«João Adelino Ribeiro, Paulo Jorge Pereira, Elísio Brandão Reaching an Optimal Mark-Up Bid through the Valuation of the Option to Sign the Contract ...»
CEF.UP Working Paper
REACHING AN OPTIMAL MARK-UP BID THROUGH THE
VALUATION OF THE OPTION TO SIGN THE CONTRACT
BY THE SUCCESSFUL BIDDER
João Adelino Ribeiro,
Paulo Jorge Pereira,
Reaching an Optimal Mark-Up Bid through the
Valuation of the Option to Sign the Contract by the
Jo˜ o Adelino Ribeiro† Paulo Jorge Pereira‡and El´sio Brand˜ o§ a, ı a April 24, 2012 Abstract 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.
JEL classiﬁcation codes: G31; D81 Keywords: optimal bidding; real options; construction projects; price determination ∗ Jo˜ o ¸˜ a Adelino Ribeiro thanks the Fundacao para a Ciˆ ncia e Tecnologia for ﬁnancial support.
e † PhD Student, Faculty of Economics, University of Porto, Portugal; email: email@example.com ‡ Assistant Professor, Faculty of Economics, University of Porto, Portugal; email: firstname.lastname@example.org § Full Professor, Faculty of Economics, University of Porto, Portugal; email: email@example.com 1 1 Introduction In this paper we aim to reach an optimal proﬁt margin in the context of a bidding contracting process using a real options approach. The model herein proposed focuses on optimizing the contractor´s price through the valuation of the option to perform 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 executing the job - does have value, as clearly established in the option pricing theory. The motivation behind our work is supported by the presence of uncertainty since the estimated costs of delivering the project will vary from the moment the price is ﬁxed until the preferred bidder has to decide whether to sign the contract or not. Even though the price remains unchanged during this period, the uncertainty in construction costs will lead to changes in the expected proﬁt margin until the contract is signed and the parties are legally bounded. 1 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 consists of a number of contractors competing to perform a particular job by submitting sealed proposals 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 (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 way more difﬁcult to reach, being probably one of the most difﬁcult decisions management has to face during the bid preparation (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 1 It should be mentioned that this risk cannot be hedged since the contractor does not know when the
bidding process will end.
2 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 winning the bid 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; Walllwork, 1999).
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 for a given contract 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 - and their models are supported by two fundamental parameters: the estimated cost of completing the project and the expected number of bidders. Gates had the merit to extend the model built by Friedman 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). All 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 but differing in the partitioning of 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 and Gates’ models, both based on bi-variate 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 parameters. An optimal mark-up value was 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 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 and – even if it is – we believe that past bidding experiences may not always be useful since the circumstances surrounding every bidding process differ from all the others. Moreover, often contractors do not possess information about which competitors will prepare and present a bid proposal, which is generally the case in public contracting processes.
Several studies suggest that decisions regarding the deﬁnition of the mark-up level were mainly 3 supported using subjective judgment, gut feeling and heuristics (Hartono and Yap, 2011), hence acknowledging the fact that managers actually do have a perception in real-world situations as to how the mark-up level will affect the probability of winning the contract. Our experience conﬁrms such: even though, in general, managers do not support their mark-up bid decisions using some sort of mathematical expression linking the price and the probability of winning, they are aware that higher mark-ups will lead to lower chances of getting the job and do have a perception of how their decision regarding the deﬁnition of the mark-up bid will affect the probability of being successful. Bearing this in mind, we decided to support our model in a mathematical expression linking the mark-up level with the probability of winning the bid that (i) respects the generally accepted inverse relationship between these two variables; (ii) allows for ﬂexibility and thus can be adapted to accommodate each contractors´ circumstances surrounding a particular bidding process. The formulation for the probability of winning that we propose will allow contractors to explicitly shape their previous perception, a determinant aspect for reaching the optimal mark-up bid, as we will demonstrate.
Most of the 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 et al. (2001), Drew and Skitmore (1992) and Shash (1993) stated 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 hand; (2) number and size of bids in hand; (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) managed 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 Techniques (Tan et al., 2008), 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).
Even though some work has been developed in the construction management ﬁeld applying the real options approach (see, for example, Espinoza, 2011; Mattar and Cheah, 2006; Ng et al., 2004;
Ng and Chin, 2004; Tseng et al., 2009; Yiu and Tam, 2006), there seems to be a lack of research contributing to the optimal mark-up debate using this methodology, motivating us to build up a 4 model embracing the real options approach and aiming to reach the mark-up level that maximizes the project expected value. This is achieved by evaluating the option to sign the contract and weighting the value of the option by the probability of winning the bid. According to our model, contractors should mark-up their bids with the amount that corresponds to the higher value of the option to sign the contract, weighted by the probability of winning the bid. Under the real options approach, this is the right perspective to follow: to the higher value of the option (weighted by the probability of winning the contract) will correspond a certain level of the proﬁt margin, this being the optimal mark-up bid. The remainder of this paper unfolds as follows. In Section 2, each of the model´s components is described and the model´s numerical solution is presented. In Section 3, a numerical example is given and a sensitivity analysis to the parameters that shape the probability of winning the bid for each mark-up value is performed, in order to evaluate the impact in the optimal mark-up ratio. In Section 4, we consider the existence of penalty costs if the successful bidder decides to not sign the contract, adapting the model accordingly and presenting the new results based on the previous numerical example. Finally, in Section 5, conclusions are given.