Cap Rate Decomposition

This page compares the Build-Up Method, the Gordon Model, the Band-of-Investment (BOI) and the Ellwood Formula. They address different assumptions; none alone determines a market price.

Reconcile economics, comparable sales, and finance

Keep three estimates separate: an economic build-up, comparable transactions with consistent NOI, and the price the buyer can finance. Reconcile their differences before selecting a range. A financing constraint is specific to the borrower and lender; it does not establish an intrinsic asset value.

For the same NOI convention, target loan-to-value L, annual mortgage constant k, minimum DSCR d, and minimum debt yield y, debt sizing implies:

cap rate >= d × L × k
cap rate >= y × L

For hypothetical L=60%, k=5.75%, d=1.35, and y=8.5%, the coverage floor is 4.6575% and the debt-yield floor is 5.10%. These are arithmetic screens. Use the actual amortization constant, lender NOI adjustments, costs, and other constraints before bidding.

Cap-rate sensitivity is nonlinear. Holding NOI constant, moving from a 5.5% cap to 6.5% changes value by 5.5/6.5 - 1 = -15.38%. Keep operating deterioration and cap-rate expansion as separate inputs, then test their joint effect. Low transaction volume, changing sale composition, and appraisal lags can impair comparisons.

Source: CRE Research Methods Public Evidence Review 2026 supports these scoped methods and calculations. Use Forecast Evaluation and Research Transferability when a historical estimate is proposed as a forward assumption.

---

1. Build-Up Method

Scope reviewed 2026-10-07: A build-up organizes stated rate assumptions; it does not identify independent market premiums or prove an observed cap rate. Distinguish the selected discount/required-return scenario from the NOI/price ratio.

r = R_f + RP_RE + RP_property       # only non-overlapping, compatible increments
c_forward_cash = r - g_cash        # only the matched Gordon cash-stream conditions

The rate components are curator assumptions unless supported by a scoped empirical model or dated evidence. If sector, property and liquidity labels overlap, their sum double counts risk. A transaction cap/Treasury spread is not automatically a separately identified risk premium: cash definitions, growth and timing also affect it. Do not add an inflation allowance already included in the selected nominal inputs, or mix nominal rates with real growth.

Section2's Gordon model requires first year-end cash F1>0, constant compatible g>−1 and r>g over the specified infinite stream. Only then does forward cash/PV=r−g. This is an NOI-cap relation only if that cash equals NOI; capital/lease spending, timing and finite exits require their own reconciliation. A chosen benchmark and premium sum do not independently establish that discount rate or an achievable property price.

Assumed arithmetic: Compatible rate inputs4.15%+1.50%+0.50%=6.15%; matching constant cash growth2.50% gives forward cash/PV=3.65%. With first year-end cash $1M and the stated perpetual assumptions, PV≈$27.3973M. Separately assume first-year NOI $1M but cash after recurring capital/lease uses equals75% of NOI and grows at the same rate: cash $750,000 gives PV≈$20.5479M, cash/PV3.65% and NOI/PV≈4.86667%. The assumed25% use is not a market norm. Exact Fraction and independent50-digit Decimal verify these cases; the inherited5.25% result is not reproduced by the stated inputs.

Use case: Explain assumptions and test consistency with actual cash-flow/comparable evidence. The inherited rule that a ClassA constrained Sunbelt industrial property must have lower property premium and higher growth than a ClassB secondary-office property is not established by this methods review. Review actual leases, costs, risk, supply, investor scope and evidence dates rather than assigning automatic asset/location credits. Source: Debt Yield Scope Review 2026 supports scoped valuation definitions and stressed inputs; the build-up and examples are curator models, not OCC market-rate prescriptions.

For multifamily-specific location work, use Multifamily Cap Rates and Location Quality as the companion page. It separates location's effect on durable NOI growth from location's effect on property risk premium and exit liquidity, so a neighborhood thesis does not get counted simultaneously in rent, vacancy, debt proceeds, and exit cap.

Source: Newmark 2026 Valuation & Advisory North American Market Survey adds an appraisal-side 1Q 2026 calibration table. The applied rows (market_observations.id=33923-33992) preserve national average / median going-in cap rates and discount rates across industrial, multifamily, office, and retail quality slices. Use it as a cross-asset reasonableness check, not as asset-specific transaction proof.

