Appraisal Formula

SUMMARY OF APPRAISAL FORMULAA) COMPOUNDED INTEREST

1. Future Value of Single Investment

FV = P (1+ r)n

Where:

FV - Future Value

P - Principal

r - interest rate

n - no. of compounding periods

Example:

Land purchased for P50,000 cash appreciates at the rate of 15% compounded annually. How

much is the land worth after 5 years? Disregard taxes, insurance and selling expenses.

Solution

FV = P (1+ r)n

FV = P 50,000 x (1 + .15)5

FV = P 100,567.90 say P 100,568

2. Future Value of Annuity

FVA = A [(1+ r)n - 1 ] r

FVA - Future Value of Annuity

A - Annual Uniform Payment

r - interest rate

n - no. of years

Example:

How much will a yearly investment of P 150,000 be after 10 years if the investor is satisfied

with a return of 12%?

Solution

FVA = A [(1+ r)n - 1 ] r

FVA = 150,000 [(1+ .12)10 - 1 ]

FVA = P 2,632,310

3. Present Value of Single Investment (Discounting or Reversion Formula)

PV = FV (1+ r)-n

Where:

PV - Present Value

FV - Future Value

r - interest rate

n - no. of compounding periods

0.12

ACEBUREAU Appraisal; ACEBU Center for Real Estate (ACRE)

Example:

What is the reversion value of a property in 2 years with an estimated market value of P12, 540,000

an interest rate of 10% per year?

Solution

PV = P (1+ r)-n

PV = P12,540,000 * (1+ .10)-2

PV = P 10,363,636.00

4. Present Value of Annuity

PVA = A [1 - (1+ r)-n ]

r

PVA - Present Value of Annuity

A - Annual Uniform Payment

r - interest rate

n - no. of years

Example:

If a property is expected to produce a yearly income of P 3,600,000 for 8 years. What is the

present value of the yearly income today if discounted at a rate of 8%.

Solution

PVA = A [1 - (1+ r)-n ]

r

PVA = 3,600,000 [1 - (1+ .08)-8

]

PVA = P 20,687,900.20

5. Amortization Formula

MA - Monthly Amortization

P - Principal Amount (Loan Amount)

r - interest rate

n - no. of months

Example:

Mr. A purchases a house and lot thru installment basis. The contract price is P 3,500,000 with a

required downpayment of 20%. Compute the monthly amortization if the loan interest rate

per year is 8% for 5 years.

M.A. = P x ( r )

1 - (1 + r)-n

0.08

M.A. = P xr

[1 - (1+ r)-n ]


Where:

P = 3,500,000 - (3,500,000 x 20%)

P = 2,800,000

n = 5yrs x 12 = 60 months

r = .08/12 = 0.006667

M.A. = P 2,800,000 x ( .006667 )

M.A. = P 56,774.44

6. Income Approach (Direct Capitalization)

Income I

Rate R

Example:

What is the value of a property consisting of land and building with an annual net operating

income of P330,000 and with an over-all capitalization rate of 12.50% is

I

R

330,000

0.125

V = P 2,640,000

7. Gross Rent Multiplier or Gross Income Multiplier (GRM or GIM)

Example 1:

Compute the Gross Rent Multiplier (GRM) of the property that rented for P 250,000 per year

and was sold a month ago at P 8,500,000.

Sales Price

Gross Rent

P 8,500,000

P 250,000

GRM = 34

1 - (1.006667)-60

Value = V =

V =

V =

GRM =

GRM =

GRM =

Sales Price or Value

Gross Rent


Example 2:

Compute the indicated value of the property that rented for P 750 per month, using a month

monthly Gross Rent Multiplier (GRM) of 100, if the expenses attribute to the property were

115 per month.

Value = GRM x Gross Rent

Value = 100 x P 750

Value = P 75,000

7. Land Residual Technique

Step 1 Compute Net Operating Income (NOI) or Net Income Before Recapture (NIBR)

if Not Given

Potential Gross Income

Less: Allowance for Vacancy & Bad debts

Equals: Effective Gross Income

Add: Other Income or Miscellaneous Income

Less: Operating Expense (Admin. Expense, RPT, Depreciation)

Equals: Net Operating Income (NOI)

Less: Mortgage Payment (Debt Servicing)

