Paulo Jorge Pereira

Optimal Investment Decisions for Two Positioned Firms Competing in a Duopoly Market with Hidden Competitors

This paper extends the literature dealing with the option to invest in a duopoly market for a leader-follower setting. A restrictive assumption embodied in the models in the current literature is that investment opportunities are semi-proprietary in that the two identified or positioned firms are guaranteed to hold at least the followers position. More competition is realistically captured in our model by introducing the concept of hidden rivals so that the places in the market can be taken not only by positioned firm but also by these hidden competitors. The value functions and the optimal triggers for the positioned firms differ materially in settings with(out) the presence of hidden rivals. Unlike existing models, our model allows for (a)symmetric market shares and investment costs for the leader and the follower. Cooperative entrance by the two positioned firms is also modelled.

Optimal subsidies and guarantees in public–private partnerships

In this paper, we analyse how certain subsidies and guarantees given to private firms in public–private partnerships should be optimally arranged to promote immediate investment in a real options framework. We show how an investment subsidy, a revenue subsidy, a minimum demand guarantee, and a rescue option could be optimally arranged to induce immediate investment, compensating for the value of the option to defer. These four types of incentives produce significantly different results when we compare the value of the project after the incentive structure is devised and also when we compare the timing of the resulting cash flows.

Reaching an Optimal Mark-Up Bid through the Valuation of the Option to Sign the Contract by the Successful Bidder

This paper aims to establish a support decision model by which an optimal mark-up (profit margin) in the context of a bidding process is reached through the valuation of the option to sign the contract assuming the contractor is chosen to perform the project. The price included in the bid proposal remains unchanged from the moment the offer is sealed until the contractor has the right - but not the obligation - to sign the contract, whereas construction costs vary stochastically throughout the period. Contractors should only sign the contract if the construction costs, at that moment, are lower than the price previously defined. We evaluate the option using an adapted version of the Margrabe (1978) exchange option formula and we also assign a probability of winning the bid for each profit margin using a function that respects the inverse relationship between these two variables. We conclude that to the higher value of the option - weighted by the probability of winning the contract - corresponds the optimal mark-up bid. Finally, we consider the existence of penalty costs which makes the model more efficient in explaining what actually takes place in some legal environments; we then conclude that the option to sign the contract and, therefore, the optimal mark-up bid are affected by their existence.

Heterogeneous beliefs and optimal ownership in entrepreneurial financing decisions

Our setting comprises one entrepreneurial firm with a growth opportunity seeking for external funding from a venture capitalist, where the entrepreneur and venture capitalist have homogeneous or heterogeneous beliefs about its growth prospects. We developed a real options model to determine the optimal ownership structure that triggers the simultaneous exercise of the growth option on the entrepreneurial firm by entrepreneurs and venture capitalists. Our results show that the more optimistic any of the parties is, the lower the post-money firm ownership that party will retain. However, optimism leads parties to delay their decision to invest in the entrepreneurial firm, by demanding higher profit triggers and investing only in more valuable entrepreneurial firms. The combination of these two effects leaves perceived returns on investment unchanged and not dependent on their own optimism.

A Two-Factor Uncertainty Model to Determine the Optimal Contractual Penalty for a Build-Own-Transfer Project

