One of the key promises of IT strategic outsourcing is to deliver greater IT service management through lower cost. However, this raises a critical question: How can one predict the service delivery cost that will deliver the promised service level agreements (SLAs)? This is particularly challenging since such prediction is mostly needed during the service engagement phase where the SLAs and the delivery cost are negotiated, and the detailed service modeling data are not available. In this paper, we propose a modeling framework that uses queueing-model-based approaches to estimate the impact of SLAs on the delivery cost. We further propose a set of approximation techniques to address the complexity of service delivery and an optimization model to predict the delivery cost subject to service-level constraints and service stability conditions. We demonstrate the applicability of the proposed methodology using data from a large IT service delivery environment.