6.1 What we count (objective function)
Goal. Convert earlier visibility (via the lane a) into fewer misses, fewer false alarms, lower working-capital cost, and cleaner reconciliations — without changing reported numbers. We measure value across four levers and sum them:
V_total := V_miss + V_ref + V_wc + V_ops # Classical magnitudes remain identical by construction: # collapse parity: phi((m,a)) = m # If needed, normalize money lenses only (not a): m_fx_norm := m_native * fx_rate(native->base) m_real := m_nominal * ( I_0 / I_t )
6.2 CFO worksheet (drop-in template)
Copy-paste this block into your planning sheet; fill inputs, the sheet computes outputs deterministically.
# Inputs (declare once per pilot) GM := gross_margin_rate R_d := daily_revenue_base # in base currency p_catch := probability_early_action_when_band_drops D_lead := average_days_of_lead_time_from_lane theta_miss := fraction_of_daily_GM_lost_on_unfixed_miss r_ref := refund_rate_base r_cb := chargeback_rate_base beta_ref := reduction_fraction_when_actioned A_ar := average_AR_balance_base WACC := annual_cost_of_capital H_base := weekly_alert_hours_now H_red := weekly_hours_reduction C_hour := blended_cost_per_hour C_impl := one_time_implementation_cost C_run := annual_run_cost # Formulas (ASCII) V_miss := GM * R_d * theta_miss * p_catch * D_lead * N_events_year V_ref := R_d * ( r_ref + r_cb ) * beta_ref * N_actioned_year V_wc := A_ar * WACC * ( D_lead / 365 ) * xi_sched # xi_sched = fraction of slippage prevented V_ops := C_hour * 52 * H_red V_total := V_miss + V_ref + V_wc + V_ops ROI_annual := ( V_total - C_run ) / ( C_impl + C_run ) # Band-trigger coupling (turn bands into p_catch) score(A++)=5, score(A+)=4, score(A0)=3, score(A-)=2, score(A--)=1 band_drop := max(0, score_prev - score_now) p_catch := p0 + p1 * band_drop # defaults: p0 := 0.10, p1 := 0.20 # Optional calm gate (reduces false positives) g_calm := 1.0 if SyZ_t >= tau_syz else rho_calm p_catch_effective := p_catch * g_calm # use this in place of p_catch if gate is enabled
6.3 Lever-by-lever cookbook (linking bands to money)
# L1 — Misses avoided (forecast vs actuals) V_miss := GM * R_d * theta_miss * p_catch * D_lead * N_events_year # Pick theta_miss from history (e.g., 0.10 if an unfixed miss knocks 10% of daily GM). # L2 — Refund/chargeback containment (reconciliation) V_ref := R_d * ( r_ref + r_cb ) * beta_ref * N_actioned_year # beta_ref measured from prior fixes (e.g., 0.20 => 20% reduction when actioned). # L3 — Working capital & borrowing cost (AR schedule) V_wc := A_ar * WACC * ( D_lead / 365 ) * xi_sched # xi_sched is the portion of slippage realistically eliminated (e.g., 0.30). # L4 — Ops toil reduction (calmer alerts) V_ops := C_hour * 52 * H_red # H_red := H_base - H_after (measure from calendars/tickets).
6.4 Cost model (transparent)
# One-time C_impl := (BI_hours + Data_hours + Audit_hours) * C_hour + Training + Dash_build # Run (annual) C_run := Infra + CI_checks + Light_maintenance + Optional_stamps_storage # Thumb rule # For a 3-KPI pilot, C_impl ~ low weeks of blended effort; C_run ~ low days per year.
6.5 Quick scenarios (plug numbers; precise arithmetic shown)
Use the same worksheet; replace with your data.
# Conservative example GM=0.45, R_d=1.2e6, theta_miss=0.05, p_catch=0.30, D_lead=5, N_events_year=6 r_ref+r_cb=0.025, beta_ref=0.15, N_actioned_year=6 A_ar=30e6, WACC=0.12, xi_sched=0.20, D_lead=5 C_hour=80, H_red=10 C_impl=150000, C_run=60000 V_miss = 0.45 * 1.2e6 * 0.05 * 0.30 * 5 * 6 = 243000 V_ref = 1.2e6 * 0.025 * 0.15 * 6 = 27000 V_wc = 30e6 * 0.12 * (5/365) * 0.20 = 9863.0137 V_ops = 80 * 52 * 10 = 41600 V_total = 243000 + 27000 + 9863.0137 + 41600 = 321463.0137 ROI_annual = (321463.0137 - 60000) / (150000 + 60000) = 1.2451
# Expected example (moderate uplift) # Same as above but theta_miss=0.08, p_catch=0.40, beta_ref=0.20, xi_sched=0.30, H_red=20. V_miss = 0.45 * 1.2e6 * 0.08 * 0.40 * 5 * 6 = 518400 V_ref = 1.2e6 * 0.025 * 0.20 * 6 = 36000 V_wc = 30e6 * 0.12 * (5/365) * 0.30 = 14794.5205 V_ops = 80 * 52 * 20 = 83200 V_total = 518400 + 36000 + 14794.5205 + 83200 = 652394.5205 ROI_annual = (652394.5205 - 60000) / (150000 + 60000) = 2.8209
# Aggressive example (high-impact flow) # theta_miss=0.10, p_catch=0.50, beta_ref=0.25, xi_sched=0.40, H_red=30 (costs unchanged) V_miss = 0.45 * 1.2e6 * 0.10 * 0.50 * 5 * 6 = 810000 V_ref = 1.2e6 * 0.025 * 0.25 * 6 = 45000 V_wc = 30e6 * 0.12 * (5/365) * 0.40 = 19726.0274 V_ops = 80 * 52 * 30 = 124800 V_total = 810000 + 45000 + 19726.0274 + 124800 = 999526.0274 ROI_annual = (999526.0274 - 60000) / (150000 + 60000) = 4.4739
Reading tip. ROI grows rapidly with D_lead, p_catch, and theta_miss. Band governance (hysteresis + optional calm gate) stabilizes p_catch by reducing false alarms.
6.6 Mapping bands to action (policy → value)
# Action table (drop-in) A++/A+ -> monitor A0 sustained 3 of 5 days -> owner RCA; update note A- once or A0 5 of 7 days -> director review, time-boxed fix A-- or 2 lanes A- in 5 days-> CFO stand-up; pre-committed playbook # Link each action to a lever forecast lane drops -> L1 (misses avoided) reconciliation lane drops -> L2 (refunds/chargebacks contained) schedule lane drops -> L3 (working capital) any lane drop reducing noise -> L4 (ops toil saved)
6.7 What goes into the executive pack (money-first)
• Before/after alert budget: hours and cost (L4) • Lead-time incidents: band drops and realized D_lead (L1/L3) • Refunds contained: rate deltas tied to action dates (L2) • Stability debt ledger: segments with persistent A0/A- and owners • ROI page: V_total, C_impl, C_run, ROI_annual
6.8 Guardrails for honest ROI
• No double counting (assign benefits once). • Declare attribution windows (e.g., 14 days post band drop for L1/L2/L3). • Freeze knobs mid-quarter to preserve comparability. • Always show collapse parity: phi((m,a)) = m. • Currency/real-terms parity: economics may use m_fx_norm or m_real; a is unchanged.
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