**Chapter 16: Income-capitalization
Methods**

**Capitalization of Site Income**

## u Straight
capitalization--assumes site value remains constant during the holding period.

## u Recapture
adjusted capitalization--assumes site value increases or decreases during the
holding period.

**Capitalization of Site Income:
Strait-line Example**

## u Strait-line
capitalization: Assume a parking lot
has an annual income of $5,000 annually.
Assume also that the appropriate capitalization rate is 10%.

## u V_{Land } = I_{Land } ÷ R_{Land
}= $5,000 ÷ .10 = $50,000

**Capitalization of Site Income: Recapture Adjusted Example**

## u Sinking
fund capitalization: Assume a parking
lot has an annual income of $5,000 annually.
The property is expected to increase in value by 10% over the ten year
holding period. Assume also that the
appropriate capitalization rate is 10%.

_{u
}V_{Land } = I_{Land }÷ R_{Land}

_{u
}R_{Land} = y_{Land} - ∆_{overall *}
a_{n }

## u V_{Land } =$5,000÷ (.10-.1_{*} .062745) =
$53,347

**Capitalization of Building Income**

## u Strait-line
capitalization--assumes the decline in the income produced by the building is a
constant percentage over its useful life. (usually not realistic.)

## u Annuity
capitalization-- assumes the income produced by the building is relatively
constant over its useful life. R_{Building} = a_{n}

_{u
}Sinking fund capitalization-- assumes the slower
decline than strait-line in the income produced by the building over its useful
life. (still not very realistic.) R_{Building} > a_{n}

**Capitalization of Building Income Strait-line Example**

## u Assume a
building has an annual income of $25,000.
The building is expected to have a useful life of 25 years. Assume also that the appropriate discount rate is 10%.

## u A building
that looses 100% of its value in 25 years, looses 1 ÷ 25 or 4% per year.

## u Therefore
the R_{Building} = 10% + 4% =14%

## u V_{Building
} = I_{Building } ÷ R_{Building
}= $25,000 ÷ 14% =
$178,500

**Capitalization of Building Income Annuity Example**

## u Assume a
building has an annual income of $25,000.
The building is expected to have a useful life of 25 years. Assume also that the appropriate discount rate is 10%.

## u R_{Building}
= y_{Land} - ∆_{overall *}
a_{n}

## u Therefore
the R_{Building} = 10% -(-1)_{ *} .010168 =

## u V_{Building
} = I_{Building } ∆ R_{Building
}= $25,000 ÷ .110168 = $226,926

**Direct capitalization**

## u Capitalizes
the value of the building and land at the same time.

_{u
}Should only be used if the appraiser has ample
evidence for the calculation of R_{overall }

