1. Internal Rate of Return (IRR) — Bisection Method
IRR is defined as the discount rate r at which the Net Present Value (NPV) of all cash flows equals zero:
There is no closed-form algebraic solution for IRR — it must be found numerically. We use the bisection method: a root-finding algorithm that repeatedly halves an interval [lo, hi] until NPV(mid) ≈ 0 to within a tolerance of 1×10⁻⁹.
14,000 bisection iterations provide precision to approximately 11 decimal places (2⁻¹⁴⁰⁰⁰ ≈ 10⁻⁴²¹⁷), far exceeding any practical requirement for real estate analysis. The bisection method is guaranteed to converge as long as NPV changes sign between lo and hi.
2. Loan Amortization & Debt Service
We compute the monthly mortgage payment using the standard amortizing loan formula:
Annual debt service = MonthlyPayment × 12. We use constant monthly payment throughout the hold period — we do not model balloon refinancing or rate resets mid-hold (see Limitations below).
3. Annual Cash Flow Projection Model
Each year of the hold period projects the following cash flow statement:
Total equity invested = down payment + closing costs + renovation/CapEx at acquisition. This is the initial negative cash flow (CF₀) used in the IRR calculation.
4. Debt Service Coverage Ratio (DSCR)
DSCR is computed for each year of the hold period. Year 1 DSCR uses Year 1 NOI (base rent, no escalation applied) and the annual debt service based on the loan terms entered. DSCR improves over time as rent escalates while debt service remains constant (for fixed-rate loans).
5. Cash-on-Cash Return
Year 1 CoC is the initial yield on equity — equivalent to the cap rate minus the loan constant when leverage is positive. As rents escalate, CoC improves each year while equity invested remains fixed (we do not model refinancing proceeds as an equity reduction).
6. Sensitivity Analysis
The sensitivity matrix runs 42 full IRR calculations (6 hold periods × 7 exit cap rates) with all other inputs held constant at the base case. This is computationally intensive — each IRR calculation runs up to 14,000 bisection iterations — but JavaScript's single-threaded execution handles the 588,000 total iterations in under 50ms on modern hardware.
7. Equity Waterfall Distribution Model
The waterfall calculator processes distributions sequentially through four tiers for each year of the hold period:
IRR is then calculated separately for LP and GP cash flows using the same bisection method described above. The GP IRR is typically extremely high in successful deals because the GP's co-invest is small relative to their total distributions (which include carried interest).
8. Key Assumptions & Limitations
| Assumption | Value / Approach | Impact / Notes |
|---|---|---|
| Cash flow timing | End-of-year (annual periods) | Standard convention. Mid-year IRRs would be ~0.5% higher for typical hold periods. |
| Rent escalation | Annual compound growth | Applied as (1 + esc)^(Y−1). Real NNN leases may escalate in 5-year steps; this smooths escalation annually. |
| Operating expenses | Fixed dollar amount, no inflation | Conservative. NNN leases typically pass through all expense inflation to the tenant. |
| Loan structure | Fixed-rate, no balloon penalty | Does not model balloon refinancing mid-hold or rate resets. For IO loans, no principal paydown during IO period. |
| Exit valuation | Cap rate applied to exit-year NOI | Does not model income haircuts at sale or vacancy at time of listing. Assumes clean NOI multiple. |
| Taxes | Not included (pre-tax) | All returns are pre-tax. Tax consequences (depreciation, capital gains, 1031 eligibility) must be analyzed separately. |
| Refinancing | Not modeled | Cash-out refinance proceeds during the hold period are not considered. This understates levered returns for value-add strategies. |
| Vacancy / credit loss | Not modeled (NNN focus) | NNN master lease structures typically have contractual income. For multi-tenant properties, apply a vacancy factor to baseRent before inputting. |
| Preferred return accrual | Compound on remaining LP capital | Accrues on outstanding LP capital balance. If distributions in a year are insufficient, the unpaid preferred return carries forward and must be paid before Tier 3. |
| IRR search range | −99.99% to +2,000% | Covers all realistic real estate return scenarios. Extremely negative IRR (below −100%) is mathematically impossible for equity investments. |