Math Examples

A tenant pays $1,400 per month for a 1,400 sq. ft. office. How much is the tenant paying per square foot per year?

$1,400 per month x 12 mo. = $16,800 per Year ÷ 1,400 sq. ft. = $12 per sq. ft. per year

Mary has purchased a home for $120,000 and obtained a loan from a local bank for 75% of the purchase price. She agreed to pay 2 discount points. Mary has placed $2,500 earnest money with the broker. How much money will Mary need at closing to complete the transaction?

$120,000 x .75 = $90,000 Loan Amount; $90,000 x .02 = $1,800 in Points (Every Point is 1% of Loan Amount) $120,000 x .25 = 30,000 Down Payment $30,000 Down Payment + $1,800 in Points = $31,800 - $2,500 Earnest Money = $29,300 Total to Bring to Closing

The sales price of a quadraplex is $150,000 and operating expenses are $30,000. What should be each unit's monthly rent for the investor to achieve a 20% rate of return?

$150,000 (value) x .20 (20% rate) = $30,000 (NOI) $30,000 (NOI) + $30,000 (OE) = $60,000 (EGI) $60,000 (EGI) ÷ 4 units = $15,000 (annual EGI per unit) $15,000 ÷ 12 = $1,250 per Month

Mr. Smith is blind, owns a home assessed at $150,000, and has lived in Florida for 6 years. The city millage rate is 8 mills, the county rate is 9 mills, and the school rate is 8 mills. What are his property taxes for the year?

$150,000 - $25,500 = $124,500 ($500 additional for blind exemption) $124,500 x .025 = $3,112.50 (city .008/county .009/school .008 = .025) amount exempt from city and county taxes $25,000 x .017 = $425 (The additional $25,000 homestead exemption only applies to city and county taxes) $3,112.50 - $425 = $2,687.50

Jane has hired Gold Star Realty to sell her house. She has closing costs and expenses of $4,200. She must net $150,000 from the sale. Jane agreed to pay Gold Star a 6% commission. At what price must the house sell for Jane to achieve her goals?

$150,000 Net + $4,200 Closing Costs and Other Expenses = $154,200 Total $154,200 ÷ .94 = $164,042.55 (Commission is 6% so Jane's share of the sale is 94%)

Percentage example: Profit or Loss A property was purchased for $140,000 and later sold for $156,500. Which represents the profit percentage earned in this transaction?

Divide what is made by what is paid. $156,500 (purchase price) - $140,000 (sales price) = $16,500 (amount made) $16,500 (amount made) ÷ $140,000 (amount paid) = .117857 or 12%

What was the total amount of the state taxes paid on the sale of a principal residence that closed last July if the sales price was $60,000 and a new mortgage was obtained in the amount of $32,500?

Documentary Stamps on the Deed: $60,000 ÷ 100 = 600 Tax Units x $.70 = $420 Documentary Stamps on the Note: $32,500 ÷ 100 = 325 Tax Units x $.35 = $113.75 Intangible Tax on the Mortgage: $32,500 x .002 = $65

The lender has agreed to a 5% loan with 2 discount points on a new home purchase. What is the approximate yield on the loan?

Effective yield rule of thumb: 2 points adds 2 x 1/8%, or 2/8% = 1/4% or .25% 5% + .25% = 5.25%

Formula example: Adjusting comparables A comparable property has sold for $235,000 and has an extra bedroom worth $19,000. The subject property is on a better lot and the lot adjustment is $10,000. Which adjustments would be made by the appraiser?

Formula: Adjustment to comparable = Comparable price - superior items + inferior items. Adjustment = Comparable price - $19,000 bedroom (superior) + $10,000 lot (inferior) Net change = $19,000 - $10,000 = $9,000 subtracted from the comparable

Formula example: Ad valorem tax with exemptions A blind widow has a homestead exemption on a property with an assessed value of $48,000. If the total millage rate is 22 mills, her annual taxes would be:

Formula: Annual taxes = Taxable value x Millage rate, where the Taxable value is the assessed value less homestead exemptions. $25,000 (basic) + $500 (widow) + $500 (blind) = $26,000 (total exemptions) $48,000 (assessed value) ‐ $26,000 (exemptions) = $22,000 (taxable value) $22,000 (taxable value) x .022 (22 mills) = $484 (annual tax amount)

Formula example: IRV formula If the net operating income is $65,000 and the capitalization rate is 6%, which of the following would represent the value of this property?

