Real estate math guide
Capitalization rate from annual NOI and market value
First find the property's annual net operating income. Then decide whether the question asks for a rate, a value or the income needed to support a value. Most mistakes happen before the division: using gross rent, subtracting the mortgage payment or forgetting to convert monthly income into an annual amount.
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The short answer
Capitalization rate = annual net operating income (NOI) / property value or price. Property value = annual NOI / decimal cap rate. Annual NOI = value x decimal cap rate. For example, $72,000 / $900,000 = 0.08, or 8%. Use property operating income before debt service and owner income taxes. Keep the income definition, treatment of reserves and time period consistent with the rate.
Reviewed October 25, 2026. Capitalization rate appears at National XI.B.2 in the June 24, 2026 PSI broker outline; the income approach also appears at III.B.4. The whole Real Estate Calculations domain has 7 of 100 scored national questions, not seven cap-rate questions. This page teaches direct-capitalization arithmetic, not a current market-rate survey or a complete appraisal assignment. All examples and questions are original.
Build the income, choose the formula, check the units
- Write down the unknown. Rate, value and required NOI are different outputs. Use R = I / V, V = I / R and I = V x R. Here I means annual property-level NOI, R is the decimal overall capitalization rate and V is the relevant total property value or price, not merely the down payment.
- Put the income on an annual basis. Multiply recurring monthly amounts by 12 when the question describes a full year. Potential rent minus the stated vacancy and collection loss, plus included other income, gives effective gross income. Follow the stated vacancy base rather than assuming every revenue source receives the same percentage deduction.
- Subtract the included operating expenses once. Taxes on the property, insurance, management, maintenance and owner-paid utilities are common examples. Keep mortgage principal and interest, owner income taxes and accounting depreciation outside standard property NOI. Distinguish an annual replacement allowance from the whole capital bill, and do not deduct a reserve a second time if the expense total already includes it.
- Use a consistent income and rate. A comparable's rate is extracted from the relevant annual NOI divided by its verified sale price. Check the income period, vacancy, expenses, replacement reserves and comparable circumstances before applying it to the subject. Do not mix a rate derived before reserves with income after reserves without a supported reconciliation.
- Convert and calculate without early rounding. An 8% cap rate is 0.08. Divide NOI by 0.08 to find value; multiplying NOI by 0.08 answers a different calculation. Retain full calculator precision until the requested final dollar or percentage rounding. Reverse-check value by multiplying it by the decimal rate.
- Keep the conclusion within the facts. For the same positive NOI, a higher positive rate gives a lower indicated value. That mathematical comparison is not a prediction that every property with a higher quoted cap rate will outperform another. A stabilized-income indication also does not establish the current as-is value of a property still being renovated or leased up. Identify which value and income period the question actually asks for.
| Find | Formula | Check before calculating |
|---|---|---|
| Effective gross income | Potential income - stated losses + other included income | Which income receives the vacancy deduction? |
| Annual NOI | Effective gross income - included operating expenses | Before debt service; consistent replacement-reserve treatment |
| Cap rate as a decimal | Annual NOI / total value or price | Multiply the quotient by 100 to state the percentage |
| Property value | Annual NOI / decimal cap rate | 8% becomes 0.08, not 8 |
| Required annual NOI | Property value x decimal cap rate | The result is annual dollars, not a percentage |
| Implied operating expenses | Effective gross income - required NOI | Do not include excluded financing costs |
| Basis-point movement | Percentage-point change x 100 | 7.5% to 8.0% is 0.5 percentage point or 50 basis points |
The distinctions that matter
| Distinction | How it works | What to notice |
|---|---|---|
| Potential income vs. effective gross income | Potential income is the stated full income schedule. Effective gross income reflects the specified vacancy and collection losses and other income. Apply each allowance to the base given. | Do not apply a rent-only vacancy allowance twice or to unrelated income. |
| Effective gross income vs. NOI | NOI is effective gross income less the included property operating expenses. Property taxes and owner-paid operating costs can belong here; debt service and owner income taxes do not. | Gross receipts are not the capitalization numerator. |
| Replacement reserve vs. actual capital expenditure | An annual allowance for future replacements is different from the entire cost of a roof replaced this year. The cited OCC and DRE methods include replacement reserves; read the question and keep the comparable-rate basis consistent. | Do not exclude every reserve merely because capital spending is treated separately. |
| Cap rate vs. mortgage rate | Cap rate relates property NOI to total value. The loan interest rate prices financing. The two rates do not become interchangeable because they happen to be numerically equal. | Use the rate identified for capitalization. |
| Cap rate vs. GRM | Cap rate uses net operating income and is a rate. Gross rent multiplier uses price / gross rent and is a multiplier. Match the monthly or annual rent basis of the multiplier. | Value / NOI is not GRM. |
| Cap rate vs. cash-on-cash return | Cap rate uses property NOI and total property price or value. A defined cash-on-cash return uses annual cash flow after the specified financing effects and the actual cash invested. | Loan terms can change the cash return without changing property NOI. |
| Cap rate vs. total investment return | One year's NOI-to-value ratio does not separately measure resale proceeds, appreciation, multiyear cash flows or every cost and risk. | A larger ratio alone does not prove a better investment. |
Work through the facts
Find the capitalization rate
Annual NOI is $72,000 and the property price is $900,000.
