Valuation
CRE Formulae Reference
A single-page consolidated reference for every key equation used across the commercial real estate knowledge base. Organized by functional category for rapid lookup during underwriting, modeling, and investment committee preparation. Asset-class-specific variants are noted inline where formulas differ materially by property type.
Also known as: CRE Formulas, Formula Cheat Sheet
Updated
1. Revenue & Income
Core Income Waterfall
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Gross Potential Rent (GPR) / Potential Gross Income (PGI) | Rent potential = sum of stated unit rents, or full-inventory rentable-area weights × rent/SF, with a matching period | State market versus in-place rent and vacant-unit reference rents. A market anchor needs the matching signed market-to-contract bridge; an in-place anchor already excludes that gap. GPR is rent potential; PGI may include other potential income under the stated definition. Inherited industrial rent ranges remain unverified by this review. See CRE Lease Structures and Expense Recovery. |
| Vacancy Loss | Sum of vacant-period rent on the matching potential-rent basis; equivalently potential rent × matching rent-weighted vacancy fraction | Physical unit/SF vacancy can replace the rent-weighted fraction only when rates and periods match appropriately. Do not multiply all PGI, including unrelated income, by a physical vacancy rate. Inherited universal asset-class vacancy ranges are unverified. See CRE Lease Structures and Expense Recovery. |
| Credit Loss | For the same rent and cutoff: collection shortfall = rent due − expected collections applied to that rent | State the denominator/period of any loss rate; shortfall may include delay and is not automatically final default loss or accounting bad debt. Inherited universal 0.5–2.0% range is unverified. See Tenant Credit Analysis Framework. |
| Concessions | Rent concession for each period = contractual rent reduction scheduled for that period | Free-rent months × matching monthly rent is a uniform-rent illustration. TI, LC and moving payments require separate cost/cash classification; do not automatically subtract capital/lease spending from GPR or deduct free rent already excluded from collected rent. See Source: Lease Weighting and Rollover Scope Review 2026. |
| Loss-to-Lease (LTL) | Positive-only occupied LTL = sum of positive market-minus-contract gaps; signed net gap = positive LTL − gain-to-lease | Match date, population, rent/area basis and period. Name any percentage denominator. Subtract the signed gap only from a matching market anchor; do not subtract it again from an in-place anchor. Snapshot gap is not a capture forecast. Inherited industrial 5–20% benchmark is unverified. See CRE Lease Structures and Expense Recovery. |
| Effective Gross Income (EGI) | Base rental income after modeled vacancy, rent concessions and credit adjustments + Recovery income + Other operating income | Match period and income convention. Other income excludes recoveries if those appear separately; count each receipt once. Parking, fees and utility income follow their actual classification. Do not treat capital/lease cash payments as automatic rent reductions. See Source: Occupancy and Expense Ratio Mechanics Review 2026. |
| Net Operating Income (NOI) | NOI = EGI − Total Operating Expenses under the stated convention | Gross recovery income requires full operating expenses; an equivalent net presentation removes the same recoveries from both sides. Reconcile actual versus underwritten reserves and capital/lease cash separately. Inherited universal industrial NNN 85–95% margin is unverified and depends on presentation. See Source: Lease Weighting and Rollover Scope Review 2026. |
| Operating Expense Ratio (OER) | $\text{OER} = \frac{\text{Stated Operating Expenses}}{\text{EGI}}$, with EGI > 0 | Same period and expense/recovery conventions required; actual versus underwritten reserves can differ. Inherited MF 35–50% / Class C claim is unverified in this review. See Source: Occupancy and Expense Ratio Mechanics Review 2026. |
| Economic Occupancy | $\frac{\text{Actual Collected Rent}}{\text{GPR}}$ | Can diverge significantly from physical occupancy due to delinquency |
| Annualized Trending NOI (T3/T12) | Hybrid annualized proxy = 4 × total T3 operating income − stated T12 operating expenses | Use complete periods, a stated cutoff and matching property/accounting scope. T3 is the three-month total; a monthly average annualizes ×12. This proxy is not actual T12 NOI or an independently supported forecast; normalize one-time income, seasonality and forward expense changes explicitly. No universal underwriting mandate is established. See Multifamily Pro Forma Modeling. |
Expense Recovery
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Expense Recovery Ratio | $\text{Recovery Ratio} = \frac{\text{Expense Reimbursements}}{\text{Total Operating Expenses}}$ | NNN (Industrial): 95–100%; Modified Gross: 60–80% |
| NNN Recovery (Office/Retail) | Tenant Pro-Rata Share × Actual OpEx | Full pass-through structure |
| Tenant Pro-Rata Share | Tenant RSF ÷ Total NRA (or occupied SF, per lease) | Basis for expense allocation |
| Base-Year Stop Recovery (Office) | $\max(0, \text{Current-Yr OpEx/RSF} - \text{Base-Yr OpEx/RSF}) \times \text{Tenant RSF}$ | Tenant pays growth above base year stop |
| Gross-Up (Variable OpEx) | Variable OpEx ÷ MAX(Occupancy, Gross-Up Floor) — typically 95% | Normalizes partial-occupancy years for recovery calculations |
| Admin / Mgmt Fee on Recoveries | Typically 3–5% of recoverable expenses added to CAM | Office standard |
| Industrial Tenant Reimbursement | $\sum_i \sum_c [\text{Active Fraction}{i,t} \times \text{Pro-Rata Share}{i,t} \times w_{i,c} \times \max(0, \text{Adjusted Expense}{c,t} - \text{Stop}{i,c,t})] + \text{Direct Billings}_{i,t}$ | Category-aware formula for blended NNN, modified-gross, base-year, and expense-stop industrial leases. See Industrial Tenant Reimbursement Modeling |
