CH 21 ***REAL ESTATE MATH REVIEW*** – Flashcards
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There are _____ square feet in an acre.
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43,560
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To determine a rectangle's square footage:
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multiple the length of one side by the length of the other side
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To convert square footage to acreage:
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divide the number of square feet by 43,560
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To convert acreage to square feet:
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multiply the number of acres by 43,560
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If you are given the dimensions only (e.g. 300' x 200'), the first number is considered to be the _____ footage
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"front"
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Example Problem #1: A parcel of land measures 400' x 400' (square). How many acres are contained in this parcel?
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400' x 400' = 160,000 square feet 160,000 sq. ft. ÷ 43,560 = 3.6731 acres
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Example Problem #2: A parcel of land is 7.5 acres. How many square feet are in the parcel?
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43,560 x 7.5 = 326,700 sq. ft.
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To calculate a sales commission:
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multiply the selling price by the commission rate
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To calculate a commission split between a broker and sales associate:
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multiply the total sales commission by the appropriate percentage that either the broker or sales associate is entitled to receive.
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To calculate the appropriate selling price so that the seller will receive a certain amount of money after paying closing costs and the sales commission, remember the following formula:
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Selling Price = Seller's Net + Closing Costs divided by 100% - Commission %
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Calculate Commission Example: Broker Gary sold a home for $375,000 with an agreed upon commission of 7.5% of the sales price. How much is the sales commission?
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$375,000 x 7.5% = $28,125
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Commission Split Example: Broker Bob has agreed to pay Salesperson Rafael two-thirds all commissions earned as a result of Rafael's efforts. If Rafael sells a property for $600,000 with an agreed upon commission of 6%, how much is Bob's share of the commission?
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$600,000 x 6% = $36,000 $36,000 ÷ 3 = $12,000
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Seller's Net Example: Seller Alexa notifies her broker that she wants to net $100,000 from the sale of her home. The seller's closing costs will be $8,000 and the broker must earn a commission of 10%. How much should the property sell for so that both the seller and broker receive the amount of money they want?
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Selling Price = Seller's Net + Closing Costs (divided by) 100% - Commission % $100,000 + $8,000 (divided by) 100% - 10% $108,000 (divided by) 90% = $120,000
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Graduated Commission Example: A broker list a property for $259,000 and agrees to accept a 5% commission on the first $100,000 of the selling price, 6% of the next $100,000, and 7% on the portion over and above $200,000. How much is the broker's total commission on a sales price of $335,300?
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$100,000 x 5% = $5,000 $100,000 x 6% = $6,000 $135,300 x 7% = $9,471 TOTAL = $20,471
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Comparable Sales Approach: Begin with identifying the sales price of the comparable property, then adjust its value either higher or lower depending on how the comparable property differs from the subject property.
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CBS (Comparable Better Subtract) CIA (Comparable Inferior Add)
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Comparable Sales Approach Example: Comp. #1 sold for $180,000. Comp #1 is identical to the subject in all aspects except that Comp #1 has a fireplace and the subject does not. If a fireplace is worth $5,000, what is the adjusted value of Comp #1?
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CBS (comp. better subtract) $180,000 - $5,000 = $175,000 adjusted value
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Cost-Depreciation Approach: Determining the value of a property using the cost-depreciation approach, a two-step math process is followed:
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Step One: Reproduction Cost ÷ Economic Life x Effective Age ======================= Total Deprecation Step Two: Reproduction Cost - Total Depreciation (calculated from Step One) + Land Value ================================== Depreciated Value of the Property
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Cost-Depreciation Approach Example: If a building is valued at $300,000, it has an economic life of 20 years and an effective age of 4 years, what is the value of the property if the lot is worth $40,000?
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Step One: $300,000 ÷ 20 x 4 ================ $60,000 Step Two: $300,000 - 60,000 + 40,000 ================ $280,000
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Income Capitalization Approach: The income capitalization approach formula is: I --(divided by)--- R X V
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I = Net Operating Income R = Capitalization Rate V = Value When you know the value of two of the letters, you can determine the value of the third letter by properly dividing or multiplying.
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Income Capitalization Example: If Net Operating Income is $40,000, and the capitalization rate is 10%, what is the value of the property?
