13.2 Deriving Capitalization Rates
Key Takeaways
- Market extraction derives Ro from comparable sales as Ro = NOI ÷ sale price, using reconstructed NOI consistent with the subject’s income definition.
- Band of investment builds Ro as a weighted average of the mortgage constant (RM) and the equity dividend rate (RE): Ro = (M × RM) + ((1 − M) × RE), where M is the loan-to-value ratio.
- The mortgage constant is annual debt service divided by the loan amount—not the contract interest rate alone; amortization and term change RM.
- Equity dividend rate (RE), also called cash-on-cash when based on before-tax cash flow, is BTCF ÷ equity investment; it is not the same as the equity yield rate (YE) used in yield capitalization.
- Prefer extracted market rates when good income-producing comps exist; use band of investment when financing terms and equity return requirements are the best evidence—or as a cross-check.
Where Do Cap Rates Come From?
Section 13.1 treated Ro as a given. ECO VI.e Derivation of capitalization rates requires two primary methods:
- Market-extracted overall rates from comparable sales
- Band of investment (mortgage + equity components)
Other classical techniques (debt coverage formula, residual techniques, built-up/summation methods) may appear conceptually, but market extraction and band of investment are the named ECO pair—master them for calculation items.
A rate is only as good as the income used to extract or the financing/equity assumptions used to build it. Garbage NOI → garbage Ro → garbage value.
Method 1 — Market Extraction
Market extraction (sales comparison for rates) observes what buyers paid relative to income:
Ro = NOI ÷ Sale price
Use stabilized, reconstructed NOI at market (or the income premise matching the appraisal), not seller’s tax depreciation-laden “profit.” Prefer comps that are:
- Same property type and competitive market
- Arms-length, recent, similar risk and upside
- Similar expense structures and lease forms
- Known or reconstructable income
Worked Extraction Table
| Comp | Sale price | Reconstructed NOI | Extracted Ro |
|---|---|---|---|
| 1 | $2,000,000 | $160,000 | 8.00% |
| 2 | $2,400,000 | $180,000 | 7.50% |
| 3 | $1,800,000 | $144,000 | 8.00% |
| 4 | $2,200,000 | $165,000 | 7.50% |
Indicated range 7.5%–8.0%. If subject is slightly inferior in location/condition, you might reconcile toward 8.0%; if superior, toward 7.5%. Simple average = 7.75%—reconciliation is judgment, not always a mean.
Subject NOI $170,000 at Ro 7.75%:
V = $170,000 ÷ 0.0775 ≈ $2,193,548 ≈ $2,190,000
Extraction Quality Controls
| Issue | Effect on extracted Ro | Fix |
|---|---|---|
| NOI includes debt service removed incompletely | NOI too low → Ro too low | Reconstruct NOI properly |
| Below-market rents left in “NOI” on fee simple job | Income low → Ro low or value later wrong | Mark rents to market for fee simple |
| Sale includes FF&E / business value | Price high → Ro low | Allocate or exclude non-realty |
| Atypical financing (seller buydown) | Price may be high | Cash-equivalent price adjustment |
| One-time CapEx year in expenses | NOI low → Ro high | Normalize expenses |
| Different reserve policy than subject | Misaligned Ro | Match reserve definition |
Worked Problem — Cash-Equivalent Caution (Conceptual Math)
Stated price $1,000,000; NOI $80,000 → face Ro = 8%.
If financing concession is worth $40,000 and cash-equivalent price is $960,000:
Ro = $80,000 ÷ $960,000 ≈ 8.33%.
Using 8% on the subject would overvalue relative to cash-equivalent market evidence.
Multiple Comps — Do Not Force a Single Sale
One perfect comp is rare. ECO expects you to understand reconciliation among extracted rates, not pure arithmetic worship. Outliers with non-market leases or partial interest sales get less weight.