Equals: Net Income Before Tax

Step 2 Analyze Income

a) Income due to Building = Building Value x Over-all rate

Where: Over-all rate = Interest rate (Land) + Recapture Rate

Recapture rate = 1/Remaining Economic Life

b) Income due to Land = NOI - Income due to Building

Step 3 Compute Land Value

Value of Land= Income due to Land x Interest Rate (Land only)

Step 4 Compute Total Property Value (TPV)

TPV = Land Value + Building Value

Example

Assume the following data:

Gross Income: P 2,350,000/year

Allowance for Vacancy & Bad debts: 5% of Gross Income/year

Operating Expense: P 220,000/year

Building Value: P 15.0M

Interest rate on Land: 8%

Economic Life of building: 40 years

Using Land Residual Technique, compute the Value of the Property:

GRM = Value or Sales Price

Gross Rent

- If Building Value is given; Land Value is Unknown


a) Compute NOI

Less: Allowance of Vac. (5% of P 2,350,000)

Less: Operating Exp.

NOI

b) Analyze Income

Income due to Bldg. = Building Value x Over-all Rate

= P 15,000,000 x (Interest Rate on Land + Recapture Rate)

Recapture Rate = 1/40 = 2.5%

= P 15,000,000 x (8% + 2.5%)

Income (Bldg) = P 1,575,000

Income due to Land = NOI - Income due to Bldg.

Income (Land) = P 2,012,500 - P 1,575,000

= P 437,500

c) Compute Value of Land

Value of Land= Income due to Land / Rate (Interest on Land only)

= 5,468,750.00

d) Compute Total Property Value

TPV = Value of Land + Value of Building

= P 5,468,750 + 15,000,000

TPV = 20,468,750.00

8. Building Residual Technique

Step 1 Compute Net Operating Income (NOI) or Net Income Before Recapture (NIBR)

if Not Given

Gross Income

Less: Allowance for Vacancy & Bad debts

Equals: Effective Gross Income

Add: Other Income or Miscellaneous Income

Less: Operating Expense

Equals: Net Operating Income (NOI)

Step 2 Analyze Income

a) Income due to Land = Land Value x Interest rate (Land only)



b) Income due to Building = NOI - Income due to Land

- If Land Value is given; Building Value is Unknown

2,350,000.00

(117,500.00)

2,232,500.00

(220,000.00)

2,012,500.00


Step 3 Compute Building Value

Value of Building= Income due to Bldg. x Over-all Rate




TPV = Land Value + Building Value

Example

Assume the following data:

Net Operating Income: P 2,350,000/year

Land Value: P 5.0M

Interest rate on Land: 8%

Economic Life of building: 40 years

Using Building Residual Technique, compute the Property Value:

a) Analyze Income

Income due to Land = Land Value x Interest rate (Land only)

= P 5,000,000 x 8%

Income (Land) = P 400,000

Income due to Bldg.= NOI - Income due to Land

Income (Bldg.) = P 2,350,000 - P 400,000

= P 1,950,000

c) Compute Value of Building

Value of Bldg.= Income due to Bldg./ Over-all Rate (Interest on land + Recapture rate)

= P 1,950,000 / (8% + 2.5%) Recapture rate = 1/Rem. Economic Life

= 18,571,428.57 = 1/40

d) Compute Total Property Value = 2.5%

TPV = Value of Land + Value of Building

= P 5,000,000 + 18,571,428.57

TPV = 23,571,428.57

9. Basic Appraisal Mathematics s

a) Area of Square = s x s s

b) Area of Rectangle= L x W

L

c) Area of Circle= π r2

r

W


b1

d) Area of Trapezoid = (b1 + b2) x h h

2

b2

e) Area of Triangle = 1/2 (b x h)

h

b

f) Volume of cube = S x S x S

S

S

g) Volume of parellelepiped = L x W x H

H

W

L

h) Volume of Cylinder = π R2 x H

i) Volume of Pyramid = B2 x H


10. Basic Statistics

Statistics - is the study of how to collect, organize, analyze and interpret numerical information.

Variable - is a quantity that may assume any set of value. (ex. Monthly income, volume, price,etc.)

Constant – is a quantity that does not change its value (ex. 12 inches = 1 foot, 1 year = 12 months)

Ungrouped data –Raw data that are not organized in any specific way

(subject to analysis & interpretation)

Grouped data – are raw data organized into groups or categories with corresponding frequencies

(distribution)

Population – the entire collection of all possible observations of a particular characteristic of interest

(ex. grades of all students who took an entrance examination)

Sample – is a representative set of observations that reflects the characteristics of the whole, that is,

the population from which it is taken.

