- Official section
- National XI.E: Rate of Return and Capitalization Rate
- Broker weight
- 7% of the national broker portion
- Expected scored items
- Real Estate Math accounts for about 7 of 100 items
Calculations topic guide
Rate of return and capitalization rate
Investment math becomes manageable when the income ladder is built in order. Start with what the property could earn, account for what it actually collects, subtract operating costs, and only then choose the return formula the question asks for.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: Effective gross income equals potential gross income minus vacancy and collection loss plus other income. NOI equals effective gross income minus operating expenses. Cap rate equals NOI divided by value. Value equals NOI divided by cap rate. Cash-on-cash return equals annual before-tax cash flow divided by cash invested. Do not subtract debt service before calculating basic NOI.
The national outline effective June 24, 2026 tests rate of return and capitalization rate. These exam calculations use simplified annual figures. A real appraisal or investment decision requires supported market income, expenses, vacancy, capitalization-rate evidence, property-specific risk, capital needs, financing, taxes, and professional judgment. This guide teaches the tested math, not investment advice or an appraisal conclusion.
The INCOME ladder for investment-property math
- Inventory annual revenue. List scheduled rent and each other income source, converting monthly amounts to annual figures.
- Normalize vacancy. Apply the stated vacancy and collection rate to the exact base identified in the question.
- Combine effective income. Subtract vacancy loss and add applicable other income to reach EGI.
- Organize expenses. Separate operating expenses from debt service, depreciation, owner taxes, and capital items.
- Make NOI. Subtract operating expenses from EGI and stop there when the question asks for NOI or cap-rate value.
- Enter the correct return formula. Use NOI/value for cap rate, NOI/rate for value, and after-debt cash flow/cash invested for cash-on-cash return.
- Audit units and direction. Annual income needs an annual rate, percentages need decimals in arithmetic, and higher cap rates should lower value when NOI is fixed.
- Requested measure
- Vacancy loss
- Formula
- Income base x vacancy rate
- Do not substitute
- Occupied income
- Requested measure
- Effective gross income
- Formula
- Potential gross income - vacancy + other income
- Do not substitute
- NOI
- Requested measure
- NOI
- Formula
- EGI - operating expenses
- Do not substitute
- After-debt cash flow
- Requested measure
- Cap rate
- Formula
- NOI / value x 100
- Do not substitute
- Cash-on-cash return
- Requested measure
- Value by direct cap
- Formula
- NOI / cap rate
- Do not substitute
- NOI x cap rate
- Requested measure
- Required NOI
- Formula
- Value x cap rate
- Do not substitute
- Gross rent
- Requested measure
- Before-tax cash flow
- Formula
- NOI - debt service
- Do not substitute
- NOI itself
- Requested measure
- Cash-on-cash return
- Formula
- Annual cash flow / cash invested x 100
- Do not substitute
- NOI / price
- Requested measure
- GRM
- Formula
- Price / gross monthly rent
- Do not substitute
- Cap rate percentage
Can you follow the calculation from facts to answer?
Build NOI from the income ladder
Scenario: An eight-unit property rents for $1,500 per unit each month. Vacancy and collection loss are 5% of scheduled rent, other annual income is $8,400, and annual operating expenses are $46,000.
- Potential rent is 8 x $1,500 x 12 = $144,000. Vacancy loss is $144,000 x 0.05 = $7,200.
- EGI is $144,000 - $7,200 + $8,400 = $145,200. NOI is $145,200 - $46,000 = $99,200.
Answer: Annual NOI is $99,200. No mortgage payment is subtracted because the question asks for NOI.
Estimate value with direct capitalization
Scenario: A comparable-supported cap rate is 8%. The subject property's stabilized annual NOI is $104,000.
- Convert 8% to 0.08.
- Value = NOI / cap rate = $104,000 / 0.08.
Answer: The direct-capitalization indication is $1,300,000. Multiplying NOI by 8% would produce the wrong direction.
