**Chapter 15**

Capitalization rates

**Theoretical basis for income capitalization**

## u Theory of
Interest: Interest is the payment for
forgoing the use of capital resources.

## u The Theory
of interest explains the difference between the value of a good at the present
time and the value to be received in the future.

**Components of Capitalization Rates**

## u
Discount rates--Return *on* Investment

## u Plus
Recapture rate--Return *of* Investment

## u R_{overall}
= y_{o} - ∆_{overall *}
a_{n
}where:

### u R_{overall} = Capitalization Rate

### u y_{o} = Discount Rate for property

### u ∆_{overall *} a_{n} =
Recapture Rate

### u ∆_{overall} = Expected change
in value during holding period.

### u a_{n} = Annualizer (converts value
over holding period into an value per year.)

**Types of Discount Rates**

## u y = General
symbol for Return *on* Investment

## u y_{o}
= Discount rate for overall property

## u y_{m}
= Discount rate on loan (mortgage loan interest)

## u y_{e}
= Discount rate on equity

## u y_{L}
= Discount rate on land

## u y_{B}
= Discount rate on building

**Components of Discount Rates**

## u Pure cost
of money

### u Base Rate

### u Inflation
Premium

### u Liquidity
Premium

## u Risk
Premium

### u Reflects
the uncertainty that the expected cash flow differs from the actual amount
received.

**Estimating Discount Rates**

## u Direct
market extraction

## u Abstraction
from Gross Income Multiplier

## u Mortgage
Equity Analysis

**Direct Market Extraction**

## u Market
research has discovered the following three comparable sales:

## u CompA CompB Comp C

## u Sale Price 200,000 210,000 150,000

## u Building
Val. 160,000 168,000 120,000

## u Net Income 24,400
22,470 16, 350

## u Useful life 25 years 50 years 40
years

## u Recapture %
4% 2%
2.5%

## u Bd.
Recapture 6,400 3,360 3,000

## u Inc After
Rcpt 18,000 19,110 13,350

## u Indicated R_{o}
9.0% 9.1% 8.9%

**Recapture Rates**

## u Strait-line
Rates

### u Assumes
recapture occurs at the same rate each year.

### u Computed by
1 ÷ useful life of improvements

## u Sinking
Fund Rates

### u Assumes
recapture occurs more rapidly toward the end of the assets useful life.

### u Computed by
computing the appropriate sinking fund factor.

**Types of capitalization rates**

## u Overall
capitalization rate

## u Equity
capitalization rate

## u Mortgage
(debt) capitalization rate

## u Land
capitalization rate

**Methods of estimating capitalization rates**

## u Direct
Market Extraction

## u Composite
Rate -- i = ƒ(base rate, inflation, risk, liquidity)

## u Return on
vs. Return of Building Capitalization Rates

## u Band of
investment analysis (Simple mortgage-equity analysis)

## u The Ellwood
formulation

## u Underwriters
method

**Direct Market Extraction**

## u Easiest and
most reliable if data is available

## u Based upon
simple valuation formula:

_{u
}V_{overall
} = I_{overall } ÷ R_{overall}

## u Steps:

### u Examine
sales of comparable properties

_{u
}Solve for the indicated overall rate by using the
Income at time of sale as I_{overall} and sales price as the V_{overall}_{ }

## u For
example, if a comparable property sold for $352,000 and its income at time of
sale was $33,440, then its indicated Return overall is .095

**Composite Rate -- i = f(base rate, inflation, risk, liquidity)**

## u Base rate +
Inflation = Treasury yield

## u Base rate +
Inflation + Liquidity = CD rate

## u Use of
bracketing certainty equivalents

### u Which is
more risky, a new Taco Bell or a USAir bond?

### u Which is
more risky, a new Taco Bell or an IBM bond?

### u Consequently,
the appropriate yield for Taco Bell should fall between the yield on a USAir
bond and an IBM bond (both found in the WSJ).

**Return on vs Return of Building Capitalization Rates**

## u Return on
Investment is the base rate desired by an investor in order to make an
investment.

## u Return of
Investment is an additional rate desired to compensate the investor for the
depreciation of the building. It is
equal to

1 ÷ (Useful life of building)

## u Return
overall for an investment is then equal to the return *on*
investment plus the return *of* investment.

**Band of Investment**

## u Weights the
investors position with the lenders

## u %Equity
investment _{* }Return on Investment + %Mortgage _{*}_{ }Rate on
Mortgage

## u What is the
indicated overall rate if an investor puts down 20%, requires a 15% rate of
return, and the bank charges 9% on the 30 year, monthly payment mortgage?

**Step 1: Compute the rate for the mortgage**

## u R_{m}=
R_{mortgage}= Total amount of payments in a year ÷ Loan Amount

## u To
calculate, simply set the loan amount (PV) as 100% or 1, then solve for the
payment like any other mortgage payment problem. Then multiply the result by the number of payments per year.

## u P/YR =12;
I/YR = 9; PV = 1; N = 360 (30 cream N); solve for PMT; _{*} 12

## u R_{m}=
.0966

**Step 2: Compute the percentage of
the investment that is mortgage**

## u Mortgage
percentage = 100% - equity percentage

## u 100% - 20%
= 80%

## u Now you
have all of the information necessary for the solution!

**Solution for Band of Investment**

## u %Equity investment
_{*} R_{equity}
= .2 _{*} .15 = .03

## u %Mortgage _{*
}Rate on Mortgage (R_{m}) = .8 _{*} .0966 =
.0773

_{u
}.03 + .0773 = .1073 = 10.73% = R_{overall}
= R_{o}

**Ellwood Mortgage Equity**

## u Based upon
a logical extension of the band of investment technique

## u Reasons
that the return overall yielded by the expected annual income does not need to
be as high if the annual cash flows are used to pay down the debt since the
investor will receive the debt reduction cash flow when the property is sold.