| Industrial Recovery Leakage | $\text{Actual OpEx} - \text{Collected Recoveries} - \text{Nonrecoverable Expenses}$ | Split into vacancy leakage, cap leakage, base-year / stop leakage, exclusions, disputes, and credit loss |
| Office Tenant Reimbursement | $\sum_i \sum_p [\text{Service Fraction}{i,t} \times \text{Tenant Area}{i,t} \times \max(0,\text{Adjusted Pool PSF}{i,p,t}-\text{Base/Stop PSF}{i,p,t}) \times w_{i,p}] + \text{Direct Service Charges}{i,t} - \text{Caps/Credits}{i,t}$ | Office-grade formula for FSG, modified gross, NNN, base-year, expense-stop, tax, electric, janitorial, and direct-service pools. See Office Tenant Reimbursement Modeling |
| Office Gross-Up Adjustment | $\text{Grossed-Up Variable Expense} = \frac{\text{Actual Variable Expense}}{\text{Actual Service Occupancy}} \times \text{Lease Gross-Up Factor}$ | Store actual OpEx separately from grossed-up recovery OpEx |
| Office True-Up | $\text{True-Up}{i,y} = \text{Actual Annual Due}{i,y} - \sum \text{Monthly Estimates Billed}{i,t} - \text{Interim Credits}{i,y}$ | Use a separate cash ledger from accrual NOI |
Lease Income Analysis
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Net Effective Rent (NER) | $\text{Rent-only monthly average} = \frac{\text{Gross face rent} - \text{Rent credits}}{\text{Positive lease months}}$ | Equivalently average the contractual rent schedule after credits; never subtract free rent twice. State whole-lease, per-unit or per-SF units and annualization. TI/LC require a separately labeled after-cost convention; this rent rate is not NOI or an investment yield. See CRE Lease Structures and Expense Recovery. Inherited TI/LC/free-rent ranges are unverified by this review. |
| Rent Escalation (Compounded) | $\text{Year } n \text{ Rent} = \text{Base Rent} \times (1 + g)^{n-1}$ | $g$ = annual escalation rate. Industrial: 2.0–3.5%/yr; some leases use CPI with floor/cap |
| Mark-to-Market Delta | $\frac{\text{Market Rent} - \text{In-Place Rent}}{\text{In-Place Rent}}$ | Rollover rent change measure |
| RUBS Revenue Lift (MF) | $\text{Units} \times \text{Monthly Rebill} \times 12$ | Typical: $500–$1,500/unit/year |
2. Valuation
Direct Capitalization & Cap Rate
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Cap Rate | $\text{Cap Rate} = \frac{\text{NOI}}{\text{Value (or Price)}}$ | Industrial Class A logistics: 4.75–5.75%; Class B: 5.50–6.75%; Value-add: 6.50–8.00%. MF: Market extraction from comparable sales |
| Direct Capitalization (Value) | $\text{Value} = \frac{\text{NOI}}{\text{Cap Rate}}$ | Inverted cap rate formula; used for quick valuation. At 5% cap, $10K NOI increase = $200K value |
| Entry Cap (Going-In) | Year 1 NOI ÷ Purchase Price | Acquisition underwriting anchor |
| Exit Cap | Matched annual terminal NOI / positive gross sale value | State forward/trailing NOI and exit date; the inherited mandatory 50–100-bp drift is unverified here. See CRE Valuation Methodologies. |
| NOI Value Multiplier | $\Delta V = \frac{\Delta \text{NOI}}{\text{Cap Rate}}$ | At 5.5% cap: $1 NOI = $18.18 value; at 6.5% cap: $1 NOI = $15.38 value |
| Broker Opinion of Value (BOV) | Stabilized Fwd NOI ÷ Market Cap Rate (cross-check with comps $/RSF or $/unit) | Disposition underwriting entry point |
Cap Rate Decomposition
| Formula | Equation | Notes |
|---|---|---|
| Build-Up Method | r = R_f + Σ incremental premiums under the stated compatible rate scenario | Non-overlapping components, cash/rate basis and evidence required. r−g is a forward cash ratio only under matched Gordon conditions; it is not automatically an NOI cap. See Cap Rate Decomposition. |
| Gordon Model Adaptation | PV_0 = F_1/(r−g) for the defined infinite growing cash stream; forward cash/PV = r−g | Require F_1 > 0, g > −1, r > g and matched cash/rate scope. Forward NOI cap equals this ratio only when selected cash equals NOI; trailing timing and capital uses change the relation. See Cap Rate Decomposition. |
| Band-of-Investment (BOI) | $R_o = (\text{LTV} \times R_m) + ((1 - \text{LTV}) \times R_e)$ | Conditional annual equity cash-yield hurdle: $R_m$ = annual mortgage constant; $R_e$ = cash dividend target, not IRR. Assumes price-funded shares and no additional cash/equity adjustments. See Cap Rate Decomposition. |
| Cap Rate Spread to Treasury | Cap Rate − 10Y Treasury Yield | Historical MF average: 150–250 bps; <100 bps = aggressive pricing |
| Ellwood Formula | $R_o = Y_E - M \times C - \Delta_{\text{value}} \times \frac{1}{S_n}$ | Conditional finite-hold model: constant annual NOI/service and defined net debt payoff; equity yield differs from current cash yield. Match principal repayment to the service schedule and use the zero-yield limit. See Cap Rate Decomposition. |
DCF & Terminal Value
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| DCF Value | Value = Σ(CF_t / (1+r)^t) + net terminal proceeds / (1+r)^n | Match cash-flow scope, dates and discount rate. Property CF includes capital/lease uses and equals NOI only when selected adjustments are zero; equity cash requires financing/allocations. Inherited industrial 7.0–9.5% rate and automatic +25–75-bp exit spread are unverified. See Industrial Valuation and Probability-Weighted Underwriting and Source: Lease Weighting and Rollover Scope Review 2026. |
| Office DCF (using PBTCF) | $\text{Value} = \sum_{t=1}^{n} \frac{PBTCF_t}{(1+r)^t} + \frac{\text{Reversion}}{(1+r)^n}$ | Use dated property cash after actual TI/LC/building CapEx and any cash reconciliation; separate reserve funding from funded spending. Net unlevered reversion uses matched forward NOI / positive exit cap less selling costs, counted once. Financing belongs in an equity model. See Office Underwriting and Lease Structures. |
| Terminal / Reversion Value | Gross terminal value = matched forward stabilized NOI / positive exit cap rate | Net proceeds additionally reflect the selected selling/terminal costs and financing scope. Discount to the same date before comparing terminal value with total DCF present value. Inherited universal industrial 55–70% share is unverified. See Industrial Valuation and Probability-Weighted Underwriting. |