Solve for the cap rate
Scenario: A property sells for $960,000 and has stabilized annual NOI of $67,200.
- Cap rate = NOI / value.
- $67,200 / $960,000 = 0.07.
Answer: The indicated cap rate is 7%. This is not automatically the buyer's cash-on-cash return.
Calculate cash-on-cash return
Scenario: A buyer invests $250,000 cash. The property produces $78,000 NOI and has $53,000 in annual debt service. No other cash-flow adjustment is stated.
- Before-tax cash flow is $78,000 - $53,000 = $25,000.
- Cash-on-cash return is $25,000 / $250,000 = 0.10.
Answer: The cash-on-cash return is 10%. Dividing the $78,000 NOI by cash invested would mix an unlevered numerator with a leveraged denominator.
Which math errors cost the most points?
- Trap
- Potential rent is the same as effective income.
- Correction
- Effective income accounts for vacancy and collection loss and may include other income.
- Trap
- Subtract the vacancy percentage itself from income.
- Correction
- First calculate the dollar loss by multiplying the correct income base by the vacancy rate.
- Trap
- Mortgage principal and interest are operating expenses.
- Correction
- Debt service is excluded from the standard NOI used in direct capitalization.
- Trap
- Depreciation is always subtracted to calculate cap-rate NOI.
- Correction
- Tax depreciation is not a property operating cash expense in the basic exam NOI formula.
- Trap
- Cap rate equals gross income divided by value.
- Correction
- The numerator in the basic direct-capitalization formula is NOI.
- Trap
- Value equals NOI multiplied by the cap rate.
- Correction
- Value equals NOI divided by cap rate. Required NOI equals value multiplied by cap rate.
- Trap
- Use 8 instead of 0.08 in a division formula.
- Correction
- Convert a percentage to decimal form before arithmetic.
- Trap
- A higher cap rate raises value when NOI stays fixed.
- Correction
- A higher denominator lowers the indicated value.
- Trap
- Cash-on-cash return and cap rate must match.
- Correction
- They use different numerators and denominators, and cash-on-cash is affected by financing.
- Trap
- A calculated value is a complete appraisal.
- Correction
- Direct capitalization depends on supported stabilized NOI and a market-derived rate, plus property-specific analysis.
Can you solve these original problems?
These questions are original study items aligned to the published outline. They are not copied, recalled, or predicted PSI questions.
1. A property has $180,000 potential gross income, 6% vacancy and collection loss, $9,000 other income, and $58,000 operating expenses. What is NOI?
- $111,200
- $120,200
- $122,000
- $131,000
Show answer and explanation
Answer: B
Vacancy loss is $10,800. EGI is $180,000 - $10,800 + $9,000 = $178,200. NOI is $178,200 - $58,000 = $120,200.
2. A property has annual NOI of $84,000 and sells for $1,200,000. What is the capitalization rate?
- 6%
- 7%
- 8.4%
- 14.29%
Show answer and explanation
Answer: B
$84,000 / $1,200,000 = 0.07, or 7%.
3. Stabilized annual NOI is $96,000 and the market cap rate is 7.5%. What is the indicated value?
- $720,000
- $1,200,000
- $1,280,000
- $1,371,429
Show answer and explanation
Answer: C
$96,000 / 0.075 = $1,280,000.
4. Which expense is normally excluded from basic NOI used in direct capitalization?
- Property insurance
- Management expense
- Mortgage debt service
- Owner-paid common-area utilities
Show answer and explanation
Answer: C
Debt service reflects the owner's financing. NOI is calculated before mortgage principal and interest.
5. An investor contributes $180,000 cash. NOI is $62,000 and annual debt service is $44,000. What is the simplified cash-on-cash return?
- 10%
- 24.44%
- 34.44%
- 68.89%
Show answer and explanation
Answer: A
Cash flow is $62,000 - $44,000 = $18,000. Cash-on-cash return is $18,000 / $180,000 = 10%.
