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

Abstract

Reaching an optimal mark-up value in the context of bidding competitions has been a research topic for more than 40 years. The model herein proposed aims to contribute to this debate by identifying and evaluating a specific real option: the option to sign the contract and perform the construction project by the selected bidder. This option constitutes 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 and the selected bidder is invited to sign the contract; (ii) flexibility is present since the selected bidder may refuse to enter into contract and 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. The model is later extended in order to consider the existence of penalty costs, borne by the selected bidder if he or she declines the invitation to sign the contract. Under these conditions, the selected bidder should only exercise the option if the difference between the price and the construction costs, at that moment, is greater than the penalty costs. Results reached using a numerical example demonstrate that the optimal price is higher when penalty costs are present.

Keywords: real options, optimal bidding, construction projects, price determination

JEL Classification: G31, D81