Implementing Fischer Black's Simple Discounting Rule

Abstract

Corporate managers typically estimate the value of capital projects by discounting the project's expected future net cash flows at the cost of capital. The capital asset pricing model (CAPM) is generally used to estimate that cost. But, as anyone who has worked on the finance or business development staff of a public company can attest, there are major challenges in applying the CAPM, including largely unresolved questions about what constitutes the “market portfolio,” how to estimate market risk premiums, and how to estimate the betas of projects.In a short article published in Financial Management in 1988, Fischer Black proposed a valuation “discounting rule” that avoids all these problems—one that involves discounting a relatively certain (as opposed to an expected or average) level of operating cash flows at the risk‐free rate. But Black's article does not address the question of how to calculate these “certainty equivalent” or “conditional” cash flows.In this article, the authors propose a way of implementing Black's rule that involves estimating the “conditional” cash flows in a three‐step procedure: Find a benchmark security that correlates with the project's cash flows; Estimate the percentiles of the distribution in which the benchmark return equals the risk‐free rate over different investment horizons; Use information from corporate managers to assess the cash flows that define the same percentiles in the cash flow distributions. As the authors point out, the virtue of Black's rule is that it shifts the focus of the analyst away from the assessment of discount factors and puts it squarely on the more challenging, and arguably more relevant, problem of estimating the project's cash flows.