ExamPassIRV formula: income, rate and value (cap rate) explained
In the IRV formula, I is net operating income (NOI), R is the capitalization rate, also called the overall capitalization rate or OAR, and V is value. The three are tied together by one relationship: I = R × V. Rearranged, R = I ÷ V and V = I ÷ R. If you know any two, you can find the third.
IRV is how the income approach turns a property's yearly income into a price, and it is a core calculation topic in Course 4 and Simulation 2. This page is about using the formula without mistakes. For what cap rates tell you about risk and the market, read the deeper guide on cap rate in commercial real estate.
In the capitalization formula, what does the I stand for?
I stands for income, and specifically net operating income: the yearly income the property produces after vacancy and operating expenses, but before any financing. It is not gross rent, not the owner's cash flow after the mortgage, and not taxable income. Using the wrong income figure is a common IRV error.
| Letter | Stands for | Usual form |
|---|---|---|
| I | Net operating income | Dollars per year |
| R | Capitalization rate (overall rate, OAR) | A percentage, used as a decimal |
| V | Value | Dollars |
How does the IRV triangle work?
Picture a triangle with I at the top and R and V side by side at the bottom. Cover the letter you want:
- Cover I: R and V sit side by side, so multiply. I = R × V.
- Cover R: I sits over V, so divide. R = I ÷ V.
- Cover V: I sits over R, so divide. V = I ÷ R.
Always enter R as a decimal. A 7.5% rate is 0.075, not 7.5. Dividing by 7.5 instead of 0.075 gives an answer 100 times too small, and the exam will have that option waiting for you.
What is the difference between NOI and gross income?
Gross income is what the property could earn before anything is taken off. NOI is what is left after the costs of running the property. The path from one to the other is always the same:
- Potential gross income: all rent at full occupancy, plus other income such as parking or laundry.
- Less vacancy and collection loss: an allowance for empty space and rent that is never collected. The result is effective gross income.
- Less operating expenses: the costs of operating the property.
- Equals net operating income.
| Deducted to reach NOI | Not deducted |
|---|---|
| Vacancy and collection loss | Mortgage principal and interest (debt service) |
| Property taxes | The owner's income tax |
| Building insurance | Depreciation (capital cost allowance) |
| Repairs and maintenance | |
| Utilities paid by the owner | |
| Property management |
Debt service is left out because NOI measures the property, not the owner's loan. Two buyers with different mortgages are buying the same income. Income tax and depreciation are left out for the same reason: they depend on the owner, not the building.
What is vacancy and collection loss?
It is the allowance for income the property will not actually receive. Vacancy covers space that sits empty between tenants. Collection loss covers rent that is billed but never paid. Questions usually give it as a percentage of potential gross income. Read carefully whether the percentage applies to rent only or to all income, including parking or laundry, because the stem will tell you and the options will punish a guess.
What is a capitalization factor?
A capitalization factor is the reciprocal of the cap rate: 1 ÷ R. Multiply NOI by the factor and you get value, which is the same as dividing NOI by the rate.
| Cap rate | Capitalization factor (1 ÷ R) |
|---|---|
| 5% | 20.00 |
| 6.5% | 15.38 |
| 7.5% | 13.33 |
| 8% | 12.50 |
| 10% | 10.00 |
A factor is handy for quick estimates. At 8%, value is 12.5 times NOI. At 5%, it is 20 times NOI. If a question says a property is "worth 12.5 times its net income," it has told you the cap rate is 8%.
How does a small rate change move value?
A lot, because R is in the denominator. Take an NOI of $186,000:
| Cap rate | Value (NOI ÷ R) | Change from 7.5% |
|---|---|---|
| 6.5% | $2,861,538 | up $381,538 (15.4%) |
| 7% | $2,657,143 | up $177,143 (7.1%) |
| 7.5% | $2,480,000 | |
| 8% | $2,325,000 | down $155,000 (6.3%) |
Half a percentage point moves this property's value by more than $150,000 in either direction. Lower rate, higher value. Higher rate, lower value. If your answer moves the other way, you have the formula upside down.
How do you solve for each letter?
One invented property, solved three ways. Halden Works, a light industrial building in Cambridge, has potential gross rent of $268,000 a year. Vacancy and collection loss is 5%. Operating expenses (taxes, insurance, maintenance, management) are $68,600. The owner pays $121,000 a year on the mortgage and claims depreciation.
First, find NOI.
- Effective gross income: $268,000 × 95% = $254,600.
- NOI: $254,600 less $68,600 = $186,000.
- The mortgage and depreciation are ignored.
Solve for V. Similar buildings trade at a 7.5% cap rate. V = I ÷ R = $186,000 ÷ 0.075 = $2,480,000.
Solve for R. A buyer agrees to pay $2,480,000 for an NOI of $186,000. R = I ÷ V = $186,000 ÷ $2,480,000 = 0.075, or 7.5%.
Solve for I. An investor wants a 7.5% return on a $2,480,000 purchase. I = R × V = 0.075 × $2,480,000 = $186,000 of NOI needed.
The three answers check each other. If they do not, one of your inputs is wrong.
What are the common IRV exam traps?
- Capitalizing the wrong income. Gross income or effective gross income in place of NOI gives a value that is far too high.
- Deducting the mortgage. Debt service is never an operating expense. Neither is the owner's income tax or depreciation.
- Skipping vacancy and collection loss. It comes off before operating expenses.
- Using the rate as a whole number. 7.5 instead of 0.075.
- Multiplying when you should divide. V = I ÷ R. Value is always much larger than NOI.
- Getting the direction wrong. A higher rate means a lower value.
- Mixing monthly and yearly figures. IRV uses annual income. Convert monthly rent first.
Frequently asked questions
In the capitalization formula, what does the I stand for? Net operating income: the yearly income after vacancy and collection loss and operating expenses, but before mortgage payments, income tax and depreciation.
What is OAR in real estate? OAR is the overall capitalization rate, the R in IRV. It is NOI divided by value for the property as a whole.
What is the capitalization factor? It is 1 divided by the cap rate. NOI multiplied by the factor gives value, so a 10% rate is a factor of 10.
Does a higher cap rate mean a higher value? No. For the same NOI, a higher rate gives a lower value, because value is NOI divided by the rate.
Is the mortgage payment deducted to find NOI? No. Debt service depends on the owner's financing, not the property, so it is never part of NOI.
How does ExamPass help you practice the IRV formula?
ExamPass gives you hundreds of original Course 4 and Simulation 2 questions, including income property calculations where every option is explained, so you can see exactly which wrong figure each distractor used. The Study notes cover the income approach step by step, and the AI Tutor can rework any calculation you miss. Plug income, rate and value into the cap rate and NOI calculator to watch how changing one moves the others. Test yourself on six worked real estate exam math practice questions, compare lease structures in gross vs net vs triple net lease, or start with the free Course 4 practice questions and Simulation 2 practice questions. See courses and pricing
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