Income-property math guide
Net operating income: from rent to NOI
Start with the rent the property could earn. Account for vacancy and collection loss, add any other income that has not already been counted, then subtract operating expenses. That gets you to NOI. The mortgage payment comes later. Most mistakes happen when an item is counted twice or a percentage is applied to the wrong subtotal.
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The short answer
Net operating income, or NOI, equals effective gross income minus property operating expenses. In a common exam setup, effective gross income is potential rent minus vacancy and collection loss plus other property income. Standard NOI excludes mortgage principal and interest, owner income taxes and accounting depreciation. Follow the question's replacement-reserve convention, keep all amounts in the same period and use the matching income definition when applying a capitalization rate.
Reviewed October 25, 2026. PSI national III.B.4 covers the income approach, and XI.B.2 covers rate of return and capitalization rate. The whole Valuation and Real Estate Calculations domains have 8 and 7 of 100 scored national broker questions respectively, with no NOI-only quota. These original exercises simplify valuation. They do not approve a loan, property value, tax return or investment.
Calculate the subtotal before moving to the next line
- Name the starting income. Is it monthly rent per unit, annual potential rent, total PGI including other income, or an EGI subtotal already adjusted for losses? Annualize only amounts that still need it.
- Calculate vacancy and collection losses from the specified bases. A combined 5% of potential rent is one deduction. Separate percentages applied to different bases cannot simply be added.
- Add other property income once. If PGI already includes parking or laundry, adding it again overstates income. If tenant reimbursements are shown as income, include the matching owner expense under the stated presentation.
- Total the operating expenses. Typical categories include real estate taxes, property insurance, management, owner-paid utilities, routine maintenance and payroll. Mortgage principal and interest, owner income taxes and depreciation are outside standard NOI.
- Read the reserve instruction. An annual replacement allowance is different from paying the full cost of a roof project. OCC underwriting includes a replacement reserve in its NOI definition; the cited Fannie Mae multifamily definition subtracts it from NOI to reach its NCF measure. Use the stated convention and avoid deducting the same reserve twice.
- Subtract the supported expense total from EGI. If the problem requests missing expenses, reverse the relationship: expenses = EGI - NOI. Preserve the sign; negative NOI does not become zero.
- Calculate only the requested result. A simplified before-tax cash flow may be NOI minus debt service. Direct-capitalization value is annual stabilized NOI divided by a decimal cap rate on a consistent basis. Neither result substitutes for the other.
| Line | Formula or treatment | Exam safeguard |
|---|---|---|
| Potential annual rent | Units x monthly rent x 12 | Use full stated occupancy; do not multiply annual rent by 12 again |
| Vacancy loss | Stated income base x vacancy rate | Subtract the loss |
| Effective gross income | PGI - vacancy and loss + other income | Do not add other income twice |
| Operating expenses | Supported operating costs and any reserve included by the stated convention | Count each item once; exclude debt service |
| NOI | EGI - operating expenses | Before debt service |
| Missing expenses | EGI - NOI | Use same period |
| Expense ratio | Operating expenses / EGI x 100 | Not cap rate |
| Simplified before-tax cash flow | NOI - stated debt service | Only when no other below-NOI items are specified |
| Cap rate | Annual NOI / value x 100 | Use annual stabilized NOI |
| Value | Annual NOI / decimal cap rate | Rate and income definitions match |
The distinctions that matter
| Distinction | How it works | What to notice |
|---|---|---|
| Potential gross rent vs. PGI | Potential gross rent concerns full rental income. PGI can include a broader potential-income definition when the problem says so. | Rent-only potential versus stated total potential. |
| PGI vs. EGI | PGI reflects full stated potential. EGI reflects vacancy and collection loss and includes qualifying other income. | Full potential versus expected collected income. |
| EGI vs. NOI | EGI is before operating expenses. NOI is the remainder after operating expenses. | Collected revenue versus property operating income. |
| Operating expense vs. debt service | Operating expense supports property operation. Debt service pays owner-specific financing. | Property cost versus loan cost. |
| Repair vs. capital expenditure | A repair ordinarily maintains current operation. A capital expenditure adds or replaces a long-lived asset or benefit. | Recurring upkeep versus long-lived investment. |
| Capital expenditure vs. reserve | A capital expenditure is a project outlay. A reserve is a periodic allowance for anticipated replacement under a stated convention. | Actual project cash versus annualized allowance. |
| NOI vs. before-tax cash flow | NOI is before financing. Before-tax cash flow subtracts stated debt service and other below-NOI cash items. | Property operation versus equity cash flow. |
| NOI vs. taxable rental income | NOI follows valuation or underwriting conventions. Taxable income follows tax rules, including deductions that NOI excludes. | Valuation measure versus tax result. |
| Actual NOI vs. stabilized NOI | Actual NOI reflects one recorded period. Stabilized NOI represents normal sustainable operation under supported assumptions. | Historical result versus normalized expectation. |
| NOI vs. GRM rent | NOI is after operating expenses and pairs with cap rate. GRM uses gross rent before explicit expense deduction. | Net-income rate input versus gross-rent multiplier input. |
Work through the facts
Build NOI from the top line
Potential annual rent is $240,000. Vacancy and collection loss equal 5% of rent, other income is $8,000, and operating expenses are $86,000.