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I ---- R X V I ----- R $40,000 ------------- = $400,000 10%
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Gross Rent Multiplier Approach: The Gross Rent Multiplier (GRM) is an easy calculation to determine the value of a property if the monthly rent is the same each month. The formula is: V ---------------------- R X M
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V = Value R = Monthly Rental Income M = Multiplier If you know the value of two of the letters, you can determine the value of the third letter by properly dividing or multiplying.
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Gross Rent Multiplier Example: If the monthly rent is $900 and the Gross Rent Multiplier is 94, what is the value of the property?
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V ---------- R X M $84,600 ------------ R X M
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Gross Income Multiplier Approach: The Gross Income Multiplier (GIM) is an easy calculation to determine the value of a property when analyzing the property's income for the entire year. The formula is: V ----------------- R X M
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V = Value R = Annual Rental Income M = Multiplier If you know the value of two of the letters, you can determine the value of the third letter by properly dividing or multiplying.
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Gross Income Multiplier Example: If the value of a property is $720,000 and the annual rental income is $60,000, how much is the gross income multiplier?
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V ---------- R X M $720,000 -------------- = 12 $60,000
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Discount Points: Discount points are pre-paid interest. For every point that a lender charges, their yield increases 1/8 of one percent. When a lender charges points, they are paid at closing by the borrower.
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One point is calculated as one percent of the loan amount; two points, two percent; etc.
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Discount Points Example: Shifty Savings and Loan is making a $90,000 loan with an annual interest rate of 7%. If the lender charges 4 discount points at closing to make the loan, what is the yield to the lender and how much will the points cost the borrower?
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$90,000 x 4% = $3,600 cost of points Four points adds 4/8 or ½ of a percent to the lender's yield
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Amortization: Amortization is the systematic process of paying down a debt through payments of principal and interest. The principal portion of the payment is the part that amortizes the debt.
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I --------- P x R x T I = Amount of interest paid in dollars P = Principal balance of a loan R = Rate of Interest T = Time length of the loan in terms of years Nine months = .75 of a year Six months = .50 of a year Three months = .25 of a year
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To amortize a loan, the steps are
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1. Loan amount x Annual interest rate = Annual interest div by 12 = Monthly interest 2. Mortgage payment (principal & interest) - Monthly interest = Principal portion 3. Principal balance of loan - principal portion of payment = New loan balance 4. Repeat same steps for next payment amortization.
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Amoritization Example: $80,000 loan for 30 years at an annual interest rate of 8% with monthly principal and interest payments of $587.01:
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$80,000 x .08 = $6,400 (annual interest) ÷ 12 = $533.33 (monthly interest) $587.01 (P&I) - $533.33 (I) = $53.68 (P) $80,000 - $53.68 = $79,946.32 new principal balance after the 1st payment. $79,946.32 x .08 = $6,395.71 ÷ 12 = $532.98 $587.01 - $532.98 = $54.03 $79,946.32 - $54.03 = $79,892.29 new principal balance after the 2nd payment.
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State Taxes: When a property sells, a Documentary Stamp Tax on the Deed is paid to the Department of Revenue regardless if the transaction is cash or financed.
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The Doc Stamp on the Deed is .70 per $100 of the purchase price. The seller usually pays this stamp tax.
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If the buyer finances the property, a new mortgage and note is created on behalf of the lender. The buyer is required to pay an Intangible Tax on the new mortgage and a Documentary Stamp Tax on the new promissory note.
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The Doc Stamp on the Note is .35 per $100 on the new debt and the Intangible Tax is .002 (2 mills) on the new debt.
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In the event a buyer assumes an existing debt, a new promissory note will be executed and a Doc Stamp will be paid (.35/$100).
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No intangible tax is levied on assumed loans.
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State Taxes Example: Sally sells her home to Dan for $159,000. Dan secures a new first mortgage from Shifty Savings and Loan in the amount of $130,000. The taxes due on this transaction are:
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$159,000 div by 100 = 1,590 (units of $100) x .70 = $1,113.00 (Doc on Deed) $130,000 div by 100 = 1,300 (units of $100) x .35 = $ 455.00 (Doc on Note) $130,000 x .002 = $260.00 (Intangible on Mortgage)
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Prorating Property Taxes: At closing, the seller's share of the annual taxes from January 1st to the day of closing must be calculated, with the seller giving this amount to the buyer.