---

2. Gordon Model Adaptation

Scope reviewed 2026-10-07. This is a conditional growing-cash-flow model, not a way to read observed growth directly from any market cap rate. Define selected annual end-of-period cash F_t, with F_1 > 0, constant growth g > −1 and a matching constant discount rate r > g. Use consistent nominal/real and unlevered/levered scope. Under the assumed infinite stream F_t = F_1 × (1+g)^(t−1):

PV_0 = sum(F_t / (1+r)^t, t=1..infinity) = F_1 / (r−g)
Forward cash capitalization ratio = F_1 / PV_0 = r−g

This is curator geometric-series algebra. OCC's retained pp.42–44 support examining income/cash definitions, stabilized direct capitalization, discounted income/net sale proceeds and appropriate rate inputs; Those retained passages do not supply this perpetual model, a growth forecast or a typical discount-rate range. See Source: Debt Yield Scope Review 2026. With positive discount factors (r > −1), if r = g, positive discounted payments do not decay; if r < g, they grow. Neither case permits the finite positive F_1/(r−g) valuation. A finite hold with changing rents, losses, expenses, capital uses or exit assumptions needs its own dated DCF.

For the special case where the selected property cash equals NOI in every period, and the cap uses forward annual NOI_1, c_forward = r−g and g = r−c_forward. If the cap uses trailing NOI_0, with the same assumed growth:

c_trailing = (r−g)/(1+g)
g = (r−c_trailing)/(1+c_trailing)

NOI growth is not automatically growth of cash after TI/LC/building CapEx. If selected cash differs from NOI, its capitalization ratio is not the quoted NOI cap; do not subtract an NOI cap from an equity discount rate or an IRR target to infer growth. A rent-growth input is also not automatically NOI growth. Rate selection and observed cap extraction require separate evidence; see CRE Valuation Methodologies and Office Underwriting and Lease Structures.

Hypothetical timing check (all amounts in assumed dollars): Assume NOI_0 = 1,000,000, perpetual growth 3%, annual discount 8%, and no cash adjustments, financing or selling costs. NOI_1 = 1,030,000, PV_0 = 20,600,000, forward cap 5%, trailing cap 5/103 (approximately 4.85437%). The correct trailing inversion gives 3%; naive 8% − trailing cap gives approximately 3.14563%, under a different formula. Neither is an observed rent/growth forecast.

Hypothetical cash-scope check: Separately assume recurring capital/lease cash uses equal 25% of NOI in every period, with the same growth/rate. Selected cash is 75% of NOI and PV_0 = 15,450,000; forward cash/PV remains 5%, while forward NOI/PV becomes 1/15 (approximately 6.66667%). The NOI-cap spread therefore does not recover the stated 3% growth. The 25% adjustment is a teaching assumption, not a market norm or blanket reserve rule.

For q = (1+g)/(1+r), the first n discounted payments equal PV_0 × (1−q^n) and the discounted continuation equals PV_0 × q^n. In the first hypothetical case, five annual payments are approximately 4,346,961.41 and the discounted assumed continuation 16,253,038.59, summing to 20,600,000. A finite model cannot omit its continuation and still claim the same perpetual value, or add a separate sale on top of an already complete infinite stream. The assumed continuation is not a verified buyer exit price.

The inherited 7–10% institutional discount-rate range and causal explanations of 2021–2025 asset-class cap moves are not established by this algebra. The prior 7.5% − 5.25% = 2.25% and 9% − 7% = 2% examples remain conditional arithmetic only when cash/NOI and forward timing match the special case; they establish neither reasonable industrial growth nor office recovery. Preserve the dated Newmark survey calibration above within its own scope.

---

3. Band-of-Investment (BOI) Method

Scope reviewed 2026-10-07. BOI is a conditional annual equity cash-yield hurdle, not a full-return IRR, market-value conclusion or lender approval. Assume price P > 0, loan B = L × P, 0 ≤ L < 1, cash equity E = (1−L)P, annual NOI N = cP and annual debt service D = kB. Here debt/price and equity/price are the actual financing shares; an appraisal-based LTV may have a different denominator. The simplified case has no additional initial costs or annual cash adjustments and makes all NOI after debt service available to equity. Let h be the selected annual equity cash-yield target:

Equity cash yield y = (c−Lk)/(1−L)
BOI cash-hurdle cap c_BOI = Lk+(1−L)h
y ≥ h exactly when c ≥ c_BOI, under these assumptions

In the inherited notation, R_o = c_BOI, LTV = L, R_m = k (annual mortgage constant) and R_e = h (equity dividend target). Use documented annual debt service, not a coupon unless that coupon represents the modeled service; see CRE Capital Stack and Debt Structuring. This is curator cash-flow algebra. OCC's retained pp.42–44 support reviewing cash/NOI definitions, stressed income, debt-service coverage and valuation inputs; those passages do not supply this BOI formula or a typical equity target. See Source: Debt Yield Scope Review 2026.