Method 2 — Band of Investment
Band of investment builds the overall rate as a weighted average of the returns required by the mortgage lender and the equity investor:
Ro = (M × RM) + (E × RE)
where:
| Symbol | Meaning |
|---|---|
| M | Mortgage ratio (loan-to-value fraction), e.g. 0.75 for 75% LTV |
| E | Equity ratio = 1 − M, e.g. 0.25 |
| RM | Mortgage constant (annual debt service ÷ loan amount) |
| RE | Equity dividend rate (also equity capitalization rate): annual before-tax cash flow to equity ÷ equity investment |
Before-tax cash flow (BTCF) ≈ NOI − Annual debt service (basic teaching model, before income tax).
Equity investment ≈ Value × E (or Purchase price − Loan).
Mortgage Constant (RM) — Not Just the Interest Rate
The mortgage constant is the total annual debt service (principal + interest) as a percentage of the original loan amount.
RM = Annual debt service ÷ Loan amount
For a fully amortizing loan, RM depends on interest rate, amortization term, and payment frequency. RM is greater than the interest rate when principal is being amortized (except interest-only, where RM equals the interest rate if no principal paydown).
| Loan type | RM vs interest rate |
|---|---|
| Interest-only | RM ≈ interest rate (annual) |
| Amortizing | RM > interest rate |
| Shorter amortization | Higher RM (more principal per year) |
| Higher interest rate | Higher RM |
Exam tip: If the stem gives the annual debt service and loan amount, compute RM directly—do not invent an amortization factor. If it gives rate, term, and LTV, you may need the payment factor (financial calculator / given factor in the stem).
Worked Mortgage Constant from Debt Service
Loan = $750,000
Monthly payment = $5,022
Annual debt service = 5,022 × 12 = $60,264
RM = $60,264 ÷ $750,000 = 0.08035 ≈ 8.04%
Note the note rate might be 7% amortizing—RM is still ~8.04%, not 7%.
Equity Dividend Rate (RE)
RE = BTCF ÷ Equity invested
BTCF = NOI − Annual debt service
RE is a one-period cash-on-cash style rate for direct cap band-of-investment. It is not the multi-period equity yield rate (YE) used in mortgage-equity yield models and DCF—those include equity build-up and reversion. Exams love this confusion.
| Rate | What it measures | Typical use |
|---|---|---|
| RE (equity dividend / equity cap rate) | Year-1 cash to equity ÷ equity | Band of investment for Ro |
| YE (equity yield) | IRR-like return on equity over holding period | Yield capitalization / mortgage-equity analysis |
| YO (property yield / discount rate) | IRR on overall property cash flows | DCF discount rate |
| Ro | NOI ÷ value, one period | Direct cap |
Full Worked Band-of-Investment Problem
Given
Typical financing and equity requirements for this property class:
- LTV M = 70% → Equity E = 30%
- Loan amount will be 0.70 × value (unknown yet—we only need rates)
- Annual mortgage constant RM = 0.092 (9.2%) from market loan terms
- Equity investors require RE = 0.12 (12% equity dividend)
Step 1 — Build Ro
Ro = (0.70 × 0.092) + (0.30 × 0.12)
= 0.0644 + 0.0360
= 0.1004 ≈ 10.04%
Step 2 — Capitalize Subject NOI
Stabilized NOI = $251,000
Value = $251,000 ÷ 0.1004 ≈ $2,500,000 (exactly $251,000 / 0.1004 ≈ $2,500,000)
Check: $2,500,000 × 0.1004 = $251,000.
Step 3 — Prove the Band (Optional Audit)
Loan = 0.70 × $2,500,000 = $1,750,000
Equity = $750,000
Annual debt service = RM × Loan = 0.092 × $1,750,000 = $161,000
BTCF = NOI − ADS = $251,000 − $161,000 = $90,000
RE check = $90,000 ÷ $750,000 = 0.12 = 12% ✓
Ro check = $251,000 ÷ $2,500,000 = 10.04% ✓
This audit is excellent exam discipline: if BTCF/equity ≠ assumed RE, arithmetic slipped.