## u Further
reasons that the annual return overall might be lower or higher if the property
appreciates or depreciates during the holding period since that appreciation or
depreciation cash flow is realized when the property is sold.

**Steps in computing the Return Overall with Ellwood**

## u Ellwood
begins with the rate of return demanded by the typical investor. This is usually determined through
interviews of typical investors.

## u Next the
annual impact of debt financing is computed.

### u Includes
impact of leverage

### u Includes
impact of debt amortization during holding period

## u Finally the
annual impact of expected appreciation or depreciation is computed.

**Computing the annual impact of debt financing**

## u Basic
formula: m(y_{e} - R_{m} + p _{*} a_{n})
where:

### u m = the percentage loan

### u y_{e}
- R_{m} = the difference between what the investor expects to earn (y_{e})
and what the lender is charging (R_{m}).

### u p = the
percentage of the loan paid off during the holding period

### u a_{n}
= annualizer (a factor which converts a
future value into an annual percentage
This is known as a sinking fund factor.)

**Calculation of p**

## u Simply
begin with 100% or 1 as the PV and calculate the percentage mortgage payment
just as any mortgage payment is calculated.

## u From the
original term of the loan, subtract the holding period and enter as N. (If there is more than one payment per year,
remember that the number of years must be multiplied by the payments per year
before entering as N.

## u Solve for
the percentage of the original balance remaining by recomputing PV.

## u Finally,
subtract the percentage remaining from 100% to determine the percentage paid
off.

**Calculation of a**_{n}

## u The
annualizer is the annual percentage of the whole necessary to invest to
accumulate that amount in the future.
It is the payment necessary to accumulate a future value.

## u Simply
enter 100% or 1 into FV.

## u Enter the number
of years into N. (Annualizers assume
only one payment per year.)

## u Enter the *investor’s*
desired rate of return (y_{e})

## u Solve for
payment. This is the annualizer.

**Computing the annual impact of appreciation or depreciation**

## u First the
expected appreciation or depreciation in the sales price (∆_{overall}) must be
determined as a percentage change in the value of the property at the time of
the valuation until the end of the expected holding period.

## u This is
usually estimated based upon percentage appreciation or depreciation of
comparable properties unless the market is not expected to react as it had in
the past.

## u This
percentage is then multiplied by the annualizer (a_{n}) to convert it
to an annual impact.

**The Complete Ellwood Formulation**

_{u
}The investor’s desired rate of return = y_{e}

## u The debt
financing component =

m(y_{e} - R_{m} + p _{*} a_{n})

## u The
appreciation/depreciation component = ∆_{overall }_{*}
a_{n}

_{u
}The entire formula is:

R_{o }= y_{e} - m(y_{e}
- R_{m} + p _{*} a_{n}) - ∆_{overall }_{*} a_{n}

**Example Ellwood problem**

## u What is the
indicated overall rate if an investor puts down 20%, requires a 15% rate of
return, and the bank charges 9% on the 30 year, monthly payment mortgage? The property is expected to depreciate 20%
over the 10 year holding period.

## u Calculate
each of the following first:

### u m

### u a_{n}

### u R_{m}

### u p

**Calculation of Debt Financing Component**

## u m = 100% -
20% investor’s equity = 80%

## u R_{m }=
.0966 (P/YR =12; I/YR=9; PV=1; N=360 (30 cream N); solve for PMT; _{*}
12)

## u p = .1057
(Original term = 30 years - 10 year holding period = 20 years remaining; 20
cream key N; solve for PV = .8943; 1 - .8942 = .1057)

## u a_{n} = .0493
(P/YR = 1; I/YR = 15; n = 10; FV = 1; solve for PMT)

## u m(y_{e}
- R_{m} + p _{*} a_{n}) = .8 (.15 - .0966 + .1057 _{*}
.0493) = .0469

**Final Calculation of Ellwood**

## u Appreciation/depreciation
component = ∆_{overall }_{*} a_{n }= -.2 _{* }_{ }.0493 = .0099

## u Thus: R_{o
}= y_{e} - m(y_{e}
- R_{m} + p _{*} a_{n}) - ∆_{overall }_{*} a_{n } = .15
- .8
(.15 - .0966 + .1057 _{*} .0493)
- (-.2 _{* }.0493)

## u .15 - .0469
+ .0099 = .1130

**Underwriter’s Method**

## u Uses market
financing terms to estimate R_{o}

## u Uses a
market implied R_{e}

## u Assumes
that investors are satisfied with financing properties at the market rates and
that the market prices the properties in accordance with the investor’s equity
requirement and the available market financing

**Underwriter’s Method Formula**

## u R_{o} = DSCR * R_{m} * m

## u Where:

### u DSCR = Debt
Service Coverage Ratio

DSCR= NOI ¸ ADS; (ADS = Annual Debt Service)

### u R_{m }=
Mortgage Capitalization Rate

### u m =
loan-to-value ratio

**Underwriter’s Method Example**

## u Market
research indicates that the appropriate financing terms for the subject
property are a DSCR of 1.3, 7.5% for 15 years, monthly payments, 70% LTV (m)

## u R_{m}
= .1112

## u R_{o}
= 1.3 * .1112 * .7 = .1012