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The COnstructive COst MOdel, COCOMO, was developed to estimate the effort measured in staff-months to complete a software project. Given an estimate of the cost per staff-month, COCOMO can be used to estimate the cost of developing software. All business enterprises involved in developing software must know their costs to maintain their long-term viability. However, COCOMO has one significant drawback. It requires that the size of the project be measured in lines of code, but function points are a better metric in measuring project size compared to lines of code. In the event that the size of the project is measured in function points, COCOMO uses a function points to lines of code converter. We present a new model that uses function points as a direct input into the model. By using actual software project data, we show that the software project data can be analyzed on a programming language by programming language basis. We claim that our proposed model takes the programming language into account through precomputed constants. We conclude that our model is superior to the existing model because it eliminates the errors introduced by arbitrary function point indices and replaces them with constants that are scientifically and statistically verifiable.