Second Worked Band Problem — Build RM from Payments
Given
- Purchase underwriting value target uses band of investment
- LTV 75%; equity 25%
- Loan $900,000 would be on a $1,200,000 value (we will derive Ro first, then apply)
- Interest 6.5%, fully amortizing; stem gives annual debt service factor such that on any loan, ADS = 0.085 × loan (RM = 8.5%)
- Equity dividend rate required = 10%
- Subject NOI = $108,000
Solution
Ro = (0.75 × 0.085) + (0.25 × 0.10)
= 0.06375 + 0.025
= 0.08875 = 8.875%
Value = $108,000 ÷ 0.08875 ≈ $1,216,901 ≈ $1,217,000
Financing at that value
Loan = 0.75 × $1,216,901 ≈ $912,676
ADS = 0.085 × $912,676 ≈ $77,577
BTCF ≈ $108,000 − $77,577 = $30,423
Equity ≈ $304,225
RE ≈ $30,423 / $304,225 ≈ 10% ✓
Third Drill — Interest-Only Band
M = 80%; interest-only rate 5.5% → RM = 5.5%
RE = 9%
Ro = (0.80 × 0.055) + (0.20 × 0.09) = 0.044 + 0.018 = 0.062 = 6.2%
NOI $310,000 → V = $310,000 ÷ 0.062 = $5,000,000
Amortizing the same 5.5% note would produce higher RM and thus higher Ro and lower value—same NOI, different debt service shape.
Debt Coverage Ratio Link (Awareness)
Lenders often require DCR = NOI ÷ ADS ≥ a minimum (e.g., 1.25).
If Max ADS = NOI / DCR, and loan = ADS / RM, you can imply a maximum LTV. Some exam outlines show:
Ro = RM × DCR × M (when equity is ignored and rate is lender-constrained)—use only if the stem frames a lender-only constraint. Standard ECO band of investment still wants both mortgage and equity bands when both are given.
Built-Up / Summation Rates (Recognition)
Older texts build a rate as safe rate + risk + nonliquidity + management − appreciation, etc. Modern practice emphasizes market extraction and band of investment. If an item mentions built-up rates, know they are a theoretical assembly of return components—not a substitute for market evidence when sales exist.
Residual Techniques (Bridge to Land Chapter)
Building residual and land residual split overall income using known land or building values and component rates—related to Ro but not the same as simple overall direct cap. You saw residual/ground rent ideas in land valuation; do not confuse RL/RB residual math with band of investment for Ro unless the stem is clearly residual.
Choosing Extraction vs Band of Investment
| Situation | Prefer |
|---|---|
| Several recent sales with supportable NOI | Market extraction |
| Thin sales but active lending and known equity cash-on-cash requirements | Band of investment |
| Both available | Extract primary; band as support/cross-check |
| Seller financing / non-market LTV in “comps” | Adjust or use band with typical M |
| Subject risk differs from comps | Adjust extracted Ro or RE/RM inputs qualitatively |
Common Exam Traps — Cap Rate Derivation
- Using interest rate as RM on an amortizing loan
- Using YE (yield) as RE (dividend) in the band formula
- Weighting with loan amount dollars incorrectly—weights are M and E as fractions of value, summing to 1.0
- Extracting Ro from price ÷ EGI (that is a reciprocal GIM-style factor, not NOI Ro)
- Averaging interest rate and equity rate without LTV weights
- Applying band Ro to BTCF instead of NOI
- Forgetting E = 1 − M
Formula Card
- Market Ro = NOI ÷ Sale price
- Ro = (M × RM) + ((1 − M) × RE)
- RM = Annual debt service ÷ Loan
- RE = (NOI − ADS) ÷ Equity
- Value = NOI ÷ Ro after Ro is derived
- RE ≠ YE; RM ≠ note rate (unless interest-only / stem equates them)
Bridge
You can now support Ro from the market or from mortgage + equity bands. Section 13.3 moves from one-period rates to yield capitalization—discount rates, property models, and a simplified DCF with cash flows and reversion. Section 13.4 applies both direct and yield frameworks to different property rights and reconciles the income approach.
A comparable sold for $1,500,000. Reconstructed stabilized NOI at the time of sale was $120,000. What overall capitalization rate is extracted from this sale?
Market financing is 75% LTV with a mortgage constant of 9%. Equity investors require a 12% equity dividend rate. What overall rate does the band of investment indicate, and what is the value if NOI is $99,000?