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 125 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 = $25,00012.5% = $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