Underwriting

CRE Return Metrics and KPIs

Commercial real estate return metrics provide different perspectives on investment performance, measuring money-weighted return over a stated interval (IRR), a stated value-to-capital multiple (Equity Multiple), or current cash yield (Cash-on-Cash). Property-level income growth (NOI) and durable cash yields are useful underwriting considerations. The inherited assertion of a marketwide institutional shift in 2026 remains unverified by this page’s mechanics reviews.

Also known as: Cash-on-Cash, Equity Multiple, IRR, Investment KPIs, Return Metrics

Updated

Candidate Return Assumptions Pending Verification

The inherited ranges below are unverified candidate underwriting inputs, not established 2026 institutional benchmarks. Before using them, identify the investor universe, strategy, geography, observation date, gross/net basis, cash-flow population and hold period. A target is a policy or forecast, not an observed realized return; IRR, multiples and cash yield also need consistent timing and valuation conventions.

StrategyCandidate IRRCandidate Equity MultipleCandidate Cash Yield
Core10% – 12%1.5x – 1.8x5% – 6%
Core-Plus12% – 15%1.8x – 2.0x6% – 7%
Value-Add15% – 20%2.0x – 2.5x4% – 6% (Post-stabilization)
Opportunistic18% – 25%+2.5x+Variable

1. Internal Rate of Return (IRR)

The money-weighted rate that makes the specified cash flows’ NPV zero. Periodic IRR is a rate per cash-flow interval; annual entries yield an annual rate, while a monthly result requires effective annualization. Dated XIRR uses supplied dates and a 365-day basis. Preserve later capital calls, zero-flow intervals and investor/fee scope; sign-changing flows can have multiple roots. See Source: MIRR and IRR Mechanics Review 2026.

Exit dependence: IRR is the solution to a cash-flow equation, not an additive sum of operating and exit return percentages. “More than 60% of IRR comes from exit” is undefined without a specified attribution method. Instead report net exit receipts separately from operating receipts, state whether a receipt share is nominal or discounted at a fixed stated rate, and stress exit price, costs and timing. Recalculate whole-investment IRR and NPV under each scenario; a change in IRR is a sensitivity, not a uniquely allocated share of the base IRR. See Sensitivity and Scenario Analysis.

Evidence gap, reviewed 2026-10-07: The inherited claims of a 150–250-bp widening versus 2021, Treasury rates of 3.5%–4.0%, and an LP-wide 60% Year-10-exit rejection threshold lack claim-specific dated support here. These are unresolved research inputs. Establish comparable target populations and dates, the Treasury maturity and observation date, and the actual investor policy before treating any figure as a market observation.

2. Equity Multiple (EMx)

A value-to-capital ratio whose numerator, denominator and reporting population must be stated. Distinguish distributions already received from total value including a residual mark:

Distributions-only equity multiple = D / C
Total-value equity multiple = (D + R) / C
C = cumulative contributions for the stated investor population, C > 0
D = cumulative distributions for that same population
R = remaining equity value at the stated as-of date and valuation basis

With consistent investor, fee/carry, currency and recall conventions, these have the same arithmetic as DPI and TVPI respectively. A modeled terminal receipt is a forecast, not a distribution already received. Include later contributions and retain gross distribution/recontribution events. Reconcile proceeds already distributed with remaining value so they are counted once. State whether distributions include non-cash value; a cash-only numerator requires that disclosure.

MOIC reporting scope: ILPA's 2025 v1.1 definitions distinguish net fund TVPI (all-purpose investor contributions), granular fund gross MOIC (investment-purpose contributions and adjusted value), gross-up fund gross TVPI (all-purpose contributions with fee/carry add-backs), and portfolio gross MOIC (fund-to-investment capital, distributions and unrealized portfolio value). These are reporting-method distinctions, not interchangeable names for one cash flow. The retained 2019 ILPA glossary uses a distributions-only LP MOIC definition; preserve the version and definition when comparing reports. This review does not implement the complete templates or certify legal compliance.

Private real estate reporting: The January 2026 NCREIF PREA paper distinguishes fund, investment and property total-value/population scope, includes recalled capital in paid-in capital, and asks readers to disclose multiple methodology. Its discussion explains why MOIC and TVPI names can be used inconsistently. Apply the relevant reporting definitions rather than treating ILPA private-equity guidance as a universal CRE rule. The paper is interpretive guidance, not a legal-compliance certification. See Source: CRE Multiple Reporting Review 2026.

