In this article, the authors provide a unified approach to joint cost allocation for situations where allocation is needed. First, with the help of an illustration, the apparent weakness of Moriarity's scheme is discussed. Later, certain desirable properties of Louderback's method are shown. Employing their "propensity to contribute" concept, the authors utilize the desirable aspects of both the Moriarity and the Louderback schemes to come up with a model which is shown to be in the core. With game-theoretic concepts, a "modified Shapley Value" to allocate the joint cost is provided.