| Net Present Value (NPV) | $\text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$ | Define dated initial investment and future cash for the same property/equity population. Positive NPV is relative to the selected inputs and rate, not proof of an achievable return; see Cap Rate Decomposition and CRE Valuation Methodologies. |
Replacement Cost & Other Value Metrics
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Replacement Cost | Define improvement cost-new separately from all-in development budget; cost-approach estimate = land + construction − supported depreciation | State date, location, specs, area and inclusions; count fees/carry/TI/LC once. No automatic market-price floor or above-cost overvaluation rule. See CRE Valuation Methodologies. Inherited $80–$150, $150–$250 and $250–$400/SF ranges are not verified benchmarks in this methods review. |
| Price per Unit (MF) | Purchase Price ÷ Total Units | Sales comp benchmark; varies widely by market and class |
| Price per RSF (Office/Industrial) | Purchase Price ÷ Total NRA (or Rentable SF) | Normalizes across buildings and tenant mixes |
| Conversion Premium / Discount (Office) | (Converted-Use Value − Conversion Cost) − As-Is Office Value | Highest-and-best-use decision metric |
| Gross Buildable Area — Resi Conversion | Existing GFA × Efficiency Factor (typically 75–85% for resi conversion) | Office-to-residential analysis |
| Resi Unit Count — Conversion | Net Residential SF ÷ Average Unit Size | Office-to-residential analysis |
3. Returns & Performance
Core Return Metrics
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Cash-on-Cash (CoC) | $\text{CoC} = \frac{\text{Annual Pre-Tax Cash Flow}}{\text{Total Equity Invested}}$ | Specify cash-flow population, period and cash-capital denominator. NOI − debt service is only a simplified bridge: reconcile TI/LC, capital spending, fees and reserve/restricted-cash movements where applicable; do not double-count reserves and spending. Forecast cash availability differs from actual LP distributions. Principal paydown and unrealized appreciation are not cash receipts. NCREIF property FCFY uses beginning market value, not cash equity. Inherited industrial Core 4–6%, Value-add 6–9% and Opportunistic 8–12%+ are unverified scenarios. See cash-yield scope and Source: Cash Yield Scope Review 2026. |
| Equity Multiple (EMx) | Distributions-only: $D/C$; total-value: $(D+R)/C$, $C>0$ | Match investor, fee/carry, currency, recall and as-of scope. Include later contributions; do not double-count distributed proceeds in residual value. A total-value 2.0× can include unrealized value; fully distributed 2.0× implies nominal gain equal to contributed capital, not a 200% profit or annualized return. Portfolio MOIC and fund TVPI can use different capital populations and fee treatments. Inherited industrial targets 1.3–1.6× / 1.6–2.2× / 2.0–3.0×+ remain unverified scenario inputs. See multiple scope and Source: Equity Multiple Scope Review 2026 and Source: CRE Multiple Reporting Review 2026. |
| Internal Rate of Return (IRR) | $0 = \sum_{t=0}^{n} \frac{CF_t}{(1 + \text{IRR})^t}$ · Periodic Excel: =IRR(values); dated Excel: =XIRR(values, dates) | Periodic equation uses equal intervals and a per-period rate; XIRR uses actual dates and a 365-day year. IRR is money-weighted; existence and uniqueness are not guaranteed. The inherited industrial ranges below remain outside this mechanics review. Industrial Core: 6–9%; Value-add: 12–18%; Opportunistic: 18–25%+ |
| One-period economic equity return (limited bridge) | (D + E_end − E_begin) / E_begin, E_begin > 0 | Assumes no additional contributions and distributions D at period end; E_end is remaining equity value after distributions. Match investor, fee/tax, valuation and period scope. Equity value changes already reflect liability changes: do not add principal paydown again. This is an economic holding-period bridge, not a universal accounting ROE, cash yield or dated IRR formula. See the scope example below. |
| DPI / RVPI / TVPI | $D/P$ · $R/P$ · $(D+R)/P = DPI + RVPI$ | $P$ = cumulative capital actually paid in ($P>0$), $D$ = cumulative distributions, $R$ = residual value at the as-of date. Match investor, currency and fee/carry scope; preserve distribution/recontribution events for recalls. A 1.0× DPI is nominal equality, not a time-adjusted return. See Source: DPI and TVPI Definitions Review 2026. |
| MIRR (Modified IRR) | $\left(\frac{FV_{\text{inflows}}}{PV_{\text{outflow magnitude}}}\right)^{1/N} - 1$ | Compound positive receipts to time $N$ at the reinvestment rate; discount every negative payment to time zero at the finance rate and use its positive magnitude. $N$ is elapsed equal periods, not entry count; rates match the interval. See Source: MIRR and IRR Mechanics Review 2026. |
| Payback Period | First observed $t$ with $B_t = \sum_{i=0}^{t} CF_i \geq 0$, starting with $B_0<0$ | Include initial and later cash payments, not just distributions. First crossing can reverse after later outflows. Use actual timing; fractional interpolation requires an explicit intra-year pattern. Discounted payback substitutes $CF_i/(1+r)^i$ with matching periodic rate. No recovery within the horizon is a valid result. See Source: Payback Mechanics Review 2026. |
Equity-return scope, reviewed 2026-10-07: The inherited “annual cash flow + principal paydown + appreciation / current equity” shortcut did not identify the valuation date or reconcile additional capital and cash uses. The limited bridge above instead compares beginning equity with ending remaining equity plus period-end distributions, assuming no additional contributions. It is synthesis for a defined example, not a formula prescribed by NCREIF: its retained property methodology separately distinguishes beginning-market-value and cash-flow-weighted denominators. Actual interim contributions/distributions require an explicitly chosen return convention and dated cash-flow analysis. Current marked equity and original cash invested are different bases. See Source: Cash Yield Scope Review 2026 and Source: CRE Loan Math Reproduction 2026.
