Real Estate Calculations

An agent was to receive 5% commission on a piece of property that listed for $30,000. How much commission would he receive if the owner reduced the selling price by 15%?

$1,275 . Correct answer. -$30,000 X 15% = $4,500 amount reduced; -$30,000 - $4,500 = $25,500 new listed price; -$25,500 X 5% = $1,275 commission.

Taxes are $2,100 per year. The tax rate is $3.00 per 100. The assessed value of the property is 40% of the estimated market value. What is the market value of the property?

$175,000 . Correct answer. -Start with $2,100 (taxes) / $3.00 (rate) x $100 = $70,000. -This is the assessed value of the property, which taxes are based on. -$70,000 (assessed value) / 0.40 (40%) = $175,000 market value.

A house sells for $54,000 and is assessed at $39,400. Annual taxes are calculated at $0.92 per 100 and are paid every 6 months. What is the semi-annual tax bill?

$181.24 . Correct answer. -Assessed Value $39,400 x .0092 = $362.48 annual taxes. -$362.48/2 = $181.24 each 6 months.

Sara is purchasing a home. How much down payment must she make if she agrees to pay $80,000 for a house and wants to make a mortgage down payment of 25%?

$20,000 . Correct answer. Determine Sara's down payment as follows: - House cost x Percentage = Down Payment- $80,000 x 0.25 (25%) = $20,000.

The current value of Pete and Martha's home minus the lot is $125,000. What did Pete and Martha originally pay assuming the home depreciated 6% per year for the past 10 years?

$312,500 . Correct answer. • First, calculate the total depreciation as follows: 6% per year x 10 years = 60% total deprecation. • Next, determine the percentage of the current value as follows: 100% original cost - 60% total depreciation = $125,000. • Finally, determine the original cost as follows: $125,000 / 0.40 = $312,500.

Murphy is going to buy 2 parcels of land. One piece of land contains 3.5 acres and a second is 0.5 square miles in area. If the price is $2,000 per acre, what would Murphy have to pay for both parcels?

$647,000 . Correct answer. •First, determine the cost of the first parcel: -3.5 acres x $2,000 per acre = $7,000. •Next, understand that 1 sq. mi. = 640 acres. •Now, apply these figures as follows: -640 acres / 2 = 320 acres in the 2nd parcel; -320 x $2,000 = $640,000 for the 2nd parcel; -$7,000 + $640,000 = $647,000. •Therefore, Murphy had to pay $647,000 for both parcels.

Harry the Homeowner purchases a new home. The purchase is financed with a conventional, amortized loan equal to $67,000. The interest rate on the loan is 8%, payable over 30 years. Harry's first monthly payment is $500. What is the loan balance after Harry's first payment?

$66,946.67 . Correct answer. - First, you must calculate the annual interest as follows: $67,000 x 0.08 = $5,360. - Next, calculate the monthly interest rate as follows: $5,360/12= $446.66. - Next, deduct that interest from his monthly payment:$500 - $446.66 = $53.34. - Now, we know that $53.34 of Harry's monthly payment is applied toward his principal. - Therefore, $67,000 (loan amount) - $53.34 (first month's principal deduction) = $66,946.67.

A developer has 25 acres, which he plans to sub-divide into 1/2 acre building lots. Of the total tract, he must dedicate 5% for streets and 15% for recreation and open space. Each lot will sell for $19,560. What is the developer's potential income?

$782,400 . Correct answer. • First, understand that the total number of acres to develop is 25. • Next, deduct 20% (5% for streets, 15% for recreation), or 5 acres. Now, you know that the number of acres to sell is 20 (25-5). • Next, multiply the 20 acres by 2 (because these are half acre lots), for a total of 40 lots. • Finally, multiply 40 lots by $19,560 = $782,400. If you forget that these were 1/2 acre lots and multiplied by 20 you may have selected $391,200.

