SSM-Audit – Economics (6.1–6.8)

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 )

# 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

# 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).

# 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.

# 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

# 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)

• 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

• 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.