- R = I / V.
- $72,000 / $900,000 = 0.08.
- 0.08 x 100 = 8%.
Answer: The cap rate on that income and price is 8%.
Find value and reverse-check it
Annual stabilized NOI is $96,000. The question supplies a supported 7.5% cap rate on the same income basis.
- 7.5% = 0.075.
- $96,000 / 0.075 = $1,280,000.
- Check: $1,280,000 x 0.075 = $96,000.
Answer: The indicated value is $1,280,000.
Find the annual income needed
A $850,000 value is based on a 6.8% cap rate.
- I = V x R.
- $850,000 x 0.068 = $57,800.
- This is property NOI, not the owner's cash after mortgage payments.
Answer: Required annual NOI is $57,800.
Build the income from monthly rents
Ten units each have potential rent of $1,200 a month. The question specifies a 5% rent-only vacancy and collection loss, $6,000 other annual income, and $50,800 total annual operating expenses including replacement reserves. The supplied cap rate is 8% on that basis.
- Potential rent: 10 x $1,200 x 12 = $144,000.
- Loss: $144,000 x 0.05 = $7,200. EGI: $144,000 - $7,200 + $6,000 = $142,800.
- NOI: $142,800 - $50,800 = $92,000. The reserve is already included; do not subtract it again.
- Value: $92,000 / 0.08 = $1,150,000.
Answer: The indicated value is $1,150,000.
Annualize monthly NOI
The question gives recurring monthly NOI of $4,200 for all twelve months and a 7% annual capitalization rate.
- Annual NOI is $4,200 x 12 = $50,400.
- $50,400 / 0.07 = $720,000.
- Using $4,200 / 0.07 would leave the income period mismatched.
Answer: The indicated value is $720,000.
Keep replacement reserves consistent
A verified comparable sold for $1,200,000. Its annual income after other operating expenses but before a $6,000 replacement allowance is $84,000. Both the comparable extraction and subject analysis use income after that allowance.
- Comparable NOI: $84,000 - $6,000 = $78,000.
- Comparable rate: $78,000 / $1,200,000 = 6.5%.
- Using $84,000 / $1,200,000 would instead produce a 7% rate on a different income basis.
Answer: Extract 6.5% on the stated after-reserve basis; do not mix the two bases.
Separate the property ratio from the investor's cash return
A property costs $1,000,000 and has $80,000 annual NOI. Assume $50,000 annual debt service, exactly $300,000 total investor cash and no other cash-flow adjustments for this example.
- Cap rate: $80,000 / $1,000,000 = 8%.
- Defined annual cash flow: $80,000 - $50,000 = $30,000.
- Cash-on-cash return: $30,000 / $300,000 = 10%.
Answer: The cap rate is 8%; the defined cash-on-cash return is 10%.
A 50-basis-point change is not a 50% change
Hold annual NOI at $96,000. Compare 7.5% with 8.0%.
- The rate rises 0.5 percentage point, or 50 basis points.
- Values: $96,000 / 0.075 = $1,280,000; $96,000 / 0.08 = $1,200,000.
- Value decreases $80,000 / $1,280,000 = 6.25%.
- The rate's relative increase is 0.5 / 7.5, about 6.67%, a different measure.
Answer: A 50-basis-point rate increase gives a 6.25% lower value here, with NOI held constant.
Mistakes to avoid
- Putting gross rent over price First calculate the specified annual NOI; gross rent belongs with a gross-income multiplier.
- Dividing annual NOI by the down payment Cap rate uses total property value or price. Cash invested is the denominator of a different return measure.
- Subtracting the loan payment in NOI Debt service belongs after property NOI in the defined cash-flow calculation.
- Using 8 instead of 0.08 Convert a percentage to its decimal before calculating value.
- Excluding all reserves or deducting one twice Read the income definition and the expense total. Keep the comparable and subject on the same basis.
- Calling every larger rate a better purchase Differences in risk, income, condition, leases and expectations require analysis beyond the formula.
