textbook summary License Math Unit 1 Summary
Basic Math in Real Estate Converting fractions to decimals
Some real estate math problems will contain fractions. While it is possible to solve the problem using fractions, it’s typically easier to convert the fraction to a decimal and then solve for the answer.
A fraction contains two numbers. The top number is the numerator; the bottom number is the denominator.
Textbook summary national practice
To convert the fraction into a decimal, divide the bottom number (numerator) into the top number (denominator).
Example:
What is ¼ as a decimal?
Converting decimals to percentages
Quickly converting decimals to percentages and vice-versa is a very important skill to learn as many student errors are caused by incorrectly converting percentages to decimals.
Converting a decimal to percentage: Formula:
Decimal number x 100 = Percentage number
Example: 0.022 x 100 = 2.2%
Converting a percentage to a decimal:
Formula:
Helpful hint!
An easy way to convert a percentage to a decimal is to simply move the decimal point two spaces to the left:
If given 5% in a question, just imagine there is a decimal point between the 5 and the percent sign and move it two spaces to the left:
When using a calculator, the answer will be in a decimal and it will need to be converted back to a percentage. To convert a decimal to a percentage, move the decimal point to the right two spaces.
Multiplying by percentages Formula:
Dividing by Percentages
The T-bar Method
The “T” method is a simple method for solving math questions that uses the three keys parts of
a math question to answer the problem.
Many real estate math problems have formulas that fit into the T-bar method. This is the basic set up of the T-bar:
The math problem will always provide two of the three parts of the T-bar needed to solve the problem.
Some problems will require two T’s to solve the problem.
How does the T-bar work?
There are two ways to use the T-bar.
1. If the math problem provides the top number and either bottom number, dividethe bottom number into the top number.
2. If the math problem provides the two bottom numbers, multiply those two numbers across to get the top number.
Example: What is 25% of 200?
Area of a Square or Rectangle
Area is the measurement of a flat surface and is expressed in square feet (SF, sq/ft). So, square footage is how large a lot or parcel is (how much area it contains).
When a rectangular lot is described using its dimensions, such as “150 feet by 300 feet,” the first dimension is the width of the lot and second dimension is the depth of the lot. Depth means how far back the lot goes if one is standing in front of it.
Formula:
Area of a Rectangle or Square= Width x Depth/Length (Horizontal) or Width x Height (Vertical) Width= Area ÷ Depth/Length (Height)
Depth/Length (Height)= Area ÷ Width
T-B ar Formula: Area of a Rectangle or Square
When using the T-bar, it doesn’t matter which side you place the width and depth/length on as
long as they are always on the bottom. The square footage is always on the top of the T-bar.
Area of a Triangle
Example
What is the area of this triangle?
Steps:
6’ B x 10’ H = 60 SF / 2 = 30 SF
Area of a Trapezoid
Trapezoids are shapes like rectangles but have uneven sides.
Formula:
Area = (L + L / 2) x H
Example:
What is the area of this trapezoid?
Steps:
1. 8’ Length + 12’ Length = 20’
2. 20’ / 2 = 10’ new Length (after adding the 2 lengths, always divide the answer by 2)
3. 10’ Length x 6’ Height = 60 SF
Area of a Trapezoid
Trapezoids are shapes like rectangles but have uneven sides.
Formula:
Area = (L + L / 2) x H
Example:
What is the area of this trapezoid?
Steps:
1. 12’ Length+ 18’ Length = 30’
2. 30’ / 2 = 15’ new Length (after adding the 2 lengths, always divide the answer by 2)
3. 15’ Length x 10’ Height = 150 SF
Square Feet to Acres conversion 1 Acre = 43,560 SF
This is a very important number to remember. It is used in many real estate math calculations.
Formula:
Acres = Total SF / 43,560
T-bar Formula for SF to Acres conversion:
Example #1:
If a lot contains 152,460 total SF, how large is the lot in acres?
Steps:
152,560 / 43,560 = 3.5 Acres
Example #2:
If a man purchases 4 acres of land, how large is the lot in square feet?
