This paper develops a dual-risk valuation theory that extends the classical discounted cash flow model by adding an analytically distinct source of risk: expectational risk. We model expectational risk through the valuation ratio \(K\) , which measures systematic distortion in projected cash flows (expectational distortion), and study its interaction with the benchmark discount rate \(c\) (market-based discounting). The objective is to embed ex-ante alpha into valuation as a structural quantity rather than treat it as an ex-post residual. Methodologically, we build an analytical framework that defines the gain of capital \(g = f(c, K)\) and the effective cost of capital \(c_{\text {eff}}\) as the internal rate that reconciles distorted expectations with fair value. We derive closed-form conditions under which discounting ceases to be equivalent to expected return, characterize the horizon behavior of \(c_{\text {eff}}\) , and establish asymptotic results for the per-period equivalent of \(g\) , denoted \(\gamma \) . The main findings show that \(K\) and \(c\) jointly determine valuation outcomes, with \(g\) providing a forward-looking measure of ex-ante alpha whenever systematic distortion persists. We prove conditions where \(c_{\text {eff}} \ne c\) , identify regimes in which short and medium horizons are most sensitive to \(K\) , and show that \(\gamma \rightarrow 0\) as the horizon lengthens, which clarifies when the expectational distortion captured by \(K\) becomes irrelevant for intrinsic value. These results reframe alpha as a structural feature of biased expectations and separate the two risk primitives: market opportunity cost (market risk) and expectational distortion (expectational risk). The framework generalizes DCF to incorporate systematic errors in cash-flow projections and yields practical guidance for enterprise valuation.
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