pp. 1-2).

> 4See, for example, Hub (2019). This report notes (p. 42) that “Exchange rate risks are more substantial in markets where exchange rates are more volatile or long-term debt or swap markets are more illiquid (such as in countries with less developed capital markets). In more mature markets, the risk of currency fluctuations is typically not substantial enough to require the Contracting Authority to provide support and exchange rates risks are addressed solely through the Private Partner’s own hedging arrangements. Where the exchange rates are more volatile, access to long term hedging may be either unavailable or too expensive”. [Furthermore] “the likelihood of debt being dominated in a foreign currency is more likely in markets where financing by multilateral or international banks may be required (e.g., in less mature markets where there is limited depth in the local debt capital markets) “.

> 5If the actual profits are easily observable, the test function can be just the profits. By referring to test functions, We just emphasize the flexibility of the mechanism to work with just an easily determined proxy for the profit.

7
While the “black box” functions can accommodate any form, including functions unrelated to exchange rate volatility, the paper discusses in greater detail three specific exchange rate guarantee mechanisms: ensuring an exchange rate level, with the government guaranteeing a specific inflation-adjusted exchange rate; a guarantee of the net present value at the beginning of the franchise; and a guarantee of equal returns among (national and non-national) partners, while not committing to a specific return. Note that in all 3 instances, the mechanism is presented to the investor/developer as an option, in principle at zero cost and decided by the investor at the contractual outset of the concession if she wants protection or not.

We then use those target functions to examine the corresponding information requirements for the regulator under two test functions, using respectively notional and real values. For many countries with limited regulatory resources, employing such guarantee mechanisms – however attractive — would be predicated on restricting information demands on the regulator. Test functions using notional values that approximate the profits with easy to check and transparent numbers – instead of the actual profits – are not only preferable in those cases, but they also reduce the probability of bilateral opportunistic behavior.

Finally, the paper examines the actual performance of the guarantee mechanism for eight countries with different currencies, with simulations based on the parameters of a 25-year highway concession which ended in 2021. Results were obtained for two target functions discussed in this paper, for countries which differ in levels of income, infrastructure assets and geographical location, but characterized by limited intervention in currency markets. The relatively small adjustments in franchise times suggest limited or zero opportunity cost for government, and the economic viability of the mechanism. Table 2 summarizes the results in case of eight different currencies against the US dollar. Given the baseline of 25 years, it is striking that the adjustment is less than 21 months (that is, 7% of the project’s length) for all but one country (Indonesia, and for the guaranteed return target function). It is equally noteworthy that if the government were to guarantee an ex-ante return in foreign currency, in 6 out of 8 instances, it would receive back excess values, while in the case of guaranteed equal returns among partners, the average extension was in little over half a year (6.5 months).

Table 2: Adjustment time (in months) required by alternative guarantee commitments

||Adjustment time (in months) fo|r a 25-year highway concession|
|---|---|---|
||Guaranteed return in Net Present<br>Value (NPV)|Guaranteed equal returns among<br>partners|
|Brazil|-14|+16|
|Mexico|-21|+5|
|Indonesia|+40|-3|
|Mozambique|+4|+13|
|Chile|-13|+5|
|Peru|-18|+1|
|Philippines|-15|+1|
|South Africa|-19|+14|

Source: own elaboration; see Section 7 and Appendix B. Note: In the case of the guaranteed equal returns among partners mechanism, negative values are associated with compensation the foreign investor must pay to the government instead of shortening the actual franchise time.

8
This paper is organized as follows. Section 2 is a brief literature review. Section 3 sets the basic model of a concession for firms and government, and the stochastic process which underlies exchange rate movements. By explicitly modelling firms and government preferences, and connecting both through an auction in which firms consortia bid for the franchise, it is shown that the guarantee mechanism bring social welfare gains if government value both consumer welfare and firm efficiency. Section 4 details the general guarantee mechanism and its functionality, which might entail either transfers among partners which have benefited more – or less – from the government guaranteeing a satisfactory concession period depending on their particular exchange rate movement, or transfer to the government in case of excess value. Section 5 illustrates the general mechanism with 3 target functions, while Section 6 discusses the information requirements regulators face if the government decides to offer such guarantees under notional and real values test functions. Section 7 presents the simulation results for two of these mechanisms and a total of 8 countries, against a 25-year actual highway concession, suggesting the applicability of the guarantee mechanism against long-term exchange rate fluctuations. Section 8 concludes.

# **2 Literature Review**

The mechanism proposed in this paper is closely related to the Least Present Value model introduced in Engel et al. (2001) as a way to mitigate demand risk by adjusting the length of the concession. This type of risk-sharing contract has been put to test successfully in Chile and, to a lesser extent, the U.K (see Engel et al. (2019) and Engel et al. (2021)). However, there are a few significant distinctions. First, this paper extends the concept of concession period adjustment to remove (in large measure) the exchange rate risk from a concession, up to now an almost intractable problem due to its cost to either private party or government. Second, and more important, the literature apparently did not draw the consequences of the link between exchange rate processes being approximated by a martingale to the provision of currency hedge by governments, its feasibility and cost. Third, the paper provides a general framework for thinking about guarantee mechanisms and their properties, suggesting a potential large menu of functional forms for target and test functions, and therefore the potential to adapt the mechanism to different country and industry circumstances. Moreover, the paper models both firm and government preferences and shows social welfare gains allowed by the mechanism under general assumptions. In particular, the paper suggests low (or even negative) opportunity cost to governments in providing guarantees against long-term exchange rate movements in the context of economic and social infrastructure projects which can be modelled as long-term concessions.

Even though currency risk is often cited as a major deterrent for private investment in infrastructure (see Vasconcelos et al. (2019), Aye et al. (2018) and Yamahaki and Breviglieri (2022)), the literature on exchange rate mitigation in long-term investment projects is relatively scarce. A study by Matsukawa et al. (2003) compares contractual arrangements that allocate exchange risk to investors, consumers and government, and argues that the optimal allocation depends on country specific characteristics. As hedge alternatives are often costly, they promote long-term local currency debt as the first best alternative to finance infrastructure projects. In countries with underdeveloped capital markets, they suggest the government 9
should protect the debt (and possibly some portion of the equity) from exchange rate volatility. Verdouw et al. (2015) agrees currency risk mitigation is inherently expensive. Therefore, they propose more local currency financing and suggest International Financial Institutions (IFIs) should move away from direct loans and towards providing financial hedging instruments and guarantees. In this context, Persaud (2023) suggests a foreign exchange guarantee mechanism that reduces the excess risk premium over actual currency risk, and implemented by a joint agency of multilateral development banks.

As an important concern for private investors, exchange rate risk has been a topic addressed by multilateral institutions in their set of recommendations to policymakers. The 2007 OECD’s Principles for Private Sector Participation in Infrastructure (see Christiansen, 2008) suggests countries remove restrictions to international capital flows, so investors can finance their operations in different currencies at competitive international rates and criticizes the experiences that imposed infrastructure tariffs linked to foreign currency fluctuation. The World Bank’s Review of Risk Mitigation Instruments for Infrastructure Financing (see Matsukawa and Habeck, 2007) distinguishes between types of risk mitigation instruments and compares the risk mitigation schemes in several projects. Regarding exchange rate risk, it notes it is a significant deterrent to investment and has been in the last 2 decades contractually mitigated by tariff indexation of foreign currency cost components (including debt and equity costs), potentially implying significant fiscal and foreign exchange liabilities to individual countries, a less than desirable outcome.

The broader issue of risk allocation and mitigation in PPPs is also tackled by Engel et al. (2014), where the authors argue that the choice of which risks to allocate to investors affects both efficiency and costs. They conclude there are good reasons to transfer construction and operation risks to the concessionaire, but advocate demand risks should probably be borne by the government. They also argue governments are not efficient at providing financial insurance, and therefore propose the firms should bear currency risk, as they can choose alternative capital structures. Albalate et al. (2015) analyzes the public and private risk allocation in road infrastructure PPPs. They identify government-provided exchange rate insurance mechanisms in Spain and Chile, while currency risk is considered borne by the investor in France, Brazil and Argentina. More recently, Engel et al. (2022b) and Engel et al. (2022a)<sup>6</sup> identify renegotiations as the major source of fiscal risk in public-private partnerships infrastructure, while pointing to variable term contracts as a mechanism to effectively reduce the probability of renegotiations on the back of the Chilean experience and the changes introduced by 2010 legislation. And it is also in this connection that this paper is related to the work of Engel and co-authors. Thus, the importance of the mechanism suggested in this paper is twofold: first, it reduces a significant entry barrier to private sector flows into a sector historically underfunded due to fiscal and other constraints emerging market and developing economies (EMDEs) face<sup>7</sup> . And second, by providing contractual flexible terms – in this case as it applies to exchange rate risk and volatility – the mechanism helps contain one of the major problems associated with concessions, namely the demand for renegotiations in view an economically inadequate risk allocation<sup>8</sup> .

> 6See as well Anderson et al. (2006) and Irwin (2007).

> 7Among other relevant references, see Fay et al. (2021) and Fay et al. (2017)

> 8In a recent paper, Acharya et al. (2022) argue that expanding the flow of private resources to infrastructure projects is predicated on government commitment in the form of guarantees, co-investment, tax subsidies and

10
Finally, expanding infrastructure investment in EMDEs has gained an unprecedented urgency in view of _climate change_ , and the fact that in the coming decades all GHG net emissions additions will originate in these countries, and they will also suffer most of the effects. The demand for both mitigation and adaptation investment will see an extraordinarily large increase, and within mitigation, energy transition looms dominant.<sup>9</sup> In this context, private finance has assumed a paramount role, and new instruments and mechanisms to attract private investment – both in terms of financial flows and direct investment - as proposed here, are likely to be regarded of first order importance to address climate change and to pursue the “net zero emission by 2050” target.

other instruments, so as to minimize the risk of expropriation and other forms of opportunistic behavior, and further suggest they are generally incentive-efficient, and could thus be construed as mechanisms to reduce the risk of renegotiation.

> 9See, for instance, International Monetary Fund (2022). Songwe et al. (2022) also states that "The world needs a breakthrough and a new roadmap on climate finance that can mobilize the $1 trillion per year in external finance that will be needed by 2030 for emerging markets and developing countries (EMDCs) other than China” with the private sector making the largest increase in financing, both foreign and domestic. In addition, a major recent statement and analysis is found in World Bank (2023).