Steps:
43,560 x 4 = 174,240 Total SF
Example #3:
If a man purchases a lot that measured 600’ x 363’ and costs $650 per acre, what was the total
cost of the lot?
1. Calculate the size of the lot in acres:
600’ x 363’ = 217,800 SF
2. Calculate the number of acres in the lot: 217,800 / 43,560 = 5 Acres
3. Calculate the price of the lot:
4. $650 per acre x 5 acres = $3,250 total cost of the lot
Front Footage
Front footage is the width of the lot and the expanse of road exposure that a lot offers. It is typically used to describe commercial lots and parcels.
Remember that when a rectangular lot is described using its dimensions, such as “150 feet by 300 feet,” the first dimension is the width of the lot and second dimension is the depth of the lot. Depth means how far back the lot goes if you were standing in front of it.
Example:
If the EZ Sales car lot is valued at $150,000 and is 300’ wide, how much is it worth per front
foot?
Steps:
$150,000 ÷ 300 = $500 per front foot
Gross Living Area
Gross Living Area, or GLA, the heated and cooled square footage of a structure that is measured using the outside dimensions.
When calculating GLA:
Only include areas that are heated and cooled.
Items excluded from the GLA typically include garages, carports, decks, and patios.
Example:
What is the GLA of this home?
Steps:
1. Don’t include the garage and the screened porch in the calculation because each is not heated or cooled.
2. Calculate the dimensions of the house: 60’ wide and 40’ deep. Add the depth of the
garage, 30’, and the remaining depth of the house, 10’, to get a total of 40’ in depth: 60’ width x 40’ depth = 2,400 SF GLA
Setbacks
Setbacks are the amount of space local zoning regulations require between the property line and any improvements.
The setback line is the boundary line that delineates the setback area.
To calculate the remaining area of the lot that can be built on, subtract the setbacks from the dimensions:
· The front yard and back yard setbacks are subtracted from the depth.
· The side yard setbacks are subtracted from the width.
Example:
On a residential lot that measures 70 feet by 100 feet, the side-yard building setbacks are 10 feet, the front-yard setback is 25 feet, and the rear-yard setback is 20 feet. What would the maximum possible area for a one-story structure be for this lot?
Steps:
1. Subtract the front yard and back yard setbacks from the depth: 100’ – 25’ – 20’ = 55’
new depth
2. Subtract the side yard setbacks from the width: 70’ – 10’ – 10’ = 50’ newwidth
3. Multiply new depth by new width: 55’ depth x 50’ width = 2,750 SF maximum possible area
Calculating Section Size
The Rectangular/Government Survey is type of legal description that describe a parcel of land using a set of fractions and the corresponding section, township and range numbers. While legal descriptions will be covered in detail in the National Appraisal chapter, students must learn how to calculate the size of the parcel described using this method.
A section is a square tract of land used in the Rectangular/Government Survey method.
A section:
· Is 1 mile wide and 1 mile deep.
· Contains 640 Acres
Example:
the S ½ of the SE ¼ of the SW ¼ of section 24, township 32 north,
Steps:
1. Ignore the text “section 24, township 32 north, range 18 east.” It doesn’t affect the answer.
2. Multiply all denominators together (the bottom number of the fraction), 2 x 4 x 4 = 32.
3. Divide 640 by that answer, 640 ÷ 32 = 20 acres.
Volume Measurement
Volume is the amount of something that a container can hold. For example, the amount of water required to fill a swimming pool is the volume of water that the swimming pool can hold.
Volume is expressed in CUBIC feet (not in square feet like area).
Formula:
Volume = Height (or Depth) x Width x Length
Example:
If a homeowner wishes to fill in an old, outdated swimming pool that measures 20’ in length, 10’ in width and is 6’ in depth with dirt, how much dirt will he need to buy in cubic feet?
Steps:
H (or D) x W X L
6’ x 10’ x 20’ = 1,200 Cu/Ft
Unit 2 Summary
License Math: Appraisal & Value
A comparative market analysis is one tool used to determine the listing value on a home. Adjusting Comparables rules:
· Never adjust the subject.
