Capitalization Rate Development

Income Streams, Rates and Factors for Direct Capitalization

Wayne Foss, MBA, MAI, CRE, Fullerton, CA USA Email: waynefoss@usa.net

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Terms and Definitions

Income Rate:

The ratio of one year’s income to the value of the property. Examples are RO, RE and RM

Discount Rate:

An interest rate used to convert future payments or receipts into present value. Examples are IRR and YO

Yield Rate:

A rate of return on capital for a specific time period. Usually expressed as a compound annual percentage rate.

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Terms and Definitions

Interest Rates:

Effective Interest Rate (i)

interest per dollar per period; the nominal annual interest rate divided by the number of conversion periods per year.

Nominal Interest Rate (I)

A stated or contract rate; an interest rate, usually annual

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Direct Capitalization

A Method used to convert an estimate of a single year’s income expectancy into an indication of value.

A capitalization technique that employs capitalization rates and multipliers extracted from sales

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Basic Formulas

I = R x V R = I / V V = I / R

V = I x F I = V / F F = V / I

Where:

I = Income

R = Capitalization Rate

V = Value

F = Factor

I

R V

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Income Streams

Potential Gross Income Effective Gross Income Net Operating Income Equity Income Mortgage Income Land Income Building Income Income to the Landlord’s leased fee interest Income to the tenant’s leasehold interest

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Income Capitalization Rates

Overall (property) capitalization rate, fee simple (RO)

Mortgage Capitalization Rate (RM)

Equity Capitalization, or equity dividend rate (RE)

Land Capitalization Rate (RL)

Building Capitalization Rate (RB)

Capitalization Rate for the leased fee position (RLF)

Capitalization Rate for the leasehold position (RLH)

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Income Factors

Potential Gross Income Multiplier (PGIM) Can be expressed as a monthly or annual multiplier

Gross Rent Multiplier (GRM) Generally expressed as a monthly multiplier

Effective Gross Income Multiplier

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Derivation of the Overall (Property) Capitalization Rate (RO)

From Comparable Sales

When Net Income is known:

RO = Net Operating Income / Sales Price

When Net Operating Income is unknown but the Effective Gross Income Multiplier is Known:

RO = Net Income Ratio / EGIM

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Overall Capitalization Rate (RO)a Weighted Rate

Example: if Net Operating Income and Sales Price are known, then Overall Capitalization Rate (RO) is calculated as:

Net Operating Income / Sales Price = RO

$100,000 $1,000,000 = 10.0%

RO is a weighted rate, between land and buildings

Land: 25% x 8.5% = 2.1% Improvements: 75% x 10.5% = 7.9% Total: 100% 10.0%

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Model for the Direct Capitalization Technique

Net Operating Income $xxx,xxx.xx

Capitalization of Income:

Income to Property divided by RO = Overall Property Value

Indicated Value per Direct Capitalization Technique

$xxx,xxx.xx

Application:

$100,000.00 $1,000,000.00

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Rates Used in the Residual Techniques

Building Capitalization Rate: Interest Rate (return on investment) Recapture Rate (return of investment)

Land Capitalization Rate: Interest Rate (return on investment)

For Assessment purposes the effective tax rate is added to each capitalization rate

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Components of theBuilding Capitalization Rate (RB)

Return on Investment (interest rate) Return of Investment (recapture rate)

Straight Line: 1 / remaining economic life I.e.: 1 20 = 5.0%

Can be calculated with other recapture assumptions

For assessment purposes add the effective tax rate Calculated as the nominal tax rate times the assessment ratio

I.e.: Assessment Ratio 50.0%, nominal tax rate 4.0% Effective tax rate = 50% x 4.0% = 2.0%

RB = Int. Rate + Recap. Rate or

RB = Int. Rate + Recap. Rate + Eff. Tax Rate

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Components of theLand Capitalization Rate (RL)

Return on Investment (interest rate)

For assessment purposes add the effective tax rate Calculated as the nominal tax rate times the

assessment ratio I.e.: Assessment Ratio 50.0%, nominal tax rate 4.0% Effective tax rate = 50% x 4.0% = 2.0%

RL = Int Rate or

RL = Int Rate + Eff Tax Rate

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Development of Capitalization Rates