Which numbers and formulas are easy to confuse?
- Terms
- Potential gross income vs. effective gross income
- Difference
- Potential gross income reflects full earning potential. Effective gross income accounts for vacancy and collection loss and includes applicable other income.
- Question cue
- Could collect versus reasonably expected to collect.
- Terms
- Effective gross income vs. NOI
- Difference
- Effective gross income is before operating expenses. NOI is what remains after those operating expenses.
- Question cue
- Collected property revenue versus operating earnings.
- Terms
- Operating expense vs. debt service
- Difference
- Operating expenses support the property's operation. Debt service reflects a particular owner's financing structure.
- Question cue
- Property cost versus capital cost.
- Terms
- NOI vs. cash flow
- Difference
- NOI is before debt service. Simplified before-tax cash flow subtracts debt service from NOI.
- Question cue
- Unlevered property performance versus money remaining after financing.
- Terms
- Cap rate vs. cash-on-cash return
- Difference
- Cap rate divides NOI by property value. Cash-on-cash divides before-tax cash flow by investor cash invested.
- Question cue
- Property yield measure versus leveraged investor yield measure.
- Terms
- Cap rate vs. discount rate
- Difference
- A cap rate converts one stabilized income measure into value. A discount rate is used to discount a series of future cash flows to present value.
- Question cue
- Direct capitalization shortcut versus discounted cash-flow analysis.
- Terms
- Capital expenditure vs. routine repair
- Difference
- A capital expenditure replaces or improves a long-lived component. A routine repair maintains ordinary operations.
- Question cue
- Long-term asset investment versus recurring operating upkeep.
- Terms
- Cap rate vs. gross rent multiplier
- Difference
- Cap rate uses NOI and a percentage. GRM uses gross rent and a multiplier without directly subtracting expenses.
- Question cue
- Net-income valuation versus gross-rent comparison.
- Terms
- Return amount vs. rate of return
- Difference
- Return amount is a dollar profit or cash flow. Rate of return divides that amount by the appropriate investment base.
- Question cue
- Dollars earned versus percentage earned on capital.
What does the outline expect you to calculate?
- Topic
- Potential gross income
- What to know
- Scheduled rent, market rent, contract rent, occupied units, vacant units, monthly rent, annual rent, full occupancy, potential gross rental income, lease step-up, concession, parking, storage, laundry, utility reimbursement, and other income
- Best exam move
- Annualize every recurring income source and keep potential rent separate from other property income when the vacancy rate applies only to rent.
- Topic
- Vacancy and collection loss
- What to know
- Physical vacancy, economic vacancy, nonpayment, bad debt, concession, turnover, market allowance, percentage of rent, percentage of gross income, occupied percentage, collection rate, stabilized assumption, and actual history
- Best exam move
- Vacancy loss = stated income base x vacancy rate; subtract the loss rather than multiplying income by the loss rate and calling it collected income.
- Topic
- Effective gross income
- What to know
- Potential gross income, vacancy, collection loss, concessions, other income, recovered expenses, parking, storage, laundry, vending, antenna, application income, late charges, reimbursements, and actual collections
- Best exam move
- Use EGI = potential gross income - vacancy and collection loss + other income unless the question's ordering defines potential gross income more broadly.
- Topic
- Operating expenses
- What to know
- Property taxes, insurance, management, utilities, repairs, maintenance, cleaning, landscaping, supplies, legal and accounting, licenses, payroll, security, trash, pest control, advertising, and replacement reserves
- Best exam move
- Subtract costs necessary to operate the property, using the categories supplied in the problem.
- Topic
- Items below NOI
- What to know
- Mortgage principal, mortgage interest, total debt service, owner income taxes, depreciation, amortization, capital improvement, acquisition cost, sale cost, distribution, and investor-specific expense
- Best exam move
- Keep financing and owner tax consequences out of the standard NOI used for direct capitalization.
