Equity free cash flow based approach to valuation of credit default option embedded in project finance
Abstract In this paper we present a novel approach towards the financial rationality assessment of commercial real estate developments being realized within a project finance framework. The proposed solution is based on Cox Ross Rubinstein (CRR) binomial lattice that is utilized to assess the price of the loan default option inherent to the financing structure of these types of projects and, consequently, their values for equity providers.
The research gap addressed in this work originates from two main sources. Firstly, our solution of default option valuation is based on equity cash flow (ECF ) - an approach commonly used in project finance and analysis of real estate projects, which according to our knowledge, has not been yet applied for such purpose. We argue that real estate projects, executed in a given project finance framework, due to their high leverage and nonrecourse debt obligations, contain embedded and particularly valuable default options and thus for practical reasons investors require real options financial layout that is based on discounted ECF . Secondly, the commonly used valuation techniques of real options included in real estate projects do not take full advantage of CRR ability to valuate real options for changing the value of the exercise price, which in the case of real estate projects, arises from the structured development of loan taking and repayment. Furthermore, contrary to closed form option pricing formulas, the presented method makes it possible to identify the optimal moment of option execution based on the loan to value ratio. In cases where the value of equity is lower than 0, rationally acting investors should abandon the project.
We support our solution with a case study embedded within a professional framework, providing further contribution to the research and practitioners’ community.
1. Introduction
In today’s turbulent economic reality and in the context of dynamically changing real estate market conditions, effective and strategically viable investment decisions become even more difficult. This situation presents multiple challenges for financial analytics, and directly exposes various deficiencies of typical DCF based investment valuation techniques, whose drawbacks have been thoroughly studied in the past by many authors (Feinstein and Lander (2002);….) The introduction of the real options concept by Stewart Myers in 1977 (Myers 1977) created a new theoretical and practical environment that allowed to address some of these issues by recognizing the strategic nature of investment process and provided rational explanation of the investors behavior and approach towards project risk assessment. This crucial concept behind the so-called “real option valuation” is based on the observation that investors are able to reduce the probability of project negative outcome through active management and consecutive decisions made upon the arrival of revised project or market data. In particular, the real options approach has been employed to explain how the existence of nonrecourse debt obligations in projects affects their intrinsic value and presents the advantages that such knowledge may bring to investors analyzing the financial rationality of a given endeavor (Gendrin, Lai, Soumare, 2007). From this point of view, having several available discounting methods to choose from (Fernandez, 2007), much of the research efforts has been focused on FCF as a platform for real options analytics (Luehrman 1998; Amram and Kalitulake, 1999; Trigeorgis, 1999). Unfortunately, application of such models, in the case of many real estate projects implemented within a given project finance framework has a limited practical usage. In the case of such projects, direct focus on investors’ returns, straightforward benchmarking with other alternative investments and the fact that the vast majority of ventures are project-financed has led to a situation where the methodology which dominated the real estate practice is the one based on equity cash flows. Its advantages for large-scale project valuation, which requires significant capital investment volumes, has been recognized and attempts have been made to improve its accuracy and applicability within the project framework (Esty, 1999). The conducted literature review has revealed only one existing model (Winsen, 2010) which employs binomial option structure to value non-recourse loan in project finance. In contrary to that, our paper focuses on providing a valuation framework for default option using equity cash flow analysis, which by taking into account the investors’ position, should make it possible to make more optimal business decisions. The proposed solution is also based on binomial trees, which in comparison to closed form solutions, is distinguished by computational flexibility and the possibility of determining the optimal moment of option exercise through investment abandon decision over the entire project lifespan. In addition, our model assumes that at each stage of the project, the logic behind the investor behavior induces two different sets of actions depending on loan to value ratio of the property (which in the case of real estate projects typically corresponds to the majority of investment vehicle value): - If equity value is higher than zero, i.e. the project value exceeds the remaining debt balance, the investors will choose to continue their engagement in the project and keep settling their credit liabilities (repayment), alternatively - If equity value is lower than zero, i.e. the project value is lower than the remaining loan balance, the investors will decide to exit the project by ceasing to repay the loan. Given the fact that investors have the right but not the obligation to undertake such actions without additional financial recourses, their perception of the project risk should decrease, having also a positive impact on their project financial rationality assessment. The remaining part of the article is organized as follows. In Section 2, we present the theoretical background of the equity free cash flow based approach to valuation of credit default option embedded in project finance. Section 3 contains our case study which presents application of the introduced methodology in a professional environment. Section 4 presents our concluding remarks.
