From unified discounting to dual-risk: A new lens on DCF valuation

Traditional discounted cash-flow (DCF) valuation often compresses uncertainty into a single discount rate. This blends two conceptually distinct objects: an external opportunity cost for priced risk and time, and belief-driven distortion in cash-flow (benefit) expectations. As a result, a valuation gap cannot be attributed cleanly to priced premia versus forecast distortion. We formalize this identification problem across common implementations, including CAPM-based discounting, WACC-plus-premium rules, and implied-cost approaches. We also argue that discounting often becomes self-referential in practice: when required-return inputs are inferred from, calibrated to, or primarily validated by the same market prices they are meant to benchmark, the opportunity-cost interpretation of discounting is violated. We develop a dual-risk framework with two primitives: a market-based cost of capital c and a valuation ratio K that captures distortion in expected benefits relative to a benchmark. The wedge captured by K can arise from forecast error, disagreement, informational frictions, behavioral distortions, or model misspecification, and it may be persistent or transitory. From ( c , K ) we derive the ex-ante gain of capital g and an effective hurdle rate c eff , decomposing expected return into benchmark discounting and expectation distortion. A parsimonious market-clearing equilibrium clarifies how heterogeneous wedges K can persist in prices under belief heterogeneity and limits to arbitrage. We then propose a proxying scheme for c and K from observable total-return prices given a chosen benchmark rate, and illustrate it on equity (VTI), gold (GLD), and Bitcoin (BTC–USD), where non-income assets can load more heavily on the wedge component. Overall, the framework offers an accessible way to separate opportunity cost from cash-flow forecast distortion within DCF valuation.