Formula: Income = Rate x Value; or Income ÷ Value = Rate $65,000 (NOI) ÷ .06 (6% cap rate) = $1,083,333 (Value)

Percentage example: Principal & interest with amortized or level payment loan How much of the second loan payment would apply to principal if the loan was originally $175,000 at 6% over 30 years with a monthly payment of $1,049.21?

Formula: Principal x Rate x Time (in months) = Interest $175,000 (initial loan) x 6% (interest) = $10,500 (12 mo. interest) $10,500 ÷ 12 = $875 (1st month interest) $1,049.21 (payment) ‐ $875 (interest part) = $174.21 (1st mo. principal part) $175,000 (original balance) ‐ $174.21 (principal paid) = $174,825.79 (new loan balance) $174,825.79 (balance at start of 2nd mo.) x 6% = $10,489.55 (12 mo. interest) $10,489.55 ÷ 12 = $874.13 (2nd month interest) $1,049.21 (payment) ‐$874.13 (interest part) = $175.08 (2nd mo. principal part)

A buyer is purchasing a home for $570,000 with a down payment of $114,000. If the buyer finances the difference, what is the loan-to-value (LTV) ratio?

Loan amount = $570,000 - $114,000 = $456,000 LTV = $456,000 loan ÷ $570,000 value = 0.8 or 80%

An investor wishes to build a 15,000 sq. ft. restaurant. The restaurant will seat 85 people. Zoning requires one parking place per 2.5 persons. Each parking space is allotted 100 sq. ft. Local building ordinances require 10% of the total parking area for driveway access. Broker Brown has 2 lots available for development. Lot A is 100 ft. × 200 ft. and lot B is 90 ft. × 210 ft. Which of the lots will fulfill the needs of the investor? lot A only

Lot A: 100 ft. x 200 ft. = 20,000 sq. ft. Lot B: 90 ft. x 210 ft. = 18,900 sq. ft. 85 people ÷ 2.5 parking = 34 spaces x 100 sq.ft. each = 3,400 sq.ft. (parking area) 3,400 sq.ft. (parking area) x .10 (10% driveway) = 340 sq.ft. (driveway access area) 15,000 sq.ft. (building) + 3,400 sq.ft. (parking) + 340 sq.ft. (driveway access) = 18,740 sq.ft. (total area needed). Therefore either lot A or lot B will work since both are larger than needed.

Nonhomestead property with an assessed value of $137,500 is sold and the closing takes place on April 12th. If the day of closing is charged to the buyer, how is the proration for taxes listed on the closing statement under the 365 day method if the millage rate is 24 mills?

Nonhomestead = no exemptions $137,500 (assessed value) x .024 (24 mills) = $3,300 (Total tax) $3,300 ÷ 365 days = $9.0411 (daily tax amount) 31 (Jan) + 28 (Feb) + 31 (Mar) + 11 (Apr) = 101 seller days $9.0411 (daily tax) x 101 (seller days) = $913.15 debit to seller and $913.15 credit to buyer

A real estate closing for a duplex is scheduled for closing on September 7, with the day of closing charged to the buyer. Monthly rent is $1,300 per unit. Which closing statement entry is correct?

Rent is prorated for the month of closing with a credit to the buyer for rent already collected for the days of buyer ownership. # buyer days = 30 - 6 = 24 days Buyer's portion = $1,300 ÷ 30 days x 24 (buyer days) x 2 units = $2,080

A property has a potential gross income of $450,000. Fixed and variable operating expenses have been calculated at $112,000 annually. The property is being operated at a vacancy rate of 2% with $4,000 being held in reserve for replacements. If the property sells for $2 million, what is the capitalization rate?

Stack formula: $450,000 (PGI) x .02 (V&C rate) = $9,000 (V&C) $450,000 (PGI) - $9,000 (V&C) = $441,000 (EGI) $441,000 (EGI) - $112,000 (OE) - $4,000 (R) = $325,000 (NOI) IRV formula: $325,000 (NOI) ÷ $2,000,000 (Value) = .1625 or 16.25% (cap rate)

If a property has an effective gross income (EGI) of $96,000 and operating expenses (OE) and reserves (R) total $45,000, what is the property value if the capitalization rate is 9%?