11
Table 3: Notation Glossary

# **3 Model**

|**Symbol**|**Usage**|
|---|---|
|T|Ex-ante expected duration of the concession, which lasts fromt=1,2,...,T,...|
|j<br>|Nationality of consortium partners, indexed by $j \in {0,1, ..., m}|
|V<sup>j</sup>(T)<br>|Value function; value of the project for frmj, expressed inj’s currency|
|V<sup>j</sup>(T)<br>|Test function; may be the actual (real) value function or an approximation (proxy)<br>which may be easier for the government to calculate and verify|
|V<br>~~j~~(T)|Target function; may be conceived as a guarantee of value for the frms|
|δt|Discount factor that brings values from yeart to year 0|
|rt|Opportunity cost for capital in periodt|
|ct|Costs of the project in periodt|
|pt|Tarif or price for the service in periodt|
|I|Investment, undertaken in periodt=0|
|qt|Consumption in periodt|
|Bt|Net beneft of the project in periodt|
|St<br>|Total consumer surplus in periodt|
|X<sup>j</sup><br>t<br>|Exchange rate in periodt, denominated in units of currencyj for each<br>unit of currency 0|
|α<sup>j</sup>|Partnerj’s share of the project|
|R<sup>j</sup>[V<sup>j</sup>(T)]<br>|Risk premium, deduced from the expected value of project|
|U<sup>j</sup>|Final value of the project utility in currencyj|
|u|Final value of the project utility for the consortium of frms|
|K|Bidding consortia, indexed byk∈{1,...,K}|
|bk|Bid submited by consortiumk|
|τ|Transfer to the government by winning consortium|
|G(T)<br>|Government’s preference|
|A<sup>j</sup>|Transfers (adjustments) between partners|
|P|Actual duration of the concession, restricted byP∈[P0,P1]|

In this section, we will describe the model and introduce the guarantee mechanism that this paper proposes. Before detailing the technical parts of the model, it is useful to understand the context for which this mechanism is conceived.

We assume that a country which fiscal (and other) restrictions wants to undertake an infrastructure project with private resources. The government tenders a concession for the services rendered by the project during a given period of time. We call this the concession period. The firm (or consortium of firms) that will explore the concession needs to commit resources and will charge tariffs for the use of the infrastructure.

We focus initially on the definition of the contract that the government offers to the consortium of firms. The basic idea is to offer a contract that is more beneficial (less risky), without creating additional burden to the government. We are specifically interested in providing protection against exchange rate risk for foreign investors. In doing so, the government 12
will increase competition by allowing for greater participation of providers of equity and debt in foreign currency, thus improving both the likelihood that the project is developed and the quality of its terms. Furthermore, the outcome of the competitive process under the guarantee would allow for the government to receive a larger payment for the right to explore the concession and/or the consumers paying a lower tariff.

Firms can form consortia with different partners to compete for the right to explore the concession. Specifically, a consortium may be composed of m + 1 firms, each of a possibly different country and interested in protection for exchange risk in its own currency. The value of the project for firm j ∈{0,1,..., m} will be denoted V<sup>j</sup> (T ), expressed in j’s currency. Here, T is the ex-ante duration of the concession, which will be important in what follows. The value functions V<sup>j</sup> (T ) will be explicitly defined below.

The general form of our guarantee mechanism consists of defining, for each j ∈{0,1,..., m}, test (real or proxy) functions V<sup>j</sup> (T ) and target functions V ~~j~~ (T ). The test functions V j(T ) may be thought as just the true value functions V<sup>j</sup> (T ). Since the true value function may be difficult to verify by the government, we allow the possibility to use as the test function a proxy V<sup>j</sup> (T ), that approximates the true value V<sup>j</sup> (T ). This test function V<sup>j</sup> (T ) may be easier for the government (and courts) to calculate and verify than the actual value function V<sup>j</sup> (T ). The main idea of the mechanism consists in guaranteeing that these test functions will meet ~~j~~ the target function V (T ), that may be conceived as a guarantee of value for the firms. In more formal notation, the main idea of the guarantee mechanism is trying to ensure that for all j ∈{0,1,..., m}, In Section 5 we give different examples of target functions, while in Section 6 we illustrate test (proxy) functions. But just to fix ideas, for now the reader can assume that the test function is the true value of the project and the target function in each currency is the value invested plus a given return over investment. In this specific case, the government is excluding all risks of the project, since it guarantees that the partners will receive the fixed return for sure.<sup>10</sup> Even if the true value functions are adopted as the test (proxy) functions V<sup>j</sup> , the left hand side of condition (1) is still subjected to currency risks. In this case, condition (1) may not be met in the initially planned period T . The second part of the mechanism is to find a termination period P for the project that guarantees that condition (1) is met. This effective termination period will be random and determined after the realization of the exchange rate process during the concession period. In other words, the guarantee of the mechanism is not exactly (1), but that the concession period will last a period P so that the value of the project at period P satisfies the target function, that is, In the rest of this section, we will define the value functions V<sup>j</sup> (T ), the preferences of the firms, that determine how they deal with risk, and the objective function of the government.

> 10 Of course, we are not recommending that the government offers such guarantee, but just illustrating a possibility.

13
The more detailed description of the mechanism is postponed to Section 4. Examples of test ~~j~~ and target functions, respectively V<sup>j</sup> and V , are discussed in Sections 5 and 6.

# **3.1 Time periods and discount factor**

Time will be divided in periods, that can be interpreted as years, although there is no formal reason for not using quarters or months, if that is convenient or necessary. The first period will be labeled period 0 and all the (present) values will be expressed with respect to this period. After that, we will have periods t = 1,2,..., T ,..., where T will denote the typical (or expected) length of the concession period. Although time is, therefore, denoted in discrete units, it will be convenient to allow continuous time in some parts of our development, namely, in the definition of the moment that the test function achieves the level of the target function.

Let 1+1rt<sup>∈(0,1)bethediscountfactorforperiodt.Inprinciple,thevalueofrtmaybe</sup> constant, in which case we would write only r. However, we can accommodate nonconstant discount factors by defining as δt the discount factor to bring values to year 0, that is, If rt = r for some opportunity cost of capital r ⩾ 0, which is fixed, then δt = (1 + r)<sup>−t</sup> .<sup>11</sup>

# **3.2 Investments, prices, costs and demand for each period**

We treat all investments as undertaken in period 0 and denote them by I. Of course, the actual investments can be spread in many different periods or years. We choose to talk about only the _present value_ of the investment in period 0 for simplicity.<sup>12</sup> This reflects the notion that period 0 corresponds to the development phase of the project (which may take more than a year), during which the project renders no service and, therefore, no revenue accrues.

Let ct be all the costs of the project and pt, the tariff or price for the service in period t. Consumers value the project as vt > pt for the services that the project provides. Consumption qt may vary with period t, but for simplicity we will assume that it does not depend on pt, that is, demand is perfectly inelastic. This is a common (and realistic) assumption in electricity markets, for instance, and is probably a reasonable approximation for infrastructure projects.<sup>13</sup> Therefore, the revenue in period t is ptqt.

In this way, the project has net benefit Bt = ptqt − ct and the total consumer surplus is St = (vt − pt)qt in period t. Of course this is expressed in the domestic currency, that is, the currency of the country where the project is located.

> 11 Below, we will consider discount rates that might vary with different countries. In this case, we will use δjt instead of δt to refer to the discount rate in currency j.

> 12 If one wants to be explicit, we can define It to be the investment made in period t and the present value of the investment is thus I = I0 + ∑<sup>T</sup> t=1<sup>δtIt.Inthiscase,weomitthedependenceofIwithrespecttoT,foramatterof</sup> convenience.

> 13Relaxing this assumption only makes the statement of our results unnecessarily more complicated. In any case, we will discuss below how the relaxation of this assumption impacts the results.

14
# **3.3 Present value of the project**

With the previous definitions, one can see that the present value of the project at period 0 is given by: where T represents the total time of the concession, that is, the time that the investors will be allowed to explore the services that the project renders.

Many terms in the expression (4) are not known at the time of the evaluation of the project: pt, qt, ct and, to some extent, even I and δt are just projections. Thus, in principle, we should consider the value V(T ) as uncertain, and write it in terms of expectation. However, the main focus of this paper is on exchange rate risks. Therefore, for simplicity we will assume that the mentioned values are known, and consider only the uncertainty with respect to the exchange rates. This will be further discussed below.

# **3.4 Partners from countries**

One of the main motivations of this paper is to deal with currency risk. To take this into account, we will assume that the project will have m + 1 partners or investors from different countries, where partner j = 0 is the domestic partner. Partner j = 0,1,..., m faces exchange X<sup>jperiodt,denominatedinunitsofcurrencyjforeachunitofcurrency0,thedomestic</sup> t<sup>in</sup> or local currency, so that X<sup>0</sup> t<sup>=1forallt.14</sup> For example, if the project is in Brazil, so that the domestic currency is the Brazilian Real and the investor j is using US dollar, then X<sup>j0.179457USD/BRL,iftheperiodtcorrespondstoendoftheyear2021.Ifweassume</sup> t<sup>=</sup> that benefit Bt = ptqt − ct is converted each period, it amounts to X<sup>j</sup> t<sup>Bt = X</sup> t<sup>j(ptqt −ct)in j’s</sup> currency. It will be useful to define the value of the project as if it is exclusively expressed in j’s currency: where we have used discounting rates specific for each j. Notice that since the initial investment I is given in the local (domestic) j = 0 currency and is realized in period t = 0. Obviously we are assuming that each period result is converted into j’s currency. Notice also that, since X<sup>0</sup> t<sup>= 1forall t, V0(T) = V(T).</sup> It is important to realize that the V<sup>j</sup> (T ) – and basically all the values discussed in this paper – refer to the value in date 0. As already mentioned, in (5) we have used δ<sup>j</sup> t<sup>,thatis,the</sup> discount rate depends on the country j. However, the model obviously allows that we assume δ<sup>j</sup> t<sup>= δtfor all j, that is, the same discount rate is used for all currencies.This flexibility allows</sup> the model to be used for different purposes, such as:

- _planning, ex ante_ : the firm has a constant opportunity cost of capital given by i, so that δ<sup>jforall j,ascommentedafter(3);</sup> t<sup>= δt = (1 + i)−t</sup>

> 14Of course, more than one partner can belong to the same country. For instance, if j and j ′ use the same currency, we would have X<sup>j</sup> t<sup>= Xj</sup> t<sup>′andthiswouldnotcreateanyproblemtoourformalism.</sup>

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- _posterior evaluation_ : δ<sup>j</sup> t<sup>takesintoaccounttheinflationincountryjand,therefore,is</sup> differentiated by country.

In other words, the model is agnostic on how the firm (or the government) define or calculate δ<sup>jitmaytakeintoaccountonlytheopportunitycostofcapitalorincludeinflationand,</sup> t<sup>:</sup> possibly, other factors. What is important is that δ<sup>j</sup> t<sup>allowstobringvaluesinthecurrencyj</sup> and time t to time 0.<sup>15</sup> In any case, whether δ<sup>j</sup> t<sup>= δtforalljornot,whatisimportantisthat</sup> the value V<sup>j</sup> (T ) in expressed in j currency at period t = 0’s value. Also, we will write δt instead of δ<sup>0</sup> t<sup>and, more generally, whenever the superscript j is omitted, the value is supposed to refer</sup> to the domestic currency 0.

