Cap Rate, IRV, GRM and Real Estate Cash-Flow Math

Three rules prevent most mistakes: pair annual NOI with an annual cap rate, pair monthly rent with a monthly GRM (and annual with annual), and keep debt service out of NOI.

What is the short formula map?

Convert a percentage to a decimal before using IRV. A 7.5% capitalization rate is 0.075.

Official source map

The New York State Department of State 77-hour curriculum requires deriving NOI, before-tax cash flow, cash-on-cash return and capitalization rate in Commercial and Investment Properties. It names the Income, Rate and Value relationship, commonly shortened to IRV.

The current Office of the Comptroller of the Currency Commercial Real Estate Lending handbook explains that direct capitalization estimates value by dividing NOI by an appropriate capitalization rate. It also defines debt-service coverage ratio as NOI divided by annual debt service.

The U.S. Department of Housing and Urban Development's rent-multiplier guidance derives a monthly gross rent multiplier by dividing comparable sale price by actual monthly rent. The current Fannie Mae Small Residential Income Property Appraisal Report displays gross monthly rent, GRM and indicated value as distinct fields. HUD's sample underwriting statement places NOI above annual debt service and net cash flow below it.

What does IRV mean?

IRV is a memory tool for three related quantities:

• I means annual income, usually NOI in direct capitalization
• R means capitalization rate
• V means value

The relationship is:

I = R × V

Cover the quantity you need:

• cover I: R × V
• cover R: I ÷ V
• cover V: I ÷ R

IRV is not a fourth valuation method. It is the algebra inside direct capitalization.

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What is a capitalization rate?

A capitalization rate, or cap rate, expresses a property's annual NOI as a percentage of value or price.

Cap rate = NOI ÷ Value

It is an unlevered property-income relationship because NOI is measured before mortgage principal and interest. Cap rate is not the mortgage interest rate, appreciation rate or investor's cash-on-cash return.

How do you calculate cap rate?

Example 1: Find the rate

A property has stabilized annual NOI of $84,000 and a value of $1,200,000.

Cap rate = $84,000 ÷ $1,200,000

Cap rate = 0.07 = 7%

The answer is 7%, not 0.07%. The decimal 0.07 converts to 7%.

How do you calculate value from NOI and cap rate?

Value = NOI ÷ Cap rate

Example 2: Find indicated value

Annual NOI is $96,000 and the problem supplies an 8% cap rate.

Value = $96,000 ÷ 0.08

Value = $1,200,000

Check by reversing the formula:

$1,200,000 × 0.08 = $96,000

How do you calculate NOI from value and cap rate?

NOI = Value × Cap rate

Example 3: Find income

A property is valued at $1,500,000 using a 6.5% cap rate.

NOI = $1,500,000 × 0.065

NOI = $97,500

What happens to value when cap rate changes?

For the same NOI, a higher cap rate produces a lower indicated value, and a lower cap rate produces a higher indicated value.

Example 4: Same income, two rates

NOI is $100,000.

At 5%:

Value = $100,000 ÷ 0.05 = $2,000,000

At 8%:

Value = $100,000 ÷ 0.08 = $1,250,000

The relationship does not say that a high or low rate is automatically desirable. An appropriate market rate reflects the income stream, property, leases, condition, location, expectations and risk considered by market participants.

Which income belongs in the cap-rate formula?

Direct capitalization uses annual NOI. It does not use:

• potential gross income
• effective gross income before operating expenses
• cash flow after debt service
• taxable income after depreciation
• one month's rent

If NOI is not supplied, construct it first:

PGI - Vacancy and collection loss = EGI

EGI - Operating expenses = NOI

Review Potential Gross Income, Effective Gross Income and NOI before applying a cap rate.

What is direct capitalization?

Direct capitalization converts one year's stabilized NOI into an indicated value using an appropriate capitalization rate.

The OCC handbook says the method fits stabilized NOI and an income stream expected to be stable. Stable doesn't mean frozen; it means the income and rate you pick should reflect how the property is expected to perform.

Direct capitalization is different from discounted cash-flow analysis, which projects multiple periods of income and a future sale, then discounts those amounts to present value.