· If the comparable is superior to the subject, subtract value from the comparable.
· If the comparable is inferior to the subject, add value to the comparable.
If the listing home has three bathrooms and the comparable only has two, you must add the estimated value of a bathroom to the sale price of the comparable home.
Gross Rent Multiplier
The Gross Rent Multiplier is an appraisal method for single family or duplexes based on the gross monthly rent.
Gross Income Multiplier
The Gross Income Multiplier is a method of appraising income-producing properties based on a multiple of the annual gross income.
Cost Approach Formula
Cost approach is another valuation or appraisal method based on the principle of substitution; the value of a building cannot be greater than the cost of purchasing a similar site and constructing a building of equal value.
Value = Land value + (Improvements + Capital additions – Depreciation)
Depreciation
Depreciation is a decrease in value due to physical deterioration, functional or economic obsolescence. Depreciation is based upon the improvements (buildings and structures) on the land, not the land itself.
Income Capitalization Formula
The Income Capitalization Formula determines the rate of return considered to be a reasonable return on investment – given the risk of income to value of the property. It also determines an income property’s value based on the income to its rate of return.
Net Operating Income (NOI, Net Income) – does not include debt payments.
The Net Operating Income is the first step to a two-step approach in determining the value of in income producing property. It is also the pro-forma used in calculating taxes for income properties.
NOI = Potential rent – Vacancy loss + Other income – Operating expenses
*Keep your focus on the formulas and calculations rather than definitions.
Unit 3 Summary License Math: Finance
Points
Annual interest is the annual amount of money someone pays to borrow money. When calculating interest remember to convert annual payments to monthly or vice versa as the question requires, and to exclude principal payments from calculations.
An amortized loan is a debt paid off over a period of time with periodic payments. An interest- only loan pays down the interest owed, none of the principle.
Interest-only loan: Total interest = Loan amount x Rate x Term in years
Amortized loan: Total interest = (Monthly PI payment x 12 x term) Loan amount
Amortization Calculation determines how much principle will be paid down each month.
· Principle Balance x Interest Rate/12 = first month’s interest
· First month’s interest subtracted from payment equals first month’s principal
· First month’s principal subtracted from the principal balance equals the NEW principle
balance.
Repeat these steps for second and succeeding months’ interest and principal payments.
Loan Constants
A loan constant is a number expressed as a percentage or decimal that calculates a mortgage payment which would retire the loan in the expressed time allotted or term of the loan.
Loan – to – Value Ratio (LTV)
The Loan-to-Value ratio shows the relationship between the amount borrowed and the appraised, market, or assessed value of the property.
Income ratio qualification
The income ratio qualification is one method lenders use to qualify a borrower.
Monthly Principal & Interest (PI) payment = Income ratio x Monthly gross income
Debt Ratio Qualification
The debt ratio qualification is another method lenders use to qualify borrowers.
*Keep your focus on the formulas and calculations rather than definitions.
Unit 4 Summary License Math: Investment
Appreciation is an increase in value over time.
Simple appreciation
Compounded appreciation
Appreciated value = Beginning value x (1+ annual rate) x (1+ annual rate)……. for the number of
years in question
Rate of Return, Investment Value, Income
The rate of return is a percentage relationship between the investment price and the returns on that investment.
Equity
Equity is the value of real estate minus any liens against the real property. Equity = Current market value – Current loan balance(s) and any other liens. Net Income (NOI) does not include debt payments.
The net operating income is the gross potential income minus vacancy and collections and other income, minus all operating expenses.
NOI = Potential rent – Vacancy loss & collection loss + Other income – Operating expenses
Cash Flow
Cash flow is the amount of money moving in and out of a business in a month. Cash flow = (Net Operating Income – Debt service) where debt service is PI payment Basis, Adjusted Basis, and Capital Gain
Capital gains are the tax profit realized from the sale of a property.
