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«Abstract Reaching an optimal mark-up value in the context of bidding competitions has been a research topic since the pionner models of Friedman ...»

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Reaching an Optimal Mark-Up Bid through the Valuation

of the Option to Sign the Contract by the Selected Bidder

† ‡ §

João Adelino Ribeiro, Paulo Jorge Pereira and Elísio Brandão


Reaching an optimal mark-up value in the context of bidding competitions has been a research topic since the pionner

models of Friedman (1956) and Gates (1967) set the standards for future discussion. The model herein proposed is based

on the existence of the option to sign the contract and perform the construction project by the selected bidder. This option constitues a real option because (i) the construction costs are uncertain, i.e., the input prices vary stochastically from the moment the bid price is established and the bid results are publicly available; (ii) flexibility is present since the selected bidder may refuse to sign the contract and not execute the project if the construction costs, at the moment the contract has to be signed, are higher than the price included in the bid proposal, and (iii) construction costs are, at least, partially irreversible. Since this real option is only available to the selected bidder, its value must be weighted by the probability of winning the bid. A maximization problem that considers the value of the option to sign the contract and the probability of winning the bid is proposed and the model’s outcome is the result of this maximization problem: to the highest value of the option to sign the contract weighted by the probability of winning the bid corresponds the optimal price (and, hence, the optimal mark-up bid). The model is later adapted in order to consider the existence of penalty costs, borne by the selected bidder if he or she refuses to sign the contract. Under these new conditions and in pure financial terms, the selected bidder should only exercise the option if the difference between the bid price and the construction costs is greater than the penalty costs, in the day the contract has to be signed. Results reached using a numerical example demonstrate that the optimal price is higher when penalty costs are present.

JEL classification codes: G31; D81 Keywords: real options; optimal bidding; investment decisions under uncertainty; price determination.

∗ PhD Student in Finance, Faculty of Economics, University of Porto, Portugal; email: 090427012@fep.up.pt † João Adelino Ribeiro ackowledges the financial support provided by FCT (Grant nº SFRH/BD/71447/2010) ‡ Assistant Professor at Faculty of Economics, University of Porto, Portugal; email: pjpereira@fep.up.pt § Full Professor at Faculty of Economics, University of Porto, Portugal; email: ebrandao@fep.up.pt Part I Introduction In this paper, we aim to reach an optimal profit margin in the context of a bidding contracting process applying the real options approach. The model herein proposed is a theoretical model whose purpose is to optimize the contractor’s price through the valuation of the option to invest in performing the project. When a contractor presents a bid to the client and assuming that the probability of winning the bid is greater than zero, the option to sign the contract and subsequently to invest in executing the project - does have value, as clearly established in the option pricing theory. The motivation behind the present work is also supported by the presence of uncertainty since the estimated costs of performing the project - the construction costs - will most likely vary from the moment the bidder computes them and defines the price to include in her or his bid proposal based on such estimate, closes the proposal, delivers the proposal to the client, and the moment the option is exercised or not, i.e., the moment the selected bidder is invited by the client to sign the contract and decides to sign it or declines the invitation. In fact, and even though the bid price remains unchanged during this period, the uncertainty in construction costs will most likely lead to changes in the project’s expected 1 profit margin until the contract is eventually signed and the parties legally bounded.

As far as the present research is concerned, contractors are firms operating in the construction industry whose business consists of executing a set of tasks previously defined by the client.

The amount of tasks to be performed constitute a project, job or work. A significant amount of projects in the construction industry are assigned through what is known as “tender” or “bidding” processes (Christodoulou (2010); Drew et al. (2001)), being this the most popular form of price determination (Liu and Ling (2005); Li and Love (1999)). A bidding process 1 We should mention that the risk deriving from the existence of uncertainty in the expected construction costs cannot be hedged since the bid participants do not know how the bidding process will end.

2 consists of a number of contractors competing to perform a particular job by submitting a sealed proposal until a certain date previously defined by the client. The usual format of a bidding process is based on the rule that - all other things being equal - the contract will be awarded to the competitor which submitted the lowest bid (Cheung et al. (2008); Chapman et al. (2000)), i.e., the lowest price. Bearing this in mind, it is easy to conclude that the client’s decision is very straightforward but the contractor’s decision on what price to bid is more difficult to reach, being probably one of the most difficult decisions construction managers have to face during the bid preparation process (Li and Love (1999)).

The construction industry is known for featuring strong levels of price competitiveness (Chao and Liu (2007); Mochtar and Arditi (2001); Ngai et al. (2002)) and the competitive pressures are probably more intense than in any other industry (Drew and Skitmore (1997); Skitmore (2002)), which often leads contractors to lower their profit margins in order to produce a more competitive bid. Thus, it is not rare to see the winning bid include a near zero-profit margin (Chao and Liu (2007)). Moreover, under-pricing in the context of competitive bidding is a common phenomenon, namely explained by the need for work and penetration strategies (Drew and Skitmore (1997); Fayek (1998); Yiu and Tam (2006)), even tough bidding below cost does not necessarily guarantee a successful result to the bidder (Tenah and Coulter (1999)).

Contractors realize that bidding low when facing strong competition increases the chance of being chosen to perform the work but they are also aware of the opposite: if the price included in their proposal is higher, the likelihood of winning the bid will definitively be lower. This inverse relationship between the level of the profit margin (commonly known in the construction management literature as the “mark-up bid”) and the probability of getting the contract is an accepted fact both in the construction industry and within the research community (see, for example, Christodoulou (2010); Kim and Reinschmidt (2006); Tenah and Coulter (1999); Wallwork (1999)).

