Forecasting the final cost with Earned Value Management (EVM) and managing contingency budgets during the project execution have been traditionally considered as two separate streams of project management research. In an attempt to combine the two areas for the purpose of reflecting the risk impact on the cost forecast, this paper presents a cost estimate at completion (CEAC) methodology adjusted with risk contingency. The proposed method is a refined Earned Schedule (ES) based nonlinear CEAC model modified with a new parameter representing the S-shaped contingency consumption as a portion of the project budget at completion. The model is validated on eight construction projects and its estimates’ accuracy and stability with a varying contingency parameter value in the early, middle, and late stages are evaluated. The cost–schedule-risk relationship represented in the model is a contribution to creating a stronger connection between EVM and contingency cost management theories through capturing the interconnected dynamics between a cost baseline and contingency accounts of ongoing projects. As a practical implication, the model is a tool for integrating the contingency consumption into nonlinear CEAC models for accurate and stable cost forecasting especially during the early and middle stages of project execution.