Parameter – is any statistical characteristic of a population, for example, the Mean and Standard

Deviation.

Measures of Central Tendency

- Statistical tools designed to give information concerning the average, or typical score of a large

number of scores.

Three Methods of measuring central tendency:

a)The Mean – arithmetic average of all scores (M=SX/n)

M – Mean

S - Summation of X

X – raw score

n – number of observations

Three Methods of measuring central tendency:

b) The Median (Mdn) - the exact midpoint of any distribution, or the point that separates the

upper half from the lower half of the distribution.

c) The Mode (Mo) - Is the measure that determines which score occurs number of times.

Frequently appearing score in the distribution.

Example:

X

120

118

115 Median = (115 + 114)/2 = 114.5

114 Mode = 114

114

112

SX 693; n = 6

Mean (simple) = SX/n

= 693/6

= 115.50


Weighted Mean – incorporates into the formula the weight of each term.

Example:

An exam was given for 3 subjects with corresponding weights-

Grade (X) Weight (W)

Exam No. 1 85 20%

Exam No. 2 90 30%

Exam No. 3 50%80 50%

100%

Weighted Mean (Mw) = 85(.20) + 90(.30) + 80(.50)

= 84

Three Methods of measuring variability (Measure of Dispersion):

a) The Range – the difference between the highest & lowest scores.

Example: If the highest score is 140; lowest is 60, range is (140 – 60) = 80

b) The Standard Deviation (SD) – Is the absolute heart & soul of variability concept. Takes into

account all scores in a distribution.

It measures how much all scores deviate or vary from the Mean (Average)

2 Methods in Computing Standard Deviation:

1. Deviation Method

2. Computational Method (Long process)

Deviation Method

Formula; SD = √Sx2/n MAD = SX/n

SD- Standard deviation

X - Raw score

M - Mean

x - deviation score

n - number of scores

SX - summation of x = (X-M)

Raw Score (X) Deviation Score x=(X-M) Absolute Dev. x2

10 10 - 6 = 4 4 16

8 8 - 6 = 2 2 4

6 6 - 6 = 0 0 0

4 4 - 6 = -2 2 4

2 2 - 6 = -4 4 16

SX 30 12 40

Mean = SX/n

M= 30/5 = 6 SD = 40 MAD = S Abs. x

5 n

SD = 2.828427 MAD = 12/5

Range = Highest - Lowest Score MAD = 2.4

= 10 - 2

Range = 8


11. Rawland Valuation (Subdivision Development Approach)

Step 1 Analyze Gross Income

Gross Income = Total Cash Price

Total Cash Price = Selling Price of Developed Lot/Sq.M. x Saleable Area

Where:

Saleable area = 70% x Gross Land Area

Step 2 Analyze Expenses

a) Development Cost

b) Administrative Expenses

c) Sales Expenses (Brokers Commission, Advertising, etc)

d) Interest on Working Capital

e) Miscellaneous Expenses

f) Contractor's Profit

Step 3 Compute Ultimate Rawland Value (URV)

URV = Gross Income - Expenses

Step 4 Compute Rawland Value/Sq.M.

Rawland Value/Sq.M. = URV x Annuity Factor

No. of Years x Gross Area

Compute Annuity Factor (if not given):

Annuity Factor = 1 - (1+r)-n

r = interest rate

n = no. of years

Example:

Mr. A offers his 10.0 hectare rawland in Lumbia, Cagayan de Oro City. Prices of developed lots in

Lumbia is at P 3,500/sq.m. Subdivision developers disclose a development cost of P 800/sq.m.

of the Gross Area; Admin., Sales & other expenses is estimated at P 21,000,000. At how much

should you buy the property given a 5 year development & sales period of 5 years?

Annuity based on a 12% interest rate is 3.60477.

a) Analyze Gross Income

Total Cash Price = Selling Price of Developed Lot/Sq.M. x Saleable Area

TCP = P 3,500/Sq.M. x 10 has x 10,000Sq.M./hectare x 70%

TCP = Php171,500,000.00

b) Analyze Expenses

Total Expense = Development Cost + Other Expenses

Total Expense = Php101,000,000.00

c) Ultimate Rawland Value = Gross Income - Total Expenses

= Php70,500,000.00

d) Compute Rawland Value/Sq.M.

