*Chapter 15
Capitalization rates*

*Theoretical basis for income
capitalization*

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

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*

Discount
rates--Return *on* Investment

Plus
Recapture rate--Return *of* Investment

R_{overall}
= y_{o} - D_{overall *} a_{n
}where:

R_{overall}
= Capitalization Rate

y_{o}
= Discount Rate for property

D_{overall *} a_{n} = Recapture Rate

D_{overall} = Expected change in value during holding period.

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

*Types of Discount Rates*

y =
General symbol for Return *on* Investment

y_{o}
= Discount rate for overall property

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

y_{e}
= Discount rate on equity

y_{L}
= Discount rate on land

y_{B}
= Discount rate on building

*Components of Discount Rates*

Pure cost
of money

Base
Rate

Inflation
Premium

Liquidity
Premium

Risk
Premium

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

*Estimating Discount Rates*

Direct
market extraction

Abstraction
from Gross Income Multiplier

Mortgage
Equity Analysis

*Direct Market Extraction*

Market
research has discovered the following three comparable sales:

CompA CompB Comp
C

Sale
Price 200,000 210,000 150,000

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

Net
Income 24,400 22,470 16, 350

Useful
life 25 years 50 years 40 years

Recapture
% 4%
2% 2.5%

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

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

Indicated
R_{o} 9.0% 9.1%
8.9%

*Recapture Rates*

Strait-line
Rates

Assumes
recapture occurs at the same rate each year.

Computed
by 1 ¸ useful life of improvements

Sinking
Fund Rates

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

Computed
by computing the appropriate sinking fund factor.

*Types of capitalization rates*

Overall
capitalization rate

Equity
capitalization rate

Mortgage
(debt) capitalization rate

Land
capitalization rate

*Methods of estimating capitalization rates*

Direct
Market Extraction

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

Return
on vs Return of Building Capitalization Rates

Band of
investment analysis (Simple mortgage-equity analysis)

The
Ellwood formulation

Underwriters
method

*Direct Market Extraction*

Easiest
and most reliable if data is available

Based
upon simple valuation formula:

V_{overall
}= I_{overall }¸ R_{overall }

Steps:

Examine
sales of comparable properties

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

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)*

Base
rate + Inflation = Treasury yield

Base
rate + Inflation + Liquidity = CD rate

Use of
bracketing certainty equivalents

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

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

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*

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

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)

Return
overall for an investment is then equal to the return ** on**
investment plus the return

*Band of Investment*

Weights
the investors position with the lenders

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

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*

R_{m}=
R_{mortgage}= Total amount of payments in a year ¸ Loan Amount

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.

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

R_{m}=
.0966

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

Mortgage
percentage = 100% - equity percentage

100% -
20% = 80%

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

*Solution for Band of Investment*

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

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

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

*Ellwood Mortgage Equity*

Based
upon a logical extention of the band of investment technique

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.

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*

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

Next
the annual impact of debt financing is computed.

Includes
impact of leverage

Includes
impact of debt amortization during holding period

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

*Computing the annual impact of debt
financing*

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

m = the
percentage loan

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

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

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*

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

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.

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

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

*Calculation of a _{n}*

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.

Simply
enter 100% or 1 into FV.

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

Enter
the ** investor’s** desired rate of return (y

Solve for
payment. This is the annualizer.

*Computing the annual impact of
appreciation or depreciation*

First
the expected appreciation or depreciation in the sales price (D_{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.

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.

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

*The Complete Ellwood Formulation*

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

The
debt financing component = m(y_{e} - R_{m} + p _{*} a_{n})

The
appreciation/depreciation component = D_{overall }_{*} a_{n }

The
entire formula is: R_{o }= y_{e} - m(y_{e} - R_{m}
+ p _{*} a_{n}) - D_{overall *} a_{n}

*Example Ellwood problem*

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.

Calculate
each of the following first:

m

a_{n
}

R_{m
}

p

*Calculation of Debt financing component*

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

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

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

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

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

*Final Calculation of Ellwood*

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

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

.15 -
.0469 + .0099 = .1130