The impacting transformations suffered by Brazil during the 1990s demanded profound changes in the eletrical sector.Decree 5.163/2004 established the Ambiente de ContrataçãoLivre (ACL), allowing participants to freely negotiate bilateral energy contracts. In Brazil, those who do so are exposed to extreme variations in spot prices, called Preço de Liquidação das Diferenças – PLD. Due to transmission capacity restrictions, PLD prices vary between the four existing submarkets: North, Northeast, South, and Southeast/Central-West. Dealing in different submarkets requires electricity generators to sell energy for local PLD and buy it for the spot price of the destination submarket. By doing so the seller may end up selling energy for a lower PLD than the buying price. Submarket swaps can be used for hedging, but what each party should be willing to pay requires investigation. Thus, to discover these prices, the Utility Theory is applied. Given that submarkets Southeast/Central-West and Northeast are currently the ones concentrating the greatest amount of transactions, these were selected for evaluation. Year 2015 was used to delimit the study. It is assumed that both parties are risk averse in a decreasing manner and that there is an equilibrium of forces in the negotiation. The final value of the contract is estimated at 10,66 reais/MWh.