Assumed arithmetic: With C=100, D=60 and R=90, the distributions multiple is 0.60× and total-value multiple is 1.50×; only 60 has been distributed. With C=100, D=200 and R=0, a fully distributed 2.00× case has nominal cash gain of 100, not 200. Receiving that 200 only at year 1 or year 10 produces the same multiple but annualized IRRs of 100% or approximately 7.18%, assuming no intervening cash flows. Neither outcome certifies inflation-adjusted preservation, taxable profit or investor liquidity at an unrealized mark.

The inherited target multiples in the table above and the claim of an institutional preference for multiples in high inflation are not verified by these definitions. Treat them as candidate underwriting assumptions pending scoped evidence and clear gross/net and horizon conventions. Reviewed 2026-10-07: Source: Equity Multiple Scope Review 2026.

3. Cash-on-Cash Return (CoC)

A stated period’s pre-tax cash flow divided by a specified cash-equity denominator. An annual cash-flow forecast is a modeled yield, not proof of cash distributed to an investor. Identify property, fund or LP scope, the period and whether the denominator is initial, cumulative or another explicitly defined cash-capital measure; current marked equity is a different basis.

For a property-level cash-availability bridge, reconcile NOI with cash operations, debt service, TI/LC, capital spending, fees and restricted cash/reserve movements as applicable. NOI minus debt service is a simplified bridge; it overstates available cash when other cash uses are omitted. Avoid deducting both a reserve transfer and the same spending funded from that reserve without reconciling releases. Investor distributions additionally depend on the agreement and retained liquidity. Separate operating cash from sale/refinance receipts and returns of capital when describing recurring income yield; principal amortization and unrealized appreciation are not cash receipts.

Related property indicator: NCREIF’s January 2015 FCFY methodology subtracts specified capital improvements from NOI and divides by beginning property market value for the quarter. It includes recurring leasing commissions, tenant improvements and building improvements, with exclusions/filtering for substantial changes. This historical property indicator is distinct from levered investor cash-on-cash return; neither its denominator nor its sampling/filter rules certify an LP distribution rate. See Source: Cash Yield Scope Review 2026.

Evidence gap, reviewed 2026-10-07: The inherited 5.5%–7.5% stabilized core-plus industrial/multifamily target is an unverified scenario input. Establish dated investor policy or a scoped survey, cash-flow basis and capital denominator before calling it a 2026 institutional benchmark.

4. Yield-on-Cost (YoC)

Stabilized annual NOI divided by the stated total project cost. Identify the stabilization date/occupancy, NOI basis and cost scope, including how land, construction, leasing, financing carry and remaining completion costs are treated. A stabilized forecast is not cash already earned, an investor distribution or a time-adjusted return.

Development spread: YoC − comparable stabilized cap rate. Match NOI and asset/date assumptions. The difference is measured in percentage points or basis points, not dollars of profit. In a static same-NOI capitalization bridge with positive cost C and cap rate c, V = NOI/c, so (V − C)/C = YoC/c − 1; this excludes transaction costs, taxes and timing. A positive spread alone does not establish an adequate risk-adjusted return or net realized profit.

Assumed arithmetic: Cost 400, annual stabilized NOI 30 and cap rate 6% give YoC 7.5%, spread 150 bps, implied value 500 and value less cost 100 (25% of cost). Holding cost and NOI constant but using a 7.5% cap gives value 400 and zero spread/gain. At cost 500, NOI 30 and cap 6%, YoC is 6% and the gain is also zero. These teaching cases are not issuer performance or construction-loan quotes. Model dated construction, lease-up and exit cash flows separately.

Evidence gap, reviewed 2026-10-07: The inherited 150–250-bp required spread and >7% construction-debt claim lack scoped dated support here. Treat them as candidate scenarios or investor-policy inputs until the asset class, geography, project risks, lender terms and observation date are established. See Source: Development Spread Scope Review 2026.

Data-centre underwriting is a useful reminder that yield-on-cost is not a generic target return; it is the bridge between demand, rent revenue, and capital intensity. Source: Cushman & Wakefield Asia Pacific Data Centre Investment Landscape 2025 names population per megawatt, rent revenue, CapEx requirements, and yield-on-cost as core APAC data-centre investment fundamentals, so YoC should be interpreted alongside demand density and capex burden rather than as a standalone hurdle.

