Real options valuation of photovoltaic power investments in existing buildings

Highlights

• Rooftop PV projects tend to be undervalued when appraised by classical NPV methods.

• GBM and Poisson jump processes are proposed for representing stochastic uncertainties.

• Uncertainty upon panel costs and tariffs give substantial value to deferral option.

• Option value provide the opportunity cost of using building rooftop for other purpose.

• Results suggest that many rooftop PV projects might be being prematurely rejected.

Abstract

Renewable power generation based on solar energy is deemed to be a key instrument to reduce the carbon footprint of modern economies. Collectively, buildings are an energy-intensive consumption sector. Therefore, existing building rooftops are seen as a target for massively deploying photovoltaic (PV) distributed generation. Nevertheless, estimating the benefits and risks of investing in rooftop PV systems is indeed a challenging task due to the large uncertainties that affect tariffs, technology costs, and regulatory policy. After reviewing the literature and identifying the current gaps, this article develops a method based on Real Options theory for appraising investments in PV generation systems to be installed on the rooftop of existing buildings. The option value of differing the investment decision and the problem of the optimal time to invest in irreversible PV assets are addressed by an advanced valuation method based on stochastic simulation, linear regression, and backward dynamic programming. In this work, returns of self-generation PV investments are subjected to uncertainties upon declining investment costs and fluctuating electricity tariffs, which are represented by appropriate exogenous stochastic processes. In order to test the practicability of the proposed decision-making framework, the valuation of an exemplary rooftop PV-system in a government building is considered. Results show that while standard appraisal methods wrongly reject the rooftop PV project now and in the future, the option valuation method finds optimal to hold the opportunity open in order to reconsider to invest later. In addition, the method provides an objective value of the opportunity cost of using the building rooftop for another purpose. The proposed valuation approach would result in better investment allocation and faster development of distributed PV power capacity contributing thereby to enhance the sustainability of current energy systems.

Introduction

General public, researchers, companies, and regulatory agencies have focused their attention on clean and sustainable energy sources because of environmental concerns and the large and paradigmatic structural changes faced by the electric industry over the last decade. Presently, fossil fuels count for a major fraction of global electricity generation and therefore they are a main anthropogenic source of carbon dioxide emissions. In this context, renewable generation technologies are regarded by policymakers as the main strategic instruments for substituting fossil fuels from the generation mix in order to meet energy sustainability and emission targets at a global scale. Photovoltaic (PV) generation is now a safe and mature technology among renewable generation types. Moreover, in many countries, solar power is currently supplying a significant part of the total electricity demand, especially in Europe [1], where it is claimed that at the end of 2020, global PV generation capacity has been estimated in 613 GW, growing at a mean annual rate of 22$\text{\%}$ over the last five years.

Buildings located in cities are the cause of near $40\text{\%}$ of global energy consumption and therefore, they play an important role in the energy market. Buildings’ energy demand seems to keep growing worldwide in the coming years [2]. Thus, the building sector represents a huge opportunity for cutting emissions by means of energy efficiency measures and the deployment of distributed renewable generation, such as rooftop PV systems. In this context, distributed renewable energy generation, such as rooftop solar photovoltaic, has grown exponentially over the past few years [1].

Renewable projects are typically capital-intensive investments also exhibiting substantial irreversibility, as assets under unfavorable scenarios can only be recovered by assuming a large or total loss in value. However, most renewable projects have some degree of strategic flexibility to decide the time to proceed with the investment. Consequently, the big challenge for decision-makers is dealing with the intricate puzzle of uncertainty, irreversibility and flexibility embedded in the PV project.

Only suboptimal investment decisions can be derived from the NPV rule when a decision-making process is characterized by irreversibility, uncertainty, and embedded flexibility [[3], [4], [5]]. Hence, the Real Option Valuation (ROV) method has been successfully used to support decision-making facing highly uncertain environments with managerial flexibility since it assesses the implied value of flexibility [6]. Strategic flexibility allows decision-makers to modify or defer investment plans in response to the arrival of new information (though never complete) that reduces the uncertainty.