Rawland Value/Sq.M. = URV x Annuity Factor

No. of Years x Gross Area

RV/Sq.M. = Php171,500,000.00 x 3.60477

5 x 100,000

RV/Sq.M. =

r

508.27 or P 510/Sq.M.


12. Appraisal of Machinery/Equipment

Estimating Reproduction Cost New (RCN) by trending of indexing (based on original acquisition cost.x Trending Factor

a)For Imported Machinery

RCN = Original Cost x Current Exchange Rate x Trend Factor

Exchange Rate at Acquisition date

Trend Factor – Kemper International Replacement Value Cost Trend

b) For Locally Manufactured Machinery

RCN = Original Cost x Local Index (from NEDA)

c) Appraisal of Machinery for Tax Purposes

RCNLD = OC x FC2 x PI x REL

FC1 EL

where:

RCNLD – Reproduction Cost New less Depreciation (DRC)

OC – Original/Acquisition Cost

FC1 – Exchange Rate (Acquisition)

FC2 – Exchange Rate (Assessment Date)

EL – Economic Life

REL – Remaining Economic Life

PI – Price Index (if available only)

Example A commercial machinery from USA was acquired, installed and in operation in

February 1999 at total original cost of $10,000,000. Re-appraisal was made in

December 2003.

Dollar Exchange Rate at the time of acquisition: Php 39.0890 to $1.00

Dollar Exchange Rate at the time of appraisal: Php 54.2033 to $1.00

Estimated Economic Life: 30 years

To compute:

RCNLD = OC x FC2 x PI x REL

FC1 EL

RCNLD = $10,000,000 x P54.2033 x 1.0 x 26/30

P39.0890

RCNLD = Php 12,018,065.00

ASSESSED VALUE: RCNLD x Assessment Level

= Php 12,018,065.00 x 80%

= Php 9,614,452.00


13. 4-3-2-1 Rule

Lot D Value of Lot D = 10% x Total Value of Property

Lot C Value of Lot C = 20% x Total Value of Property

Lot B Value of Lot B = 30% x Total Value of Property

Lot A Value of Lot A = 40% x Total Value of Property

14. Market Data Approach

SUBJECT COMPARABLE 1

VALUE ? P xxxx.xx

Adjustment(s)

Time (if applicable) +

Location (+/-)

Size (+/-)

Shape (+/-)

Topography (+/-)

Terrain (+/-)

Corner Influence (+/-)

Adjusted Value

Weight X%

Indicated Value = (Price of Comparable - Adjustments) x Weight

If Comparable is SUPERIOR

COMPARABLE (Subtract Adjustment Factor)

If Comparable is INFERIOR

COMPARABLE (Add Adjustment Factor)

14. Cost Approach

Step 1 Value Land by Market Data Approach

Step 2 Compute Replacement Cost, New (RCN)

RCN = Cost of Replacement/Sq.M. x Floor Area (in Sq.M.)

Less: a) Physical Deterioration , SLM = Actual Age / Economic Life

b) Functional Obsolescence (if any)

c) Economic Obsolescence (if any)

Equals: Depreciated Replacement Cost (DRC)


TPV = Land Value + Depreciated Replacement Cost (Building)

ROAD

COMPARABLE 2

P yyyy.yy

SUBJECT

( - )

( + )

+

(+/-)

(+/-)

(+/-)

(+/-)

(+/-)

(+/-)

(+/-)

Y%

(+/-)

(+/-)

(+/-)

100% - X% -Y%

COMPARABLE 2

P zzzz.zz

+

(+/-)

(+/-)


Example

Subject Property House and Lot

Location Pine Street, P.N. Roa Valley Subd., Cagayan de Oro City

Land Area (Sq.M.) 182

Building Single-storey residential house; High cost; Year built - 2004, well-maintained

Floor Area (Sq.M.) 146

VALUATION BY COST APPROACH per Sq.M.

LAND: 182 Sq.M. @ Php1,500

per Sq.M.

IMPROVEMENT: (Residential Building)

Reproduction Cost, New 146 Sq.M. @ Php15,000

a) Physical Deterioration - Straight Line Method (SLM) - 6/40 x 100%

b) Functional Obsolesence - -5%

c) Economic Obsolesence - 0%

Depreciated Replacement Cost (DRC)

TOTAL PROPERTY VALUE

2,027,775.00

2,300,775.00

MARKET VALUE

273,000.00

2,190,000

328,500.00

2,134,500.00

106,725.00

0.00

2,027,775.00


Appraisal Formula

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