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The number of days from January 1st and the cost of the taxes per day must be determined.
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Prorating Property Taxes Example: Prorate the taxes between the buyer and seller if the day of closing is March 14th, annual taxes are $2,200, and the day of closing belongs to the seller (the seller pays the taxes for March 14th):
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Step One: Calculate the number of days between January 1st and March 14 31 + 28 + 14 = 73 days Step Two: Calculate the daily tax rate by dividing the annual taxes by 365 days: $2,200 ÷ 365 = $6.02739726 (don't round up the decimal) Step Three: Multiply the daily tax rate by the number of days $6.02739726 x 73 = $440.00
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Prorating Rent: At closing, the buyer's share of the monthly rent from the day of closing until the last day of the month must be calculated, with the seller giving this amount to the buyer.
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The number of days from closing until the end of the month and the cost of the rent per day must be determined.
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Prorating Rent Example: Prorate the rent between the buyer and seller if the day of closing is March 24th, the monthly rent is $1,000, and the day of closing belongs to the seller (the seller gets the rent for March 24th):
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Step One: Prorate Calculate the number of days of rent the buyer is entitled to (March 25th through March 31st) 25, 26, 27, 28, 29, 30, 31 = 7 days ------------------------------------------------------------ Step Two: Calculate the daily rate by dividing the monthly rent by the number of days in the subject month $1,000 ÷ 31 = $32.25806451 (don't round up the decimal) ------------------------------------------------------------ Step Three: Multiply the daily rental rate by the number of days $32.25806451 x 7 = $225.81
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Before Tax vs. After Tax: When asked to analyze an investor's choice, select the investment that provides the greatest return after taxes. If the selection provides the before-tax return, we must convert the before tax-return percentage to an after-tax return percentage
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When comparing the returns on investments, it is only helpful to compare AFTER TAX rate of return. On an exam, convert all before tax returns to AFTER TAX returns.
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For example, if a person is in a 30% tax bracket, that means they get to keep 70% of their money after taxes. To calculate a 22% return before taxes and convert it to AFTER TAX rate of return, multiply by the percentage that a taxpayer gets to keep.
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That will convert a before tax return to an AFTER TAX return. On the test, choose the answer that gives the greatest AFTER TAX rate of return.
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Before Tax vs. After Tax Example: If a person is in a 32% tax bracket, which of the following represents the most desirable investment? a. 22% Before Taxes b. 20% Before Taxes c. 18% After Taxes d. 16% After Taxes
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Step One: Convert the before tax returns to after tax returns: a. = .22 x 68% = 14.96% after taxes b. = .20 x 68% = 13.6% after taxes Step Two: Compare all the after tax returns and select the highest one a. = 14.96% b. = 13.6% c. = 18% d. = 16% Step Three: Select the highest after tax return choice Answer: C 18% after taxes
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OFFICE BUILDING SQUARE FOOTAGE Sometimes the student is asked to calculate how many offices will fit in a multi-floor office location.
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FIRST: FIGURE OUT HOW MUCH SQUARE FOOTAGE IS AVAILABLE FOR ONE FLOOR. SECOND: CALCULATE HOW MANY OFFICES CAN BE FITTED ON ONE FLOOR. THIRD: MULTIPLY THE NUMBER OFFICES ON ONE FLOOR BY THE NUMBER OF FLOORS
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Square Footage / Office Building Example: Donald wants to rent out 3 floors of a bank building that measure 55,000 square feet each. On each floor, 30% of the square footage must be set aside for hallways, elevators, stairs, and other common areas. Donald decides that each office needs to be at least 1,400 square feet. How many offices can Donald fit if he rents out all 3 floors?
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1) Determine how much square footage is available for offices on one floor 55,000 x 70% = 38,500 square feet 2) Divide the number of available square feet by the size of each office 38,500 ÷ 1,400 = 27.5 offices. NEVER ROUND UP AT THIS STAGE. Therefore there are 27 offices on one floor 3) Multiply the number of offices by the number of floors to be rented 27 X 3 = 81 offices
