""" Amanah — five-year portfolio model, three scenarios. DISCIPLINE (this is the whole point of the file) ------------------------------------------------ Every input below is one of: SOURCED — a published figure with a citation id in ../_research/CITATIONS.json DECISION — a number the founders choose (a salary, a fee, a target). Not a claim about the world. Labelled as a decision so nobody reads it as research. DERIVED — computed here from SOURCED and DECISION inputs by the code below. MEASURE — cannot honestly be known before the first contracts run. Modelled as a range and flagged on the slide as something to measure, not assume. No input is a "class typical". If it is not sourced and not a decision, it is a MEASURE and the deck says so. MECHANICS --------- A murabaha is a sale, not a loan: Amanah buys the equipment and resells it at a disclosed markup payable in instalments. Economically the profit accrues on the declining unpaid balance, so the portfolio is modelled as a monthly cohort engine — originate each month, amortise each cohort over its term, accrue profit on the outstanding balance. That is arithmetic, not an assumption. """ import json, pathlib # ── SOURCED anchors (ids refer to CITATIONS.json) ──────────────────────────── SOURCED = { "prime_rate": (0.0675, "C9", "US bank prime loan rate, 9 Sep 2026"), "sofr": (0.0362, "C10", "SOFR, 10 Sep 2026"), "bbb_corp_yield": (0.0586, "C11", "ICE BofA BBB US corporate effective yield, 10 Sep 2026"), "elfa_small_ticket_co": (0.0072, "C14", "ELFA small-ticket charge-off rate, June 2026"), "elfa_industry_co": (0.0054, "C14", "ELFA industry-wide charge-off rate, June 2026"), "bank_ci_chargeoff": (0.0058, "C13", "Fed net charge-off rate, business loans, Q2 2026"), "usury_ceiling": (0.25, "C3", "Michigan criminal-usury ceiling, MCL 438.41"), "sales_tax": (0.06, "C5", "Michigan sales tax rate, MCL 205.52(1)"), "ucc_file_fee": (15.0, "C19", "UCC-1 filing fee, MCL 440.9525(1)"), "ucc_search_fee": (6.0, "C19", "UCC search fee, MCL 440.9525(2)"), } # ── Scenarios ──────────────────────────────────────────────────────────────── # Each entry carries its class so the deck can print it beside the number. SCENARIOS = { "pessimistic": { "label": "Pessimistic", "capital_y1": (1_500_000, "DECISION", "seed equity actually raised in year one"), "capital_added": ([0, 0, 500_000, 0, 500_000], "DECISION", "further equity by year"), "profit_rate": (0.095, "MEASURE", "price the market will bear, below plan"), "avg_ticket": (60_000, "MEASURE", "deals land at the small end"), "term_months": (36, "DECISION", "standard contract term"), "deals_per_month": ([1, 2, 3, 4, 4], "MEASURE", "origination pace by year"), "utilisation": (0.60, "MEASURE", "share of capital sitting in earning contracts"), "net_loss_rate": (0.030, "MEASURE", "annual net loss on average earning assets — 4.2x the ELFA small-ticket rate"), "opex_y1": (395_000, "DECISION", "year-one operating budget"), "opex_growth": (0.08, "DECISION", "annual operating cost growth"), "origination_cost": (900, "DECISION", "direct cost to close one contract"), "prepay_rate": (0.06, "MEASURE", "annual share of balances settled early"), "doc_fee": (750, "DECISION", "documentation fee per contract — must be actual cost recovery, not a disguised return"), "leverage": (0.0, "DECISION", "no funding facility — all equity"), "cost_of_funding": (0.075, "MEASURE", "profit rate payable on a Shariah-compliant funding facility"), }, "base": { "label": "Base", "capital_y1": (2_500_000, "DECISION", "seed equity actually raised in year one"), "capital_added": ([0, 1_500_000, 2_000_000, 2_000_000, 2_000_000], "DECISION", "further equity by year"), "profit_rate": (0.115, "MEASURE", "prime + 4.75 points; ceiling is 25% by statute"), "avg_ticket": (95_000, "MEASURE", "midpoint of the stated 25k-250k band, weighted low"), "term_months": (36, "DECISION", "standard contract term"), "deals_per_month": ([2, 4, 7, 10, 13], "MEASURE", "origination pace by year"), "utilisation": (0.80, "MEASURE", "share of capital sitting in earning contracts"), "net_loss_rate": (0.014, "MEASURE", "annual net loss — about 2x the ELFA small-ticket rate, for a new book"), "opex_y1": (395_000, "DECISION", "year-one operating budget"), "opex_growth": (0.12, "DECISION", "annual operating cost growth"), "origination_cost": (750, "DECISION", "direct cost to close one contract"), "prepay_rate": (0.08, "MEASURE", "annual