The power industry is a classic example of a sector with capital-intensive investments. This fact and the increasing uncertainties introduced with deregulation of electricity markets have become the ROV a particularly suitable framework for assessing investments in power infrastructure. Hence, ROV has been successfully applied to generation projects considering different types of options and uncertainties. In fact, flexible investments in nuclear power stations, hydroelectric plants and renewable energy projects have been appraised by ROV [[7], [8], [9]]. In addition, ROV are used in selecting generation technologies and in the optimal scheduling of multi-fuel power plants [[10], [11], [12], [13]]. Although this technique has grown in importance, the use of ROV in the context of renewable generation investments is still limited. Literature on the application of ROV to PV investments is even sparser.

Thus, the latest and highest quality articles have explored the use of the ROV approach in transmission planning decisions [14,15], and in generation expansion investments. Accordingly, authors in Ref. [16] have provided a survey of the ROV method applied to electricity generation projects. In addition, one of the most recent papers [17] carries out an exploration of the ROV method to support renewable generation decision-making in developing countries. Particularly, this work provides a state-of-the-art survey about ROV applied to renewable energy generation. Important and recent research applications of ROV to generation technologies includes: hydroelectric projects [16,18,19], wind power [[20], [21], [22], [23], [24], [25]] and photovoltaic energy [26,27].

In addition, the work in Ref. [28] presents an investment planning model that integrates learning curve information on renewable power generation technologies into a dynamic programming formulation featuring real option analysis, in which the empirical analysis is based on data for the Turkish electricity supply industry. In Ref. [25], an analysis of investments in wind generation at the Baltic Sea was conducted, in which three different incentive schemes were considered (feed-in tariffs, feed-in premiums and tradable green certificates). Moreover, authors in Ref. [20] applied ROV to a wind generation project considering the electricity price, the amount of energy and government subsidies in the UK. Similarly, the proposal in Ref. [29] applied ROV to a wind generation project in Taiwan from which they conclude that the investment value increases as a result of an increase in the length of time taken to exercise the option, the risk-free discount rate, the price of the underlying asset and volatility. In Ref. [23], a ROV-based method to valuate small wind turbine generation was proposed.

Furthermore, in order to find a price for encouraging hydro-power projects in Norway, an ROV-based model was developed by Bockman [18]. Likewise, in Ref. [19] the ROV method has been applied for a hydroelectric generation project to estimate the value of the investment opportunity and also to find the incentive-price based on a price forecast.

Even though there is a significant amount of research that applies the ROV method in the context of renewable energy investments, the contributions to the field of photovoltaic projects based on ROV are still scarse. Moreover, financial analyses are developed considering specific countries with different policy regulations, therefore limiting the generalization. In addition, according to Ref. [30], distributed photovoltaic generation does not compete for land use and therefore, it should be analyzed from the standpoint of the final consumer who perceives electricity prices rather than electricity generation costs. Incorporating PV to existing buildings is one case belonging to this category, which will be addressed in this work.

One of the latest papers [31] suggests an ROV-based model for evaluating large-scale photovoltaic generation plants in China, considering tariffs, investment cost, conventional energy cost and changes of unit generating capacity. Additionally, in Ref. [32] an optimal level of feed-in tariffs policy in 30 provinces of China for photovoltaic power generation is estimated based on ROV, but not for residential users. Also, Gomes [33] addresses a DCF-based technical-economic analysis considering a policy for the integration of PV systems in Brazil, and the potential penetration of PV-based distributed generation in residential buildings is estimated.