Obviously, partner j will have just a share α<sup>j</sup> of the project, with ∑<sup>m</sup> j=0<sup>αj=1.Sincewe</sup> can just drop partners with zero participation, we will assume that α<sup>j</sup> > 0 for all j = 0,1..., m. Therefore, each period t partner j receives X<sup>j</sup> t<sup>αj(ptqt −ct)initscurrency.Thisimpliesthat</sup> the value for partner j is Therefore, α<sup>j</sup> V<sup>j</sup> (T ) is the value for partner j of its participation in the project.

As observed before, the above values are uncertain, but for simplicity, we will focus our attention only on the uncertainty with respect to the exchange rate. Thus, we denote by Et[⋅] the expectation with respect to exchange rates (in the foreign currencies).

If the expectation with respect to the future value of some exchange rate is its current value, as it is usually assumed in many financial markets, then the expected value of V<sup>j</sup> (T ) is just the value V(T ) converted to the j currency at the current exchange rate. In order to formalize this result, we need an assumption about the nature of the underlying stochastic process governing exchange rate dynamics. This will be done in Section 3.

# **3.5 Firms’ preference**

We assume that firms are risk averse and deduce from expected values a risk premium R<sup>j</sup> [V<sup>j</sup> (T )] that depends on the volatility of the value of the project V<sup>j</sup> (T ). Therefore, the final value of the project utility in currency j is: Of course partner j with fraction α<sup>j</sup> of the project will evaluate its stake at α<sup>j</sup> U<sup>j</sup> . From this, we can define the value of the project for the consortium of firms, denoted just u, as: where we have omitted the dependence on T for simplicity and converted all values to the domestic currency.

> 15Figure 1 below and the discussion that follows it help to further understand the roles that δjt<sup>andδtplayin</sup> our model.

16
For most of the paper, we will focus on only one consortium of firms that will execute the project. Thus, for most of the paper we do not need to make a special notation on the value of the project for the consortium, as in (7). However, to discuss the competition for the government concession, we will need to introduce a notation differentiating the values for each consortium. In this case, the value u that appears in (7) will appear with a subscript, as explained below.

# **3.6 The competition of different consortia for the project**

In most of the paper we will consider only one consortium of firms building the infrastructure the project and exploring its service. Although this is convenient for most of the results of the paper, the analysis of the bidding process requires that we model how different consortia compete for the right to build the infrastructure and explore its service.

We will model this competition as an auction among K consortia. The consortium k ∈ {1,..., K} submits a bid bk after learning/estimating value uk for the project, where the reader can think of the value uk coming from an aggregation of the different values for the firms which form the consortium k as in (7). We will assume that the the distribution of the values of the consortia are independent and identically distributed according to cumulative distributive functions (c.d.f.) F ∶ R →[0,1], that is,<sup>16</sup> The difference in values for the consortia arises from possible difference in costs and managerial expertise. The symmetry assumption is not extremely important for our results, that might hold under asymmetric distributions as well. However, symmetry allows us to use many convenient results in auction theory. Moreover, this may be a reasonable assumption at this level because, although the firms in different countries will have values that are very different, they can participate in consortia of different composition. Therefore, taking into account the possibility of consortia made with firms of different countries, each consortium can be viewed, ex ante, more or less symmetrically with respect to other ones.

# **3.7 Government’s preference**

We assume that the firms competing for the project make a transfer τ to the government.<sup>17</sup> This can be done at the beginning of the concession period or be the present value of transfers made during the concession period.<sup>18</sup> We assume that the government’s preference is based on the consumer surplus S(T ) = ∑<sup>T</sup> t=1<sup>δt(vt−pt)qt,thevalueV(T)oftheproject(withaweightfactorμ∈[0,1]furtherdis-</sup>

> 16 In fact, later we will consider two c.d.f.s: F0 when the guarantee mechanism is not used, and F1 if the guarantee mechanism is adopted. This will be further explained in Subsection 4.4 below.

> 17We can model the situation in which the government pays a _subsidy_ to the firm for completing the project by assuming that τ < 0.

> 18In principle, this could include taxes as well. However, since taxes can come in different forms and be complex, we avoid discussing them in detail here and focus only on transfers directly related to the concession contract.

17
cussed below) and the transfer τ: Recall that τ includes the (present value) of the fees paid to the government for the concession rights (which may be zero) or all subsidies offered by the government (which will enter with a negative sign).This total transfer can be used by the government for promoting other social or public goals. The factor μ represents the weight that the government puts on the benefits obtained by the project. If μ = 1, the government values the benefits on par with the consumer surplus, thus pursuing efficiency. If μ = 0, the government is interested only on the consumer surplus and the transfers τ, and disregards the benefits accrued to the firms. In any case, notice that the government takes into account the total net benefit of the project V(T ) and not the firms’ expected utility U<sup>j</sup> introduced above. This is justified for two reasons. First, taking into account U<sup>j</sup> would make the government objective vary with the composition of the consortium of firms and their shares in the project. Second, U<sup>j</sup> deducts a risk premium that is faced by the firms but is not relevant for the government. Indeed, we assume that the government is risk neutral. This last assumption is justified by Arrow and Lind (1970), who argue that the government can spread risk better than firms. At this point the reader may ask: but G(T ) does not depend on the exchange rates and, therefore, will not be subjected to the uncertainty that we have previously specified. Although that is true, the guarantee mechanism that this paper proposes makes the actual concession length T dependent on the exchange rates. ̃ Therefore, rather than a certain period T , we will work with a random variable T , that depends on the exchange risks. In this case, by saying that the government is risk neutral, we are assuming that it is trying to maximize E[G(T<sup> ̃</sup> )].

We assume that the government may choose pt and τ, subject to the incentive constraints defined by the preferences of the firms. Indeed, by reducing pt (considering the demand qt inelastic) and/or increasing τ, the government improves G(T ), but decreases U<sup>j</sup> , making the project less attractive to firms. In the limit, no firm would undertake the project. Alternatively, by reducing τ, the government can expect firms to reduce the price pt that firms require to participate in the project.

More specifically, we will consider two polar cases, both of which have occurred in the real world. In the _price competition_ case, the government fixes τ (for instance, τ = 0) and organize the bidding competition around the price pt (usually taking at a fixed real value, that is, δtpt = p for all t). The firm that offers the lowest price wins. In the _concession competition_ case, the government fixes prices pt and organizes an auction for the concession right. The firm that offers the highest payment τ wins the competition. The specific models of these two competition cases will be further discussed below.

# **4 The general guarantee mechanism**

In this section, we develop mechanism of guarantees and explain in more detail how it works. Recall that the main idea was described at the beginning of Section 3. It consist of adjusting the concession period in order to provide the guarantee to partners. This guarantee will take 18
~~j~~ the form of a target function V (T ) for each partner j, that is, the purpose is to guarantee that (a proxy for) the value for partner j, V<sup>j</sup> (T ), is at least as high as the target function V ~~j~~ (T ). In this section, we will simplify notation and denote the test functions V j(T ) simply as the value functions V<sup>j</sup> (T ). This will create no restriction since we will not make use of any specific properties of V<sup>j</sup> (T ) nor its particular definition given in (5). Since an important case that interests us is exactly when the proxy functions are exactly equal to the value functions, V<sup>j</sup> (T ) = V<sup>j</sup> (T ), this simplification has the advantage of helping understanding.

As explained in Section 3, the method requires finding the period P such that Obviously, partner j that owns share α<sup>j</sup> of the total project, will receive only α<sup>j</sup> V<sup>j</sup> (P). In any case, (9) guarantees that this partner receives the corrresponding fraction of the target ~~j~~ function, that is, α<sup>j</sup> V<sup>j</sup> (P) ⩾ α<sup>j</sup> V (P).

Since different currencies will lead to different values for different partners, and therefore, different target functions, the condition expressed by (9) might in principle lead to different end dates for the project. This is obviously not convenient, since the project needs a definitive time for the concession to end. A solution could be to use the longer P, that makes all restrictions (9) satisfied. While this guarantees that all partners achieve their target values, it also implies that some partners will have a large advantage over others. Instead, we propose to introduce transfers (that we will call adjustments) between partners. It will be established that the project produces enough resources in order to meet the guarantees made for all partners, but there will be adjustments between them to guarantee that all targets are satisfied at the earliest possible concession period P. We discuss the transfers among partners in more detail in the next subsection.

# **4.1 The definition of the concession period**

Our main task is to show that the proposed mechanism can work under certain conditions. For this, it is of central importance to discuss the transfers among partners. As anticipated above, those transfers are what allow the mechanism to be practical. In fact, the definition of the concession period, which we name a “satisfactory concession period” needs to be introduced together with the transfers (adjustments) among partners. This is accomplished by the following:

**Definition 1.** _We say that_ P ∈ R++ _is a satisfactory concession period if there exist adjustments_ A<sup>j</sup> ∈ R _, for_ j = 0,1..., m _, such that:_<sup>19</sup>

_1. the adjustments are just transfers between the partners, that is,_ _and_

> 19Note that we do not restrict the satisfactory concession period to be restricted to integers, as previously commented in Subsection 3.1.

19
_2. for all_ j = 0,1..., m _,_<sup>20</sup> Recall that all V<sup>j</sup> (P) are given at period t = 0 values. Thus, the adjustments are also expressed in those values.<sup>21</sup> More specifically, all the adjustments are given in the domestic currency at period 0 values. This allows us to add them with respect to the shares that each partner has, as (10) requires. Notice also that the definition of satisfactory concession period P modifies (9) to include the adjustments (transfers) converted to j currency and changes it to (11).

The main question is under what conditions we can find a satisfactory concession period that guarantees, as Definition 1 requires, that all partners receive at least the value assigned by their target functions. The conditions are in fact simple and are given by the following: **Theorem 1.** _Assume that the functions_ V<sup>j</sup> , V ~~j~~ , Xj ∶[P0, P1] → R++ _are continuous and_ _that is, the value of the target functions are necessarily satisfied at the end of maximum concession period_ P1 _. Then there exists the lowest satisfactory concession period, that is, there exists_ P ∈[P0, P1] _such that_ P _is a satisfactory concession period and if_ P<sup>′</sup> ∈[P0, P1] _is also a satisfactory concession period, then_ P ⩽ P<sup>′</sup> _._

**Remark 2.** _As already mentioned at the beginning of this section, in Theorem 1 we do not use the specific formula_ (5) _that defines the value functions_ V<sup>j</sup> (P) _. That is, those functions are treated as “black box” functions without specific form. Therefore,_ V<sup>j</sup> (P) _could be any “real” or_ ~~j~~ _“proxy” test function_ V<sup>j</sup> _against which the (also arbitrary) target function_ V (P) _is compared. This will allow us to work with different specifications of the mechanism illustrated in Sections 5 and 6._

Theorem 1 is proved in Appendix A. The proof also establishes the specific value of the adjustments among partners that should be implemented. Since these adjustments may be important for the illustrations of specific mechanisms in Section 5, we reproduce those formulas here. For j = 1,..., m define the adjustment and for j = 0, define If all the conditions (11) are to hold with equality for the satisfactory concession period P, the above adjustments are unique. If one or some of the inequalities in (11) are allowed to be strict, then we would have an infinity of possible adjustments.

