When is it worth measuring a covariate in a randomized clinical trial?

In a randomized clinical trial, an experimenter can increase statistical power by including a covariate (e.g., a pretest). This will generally reduce the total number of participants needed to achieve a specified level of power. However, it will also increase the cost per participant. Thus, the question arises, "When do the savings incurred by needing fewer participants exceed the costs incurred by measuring each participant on the covariate?" A simple closed form expression is derived that applied researchers can use in the design phase of studies to answer this question.