Sensitivity of the Discount Rate to the Expected Payoff in Project Valuation

A routine method in business is to value risky capital investment projects by discounting their expected cash payoffs at ‘risk‐adjusted’ discount rates. Discount rates are purportedly allied to projects in ‘the same risk‐class,’ but there is little clarity about what makes a risk class. The capital asset pricing model (CAPM) gives two mathematically equivalent definitions. One is that assets in the same risk class have the same ‘beta,’ and the other is that they have the same ratio of payoff mean to payoff covariance (with ‘the market’). The second depiction, albeit widely unknown, is more interesting in terms of cash flow fundamentals. Its implication is that the ‘denominator’ (risk‐adjusted discount rate) depends on its own ‘numerator’ (expected payoff). In practical circumstances, the CAPM price‐implied discount rate can be highly sensitive to changes in the expected payoff, contradicting the convention of discounting an expected cash flow at some fixed ‘risk‐adjusted’ rate regardless of its dollar amount.