Capital gain = Amount realized – Adjusted basis, where Amount realized = Sale price – Selling costs
Adjusted basis = Beginning basis + Capital improvements – Total depreciation
Depreciable basis = Initial property value + Capital improvements – Land value
Investment Property Income Tax Liability
Tax liability is the amount of taxes owed.
Tax liability = (NOI + Reserves – Interest expense – Depreciation) x Tax bracket
Return on Investment
Return on investment is the ratio between the net profit and the cost of investment.
ROI = NOI ÷ Price
Return on equity is the ratio between the cash flow and equity in a property.
ROE = Cash flow ÷ Equity
*Keep your focus on the formulas and calculations rather than definitions.
Unit 5 Summary
License Math: Leases; Taxation; Commissions; and Seller’s Net
Percentage Lease Rent Calculation
A percentage lease is when the landlord receives a percentage of gross sales or net profits as the rental payment for a property.
Monthly percentage rent = Sales times Percent Sales charged
Rent Escalations
Rent escalation is a way to determine the dollar amount of a rent increase.
New rent = current rent x (100% + escalation rate)
Converting Millage or Mill Rates
A mill rate is equal to one-tenth of one cent and is used to state the property tax. The millage rate is the tax rate stated in tenths of a cent.
1 mill = $.001; a mill rate of 1 mill per $1,000 = .1%; a 1% tax rate = 10 mills
Taxable Value
Tax = 1,000 x Mill rate
Tax Base
The tax base is the total tax-assessed value of all real property in a particular jurisdiction.
Tax base = Assessed valuations – Exemptions
Tax Rate, Base, and Requirement
Tax requirement
Tax rate = Tax base
Tax requirement
Tax base = Tax rate
Tax requirement = Tax base x Rate
Commission Splits
Commission splits determine how much each licensee involved in the sale earns when a property closes. No standard commission split exists.
· Total commission = Sale price x Commission rate
· Co-brokerage split = Total commission x listing side or sale side brokerage percent
· Agent commission = Brokerage percent x Agent percent
· Broker commission after agent payment = Brokerage percent – Agent payment
Seller’s Net
Seller’s Net is the amount that the seller profits (gets to keep in his pocket) after paying the
expenses involved in the sale (commission rate, closing costs and any existing mortgage).
Formula:
Sale Price – (sale price x commission % paid) – Other closing costs – Loan balance = Seller’s Net
Minimum Listing Price
The Minimum Listing Price is the lowest amount that the seller can list the property for and still cover all of his expenses (commission, closing costs and existing mortgage) and make the desired profit.
Formula:
(Desired Seller’s net profit + Loan payoff + closing cost = Seller’s gross profit) ÷ Seller’s % =
Minimum Listing Price
*Keep your focus on the formulas and calculations rather than definitions
Unit 6 Summary
License Math: Contracts; Closing Costs; Insurance
Percentage of Listing Price Calculation
Percentage of listing price is a ratio of the offer to the listing price.
Percentage of listing price = Offer ÷ Listing price
Earnest Money Deposit Calculation
This calculation is used to determine an appropriate amount of earnest money to include with an offer.
Deposit = Offering price x required or market-accepted percentage
30-Day 12-Month Method
This method of calculations uses 30 days for every month regardless of the actual numbers of days in each month.
Monthly amount = Annual amount ÷ 12 Daily amount = Monthly amount ÷ 30
Proration = (Monthly amount multiplied by the # months) + (Daily amount multiplied by the # days)
365-Day Method
This calculation for prorations uses the actual number of days for each month.
Annual amount or Monthly amount Daily amount = 365 Length of month
Proration = Daily amount multiplied by the # days
Income Received in Advance
Investment properties collect rent each month. The amount of rent is prorated between the buyer and seller for the month in which the sale takes place.
Taxes on properties are usually paid at the end of a set time period, not the beginning. The amount of taxes for the time period is prorated between the buyer and seller.
Recovery with Co-Insurance Clauses
Insurance companies include co-insurance clauses to share the risk of insuring a property.
% Replacement cost covered
Recovery = Damage claim x Minimum coverage requirement
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