5. Risk-Adjusted Metrics (2026 Additions)

These 2026 additions reflect the specific credit and refinancing pressures of the current cycle. The concepts are durable; the numerical thresholds and which metric is binding can change as capital markets reset.

Debt Yield Sensitivity

Debt yield divides stated annual underwritten NOI by a specified debt amount greater than zero. Define the NOI adjustments, as-of/stabilization basis and whether the denominator is senior balance, total debt or another agreement-defined exposure. A senior-only ratio and an all-debt ratio are different measures. Debt yield is not the lender’s coupon, realized investment yield or guaranteed recovery.

For fixed NOI and debt amount, the ratio does not contain interest rate, amortization or cap rate. Those assumptions still affect DSCR, valuation, approved proceeds and the investment’s risk. If a positive minimum debt yield applies, its standalone sizing cap is Underwritten NOI / Minimum Debt Yield; compare all applicable DSCR, LTV and other limits. A cap is not a guaranteed commitment. Nonpositive NOI cannot support a positive loan under a positive minimum in this simple test.

Assumed sizing: Annual NOI $1M, a 10% debt-yield input and 65% LTV on $20M value give standalone caps of $10M and $13M. At assumed 1.25× DSCR with interest-only 8% debt, the DSCR cap is also $10M. At 10% interest it falls to $8M, while the debt-yield cap stays $10M. The binding test therefore changes with the full constraint set; debt yield is not automatically binding whenever cap rates are compressed. These are hypothetical inputs, not loan quotes or universal policy floors.

Rate-level counterexample: Retain annual NOI $1M, minimum debt yield10% and minimum DSCR1.25×, but separately assume value $10M and maximum LTV65%. At IO10%, DSCR permits $8M; at IO4%, it permits $20M. Debt yield permits $10M in both, while LTV permits $6.5M and binds in both. These assumed cases show why neither a high-rate nor low-rate label determines the minimum. Exact Fraction and independent50-digit Decimal reproduce the caps. Loan costs/reserves, commitments and other restrictions can further reduce net available funding; the simple minimum is not an approval.

Evidence gap, reviewed 2026-10-07: The inherited 8.5%–10.5% institutional floor and claim of a marketwide 2024–2025 shift toward debt yield are not established by the reviewed OCC definition. OCC’s retained passage describes property/market differences and use alongside DSCR/LTV, not a universal numerical minimum. Obtain the actual dated lender/product terms. See Source: Debt Yield Scope Review 2026 and CRE Capital Stack and Debt Structuring.

OpEx Efficiency Ratio

Define OER here as stated operating expenses / positive effective gross income (EGI) for the same period. Identify actual versus underwritten expenses, reserve treatment and gross versus net expense-recovery presentation before comparing properties. A lower ratio alone does not establish a valuation premium: revenue mix, deferred work and expense allocation can change the ratio without improving cash available to equity.

Evidence gap, reviewed 2026-10-07: The inherited claim that an expense ratio below 35% commands a valuation premium is not established by the retained methodological evidence. Obtain comparable asset/lease scopes and dated valuation evidence. See Source: Occupancy and Expense Ratio Mechanics Review 2026.

Break-Even Occupancy

Debt-service break-even solves the stated income model for NOI equal to modeled debt service. The shortcut (fixed operating expenses + debt service) / GPR assumes rent is proportional to occupancy, full collection, no concessions, no other income/recoveries and expenses that do not change with occupancy. It is not automatically physical occupied SF/units or a threshold covering every cash obligation. Capital costs, fees and reserve funding require a separate cash reconciliation.

Use Sensitivity and Scenario Analysis for the conditional formula and collection/variable-cost example, and Office Sensitivity and Scenario Analysis for office rollover and recovery stress. Inherited NNN industrial 40–50% and other universal targets remain unverified benchmarks; lease obligations, income, debt and the selected break-even objective govern the result. See Source: Occupancy and Expense Ratio Mechanics Review 2026.

6. Fund-Level Return Metrics

These metrics support commingled-fund and multi-asset monitoring; some, including MIRR and payback, can also be calculated for individual deals. Define the investor population, cash-flow scope and period before comparing results.