- Calling 7.5% to 8% a 0.5% relative increase That is 0.5 percentage point, or 50 basis points. Relative change uses the original rate as denominator.
Check your understanding
These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.
1. Annual NOI is $84,000 and price is $1,200,000. What cap rate results?
- 10%
- 14.29%
- 0.7%
- 7%
Show answer and explanation
Answer: D. 7%
$84,000 / $1,200,000 = 0.07 = 7%. Dividing price by NOI reverses the ratio.
2. Annual NOI is $75,000. What value is indicated at a 6% cap rate?
- $125,000
- $450,000
- $4,500
- $1,250,000
Show answer and explanation
Answer: D. $1,250,000
Convert 6% to 0.06, then divide: $75,000 / 0.06 = $1,250,000. Check: $1,250,000 x 0.06 = $75,000.
3. A $640,000 value uses an 8.5% cap rate. What annual NOI supports it?
- $5,440
- $59,200
- $54,400
- $75,294.12
Show answer and explanation
Answer: C. $54,400
NOI = $640,000 x 0.085 = $54,400. Income, rather than value, is the unknown.
4. Annual potential rent is $120,000. Deduct 5% vacancy from rent only, add $4,000 other income, then subtract $38,000 operating expenses. What NOI results?
- $80,000
- $79,800
- $82,000
- $76,000
Show answer and explanation
Answer: A. $80,000
Loss is $6,000. EGI = $120,000 - $6,000 + $4,000 = $118,000. NOI = $118,000 - $38,000 = $80,000. Applying vacancy to other income would produce the wrong $79,800 answer.
5. Recurring monthly NOI is $3,500 for a full year. What value is indicated at a 7% annual cap rate?
- $294,000
- $500,000
- $600,000
- $50,000
Show answer and explanation
Answer: C. $600,000
Annualize first: $3,500 x 12 = $42,000. Then $42,000 / 0.07 = $600,000. The $50,000 answer incorrectly uses monthly NOI with an annual rate.
6. EGI is $120,000. A $1,100,000 value and 7% cap rate are supplied. What annual operating expenses are implied?
- $50,000
- $36,000
- $77,000
- $43,000
Show answer and explanation
Answer: D. $43,000
Required NOI = $1,100,000 x 0.07 = $77,000. Expenses = $120,000 - $77,000 = $43,000.
7. NOI remains $80,000. What happens to the indicated value when the cap rate rises from 8% to 10%?
- It rises from $800,000 to $1,000,000
- It falls by exactly 2%
- It stays $1,000,000 because income is unchanged
- It falls from $1,000,000 to $800,000
Show answer and explanation
Answer: D. It falls from $1,000,000 to $800,000
$80,000 / 0.08 = $1,000,000; $80,000 / 0.10 = $800,000. The value decrease is 20%, not the two-percentage-point change in the rate.
8. A comparable sold for $1,200,000. Annual income before its $6,000 replacement allowance is $84,000. Which cap rate uses income after the allowance?
- 7%
- 7.5%
- 6%
- 6.5%
Show answer and explanation
Answer: D. 6.5%
After-reserve NOI is $78,000. $78,000 / $1,200,000 = 0.065, or 6.5%. The 7% answer uses the before-reserve amount instead.
9. A cap rate moves from 7.5% to 8.0%. How large is the rate movement in basis points?
- 5 basis points
- 6.67 basis points
- 500 basis points
- 50 basis points
Show answer and explanation
Answer: D. 50 basis points
The difference is 0.5 percentage point. Each percentage point is 100 basis points, so the movement is 50 basis points. About 6.67% is the relative rate increase, not the basis-point movement.
10. NOI is $12,345 and price is $175,000. What is the cap rate rounded to two decimal places as a percentage?
- 0.07%
- 7.50%
- 7.05%
- 7.00%
Show answer and explanation
Answer: C. 7.05%
$12,345 / $175,000 = 0.070542857...; multiply by 100 for 7.0542857...%. Round the final percentage to 7.05%, rather than rounding the decimal rate too early.
Common questions
What is the capitalization-rate formula?
Annual NOI divided by total property value or price gives the decimal cap rate. Multiply the quotient by 100 to express a percentage. With $72,000 NOI and $900,000 price, the result is 0.08, or 8%.
How do I calculate value using the IRV formula?
Use V = I / R: divide annual NOI by the decimal capitalization rate. IRV is a memory aid for income, rate and value; it does not change which income or rate the facts support. $96,000 / 0.075 gives $1,280,000.
How do I find NOI when value and rate are given?
Multiply value by the decimal cap rate. A $850,000 value at 6.8% implies $57,800 annual NOI. Do not multiply NOI by the rate when the question instead asks for value.
