A Note on the Apparent Bias of Net Revenue Estimates for Capital Investment Projects

CONSIDER JOE. His job is evaluating potential investment projects for the XYZ Corporation. For each proposed project, Joe carefully estimates expected cost and revenue streams and calculates expected net present values and rates of return. Management takes Joe's reports, selects the projects that appear desirable for implementation, and rejects the rest. When the life of the project has ended, actual cash flows are determined and compared with Joe's estimates. It's clear that, on the average, the investments that have been undertaken have not turned out so well as Joe predicted. Joe is puzzled. He feels he is as unbiased as possible in making his estimates. He is fully aware, of course, that since he cannot predict the future with complete accuracy, that some estimates will be high and some low, and that a different amount of variability ought to be associated with each. But he feels that in the long run his errors ought nearly to balance out, leaving net realized cash flows, on average, equaling those he predicted. Management is puzzled, too. They respect Joe's skill in making the estimates, yet they feel that he must be making some systematic errors. Should they direct Joe deliberately to bias cost estimates upwards, or revenue estimates downwards, or both, in order to compensate for these errors? Not necessarily. It is possible that Joe is indeed turning in unbiased estimates, but that the selection process yields a set of investments that will, typically not perform so well as Joe has estimated. If Joe's estimates are unbiased, the estimates associated with a random selection of the projects Joe has evaluated will be unbiased too. But the selection of investments to be implemented is not a random process. Expected net present value or discounted rate of return strongly influences management's decision to accept or reject a potential project. The higher the estimated net present value or rate of return for a project, the more probable, ceteris paribus, it is that the project will be accepted. Thus for any specified project, acceptance may be more likely if Joe has underestimated costs or overestimated revenues, and less likely if Joe has overestimated costs or underestimated revenues. Therefore, relatively more projects may be selected that turn out more poorly than Joe predicted, and relatively fewer may turn out better, than if the selection process had been random. A more formal statement in the context of net present value estimation can be made as follows: Let V stand for the actual net present value of the capital project, V' for Joe's estimate of this net present value, A for whatever is assumed about the accuracy of V', and PSS for the project selection strategy