Is cap rate the same as return on investment?

No. Cap rate relates property NOI to property value without subtracting debt service. An investor's return can be affected by financing, cash invested, capital expenditures, taxes, sale proceeds and holding period.

Cap rate is useful, but it is not a complete investment decision.

What is gross rent multiplier?

Gross rent multiplier, or GRM, is a market comparison between sale price and gross rent.

GRM = Sale price ÷ Gross rent

The rent and multiplier must use the same time period:

• monthly price-to-rent relationship produces monthly GRM
• annual price-to-rent relationship produces annual GRM

GRM is a multiplier, not a percentage.

How do you derive a monthly GRM?

Example 5: Comparable sale

A comparable rental property sold for $540,000 and had gross monthly rent of $4,500.

Monthly GRM = $540,000 ÷ $4,500

Monthly GRM = 120

The unit is 120 months of gross rent. Do not write 120%.

How do you estimate value with GRM?

Indicated value = Subject gross rent × Market-derived GRM

Example 6: Apply monthly GRM

The subject property has gross monthly rent of $4,800. Supported comparable analysis produces a monthly GRM of 120.

Indicated value = $4,800 × 120

Indicated value = $576,000

The multiplier should come from comparable market evidence, not from the subject's desired listing price.

How do you reconcile several comparable GRMs?

Calculate each comparable, then select a supported multiplier after considering comparability.

Example 7: Three comparable sales

Simple average for this educational problem:

(116.47 + 120.00 + 116.67) ÷ 3 = 117.71

If the subject's gross monthly rent is $4,600:

Indicated value = $4,600 × 117.71 = $541,466

An actual appraisal does not have to use a simple average. Comparable quality and adjustments matter.

What is the difference between monthly and annual GRM?

They express the same price-rent relationship on different time scales.

Using the $540,000 sale and $4,500 monthly rent:

Annual rent = $4,500 × 12 = $54,000

Annual GRM = $540,000 ÷ $54,000 = 10

Monthly GRM = 120

Annual GRM = Monthly GRM ÷ 12

Both methods indicate $540,000 when the correct rent period is used.

Period-mismatch trap

Do not multiply annual rent of $54,000 by monthly GRM of 120. That would create an unsupported value of $6,480,000.

Does GRM account for operating expenses?

No. GRM uses gross rent. It does not directly deduct vacancy, collection loss or operating expenses.

Two properties can have the same rent and different expenses. Their GRMs may look similar even though their NOIs differ. That is why GRM is a quick market indicator rather than a substitute for a complete income and expense analysis.

What is gross income multiplier?

Gross income multiplier, often abbreviated GIM, can use annual gross income rather than rent alone. A problem may include other property income in its gross-income measure.

If the problem defines different income bases, keep them straight:

• GRM uses stated gross rent
• GIM uses stated gross income
• direct cap uses NOI

What is before-tax cash flow?

In the curriculum's simplified cash-world statement:

Before-tax cash flow = NOI - Annual debt service

Debt service includes the required principal and interest payments for the period. Other below-NOI cash items can exist in a real analysis, so follow the statement given in the problem.

Example 8: Find before-tax cash flow

A property has:

• annual NOI: $150,000
• monthly debt service: $8,500

Annual debt service:

$8,500 × 12 = $102,000

Before-tax cash flow:

$150,000 - $102,000 = $48,000

The debt service is not subtracted when finding NOI. It is subtracted after NOI.

What is debt-service coverage ratio?

Debt-service coverage ratio, or DSCR, compares property NOI with required annual debt service.

DSCR = NOI ÷ Annual debt service

Example 9

Using NOI of $150,000 and annual debt service of $102,000:

DSCR = $150,000 ÷ $102,000

DSCR = 1.4706, or about 1.47

A ratio of 1.47 means the stated NOI is 1.47 times the stated annual debt service. It is not a 147% cap rate.

There is no universal “passing” DSCR. Each lender sets its own minimum based on the loan, the property and its underwriting policy.

What is cash-on-cash return?

Cash-on-cash return, also called an equity dividend rate in the curriculum, compares before-tax cash flow with the investor's actual cash invested.