2. The model
We set up the model of valuating credit default options in project finance using an equity cash flow approach. Figure 1 below illustrates eight stages of the credit default option valuation.
Diagram 1
Stages of the model
Calculation of standard NPV ECF based on the cost of equity determined by Stage 1 CAPM model and Hamada equation assuming hypothetical D/E ratio and target loan repayments schedule
Preliminary calculations of market values of equity at every stage of the Stage 2 project based on ECF estimation and initial costs of equity calculated based on hypothetical D/E ratio.
Application of Excel’s solver software to transform the hypothetical D/E in cost of equity capital estimation into a real D/E within the following Stage 3 constraints: D/E in cost of equity estimation = D/E at each stage of NPV
calculation; results in final NPV ECF calculation
Stage 4 Market WACC calculation based on real D/E and D/(D+E) ratios
PV FCF and NPV FCF calculation based on market WACC, where NPV FCF = Stage 5 NPV ECF
Monte Carlo simulations of standard deviation of lognormal rate of return (r) Sage 6 calculated based on PV FCF and chosen risk factors
Application of RCR method refined by Copeland and Antikarov (2001) in Stage 7 construction of event tree based on PV FCF
ECF decision tree construction; application of RCR option pricing in valuation Stage 8 of credit default option. Assumption: rational decision on the date of default option expiration: MAX ( ,where 0 means the decision to default ; 0) Source: Compiled by the authors.
The starting point of the analysis is the valuation of the project without flexibility, using the standard net present value method (stage 1). According to Fernandez (2007), there are ten cash flow discounting methods, which, if properly applied, should lead to identical NPV results but different IRR (Mielcarz and Mlinari č 2014). From those, the two most popular include ECF and FCF techniques. (1)
NPV FCF = NPV ECF
Since our model takes the equity providers’ perspective into account, we use expected equity cash flow (ECF) and hence, the required return on equity (K e).We estimate the required return on equity using the capital asset pricing model (CAPM):
(2)
Ke= R F+ βLPM
To adjust the market β for leverage effects, we use Hamada formula (Hamada, 1972), which defines the relationship between the levered beta to the asset beta ( βU). This is:
(3)
βL= βU + (D/E) βU (1-T)
The above equation implies that with changes in the company leverage, the subsequent periods discount rates will also vary, contributing to additional business uncertainty. However, during the stages 1 of the model (see Diagram 1), we deal with the preliminary stage of valuation using hypothetical D/E ratios, which results in preliminary NPV values. The stage 2 also involves calculation of preliminary equity market value at every individual cash flow time period (t). This is done by discounting the outstanding ECF to the end of each subsequent period of analysis and just like in the first step, we use the cost of equity based on hypothetical D/E ratios.
(4)
Et=PV t+1 [Ke t+1 ;ECF t+1 ]
In the stage 3, the preliminary NPV and preliminary equity values at every individual cash flow time period are being transformed into final market values, for which purpose the Excel’s solver optimization software is used. To achieve the result, the constrain is set that the D/E ratios in cost of equity estimation (according to formula 3 and further 2) for a given time period must be equal to D/E ratios of the same period, where E t is calculated based on formula 4. This final NPV value along with the option of credit default will determine the true value of the project finance company with flexibility. Subsequently, at stage 4 , the final market values of equity – obtained in the previous step - make it possible to calculate the time-varying, market weighted average cost of debt and shareholder’s equity after tax (WACC).
(5)
WACC t=[E t-1Ke t+D t-1Kd t(1-T)] / [E t-1 + Dt-1]
Arriving at WACC based on market values, we move to stage 5 and are then able to discount
FCF of a given project and thus calculate NPV FCF ., where NPV FCF is the difference between the present value of operational FCFs (PV FCF ) and the present value of investment outflows
(PV I). As we stated before, the value of the NPV based on FCF is calculated using market WACC (formula 5) and will be equal to the NPV based on ECF.
At stage 6 , the PV FCF is the basis for continuous compounding returns (r) calculation (Copeland and Antikarov, 2001), which is subsequently used to estimate its standard deviation ( σ) by means of Monte Carlo simulation software.
(6)