> 20In this section, it will be convenient to maintain the time explicitly denoted in the notation of Xj(T ), instead of just X<sup>j</sup> T<sup>.</sup>

> 21In real world implementations of our guarantee mechanisms, it will be natural to convert them to period P values. This is, of course, straightforward, but would complicate our notation and we refrain from doing this.

20
**Remark 3.** _Condition_ (12) _in Theorem 1 is in fact stronger than what is actually necessary for the theorem to hold. In the proof of Theorem 1 in the appendix, we show that the following condition is sufficient for its conclusion:_

_where_ α = (α<sup>0</sup> , α<sup>1</sup> ,..., α<sup>m</sup> ) _. That is, in the appendix we show that_ (12) _implies_ (15) _, which means that_ (15) _is a weaker condition than the (simpler one) stated in Theorem 1. Notice that_ (15) _is just the requirement that the weighted value of the project (reflecting the participation of each partner) is above the weighted value of the target value. In this way it is easy to understand why_ (15) _is weaker than_ (15) _: this last condition could fail for some partner_ j _, but the overall weighted value still be above the target because the lack of value for partner_ j _is compensated by the excess of a different partner._ In fact, it is useful to formally state the following result: ~~α~~ **Lemma 4.1.** _If_ V<sup>α</sup> (P) ⩾ V (P) _then_ P _is a satisfactory concession period._ In other words, the condition on weighted value functions (15) is sufficient for having a satisfactory concession period.

# **4.2 Transfer to the government in case of excess value**

~~α~~ The difference V<sup>α</sup> (P)− V (P) defines the excess value that is left to the partners at the end of the satisfactory concession period. This is nonnegative and it can be strictly positive. In the latter case, we could stipulate that the excess value had to be transferred to the government. This is not necessary for the general mechanism, but it might seem advisable as an additional rule. Therefore, we discuss this in more detail in this subsection. Instead of leaving the possible excess value to the participants, the government should require that this excess value is returned to it, in order to insure symmetrical conditions. Thus, if that is, if the project gives a combined value for the partners that is above the target at the first possible concession deadline P0, then we would require that the partners make the transfer of the excessive amount ~~α~~ to the government. On the other hand, if V<sup>α</sup> (P0) − V (P0) ⩽ 0, then Theorem 1’s proof ~~α~~ guarantees that V<sup>α</sup> (P) = V (P) at the satisfactory concession period P. In this case, no transfer to the government would be necessary (just transfers or adjustments among the partners).

If we adopt this rule, then we obtain two consequences. First, each partner receives exactly ~~j~~ α<sup>j</sup> V<sup>j</sup> (P) = α<sup>j</sup> V (P) at the end of the satisfactory concession period P. Second, the adjustments A<sup>j</sup> defined by (13) and (14) are the unique possible adjustments, which gives the extra benefit of avoiding possible disputes among partners over the division of the excess value.

21
It is important to notice, however, that the adoption of this rule _does not_ imply that the ~~j~~ partners do not face risks or receive a predetermined value. Indeed, the functions V (P) may not be constant (as in the case the government guarantees a net present value) and may be defined only at period P (in view of demand, construction, and other risks other than exchange rate). That is, they can be unknown and uncertain ex ante. In fact, we could even have V ~~j~~ (P) = V j(P), in which case no guarantee is provided. What determines the level of certainty that is provided for the partners is defined exactly by the specific format that the ~~j~~ functions V (P) assume. We next evaluate the proposed general mechanism from the point of view of its consequences to the bidding process and the government objectives. Section 5 will discuss specific guarantee mechanism and corresponding target functions. But before this, we will discuss the source of difference between partners in different countries and give conditions to show that those differences are related only to risk aversion with respect to exchange rate.

# **4.3 Foreign partners and their values**

We want to highlight that the guarantee mechanism does not introduce any special advantages to the foreign partners. Indeed, it only corrects for the exchange rate risks that foreign partners face. In other words, if all partners were risk neutral with respect to currency risks, they would be on an equal footing in evaluating the project. In order to establish this, we will introduce the assumption that the exchange rates form a martingale. This is supported by recent economic literature, such as Phillips and Jin (2014) and Fong et al. (1997), among others.

Let us assume for a moment that δ<sup>j</sup> t<sup>= δtforeachj,thatis,thediscountrateisthesame</sup> for all currencies. In this case, our main assumption takes the following form: which is just the standard formulation of a martingale assumption, that is, the expected value of the exchange rate is just the current value.

In order to take into account the possibility that the discount rates are different, let us assume for a moment that the exchange rates are known. Consider Figure 1. In this figure, point A corresponds to values in the currency j in time t = 0; point B corresponds to values in currency j in time t; point C corresponds to values in the domestic currency (0) in time t; point D corresponds to values in the domestic currency in time t = 0.

<!-- Start of picture text --> δ j<br>t<br>A B<br>currency j time<br>X j 0 δt X j t<br>D C<br>currency 0 time<br>time 0 time t<br><!-- End of picture text --> Figure 1: Exchange and discount rates in times 0 and t 22
To bring values in point B to point A, we must use the discount rate in currency j from time t (to time 0), which is denoted δ<sup>j</sup> t<sup>.TobringvaluesfrompointCtopointB,wemust</sup> apply the exchange rate X<sup>j</sup> t<sup>.TobringvaluesfrompointCtopointD,wemustdepreciatethe</sup> domestic currency using the depreciation factor δt. To bring values from point D to point A, we must apply the exchange rate X<sup>j</sup> 0<sup>.Now,ifwewanttoconvertvaluesinpointCtopoint</sup> A, there are two possible pathways: 1) we can convert from C to B and then from B to A; or 2) we can convert from C to D and then from D to A. In the first pathway, we obtain the convergence coefficient δ<sup>j</sup> t<sup>Xj</sup> t<sup>;inthesecond,weobtainδtXj</sup> 0<sup>.Ifthereisnouncertainty,an</sup> arbitrage condition would impose that the two coefficients must be the same, otherwise an investor would have an arbitrage opportunity. Therefore, the following relation must hold if there is no uncertainty: Our main assumption just introduces back the uncertainty into (19). Indeed, if only the _expectation_ of X<sup>j</sup> t<sup>isknown,thenitisnaturaltoassume:</sup>

**Assumption 1** (Martingale Assumption) **.** _For any_ j _,_

Notice that if we assume that δ<sup>jThat is, if the depreciation</sup> t<sup>= δt, then (20) simplifies to (18).</sup> in all currencies are the same, then Assumption 1 just requires that the exchange rates are martingales. On the other hand, the only difference between (19) and Assumption 1 is the uncertainty in the future exchange rates. Therefore, we can say that Assumption 1 is just a martingale condition, adjusted for a possible difference in depreciation. This assumption allows us to show that the _expected_ value of the project is the same for all currencies, as formalized by the following:<sup>22</sup>

**Lemma 4.2.** _Let Assumption 1 hold. Then_

Notice that this result suggests that the value of the project for all partners will be unaffected by the currency used. This might induce the reader to think that risk neutral firms will not appreciate the kind of exchange rate protection that we are considering in this paper. However, even risk neutral firms may benefit from this mechanism because they may lack relevant information regarding the underlying exchange rate dynamics. In any case, in our experience, most investors express strong concerns regarding the exchange rate uncertainty and would like to have mechanisms to curb such risks. Moreover, firms are generally not risk neutral for large stakes. As discussed in Subsection 3.5, it is natural to assume that foreign firms deduce a risk premium from the expected values that they perceive in the projects. The guarantee mechanism affects (reduces) the risk premium R<sup>j</sup> [V<sup>j</sup> (T )] that appears in (6), but it does not necessarily improve the value function for the partners. In particular, the guaran-

> 22In any case, it should be highlighted that the mechanism proposed in this paper do not depend on this assumption and may be considered even if it is not satisfied.

23
tee mechanism does not favor any particular firm.<sup>23</sup> This observation leads to an important remark with respect to the adoption of this mechanism.

**Remark 4.** _Throughout the paper we have been referring to foreign firms as participating in the consortium as partners, thereby supplying equity in foreign currency. However, this is not necessarily the case as domestic firms can procure equity in different countries and may be interested in protecting these values. Even if the consortium is made only of domestic firms, they may decide to protect a fraction of the project in various currencies, in order to hedge themselves with respect to credit that they have taken. In particular, the consortium may define the fractions_ α<sup>j</sup> _protected for each currency in a completely arbitrary way._

# **4.4 Impact of the mechanism on the bidding process**

Recall from section 3.6 that there are K consortia competing for the project and consortium k ∈{1,..., K} values the project at uk. All uk are independent and identically distributed. As anticipated in footnote 16, we consider two cumulative distributive functions (c.d.f.) for the values uk: when there is _no_ guarantee mechanism, the c.d.f. is F<sup>0</sup> ∶ R →[0,1] and when the guarantee mechanism is in place, the c.d.f. is F<sup>1</sup> ∶ R →[0,1].

Let us remember from (7) that the values uk are obtained as the weighted sum of values U<sup>j</sup> of the partners of consortium k ∈{1,..., K}.<sup>24</sup> In turn, the values U<sup>j</sup> are given by expression (6), which takes into account a risk premium R<sup>j</sup> . It is natural to assume that the introduction of the guarantee mechanism reduces the risks for each partner j and, therefore, increases the value U<sup>j</sup> . As a result, the values uk are likely to be higher if it exists at least one partner supplying equity in foreign currency in consortium k. We formalize this intuitive and natural condition as the following:

**Assumption 2.** F<sup>1</sup> _first-order-stochastically dominates_ F<sup>0</sup> _, that is,_ F<sup>1</sup> (x) ⩽ F<sup>0</sup> (x) _, for all_ x ∈ R _._ A particular case of interest is when F<sup>1</sup> is just a location shift of F<sup>0</sup> , that is,

Of course, (21) implies Assumption 2.

We will use this assumption to show the benefits of the introduction of the guarantee mechanism in the following:

**Proposition 4.3.** _Let Assumption 2 hold. Then the introduction of the guarantee mechanism increases the expected revenue of the bidding process._

In the particular case in which (21) holds, we can have a very clear expression by how much the revenue increases, as the following result establishes.