Public-Private Partnerships (PPP) became one of the most common types of public procurement arrangements and Build-Own-Transfer (BOT) projects, awarded through adequate bidding competitions, have been increasingly promoted by governments. The theoretical model herein proposed is based on a contractual framework where the government grants leeway to the private entity regarding the timing for project implementation. However, the government is aware that delaying the beginning of operations will lead to the emergence of social costs, i.e., the costs that result from the corresponding loss of social welfare. This fact should motivate the government to include a contractual penalty in case the private firm does not implement the project immediately. The government also recognizes that the private entity is more efficient in constructing the project facility. Considering both the existence of social costs and the private firm’s greater efficiency, the model’s outcome is the optimal value for the legal penalty the government should include in the contract form. A two-factor uncertainty approach is adopted, where the facility construction costs and the cash-flows to be generated by running the subsequent activities follow geometric Brownian motions that are possibly correlated. Adkins and Paxson (2011) quasianalytical solution is followed since homogeneity of degree one can not be invoked in all of the model’s boundary conditions. Sensitivity analysis reveals that variations both in the correlation coefficients and in the standard deviations have a strong impact on the optimal contractual penalty. Sensitivity analysis also demonstrates that there is a level of social costs above which the inclusion of a legal penalty is necessary and, similarly, that there is a level for the comparative efficiency above which the inclusion of a legal penalty is not justifiable. The analytical solution to determine each of these values is presented. Finally, the effects of including a non-optimal penalty value in the contract form, which result from overestimating or underestimating the selected bidder’s real comparative efficiency are examined, using a numerical example. Results demonstrate that overestimating (underestimating) the selected bidder’s real comparative efficiency leads to the inclusion of a below-optimal (above-optimal) value for the legal penalty in the contract and produces effects that the government would prefer to prevent.

Optimal contingent payment mechanisms and entrepreneurial financing decisions

Abstract We explore Contingent Payment Mechanisms (also known as Contingent Earn-Outs) as a capital raising strategy surrounding Entrepreneurial Financing decisions. Unlike previous literature, which investigates how Contingent Payment Mechanisms are used within the context of mergers and acquisitions, we show how an optimum contingent payment might be designed so that one Entrepreneur and one external equity provider – taken as a Venture Capitalist – are simultaneously and jointly willing to support a given Entrepreneurial Firm and its growth strategy. We show that such optimum contingent payment might be designed for a range of different types of contingent payments, for which we present a novel taxonomy. As closed-form solutions underlay the terms of such optimum contingent payments, we provide a tractable analytical tool for Entrepreneurs and Venture Capitalists to easily contract these Contingent Payment Mechanisms.

Volume Uncertainty in Construction Projects: A Real Options Approach

The levels of uncertainty surrounding construction projects are particularly high and construction managers should be aware that adequately managing the effects of the different types of uncertainty may lead to an increase in the project’s final Net Present Value (NPV). The model proposed focus on the impact that a specific type of uncertainty - volume uncertainty - may produce in the project’s expected NPV. Volume uncertainty is present in most construction projects since managers do not know, during the bid preparation stage, the exact volume of work that will be executed during the project’s life cycle. Volume uncertainty leads to profit uncertainty and the model integrates a discrete-time stochastic variable, designated as “additional value”, i.e., the value that does not directly derive from the execution of the tasks specified in the bid documents, and which can only be quantified with precision by undertaking an incremental investment in human capital and technology. The model determines that, even only recurring to the skills of their own experienced staff, contractors will produce a more competitive bid, provided that the expected amount for the additional profit is greater than zero. However, construction managers often need to hire specialized firms and highly skilled professionals in order to quantify, with accuracy, the expected amount of additional value and, hence, the precise impact of such additional value in the optimal bidding price. Based on the option to sign the contract and to perform the project by the selected bidder, identified and evaluated by Ribeiro et al. (2013), the model’s outcome is the threshold value for this incremental investment. A decision rule is then reached: construction managers should invest in human capital and technology provided that the cost of such incremental investment does not exceed the predetermined threshold value. The model also proposes new forms of reaching the optimal bidding price, considering solely the effects of the non-incremental investment and also considering the possible impact of the incremental investment in human capital and technology.

The Optimal Timing for the Construction of an Airport

In this paper we study the option to invest in a new airport, considering that the benefits of the investment behave stochastically. In particular, the number of passengers, and the cash flow per passenger are both assumed to be random. Additionally, positive and negative shocks are also incorporated, which seems to be realistic for this type of projects. Accordingly, we propose a new real options model which combines two stochastic factors with positive and negative shocks.