MIRR (Modified Internal Rate of Return)

As of 2026-10-07, MIRR is reviewed here as a periodic cash-flow calculation, not a market-return benchmark. IRR is a rate that makes the specified cash flows' NPV zero; that equation does not measure the wealth actually achieved by reinvesting distributions. MIRR explicitly selects financing and reinvestment rates. Neither metric alone guarantees a realized return. See Source: MIRR and IRR Mechanics Review 2026.

For cash flows CF_0 through CF_N at equally spaced times, with N > 0, define positive receipts and negative payments from one investor's perspective:

PV_outflows = sum(-CF_t / (1 + finance_rate)^t for CF_t < 0)
FV_inflows = sum(CF_t × (1 + reinvest_rate)^(N - t) for CF_t > 0)
MIRR = (FV_inflows / PV_outflows)^(1/N) - 1

Positive cash flows are compounded forward to the terminal period; all negative cash flows, including later capital calls, are discounted to time zero and expressed as a positive outflow magnitude. N counts elapsed periods, not cash-flow entries: six annual entries from time zero through year five span five periods. Rates must match the interval and exceed -100%; the calculation needs both payment and receipt cash flows. Keep zero-flow periods in their positions.

  • Rate inputs: document the modeled financing cost and reinvestment opportunity. Inherited 8%–10% reinvestment and 6%–8% finance ranges are provisional scenarios, not verified current market norms or automatic cost-of-equity/debt substitutions.
  • Timing: standard spreadsheet MIRR uses regular periods. Monthly MIRR is a monthly result; effective annualization is (1 + monthly_MIRR)^12 - 1. For irregular dates, define a dated financing/reinvestment convention; do not silently compress dates into periodic slots. Excel XIRR(values, dates) separately solves a dated IRR using a 365-day basis and is not a MIRR calculation.
  • Interpretation: compare sensitivities under explicit assumptions. MIRR can change when either modeled rate changes and is not guaranteed to be below IRR. Sign-changing cash flows can have multiple IRR roots; a solver result is not proof of uniqueness.

Reproduced publisher example: Microsoft's periodic sample [-120000, 39000, 30000, 21000, 37000, 46000], with 10% finance and 12% reinvestment rates, has positive outflow PV of $120,000 and terminal inflow FV of $217,297.49504. Five-period MIRR is approximately 12.6094%, consistent with the publisher's whole-percent display of 13%. The finance rate has no effect in this particular sample because its only outflow occurs at time zero; later outflows change that sensitivity. This is a spreadsheet example, not an observed CRE investment return.

DPI (Distributions to Paid-In Capital)

As of 2026-10-07, the reviewed definitions use cumulative contributions actually paid in, not unfunded commitments, unpaid calls or only capital deployed into assets. Distributions include cash and appropriately valued in-kind amounts under the selected reporting convention. Specify the same investor population, as-of date, currency, fee/carry basis and recall treatment for every component. See Source: DPI and TVPI Definitions Review 2026.

P = cumulative paid-in capital (P > 0)
D = cumulative distributions
R = residual value at the reporting date
DPI = D / P
RVPI = R / P
TVPI = (D + R) / P = DPI + RVPI
  • DPI < 1.0×: Distributions are below cumulative paid-in capital. This alone does not establish a J-curve, loss or underperformance; residual value and timing remain relevant.
  • DPI = 1.0×: Distributions equal cumulative paid-in capital in nominal reported amounts. This is not proof of an inflation-adjusted or hurdle-rate break-even, liquidation, zero remaining value or a particular legal/tax allocation between capital and profit.
  • Thresholds: The inherited 1.5× watchpoint is a provisional scenario, not a verified target for most institutional PE real estate funds. Compare definitions, vintage and strategy before treating a multiple as a benchmark.
  • Realized versus residual: DPI records distributions; RVPI reflects marked residual value, which is not yet distributed cash. Their sum equals TVPI only with matching scope and denominator. Do not compare a gross asset multiple directly with a net LP multiple.
  • Recalls: Under the reviewed GIPS/ILPA definitions, record an actual recallable distribution in D and its subsequent recontribution in P. Do not erase both ledger events or cap cumulative paid-in capital at the original commitment. The agreement separately determines whether and how much capital can be recalled.

