Component unit pricing (CUP) theory presents a fresh approach to item pricing, described as the process of distributing the overall price among its constituent component items. This theory provides explanation and proof that different distributions of mark-up among the items of a project produce different levels of reward for contractors, while exposing them to different degrees of risk. The theory describes the three identified sources of these rewards, namely those of improved cash flow, escalation in compensation and valuations of likely variations. In addition, it also provides the first explanation of the three risks involved, namely the risk of 'rejection', the risk of 'reaction' and the risk of 'being wrong'. In combination, it provides a means by which both the rewards as well as these risks can now be measured given any pricing scenario. This theory gives effect to fuzzy constraints on the price of each item, providing a scientific basis by which to identify more extreme prices when pursuing more profit and more restrained prices when seeking to reduce risk. Overall, it provides a basis by which to moderate these two objectives in the pursuit of the maximization of a contractor's utility. A test on a hypothetical project indicates an improvement of more than 150% on utility, if a contractor applies this theory, compared to the position when balanced prices are used instead.