- Vacancy and collection loss are $240,000 x 0.05 = $12,000.
- EGI is $240,000 - $12,000 + $8,000 = $236,000.
- NOI is $236,000 - $86,000 = $150,000.
Answer: The property's annual NOI is $150,000.
Calculate management from EGI
A property has EGI of $210,000. Management is 6% of EGI, and other operating expenses are $70,400. What is NOI?
- Management expense is $210,000 x 0.06 = $12,600.
- Total operating expenses are $12,600 + $70,400 = $83,000.
- NOI is $210,000 - $83,000 = $127,000.
Answer: Annual NOI is $127,000.
Recover missing operating expenses
A property has EGI of $185,000 and NOI of $112,000. What operating-expense total is implied?
- Use operating expenses equals EGI minus NOI.
- $185,000 - $112,000 = $73,000.
- No vacancy adjustment is needed because EGI is already supplied.
Answer: Implied annual operating expenses are $73,000.
Keep debt service below NOI
EGI is $310,000, operating expenses are $115,000, and annual mortgage debt service is $92,000. Find NOI and simplified before-tax cash flow.
- NOI is $310,000 - $115,000 = $195,000.
- Debt service is not an operating expense.
- Before-tax cash flow is $195,000 - $92,000 = $103,000.
Answer: NOI is $195,000 and simplified before-tax cash flow is $103,000.
Handle a capital project correctly
EGI is $180,000, recurring operating expenses are $68,000, and the owner pays $90,000 for a major roof replacement. The exam problem classifies the roof as a capital expenditure and gives no annual reserve.
- Use the problem's classification rather than putting the full roof project into recurring operations.
- NOI is $180,000 - $68,000 = $112,000.
- The $90,000 project affects capital cash needs outside this simplified NOI.
Answer: NOI is $112,000 under the stated convention.
Use NOI to indicate value
A stabilized annual NOI of $96,000 is paired with a supported 7.5% overall capitalization rate. What value is indicated?
- Convert 7.5% to 0.075.
- $96,000 / 0.075 = $1,280,000.
- The result depends on NOI and rate being defined consistently.
Answer: The direct-capitalization indication is $1,280,000.
Annualize a monthly rent roll
Eight units each have potential rent of $1,500 a month. Combined vacancy and collection loss is 6% of that rent. Annual parking income of $3,600 is additional and is not subject to that loss. Annual operating expenses, including any required reserve, total $54,800.
- Potential annual rent: 8 x $1,500 x 12 = $144,000.
- Loss: $144,000 x 0.06 = $8,640. EGI: $144,000 - $8,640 + $3,600 = $138,960.
- NOI: $138,960 - $54,800 = $84,160.
Answer: Annual NOI is $84,160.
Other income is already in PGI
Annual PGI is $252,000 and already includes $12,000 of parking income. The stated total vacancy and collection deduction is $12,000. Operating expenses are $90,000.
- EGI: $252,000 - $12,000 = $240,000.
- Do not add the parking income again.
- NOI: $240,000 - $90,000 = $150,000.
Answer: NOI is $150,000, not $162,000.
Two reserve presentations, clearly labeled
Annual EGI is $200,000 and operating expenses before a $6,000 replacement allowance are $90,000. Compare a problem defining NOI after that allowance with one reporting NOI before it and a separate after-reserve subtotal.
- If the definition includes the allowance in NOI: $200,000 - $90,000 - $6,000 = $104,000 NOI.
- If it reports NOI before the allowance: NOI is $110,000, followed by an after-reserve subtotal of $104,000.