**Lemma 4.4.** _Let_ (21) _holds. Then, the expected revenue with the guarantee mechanism is increased by_ a _, where_ a > 0 _is the number that makes_ (21) _hold._

> 23Some specifications of the mechanism _may_ indeed favor some firms. For this, the guarantee V ̄j may be high or very generous for some j and not for others. This is formally allowed in the specification above. However, in principle the guarantee mechanism does not need to favor any currency. This can be accomplished by requiring that the target function (adjusted for the exchange rate) is the same for all partners, that is, V<sup> ̄j</sup> /X<sup>j</sup> 0<sup>=V ̄0.</sup>

> 24It would be more correct to talk about values Uj,k of partner j of consortium k. We avoid this notation for simplicity.

24
<!-- Start of picture text --> 1 1<br>F 0 F 1 F 0 a F 1<br>a<br>0 0 x x + a<br>(a) F 0 and F 1 satisfy Assumption 2 (b) F 0 and F 1 satisfy (21)<br><!-- End of picture text --> Figure 2: Illustration of Assumption 2

# **4.5 Impact of the mechanism on the government’s objective**

The mechanism proposed above converts the concession period of the project, initially projected to be T , into a random variable T<sup> ̃</sup> that depends on the realization of the exchange rates X<sup>jforj = 1,...,mandthesatisfactionofthecondition(9),thatis,thatthetestfunctionsare</sup> t<sup>,</sup> at least as large as the target functions.

Recall from Section 3.7 that the government is interested in maximizing G(T ). Since T is now a random variable T<sup> ̃</sup> , then the objective function of the government is, naturally, E[G(T<sup> ̃</sup> )].<sup>25</sup> From the comments above, it is clear that the distribution of T<sup> ̃</sup> ∈[P0, P1] depends not only on the exchange rate process for all currencies, but also on the test and target functions. Since we are not making particular assumptions on the test and target functions in this section, we will assume directly something about the random variable T<sup> ̃</sup> , namely:

**Assumption 3.** _The expectation of_ T<sup> ̃</sup> _is equal to the original predefined concession period_ T ∈ [P0, P1] _, that is,_ T = E[T<sup> ̃</sup> ] _._

Assumption 3 requires that if the government wants to achieve a particular concession period, it might adjust the test and targets functions so that the expected value of the concession is just this target period. Thus, we can interpret T = E[T<sup> ̃</sup> ] as the period that the government is aiming at. Another interpretation of Assumption 3 is that the government wants to implement the expectation of T<sup> ̃</sup> , which is defined as T .

We want to provide sufficient conditions to show that, holding T constant, the expectation E[G(T<sup> ̃</sup> )] is just the initial planned valued G(T ), where the proposed mechanism was not in place. This means that the introduction of the mechanism does not modify the expected value for the government. For this, we introduce the following:

**Assumption 4.** _For all_ t _,_ δtpt = p; δtct = c; δtvt = v _and_ qt = q _._

From an _ex ante_ point of view, it is a normal practice to estimate the future values of pt, qt, ct and vt at a constant, present value. Assumption 4 just formalizes this standard practice. Therefore, it can be considered a mild assumption. With this, we have following:

**Proposition 4.5.** _Let Assumptions 1, 3 and 4 hold. Then the government payoff expectation is the same as the originally planned value, that is,_ E[G(T<sup> ̃</sup> )] = G(T ) _._

> 25Recall that in Section 3.7 we have argued, from Arrow and Lind (1970), that the government should be concerned with expected values.

25
ved NmOe eS —— “
<!-- Start of picture text --> te | eeeSS<br>eS ——— ——<br><!-- End of picture text -->
by: ~~j~~ Notice that the right-hand expression above _does not_ depend on P, that is, V (P) is constant for all P ⩾ P0. In this way, the exchange rate g<sup>j</sup> is guaranteed at the time T = P0. If the exchange rate is favorable for partner j, then this partner will pay the government an adjustment to bring it back to the level g<sup>j</sup> if the rule discussed in Subsection 4.2 is in place, or keep this value if not. On the other hand, if the exchange rate is not favorable, the concession may be extended. Our task now is to provide sufficient conditions for the assumptions in Theorem ~~j~~ 1 when V (P) is defined by (24). We need to bound the values of the exchange rates (they cannot become arbitrarily large or low), that is:

**Assumption 5** (Exchange rate is bounded) **.** _Assume that for each_ j _, there exist_ <u>ej, e</u><sup>~~j~~</sup> _such that_ <u>e</u><sup>~~j~~</sup> ⩾ <u>ej > 0</u> _and_ X<sup>j</sup> 0<sup>∈</sup><sup><u>[e</u></sup> j, <u>e</u><sup>~~j~~</sup> ] _for all_ P ⩽ P1 _._

If the guaranteed exchange is sufficiently low, given the values of P0, P1 and the minimal and maximal benefits that the project produce, then the assumption (12) holds. More formally, we have the following:

**Lemma 5.1.** _Let Assumption 5 hold. Assume that_ Bt = ptqt − ct ∈ <u>[B,</u> B] _, with_ B ⩾ <u>B</u> > 0 _and_ δt = 1 _for all_ t _. If_ V<sup>j</sup> (T ) = V<sup>j</sup> (T ) _and_

_then Theorem 1 holds._

# **5.2 Guaranteed return**

Let us assume that the guarantee is a given net present value N set at the beginning of the franchise. For simplicity, let us assume in this subsection that there are just two partners in the consortium, that is, m = 1. The target function in this case is: That is, the target is a previously agreed upon present value that has to be reached by both the domestic and foreign partner in their respective currencies in order for the franchise to end. This particular value can be set through a least present value bidding mechanism<sup>27</sup> . We will who below that the following assumption is sufficient for the conclusion of Theorem 1.

**Assumption 6** (Net present value is bounded) **.** _There exist_ a, b ∈ R++ _such that_ X<sup>1</sup> P<sup>⩾a</sup><sup>_and_</sup> 27While optimal auction design would ultimately depend on contract-specific characteristics, a risk neutral government may accept bids in both domestic and foreign currency.

28
BP ⩾ b _,_ ∀P ∈[P0, P1] _, and:_ The mathematical condition required by Assumption 6 is numerically illustrated below, since the complexity of (26) does not allow a straightforward interpretation. Its motivation, however, should be clear: it sets a lower bound on the exchange rate and the net benefits for a given maximum duration of the project. Indeed, (26) requires that the P1 is sufficiently large such that, even if the benefits are very low in terms of foreign currency and the exchange rate is very unfavorable to the external investor, there will be enough time for him to achieve the previously guaranteed return.

~~α~~ **Lemma 5.2.** _Assumption 6 implies that_ V<sup>α</sup> (P1) ⩾ V (P1) _, that is, the conditions of Theorem 1 are satisfied._

# **5.3 Guaranteed equal returns among partners**

A modification of the above example is that the target function for the foreign partner be defined by the return obtained by the domestic partner at period T . As in the previous subsection, let us assume for simplicity that there are just two partners, the domestic j = 0 and the foreigner, j = 1. An endogenous target function based on franchise parameters can be particularly useful for countries that auction their infrastructure concessions by the lowest tariff or highest bestowal. In order to ensure a level playing field for all investors, the government may be interested in providing an insurance against exchange-rate fluctuation without necessarily guaranteeing a fixed rate of return — that is, eliminating exchange-rate risk without eliminating demand and construction risk. This can be accomplished by letting the return r<sup>0</sup> to be determined as the return of the project in domestic currency at period T = P0: With this, we can define: ~~1~~ Let us adopt the rule discussed in Subsection 4.2, that is, if at P0 = T , V<sup>1</sup> (P0) > V (P0), the ~~1~~ difference V<sup>1</sup> (P0) − V (P0) is returned to the government. From (5) and (27), we can calculate this as: After period T , the domestic partner transfers all the benefits of the project to the foreigner partner. Therefore, the totality of the project’s additional benefits in periods T + 1, T + 2,..., P 29
are added to the foreign investor’s previous benefits.

Since the target function and test function for the domestic investor are equal by default, the validity of the assumption of Theorem 1 depends only on the foreign investor. Similar to Subsection 5.2, the return of the foreign investor relies on the range of the exchange rate and the benefits, with the distinction that since the target function is endogenously defined by the project in period T , we need to impose restrictions on the exchange rate fluctuation only after T = P0.

**Assumption 7** (Both exchange rate and revenue are bounded) **.** _There exist_ a, b ∈ R++ _such that_ XP ⩾ a _and_ BP ⩾ b _,_ ∀P ∈(P0, P1] _, and:_

_where_ T = P0 _._ Similar to Subsection 5.2, we set minimum values for the exchange-rate and benefits for a minimum period P1. However, unlike Subsection 5.2, the boundaries also depend on endogenous values r<sup>0</sup> T<sup>andV1(T),thatis,thedifferencebetweenthepresentvalueofthe</sup> project for the domestic and foreign investors in T . If the exchange rate is unfavorable to the foreign partner before T , the maximum period P1 must be greater, even more so if the exchange rate continues to be unfavorable after the extension.

In these illustrative target functions, clearly a favorable exchange rate does not create a problem for the supplier of equity in foreign currency. She simply returns the excess to the government. However, if the exchange rate conditions are unfavorable, we establish fluctuation boundaries such that an extension of the concession period satisfies the target commited or guaranteed by the government. Of course, the mechanism guarantees only exchange rate within the boundaries assumed above. If the level of depreciation falls outside of those boundaries, then the guarantee would be honored only up to that limits previously<sup>28</sup>

# **6 Specific guarantee mechanisms: test functions**

In this section, we compare the informational requirements for the regulator of alternative test functions characterized respectively by notional (or proxy) and real values, and for different guarantee mechanisms discussed in Section 5. Notional (or proxy) values might be particularly useful for countries with limited regulatory resources and as a means to deal with the growing

> 28 It is important that those limits are explicitly defined before the competitive bidding for the project, since they influence the value of the project for the partners.

30
regulatory burden associated with private capital to infrastructure. Indeed, countries suffer with a lack of specialized and experienced human capital to staff agencies, and their eventual use as political currency affected the quality of regulation, the credibility of the agencies and the perception of society that decisions are sometimes not technically grounded or less than transparent.

Several countries facing such constraints, have sought simpler or less costly alternatives: a multisector agency, thereby avoiding fragmentation of resources and being guided by OECD “Best Practice” recommendations;<sup>29</sup> regulation by contract, where the burden lies in spelling out in the greatest details the rights and obligations of the regulated entity; and contracting out regulatory reviews to independent third parties. Any such alternative faces problems in attending the objectives of ringfencing from undue political interference, reducing the regulatory risk premium, improving regulatory predictability, and avoiding contract renegotiation.