What is deducted to calculate NOI?
Begin with the defined effective gross income and deduct the included operating expenses. Property taxes, insurance, management, repairs and owner-paid utilities are common examples. Mortgage principal and interest, owner income taxes and accounting depreciation are excluded from the ordinary property-level calculation. Read any stated reserve treatment.
Are property taxes different from income taxes here?
Yes. Real property taxes can be a property operating expense. The owner's personal or entity income tax is a different item. Do not exclude property taxes merely because the words income taxes appear in the NOI exclusions.
Are replacement reserves included in NOI?
Definitions must be checked. The cited OCC underwriting method and DRE teaching example deduct an annual replacement allowance in determining NOI. An actual capital project is different from that allowance. Follow the stated problem and keep comparable extraction and subject capitalization on the same basis; do not invent or double-count a reserve.
Can I use monthly NOI?
Annualize a recurring monthly amount before combining it with an annual rate. If monthly NOI is $4,200 for a full year, annual NOI is $50,400. A short lease-up month may not represent a stabilized year, so do not automatically multiply every isolated month by twelve.
How do vacancy and other income affect the calculation?
Apply vacancy and collection loss to the income base specified. Then add other income where the problem places it. If laundry income is stated after its own loss allowance, do not automatically deduct the rent-vacancy percentage from it again. Consistency matters more than a memorized order without defined inputs.
How is a market cap rate extracted?
Divide a verified comparable sale's relevant annual NOI by its sale price. Compare income timing, vacancy, expenses, reserves, property rights, transaction circumstances and the properties themselves before selecting a subject rate. A computed comparable ratio is evidence to analyze, not an automatic rate for every building nearby. A stabilized projection and current as-is operating income must not be silently substituted for one another.
Does a higher cap rate always mean a better investment?
No. Holding positive NOI constant, a higher positive rate produces a lower value indication. Properties can have different risks and income expectations. Neither a high advertised ratio nor the direct-capitalization result proves future cash flow or total investment performance.
Is cap rate the same as mortgage interest or cash-on-cash return?
No. Mortgage interest prices borrowed funds. Cap rate uses property NOI and total property value. For a stated cash-on-cash calculation, divide the defined annual cash flow after financing and other specified adjustments by the actual investor cash. Read the definitions rather than switching denominators.
How is cap rate different from GRM?
Cap rate uses net operating income. GRM relates price to gross rent and is a multiplier. Use the same monthly or annual rental basis that was used to derive the multiplier. A gross-income multiplier and a net-income rate are not simple reciprocals.
What are basis points and percentage points?
One percentage point equals 100 basis points. A move from 7.5% to 8.0% is 50 basis points. Its relative increase is about 6.67%. With the same $96,000 NOI, the value falls from $1,280,000 to $1,200,000, a separate 6.25% change.
How should I round a cap-rate answer?
Keep full working precision, then round the requested final amount. To report a percentage to two decimal places, first convert the decimal quotient into percent. For $12,345 / $175,000, that gives 7.0542857...%, reported as 7.05%. A problem's express instruction controls. Do not round 0.070542857 to 0.07 before converting it to the requested percentage.
Does the formula alone establish appraised value?
It produces an indication from the chosen income and rate. The cited Fannie Mae single-family Selling Guide discusses an income approach based on comparable rent and GRM and does not accept reliance solely on that approach. It is a separate lender-policy context, not authority to apply its GRM procedure to every commercial cap-rate problem. Supported professional valuation requires the appropriate assignment analysis.
Are these current Illinois market rates or official exam questions?
No. Every number here is an invented teaching input, not an October 2026 market quote or a guaranteed investment return. These are original questions aligned to the cited PSI outline. Practice results identify arithmetic or concept gaps; they are not a validated passing prediction.
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Official sources and scope
Checked October 25, 2026. The identified PSI outline, DRE arithmetic chapter, relevant OCC handbook provisions, current Fannie Mae topic and SEC glossary were read. The DRE chapter is foundational teaching material; OCC and Fannie Mae examples have their stated lender scopes. Two original references returned access errors and were not relied on. All numbers are teaching examples, independently checked, rather than current local cap-rate observations.
- PSI June 24, 2026 broker outline: calculations and income valuation
- California DRE Reference Book chapter 15: overall-rate and income arithmetic
- OCC Commercial Real Estate Lending handbook: income and value analysis
- Fannie Mae B4-1.3-10: separate income-approach lender context
- SEC Investor.gov glossary: basis point
This is exam preparation, not advice for a specific transaction. State law and the applicable facts control. Our editorial and corrections process explains how to report an issue.