"""GreyScienx armchair model for inheritance in a long-life society. The model compares inheritances received at ages 40, 55, 70 and 85 with a living transfer at 35. It also tests capital compounding, first-home timing, business runway, simplified South African transfer-tax wedges, parental retirement reserves and three-generation wealth paths. All money is constant 2026 rand. The results are scenarios, not forecasts or tax advice. """ from __future__ import annotations import json import re import sys from pathlib import Path import matplotlib.pyplot as plt import numpy as np ROOT = Path(__file__).resolve().parents[1] WORK_DIR = ROOT / "work" / "inheritance-after-retirement" ASSET_DIR = WORK_DIR / "assets" RESULTS_PATH = WORK_DIR / "model_results.json" CSS_PATH = Path(r"C:\Users\Deriv\Desktop\GreyScienx\app\globals.css") STYLE_HELPER = Path( r"C:\Users\Deriv\Desktop\GreyScienx\skills\greyscienx-editorial-pdf\scripts" ) if str(STYLE_HELPER) not in sys.path: sys.path.insert(0, str(STYLE_HELPER)) try: from greyscienx_style import configure_matplotlib # type: ignore except Exception: configure_matplotlib = None def load_brand_tokens() -> dict[str, str]: defaults = { "black": "#131200", "true-black": "#000000", "coral": "#f26157", "white": "#fbfffe", "grey-100": "#f0f1f2", "grey-300": "#cccccc", "grey-500": "#777777", "grey-700": "#3d3d3d", } if CSS_PATH.exists(): css = CSS_PATH.read_text(encoding="utf-8") for key in list(defaults): match = re.search(rf"--{re.escape(key)}\s*:\s*(#[0-9a-fA-F]{{6}})", css) if match: defaults[key] = match.group(1) return defaults TOKENS = load_brand_tokens() BLACK = TOKENS["black"] TRUE_BLACK = TOKENS["true-black"] CORAL = TOKENS["coral"] WHITE = TOKENS["white"] GREY_100 = TOKENS["grey-100"] GREY_300 = TOKENS["grey-300"] GREY_500 = TOKENS["grey-500"] GREY_700 = TOKENS["grey-700"] def set_plot_style() -> None: configured = False if configure_matplotlib is not None: try: configure_matplotlib(CSS_PATH) configured = True except Exception: pass if not configured: plt.rcParams.update( { "font.family": "sans-serif", "font.sans-serif": ["Segoe UI", "Arial", "DejaVu Sans"], "font.size": 9.0, "axes.edgecolor": BLACK, "axes.labelcolor": BLACK, "axes.titlecolor": BLACK, "xtick.color": BLACK, "ytick.color": BLACK, "text.color": BLACK, "figure.facecolor": WHITE, "axes.facecolor": WHITE, "savefig.facecolor": WHITE, } ) plt.rcParams["axes.unicode_minus"] = False def figure_header(fig: plt.Figure, field: str, title: str, subtitle: str) -> None: fig.add_artist( plt.Line2D( [0.065, 0.965], [0.955, 0.955], transform=fig.transFigure, color=CORAL, linewidth=4.0, solid_capstyle="butt" ) ) fig.text(0.065, 0.918, field.upper(), color=CORAL, fontsize=8.5, fontweight="bold", ha="left", va="top") fig.text(0.065, 0.878, title, color=BLACK, fontsize=17, fontweight="bold", ha="left", va="top") fig.text(0.065, 0.826, subtitle, color=GREY_700, fontsize=8.4, ha="left", va="top") def style_axis(ax: plt.Axes, grid_axis: str = "y") -> None: ax.spines["top"].set_visible(False) ax.spines["right"].set_visible(False) ax.spines["left"].set_color(BLACK) ax.spines["bottom"].set_color(BLACK) ax.grid(axis=grid_axis, color=GREY_300, linewidth=0.6) ax.grid(axis="x" if grid_axis == "y" else "y", visible=False) ax.set_axisbelow(True) def save_figure(fig: plt.Figure, name: str) -> Path: ASSET_DIR.mkdir(parents=True, exist_ok=True) path = ASSET_DIR / name