Assumed snapshot: $100 paid in, $60 distributed and $90 residual value give DPI 0.60×, RVPI 0.90× and TVPI 1.50×. If the $100 includes $10 used for fees or still awaiting investment, $90 deployed into companies is a different denominator; $110 of issued calls with $10 unpaid or $150 committed is also different. This scenario is not an actual fund return.

Assumed recall case: contribute $100, receive a $40 distribution and subsequently recontribute $20 under permitted recall terms. Cumulative P is $120 and D is $40. With $80 residual value, DPI is about 0.3333×, RVPI about 0.6667× and TVPI 1.00×. Original commitment of $100 is not the paid-in denominator; the example assumes recall permission and does not establish a universal right to exceed commitments.

DPI ignores elapsed time. Receiving $100 for an initial $100 after one year or ten years produces the same 1.00× DPI; at an explicitly assumed 8% annual discount rate, the respective NPVs are approximately -$7.41 and -$53.68. Use dated returns and valuation alongside multiples; neither scenario certifies current market discount rates.

Payback Period

A capital-recovery screen for a defined investor or project cash-flow population. Simple payback ignores the time value of money; discounted payback uses a stated discount rate. Neither measures total investment return or guarantees that later capital calls cannot reverse an earlier recovery.

CF_i = Relevant Cash Receipts_i − Relevant Cash Payments_i
B_t = Sum of CF_i from i = 0 through t, including initial investment
First-crossing simple payback = First observed t with B_t ≥ 0, if B_0 < 0
Discounted balance = Sum of CF_i / (1 + r)^i from i = 0 through t

Use matching cash-flow and rate intervals in the periodic discounted equation. Preserve later contributions and recall payments as negative cash flows. The first-crossing convention is explicit here; nonconventional flows can produce multiple crossings, so report the later reversal and any subsequent recovery. If the balance never reaches zero within the modeled horizon, report that outcome rather than inventing a payback date.

End-of-year receipts give an observed year-end recovery date. A fractional-year estimate assumes an intra-year receipt pattern; dividing the unrecovered balance by the next year's cash flow is not valid for a lump sum arriving at year-end. The initial-investment/annual-net-inflow shortcut requires constant positive net cash inflows starting in year one and no additional investment; it must use the same timing convention.

Assumed cash-flow checks: With [-100, 60, -80, 50, 70] at years 0–4, balances are [-100, -40, -120, -70, 0]; recovery is at year 4. Comparing distributions only with the initial 100 would incorrectly report year 3. With [-100, 120, -50, 40], the year-1 crossing reverses in year 2 and recovery occurs again in year 3. These are teaching cases, not fund performance.

Payback omits cash flows after the selected recovery point; use NPV and dated returns alongside it. The inherited 5–6-year target within a 7–10-year value-add hold is an unsupported candidate underwriting policy, not a verified institutional market norm. Review scope and arithmetic as of 2026-10-07: Source: Payback Mechanics Review 2026.

NAV (Net Asset Value)

NAV is the value of all fund assets less all fund liabilities under the stated accounting or valuation basis. It is a valuation measure used in open-end fund monitoring and subscription/redemption processes; it is not itself a performance return or a guarantee of liquidity.

NAV = Value of All Fund Assets − All Fund Liabilities
NAV per Unit = NAV Allocated to a Unit Class / Units Outstanding in That Class

Include cash, receivables and other assets as well as properties, and accrued fees and other liabilities as well as debt. Property value less mortgage debt is a property-equity calculation; it need not equal fund NAV. State the valuation basis and date. A single-class fund can use total NAV divided by total units; different classes require their own allocations and rights.

  • Valuation frequency: Reporting frequency, internal valuation updates and independent external appraisals are distinct. The NCREIF open-end index context uses quarterly valuations; this does not establish a universal quarterly independent-appraisal requirement for every institutional fund.
  • Redemption pricing: Review the vehicle's pricing policy, notice periods, windows, available cash and deferral/queue provisions. NAV-based redemption is a governed process. A negotiated secondary transfer price can differ from reported NAV; it is a separate transaction price, not a universal subscription/redemption quote.
  • Limitation: Appraisal-based property marks can lag transaction evidence and smooth reported NAV changes. Reported NAV need not equal executable sale proceeds. Subscriptions, distributions and other capital movements also affect total NAV, so its change alone is not a return calculation.
  • Historical evidence gap, reviewed 2026-10-07: The inherited claims of 8–15% open-end NAV declines in 2023–2024, $5–8B peak ODCE redemption queues and stabilization in late 2025 are unsupported by the cited fund-structure verification. They are unresolved research inputs, not accepted market observations. Establish the fund universe, measurement dates, NAV/return definition and queue convention before using those figures.