share of balances settled early"), "doc_fee": (750, "DECISION", "documentation fee per contract — must be actual cost recovery, not a disguised return"), "leverage": (1.0, "DECISION", "funding facility at 1x equity — from YEAR THREE, not year two (R03)"), "cost_of_funding": (0.081, "MEASURE", "SOFR 3.62% + 450bp. R03: a first-time book cannot borrow at prime + 25bp"), }, "optimistic": { "label": "Optimistic", "capital_y1": (4_000_000, "DECISION", "seed equity actually raised in year one"), "capital_added": ([0, 3_000_000, 4_000_000, 5_000_000, 6_000_000], "DECISION", "further equity by year"), "profit_rate": (0.125, "MEASURE", "prime + 5.75 points; ceiling is 25% by statute"), "avg_ticket": (120_000, "MEASURE", "deals land toward the upper half of the band"), "term_months": (36, "DECISION", "standard contract term"), "deals_per_month": ([3, 7, 12, 17, 22], "MEASURE", "origination pace by year"), "utilisation": (0.90, "MEASURE", "share of capital sitting in earning contracts"), "net_loss_rate": (0.008, "MEASURE", "annual net loss — close to the ELFA small-ticket rate"), "opex_y1": (395_000, "DECISION", "year-one operating budget"), "opex_growth": (0.15, "DECISION", "annual operating cost growth"), "origination_cost": (650, "DECISION", "direct cost to close one contract"), "prepay_rate": (0.10, "MEASURE", "annual share of balances settled early"), "doc_fee": (750, "DECISION", "documentation fee per contract — must be actual cost recovery, not a disguised return"), "leverage": (2.0, "DECISION", "facility at 2x equity from year three"), "cost_of_funding": (0.071, "MEASURE", "SOFR 3.62% + 350bp — the best a seasoned book might reach"), }, } def v(x): """unwrap (value, class, note) tuples""" return x[0] if isinstance(x, tuple) else x def run(s, years=5): ticket = v(s["avg_ticket"]); term = v(s["term_months"]) rate = v(s["profit_rate"]); util = v(s["utilisation"]) loss = v(s["net_loss_rate"]); prepay = v(s["prepay_rate"]) dpm = v(s["deals_per_month"]); origcost = v(s["origination_cost"]) doc_fee = v(s["doc_fee"]); lev = v(s["leverage"]); cof = v(s["cost_of_funding"]) capital = v(s["capital_y1"]); added = v(s["capital_added"]) opex = v(s["opex_y1"]); opexg = v(s["opex_growth"]) months = years * 12 cohorts = [] # (remaining_balance, monthly_principal, months_left) out = [{"originations_n":0,"originations_$":0.0,"profit_income":0.0,"losses":0.0, "opex":0.0,"orig_cost":0.0,"avg_earning":0.0,"capital":0.0, "fee_income":0.0,"funding_cost":0.0,"avg_debt":0.0} for _ in range(years)] equity = capital monthly_rate = rate / 12.0 monthly_loss = loss / 12.0 monthly_prepay = prepay / 12.0 for m in range(months): y = m // 12 if m % 12 == 0: equity += added[y] if y < len(added) else 0 out[y]["capital"] = equity opex_y = opex * ((1 + opexg) ** y) # capacity check — you cannot deploy capital you do not have outstanding = sum(c[0] for c in cohorts) # leverage from YEAR THREE. R03: nobody underwrites a warehouse line against a # book with less than two years of performance data. facility = equity * lev if y >= 2 else 0.0 room = max(0.0, (equity + facility) * util - outstanding) want = dpm[y] if y < len(dpm) else dpm[-1] can = int(min(want, room // ticket)) if can > 0: cohorts.append([can * ticket, (can * ticket) / term, term]) out[y]["originations_n"] += can out[y]["originations_$"] += can * ticket out[y]["orig_cost"] += can * origcost out[y]["fee_income"] += can * doc_fee # accrue on declining balances, amortise, apply loss and prepayment bal_start = sum(c[0] for c in cohorts) out[y]["profit_income"] += bal_start * monthly_rate out[y]["losses"] += bal_start * monthly_loss out[y]["avg_earning"] += bal_start / 12.0 drawn = max(0.0, bal_start - equity * util) # facility is drawn only above equity capacity drawn = min(drawn, facility) out[y]["funding_cost"] += drawn * (cof / 12.0) out[y]["avg_debt"] += drawn / 12.0 alive = [] for c in cohorts: c[0] -= c[1] # scheduled principal c[0] -= c[0] * monthly_prepay # early settlement c[2] -= 1 if c[2] > 0 and c[0] > 1: alive.append(c) cohorts = alive out[y]["opex"] = opex_y rows = [] cum = 0.0 for y in range(years): o = out[y] pretax = (o["profit_income"] + o["fee_income"] - o["losses"] - o["opex"] - o["orig_cost"] - o["funding_cost"]) cum += pretax rows.append({ "year": y + 