Real estate · super (composes 4 primitives)
Real estate investment chain
Type the deal once. We chain cap rate, cash-on-cash, the actual mortgage payment on your terms, after-tax cash flow with depreciation, and a 5-year projection with appreciation + amortization paydown.
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Inputs
Load a preset
Result
Cap rate 5.22% · CoC -3.3% · Year-1 cash flow -$2,943.
Action: CoC -3.3% — typical buy-hold target. Stress test for rent drop 5% + vacancy +5% before signing.
- 1
Net operating income
$16,704
$26,784 eff gross − $10,080 opex
- 2
Cap rate
5.22%
NOI / purchase price
- 3
Mortgage P&I
$1,637/mo · $19,647/yr
$240,000 at 7.250% for 30 yrs
- 4
Year-1 cash flow (pre-tax)
-$2,943
NOI − annual debt service
- 5
- 6
After-tax cash flow
-$2,943
Depreciation $9,309 shields $9,309 of NOI
- 7
5-yr equity + cumulative cash flow
$41,745
Equity $144,459 (value $370,968 − balance $226,509) + -$14,713 cash flow
- 8
Approximate IRR (equity-only, 5 yr)
21.4%
Approximate — assumes you sell at year 5 for projected value
Assumptions & notes
- OpEx default 35% of gross — typical for SFR/small multifamily including PM. Drops to ~25% for self-managed.
- Depreciation is straight-line 27.5 yr residential (39 yr commercial). Recapture at sale is ignored here.
- IRR is a rough 5-yr equity-only approximation, not a full DCF.
Continue the housing path
Keep going from Real estate investment chain
Real-estate decisions compound: affordability changes refi risk, refi terms change investment returns, and investment math changes how much house is actually safe.
Try another scenario
Jump between the buyer, refi, and investor presets without leaving the super-calculator layer.
Affordability scenarios
Refi scenarios
Investor scenarios
Companion tools on mitchreise.com
Keep ShowMath as the formula layer, then jump to Reise Tools for richer dashboards, comparison panels, and adjacent housing workflows.
Multi-scenario comparison
What if — ±20% on one input
| Scenario | Purchase price | Headline | Δ vs baseline | Magnitude |
|---|---|---|---|---|
| −20% (cautious) | $256,000 | Cap rate 6.53% · CoC 1.4% · Year-1 cash flow $987. | 0 | |
| Baseline | $320,000 | Cap rate 5.22% · CoC -3.3% · Year-1 cash flow -$2,943. | 0 | |
| +20% (aggressive) | $384,000 | Cap rate 4.35% · CoC -6.5% · Year-1 cash flow -$6,872. | 0 |
Try the input with the highest sensitivity (above). The Δ column shows the dollar swing from a 20% move — that's how much room you have for a counter, raise, or hedge.
Goal seek
Solve for an input value
Pick the input you want to vary and the output you care about. We'll find the input value that gets you to the target. Bisection-based; converges in < 50 iterations.
Monte Carlo simulation
Distribution under input uncertainty (500 trials)
We perturb every numeric input with normal-distributed noise (10–25% sigma depending on input type) and run 500 compute trials. The output is a probability distribution, not a single number — closer to how finance actually works.
Most-leveraged inputs (sensitivity analysis)
Where to focus — what moves the answer most
Each input perturbed ±10%; measured impact on Net operating income. Higher elasticity = bigger lever.
- 1
Monthly rent (gross)
Elasticity ↑ 1.00× — 10% change in this input increases Net operating income by 10.0%.
- 2
Operating expenses (% of gross rent)
Elasticity ↓ 0.60× — 10% change in this input decreases Net operating income by 6.0%.
- 3
Vacancy + bad-debt allowance (%)
Elasticity ↓ 0.12× — 10% change in this input decreases Net operating income by 1.2%.
- 4
Purchase price
Elasticity ↕ 0.00× — 10% change in this input affects Net operating income by 0.0%.
ShowMath is the only calc site that surfaces this. Adjust the highest-leverage input first — that's where small moves create big results.
Chain payload (for the 3D constellation)
{
"slug": "real-estate-investment",
"depth": 1,
"primitives": [
"cap-rate-calculator",
"cash-on-cash-return",
"mortgage-calculator",
"rental-income-calculator"
],
"composes": [],
"chain": [
{
"key": "noi",
"label": "Net operating income",
"primitive": "rental-income-calculator",
"numeric": 16704
},
{
"key": "cap_rate",
"label": "Cap rate",
"primitive": "cap-rate-calculator",
"numeric": 5.220000000000001
},
{
"key": "mortgage",
"label": "Mortgage P&I",
"primitive": "mortgage-calculator",
"numeric": 1637.2230721348562
},
{
"key": "cash_flow",
"label": "Year-1 cash flow (pre-tax)",
"numeric": -2942.6768656182758
},
{
"key": "cash_on_cash",
"label": "Cash-on-cash return",
"primitive": "cash-on-cash-return",
"numeric": -3.3439509836571317
},
{
"key": "after_tax_cash_flow",
"label": "After-tax cash flow",
"numeric": -2942.6768656182758
},
{
"key": "five_year",
"label": "5-yr equity + cumulative cash flow",
"numeric": 41745.25410029833
},
{
"key": "irr_approx",
"label": "Approximate IRR (equity-only, 5 yr)",
"numeric": 21.443032569400856
}
]
}The chain explained
Each step above corresponds to a primitive calculator. Click any to see the stand-alone version with its own explainer + sources.
- cap rate calculatorshipping soon
- cash on cash return
- mortgage calculatorshipping soon
- rental income calculatorshipping soon
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