Cash-on-cash return = Before-tax cash flow ÷ Cash invested

Example 10

Before-tax cash flow is $48,000 and the investor has $600,000 of cash invested.

Cash-on-cash return = $48,000 ÷ $600,000

Cash-on-cash return = 0.08 = 8%

Cash-on-cash return differs from cap rate because it uses after-debt cash flow and investor cash, not NOI and total property value.

How do leverage and cash flow interact?

Borrowed money can reduce the cash invested, but debt service also reduces cash flow. Leverage can magnify favorable or unfavorable equity results.

Example 11: Same property, different financing

A property has value of $1,000,000 and NOI of $80,000, so its cap rate is 8% regardless of the two simplified financing choices below.

Scenario A:

• cash invested: $1,000,000
• debt service: $0
• before-tax cash flow: $80,000
• cash-on-cash return: $80,000 ÷ $1,000,000 = 8%

Scenario B:

• cash invested: $300,000
• annual debt service: $58,000
• before-tax cash flow: $80,000 - $58,000 = $22,000
• cash-on-cash return: $22,000 ÷ $300,000 = 7.33%

The cap rate stays 8% because NOI and property value did not change. The cash-on-cash return changes because financing changed.

What is after-tax cash flow?

After-tax cash flow considers income-tax effects after before-tax cash flow. A simplified problem may state:

After-tax cash flow = Before-tax cash flow - Income-tax liability

If the tax calculation produces a tax saving, the problem may add that saving instead. Depreciation, basis, interest deductions, passive-activity rules and the taxpayer's circumstances can affect the result.

On the exam, use only the tax amount and direction the problem gives you. You can't work out an investor's tax bill from NOI alone.

How do you solve a combined income and value problem?

Example 12: From rent roll to value and cash flow

A property has:

• potential gross income: $300,000
• vacancy and collection loss: 6% of PGI
• operating expenses: $108,000
• market cap rate supplied by the problem: 7.5%
• annual debt service: $90,000
• investor cash: $500,000

Vacancy and collection loss:

$300,000 × 0.06 = $18,000

EGI:

$300,000 - $18,000 = $282,000

NOI:

$282,000 - $108,000 = $174,000

Indicated value:

$174,000 ÷ 0.075 = $2,320,000

Before-tax cash flow:

$174,000 - $90,000 = $84,000

Cash-on-cash return:

$84,000 ÷ $500,000 = 16.8%

DSCR:

$174,000 ÷ $90,000 = 1.9333, or about 1.93

Each result answers a different question. Do not call the 16.8% cash-on-cash return a cap rate.

What mistakes cause the most wrong answers?

Using EGI instead of NOI in IRV

Subtract operating expenses before capitalizing income.

Dividing by 7 instead of 0.07

Convert percentages to decimals.

Multiplying when value requires division

In IRV, value equals income divided by rate.

Calling GRM a percentage

GRM is a multiplier derived from price divided by gross rent.

Mixing monthly rent with annual GRM

Match the rent period to the multiplier period.

Deducting expenses from rent before applying GRM

GRM uses gross rent. Direct capitalization uses NOI.

Putting debt service inside NOI

Financing comes below the NOI line.

Treating cap rate and cash-on-cash return as the same

Cap rate uses NOI and property value. Cash-on-cash uses after-debt cash flow and investor cash.

Assuming a larger metric is better without context

Rates and multipliers must be interpreted with property, market, financing and risk information.

What is a reliable exam-day workflow?

1. Label every income figure as PGI, EGI, NOI or cash flow.
2. Annualize figures used with an annual cap rate.
3. Convert the cap-rate percentage to a decimal.
4. Choose the correct IRV operation.
5. Reverse the formula to check the result.
6. For GRM, identify monthly or annual rent.
7. Derive the multiplier from comparable evidence when requested.
8. Keep operating expenses out of GRM and debt service out of NOI.
9. Subtract annual debt service to find simplified before-tax cash flow.
10. Use the correct denominator for DSCR or cash-on-cash return.

Use Part, Rate and Whole for New York Real Estate Math for percentage setup and the New York real estate math formula map for the broader exam formula set.

Can you solve these original practice questions?