- These are two reporting conventions for the same stated allowance. Do not subtract another $6,000 from the $104,000 after-reserve result. Before applying a cap rate, confirm that its income definition matches the chosen numerator.
Answer: Use the problem's defined NOI and keep the reserve deduction to one occurrence.
Match a reimbursement to its expense
Collected annual rent is $200,000. Tenants also reimburse $18,000 of owner-paid property taxes. Operating expenses of $50,000 include those taxes; no other adjustments apply.
- Gross presentation: EGI is $218,000 and expenses are $50,000. NOI is $168,000.
- A consistent net presentation removes the $18,000 from both sides: $200,000 - $32,000 = $168,000.
- Adding the reimbursement while removing the related expense would overstate NOI.
Answer: Both consistent presentations give $168,000 NOI.
Two percentages use different bases
Potential annual rent is $240,000. Vacancy is 10% of potential rent. Collection loss is then 2% of the rent remaining after vacancy. There is no other income. Operating expenses are $80,000.
- Vacancy: $240,000 x 0.10 = $24,000. Remaining rent: $216,000.
- Collection loss: $216,000 x 0.02 = $4,320. EGI: $211,680.
- NOI: $211,680 - $80,000 = $131,680. Applying 12% directly to $240,000 would use the wrong base.
Answer: NOI is $131,680 under these explicit loss assumptions.
Self-management does not erase a stated allowance
Annual EGI is $100,000. Other operating costs are $30,000. The problem requires a normalized management allowance of 5% of EGI even though the current owner self-manages.
- Management allowance: $100,000 x 0.05 = $5,000.
- Total defined expenses: $30,000 + $5,000 = $35,000.
- NOI: $100,000 - $35,000 = $65,000. The owner's actual unpaid time does not cancel the supplied normalized expense.
Answer: Use $65,000 NOI for the stated analysis.
Mistakes to avoid
- Call potential gross income NOI. First account for vacancy, other income, and operating expenses.
- Subtract the vacancy percentage from income as a dollar amount. Multiply the correct income base by the decimal rate to find dollar loss.
- Add other income twice. Read whether the problem includes it inside PGI before adding it to reach EGI.
- Use an expense percentage on the wrong income base. Apply management or another percentage to PGI, EGI, or collected rent exactly as stated.
- Subtract mortgage principal and interest in NOI. Debt service is owner financing and belongs below standard property-level NOI.
- Subtract accounting depreciation from NOI. Depreciation can affect taxable income but is excluded from standard appraisal NOI.
- Treat a major addition as an ordinary annual expense. Use the stated capital or reserve convention rather than distorting one year's operations.
- Assume owner self-management means zero management expense. A stabilized analysis may include a supported market management cost even without a current payment.
- Use monthly NOI with an annual cap rate. Annualize NOI before using an annual capitalization relationship.
- Treat Schedule E net income as appraisal NOI. Tax reporting and appraisal NOI use different expense and depreciation conventions.
- Call NOI cash flow after debt service. NOI is before financing; after-debt cash flow subtracts debt service later.
- Assume a higher NOI alone proves a better property. Value, risk, growth, leases, condition, capital needs, and the income period still matter.
Check your understanding
These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.
1. Potential annual rent is $200,000, combined vacancy and collection loss is 5% of that rent, additional other income is $10,000, and annual operating expenses are $70,000. No other adjustments apply. What is NOI?
- $140,000
- $120,000
- $190,000
- $130,000
Show answer and explanation
Answer: D. $130,000
Vacancy is $10,000, EGI is $200,000, and NOI is $200,000 - $70,000 = $130,000.
2. EGI is $180,000 and operating expenses are $72,000. What is NOI?
- $252,000
- $108,000
- $2,500
- $72,000
Show answer and explanation
Answer: B. $108,000
$180,000 - $72,000 = $108,000.
3. Which item is normally excluded from standard property-level NOI?
- Mortgage debt service
- Property insurance
- Management expense
- Owner-paid utilities
Show answer and explanation
Answer: A. Mortgage debt service
Owner financing is subtracted below NOI when a later cash-flow measure is requested.
4. EGI is $150,000 and NOI is $90,000. What operating expenses are implied?
- $45,000
- $60,000
- $90,000
- $240,000
Show answer and explanation
Answer: B. $60,000
$150,000 - $90,000 = $60,000.