One recurrent problem in regulation is bilateral opportunistic behavior whereas governments have an incentive for expropriating private investors and the latter to gouge consumers, in face of incomplete contracts and information asymmetry respectively, even if it were rational to avoid such behavior from a longer-term perspective. Often, it is the perception in government that the private sector is hiding or distorting information that generates undue friction. To address this issue, one possible criterion for choosing the guarantee mechanism proposed in this paper is the volume of information required, on the presumption that minimizing such requirements decreases information asymmetry between the government and the operator. This is most relevant for governments which face problems accessing accurate operator information and adequately processing such information.<sup>30</sup>

# **6.1 Notional costs and investment**

In general, it might be very difficult for governments to verify the costs of a firm. This opens the possibility of misrepresentation of costs in order to manipulate the application of the guarantee mechanism. One way to avoid this is to consider notional costs, which are defined before the beginning of the project, instead of true or realized/reported costs. For this, it would be necessary to define a sequence of predefined costs <u>ct.</u><sup>31</sup> We will comment in a moment about options to define these predefined costs. We could also consider a notional value for investments, I, if it may be difficult to verify the total amount invested. In this case, the test functions with notional costs can be as follows:

> 29The OECD has advanced 7 principles of best practice: role clarity; preventing undue influence and maintaining trust; independence for decision-making, based on solid governance; accountability and transparency; engagement with stakeholders; adequate funding; and performance evaluation.

> 30According to a major World Bank report, “most developing and transition economies do not have wellestablished cost accounting and auditing systems. And as noted, they often lack regulatory expertise. Thus the information and human capital requirements of different regulatory mechanisms are important.” See Kessides et al. (2004) (p. 122 and passim.)

> 31 As the following discussion makes clear, what needs to be predefined is not exactly the value of <u>ct, but the rule</u> that defines it. If the government tries to define <u>ct</u> a posteriori, then there will be opportunities for manipulation and the guarantee mechanism would not guarantee anything.

31
Perhaps the simplest possibility for the definition of the notional costs is to define them as constant, that is, ct = c for all t. They can also be defined as constant in real terms, that<sup>ct = c.</sup> is, ct = δ<sup><u>c</u></sup> t<sup>,sothat δtHowever,morecomplexschemescanbeconceived.Forexample,</sup> it can be stipulated that the notional costs will be defined by a particular index of prices it, widely available and not manipulable. For instance, this index could be international oil prices. Maybe some price indices can be found that are directly linked with the costs of the particular industry in question. In this case, one can define ct = itc.<sup>32</sup> Similar comments can be applied to the investment. In any case, as the reader can see, the definition is very flexible.

# **6.2 Notional demand**

Another topic that may be difficult to verify in certain cases is demand. As in the previous case, one can define notional demand qt. In this case, the test (proxy) function can be defined as: The notional demand can be defined by a fixed quantity, that is, qt = q. Alternatively, it can be defined as growing following a given index it, such as population growth or economic growth. In this case, qt = itq.

# **6.3 Notional prices**

Prices are, in general, easier to verify and it might not be necessary to use notional values for it. However, as we commented in Subsection 4.5, the government might be interested in letting the consortium define the price freely in order to maximize revenue. In this case, since the price will be determined exclusively by the consortium, it might be convenient to fix a notional price for the purpose of the guarantee mechanism. In this case, the government may define a notional price pt and the corresponding test (proxy) function is: As before, the notional price may be fixed, pt = p or adjusted by some index it, that is, pt = itp.

# **6.4 Notional and real values**

Of course we can combine all of the previous cases, by defining notional values pt, qt, ct and I. In fact, the logic may be extended also to the discount rates δ<sup>j</sup> t<sup>.Theformofthesenotional</sup> values is, to some extent, arbitrary. A particular case of interest is, of course, that they are the real values.

> 32Here, we are obviously denoting by it the accumulated adjustment from time 0 to time t.

32
In any case, giving the target values above, the general test (proxy) functions V<sup>j</sup> (P) can be defined by The choice of which notional or real values to use will depend, of course, in the special cases. An important aspect to consider is the institutional maturity and stability of the country. Using notional values may be better in a situation of poor institutional development. However, the use of notional values increase the risks for companies, since it introduces the possibility that the test or proxy functions do not approximate well their real profits. An important question to ask in this context is how much risk should be borne by the firms and how much by the government.<sup>33</sup> On the other hand, if the test function is the true value and the target functions are guaranteed returns, the government is eliminating all risks for the firms, thus absorbing more than its fair share. Insofar as government may also be in a weak position to manage effectively risks of certain nature or exogenous shocks, this should be avoided. In our view, a good starting point can be that the private party absorbs risks associated with demand and costs, on the presumption that price (tariff of the service) is preset at the beginning of the period and corrected by a certain rule established in contract. That is, the contract establishes only notional values for demand and costs, qt and ct, respectively, but use real values for pt.

# **6.5 Information requirements under different target functions and alternative test functions**

Below we summarize the information requirements for regulators of the 3 guarantee mechanisms discussed in this paper, and under two types of test functions, respectively with notional and real values. In all cases, the exchange rate of interest to partner j at time t X<sup>j</sup> t<sup>isdirectly</sup> observable in markets; by the same token, the discount factor δi is also market observable; the tariff p is set and publicized; and the share of α<sup>j</sup> of partner j is contractually observable.

Table 4 indicates that for countries with limited regulatory resources, the use of notional or proxy test functions would be preferable, though service levels would still need to be observed and assessed independently by the regulator or third party to ensure the provider is fulfilling its obligations. In terms of real values, target functions in 5.2 and 5.3 would be preferable insofar as they demand or can do with less information from the private party.

33Although we have argued that the government should be risk neutral, it is probably better to avoid widespread protection, not exactly because of risk aversion, but because moral hazard. Indeed, due to informational asymmetries, the government may be put in disadvantage in certain contractual arrangements.

33
Table 4: Information requirements for regulators under alternative guarantee mechanisms

|||Target Functions|
|---|---|---|
||Guarantee an<br>Exchange Rate (5.1)|Guarantee a Return<br>(5.2)<br>Guarantee<br>Equal<br>Return<br>Among<br>Partners (5.3)|
|Notional<br>(or proxy)<br>Values<br>(for I, q,<br>and<br>c<br>fxed and<br>known in<br>advance)|For the three mechan<br>lators is directly obser<br>the market at minima<br>plied by the regulated<br>and (bi-lateral) oppor<br>values would only req<br>regulator and investor<br>quantity.|isms, all information required by regu-<br>vable, contractually set or gleaned from<br>l cost; conversely, none needs to be sup-<br> entity, which minimizes renegotiations<br>tunistic behavior.<br>The use of notional<br>uire an underlying model verifed by both<br>that relates investment, costs, tarif and|
|Real Val-<br>ues (forI,<br>q andc)|In<br>order<br>to<br>calcu-<br>late<br>excess<br>beneft<br>caused by the ex-<br>change rate guaran-<br>tee and therefore de-<br>termine<br>the<br>exten-<br>sion of T, the reg-<br>ulator would require<br>real values for I, q<br>and c for each pe-<br>riod.|The regulator must be able to calculate<br>the real I and real net Beneft B for each<br>period.<br>The government does not need<br>to observe individual q and c values di-<br>rectly in every period, even though doing<br>so may reduce opportunistic behavior by<br>the incumbent. If the regulator faces in-<br>formation restrictions, it can audit the in-<br>cumbent on a random basis.|

# **7 Simulating alternative guarantee mechanisms in a real life highway concession**

In this section, we investigate the behavior of the proposed mechanisms using data from CCR NovaDutra, a highway franchise taken place in Brazil from 1996 to 2020. We test target functions from Subsections 5.2 and 5.3 with profit functions constructed under a broad array of different exchange rate scenarios.<sup>34</sup> For that, we suppose the same project have taken in eight developing countries characterized by limited currency market interventions between 1996 and 2020: Brazil, Mexico, Indonesia, Mozambique, Chile, South Africa, Peru and the Philippines. Table 5 compares selected indicators among these countries and shows they are diverse in terms of income, export composition, population and private investment in infrastructure.

> 34 For detailed information about the project, see Appendix B. Due to lack of data regarding prices and demand, it was not possible to simulate the target function discussed in Subsection 5.1 nor propose a test function based on notional values that would be consistent with the project’s cost structure.

34
~~<u>|</u>~~

<!-- Start of picture text --> Brazil Chile Indonesia Mexico<br>8 120100 rae<br>no \A\<br>60<br>Mozambique Peru Phillipines South Africa<br>120<br>100 Ne as<br>60<br>80 yee \*\.<br>1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 aear<br><!-- End of picture text -->
# **7.1 Guaranteed return**

For this Subsection, we will use the target functions outlined in 5.2, that is: We defined N by applying a 5.88% compound rate for 25 periods on the total investment denominated in each local currency.<sup>35</sup> It is important to note, however, that this value can be determined in different ways for distinct countries, including a least present value auction that captures the market’s expected return for a given project in a country with certain characteristics. Therefore, the franchise will be terminated when the value in mixed currency is ~~α~~ at least as high as the target function in mixed currency (that is, V<sup>α</sup> ⩾ V as defined in (15). Results for the simulations are shown in Table 6.

35 This is the internal rate of return of the project when α = 0, obtained using data from the project and Brazil’s CPI inflation as the discount factor. This is further clarified in Appendix B.

36
~~α~~ Table 6: V<sup>α</sup> (by year) and V for each country (in billion LCU)

|Year|Brazil|Mexico|Indonesia|Mozambique|Chile|Peru|Philippines|South Africa|
|---|---|---|---|---|---|---|---|---|
|1996|0.07|0.07|0.07|0.07|0.07|0.07|0.07|0.07|
|1997|0.22|0.20|0.24|0.21|0.21|0.21|0.22|0.22|
|1998|0.39|0.32|0.32|0.37|0.37|0.36|0.40|0.38|
|1999|0.58|0.39|0.36|0.49|0.50|0.49|0.48|0.50|
|2000|0.73|0.50|0.50|0.67|0.68|0.65|0.66|0.68|
|2001|0.98|0.60|0.58|0.91|0.90|0.81|0.86|0.91|
|2002|1.18|0.71|0.59|1.03|1.09|0.97|1.00|1.09|
|2003|1.37|0.91|0.68|1.16|1.26|1.22|1.26|1.15|
|2004|1.53|1.13|0.84|1.28|1.54|1.51|1.56|1.34|
|2005|1.64|1.34|0.95|1.49|1.84|1.85|1.83|1.66|
|2006|1.83|1.58|1.04|1.71|2.27|2.24|2.06|2.03|
|2007|2.01|1.83|1.19|1.89|2.53|2.60|2.30|2.36|
|2008|2.25|2.10|1.39|1.97|3.21|2.93|2.57|2.83|
|2009|2.57|2.52|1.41|2.24|3.32|3.33|2.92|3.08|
|2010|2.74|2.72|1.52|2.59|3.70|3.75|3.23|3.25|
|2011|3.01|3.02|1.70|2.55|4.41|4.26|3.59|3.60|
|2012|3.54|3.43|1.92|2.75|4.82|4.72|3.98|4.16|
|2013|4.00|3.69|2.26|3.03|5.59|5.34|4.44|4.86|
|2014|4.44|4.08|2.39|3.32|6.53|6.02|4.96|5.48|
|2015|5.37|4.78|2.65|3.92|7.49|6.84|5.47|6.23|
|2016|5.68|5.52|2.76|4.87|7.78|7.55|6.07|6.92|
|2017|5.73|5.77|2.93|4.77|8.07|8.00|6.73|6.86|
|2018|6.45|6.11|3.20|4.79|**9.20**|8.70|7.29|7.17|
|2019|**6.95**|**6.41**|3.29|5.04|-|**9.34**|**7.68**|**7.80**|
|2020|-|-|3.47|5.47|-|-|-|-|
|V<br>~~α~~|6.89|6.18|4.06|5.60|9.07|9.04|7.85|7.41|

Note: Bold values indicate that the test function is at least as high as the target function (shown in the last line) and therefore the franchise is terminated.