Practice 1

NOI is $72,000 and value is $900,000. What is the cap rate?

A. 0.8%
B. 8%
C. 12.5%
D. 80%

Answer: B. $72,000 ÷ $900,000 = 0.08 = 8%.

Practice 2

NOI is $135,000 and the cap rate is 7.5%. What is indicated value?

A. $10,125
B. $1,012,500
C. $1,800,000
D. $10,125,000

Answer: C. $135,000 ÷ 0.075 = $1,800,000.

Practice 3

Value is $2,000,000 and the cap rate is 6%. What is NOI?

A. $12,000
B. $120,000
C. $333,333
D. $3,200,000

Answer: B. $2,000,000 × 0.06 = $120,000.

Practice 4

A comparable sold for $600,000 and rents for $5,000 per month. What is monthly GRM?

A. 10
B. 100
C. 120
D. 1,200

Answer: C. $600,000 ÷ $5,000 = 120.

Practice 5

The subject's gross monthly rent is $5,200 and the market-derived monthly GRM is 120. What is indicated value?

A. $43,333
B. $520,000
C. $624,000
D. $7,488,000

Answer: C. $5,200 × 120 = $624,000.

Practice 6

NOI is $180,000 and annual debt service is $120,000. What are before-tax cash flow and DSCR?

A. $60,000 and 1.5
B. $60,000 and 3.0
C. $120,000 and 1.5
D. $300,000 and 0.67

Answer: A. Cash flow is $180,000 - $120,000 = $60,000. DSCR is $180,000 ÷ $120,000 = 1.5.

Practice 7

Before-tax cash flow is $45,000 and cash invested is $500,000. What is cash-on-cash return?

A. 4.5%
B. 9%
C. 11.11%
D. 90%

Answer: B. $45,000 ÷ $500,000 = 0.09 = 9%.

Practice 8

Which statement is accurate?

A. GRM directly accounts for operating expenses.
B. Debt service is deducted to calculate NOI.
C. Direct capitalization uses NOI divided by cap rate.
D. Monthly rent should be multiplied by annual GRM.

Answer: C. GRM uses gross rent, debt service comes below NOI, and rent must match the multiplier period.

Frequently asked questions

What is the IRV formula?

Income equals rate times value. Rate equals income divided by value. Value equals income divided by rate.

How do I calculate cap rate?

Divide annual NOI by property value or price and express the result as a percentage. For example, $84,000 NOI on a $1,200,000 property is a 7% cap rate.

How do I calculate value from NOI?

Divide stabilized annual NOI by the cap rate written as a decimal. $96,000 divided by 0.08 indicates a value of $1,200,000.

What is GRM?

Gross rent multiplier is comparable sale price divided by comparable gross rent for the same time period.

Is GRM based on net income?

No. GRM uses gross rent and does not directly deduct vacancy or operating expenses.

What is before-tax cash flow?

In a simplified property statement, it is NOI minus annual debt service.

What is DSCR?

Debt-service coverage ratio is NOI divided by annual debt service.

What is cash-on-cash return?

It is before-tax cash flow divided by the investor's cash invested.

Is cap rate the same as mortgage interest rate?

No. Cap rate relates property NOI to value. Mortgage interest rate prices borrowed money.

Does New York publish an official number of cap-rate questions?

No. The curriculum requires the concepts, but the Department of State does not publish a topic-level question count or weighting.

Sources and verification notes

The calculations, scenarios and practice questions are original teaching examples. They do not value a real property, pick a market cap rate or recommend an investment.

• New York State Department of State, Real Estate Salesperson 77-Hour Curriculum
• New York State Department of State, Real Estate Salesperson
• Office of the Comptroller of the Currency, Commercial Real Estate Lending handbook
• U.S. Department of Housing and Urban Development, Rent multipliers
• Fannie Mae, Small Residential Income Property Appraisal Report
• U.S. Department of Housing and Urban Development, Sample loan underwriting statement

Use this lesson for education and exam preparation. For an actual property, verify the rent roll, leases, expenses, stabilized NOI, comparable sales, market-derived rate, financing, capital needs and investor objectives with qualified professionals.