fig.savefig(path, dpi=280, bbox_inches="tight", facecolor=WHITE) plt.close(fig) return path TRANSFER = 1_000_000.0 RECEIPT_AGES = [35, 40, 55, 70, 85] FINAL_AGE = 100 START_MONTHLY_SALARY = 30_000.0 REAL_WAGE_GROWTH = 0.012 SALARY_SAVING_RATE = 0.03 PORTFOLIO_RETURN = 0.04 HOME_PRICE = 1_800_000.0 HOME_DEPOSIT = 0.20 * HOME_PRICE BUSINESS_CAPITAL = 250_000.0 def future_value(amount: float, years: int, rate: float) -> float: return amount * ((1 + rate) ** years) def donation_tax(gift: float) -> float: """Simplified 2026/27 donation tax for one natural-person donor.""" taxable = max(0.0, gift - 150_000.0) return 0.20 * min(taxable, 30_000_000.0) + 0.25 * max(0.0, taxable - 30_000_000.0) def estate_duty(net_estate: float) -> float: """Simplified duty after only the R3.5m general abatement.""" dutiable = max(0.0, net_estate - 3_500_000.0) return 0.20 * min(dutiable, 30_000_000.0) + 0.25 * max(0.0, dutiable - 30_000_000.0) def gift_from_total_budget(budget: float) -> float: """Largest gift when the tax must also be paid from the donor's budget.""" low, high = 0.0, budget for _ in range(100): mid = (low + high) / 2 if mid + donation_tax(mid) <= budget: low = mid else: high = mid return low def deposit_age_without_transfer() -> int: balance = 0.0 for age in range(25, 101): salary = START_MONTHLY_SALARY * 12 * ((1 + REAL_WAGE_GROWTH) ** (age - 25)) balance *= 1 + PORTFOLIO_RETURN balance += salary * SALARY_SAVING_RATE if balance >= HOME_DEPOSIT: return age return 101 def retirement_reserve(lifespan: int, parent_age: int = 65) -> float: annual_income_gap = 5_000.0 * 12 care_buffer = 500_000.0 years = max(0, lifespan - parent_age) if years == 0: income_reserve = 0.0 else: income_reserve = annual_income_gap * (1 - (1 + 0.03) ** (-years)) / 0.03 return income_reserve + care_buffer def dynasty_paths() -> dict[str, float]: initial = 2_000_000.0 elder_return = 0.04 gen1_estate = future_value(initial, 35, elder_return) gen1_receipt = gen1_estate - estate_duty(gen1_estate) gen2_estate = future_value(gen1_receipt, 30, elder_return) late_final = gen2_estate - estate_duty(gen2_estate) def early_path(recipient_return: float) -> float: gen1_gift = gift_from_total_budget(initial) gen1_wealth_at_65 = future_value(gen1_gift, 30, recipient_return) gen2_gift = gift_from_total_budget(gen1_wealth_at_65) return future_value(gen2_gift, 35, recipient_return) return { "late_bequests_4pct": late_final, "early_gifts_4pct": early_path(0.04), "early_gifts_5pct": early_path(0.05), "no_tax_neutral_4pct": future_value(initial, 65, 0.04), } def make_results() -> dict: timing = { str(age): { str(int(rate * 100)): future_value(TRANSFER, FINAL_AGE - age, rate) for rate in (0.02, 0.04, 0.06) } for age in RECEIPT_AGES } purpose_shares = { "35": [0.40, 0.30, 0.15, 0.10, 0.05], "40": [0.35, 0.30, 0.15, 0.15, 0.05], "55": [0.20, 0.15, 0.10, 0.40, 0.15], "70": [0.05, 0.05, 0.00, 0.50, 0.40], "85": [0.00, 0.00, 0.00, 0.30, 0.70], } baseline_home_age = deposit_age_without_transfer() opportunity = {} for age in RECEIPT_AGES: purchase_age = age if age <= baseline_home_age else baseline_home_age opportunity[str(age)] = { "first_home_purchase_age": purchase_age, "years_earlier_than_baseline": max(0, baseline_home_age - age), "business_runway_to_65": max(0, 65 - age), } tax_examples = {} for budget in (1_000_000.0, 10_000_000.0, 40_000_000.0): gift = gift_from_total_budget(budget) bequest = budget - estate_duty(budget) tax_examples[str(int(budget))] = { "donor_budget": budget, "living_gift_received": gift, "donations_tax": budget - gift, "bequest_received": bequest, "estate_duty": budget - bequest, } safe_transfers = { str(lifespan): { str(int(wealth)): max(0.0, wealth - retirement_reserve(lifespan)) for wealth in (2_000_000.0, 5_000_000.0, 10_000_000.0) } for lifespan in (85, 100, 120) } compounding_80 = { str(int(rate * 100)): future_value(TRANSFER, 80, rate) for rate in (0.02, 0.04, 0.06) } return { "study": "Inheritance After Retirement", "prices": "constant 2026 rand", "core_assumptions": { "transfer": TRANSFER, "final_age": FINAL_AGE, "start_monthly_salary": START_MONTHLY_SALARY, "real_wage_growth": REAL_WAGE_GROWTH, "salary_saving_rate": SALARY_SAVING_RATE, "portfolio_return": PORTFOLIO_RETURN, "home_price": HOME_PRICE, "home_deposit": HOME_DEPOSIT, "business_capital": BUSINESS_CAPITAL, }, "value_at_100": timing, "purpose_shares": purpose_shares, "baseline_first_home_age": baseline_home_age, "opportunity": opportunity, "tax_examples": tax_examples, "safe_transfers": safe_transfers, "dynasty_paths": dynasty_paths(), "compounding_80_years": compounding_80, "warnings": [ "Receipt ages and uses are scenarios, not forecasts of South African households.", "Tax cases simplify 2026/27 rules and exclude CGT, transfer duty, spouse deductions, trusts, expenses and avoidance.", "The dynasty model assumes fixed real returns, 100-year lives and 30-year generation gaps.", "The safe-transfer test is an illustrative reserve rule, not financial advice.", ], } def make_figures(data: dict) -> None: set_plot_style() # Figure 1: value at age 100 by transfer age and return. fig, ax = plt.subplots(figsize=(10.6, 5.5)) figure_header( fig, "Figure 1", "Inheritance loses economic runway as it arrives later", "Value at age 100 of R1 million received at each age; age 35 is a living-transfer reference." ) styles = [ ("2", GREY_500, ":", "D", "2% real return"), ("4", BLACK, "--", "s", "4% real return"), ("6", CORAL, "-", "o", "6% real return"), ] for key, color, line, marker, label in styles: values = [data["value_at_100"][str(age)][key] / 1e6 for age in RECEIPT_AGES] ax.plot(RECEIPT_AGES, values, color=color, linestyle=line, marker=marker, linewidth=2.2, markersize=6, label=label) ax.axvline(65, color=GREY_300, linewidth=1.2) ax.text(65, ax.get_ylim()[1] * 0.93, "conventional retirement age", rotation=90, ha="right", va="top", color=GREY_700, fontsize=8) ax.set_xlabel("Age when capital arrives") ax.set_ylabel("Value at age 100, R million") ax.set_xticks(RECEIPT_AGES, ["35 gift", "40", "55", "70", "85"]) style_axis(ax) ax.legend(loc="upper right", frameon=False, ncol=1) fig.subplots_adjust(left=0.09, right=0.92, bottom=0.14, top=0.75) save_figure(fig, "inheritance-timing.png") # Figure 2: the purpose of capital changes with receipt age. fig, ax = plt.subplots(figsize=(10.6, 5.5)) figure_header( fig, "Figure 2", "Capital gradually changes from formation to transmission", "Illustrative allocation of a transfer by recipient age; shares sum to 100 percent." ) categories = ["Home formation", "Business / study", "Debt reduction", "Retirement / care", "Onward transfer"] colors = [CORAL, BLACK, GREY_700, GREY_300, GREY_500] hatches = [None, None, "//", "..", "xx"] y_positions = np.arange(len(RECEIPT_AGES)) left = np.zeros(len(RECEIPT_AGES)) for