A Note on the Equivalence of Certain Capital Budgeting Criteria.

Abstract When a proposed capital project is evaluated at the firm's cost of capital, the present value V may be compared to the project's initial cost C in two different ways, (V-C), or (V-C)/C. Alternatively, one may determine the rate of discount i, which equates the present value of a payoff stream to its initial cost and which is often referred to as the internal rate of return. Proposed projects may then be ranked on the basis of the order of magnitude of (V-C), (V-C)/C, or i, and choices made on the basis of the familiar decision rule corresponding to each ranking procedure. The method which ranks projects on the basis of (V-C)/C, however, can be shown to be equivalent to a ranking on the basis of V/C, a quantity sometimes called the profitability index. The purpose of this note is two-fold. First, to set forth conditions for which, the ranking of proposed projects on the basis of (V-C) will correspond to the ranking on the basis of(V-C)/C, the ranking on the basis of i will conform to the ranking on the basis of(V-C)/C, and the rankings in both the mentioned statements will not correspond. Second, to draw attention to the fact that the (V- C)/C ranking is not equivalent to the (V-C) ranking.