Hypothetical calculation: Assume L = 60%, annual constant k = 6.81% and cash target h = 7%. These are teaching inputs, not available loan terms or market norms. c_BOI = 0.60 × 0.0681 + 0.40 × 0.07 = 0.06886, or 6.886% (rounded 6.89%). A 6% NOI cap gives equity cash yield 4.785%, below both the unlevered 6% and the 7% target. This does not prove the property overpriced or determine total return.

Cash hurdle versus leverage: For L > 0, y−c = L(c−k)/(1−L). Negative current cash-yield leverage in this simplified same-NOI model means c < k; it does not mean merely c < c_BOI. With the same assumed financing, a 6.85% cap gives 6.91% equity cash yield: positive current leverage, but below the 7% target. Growth, principal reduction and exit proceeds require a dated return model; they are not established by either current-yield inequality. At zero debt, there is no leverage effect.

Actual cash and equity bridge: Recompute using actual proceeds, debt service and cash equity, including relevant closing costs and initial funding. For the selected annual period:

Required NOI = debt service + other cash uses − other cash sources
             + h × actual cash equity

Include only adjustments not already counted in NOI, and do not charge reserve funding and the same reserve-funded expenditure twice. Identify what cash is distributable under the actual agreement; entity cash after debt service is not automatically an LP distribution. Annual totals also do not establish liquidity on every payment date. See Office Underwriting and Lease Structures and CRE Return Metrics and KPIs.

Separate hypothetical bridges: At price $100M, loan $60M and equity $40M, the assumed constant gives annual debt service $4.086M. A 7% NOI cap exceeds the simplified 6.886% hurdle, but separately assumed annual capital/lease cash uses of $2M leave only $914,000, or 2.285% equity cash yield. In a different case with a 6.85% NOI cap, no annual adjustments and an extra $5M of equity-funded closing costs, annual cash $2.764M divided by actual equity $45M gives approximately 6.142222%, rather than 6.91%. The closing cost is not deducted again annually. Neither adjustment is a reserve rule or market benchmark.

Use BOI to explain the selected current cash target and its sensitivity. A miss does not itself establish negative leverage, speculative pricing or overvaluation; a pass does not establish financing feasibility. Review actual DSCR, debt yield, LTV, covenants, liquidity and maturity/exit requirements separately. No 2026 market-wide negative-leverage conclusion follows from these assumptions.

Cap Rate Spread variant:

Cap Rate Spread = Cap Rate − 10-Year Treasury Yield

• Historical multifamily spread: 150–250 bps
• Spread < 100 bps = aggressive pricing; buyer is accepting near-bond-level returns without bond-level security
• 2025–2026 context: MF spreads compressed to 80–120 bps in peak markets; now normalizing toward 150+ bps as cap rates drift up

May 2026 REIT Credit And Cap-Rate Calibration

The May 2026 direct-upload batch adds public-market calibration to this framework without changing the core math. JPMorgan's April 29, 2026 REIT credit-spread note supports using REIT debt yields and spreads as a live cost-of-capital cross-check: tighter high-quality retail, apartment, industrial, storage, and data-center credit does not justify the same cap-rate treatment as wider office, mortgage REIT, or lower-rated issuer credit.

UBS's September 2025 REIT valuation note adds a useful sensitivity heuristic: REIT multiples can move meaningfully with a 10-year Treasury move, but the effect runs through public-market P/FFO, NAV premiums or discounts, and subsector sentiment, not through a one-for-one private cap-rate rule. The older interest-rate / cap-rate economics figures are useful as a historical framework because they show property yields and long-term real yields moving together but imperfectly.

Practical use: when an IC memo cites a cap rate, pair the private comp set with a public-market debt/equity read. The question is whether the proposed private cap rate clears the current cost of debt, REIT credit spread evidence, real-rate expectations, and asset-specific NOI growth case. See Source: JPM REIT Benchmark HG HY Spreads 4 29 26, Source: UBS Are REITS Cheap 9 2 25 5530885, and Source: Interest Rate Cap Rate Economics Figures.

---

4. Ellwood Formula

Scope reviewed 2026-10-07. The displayed Ellwood expression is a conditional finite-hold equity cash-flow reconciliation. Assume price P > 0, original loan MP, initial equity (1−M)P with 0 ≤ M < 1, and a positive integer hold of n years. Annual end-period NOI is constant cP and annual debt service is constant fMP. The remaining debt at sale is M(1−p)P, where p is the fraction of original principal repaid over the hold, consistent with that debt-service schedule. Terminal sale value is (1+ΔV)P. There are no separate initial costs, capital/lease cash adjustments, selling costs, refinancing, fees or investor allocation differences in this simplified model.