3 Competitive bidding has been a subject of research since the important papers of Friedman (1956) and Gates (1967) set the standards for future discussion. Both models proposed a probabilistic approach to determine the most appropriate mark-up value and were supported by the definition of a relationship between the mark-up level and the probability of winning the bid. For that purpose, the two authors assumed the existence of previous bidding data leading to the definition of the bidding patterns of potential competitors. Gates (1967) had the merit to extend the model built by Friedman (1956) and turned it into a general strategic model, with general applicability, setting the foundations for what is now commonly known as “Tendering Theory” (Runeson and Skitmore, 1999). Later attempts to establish a relationship between the probability of winning the contract and the level of the profit margin were based on previous bidding data – in line with the mentioned pioneer models. Carr (1982) proposed a model similar to Friedman’s model but differing in the partitioning of the underlying variables: Friedman (1956) used a single independent variable, a composite “bid-to-cost” ratio, whereas Carr (1982) crafted his model around two distributions: one that standardizes the estimated cost of the analyzing bidder to that of all competitor bids, and another that standardizes the bids of an individual competitor against that of the analyzing bidder’s estimated costs. More recently, Skitmore and Pemberton (1994) presented a multivariate approach by assuming that an individual bidder is not restricted to data for bids in which he or she has participated, as in the case of Friedman (1956) and Gates (1967) models, both based on bivariate approaches. Instead, the bidder is able to incorporate data for all auctions in which competitors and potential competitors have participated, regardless of the individual bidder’s participation. This methodology had the merit of increasing the amount of data available for estimating the model’s parameters. An optimal mark-up value is then reached against known competitors, as well as other types of strategic mark-ups.

Past research seems to suggest that it would be difficult to establish a link - with general applicability - between the mark-up level and the probability of winning the bid. Contractors 4 may recur to previous bidding data and assume that bidders are likely to bid as they have done in the past in order to shape the relationship that best describes their specific situation.

However, as Fayek (1998) stated, past bidding information is not always available. Chapman et al. (2000) argued that many managers consider that the information required by quantitative models is too difficult, too expensive or impossible to compile.To clearly understand what researchers mean by “past bidding information”, we should distinguish between two different types of bidding data: (i) the one that is available to all contractors and comprises the estimates carried out by the client’s engineers for the execution of each task or set of tasks, the price of each competitor for the execution of such task or set of tasks and, obviously, the final bid price of each competitor, i.e., the price of executing all the tasks included in the bid package; (ii) the real empirical data each contractor (eventually) compiles concerning the results reached in past bidding competitions when a specific mark-up level was included in the bid proposal. This means that the first type of data is publicly available and allows researchers to reach, through the application of several models and methodologies, what is commonly known as “theoretical probabilities”. These probabilities are computed based on data which is not real empirical data. Real empirical data is private information that contractors seldom share, meaning that this information is rarely observable and is, therefore, private knowledge of each contractor.2 However, we recognize that assuming bidders are likely to bid as they have done in the past becomes inevitable, regardless of the type of data in question. In fact, utilizing past bidding information is only useful if one assumes that other bidders will decide in the future in the same way they have decided in the past. Still, and even though we agree that this assumption (which has been adopted since the pioneer works Friedman (1956) and Gates (1967)) may be considered some what restrictive, we sympathize with Crowley (2000) when this researcher states that bid models do not predict the future, but simply organize past 2 Chapman et al. (2000) observed that some managers argue that collecting the necessary information to apply quantitative models is too difficult, to expensive or even impossible, which leads us to conclude that not all contractors actually compile data from previous bidding competitions.

5bidding information in a way that is meaningful to current bid decisions.3

Most of the more recent contributions to the optimal mark-up bid debate have been concerned with the selection of factors construction managers should take into account when deciding what price to bid (Christodoulou, 2010). Research by authors such as Drew and Skitmore (1992), Shash (1993) and Drew et al. (2001) observed that different bidders apply different mark-up policies, which may be variable or fixed. These authors list a long set of factors aiming to explain the rationale behind mark-up bidding decision making: (1) amount of work in hands; (2) number and size of bids in hands; (3) availability of staff, including architects and other supervising officers; (4) profitability; (5) contract conditions; (6) site conditions; (7) construction methods and programme; (8) market conditions and (9) identity of other bidders, to name the ones they considered to be the most prominent. In general terms, factors are grouped in different categories and we sympathize with the 5 categories defined by Dulaimi and Shan (2002): (1) project characteristics; (2) project documentation;

(3) contractor characteristics; (4) bidding situation and (5) economic environment. Following this line of thought, innovative research on the subject has been embracing more sophisticated methodologies. The paper by Li and Love (1999) manages to combine rule-based expert systems with Artificial Neural Networks (ANN) in the context of mark-up bid estimation, following previous research conducted by Li (1996), Moselhi et al. (1991), amongst others. In fact, the most recent and innovative models use ANN (as in Christodoulou (2010) and Liu and Ling (2005)) or Goal Programming Technique (Tan et al. (2009)), where those determinants (or attributes) provide the ground where models are built upon, thus recognizing the crucial importance of possessing a strong knowledge of the factors influencing the contractors bid mark-up decision for the purpose of identifying the optimal mark-up level (Dulaimi and Shan (2002)).

3 We believe that past bidding information is, in fact, the best tool construction managers may use to create a perception as of how bidders will tend to act in the future. However, since each project has characteristics that distinguishes it from all other past projects, we believe construction managers should also consider the specific features of the current bid process, when establishing the mark-up bid.

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