- Topic
- Net operating income
- What to know
- Annual NOI, stabilized NOI, trailing operations, forecast income, operating statement, recurring revenue, normalized expense, one-time expense, non-operating item, property performance, income approach, and value basis
- Best exam move
- NOI = EGI - operating expenses. Check that the result is annual when the cap rate is annual.
- Topic
- Direct capitalization
- What to know
- Income approach, stabilized annual NOI, capitalization rate, overall rate, market-derived rate, comparable sale, property value, present worth, risk, investor expectation, single-year income, perpetuity shortcut, and appraisal judgment
- Best exam move
- Use NOI, not gross rent and not after-debt cash flow, with the basic cap-rate formula.
- Topic
- IRV formula triangle
- What to know
- Income, rate, value, NOI divided by value, NOI divided by cap rate, value multiplied by rate, decimal conversion, percentage conversion, reverse calculation, and reasonableness
- Best exam move
- Cover the requested letter: I = R x V, R = I / V, and V = I / R.
- Topic
- Capitalization-rate interpretation
- What to know
- Current income, price, required return, market evidence, perceived risk, location, property condition, tenant quality, lease term, growth expectation, supply, investor demand, volatility, useful life, and financing conditions
- Best exam move
- With NOI held constant, a higher cap rate means lower indicated value and a lower cap rate means higher indicated value.
- Topic
- Cash flow and debt service
- What to know
- NOI, annual principal and interest, debt service, before-tax cash flow, capital expenditure, reserve, lender payment, leverage, positive cash flow, negative cash flow, and investor distribution
- Best exam move
- For the simplified exam formula, before-tax cash flow = NOI - annual debt service, then follow any stated capital-cost adjustment.
- Topic
- Rate of return
- What to know
- Return on investment, annual profit, initial investment, cash invested, cash-on-cash return, equity return, holding period, appreciation, sale proceeds, total return, percentage yield, and denominator selection
- Best exam move
- Match the numerator and denominator to the named return: profit over investment is not the same as NOI over value.
- Topic
- Multiplier comparisons
- What to know
- Gross rent multiplier, gross income multiplier, monthly rent, annual income, sale price, cap rate, NOI, expenses, quick comparison, unit consistency, market extraction, and valuation limit
- Best exam move
- GRM uses gross rent and a multiplier, while direct capitalization uses NOI and a percentage rate.
How should you drill this calculation?
- Session
- 1. Build the income ladder
- Focus
- Potential rent, annualization, vacancy, collection loss, concessions, other income, EGI, and NOI sequence
- Proof you are ready
- Build ten complete operating statements from unsorted facts.
- Session
- 2. Classify expenses
- Focus
- Operating expense, debt service, depreciation, income tax, capital expenditure, reserve, routine repair, and owner-specific cost
- Proof you are ready
- Classify forty line items and explain every excluded item.
- Session
- 3. Master IRV
- Focus
- NOI, cap rate, value, formula triangle, decimal conversion, reverse-solving, and direction check
- Proof you are ready
- Solve fifteen mixed income, rate, and value questions at 90% accuracy.
- Session
- 4. Compare return measures
- Focus
- Cap rate, before-tax cash flow, cash invested, cash-on-cash return, total return, leverage, and denominator selection
- Proof you are ready
- Explain why two return rates on the same property can differ without either being wrong.
- Session
- 5. Separate cap rate and GRM
- Focus
- NOI, gross rent, percentage rate, multiplier, monthly unit, annual unit, expenses, and comparable sale
- Proof you are ready
- Identify the correct method and units in twenty short prompts.
- Session
- 6. Apply INCOME
- Focus
- Revenue, vacancy, other income, EGI, operating expenses, NOI, debt service, formula choice, percentage conversion, and reasonableness
- Proof you are ready
- Score at least 90% on fresh mixed income-property calculations.