idx, category in enumerate(categories): vals = np.array([data["purpose_shares"][str(age)][idx] * 100 for age in RECEIPT_AGES]) bars = ax.barh(y_positions, vals, left=left, color=colors[idx], height=0.62, label=category, hatch=hatches[idx], edgecolor=BLACK if hatches[idx] else colors[idx], linewidth=0.6 if hatches[idx] else 0) for bar, value, start in zip(bars, vals, left): if value >= 15: text_color = WHITE if idx in (1, 2, 4) else BLACK ax.text(start + value / 2, bar.get_y() + bar.get_height() / 2, f"{value:.0f}%", ha="center", va="center", color=text_color, fontsize=8, fontweight="bold") left += vals ax.set_xlabel("Share of transfer") ax.set_ylabel("Age when capital arrives") ax.set_yticks(y_positions, [str(age) for age in RECEIPT_AGES]) ax.set_xlim(0, 100) style_axis(ax, grid_axis="x") ax.legend(loc="lower center", bbox_to_anchor=(0.5, -0.37), ncol=3, frameon=False) fig.subplots_adjust(left=0.11, right=0.97, bottom=0.32, top=0.75) save_figure(fig, "capital-purpose.png") # Figure 3: capital access for home and enterprise formation. fig, axes = plt.subplots(1, 2, figsize=(10.6, 5.3)) figure_header( fig, "Figure 3", "Late inheritance misses the first-home and enterprise windows", "R30,000 starting monthly salary; 3 percent salary saving; R360,000 home deposit; retirement at 65." ) ages = RECEIPT_AGES baseline = data["baseline_first_home_age"] purchase = [data["opportunity"][str(age)]["first_home_purchase_age"] for age in ages] axes[0].bar(range(len(ages)), purchase, color=[CORAL, CORAL, GREY_500, GREY_500, GREY_500]) axes[0].axhline(baseline, color=BLACK, linestyle="--", linewidth=1.4, label=f"No transfer: age {baseline}") axes[0].set_xticks(range(len(ages)), [str(age) for age in ages]) axes[0].set_xlabel("Age when transfer arrives") axes[0].set_ylabel("Age of first-home purchase") axes[0].set_title("First-home entry") axes[0].set_ylim(25, 58) axes[0].legend(frameon=False, loc="upper left") for x, value in enumerate(purchase): axes[0].text(x, value + 0.8, str(value), ha="center", fontsize=8) style_axis(axes[0]) runway = [data["opportunity"][str(age)]["business_runway_to_65"] for age in ages] axes[1].bar(range(len(ages)), runway, color=[CORAL, CORAL, GREY_500, GREY_300, GREY_300]) axes[1].set_xticks(range(len(ages)), [str(age) for age in ages]) axes[1].set_xlabel("Age when transfer arrives") axes[1].set_ylabel("Years before age 65") axes[1].set_title("Runway for a capital-funded business") axes[1].set_ylim(0, 34) for x, value in enumerate(runway): axes[1].text(x, value + 0.8, str(value), ha="center", fontsize=8) style_axis(axes[1]) fig.subplots_adjust(left=0.08, right=0.97, bottom=0.15, top=0.70, wspace=0.25) save_figure(fig, "housing-business-windows.png") # Figure 6: three-generation paths. fig, ax = plt.subplots(figsize=(10.6, 5.4)) figure_header( fig, "Figure 6", "Earlier ownership matters only when the heir can use it better", "Gen 0 starts with R2m at 65; Gen 2 is measured at 70; simplified transfer taxes included." ) labels = ["Late bequests\n4% return", "Early gifts\n4% return", "Early gifts\n5% return"] keys = ["late_bequests_4pct", "early_gifts_4pct", "early_gifts_5pct"] values = [data["dynasty_paths"][key] / 1e6 for key in keys] bars = ax.bar(range(3), values, color=[BLACK, GREY_500, CORAL], width=0.62) benchmark = data["dynasty_paths"]["no_tax_neutral_4pct"] / 1e6 ax.axhline(benchmark, color=BLACK, linestyle=":", linewidth=1.4, label=f"No-tax 