Going deeper into the analysis of photovoltaic project valuation, in Ref. [26] the authors argue that investors find more attractive to delay the investment in PV technologies while preparing Solar Ready Buildings in order to adopt PV technologies in the future when their prices are lower, energy prices are higher, or stricter environmental regulations are in place. However, this work uses a binomial tree for solving the option valuation problem, with the consequent limitations and simplifications inherent to this method. Drawbacks of this analytical approach to option valuation are overcome by advanced numerical techniques based on stochastic simulation, such as the well-known Least-Square Monte Carlo (LSM) method [34]. According to Ref. [35], complex real investments with embedded real options and multiple uncertain state variables can be economically evaluated by extending the LSM method, despite the fact that it was originally thought for valuing American financial options. The LSM approach has been successfully applied in various industries such as R $\&$ D projects [36], Internet companies [37] and pharmaceutical companies [38]. In fact, assessing ROV in power investments by using the LSM method is a recent development and the review of the literature in the field reflects a still limited use of this valuation tool. Works like [[39], [40], [41]] have applied LSM to the power generation sector while in the power transmission sector, LSM has been used by Refs. [42,43] for assessing investments in flexible AC transmission devices (FACTS). Additionally, a recent work [44] has conducted an economic research based on LSM for investment decisions faced by solar panels producers.

In addition, research on the economic benefits of installing PV generation on existing buildings that were not originally designed for PV generation should be conducted. Authors in Ref. [45] have contributed by using the ROV method to estimate the opportunity cost of designing a building with the capability of install mechanical cooling in the future only if natural ventilation is not sufficient. Additionally, authors in Ref. [46] have conducted research with the aim of finding the social acceptance (public perceptions) of different renewable energy technologies for buildings in Helsinki. However, adopting onsite renewable generation in existing buildings has not been properly analyzed, not only from a technical perspective, but also in terms of the regulatory policies, the financial aspects, and the long-term uncertainties. Moreover, research on the photovoltaic investment decision-making process in existing buildings based on ROV is not readily available in the literature and finding ROV properly solved by using the LSM approach is even more infrequent.

Review of the current literature reveals a considerable gap between modern finance methods and conventional decision frameworks used by practitioners when assessing PV projects for self-generation. Because of this, many onsite PV generation projects might be being discarded too early. Accordingly, research focused on reducing this gap is urgently needed in order to improve allocation of capital resources, reduce overall supply costs, and enhance reliability and sustainability of current energy systems.

Finally, Fig. 1 graphically illustrates a summarized classification of the surveyed literature in order to facilitate the analysis of the overlapping fields of renewable energy, sustainable buildings and valuation methods according to the applications and the methods used.

In order to make a contribution to the field of valuation of distributed renewable energy systems and aid in decision-making, in this work we introduce a methodological framework to assess rooftop solar photovoltaic investment projects in existing buildings based on the ROV approach. The option valuation problem is solved by means of the LSM method. Uncertainties regarding tariff prices and investment costs were incorporated by specifying suitable stochastic processes and applying Monte Carlo simulation. The option to defer the rooftop PV investment was taken into account; therefore, the question of when to invest is answered after a real options analysis. In addition, a discussion of capital cost and option expiration time is examined by a sensitivity analysis. The sensitivity analysis performed allows creating decision regions and determining threshold values for triggering immediate investments. This framework also provides quantitative support for the decision-making process as concerns the best timing for the investment. To demonstrate the numerical practicability of the proposed approach, the assessment of a PV project deployed on the rooftop of a large government office building was taken as an exemplary case study.

In the next section, background on concepts and methods in Real Option valuations is summarized. Also, the advantages of simulative techniques over analytical valuation methods are highlighted. In Section 3, the stochastic simulation method is introduced and a framework for evaluating solar generation investments in buildings is proposed. Section 4 presents a numerical example of a PV project installed on the rooftop of an existing large office building in order to test the option-based valuation methodology proposed in this work. Quantitative results and a sensitivity analysis are provided in order to demonstrate the feasibility and usefulness of the proposed valuation method. Finally, the discussion provided in Section 5 concludes the article.