Interest Rate or Discount Rate

Net Operating Income $100,000 Overall Capitalizaton Rate (RO) 10.0%

Less Recapture Less Recapture$750,000 x 2.0% = $15,000 75.0% x 2.0% = 1.5%

Residual for Return on Investment $85,000 Residual for Return on Investment 8.5%

Development of Rate$85,000 $1,000,000 = 8.5%

Band of InvestmentDollars

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Development of Capitalization Rates

Land Capitalization Rate (RL) and Building Capitalization Rate (RB)

Rate to the Land (RL)

Interest Rate 8.5%

Rate to the Building (RB)

Interest Rate 8.5% Recapture Rate 2.0% Total: 10.5%

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Development of Capitalization Rates

Equity Capitalization Rate (RE)

Net Operating Income $100,000 Overall Capitalizaton Rate (RO) 10.0%

Less Mortgage Requirement Less Mortgage Requirement$650,000 x 7.98% = $51,870 65.0% x 7.98% = 5.19%

Residual for Return on Equity $48,130 Residual for Return on Equity 4.81%

Development of Rate Development of Rate$48,130 $350,000 = 13.75% 4.81% 35.0% = 13.75%

Dollars Band of Investment

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Development of Capitalization Rates

Mortgage Capitalization Rate (RM)

By definition, the Mortgage Capitalization Rate is the relationship between annual debt service and the balance of the loan.

At the beginning of the loan term, the Mortgage Capitalization Rate is equal to the annual mortgage constant.

For Example:

Loan = $650,000.00 Term = 30 yearsInterest Rate = 7.0% Amortization Type = Monthly Amortization Factor = .006653 Annual Payment = $51,893.40

RM = $51,893.40 $650,000.00 = 7.98%

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Development of Capitalization Rates

Leased Fee Capitalization Rate (RLF)

If Net Operating Income is Equal to Market Net Operating IncomeIncome Value = Rate

$100,000 $1,000,000 = 10.0%

If Net Operating Income is Greater Than Market Net Operating Income

$120,000 $1,100,000 = 10.9%

If Net Operating Income is Less Than Market Net Operating Income

$80,000 $900,000 = 8.9%

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Development of Capitalization Rates

Leasehold Capitalization Rate (RLH)

If Net Operating Income is Equal to or Greater Than Market Net Operating Income, there is no value to the leasehold position.

If Net Operating Income is Less Than Market Net Operating Income

Market NOI $100,000Contract NOI $80,000Savings to Leasehold $20,000

Income Value = Rate$20,000 $150,000 = 13.3%

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The Residual Techniques

The Building Residual Technique

What is Known:

1. Net Operating Income

2. Land Value

What is Unknown: Improvement Value

The Land Residual Technique

What is Known:

1. Net Operating Income

2. Depreciated Value of the Improvements

What is Unknown: Land Value

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Model for the Building Residual Technique

Net Operating Income $xxx,xxx.xx

Less Income Available to the Land:

Land Value times RL : -$ xx,xxx.xx

Income Available to the Improvements: $xxx,xxx.xx

Capitalization of Income:

Income to Improvements divided by RB = Building Value

Plus Land Value $xxx,xxx.xx

Indicated Value per Building Residual Technique

$xxx,xxx.xx

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Example for the Building Residual Technique

Net Operating Income $100,000.00

Less Income Available to the Land:

$250,000.00 x 8.5% : -$ 21,250.00

Income Available to the Improvements: $ 78,750.00

Capitalization of Income:

$78,750.00 10.5% = $750,000.00

Plus Land Value $250,000.00

Indicated Value per Building Residual Technique

$1,000,000.00

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Model for the Land Residual Technique

Net Operating Income $xxx,xxx.xx

Less Income Available to the Improvements:

Improvements Value times RB : -$ xx,xxx.xx

Income Available to the Land: $xxx,xxx.xx

Capitalization of Income:

Income to Land divided by RL = Land Value

Plus Improvements Value $xxx,xxx.xx

Indicated Value per Land Residual Technique

$xxx,xxx.xx

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Example for the Land Residual Technique

Net Operating Income $100,000.00

Less Income Available to the Improvements:

$750,000.00 x 10.5% : -$ 78,750.00

Income Available to the Land: $ 21,250.00

Capitalization of Income:

$21,250.00 8.5% = $250,000.00

Plus Improvements Value $750,000.00

Indicated Value per Land Residual Technique

$1,000,000.00

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So That’s Capitalization Rate Development

Wayne Foss, MBA, MAI, CRE, Fullerton, CA USA Email: waynefoss@usa.net