Stack formula: $96,000 (EGI) - $45,000 (OE + R) = $51,000 (NOI) IRV formula: $51,000 (NOI) ÷ .09 (9% cap rate) = $566,666.67 (Value), rounded up to the nearest dollar as $566,667

How many acres are contained in the NW 1/4 of NE 1/4 and W 1/2 of NE 1/4 of NE 1/4, Section 12? 160

Watch for the word "and" in this legal description and calculate as 2 separate parcels. 640 ÷ 4 ÷ 4 = 40 Acres; 640 ÷ 2 ÷ 4 ÷ 4= 20 Acres; 40 Acres + 20 Acres = 60 Acres

Real estate property taxes are $1,900. Millage rates for the property total 28 mills with no exemptions. What is the assessed value of the property?

Work backward. If assessed value x millage rate = tax, then tax ÷ millage rate = assessed value. $1,900 tax ÷ .028 (28 mills) = $67,857 assessed value

A 20‐unit apartment building located adjacent to a race track, suffers a $2,000 loss in net income each month because of location. Assuming a 12% rate of capitalization, what is the loss in value as a result of the race track?

$2,000 loss per month x 12 months = $24,000 annual loss $24,000 annual loss ÷ .12 = $200,000 loss in value

Mrs. Smith sold two 60‐acre tracts for $2,000 per acre. Profit on one sale was 20%; loss on the other sale was 20%. What was her loss or gain?

$2,000 x 60 = $120,000 Sale Price for each Tract $120,000 ÷ 1.20 = $100,000 Originally Paid for Tract with 20% Profit $120,000 ‐ $100,000 = $20,000 Profit $120,000 ÷ .80 = $150,000 Originally Paid for Tract with 20% Loss $120,000 ‐ $150,000 = ($30,000) Loss $20,000 ‐ $30,000 = ($10,000) Net Loss

A building rents for $20 per square foot based on a CPI (rent index) of 1.5. If the CPI increases to 1.8, what would be the new rent per square foot?

$20 (rent per sq. ft.) ÷ 1.5 (old CPI) = $13.3333 $13.3333 x 1.8 (new CPI) = $24 (new rent per sq. ft.)

A lot measures 240' x 660' and costs $21,780 per acre. What is the cost per square foot?

$21,780 per acre ÷ 43,560 sq. ft. per acre = $.50

An income-producing property has an gross income of $30,000 and expenses of $12,000. The rate of return expected is 12%. What is the value of the property?

$30,000 - $12,000 = $18,000 $18,000 ÷ .12 = 150,000

An apartment complex has 3 apartments rented for $400 each, 6 apartments rented for $360 each, and 6 apartments rented for $350 each. All apartments are rented on a monthly basis with rental payments due on or before the first of each month. If the gross rent multiplier is 55, what is the value of the property?

$400 x 3 = $1,200 $360 x 6 = $2,160 $350 x 6 = $2,100 $1,200 + $2,160 + $2,100 = $5,460 total monthly rent $5,460 x 55 GRM = $300,300 property value

A buyer acquires 3 lots for a total price of $44,000. The second lot cost $4,000 more than the first lot and the third lot cost $6,000 more than the second. What was the cost of the first lot?

$44,000 - $4,000 - $4,000 - $6,000 = $30,000 $30,000 ÷ 3 = $10,000 Lot 1: $10,000 Lot 2: $10,000 + $4,000 = $14,000 Lot 3: $14,000 + $6,000 = $20,000

What are the state taxes due on the sale of a homestead if the sales price is $48,750, a mortgage is assumed with a balance of $38,750, a new purchase money mortgage of $7,600 is to be held by the seller, and a binder deposit of $1,500 is paid to the broker?

$48,750 (sales price) ÷ 100 = 487.5 = 488 Tax Units (rounded up) Doc stamp tax on deed: 488 tax units x $.70 = $341.60 $38,750 (assumed loan) ÷ 100 = 387.5 = 388 Tax Units $7,600 (new PMM) ÷ 100 = 76 Tax Units Doc stamp tax on assumed mortgage: 388 tax units x $.35 = $135.80 Doc stamp tax on new PMM: 76 tax units x $.35 = $26.60 Intangible tax: $7,600 (new PMM) x .002 = $15.20 State taxes due: $341.60 + $135.80 + $26.60 + $15.20 = $519.20

If a commercial property rents for $5 per square foot based on an index of 1.5, what will the new price be if the index changes to 1.8?