5. Which income measure is the appropriate numerator for the stated stabilized direct-capitalization analysis?
- Seller net proceeds
- Mortgage loan amount
- Annual stabilized NOI
- Monthly gross rent
Show answer and explanation
Answer: C. Annual stabilized NOI
Use annual stabilized NOI for this stated analysis, with the same income and reserve definition used to derive the cap rate. Gross rent, sale proceeds and loan principal are different measures.
6. Monthly NOI is $7,000. An appropriate annual cap rate is 7%. What simplified direct-capitalization value results?
- $100,000
- $84,000
- $490,000
- $1,200,000
Show answer and explanation
Answer: D. $1,200,000
Annualize: $7,000 x 12 = $84,000. Then divide $84,000 by 0.07. Do not capitalize one month as if it were the annual income.
7. EGI is $200,000. Other operating expenses are $90,000. The problem expressly defines NOI after a separate $6,000 annual replacement allowance. What is NOI?
- $98,000
- $110,000
- $104,000
- $116,000
Show answer and explanation
Answer: C. $104,000
Subtract the $90,000 and the $6,000 allowance once: $104,000. The question expressly supplies the convention.
8. Collected rent is $200,000, tenant tax reimbursements are $18,000, and operating expenses of $50,000 include those taxes. No other items apply. What is NOI?
- $150,000
- $186,000
- $218,000
- $168,000
Show answer and explanation
Answer: D. $168,000
Include both the reimbursement and its related expense: $200,000 + $18,000 - $50,000 = $168,000.
9. EGI is $180,000, operating expenses are $72,000 and property value is $1,800,000. What is the operating-expense ratio used in this lesson?
- 6%
- 60%
- 4%
- 40%
Show answer and explanation
Answer: D. 40%
Operating expenses divided by EGI are $72,000 / $180,000 = 0.40. The 6% figure would be NOI divided by value, a different ratio.
10. Potential rent is $240,000. Vacancy is 10% of potential rent, and collection loss is 2% of rent remaining after vacancy. No other income applies. What is EGI?
- $211,680
- $235,200
- $211,200
- $216,000
Show answer and explanation
Answer: A. $211,680
After $24,000 vacancy, rent is $216,000. The 2% collection loss is $4,320, leaving $211,680. Adding the percentages ignores the stated bases.
11. For a stabilized analysis, the problem requires a $5,000 market management allowance. The owner currently self-manages without a cash payment. What should the solver do?
- Deduct it twice as both labor and a reserve
- Use the stated $5,000 normalized allowance
- Omit it because no check was written
- Replace it with the owner's mortgage interest
Show answer and explanation
Answer: B. Use the stated $5,000 normalized allowance
NOI analysis can use supported normalized expenses that are not immediate cash payments. The supplied management instruction controls this calculation.
12. EGI is $120,000 and defined operating expenses are $135,000. What is NOI?
- Negative $15,000
- $255,000
- $0
- $15,000
Show answer and explanation
Answer: A. Negative $15,000
$120,000 - $135,000 = negative $15,000. Retain the shortfall rather than imposing an unsupported zero floor.
Common questions
What is the net operating income formula?
NOI equals effective gross income minus property operating expenses. A common exam waterfall is potential gross income minus vacancy and collection loss plus qualifying other property income, then minus operating expenses. Keep every amount on the same annual or monthly basis.
What is potential gross income?
Potential gross income, or PGI, represents the full income potential under the rent and occupancy assumptions stated by the problem. It commonly begins with scheduled or market rent at full occupancy and full collection before vacancy and collection loss.
What is effective gross income?
Effective gross income, or EGI, is the income level after vacancy and collection loss and after adding qualifying other property income under the stated convention. If a problem already includes other income in PGI, do not add it again.
Which expenses are included in NOI?
Typical categories include property taxes, property insurance, management, owner-paid utilities, routine repairs, maintenance and payroll. Use the ownership and lease facts: a cost paid directly by a tenant is not automatically an additional owner expense. Follow any stated normalized expense or reserve instruction rather than import every line from an owner's tax return.
Is mortgage debt service included in NOI?
No under the standard property-level formula. Mortgage principal and interest depend on owner financing. NOI is before debt service. Subtract debt service later if the question asks for before-tax cash flow or a debt-coverage measure.
Is depreciation included in NOI?
Accounting or tax depreciation is excluded from standard appraisal NOI. It can reduce taxable rental income, but it is a noncash tax or accounting allocation rather than a property operating outlay in the basic valuation formula.