Assumed arithmetic: Beginning equity 100, ending equity 120 after a period-end distribution of 10 give gain 30 and one-period economic return 30%. Dividing that same gain by ending equity gives 25%, a different ratio. If the 20 equity-value increase consists solely of 15 property appreciation and 5 debt reduction, those components are already inside E_end − E_begin; adding another 5 for paydown would count it twice. This scenario assumes consistent valuations, no additional capital, fees/tax effects or other assets/liabilities changing, and is not an observed investment return.
Development Returns
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Yield on Cost (YoC) / Return on Cost | $\text{YoC} = \frac{\text{Stabilized NOI}}{\text{Total Development Cost}}$ | Stabilized annual NOI divided by defined total cost; disclose stabilization and land/construction/leasing/financing cost scope. A forecast yield is not IRR or an LP cash distribution. Inherited 6.5–8.5% and 100–200+ bps are unverified scenario inputs. See Source: Development Spread Scope Review 2026. |
| Development Spread | $\text{Dev Spread} = \text{YoC} - \text{Market Cap Rate}$ | Match NOI, valuation date and comparable stabilized asset assumptions. Spread is a rate difference, not a profit margin or proof of adequate risk compensation. Inherited >100-bp and <75–100-bp rules are unverified policy/scenario inputs. See development-spread scope. |
| Value Created (Developer Profit) | $\frac{\text{Stabilized NOI}}{\text{Cap Rate}} - \text{TDC}$ | Static implied property value less stated cost, before omitted transaction/tax/carry effects; not automatically realized profit or investor equity. Under matching NOI assumptions, gain on cost = YoC / cap rate − 1, not YoC − cap rate. |
| Profit on Cost | $\frac{\text{Stabilized Value} - \text{TDC}}{\text{TDC}}$ | State valuation, cost and transaction/tax scope; not an annualized return. Inherited 15–20%, 20–35% and 35%+ thresholds are unverified candidate policy inputs, not certified institutional norms. |
| Residual Land Value | $\text{Stabilized Value} - \text{TDC (excl. land)} - \text{Required Profit}$ | Maximum justifiable land price; if asking > residual → walk away |
Hold vs. Sell
| Formula | Equation | Notes |
|---|---|---|
| Marginal Hold IRR | IRR of remaining CFs using current market value as Day 0 investment | Sell when Marginal Hold IRR < Redeployment IRR (net of friction) |
| 1031 Exchange Tax Savings | $\text{Tax Deferred} = \text{Gain} \times \text{Effective Tax Rate}$ | Gain = Sale Price − Adjusted Basis; deferred if proceeds reinvested in like-kind property within 180 days. Typical savings: 15–30% of gross sale proceeds |
4. Debt & Leverage
Loan Sizing Metrics
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Loan-to-Value (LTV) | $\text{LTV} = \frac{\text{Loan Amount}}{\text{Property Value}}$ | Industrial permanent: 55–65%; Bridge/construction: 65–75%. Agency MF: max 80%; HUD ML 2025-03: 87% market-rate category / 90% qualifying affordable or rental-assistance categories, with cash-out and statutory limits separate; CMBS: 70–75% |
| Loan-to-Cost (LTC) | $\text{LTC} = \frac{\text{Loan Amount}}{\text{Total Project Cost}}$ | Construction: 60–70%; Bridge MF: 70–80%; Industrial permanent: 55–65% |
| Debt Service Coverage Ratio (DSCR) | $\text{DSCR} = \frac{\text{NOI}}{\text{Annual Debt Service (P+I)}}$ | Industrial permanent min: 1.20–1.35×; Bridge IO: 1.10×. Agency MF min: 1.25×; HUD ML 2025-03: 1.15× market-rate category / 1.11× qualifying affordable or rental-assistance categories; see Source: HUD Multifamily Underwriting Primary Review 2026 |
| Debt Yield | $\text{Debt Yield} = \frac{\text{NOI}}{\text{Loan Amount}}$ | Specify annual underwritten NOI and positive debt/exposure denominator. Holding both fixed, interest/amortization/cap rates do not enter this ratio; they still affect other constraints and approved proceeds. Not lender coupon or realized cash return. Inherited Industrial CMBS 8–10% and CMBS MF 7–8% floors are unverified scenarios; agency tests require product/lender review. See Source: Debt Yield Scope Review 2026. |
| Mortgage Constant (Kd / Rm) | $K_d = \frac{\text{Annual Debt Service}}{\text{Loan Amount}}$ | Function of rate + amortization; e.g., 5.5%/30yr ≈ 6.81% |
| Max Loan by DSCR | $\frac{\text{NOI} / \text{Min DSCR}}{K_d}$ | Positive annual debt constant and positive minimum coverage required; use matched lender income/service definitions. A rate level alone does not establish binding. See CRE Return Metrics and KPIs. |
| Max Loan by LTV | $\text{Appraised Value} \times \text{Max LTV}$ | Standalone cap under the actual value basis and maximum LTV; compare all applicable limits. Low rates or rising values alone do not establish binding. See CRE Return Metrics and KPIs. |
| Max Loan by Debt Yield | $\text{NOI} \div \text{Min Debt Yield}$ | Standalone cap only when a positive minimum applies; positive NOI required for positive proceeds. Compare every applicable DSCR, LTV and other limit. No automatic binding test follows from cap-rate compression; see constraint example. |
| Binding Loan Constraint | Minimum of all applicable loan-sizing limits | Use the three-test expression when each test applies; not every agency product is attested to have an independent debt-yield minimum. |
| Loan per Unit (MF) | Loan Amount ÷ Total Units | Comparison metric; verify actual program/lender restrictions. FHFA one- through four-unit conforming limits and annual Enterprise multifamily purchase caps are different scopes, not universal per-apartment ceilings. See Source: Agency Limit Scope Primary Review 2026. |
Debt Service & Loan Math
For the level-payment formulas, assume fixed nominal annual interest divided by 12, equal monthly payments at period end, and no fees, IO period, irregular periods or day-count adjustment. r is the monthly rate; N is amortization months and p is payments elapsed. At zero interest, payment is Loan / N and balance after p payments is Loan × (1 − p / N). Use actual lender definitions and schedules for DSCR; NOI/P&I is a simplified model, not every program's definition. Source: CRE Loan Math Reproduction 2026 records primary-method boundaries and independently reproduced examples.