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

## u Assume a
property has an annual income of $30,000 and the appropriate discount rate is
10.5%.

## u V_{Overall
} = $30,000 ÷ .105 =
$285,714

**Residual techniques**

## u Site
residual technique

## u Building
residual technique

## u Property
residual technique

## n Basic
Relationships

_{u
}V_{Overall
} = V_{Land }+ V_{Building
}

_{u
}I_{Overall
} = I_{Land }+ I_{Building}

_{u
}I_{Land }= V_{Land * }R_{Land}

_{u
}I_{Building
}= V_{Building * }R_{Building}

_{u
}V_{Land
} = I_{Land } ÷
R_{Land}

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

_{u
}R_{Land }= Return on Investment_{}

### u R_{Building} = R_{Land }+
1 ÷ (Useful life of building)

**Land Residual Problem**

## u Given the
following for a proposed property:

### u Return on
Land Investment (R_{L}) = 10%

### u Useful life
of building = 25 years

### u Building
Cost = $300,000

### u Expected
NOI = $65,000, What is the Value?

## u R_{Building}
= R_{Land }+ 1 ÷ (Useful life of building)

= 10% + 1 ÷ 25 = 10% + 4%
= 14%

_{u
}I_{Building }=V_{Building * }R_{Building
}= 300,000_{*}14%= 42,000_{}

## u
I_{Land}
= I_{Overall } - I_{Building }= 65,000 -
42,000 = 23,000

## u
V_{Land
} = I_{Land } ÷ R_{Land }= $23,000 ÷
10% = $230,000

## u
V_{Overall
}=V_{Land}+V_{Building }=230,000 +300,000 = $530,000

**Building Residual Problem**

## u Given the
following for a proposed property:

### u Return on
Land Investment (R_{L}) = 10%

### u Useful life
of building = 40 years

### u Land Cost =
$100,000

### u Expected
NOI = $35,000, What is the Value?

## u R_{Building}
= R_{Land }+ 1 ÷ (Useful life of building)

= 10% + 1 ÷ 40 = 10% +
2.5% = 12.5%

_{u
}I_{Land }=V_{Land * }R_{Land }=
100,000_{*}10%= 10,000_{}

## u
I_{Building}
= I_{Overall } - I_{Land}
=
35,000 - 10,000 = 25,000

## u
V_{Building
} = I_{Building } ÷ R_{Building} =
$25,000÷12.5% = $200,000

## u
V_{Overall
}=V_{Land}+V_{Building }=100,000 +200,000 = $300,000

**Property Residual Technique**

## u The value
of an income producing property is the present value of the income stream plus
the present value of the sales price at end useful life.

_{u
}V_{Overall }=V_{Income during useful life}+V_{Reversion}

## u Research
indicates that a property is expected to generate $20,000 per year income
during its 25 year useful life, that the property should sell for $90,000 at
the end of that life, and that the appropriate capitalization rate is 10%.

## u V_{Overall
}= PVA ($20,000, 10%, 25years)

+ PV_{Lump Sum}
($90,000, 25 years, 10%)

## u V_{Overall
}= $181,541 + $8,307 = $189,848

**Mortgage-equity Capitalization**

## u Divides the
property income into two streams:
Income to the mortgage and Income to the owner.

_{u
}I_{Overall } = I_{Mortgage}+ I_{Owner}

_{u
}V_{Overall }=V_{Mortgage}+V_{Equity}

## u V_{Mortgage}
may be determined by the DSCR

### u DSCR = NOI ÷ Annual Debt Service

### u Therefore
ADS = NOI ÷ DSCR

### u Knowing ADS
and market financing terms, the appraiser can solve for V_{Mortgage} :
Known--P/YR, I/YR, Number of years; Compute PV

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

**Mortgage-equity Capitalization Example**

## u Assume a
DSCR of 1.39, market financing of 9% for 20 years paid monthly, an annual property
income of $5,000, and an equity capitalization rate of 12%.

## u ADS = NOI ÷ DSCR =
$5,000 ÷ 1.39 =
$3,597 (MDS=3597 ÷ 12 =
299.75)

## u V_{Mortgage}
= PVA (299.75, 9%, 20 years) = $33,315.70

## u I_{Equity}
= $5,000 - $3,597 = $1403

## u V_{Equity}=
I_{Equity} ÷ R_{Equity
}= $1,403 ÷ .12 =
$11,692

## u V_{Overall
}=V_{Mortgage}+ V_{Equity}= $33,316 + $11,692 = $45,008

**Capitalization of Cash Flows**

## u Also called
the Discounted Cash Flow Technique

_{n}

## u V_{Overall
}= ∑ __BFCF___{t} + __ PR___{n} _{.}

t =1 (1+y_{o})^{t }(1+y_{o})^{n}

### u where: BFCF_{t} is the NOI + Reserves in year t

### u PR_{n}=
proverty reversion (sales price) in year n

### u y_{o}
= appropriate discount rate

_{n}

## u V_{equity
}= ∑ __BTCF___{t} + __ ER___{n} _{.}

t =1 (1+y_{e})^{t }(1+y_{e})^{n}

#### u where: BTCF_{t} is the BFCF - ADS in year t

#### u ER_{n}= equity reversion (PR - Mtg. Bal) in
year n

#### u y_{e} = equity yield rate