Are capital expenditures included in NOI?
The full cost of a major capital project is generally outside ordinary annual operating expenses. An annual replacement allowance is different. OCC's cited underwriting definition includes that reserve in NOI; the cited Fannie Mae multifamily definition subtracts the reserve from NOI to reach its NCF measure. The problem should identify the convention. Do not silently choose the definition that produces the larger answer. Read the operating-statement headings and the express reserve instruction before doing the calculation.
How do you find missing operating expenses?
Subtract NOI from EGI. If EGI is $180,000 and NOI is $108,000, operating expenses are $72,000. In reverse, EGI = NOI + operating expenses. Do not substitute PGI for EGI when vacancy or other income adjustments still remain.
Is NOI the same as profit or cash flow?
No. NOI is property income before financing, owner income taxes, and accounting depreciation. Profit, taxable income, and investor cash flow can include debt service, capital spending, tax items, sale costs, and other facts outside the standard NOI calculation.
Are these official Illinois broker exam questions?
No. The examples and questions are original. They follow the identified PSI outline topics and named valuation references. The source notes distinguish an older teaching reference from current published lender definitions. This short set is not a validated readiness test.
Do property taxes belong in NOI if income taxes do not?
Ordinary property taxes are a property operating expense under the basic formula. The owner's personal or entity income taxes are different. Do not remove real estate taxes merely because an answer explanation excludes owner income taxes.
Does PGI always exclude parking and other income?
No. Read the definition supplied. PGI may already include potential parking, laundry or other property income. If it does, do not add the same amount again. If the question starts with rent only and separately supplies additional other income, add it at the appropriate step.
Which income amount do I use for the vacancy percentage?
Use the stated base. A loss equal to 5% of potential rent is different from 5% of all potential income when other income is present. If vacancy and collection losses use different bases, calculate them separately. A combined allowance on one base is a different premise.
How do tenant reimbursements affect NOI?
Keep the income and expense presentation consistent. A reimbursement may appear in income when the matching owner-paid cost is in operating expenses. Removing both can give the same NOI. Including the reimbursement while excluding that expense, or including the expense while omitting the reimbursement, distorts the result.
Can I use monthly NOI with an annual cap rate?
Annualize first. Monthly NOI of $7,000 gives annual NOI of $84,000. At an appropriate annual cap rate of 7%, the simplified indication is $84,000 / 0.07 = $1,200,000. The income period and expense definition must match the rate.
What is the operating-expense ratio?
For the convention used here, divide operating expenses by EGI and multiply by 100. Expenses of $72,000 divided by EGI of $180,000 give 40%. A cap rate instead compares annual NOI with value or price; these are different denominators and different questions.
Does a vacant unit mean stabilized vacancy is exactly its current vacancy?
No. Actual results describe a recorded period. Stabilized analysis uses supported expectations about normal operation, including market vacancy and appropriate expenses. Use the period requested; do not quietly replace an as-is or actual-year problem with a more favorable stabilized forecast.
Is Fannie Mae multifamily NCF the same as cash after the mortgage?
Not under the cited definition. It subtracts the underwritten replacement-reserve expense from NOI, whether or not reserve deposits are actually made. It is not a universal label for cash left after all debt service, capital spending and taxes. Read the definition attached to each measure.
Can NOI be negative?
Yes. If the stated EGI is $120,000 and operating expenses are $135,000, NOI is negative $15,000. That indicates an operating shortfall for the defined period. Do not change it to zero or treat a negative direct-capitalization result as a reliable market-value conclusion.
Why is tax-return rental income different from appraisal NOI?
IRS rental reporting can include items and deductions that do not belong in standard appraisal NOI, including tax depreciation, and cash-basis timing can differ from a normalized operating analysis. A refundable security deposit is also not automatically rental income. This comparison does not determine a particular owner's tax deduction or filing treatment.
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Official sources and scope
Checked October 25, 2026 against the identified PSI outline, OCC handbook passages, current Fannie Mae definitions and IRS rental-reporting explanation. The older California DRE chapter supports basic valuation arithmetic. These sources use different reporting conventions; the exercises state which definition applies. Examples, rates and property amounts are invented for practice.
- PSI June 24, 2026: national III.B.4 income approach and XI.B.2 capitalization
- 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
- Fannie Mae multifamily: defined NCF subtracts replacement reserve from NOI
- IRS Topic 414: rental reporting differs from appraisal NOI
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.