4% benchmark: R{benchmark:.1f}m") for bar, value in zip(bars, values): ax.text(bar.get_x() + bar.get_width() / 2, value + 0.8, f"R{value:.1f}m", ha="center", fontsize=9, fontweight="bold") ax.set_xticks(range(3), labels) ax.set_ylabel("Gen 2 wealth at age 70, R million") style_axis(ax) ax.legend(frameon=False, loc="upper left") fig.subplots_adjust(left=0.10, right=0.97, bottom=0.19, top=0.72) save_figure(fig, "dynasty-paths.png") # Figure 5: eighty years of compounding. fig, ax = plt.subplots(figsize=(10.6, 5.3)) figure_header( fig, "Figure 5", "Eighty years turns small return differences into dynasties", "Future value of R1m in constant 2026 rand; log scale keeps all three outcomes visible." ) rates = [2, 4, 6] values = [data["compounding_80_years"][str(rate)] / 1e6 for rate in rates] bars = ax.bar(range(3), values, color=[GREY_500, BLACK, CORAL], width=0.58) ax.set_yscale("log") ax.set_xticks(range(3), [f"{rate}% real" for rate in rates]) ax.set_xlabel("Annual return") ax.set_ylabel("Value after 80 years, R million (log scale)") for bar, value in zip(bars, values): ax.text(bar.get_x() + bar.get_width() / 2, value * 1.14, f"R{value:.1f}m", ha="center", fontsize=9, fontweight="bold") style_axis(ax) fig.subplots_adjust(left=0.11, right=0.97, bottom=0.15, top=0.72) save_figure(fig, "eighty-year-compounding.png") # Figure 4: safe transfer frontier. fig, ax = plt.subplots(figsize=(10.6, 5.5)) figure_header( fig, "Figure 4", "A parent cannot gift wealth that may finance another 55 years", "Safe gift after reserving a R5,000 monthly income gap plus R500,000 care buffer at age 65." ) wealths = [2, 5, 10] x = np.arange(len(wealths)) width = 0.23 cases = [(85, CORAL, "-", "Life to 85"), (100, BLACK, "//", "Life to 100"), (120, GREY_500, "..", "Life to 120")] for offset, (lifespan, color, hatch, label) in enumerate(cases): vals = [data["safe_transfers"][str(lifespan)][str(int(w * 1e6))] / 1e6 for w in wealths] bars = ax.bar(x + (offset - 1) * width, vals, width=width, color=color, hatch=hatch, edgecolor=BLACK if hatch else color, linewidth=0.6, label=label) for bar, value in zip(bars, vals): ax.text(bar.get_x() + bar.get_width() / 2, value + 0.12, f"{value:.1f}", ha="center", va="bottom", fontsize=7.4) ax.set_xticks(x, [f"R{w}m" for w in wealths]) ax.set_xlabel("Parent wealth at age 65") ax.set_ylabel("Illustrative safe living transfer, R million") style_axis(ax) ax.legend(loc="upper left", frameon=False, ncol=3) fig.subplots_adjust(left=0.10, right=0.97, bottom=0.15, top=0.72) save_figure(fig, "safe-transfer-frontier.png") def main() -> None: WORK_DIR.mkdir(parents=True, exist_ok=True) ASSET_DIR.mkdir(parents=True, exist_ok=True) data = make_results() RESULTS_PATH.write_text(json.dumps(data, indent=2), encoding="utf-8") make_figures(data) display = { "value_at_100_4pct_m": { age: round(values["4"] / 1e6, 2) for age, values in data["value_at_100"].items() }, "baseline_first_home_age": data["baseline_first_home_age"], "dynasty_paths_m": { key: round(value / 1e6, 2) for key, value in data["dynasty_paths"].items() }, "compounding_80_years_m": { key: round(value / 1e6, 2) for key, value in data["compounding_80_years"].items() }, "safe_transfer_r2m": { life: round(values["2000000"] / 1e6, 2) for life, values in data["safe_transfers"].items() }, } print(json.dumps(display, indent=2)) if __name__ == "__main__": main()