1, "capital": round(o["capital"]), "deals": o["originations_n"], "originated": round(o["originations_$"]), "avg_earning_assets": round(o["avg_earning"]), "profit_income": round(o["profit_income"]), "fee_income": round(o["fee_income"]), "funding_cost": round(o["funding_cost"]), "avg_debt": round(o["avg_debt"]), "credit_losses": round(o["losses"]), "opex": round(o["opex"]), "origination_cost": round(o["orig_cost"]), "pretax": round(pretax), "cumulative_pretax": round(cum), "return_on_equity": round(pretax / o["capital"], 4) if o["capital"] else 0.0, "yield_on_assets": round(o["profit_income"] / o["avg_earning"], 4) if o["avg_earning"] else 0.0, }) return rows def breakeven_month(s): """first month in which trailing-12 pretax turns positive — DERIVED, not claimed""" rows = run(s, years=5) for r in rows: if r["pretax"] > 0: return r["year"] return None if __name__ == "__main__": result = {"sourced": {k: {"value": a, "citation": b, "note": c} for k, (a, b, c) in SOURCED.items()}, "scenarios": {}} for key, s in SCENARIOS.items(): rows = run(s) result["scenarios"][key] = { "label": s["label"], "inputs": {k: {"value": v(val), "class": val[1], "note": val[2]} for k, val in s.items() if isinstance(val, tuple)}, "years": rows, "first_profitable_year": breakeven_month(s), "five_year_pretax": rows[-1]["cumulative_pretax"], } pathlib.Path("model-output.json").write_text(json.dumps(result, indent=1)) for k, sc in result["scenarios"].items(): print(f"\n=== {sc['label']} (first profitable year: {sc['first_profitable_year']})") print(f"{'yr':>3} {'capital':>11} {'deals':>6} {'originated':>12} {'avg assets':>12} {'profit':>10} {'losses':>9} {'opex':>9} {'pretax':>11} {'cum':>12} {'ROE':>7}") for r in sc["years"]: print(f"{r['year']:>3} {r['capital']:>11,} {r['deals']:>6} {r['originated']:>12,} " f"{r['avg_earning_assets']:>12,} {r['profit_income']:>10,} {r['credit_losses']:>9,} " f"{r['opex']:>9,} {r['pretax']:>11,} {r['cumulative_pretax']:>12,} {r['return_on_equity']*100:>6.1f}%") # ── DERIVED diagnostics — the numbers that decide whether this is a business ── def breakeven_earning_assets(s, extra_opex=0.0): """Earning assets required before the book pays for its own overhead. CORRECTED 2026-09-14 after council round R03. The first version was opex / (profit rate - loss rate), which omitted two real costs and understated the answer by about a third: * the funding cost on the share of assets funded by the facility rather than by equity, and * nothing about utilisation — but note the answer is expressed in EARNING ASSETS, so the utilisation drag belongs in the capital required to carry them, reported separately below. Two lineages (Google, Mistral) raised the funding omission independently. """ y = v(s["profit_rate"]); l = v(s["net_loss_rate"]); o = v(s["opex_y1"]) + extra_opex lev = v(s["leverage"]); cof = v(s["cost_of_funding"]) debt_share = lev / (1.0 + lev) if lev > 0 else 0.0 # of earning assets net_yield = y - l - debt_share * cof return o / net_yield if net_yield > 0 else None def capital_required(s, extra_opex=0.0): """Capital needed to CARRY the break-even book: earning assets are only a fraction of capital deployed, and the facility supplies part of them.""" ea = breakeven_earning_assets(s, extra_opex) if ea is None: return None lev = v(s["leverage"]); util = v(s["utilisation"]) equity_share = 1.0 / (1.0 + lev) if lev > 0 else 1.0 return ea * equity_share / util def net_yield(s): y = v(s["profit_rate"]); l = v(s["net_loss_rate"]) lev = v(s["leverage"]); cof = v(s["cost_of_funding"]) debt_share = lev / (1.0 + lev) if lev > 0 else 0.0 return y - l - debt_share * cof def sensitivity(base_key="base", years=5): """One variable at a time — L-9: never move two and attribute to one.""" import copy base = SCENARIOS[base_key] ref = run(base, years)[-1]["pretax"] moves = { "profit_rate": [-0.02, +0.02], "net_loss_rate": [+0.02, -0.006], "utilisation": [-0.20, +0.10], "opex_y1": [+100_000, -100_000], "avg_ticket": [-30_000, +30_000], "cost_of_funding": [+0.03, -0.02], "leverage": [-1.0, +1.0], } rows = [] for k, deltas in moves.items(): line = {"driver": k, "base_value": v(base[k]), "reference_pretax_y5": round(ref)} for i, d in enumerate(deltas): s2 = copy.deepcopy(base) val = v(s2[k]) + d if k == "leverage": val = max(0.0, val) s2[k] = (val, s2[k][1], s2[k][2]) line[f"{'down' if i == 0 else 'up'}_value"] = round(val, 4) line[f"{'down' if i == 0 else 'up'}_pretax_y5"] = round(run(s2, years)[-1]["pretax"]) rows.append(line) rows.sort(key=lambda r: -abs(r["up_pretax_y5"] - r["down_pretax_y5"])) return rows