<![CDATA[Capital investment appraisal requires accounting and finance professionals to explain whether a proposed expenditure clears the firm's hurdle rate, not merely to report an Internal Rate of Return (IRR) generated by software. Conventional manual IRR procedures often separate the Net Present Value (NPV) decision at the Required Rate of Return (RRR) from rate discovery and interpolate across arbitrarily selected brackets. This study develops the Evbayiro RRR-First Method as a decision-anchored appraisal procedure: it tests NPV at the RRR, forms an adjacent one-percentage-point sign-changing bracket, and applies Three-Point Curvature Closure (E3C). Its accounting and finance contribution is to integrate hurdle-rate governance, transparent decision communication, and reproducible manual computation in one workflow. The validation uses sourced conventional and non-conventional worked examples and 88,556 public-company cash-flow proxy cases constructed from SEC EDGAR/Companyfacts data and Damodaran industry WACC proxies; 76,657 cases produced applicable brackets. Iterated E3C returned an in-bracket estimate for every applicable case, met scaled zero-NPV residual thresholds of 10^-8 in 99.69% and 10^-12 in 98.80% of cases, and required a median of two closure cycles versus 33 bisection iterations. One-step E3C materially improved on two-point interpolation while retaining calculator-based feasibility. The method does not replace NPV or automated solvers; rather, it provides practitioners, accounting educators, and professional examination bodies with a traceable way to connect the hurdle-rate decision to IRR estimation and to interpret multiple-IRR cases without displacing NPV as the controlling rule.]]>
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