| Formula | Equation | Notes |
|---|---|---|
| Monthly P&I Payment | $\text{Loan} \times \frac{r(1+r)^n}{(1+r)^n - 1}$ where $r$ = monthly rate, $n$ = months | Standard amortizing payment formula |
| Balloon Balance | $\text{Loan} \times \frac{(1+r)^N - (1+r)^p}{(1+r)^N - 1}$ where $N$ = amort months, $p$ = term months | Remaining principal at loan maturity |
| Interest During Construction (IDC) | $\text{IDC} = \sum_j B_j r_j \Delta t_j$ | Split actual interest-bearing balances/rates into contractual year-fraction intervals; include financed-interest postings when applicable. Fixed-rate average balance is time-weighted, not a universal 50–60% factor. Fees and funding sources are separate. See Construction Loan Mechanics and Development Risk. |
| WACC | $\text{WACC} = (%{\text{debt}} \times k_d) + (%{\text{mezz}} \times k_m) + (%_{\text{equity}} \times k_e)$ | Normalize nonnegative shares to 100%; state valuation/funding bases and compatible cost/tax definitions. Debt cost is not the mortgage constant, and equity cost is not a current cash target. A blend is not automatically a property cap or discount rate. See CRE Valuation Methodologies. |
Leverage Tests
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Current Cash-Yield Leverage Test | Compare Cap Rate to annual Mortgage Constant ($K_d$) using the same NOI | In the simplified model, cap above/below $K_d$ raises/lowers current pre-tax cash yield. This does not determine total-return IRR or a market-wide 2024–2025 result. |
| Current Cash-Yield Spread | Cap Rate − annual Mortgage Constant | A coupon comparison applies only when it represents the modeled debt service, such as simplified full-term IO. Fees, reserves and capital costs require separate treatment. |
| Levered vs. Unlevered IRR | Compute IRR from each complete cash-flow series, including initial investment and exit proceeds | A cap-rate/coupon or mortgage-constant comparison alone cannot establish the IRR ordering. Include principal balances, fees, timing, capital costs and sale proceeds. |
| Break-Even Occupancy (Fixed-Cost Shortcut) | $\frac{\text{Fixed Operating Expenses} + \text{Debt Service}}{\text{GPR}}$, with GPR > 0 | Full collection, proportional rent, no other income/recoveries and occupancy-independent costs only. Not automatically physical occupancy or all-cash break-even; inherited asset-class targets are unverified. See Sensitivity and Scenario Analysis. |
Debt Sizing Waterfall (Quick Reference)
Step 1: Max Loan (LTV) = Appraised Value × Max LTV Step 2: Max Loan (DSCR) = (Underwritten NOI ÷ Min DSCR) ÷ Mortgage Constant Step 3: If required, Max Loan (Debt Yield) = Underwritten NOI ÷ Min Debt Yield Step 4: Binding constraint = minimum of applicable limits, including other program/lender restrictions. The lender-defined cash-flow numerator and underwriting payment schedule govern DSCR. Step 5: Equity required = Total Cost − Binding Loan Amount
5. CapEx & Reserves
Industrial / Office CapEx
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| CapEx Reserve (Annual) — Office | NRA × $/RSF reserve | Class A: $0.25–$0.75/SF; Class B/C: $0.75–$1.50+/SF |
| TI Allowance — New Lease | RSF × $/RSF market TI | Office: $40–$100+/SF Class A. Industrial: $2–$15/SF |
| TI Allowance — Renewal | Typically 40–60% of new-lease TI (office); 50% (industrial) | |
| Leasing Commission — New | Typically 4–6% of aggregate lease value | Standard across office and industrial |
| Leasing Commission — Renewal | Typically 50% of new-deal commission rate (office); 2–3% of value (industrial) | |
| Effective Useful Life (EUL) Rule | Replace if Remaining Useful Life < Hold Period; otherwise reserve | CapEx triage decision rule |
Multifamily CapEx & Reserves
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Replacement Reserve (MF) | $/unit/year × total units | Typical: $200–$500/unit/year |
| Turnover Cost Savings | Units × ΔTurnover Rate × Cost per Turn | Cost per turn: $1,500–$4,000 + vacancy loss |
| Renovation ROI (Unlevered) | $\frac{\text{Annual Rent Premium} \times 12}{\text{Renovation Cost per Unit}}$ | e.g., $300/month premium ÷ $25K cost = 14.4% unlevered ROI |
| NOI Impact on Value | $\frac{\Delta \text{NOI}}{\text{Cap Rate}}$ | At 5% cap, $50K OpEx savings = $1M value creation |
Development Cost Structures
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Total Development Cost (TDC) | $\text{TDC} = \text{Land} + \text{Hard Costs} + \text{Soft Costs} + \text{Carry Costs}$ | Industrial Class A bulk: $80–$150/SF; Cold storage: $150–$250/SF; Life sciences: $250–$400/SF. MF garden: $150K–$225K/unit; Mid-rise: $225K–$350K; High-rise: $350K–$600K+ |
| Hard Cost Ratio | $\text{Hard Cost %} = \frac{\text{Hard Costs}}{\text{TDC}}$ | 60–70% of TDC for standard industrial |
| Cost per Unit (MF) | TDC ÷ Total Units | Garden: $150K–$225K; Mid-rise: $225K–$350K; High-rise: $350K–$600K+ |
| Operating Deficit Reserve (ODR) | $\sum_{m=1}^{\text{Stabilization}} (\text{OpEx}_m + \text{Debt Service}_m - \text{Rent}_m)$ | MF: typically $2,000–$5,000/unit; funded at construction loan closing |
| Floor Area Ratio (FAR) | $\frac{\text{Total Buildable Floor Area}}{\text{Lot Area}}$ | Zoning constraint determining max density |
6. Tax & After-Tax
Depreciation
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Straight-Line Depreciation — Commercial (39yr) | $\text{Annual Deduction} = \frac{\text{Building Cost Basis}}{39}$ | Nonresidential real property. Industrial: Land is 15–30% of purchase price (higher in constrained markets) |