Do not count recognition as mastery. Close the notes and explain the rule, apply it to a new fact pattern, and identify why each distractor fails.
Build speed without skipping the setup
From concept to decision
Drill this topic, then review the explanation
Pass Illinois gives you original national and Illinois questions, topic-by-topic study, clear explanations, timed practice, flashcards, progress tracking, and Math Coach. Start free, find the weak distinction, and focus the next session there.
Questions students ask about Rate of Return and Capitalization Rate
What is net operating income in real estate?
Net operating income, or NOI, is the property's effective income minus reasonably necessary operating expenses. A standard exam setup begins with potential rental income, subtracts vacancy and collection loss, adds other property income, and then subtracts operating expenses. NOI is calculated before mortgage debt service, owner income taxes, and depreciation unless a question expressly defines another measure.
What is the capitalization-rate formula?
Capitalization rate equals annual NOI divided by property value or price. In decimal form, cap rate = NOI / value. The same relationship can be rearranged as value = NOI / cap rate or NOI = value x cap rate. Convert the percentage to a decimal before dividing or multiplying.
How do you estimate value using a cap rate?
Divide the property's stabilized annual NOI by the market-derived capitalization rate. If annual NOI is $72,000 and the cap rate is 8%, estimated value is $72,000 / 0.08 = $900,000. This is a direct-capitalization estimate, not a guarantee of sale price or a substitute for a complete appraisal.
What expenses are included in NOI?
Typical operating expenses include property taxes, property insurance, management, owner-paid utilities, routine repairs and maintenance, supplies, cleaning, landscaping, and other costs necessary to operate the property. Use the expense facts given in the exam question because classification and reserves can vary by assignment and market practice.
Is a mortgage payment an operating expense for cap-rate NOI?
No in the standard direct-capitalization calculation. Financing is specific to the owner, while NOI measures the property's operating performance before debt service. Mortgage principal and interest are subtracted later when calculating before-tax cash flow, not when calculating the unlevered NOI used in the basic cap-rate formula.
What is cash-on-cash return?
Cash-on-cash return compares annual before-tax cash flow with the investor's actual cash invested. The formula is annual cash flow / cash invested x 100. It is financing-sensitive because debt service affects cash flow and borrowing affects the amount of cash invested.
Is cap rate the same as cash-on-cash return?
No. Cap rate compares NOI with property value and generally ignores the investor's financing. Cash-on-cash return compares after-debt-service cash flow with the investor's cash investment. The rates can differ sharply on the same property.
What happens to value when the cap rate rises?
If NOI stays constant, value falls when the cap rate rises because value = NOI / cap rate. If NOI is $60,000, a 6% cap rate indicates $1,000,000, while an 8% cap rate indicates $750,000. A higher required return is commonly associated with higher perceived risk, all else equal.
Should vacancy be deducted before calculating NOI?
Yes when the problem provides a vacancy and collection allowance. Subtract it from potential gross income to reach effective gross income, then subtract operating expenses. If vacancy is given as a percentage, read carefully whether it applies only to rent or to all potential income.
Are these actual PSI exam questions?
No. The questions are original and aligned to the public Real Estate Math outline effective June 24, 2026. The valuation concepts are grounded in primary federal and current Fannie Mae guidance reviewed through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- HUD Handbook Chapter 7, Income Approach to Value
- Federal banking agencies, valuation concepts for income-producing real estate
- Office of the Comptroller of the Currency commercial real estate resources
- Fannie Mae Selling Guide, cost and income approaches to value
- Fannie Mae Multifamily Guide, capitalization-rate derivation
- HUD definition of net operating income
The current official outline controls the tested scope. Statutes, regulations, and official agency materials control when a general study rule and a jurisdiction-specific rule differ.
Editorial status
Checked against primary sources
The Pass Illinois editorial team last checked this guide on August 1, 2026. Every practice question is an original study item, and the source links above let you verify the rules that support the lesson.