These results mean the franchise would end in 2018 in Chile, and in 2019 in Mexico, Brazil, Peru, Philippines and South Africa. If we assume revenue and cost as constant for every month throughout the year, the mechanism would shorten the concession by 21 months in Mexico, 14 months in Brazil, 13 months in Chile, 18 months in Peru, 15 months in Philippines and 19 months in South Africa. However, the project in Indonesia and Mozambique would be extended beyond 25 years, until they generated additional 590,772 USD in Indonesia and 128,108 USD in Mozambique. By contrasting these values with 2020 benefits (178,979 USD for Indonesia and 423,363 USD for Mozambique) and assuming yearly revenue as constant each month, we can see that if the benefits and exchange rate from 2020 remained constant, the project would be extended by less than one year in Mozambique (more precisely, 4 months) and less than four years (40 months) in Indonesia.

37
# **7.2 Guaranteed equal returns among partners**

In this Subsection, we will use the target function outlined in Subsection 5.3, that is: Using the project data and each discount factor, it becomes possible to compute the project’s effective return rate in each country after the 25 years of the franchise (T = 25). For that, we use Equation (27).

Table 7: Yearly return rate for the domestic investor at T=25

|Country|r<sup>0</sup><br>T|
|---|---|
|Brazil|5.88%|
|Mexico|6.09%|
|Indonesia|5.45%|
|Mozambique|5.38%|
|Chile|6.47%|
|South Africa|6.11%|
|Peru|6.52%|
|Philippines|6.31%|

Using these values, we calculate the value of the target functions for the foreign partners in each country and compare it with test functions. Results are shown in Table 8.

Table 8: Target and Test function at T=25 for each country.

|Country|V<sup>1</sup>(T)|V<br>~~1~~(T)|V<sup>1</sup>(T)−<br>V<br>~~1~~(T)|
|---|---|---|---|
|Brazil|2583574|2402383|181191|
|Mexico|441460|427495|13965|
|Indonesia|531|543.5|-12.6|
|Mozambique|195085|184045|11039|
|Chile|10332.7|9945.8|387|
|South Africa|676789|626224|50565|
|Peru|1885423|1875655|9768|
|Philippines|125239|123940|1299|

~~1~~ The values of V<sup>1</sup> (T ) and V (T ) are vastly different between the countries and don’t mean anything on their own as we are considering equal It and Bt in local currency across vastly different exchange rates. Therefore, it is useful to compare the magnitude of the adjust compared to the revenue in USD for the last year of the franchise (2020) in each country.

38
Table 9: Extension of the concession period by country

|Country|V<sup>1</sup>(T)−<br>V<br>~~1~~(T)|δX2020B2020|# of months of extension|
|---|---|---|---|
|Brazil|181191|138333|16|
|Mexico|13965|33102|5|
|Chile|387|978.4|5|
|Indonesia|-12.5|50.6|-3|
|South Africa|50565|43243|14|
|Peru|9768|204071|1|
|Philippines|1299|14372|1|
|Mozambique|195085|184045|14|

Table 9 shows that if the transfer rules from Subsection 4.2 were adopted, the compensation the foreign investor would have to pay to the government in Indonesia is equivalent to 3 months of the benefits of the project in 2020 – that is, 25% of the yearly profit. Moreover, if the benefit of the project stayed the same as in 2020 for the subsequent years, the extension of the project in Mexico, Chile and Philippines would last a fraction of one year, and in Mozambique, South Africa and Brazil less than two years.

# **8 Conclusion**

Currency risk remains a significant deterrent to foreign investment flows to developing and emerging economies, particularly for long-duration infrastructure investments. Given the nature of such long-term investments, that take place in non-tradable sectors for which natural hedge is unlikely, hedging instruments are frequently costly, if at all available. Therefore, the search for hedging substitutes is a policy priority for countries in need to build or modernize their infrastructure.

This paper shows that a mechanism which adjusts the length of a concession contract as a means to protect investors supplying equity (and debt) denominated in foreign currency would not only be feasible but provide the government with a gain measured against a social welfare function which values both consumer (user) surplus and the efficiency of firms providing the service, even if the government were not to charge for providing hedge. This would be selfintuitive to the extent that by providing hedge to suppliers of foreign capital, governments attract a larger number of competitors which bring a lower tariff to consumers or greater revenues to government, or both.

Two additional features should be underlined. The mechanism is symmetric. For those that opt for it would either benefit from an extension in the concession contract – if the currency moves against them – or conversely return the excess gains to the government, without altering the original concession length. The mechanism is adaptable to countries with limited regulatory resources insofar as the tests to establish if the partner supplying capital in foreign currency should return excess gains to the government or enjoy additional concession time can be conducted in notional or proxy values, thereby minimizing the probability of (bilateral) opportunistic behavior, while eventually facilitating court decisions.

Finally, the empirical tests provide evidence that using the numbers of a real world 2539
year highway concession, the variation in concession length resulting from the government of 8 countries hypothetically providing a guarantee mechanism under alternative formats or functions are relatively small. It is striking that the mechanism works across countries at different levels of development and with 8 currencies which the only common denominator is the exchange rate regime, namely, they operate with very limited Central Bank intervention.

We conclude that the mechanism proposed, modelled and tested in this paper, would be a valuable addition to the toolkit of emerging and developing countries which have as a policy objective the provision of better infrastructure services to the population and firms. Such services more often than not depend on significant capital and operational expenditures over many years, and outside the reach for many countries facing fiscal restrictions. Even if this were not the case, private capital and operators normally bring about significant efficient gains due to superior governance and management. The guarantee mechanism reduces what is generally regarded as a binding entry barrier for many investors: currency risk. And it is shown that it does with relatively small variations in concession length and positive gains in social welfare.

# **A Proofs**

## **A.1 Proof of of Theorem 1**

In this appendix we provide a proof of Theorem 1. To establish this result, it will be convenient to define the following function: Also, it will be important to convert back the value for partner j, α<sup>j</sup> V<sup>j</sup> (T ), to the domestic −1 currency at period T , that is just (X<sup>j</sup> T<sup>)</sup> α<sup>j</sup> V<sup>j</sup> (T ). The collection of those values define a virtual value for the project that depends on the vector of shares α = (α0,..., αm) and it is given by: This “mixed” value of the project will be used to prove Theorem 1. Indeed, we have the following: ~~α~~ The problem will be to find the period P such that V<sup>α</sup> (P) = V (P).

**Lemma A.1.** _If there is_ P ∈[P0, P1] _such that_

_and_ _then_ P _satisfies the conditions of Theorem 1._ _Proof._ Let P satisfy the assumptions above. We have to show two things: 1) P is a satisfactory concession period; and 2) if P<sup>′</sup> is also a satisfactory period, then P ⩽ P<sup>′</sup> .

40
For j = 1,..., m define the adjustment and for j = 0, define Therefore, which establishes (10). Now we will verify (11) for j = 1,..., m. By definition, that is, (11) is satisfied with equality. Now, for j = 0, we have: where the last inequality comes from (33). This shows that (11) is satisfied for all j = 0,1,..., m. This shows that P is a satisfactory concession period.

Now, we will show the second claim by contradiction. That is, assume that P<sup>′</sup> ∈ <u>[P0,</u> P1] ~~α~~ is also a satisfactory concession period and P<sup>′</sup> < P. Then (34) implies that V<sup>α</sup> (P) < V (P). Since P<sup>′</sup> is also a satisfactory concession period, there exists adjustments A<sup>j</sup> such that (10) and (11) hold. From (11), we have for all j = 0,1,..., m. From (11), we have 41
~~α~~ which contradicts V<sup>α</sup> (P) < V (P). The contradiction concludes the proof.

Therefore, we can conclude the proof of Theorem 1 as follows.

_Proof._ We want to show that there exists P ∈[P0, P1] satisfying the conditions of Lemma A.1. ~~α~~ Note that if V<sup>α</sup> (P0) ⩾ V (P0) then P = P0 satisfies those conditions. Therefore, assume that ~~α~~ V<sup>α</sup> (P0) < V (P0). From the assumptions, is continuous in P and d(P0) < 0. If we can show that d(P1) ⩾ 0, there exists P such d(P) = 0 and P<sup>′</sup> ∈[P0, P1], P<sup>′</sup> < P implies d(P<sup>′</sup> ) < 0, that is, P is the smallest zero of the function P ↦ d(P). This P would satisfy therefore (33) and (34). Thus, it is sufficient to show that d(P1) ⩾ 0. Notice that ~~j~~ where the inequality at the end holds because V<sup>j</sup> (P1) ⩾ V (P1) for every j.

# **A.2 Other proofs**

_Proof of Lemma 4.1._ Let the adjustments A<sup>j</sup> be defined by (13) and (14). Then, which establishes condition 1 of Definition 1. For condition 2, let j ∈{1,..., m}. Then, ~~0~~ For j = 0, recall that X<sup>0</sup> 0<sup>= X0 = 1.Itissufficienttoshowthat α0 [V0(P) + A0 −</sup> V (P 0. )] ⩾ Therefore condition 2 of Definition 1 holds for all j ∈{0,1,..., m}, which concludes the proof.