| Straight-Line Depreciation — Residential (27.5yr) | $\frac{\text{Depreciable Basis}}{27.5}$ | MF: Depreciable basis = acquisition cost + closing costs − land value. Land typically 15–25% of total |
| Depreciable Basis | Purchase Price + Closing Costs + Capital Improvements − Land Value | Foundation for all depreciation calculations |
| Year 1 Depreciation with Cost Seg + Bonus (MF) | $(5\text{yr Property} \times 100%) + (15\text{yr Property} \times 100%) + \frac{27.5\text{yr Property}}{27.5}$ | 100% bonus for 5yr/15yr components (post-OBBBA January 2025); 27.5yr = straight-line only |
| Cost Segregation Benefit (Industrial) | $\text{Accelerated Deduction} = \text{Reclassified Amount} \times \text{Applicable %}$ | 5-year property: 100% bonus; 15-year: 100% bonus. Industrial: 25–35% of building cost typically reclassified (high due to site improvements, paving, dock equipment) |
Taxable Income & Liability
| Formula | Equation | Notes |
|---|---|---|
| Taxable Income (Operations) | NOI − Mortgage Interest − Depreciation − Amortizable Costs | Annual operating tax basis |
| Tax Liability (Operations) | Taxable Income × Marginal Tax Rate | Federal + state combined |
| Before-Tax Levered Cash Flow | NOI − Debt Service − TI/LC − CapEx Reserves | Office / industrial pre-tax equity cash flow |
| After-Tax Cash Flow (ATCF) | Before-Tax Levered CF − Income Tax Liability | True after-tax equity return |
| After-Tax IRR | IRR of after-tax cash flows (operating CF net of tax; sale CF net of cap gains + recapture) | AT-IRR typically 70–85% of pre-tax IRR depending on depreciation benefits |
Sale Taxation
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Adjusted Basis at Sale | Original Basis − Accumulated Depreciation + Capital Improvements | Foundation for gain calculation |
| Gain on Sale | Net Sale Price − Adjusted Basis | Gross taxable gain before character split |
| §1250 Depreciation Recapture Tax | $\min(\text{Gain}, \text{Accumulated Depreciation}) \times 25%$ | Applies to real property depreciation upon sale (max 25% rate) |
| §1245 Recapture (Cost Seg Components) | Gain attributable to personal property depreciation × ordinary rates (up to 37%) | Applies to accelerated 5yr/15yr cost seg components |
| Capital Gains Tax | (Gain on Sale − Depreciation Recaptured) × LTCG Rate (20% + 3.8% NIIT) | Long-term capital gain on residual gain |
| Effective Combined Rate | Federal LTCG + state + recapture | Typical range: 25–35% combined |
| After-Tax Sale Proceeds | Net Sale − Loan Payoff − Recap Tax − Cap Gains Tax | Equity distributions at disposition |
Tax Credit Programs
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Max LIHTC Gross Rent | Imputed Income Limit × 30% ÷ 12 | Imputed household size: 1 person for no separate bedroom; 1.5 persons per bedroom for units with bedrooms. Use current HUD MTSP limits. |
| Max LIHTC Owner Rent | Max LIHTC Gross Rent − Utility Allowance − Mandatory Rent-Like Charges | UA follows the applicable Section 42 / agency method; energy retrofits increase collectible rent only when documented and allowed. |
| Applicable Fraction | Lesser of Low-Income Unit Fraction or Low-Income Floor-Area Fraction | Use building-level unit and floor-area schedules; mixed-income floor-area differences can bind unexpectedly. |
| Qualified Basis | Adjusted Eligible Basis × Applicable Fraction | Eligible basis excludes land, nondepreciable costs, many reserves, syndication costs, and other nonqualified / reduced costs. See LIHTC Calculation Mechanics. |
| Annual LIHTC Credit | Qualified Basis × Applicable Percentage | Applicable percentage depends on the 9% or 4% path and IRS rates / statutory floors. |
| 4% Bond Test Ratio | Qualifying Tax-Exempt Bond Proceeds ÷ Aggregate Basis | Legacy path is 50%; post-2025 25% path requires bonds after 2025, at least 5% aggregate-basis bond financing, and statutory timing / placed-in-service conditions. |
| Tax Credit Equity (LIHTC) | Annual Credit × 10 × Credit Price ($/$1) | Credit price is current-market and deal-specific; March 2026 evidence was broadly mid/high $0.70s to low/mid $0.90s. Sensitize pricing. |
| Net Usable Tax Credit Equity | Gross Tax Credit Equity − Fees / Holdbacks / Adjusters / Delayed Pay-Ins | Treat investor installments as timed sources, not all-cash-at-closing proceeds. |
7. Syndication & Waterfall
| Formula | Equation | Notes |
|---|---|---|
| Preferred Return (Cumulative) | For a stated simple convention: sum(eligible capital balance × annual rate × year fraction) | Constant equity × rate × years requires an unchanged base. Track paid/unpaid pref and capital return separately; compounding and IRR hurdles require their own definitions. See Equity Waterfall and Promote Structures. |
| GP Promote / Carried Interest | Agreed GP allocation of eligible profit under the signed tiers/hurdles | Specify capital return, pref, carry base, catch-up and clawback; a stated hurdle alone does not define entitlement or guarantee alignment. See Equity Waterfall and Promote Structures. |
| Catch-Up Tranche | Under the shared simplified assumptions only: C = pH / (g−p), with H>0 and 0<p<g≤1 | H = LP pref profit already paid; p = GP profit target; g = GP tranche share; prior GP carry zero. Full and slow catch-up differ, and available cash may not clear the tranche. See Equity Waterfall and Promote Structures. |
| LP Net IRR | Zero-NPV return on complete LP contributions and distributions after applicable fees and promote | Match actual timing and the periodic/dated convention; project returns do not establish partner returns. See CRE Return Metrics and KPIs. |
