Rent vs Buy

Methodology

Symmetric framing

Both households start with the same liquid wealth W₀ = down payment + buy-side closing costs. At t = 0 the renter invests W₀; the buyer spends it on the purchase. Each month, the side with the lower outflow invests the differential. Annual tax effects (HRA refund, MID benefit, mutuo deduction, EWF add-back, Box 3 drag, IT bollo) are netted into the buy-side cash flow once a year so they ripple through the differential.

Net worth definitions (asymmetric on purpose)

  • Buy: (V − L) + P_buy. The accounting view of home equity plus portfolio. We do not subtract sale-side transaction costs or a notional home capital-gains tax — if you sold today, ~6–10% in agent/notary/ transfer costs would come off.
  • Rent: P_rent − unrealizedCGT(P_rent). The country-specific capital-gains tax that would be owed on liquidation is subtracted (US LTCG ± NIIT, IT 26%/12.5%, NL 0% because Box 3 is paid annually).

Mortgage

Annuity (standard amortization): M = L₀ · r / (1 − (1 + r)^−n) with r = monthly rate, n = term in months. Monthly split: interest = balance × r; principal = M − interest.

Portfolio

Two buckets: equity ETF and government bonds, allocation slider, monthly returns via (1 + annual)^(1/12) − 1, annual rebalance to target. Cost basis is tracked per bucket so realization tax is computed correctly.

United States

  • Closing costs default 3% of price.
  • Property tax = rate × home value (annual, applied monthly).
  • PMI = pmiRate × original loan, while LTV > 80%.
  • Itemize vs standard each year. Itemized = deductible mortgage interest (interest scaled by min(1, $750k/avgBalance)) + min($10k SALT cap, property + state-local income). If itemized > standard deduction (2025: $15k single / $30k MFJ), we apply the federal marginal rate to the excess.
  • Realization tax on rent portfolio: LTCG rate (default 15%) + NIIT 3.8% if toggled.

Netherlands

  • One-time: 2% transfer tax (overdrachtsbelasting), or 0% for first-time buyers below the threshold (~€525k); ~1.5% notary + advisor; NHG premium 0.6% of loan when applicable.
  • Recurring: OZB ~0.1% × WOZ; Eigenwoningforfait at 0.35% of WOZ (2.35% above ~€1.31M).
  • HRA: deductible at min(marginal rate, ceiling ≈ 36.97%) — only for annuity products. Net annual buy-side tax effect = min(marginal, ceiling) × interestPaid − marginal × EWF.
  • Box 3: 2025 transition deemed yield × 36% on portfolio above the per-person threshold (~€57k single, doubled if partnered). v1 treats the whole portfolio as the "investments" bucket.

Italy

  • One-time (prima casa, private seller, non-luxury A/2–A/7):
    • Imposta di registro: 2% × cadastral value
    • Imposta ipotecaria + catastale: €100 fixed (€50 + €50)
    • Notary 1.5% (parameter)
    • Real-estate agent 3% + 22% IVA (parameter)
  • Recurring: TARI flat (annual); IMU exempt (prima casa, non-luxury).
  • Mutuo deduction: 19% × min(interest paid in year, €4,000) — credit against IRPEF, prima casa only.
  • 0.2% bollo on portfolio market value, annually.
  • Realization (rent-side CGT): 26% on equity ETF gains, 12.5% on Italian/EU government bond gains.

Policy simulation (v1.1)

Several thresholds are inflation-indexed in real life: the NL Box 3 allowance, the US standard deduction and SALT cap, the IT mutuo cap, etc. Each of those exposes a sibling annual-growth field. At year tick N, the engine evaluates the parameter as base × (1 + growth)^(N − 1), so year 1 always matches the base value and growth compounds geometrically afterwards.

Set the growth to 0% for "frozen at today's value" (this is what historic IT mutuo caps look like). Use 2% to approximate CPI indexation. Negative values let you simulate cuts (e.g. SALT cap halving in year 5 — though we only support smooth compounding, not step changes; that's a v2 feature).

One-time costs (transfer tax, registration tax, NHG/first-time-buyer thresholds, cadastral value for closing) aren't escalated since they only fire at t = 0.

Open assumptions (v1)

  • Dividend withholding tax on equity ETFs ignored.
  • NL Box 3: whole portfolio in the "investments" bucket — bond/cash distinction is v2.
  • IT: distributions ignored, taxes only at realization.
  • Maintenance is a flat % of value — no shock years.
  • HOA / TARI / insurance are flat — no inflation modeled.
  • NL partnered case uses the same marginal rate for both partners (v1 simplification).
  • Italy luxury homes (A/1, A/8, A/9) are excluded — IMU exemption assumed.
  • Annual rebalance treated as cost-basis-preserving (a v1 simplification).