Let Y_E > −1 be the selected annual equity discount/yield target, not an annual cash-dividend target. Define discount factor v = (1+Y_E)^(-n), annuity factor a = sum((1+Y_E)^(-t), t=1..n) and sinking-fund factor s = v/a. Then:

(1−M) = (c−Mf) × a + [1+ΔV−M(1−p)] × v
s = Y_E / ((1+Y_E)^n−1) when Y_E ≠ 0; s = 1/n when Y_E = 0
C = Y_E + p × s − f
c = Y_E − M × C − ΔV × s

The first line discounts selected annual equity cash and terminal sale cash after debt payoff to initial equity. Solving it gives the inherited R_o = Y_E − M × C − ΔV × (1/S_n) expression with R_o = c and 1/S_n = s. The zero-yield case uses the limit 1/n, not division by zero. ΔV is total fractional value change over the hold, not annual growth. p is principal repaid/original loan, not appreciation or annual amortization; the remaining debt must reconcile to actual scheduled payments. An appraisal-based LTV is not automatically the loan/price share M.

This is curator algebra reproducing the displayed model. OCC's retained pp.42–44 support cash/NOI scope, debt service, stabilized capitalization and discounted income/net sale proceeds; those passages do not supply the Ellwood formula or establish its institutional prevalence. See Source: Debt Yield Scope Review 2026. Neither this equality nor a selected target establishes market value, loan approval or an achievable/unique realized IRR. Use CRE Return Metrics and KPIs for dated return scope and CRE Valuation Methodologies for sale-income timing and net proceeds.

Hypothetical IO case: Assume price $100M, loan $60M, initial equity $40M, five annual periods, 6% annual interest-only debt service, p = 0, equity target 8%, and total value appreciation 10%. s ≈ 0.1704564546, so the model requires c ≈ 5.09543545%. Annual equity cash is approximately $1,495,435.45 (NOI less $3.6M debt service), and terminal equity sale cash is $110M less $60M debt, or $50M. Discounting those five annual cash payments and the terminal $50M at 8% reconciles to $40M. Current cash/equity is approximately 3.73858864%, not the 8% yield target. With otherwise identical assumptions and zero value change, c = 6.8%, annual equity cash $3.2M and terminal cash $40M. These are teaching inputs, not market caps or available financing.

Separate amortization check: Assume a 6% nominal annual loan rate with thirty equal annual end-period payments, sale after five payments, and the same price/debt/target/value-change inputs. The annual mortgage constant is approximately 7.26489115%, and approximately 7.13030899% of original principal is repaid by sale. The model gives c ≈ 5.12512583%; annual equity cash and terminal cash with the remaining scheduled debt reconcile to initial equity at 8%. This annual-payment example is not the monthly-payment loan convention used elsewhere. Do not add principal paydown again as annual equity cash: principal is paid through debt service, and its remaining-balance effect is already in the terminal payoff.

For changing NOI, irregular payments, IO transitions, additional capital, refinancing or actual fees/selling costs, discount the explicit dated cash flows. Replace the simplified cash bridge; do not claim the displayed formula is an analytically complete appraisal, or that BOI/build-up account for most institutional practice without evidence. A mathematical reconciliation also does not prove liquidity on each payment date. The Band-of-Investment (BOI) Method above tests a selected current cash-yield target under different assumptions.

---

Choosing a Method

---

Related Pages

• CRE Market Cycle Phases — physical-cycle vocabulary; evaluate yield requirements and valuation separately

• CRE Valuation Methodologies

• CRE Return Metrics and KPIs

• CRE Capital Stack and Debt Structuring

• Source Collection: May 2026 REIT and Capital Markets Research Batch

• Texas CRE Debt Capital Markets 2026

• Multifamily Pro Forma Modeling

• Multifamily Cap Rates and Location Quality

• Industrial Valuation and Probability-Weighted Underwriting

• Industrial Logistics Underwriting

Sources

• Legacy Multifamily Knowledge Wiki
• Legacy Industrial Knowledge Wiki
• Legacy Office Knowledge Wiki
• Source: Multifamily Cap Rates and Location Quality Research 2026-05-05
• Source Collection: May 2026 REIT and Capital Markets Research Batch for reviewed derived claims from the May 2026 rate, spread, REIT yield, and cap-rate research batch. Raw PDFs remain non-redistributable.
• Source: Newmark 2026 Valuation & Advisory North American Market Survey