| GP Share of a Residual Profit Tier | p + o(1−p), only when promote p goes solely to GP before ownership split o | Assumed 20% promote and 10% ownership give 28% of this tier, not all distributions including returned capital. See Equity Waterfall and Promote Structures. |
| Acquisition Fee | Contractual eligible acquisition base × agreed rate, subject to terms | Identify services, payee, closing conditions and offsets. The inherited 1–3% is not a verified market norm; tax treatment is outside this methods review. See GP Fee Structures. |
| Asset Management Fee | Sum of period-specific contractual base × rate, with the agreement’s period convention | Specify EGI, committed/invested capital, unrealized cost or another base; annual and period-income bases require different time treatment. Reconcile waivers, minimums and offsets once. See GP Fee Structures. |
| Construction Management Fee | Eligible agreed construction-cost base × agreed rate, subject to terms | Define hard/soft costs, services, payment dates and any fee inclusion; do not add a fee already in the budget twice. The inherited 5–10% is an unverified scenario range. See GP Fee Structures. |
| Disposition Fee | Contractual eligible sale base × agreed sponsor rate, subject to terms | Identify service, payee, closing trigger and offsets; separate GP compensation from brokerage. The inherited 0.5–1.5% is not a verified market norm. See GP Fee Structures. |
8. Leasing & Tenant Analysis
Lease Term & Rollover
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Weighted Average Lease Term (WALT) | $\frac{\sum w_i T_i}{\sum w_i}$, with nonnegative stated weights and positive total weight | $T_i$ is remaining term at the same as-of date. State area or total annual rent basis, lease scope and option/break treatment. Rent per SF is a different weight. Inherited cap-rate adjustments are unverified; see Source: Lease Weighting and Rollover Scope Review 2026. |
| Rollover Exposure (Year) | Expiring leased RSF ÷ stated total NRA (positive denominator) | Area share; use expiring annual rent ÷ stated total annual rent for a separately scoped rent share. Scheduled expiry is not complete income loss. See Sensitivity and Scenario Analysis. |
| Retention Ratio | Renewed RSF ÷ expiring RSF in the same defined cohort (positive denominator) | Area-retention convention; not automatically tenant-count retention or a tenant-specific renewal probability. Match issuer denominator definitions. Inherited 65–80% range is unverified; see Source: Lease Weighting and Rollover Scope Review 2026. |
| Renewal Probability Weighting | Expected collected rent in period t = Σ(p_s × collected rent_s,t) | Exhaustive, mutually exclusive lease paths; p_s ≥ 0 and Σp_s=1. Use period lease schedules and consistent units. NOI and after-capital cash are separate; see Sensitivity and Scenario Analysis. Inherited universal 3–9-month downtime range is unverified. |
Tenant Economics
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Occupancy Cost Ratio | $\text{Occ. Cost} = \frac{\text{Total Rent + OpEx}}{\text{Tenant Revenue}}$ | Industrial: 2–8% of revenue (very low vs. retail at 8–15%) |
| Rent-to-Income Ratio (RTI) | $\frac{\text{Monthly Rent}}{\text{Monthly Gross Household Income}}$ | MF target: <30%; >35% = affordability stress |
| Concession Value (Office) | (Free-Rent Months × Monthly Rent) + (Above-Market TI × RSF) + Moving Allowance | Total landlord cost of incentive package |
9. Market Analysis
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Net Absorption | Occupied SF (or Units) End − Occupied SF (or Units) Start | Compared against supply pipeline to project rent growth |
| Supply Pipeline Pressure | $\frac{\text{Units / SF Under Construction}}{\text{Existing Inventory}}$ | MF: >5% = elevated oversupply risk; compare against historical absorption |
| Break-Even Rent | $R = \frac{O+D+A+Y-H}{S \times p \times q}$, with positive occupied/collected area | Annual rent/SF for stated cash uses and hurdle. $Y=yE$ is an annual cash-yield requirement, not an IRR target. Hold other inputs fixed or solve the actual model; see Sensitivity and Scenario Analysis for variables, limits and monthly MF version. |
10. Sensitivity & Scenario Analysis
| Technique | Approach | Notes |
|---|---|---|
| Exit Cap × Rent Growth Grid | Recompute the full dated cash model for each chosen cap/rent-growth pair | Select ranges and rank drivers for the actual model; inherited universal ±50–100/±100–200-bp ranges and top-two ranking are unverified here. Rent growth is not automatically NOI growth. See Sensitivity and Scenario Analysis. |
| Tornado / Sensitivity Analysis | Vary one input ±Δ, hold others constant; rank by impact on IRR / EMx | Identifies key value drivers |
| Scenario Matrix | Define coherent paths with full period income, expense, capital and financing schedules | Case names and fixed shock bands are not universal standards. State evidence or assumed status, outcome scope and liquidity/covenant effects. A stress menu is not a probability distribution; weighted expected results need exhaustive, mutually exclusive paths and normalized nonnegative probabilities. See Sensitivity and Scenario Analysis. |
| Break-Even Occupancy (Sensitivity) | Solve the stated income/expense model for NOI = Debt Service (DSCR = 1.0× with positive debt service) | Conditional debt-service threshold; reconcile collections, recoveries, variable expenses and additional cash uses. See Sensitivity and Scenario Analysis. |
| Break-Even Cap Rate | Cap rate at exit that yields EMx = 1.0× (return-of-capital threshold) | Exit risk floor |
| NPV of Decision | $\text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$ | Used for hold vs. sell, CapEx, and lease decisions; NPV > 0 = value-creating |
