Query processing remains one of the important challenges of Object-Oriented Database Management Systems. Cost based query optimization involves creating alternative executing plans for a given query and executing the least costly one within a cost model framework. In Object-Oriented Database Management Systems (OODBMSs) objects may store references to other objects (precomputed joins), and therefore path expressions are used in query languages. The cost formulas for explicit joins and the selectivities of attributes and joins are well-known in the relational model and there is a need for a similar work for object-oriented queries involving path expressions. This information is necessary for deciding whether to use pointer chasing or to convert the path expressions into explicit joins and also for deciding on the execution order of path expressions. In this paper, we provide a cost model that includes the formulas for the costs and selectivities of forward and backward path traversals.