$5 ÷ 1.5 = 3.3333 3.3333 x 1.8 = $6

Percentage example: Net listing A seller wants to net $50,000 after paying off a loan of $65,000 and a real estate commission of 5%. Which list price would give the seller his or her net?

$50,000 (seller's net) + $65,000 (loan payoff amount) = $115,000 (total) 100% - 5% (commission rate) = 95% (or .95) $115,000 (total) ÷ .95 = $121,052.63 (listing price)

The sales price of a property is $62,300. The brokers have agreed to split the 7% brokerage fee equally between the listing and selling brokers. The selling broker has agreed to pay 60% to the sales associate from his share of the commission. How much will the sales associate receive?

$62,300 (sales price) x .07 (total commission) ÷ 2 brokers = $2,180.50 $2,180.50 x .60 (60% to the Sales associate) = $1,308.30 (to sales associate)

A house is valued at $65,000. The monthly rent is $500, monthly debt service is $375, and annual taxes are $840. If there are no other expenses, what is the gross rent multiplier (GRM)?

$65,000 ÷ $500 = 130 GRM

Percentage example: Interest only loans If an interest only loan has monthly payments of $825 and an interest rate of 5%, what was the original loan balance?

$825 (monthly payment) x 12 months = $9,900 (1 year of payments) $9,900 ÷ .05 (5% interest) = $198,000 (original loan balance)

An investor assumes a first mortgage loan of $88,000 at 8% and the seller takes back a second mortgage of $19,000 at 11%. The overall rate on both mortgages would be:

$88,000 (1st mortgage) x .08 (8%) = $7,040 (1st mortgage interest) $19,000 (2nd mortgage) x .11 (11%) = $2,090 (2nd mortgage interest) $7,040 + $2,090 = $9,130 (total interest on both loans) $88,000 (1st) + $19,000 (2nd) = $107,000 (total loan amount) $9,130 interest ÷ $107,000 loan amount = .085 or 8.5%

A real estate sales associate's agreement with their broker gives the sales associate 60% of all commissions earned by the firm. If a property sells for $145,000 and the firm earns a 6% commission, what would be the sales associate's share?

1. 145,000 x .06=8700 2. 8700 x .60=5,220

A quoted interest rate on a conventional loan is 5.5%. However, once the discount points are added, the annual percentage rate is 6%. How many points did the bank charge?

1/2% Increase = 4/8 or 4 Points

A lot measuring 100 ft. by 218 ft. would be approximately what size?

100 ft. x 218 ft. = 21,800 sq. ft. 21,800 sq. ft. ÷ 43,560 sq. ft. per acre = .50 sq. ft. = 1/2 acre

If you purchased property for 60% of the asking price and later resold the property for 100% of the original asking price, what is your profit?

100% - 60% Paid = 40% Made; 40% (Made) ÷ 60% (Paid) = 66.66% or 66 2/3% Profit

Mrs. Levine found a property for sale at 80% of market value. After she purchased it, she resold it for full market value. What percentage of profit did Mrs. Levine earn?

100% ‐ 80% Paid = 20% Made 20% Made ÷ 80% Paid = 25% Profit

A 3 bedroom, 2 bath home contains 1200 square feet. If the appraiser estimates the rent to be $.375 per square foot and the gross rent multiplier (GRM) is 125, the value of the property is:

1200 sq. ft. x $.375 rent per sq. ft.= $450 rent $450 rent x 125 GRM = $56,200

If a lot has 150 feet of road frontage and 150 feet of depth, and there is a requirement for 15 feet of setback from the road, how many square feet are usable?

150' x 150' = 22, 500 sq. ft. (lot) 150' frontage x 15' setback = 2,250 sq. ft. (unusable) 22,500 - 2,250 = 20,250 sq. ft. (usable)

Square footage example: Size of lot after setback A lot measures 165 feet by 165 feet. If there are setbacks on all four sides of 10 feet, what square footage could be developed on this lot?