11. Disposition & Transaction Costs
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Net Sale Proceeds | Sale Price − Broker Commission − Transfer Tax − Legal − Loan Payoff − Prepayment Penalty | Industrial: Commission 1–4%; Transfer tax 0–2%; Legal $25K–$100K; Total seller transaction costs: 1.5–5.0% of sale price |
| Seller Credits | Unfunded TI + Deferred Maintenance + Free-Rent Burn-Off | Office disposition; negotiated adjustments to gross price |
| Disposition Fee | Agreed sponsor disposition fee, reconciled with other closing charges | Use the same definition as Section 7 and GP Fee Structures. Brokerage is a separate agreement/service; deduct each actual cost once. The conflicting inherited “typically 1–2%” range is unverified here. |
12. ESG & Sustainability (Industrial)
| Formula | Equation | Notes / Benchmarks |
|---|---|---|
| Solar Simple Payback | $C_0/S$ only for constant positive annual net cash savings from year one; otherwise use cumulative net cash flow | Match system-owner or host scope, costs and receipt timing. Model actually received incentives at their dates rather than assuming immediate tax-credit cash. Inherited 4–8 years is an unsupported scenario range. A host making no system investment has no such investment to recover; PPA savings and developer payback are separate calculations. See solar cash-flow scope and Source: Payback Mechanics Review 2026. |
| Green Premium on Value | $\Delta V = \frac{\text{NOI}}{\text{Cap Rate} - \Delta r} - \frac{\text{NOI}}{\text{Cap Rate}}$ | $\Delta r$ = cap rate compression from green features (typically 15–30 bps for LEED + solar + EV). ~$1.4M–$2.9M value increase on a $5M NOI asset |
| Building Performance Standard Penalty | $\text{Annual Penalty} = \text{Excess Emissions (tCO}_2) \times \text{Penalty Rate}$ | NYC LL97: $268/ton CO₂ over limit. 500K SF industrial exceeding limit by 20%: $200K–$500K+/year |
Pro Forma Cascade (Quick Reference)
Stated rent potential (matching unit/area and monthly/annual basis)
− Vacant-unit rent on that same basis
− Occupied signed market-to-contract gap only for a market-rent anchor; an in-place anchor already excludes it. See CRE Lease Structures and Expense Recovery.
− Additional identified credit adjustments (do not deduct vacancy again; broad asset-class loss ranges require separate review)
− Only additional rent concessions not already excluded by the anchor or contractual schedule
- Other Income (parking, pet fees, storage, laundry, package / amenity income, RUBS, antenna, expense recoveries)
= EGI
− Defined operating expenses on a consistent gross/net basis; broad asset-class ratios require scoped evidence. See Multifamily Pro Forma Modeling.
= NOI
− Actual TI/LC and building CapEx payments after cash reconciliation; reconcile reserve movements separately without counting funded spending twice
= Property Before-Tax Cash Flow (PBTCF) — selected property cash scope; see Office Underwriting and Lease Structures
− Debt Service
= Before-Tax Levered Cash Flow (BTCF) — simplified operating bridge; complete equity models also include loan proceeds/payoffs, deal costs, retained cash and allocations
− Income Tax Liability
= After-Tax Cash Flow (ATCF)
Negative Leverage Test (Quick Reference)
Negative leverage exists when: Mortgage Constant ($K_d$) > Cap Rate
Every dollar of debt reduces equity CoC return.
Example: If $K_d = 6.81%$ and Cap Rate $= 5.25%$ → negative leverage of 156 bps.
This is a current-yield screen. Test NOI, capital costs, debt amortization, fees and exit scenarios in the full return model; growth or appreciation is not guaranteed to offset the cash-yield shortfall.
Related Pages
- CRE Return Metrics and KPIs
- CRE Valuation Methodologies
- CRE Capital Stack and Debt Structuring
- Cap Rate Decomposition
- CRE Tax and After-Tax Underwriting
- Equity Waterfall and Promote Structures
- Sensitivity and Scenario Analysis
- CRE Lease Structures and Expense Recovery
- Industrial Tenant Reimbursement Modeling
- Office Tenant Reimbursement Modeling
- CRE Supply Pipeline and Construction Analysis
- Multifamily CapEx Budgeting
- Multifamily Pro Forma Modeling
- Multifamily Value-Add Renovation
- Multifamily Ancillary Income Programs
Provenance
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Source: Lease Weighting and Rollover Scope Review 2026 — lease weighting, area/rent exposure and retention-denominator scope only.
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Source: Occupancy and Expense Ratio Mechanics Review 2026 — conditional occupancy/OER mechanics and assumed examples only.
This page consolidates three asset-class-specific formula cheat sheets from the legacy Notion export:
| Source File | Asset Class |
|---|---|
| Formulae Cheat Sheet | Industrial |
| Formulae Cheat Sheet | Multifamily |
| Formulae Cheat Sheet | Office |
The consolidation preserved the legacy source files unchanged. Canonical formulas and interpretations are subsequently reviewed independently; the October 7, 2026 loan-math pass clarifies payment conventions, zero-rate limits and the distinction between current cash yield and total-return IRR. Other inherited benchmarks remain subject to factual review.
Consolidated: 2026-04-09
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Source: GP Fee Mechanics Review 2026 — sponsor fee bases, periods and offsets only; no tax or market-range attestation.
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Source: ILPA Waterfall Scope Review 2026 — preferred-return/catch-up scope and hypothetical tier-share mechanics only.