See Source: ILPA Waterfall Scope Review 2026 for the retained ILPA NAV glossary definition and Fund Structure Verification 2026-04-21 for scoped open-end valuation and liquidity framing.

Metric Failure Modes

No metric is neutral. Each one highlights a different part of the return story and hides a different risk.

  • IRR: can over-reward short hold periods, early exits, and terminal-value assumptions that are too generous.
  • Equity Multiple: measures a stated value-to-capital ratio, not dollar profit or annualized return. A total-value multiple can include unrealized marks; a distributions-only multiple excludes them.
  • Cash yield: is useful for current income but can ignore back-end capital risk or deferred CapEx.
  • NAV: supports open-end portfolio monitoring but can smooth volatility because appraisal marks lag transaction markets.
  • DPI: is useful for realized return discipline but often advantages older harvested funds relative to younger funds still carrying unrealized value.

That is why return metrics should be read in combination with vehicle structure, portfolio role, and the actual source of the return. A strong-looking metric can still be telling the wrong story if the hold period, liquidity regime, or realization path is not explicit.

Which Metrics Fit Which Mandates

MandatePrimary metricsWhy
CoreCash yield, unlevered return, NAV stabilityIncome durability and downside protection matter more than velocity
Core-PlusCash yield, net IRR, Equity MultipleThe investor still wants current income, but with measured execution upside
Value-AddNet IRR, Equity Multiple, payback periodExecution and realization timing drive the return story
OpportunisticNet IRR, Equity Multiple, Yield-on-CostBasis creation and high-conviction upside matter more than early current income
Open-EndNAV, total return, cash yieldThe vehicle is designed for periodic liquidity and standing portfolio monitoring
Closed-EndNet IRR, DPI, TVPI / MOICThe vehicle is judged through drawdown, realization, and finite-life harvest discipline

Use Open-End and Closed-End Fund Structures when the vehicle design itself is the main question. Use Portfolio Construction and Risk Budgeting when the issue is how much of the portfolio should consume this return profile. Use Hold, Sell, and Refinance Decision Framework when the return debate is really about the next use of capital rather than the current mark.

Coconut Grove Case: Price Change Versus Investor Return

Source: Coconut Grove Office Flipped For $15M Gain After One Year reports purchase and resale prices for 3250 Mary Street. Its headline “gain” is not a net-profit or IRR measure. Build dated property and investor cash flows separately, including acquisition costs, capital work, interim income, sale costs, debt and investor fees. Exact holding period and complete cost basis need verification; do not annualize the headline. Office Disposition and Exit Strategy tests net sale proceeds, while Hold, Sell, and Refinance Decision Framework compares alternatives from the owner's current position.

Related Pages

Sources

  • Source: Occupancy and Expense Ratio Mechanics Review 2026 — conditional occupancy/OER mechanics and assumed examples only.
  • Source: CRE Multiple Reporting Review 2026 — private real estate level/denominator definitions and reproduced aggregate teaching-table multiples.
  • Source: Equity Multiple Scope Review 2026 — realized/total-value multiples, reporting populations and assumed arithmetic; not market target ranges.
  • Source: Payback Mechanics Review 2026 — timing, cumulative net cash flow and solar ownership/rate-model scope only.
  • Source: ILPA Waterfall Scope Review 2026 — NAV accounting definition only; the fund-structure verification supplies valuation/liquidity context.
  • Fund Structure Verification 2026-04-21 — open-end index and governed-liquidity scope; not the historical decline or queue figures.
  • Legacy Industrial Knowledge Wiki
  • 2026 Q2 Market Research Sprint
  • Investment Fundamentals Sprint Research 2026
  • CBRE 2026 Investment Outlook / Deloitte 2026 Real Estate Forecast
  • Source: MIRR and IRR Mechanics Review 2026 — periodic/dated return mechanics only; other market benchmarks remain outside this verification.
  • Source: DPI and TVPI Definitions Review 2026 — paid-in, distribution, residual-value and recall definitions; explicitly assumed arithmetic.