International Review of Business, Trade, and Economics
Temporal Robustness and Valuation Closure in Corporate Finance: A Closed-Loop Test of Broken-Date Floating-WACC and Full-Year Fixed-WACC Regimes
Abstract
Hany Hassanien Badr
This paper studies whether a closed-loop corporate-finance valuation system preserves its core economic identities when the valuation regime changes from a broken-date, floating-WACC structure to a full-year, fixed-WACC structure. The two scenarios are deliberately not treated as a clean one-factor experiment. Scenario A is valued on 14 September 2005, uses a 108/365 first-period fraction and maturity-specific floating WACC inputs, and follows the baseline operating path. Scenario C begins at a full-year boundary, uses a fixed WACC of 17.6754%, and embeds a 5% higher sales path that propagates into NOPLAT, ROIC, economic profit, FCFF, and value. The research therefore separates within-regime identity tests from cross-regime descriptive comparisons. Four findings are central. First, both scenarios satisfy exact cash-flow conservation across the active 2005-2009 forecast horizon: FCFF equals NOPLAT less net investment, gross cash flow less gross investment, and the financing flow serving investors. Second, claim-level conservation holds year by year: FCFF equals FCFE/quasi-equity cash flow plus debt movements plus after-tax interest. Third, Scenario C produces exact DCF-residual-income closure at operating value 74,268.4586, equity value 73,718.4586, and model per-share value 335.0839. Scenario A produces near, but not exact, closure. On a single schedule-consistent analytical basis, the DCF operating value is 71,169.1793 and the residual-income operating value is 71,327.6925, a residual of 158.5132 model units, or approximately 0.2225% on a symmetric valuation-error basis. Fourth, the paper derives a general discount-factor closure condition. If D_t is the discount factor for period t and k_t is the capital-charge rate used in residual income, DCF and residual-income valuation close exactly when D_{t-1}=(1+k_t)D_t; equivalently, k_t*=D_ {t-1}/D_t-1. The fixed-WACC full-year case satisfies this recursion exactly, whereas the broken-date floating-WACC case does not when maturity-specific direct-power discount factors are paired with a different capital-charge timing convention. Replacing the capital-charge sequence with the implied forward sequence restores closure to machine precision. A date-normalized diagnostic bridge also shows why the raw values near 321 and 335 per share cannot be interpreted as a simple fixed-versus-floating WACC effect. Holding Scenario A operations constant, moving from the broken date to a full-year basis lowers operating value from 71,169.18 to 63,504.84; changing only the full-year discount architecture to Scenario C’s fixed WACC lowers value by a further 19.33; replacing Scenario A operations with Scenario C operations then raises value by 10,782.95 to 74,268.46. Valuation convergence is therefore treated as a structural property governed by capital continuity, claim conservation, discount-factor recursion, and temporal alignment rather than as a coincidence of headline values.