import json from dataclasses import asdict, dataclass from pathlib import Path from typing import Optional ROOT = Path(__file__).resolve().parents[1] RESULTS_PATH = ROOT / "source" / "economics-of-living-together" / "model_results.json" @dataclass class Scenario: name: str separate_expense: float separate_rent: float cohabit_expense: float cohabit_rent: float income_growth: float expense_growth: float gross_investment_return: float investment_fee_drag: float investment_tax_drag: float debt_rate: float moving_cost: float pension_rate: float child_monthly_cost: float family_remittance: float care_reduction: float care_start_age: int care_end_age: int property_price_40: float deposit_rate: float purchase_cost_rate: float mortgage_real_rate: float home_real_growth: float owner_cost_rate: float inheritance_age: Optional[int] inheritance_amount: float retirement_expense_factor: float income_shocks: tuple emergencies: tuple death_age: Optional[int] funeral_cost: float @property def net_investment_return(self): return self.gross_investment_return - self.investment_fee_drag - self.investment_tax_drag SCENARIOS = ( Scenario( name="Best case", separate_expense=44_800, separate_rent=19_000, cohabit_expense=34_800, cohabit_rent=12_000, income_growth=0.015, expense_growth=0.010, gross_investment_return=0.055, investment_fee_drag=0.005, investment_tax_drag=0.000, debt_rate=0.070, moving_cost=20_000, pension_rate=0.10, child_monthly_cost=3_500, family_remittance=500, care_reduction=0.00, care_start_age=36, care_end_age=36, property_price_40=1_800_000, deposit_rate=0.20, purchase_cost_rate=0.05, mortgage_real_rate=0.035, home_real_growth=0.015, owner_cost_rate=0.015, inheritance_age=55, inheritance_amount=500_000, retirement_expense_factor=0.70, income_shocks=(), emergencies=(), death_age=None, funeral_cost=0, ), Scenario( name="Average case", separate_expense=44_800, separate_rent=19_000, cohabit_expense=36_300, cohabit_rent=13_000, income_growth=0.0075, expense_growth=0.0075, gross_investment_return=0.045, investment_fee_drag=0.0075, investment_tax_drag=0.0075, debt_rate=0.080, moving_cost=30_000, pension_rate=0.08, child_monthly_cost=5_000, family_remittance=1_500, care_reduction=0.20, care_start_age=36, care_end_age=42, property_price_40=1_900_000, deposit_rate=0.20, purchase_cost_rate=0.06, mortgage_real_rate=0.045, home_real_growth=0.000, owner_cost_rate=0.018, inheritance_age=55, inheritance_amount=200_000, retirement_expense_factor=0.80, income_shocks=((30, 1, 6, 1.00), (50, 0, 12, 0.50)), emergencies=((50, 100_000),), death_age=None, funeral_cost=0, ), Scenario( name="Worst case", separate_expense=47_000, separate_rent=20_000, cohabit_expense=42_500, cohabit_rent=14_500, income_growth=0.000, expense_growth=0.005, gross_investment_return=0.025, investment_fee_drag=0.010, investment_tax_drag=0.005, debt_rate=0.030, moving_cost=50_000, pension_rate=0.04, child_monthly_cost=6_500, family_remittance=2_500, care_reduction=0.40, care_start_age=36, care_end_age=45, property_price_40=2_100_000, deposit_rate=0.20, purchase_cost_rate=0.08, mortgage_real_rate=0.065, home_real_growth=-0.010, owner_cost_rate=0.022, inheritance_age=None, inheritance_amount=0, retirement_expense_factor=0.90, income_shocks=((28, 1, 12, 1.00), (43, 0, 9, 1.00), (58, 1, 60, 0.50)), emergencies=((58, 250_000),), death_age=63, funeral_cost=100_000, ), ) def monthly_rate(annual): return (1 + annual) ** (1 / 12) - 1 def mortgage_payment(principal, annual_real_rate, months): rate = monthly_rate(annual_real_rate) if rate == 0: return principal / months return principal * rate / (1 - (1 + rate) ** -months) def simulate(scenario, move_age): liquid = 0.0 pension = 0.0 home_value = 0.0 mortgage_balance = 0.0 mortgage_payment_monthly = 0.0 mortgage_months_left = 0 homeowner = False purchase_age = None move_month = (move_age - 25) * 12 net_investment_monthly = monthly_rate(scenario.net_investment_return) debt_monthly = monthly_rate(scenario.debt_rate) home_growth_monthly = monthly_rate(scenario.home_real_growth) mortgage_rate_monthly = monthly_rate(scenario.mortgage_real_rate) milestones = {25: 0.0} series = [(25.0, 0.0)] cumulative_living_expense = 0.0 cumulative_child_cost = 0.0 cumulative_remittance = 0.0 cumulative_income_lost = 0.0 cumulative_care_income_lost = 0.0 cumulative_pension_contributions = 0.0 cumulative_investment_drag = 0.0 death_month = None if scenario.death_age is None else (scenario.death_age - 25) * 12 for month in range(50 * 12): age = 25 + month / 12 years = month / 12 expense_growth_factor = (1 + scenario.expense_growth) ** years salary_growth_factor = (1 + scenario.income_growth) ** years salaries = [30_000 * salary_growth_factor, 20_000 * salary_growth_factor] if scenario.death_age is not None and age >= scenario.death_age: salaries[0] = 0.0 if age >= 65: salaries = [0.0, 0.0] if scenario.care_start_age <= age < scenario.care_end_age: reduction = salaries[1] * scenario.care_reduction salaries[1] -= reduction cumulative_care_income_lost += reduction shock_loss = 0.0 for shock_age, person, duration, loss_fraction in scenario.income_shocks: start = (shock_age - 25) * 12 if start <= month < start + duration: loss = salaries[person] * loss_fraction salaries[person] -= loss shock_loss += loss cumulative_income_lost += shock_loss cash_income = sum(salaries) # Retirement contributions are modelled outside the stated disposable salary. pension_contribution = scenario.pension_rate * cash_income if age < 65 else 0.0 pension = pension * (1 + net_investment_monthly) + pension_contribution cumulative_pension_contributions += pension_contribution # At retirement the accumulated pension becomes available to fund consumption. if month == (65 - 25) * 12: liquid += pension pension = 0.0 liquid_growth_rate = net_investment_monthly if liquid >= 0 else debt_monthly before_growth = liquid liquid *= 1 + liquid_growth_rate # Difference between gross and net return is an approximate fee/tax opportunity cost. if liquid > 0 and before_growth > 0: gross_m = monthly_rate(scenario.gross_investment_return) cumulative_investment_drag += max(0.0, before_growth * (gross_m - net_investment_monthly)) if homeowner: home_value *= 1 + home_growth_monthly if mortgage_months_left > 0: interest = mortgage_balance * mortgage_rate_monthly principal_paid = min(mortgage_balance, mortgage_payment_monthly - interest) mortgage_balance -= principal_paid mortgage_months_left -= 1 # Attempt to buy annually from age 40 through age 50 if a six-month cash buffer remains. if (not homeowner and 40 <= age <= 50 and month % 12 == 0): candidate_price = scenario.property_price_40 * (1 + scenario.home_real_growth) ** (age - 40) upfront = candidate_price * (scenario.deposit_rate + scenario.purchase_cost_rate) required_buffer = 6 * scenario.cohabit_expense * expense_growth_factor if liquid >= upfront + required_buffer: homeowner = True purchase_age = int(age) home_value = candidate_price mortgage_balance = candidate_price * (1 - scenario.deposit_rate) mortgage_months_left = 20 * 12 mortgage_payment_monthly = mortgage_payment( mortgage_balance, scenario.mortgage_real_rate, mortgage_months_left ) liquid -= upfront # Housing and non-housing living costs are kept separate after a purchase or death. if age < move_age: rent = scenario.separate_rent * expense_growth_factor nonhousing = (scenario.separate_expense - scenario.separate_rent) * expense_growth_factor else: rent = scenario.cohabit_rent * expense_growth_factor nonhousing = (scenario.cohabit_expense - scenario.cohabit_rent) * expense_growth_factor if age >= 65: nonhousing *= scenario.retirement_expense_factor if scenario.death_age is not None and age >= scenario.death_age: nonhousing *= 0.65 if homeowner: housing = (mortgage_payment_monthly if mortgage_months_left > 0 else 0.0) housing += home_value * scenario.owner_cost_rate / 12 else: housing = rent child_cost = 0.0 for birth_age in (36, 39): child_age = age - birth_age if 0 <= child_age < 18: child_cost += scenario.child_monthly_cost * expense_growth_factor elif 18 <= child_age < 22: child_cost += 0.50 * scenario.child_monthly_cost * expense_growth_factor remittance = 0.0 if 30 <= age < 65: remittance = scenario.family_remittance * expense_growth_factor expense = housing + nonhousing + child_cost + remittance cumulative_living_expense += housing + nonhousing cumulative_child_cost += child_cost cumulative_remittance += remittance one_off = 0.0 if month == move_month: one_off += scenario.moving_cost if scenario.inheritance_age is not None and month == (scenario.inheritance_age - 25) * 12: liquid += scenario.inheritance_amount for event_age, amount in scenario.emergencies: if month == (event_age - 25) * 12: one_off += amount if death_month is not None and month == death_month: one_off += scenario.funeral_cost liquid += cash_income - expense - one_off net_home_equity = 0.95 * home_value - mortgage_balance if homeowner else 0.0 net_worth = liquid + pension + net_home_equity end_age = 25 + (month + 1) / 12 series.append((end_age, net_worth)) if end_age in (35, 45, 55, 65, 75): milestones[int(end_age)] = net_worth return { "move_age": move_age, "net_worth": series[-1][1], "milestones": milestones, "series": series, "purchase_age": purchase_age, "home_value": home_value, "mortgage_balance": mortgage_balance, "liquid": liquid, "pension": pension, "living_expense": cumulative_living_expense, "child_cost": cumulative_child_cost, "remittance": cumulative_remittance, "income_lost": cumulative_income_lost, "care_income_lost": cumulative_care_income_lost, "pension_contributions": cumulative_pension_contributions, "investment_drag": cumulative_investment_drag, } def money(value): sign = "-" if value < 0 else "" return f"{sign}R{abs(value):,.0f}" if __name__ == "__main__": output = { "model_label": "Gauteng lifetime household-consolidation model", "currency": "constant 2026 rand", "ages": [25, 75], "salary_inputs_monthly": [30_000, 20_000], "scenarios": [], } for scenario in SCENARIOS: early = simulate(scenario, 25) late = simulate(scenario, 35) output["scenarios"].append( { "name": scenario.name, "assumptions": asdict(scenario), "early_move_age": 25, "late_move_age": 35, "early_net_worth_age_75": early["net_worth"], "late_net_worth_age_75": late["net_worth"], "age_75_gap": early["net_worth"] - late["net_worth"], "early_milestones": early["milestones"], "late_milestones": late["milestones"], "early_purchase_age": early["purchase_age"], "late_purchase_age": late["purchase_age"], "living_cost_saved": late["living_expense"] - early["living_expense"], "child_cost": early["child_cost"], "family_remittance": early["remittance"], "income_lost_to_shocks": early["income_lost"], "income_lost_to_care": early["care_income_lost"], "early_pension_contributions": early["pension_contributions"], "early_investment_drag": early["investment_drag"], } ) print(f"\n{scenario.name}") print("age,early,late,gap") for age in (25, 35, 45, 55, 65, 75): e = early["milestones"][age] l = late["milestones"][age] print(f"{age},{money(e)},{money(l)},{money(e-l)}") print(f"purchase_age_early={early['purchase_age']}") print(f"purchase_age_late={late['purchase_age']}") print(f"living_cost_saved={money(late['living_expense']-early['living_expense'])}") print(f"child_cost={money(early['child_cost'])}") print(f"remittance={money(early['remittance'])}") print(f"income_lost_shocks={money(early['income_lost'])}") print(f"income_lost_care={money(early['care_income_lost'])}") print(f"pension_contributions={money(early['pension_contributions'])}") print(f"investment_drag_early={money(early['investment_drag'])}") RESULTS_PATH.parent.mkdir(parents=True, exist_ok=True) RESULTS_PATH.write_text(json.dumps(output, indent=2), encoding="utf-8") print(f"model_results={RESULTS_PATH}")