42
_Proof of Lemma 4.2._ This is an easy application of the properties of the expectation: _Proof of Proposition 4.3._ Since we are assuming symmetry (the distribution for all bidders is the same), independence and risk neutrality with respect to the actual outcomes of the auction,<sup>36</sup> the Revenue Equivalence Theorem applies and the auction format is not relevant to determine the expected revenue from the auction.<sup>37</sup> In fact, in this private value setting, the expected revenue is just the expected value of the second highest valuation. The probability that the second highest valuation is less than x is given by G<sup>i</sup> (x) = F<sup>i</sup> (x)<sup>K</sup> + KF<sup>i</sup> (x)<sup>K−1</sup> [1 − F<sup>i</sup> (x)],<sup>38</sup> for i = 0,1, depending whether the guarantee mechanism is in place or not. We will show that G<sup>1</sup> (x) ⩽ G<sup>0</sup> (x) for all x ∈ R, that is, G<sup>1</sup> first order stochastically dominates G<sup>0</sup> . This is sufficient for the conclusion of the theorem since, as it is well known, it implies that the expectation with respect to G<sup>1</sup> is higher than the expectation with respect to G<sup>0</sup> . The proof of the dominance of G<sup>1</sup> is elementary, but included for reader’s convenience.

Fix x ∈ R and define t = F<sup>1</sup> (x) ∈[0,1] and s = F<sup>0</sup> (x) − F<sup>1</sup> (x) ∈[0,1], with t + s ∈[0,1]. Then, Since t + s ∈[0,1], K −(K − 1)(t + s) ⩾ 1 and from the binomial formula and t, s ⩾ 0, we have (t + s)<sup>K−1</sup> − t<sup>K−1</sup> ⩾(K − 1)t<sup>K−2</sup> s. Using these two inequalities in (35), we obtain that is, G<sup>0</sup> (x) ⩾ G<sup>1</sup> (x), which is what we needed to show.

> 36In other words, the participants may have risk aversion with respect to exchange rate, for instance. The assumption of risk neutrality here is restricted to the auction itself.

> 37See Menezes and Monteiro (2004) for the Revenue Equivalence Theorem.

> 38See, for instance, Menezes and Monteiro (2004, p. 19).

43
_Proof of Lemma 4.4._ Using the notation in the proof of Proposition 4.3, the revenue in situation i = 0,1 is ∫R xdG<sup>i</sup> (x). Since F<sup>1</sup> (x + a) = F<sup>0</sup> (x), we have Therefore, This establishes the result.

_Proof of Proposition 4.5._ Under the stated assumptions, G(T ) is given by: Where μ ∈ R<sup>+</sup> is how the government values the social benefit brought about by the firm and τ is the transfers to the governments. Therefore, G(T ) is an affine function of T and E[G(T<sup> ̃</sup> )] = G(E[T<sup> ̃</sup> ]). Since by assumption E[T<sup> ̃</sup> ] = T , we conclude that E[G(T<sup> ̃</sup> )] = G(T ), as we wanted to show.

~~j~~ _Proof of Lemma 5.1._ We will first observe that (12) holds, that is, V<sup>j</sup> (P1) ⩾ V (P1). Indeed, ~~j~~ where the last inequality comes from (25). Since V<sup>j</sup> and V are continuous and (12) is verified, the assumptions of Theorem 1 are satisfied and the result follows.

_Proof of Lemma 5.2._ Let us denote α<sup>0</sup> = α and α<sup>1</sup> = 1 − α. Observe that, since X<sup>1</sup> (P1) ⩾ a and 44
B(P1) ⩾ b, V<sup>α</sup> (P1) satisfies: Thus: ~~α~~ From Assumption 6, we have V<sup>α</sup> (P1) ⩾ V (P1): _Proof of Lemma 5.3._ Since X(P) ⩾ a and B(P) ⩾ b, V<sup>1</sup> (P) satisfies: From (30): 45
# **B Simulations’ data**

The project data used for the simulations in Section 7 stems from CCR NovaDutra, a highway franchise in Brazil that was in place between 1996 and 2020. Yearly revenue, operational cost and investment data in current values can be seen in Table 10.

Table 10: CCR Nova Dutra – Yearly Revenue (pqt), Investment (It) and Cost (ct)

|Year|pqt|It|ct|
|---|---|---|---|
|1996|82,791|114,950|17,108|
|1997|202,782|133,364|44,662|
|1998|225,373|20,2307|53,149|
|1999|243,209|131,520|128,332|
|2000|281,570|73,650|85,060|
|2001|314,398|75,917|114,949|
|2002|353,779|33,661|157,616|
|2003|394,573|49,846|62,152|
|2004|500,107|70,063|81,315|
|2005|551,542|88,297|65,218|
|2006|611,791|75,866|79,655|
|2007|665,577|100,411|86,238|
|2008|748,324|159,720|92,432|
|2009|782,241|172,692|160,625|
|2010|900,052|203,472|79,348|
|2011|993,056|229,810|83,078|
|2012|1,050,626|197,592|82,509|
|2013|1,113,905|219,078|79,813|
|2014|1,150,439|241,056|77,840|
|2015|1,168,369|137,177|87,125|
|2016|1,210,658|89,337|87,664|
|2017|1,297,371|165,574|84,563|
|2018|1,350,917|172,908|93,001|
|2019|1,429,118|39,262|211,450|
|2020|1,320,042|102,489|143,212|
|Sum|18,942,610|3,280,019|2,338,114|

Source: own elaboration with data from Brazil’s Ministry of Infrastructure. Note: To keep notation of investment as a one-time disbursement (I0), one could consider investment to be zero and include it as part of operational cost ct.

To perform simulations for each of the eight countries, we use national Consumer Price Index rates as discount factor δt and inflation adjusted US Dollar exchange rates Xt. These values are shown in Tables 11 and 12.

46
Table 11: Inflation rate (it) and exchange rate (Xt) by country.

||Bra|zil|Mex|ico|Ind|onesia|Moza|mbique|
|---|---|---|---|---|---|---|---|---|
||it (%)|Xt|it (%)|Xt|it (%)|Xt|it (%)|Xt|
|1996|9,6|0,99|27,7|0,13|6,0|0,00042|48,5|0,089|
|1997|5,2|0,95|15,7|0,14|10,3|0,00023|7,4|0,091|
|1998|1,7|0,89|18,6|0,14|77,6|0,00023|1,5|0,088|
|1999|8,9|0,60|12,3|0,15|1,9|0,00027|2,9|0,083|
|2000|6,0|0,61|9,0|0,16|9,3|0,00021|12,7|0,076|
|2001|7,7|0,50|4,4|0,17|12,5|0,00021|9,1|0,059|
|2002|12,5|0,45|5,7|0,17|9,9|0,00026|16,8|0,059|
|2003|9,3|0,45|4,0|0,15|5,2|0,00029|13,4|0,065|
|2004|7,6|0,50|5,2|0,15|6,5|0,00027|12,7|0,076|
|2005|5,7|0,61|3,3|0,15|17,1|0,00029|7,2|0,077|
|2006|3,1|0,69|4,1|0,16|6,6|0,00033|13,2|0,076|
|2007|4,5|0,78|3,8|0,16|6,6|0,00032|8,2|0,079|
|2008|5,9|0,84|6,5|0,16|10,2|0,00030|14,5|0,093|
|2009|4,3|0,81|3,6|0,14|2,8|0,00035|3,8|0,085|
|2010|5,9|0,96|4,4|0,15|7,0|0,00039|12,4|0,076|
|2011|6,5|1,04|3,8|0,15|3,8|0,00039|11,2|0,096|
|2012|5,8|0,92|3,6|0,15|4,3|0,00037|2,6|0,099|
|2013|5,9|0,87|4,0|0,15|7,7|0,00031|4,3|0,096|
|2014|6,4|0,84|4,1|0,15|8,4|0,00033|2,6|0,093|
|2015|10,7|0,65|2,1|0,13|3,4|0,00031|3,6|0,075|
|2016|6,3|0,66|3,4|0,11|3,0|0,00032|17,4|0,055|
|2017|3,0|0,72|6,8|0,12|3,6|0,00032|15,1|0,062|
|2018|3,8|0,64|4,8|0,12|3,1|0,00030|3,9|0,066|
|2019|4,3|0,61|2,8|0,12|2,7|0,00032|2,8|0,064|
|2020|4,5|0,48|3,2|0,11|1,6|0,00031|3,1|0,059|

Source: own elaboration with data from the International Financial Statistics (IMF).

47
Table 12: Inflation rate (it) and exchange rate (Xt) by country.

||C|hile|South|Africa|Pe|ru|Phili|ppines|
|---|---|---|---|---|---|---|---|---|
||it (%)|Xt|it (%)|Xt|it (%)|Xt|it (%)|Xt|
|1996|6,6|0,0024|9,3|0,23|11,5|0,41|7,5|0,038|
|1997|6,1|0,0024|6,2|0,23|8,6|0,40|5,6|0,035|
|1998|4,7|0,0023|9,0|0,20|7,2|0,38|9,2|0,027|
|1999|2,3|0,0020|2,2|0,18|3,5|0,34|5,9|0,029|
|2000|4,5|0,0019|7,0|0,17|3,8|0,33|4,0|0,026|
|2001|2,6|0,0016|4,6|0,14|2,0|0,32|5,3|0,023|
|2002|2,8|0,0015|13,5|0,12|0,2|0,32|2,7|0,023|
|2003|1,1|0,0018|-1,6|0,17|2,3|0,32|2,3|0,022|
|2004|2,4|0,0019|2,2|0,19|3,7|0,33|4,8|0,022|
|2005|3,7|0,0021|2,0|0,19|1,6|0,34|6,5|0,023|
|2006|2,6|0,0020|4,8|0,19|2,0|0,33|5,5|0,025|
|2007|7,8|0,0023|7,6|0,19|1,8|0,35|2,9|0,028|
|2008|7,1|0,0018|9,3|0,17|5,8|0,38|8,3|0,030|
|2009|-2,6|0,0022|6,2|0,18|2,9|0,38|4,2|0,029|
|2010|3,0|0,0025|3,3|0,20|1,5|0,40|3,8|0,032|
|2011|4,4|0,0022|6,3|0,21|3,4|0,41|4,7|0,034|
|2012|1,5|0,0024|5,8|0,20|3,6|0,44|3,0|0,035|
|2013|2,8|0,0022|5,2|0,17|2,8|0,43|2,6|0,035|
|2014|4,6|0,0020|5,3|0,16|3,4|0,42|3,6|0,034|
|2015|4,4|0,0018|5,2|0,14|3,4|0,39|0,7|0,034|
|2016|2,7|0,0019|7,1|0,13|3,6|0,37|1,3|0,032|
|2017|2,3|0,0021|4,5|0,15|3,0|0,39|2,9|0,030|
|2018|2,6|0,0018|4,4|0,15|1,5|0,38|5,2|0,030|
|2019|3,0|0,0017|4,0|0,14|2,3|0,38|2,5|0,031|
|2020|3,0|0,0018|3,1|0,13|2,0|0,36|2,6|0,032|

Source: Own elaboration with data from the International Financial Statistics (IMF).

In Subsection 7.2, we use the rate of return of the project to estimate NPV target functions for each country. This rate (5.88%) is obtained through Equation B, where pqt, ct and It are shown in Table 10 and δt is obtained using Brazil’s inflation rate it in Table 11.

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