Chapter 16: Income-capitalization Methods

Capitalization of site income

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

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

Capitalization of Site Income: Strait-line Example

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

VLand = ILand ¸ RLand = \$5,000 ¸ .10 = \$50,000

Capitalization of Site Income: Recapture Adjusted Example

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%.

VLand = ILand ¸ RLand

RLand = yLand - Doverall * an

VLand =\$5,000¸(.10-.1* .062745) = \$53,347

Capitalization of Building Income

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

Annuity capitalization-- assumes the income produced by the building is relatively constant over its useful life. RBuilding = an

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.) RBuilding > an

Capitalization of Building Income Strait-line Example

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%.

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

Therefore the RBuilding = 10% + 4% =14%

VBuilding = IBuilding ¸ RBuilding = \$25,000 ¸ 14% = \$178,500

Capitalization of Building Income Annuity Example

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%.

RBuilding = yLand - Doverall * an

Therefore the RBuilding = 10% -(-1) * .010168 =

VBuilding = IBuilding ¸ RBuilding = \$25,000 ¸ .110168 = \$226,926

Direct capitalization

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

Should only be used if the appraiser has ample evidence for the calculation of Roverall

VOverall = IOverall ¸ ROverall

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

VOverall = \$30,000 ¸ .105 = \$285,714

Residual Techniques

Site residual technique

Building residual technique

Property residual technique

Basic Relationships

VOverall = VLand + VBuilding

IOverall = ILand + IBuilding

ILand = VLand * RLand

IBuilding = VBuilding * RBuilding

VLand = ILand ¸ RLand

VBuilding = IBuilding ¸ RBuilding

RLand = Return on Investment

RBuilding = RLand + 1 ¸ (Useful life of building)

Land Residual Problem

Given the following for a proposed property:

Return on Land Investment (RL) = 10%

Useful life of building = 25 years

Building Cost = \$300,000

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

RBuilding = RLand + 1 ¸ (Useful life of building)
= 10% + 1
¸ 25 = 10% + 4% = 14%

IBuilding =VBuilding * RBuilding = 300,000*14%= 42,000

ILand = IOverall - IBuilding = 65,000 - 42,000 = 23,000

VLand = ILand ¸ RLand = \$23,000 ¸ 10% = \$230,000

VOverall =VLand+VBuilding =230,000 +300,000 = \$530,000

Building Residual Problem

Given the following for a proposed property:

Return on Land Investment (RL) = 10%

Useful life of building = 40 years

Land Cost = \$100,000

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

RBuilding = RLand + 1 ¸ (Useful life of building)
= 10% + 1
¸ 40 = 10% + 2.5% = 12.5%

ILand =VLand * RLand = 100,000*10%= 10,000

IBuilding = IOverall - ILand = 35,000 - 10,000 = 25,000

VBuilding = IBuilding ¸ RBuilding = \$25,000¸12.5% = \$200,000

VOverall =VLand+VBuilding =100,000 +200,000 = \$300,000

Property Residual Technique

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.

VOverall =VIncome during useful life+VReversion

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%.

VOverall = PVA (\$20,000, 10%, 25years) + PVLump Sum (\$90,000, 25 years, 10%)

VOverall = \$181,541 + \$8,307 = \$189,848

Mortgage-equity Capitalization

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

IOverall = IMortgage+ IOwner

VOverall =VMortgage+VEquity

VMortgage may be determined by the DSCR

DSCR = NOI ¸ Annual Debt Service

Therefore ADS = NOI ¸ DSCR

Knowing ADS and market financing terms, the appraiser can solve for VMortgage : Known--P/YR, I/YR, Number of years; Compute PV

VEquity = IEquity ¸ REquity

Mortgage-equity Capitalization Example

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%.

ADS = NOI ¸ DSCR = \$5,000 ¸ 1.39 = \$3,597 (MDS=3597 ¸ 12 = 299.75)

VMortgage = PVA (299.75, 9%, 20 years) = \$33,315.70

IEquity = \$5,000 - \$3,597 = \$1403

VEquity= IEquity ¸ REquity = \$1,403 ¸ .12 = \$11,692

VOverall =VMortgage+VEquity= \$33,316 + \$11,692 = \$45,008

Capitalization of Cash Flows

Also called the Discounted Cash Flow Technique

n

VOverall = S BFCFt + PRn .
t =1 (1+yo)t (1+yo)n

where: BFCFt is the NOI + Reserves in year t

PRn= proverty reversion (sales price) in year n

yo = appropriate discount rate
n

Vequity = S BTCFt + ERn .
t =1 (1+ye)t (1+ye)n

where: BTCFt is the BFCF - ADS in year t

ERn= equity reversion (PR - Mtg. Bal) in year n

ye = equity yeild rate