165 ft. (side length of lot) ‐ 20 ft. (10 ft. setback x 2 for each end of side)= 145 ft. (usable side length) 145 ft. x 145 ft. = 21,025 sq. ft (available for development)

Your lot has 180 ft on Elm Street and there are houses on both sides of the street. The city is paving Elm Street at a cost of $24 per foot. The city has agreed to pay 30% of the paving cost and the owners will be assessed for the remainder. Your paving assessment will be:

180 ft. x $24 per ft. = $4,320 Total Paving Cost Owners' share = 100% - 30% City's share = 70% $4,320 x .70 (Owners' Share) = $3,024 $3,024 ÷ 2 (you plus the owner across the street) = $1,512 per owner

The owner of a warehouse that goes 3 stories up wants to subdivide each of its floors into 10 x 20 foot bins and rent each bin for $6.00 per month. The building is 200 feet by 120 feet on each floor. 20% of each floor will be unusable because of elevators, closets, bathrooms, and hallways. What will be the owner's annual income?

200 x 120 x 3 floors = 72,000 sq ft 72,000 x .80 usable = 57,600 sq ft 10 x 20 bins = 200 sq ft per bin 57,600 ÷ 200 + 288 bins 288 bins x $6 x 12 months = $20,736 annual income

Calculate the gross income of an apartment building containing 5 units: 3 units bring in $350 per month; one unit brings in $300 per month; and one unit brings in $75 per week

3 x $350 x 12 months = $12,600 1 x $300 x 12 months = $3,600 1 x $75 x 52 weeks = $3,900 $12,600 + $3,600 + $3,900 = $20,100 Total gross income

Annual real estate taxes are $1,838. The day of closing is April 15 and belongs to the seller. If the 365‐day method is used, how should the proration be handled?

31 + 28 + 31 + 15 = 105 days of seller ownership. $1,838 annual taxes ÷ 365 days = $5.0356 daily tax $5.0356 x 105 days = $528. 74 debit to seller, credit to buyer

Square footage example: Reproduction cost A home measures 60 feet by 30 feet and has a detached garage that measures 30 feet by 20 feet. If the cost to reproduce the living area is $95 per square foot and the cost to reproduce the garage area is $35 per square foot, what is the reproduction cost of the home?

60 ft. x 30 ft. = 1,800 sq. ft. (living area) 1,800 sq. ft. x $95 cost per sq. ft. (living area) = $171,000 (cost to reproduce living area) 30 ft. x 20 ft. = 600 sq. ft. (garage) 600 sq. ft. x $35 cost per sq. ft. (garage) = $21,000 (cost to reproduce garage) $171,000 (living area) + $21,000 (garage) = $192,000 (reproduction cost)

Square footage example: # Lots for a parcel of land A developer purchases a 65 acre tract to develop into lots of 8,500 square feet each. How many lots could be developed if roads total 900 feet in length and 30 feet in width and there is a common area of 400,000 square feet?

65 acres x 43,560 sq. ft. per acre = 2,831,400 sq. ft. 900 ft. x 30 ft. = 27,000 sq. ft (roads) 2,831,400 sq. ft. (total) - 27,000 sq. ft. (roads) - 400,000 sq. ft. (common) = 2,404,400 sq. ft. (available for lots) 2,404,400 sq. ft. (available) ÷ 8,500 sq. ft. (each lot size) = 282.87 or 282 lots Round down for the number of full lots

Broker Smith is preparing a comparative market analysis on a residence. She determines inflation has been 10% each year. The current market values each bedroom at $12,000 and each bathroom at $5,000. The subject property has 3 bedrooms and 2 baths. The following table shows the available comparables. If equal weight is given to each comparable, what is the value of the subject property?

A: $86,000 x .10 = $8,600 Inflation for 1 Year $86,000 + $8,600 Inflation ‐ $5,000 Adjustment for Bath = $89,600 B: $92,000 x .05 = $4,600 Inflation for 6 Months $92,000 + $4,600 Inflation ‐ $12,000 Adjustment for Bedroom = $84,600 C: $73,000 + $12,000 Adjustment for Bedroom = $85,000 (Inflation not a Factor) ($89,600 + $84,600 + $85,000) ÷ 3 = $86,400 Estimated Value