3. Amortization/monthly installment payments

3. Amortization/Monthly Installment Payments: On the exam, you may be asked to create part of an amortization schedule to show what the monthly payments would be (interest and principal) for a few months or to show what the principal balance would be after a few months. Using the example above: "What are Sam's principal and interest payments (installment payments) for 3 months?""What is the principal balance of the loan owed at by Sam the end of 3 months? " First month's principal, interest, and principal balance: Monthly payment - Month's interest = Amount paid towards principal $1,711.88 - $1,381.88 = $330 first month's principal Principal balance- Amount paid toward principal = New principal balance $301,500 - $330 = $301,170 "What are Sam's principal and interest payments (installment payments) for 3 months?""What is the principal balance of the loan owed at by Sam the end of 3 months? " Second month's principal, interest, and principal balance: Loan balance x Annual interest rate = Annual interest $301,170 x 0.055 = $16,564.35 $16,564.35/12 = $1,380.36 second month's interest $1,711.88 - $1,380.36 = $331.52 second month's principal $301,170 - $331.52 = $300,838.48 principal balance at the end of second month What are Sam's principal and interest payments (installment payments) for 3 months?""What is the principal balance of the loan owed at by Sam the end of 3 months? " Third month's principal, interest, and principal balance: $300,838.48 x 0.055 = $16,546.12 $16546.12/12 = $1378.84 third month's interest $1,711.88 - $1,378.84 = $333.04 third month's principal $300,838.48 - $333.04 = $300,505.44 principal balance at end of third month

Capitalization Rate

As previously discussed, The Cap Rate is the estimated annual percentage of return on an income-producing property, established by dividing the NOI with the sales price (NOI/Sales Price = Capitalization Rate). The appraiser estimates the sales price using the Market Data Approach with comparable properties.

Which of the following formulas is used to determine annual real estate taxes?

Assessed value x Tax rate . Correct answer. Annual taxes are calculated by this formula: ANNUAL TAXES = ASSESSED VALUE x TAX RATE. Market value, sales price or appraised value are determined by other elements.

Gross Rent Multipliers

Consider the following example calculation of a monthly gross rent multiplier: Determine the average gross rent multiplier by adding each rent multiplier and dividing by the total number of rent multipliers added as follows: 120 + 123.19 + 121.68 + 118.75 + 121.92 = 605.54. Next, divide the sum of all rent multipliers by the total number of rent multipliers used to arrive at the average as follows: 605.54 / 5 = 121.108. Finally, round the number as follows: 121.108 = 121.11. The Average Gross Rent Multiplier is: 121.11. GRM: EXAMPLE: Consider the following example calculation of a monthly gross rent multiplier: An appraiser can apply the estimated GRM to the projected gross rents of the subject property. For example, if the appraiser had determined that the market rent for the subject property is $700 per month, the estimated value of the subject property would be: Gross Rent x GRM = Market Value; $700 x 121.11 = $84,777.

2. Interest Rates/Interest Amounts: Interest is the cost of borrowing money. A borrower's interest rate is stated in a note, and is expressed as an annual rate. EXAMPLE: "Sam bought a house for $335,000. He got an interest rate of 5.5%, on a 90% loan for 30 years. His monthly payment is $1,711.88. How much interest did Sam pay the lender in his first payment?" Solution:

First, you need to figure out how much the loan is: - LTV ratio x Sales price = Loan amount- 0.9 x $335,000 = $301,500. Next, you need to find the amount of annual interest Sam pays: - Loan amount (principal balance) x Annua linterest rate = Annual interest- $301,500 X 0.055 = $16,582.50

Transfer Tax - EXAMPLE: "A home sells for $377,000 in the State of Progress. Assuming a transfer tax of $1.75 per $600 of sales price, how much tax must the seller pay?"

Formula: (Sales Price / Unit of Measure) x Tax Rate per Unit = TaxSolution: First, realize that the tax rate is not expressed in a unit of measure conducive to moving the decimal (such as $1.75 per $1,000), as in previous examples. Therefore, you must determine how many $600 units are in the total sale price of $377,000 by dividing $377,000 by $600 as follows: $377,000 / $600 = $628.3333. Next, multiply the number of units by the tax rate to arrive at the solution as follows: $628.3333 x $1.75 = $1,099.5833. The seller must pay $1,099.58 (rounded down) in transfer taxes.

Total Money needed by buyer at closing

Frequently, a buyer will ask the agent how much the buyer should bring to closing. the answer is a matter of simple math. Total Money Needed at Closing EXAMPLE: "Buyer entered a contract to purchase Seller's house for $247,000. She was getting a loan to finance 90 percent of the purchase price. Her closing costs were estimated by the lender to be $1,225. She had already placed a deposit on the property of $5,000. How much does buyer need to bring to closing?" Formula: Purchase price - Amount financed + Closing costs - Deposit already paid = Amount needed to bring to closingSolution: 247,000 - (0.9 x 247,000) + 1,225 - 5,000 = $20,925.

General Math Concepts

General Math Concepts a. Equations: Answer story problems by converting narrative text into numeric equations, inserting supplied variables, and performing simple calculations (adding, subtracting, dividing, or multiplying) to determine missing variables. b. Scrap Paper: PSI examiners will provide you with scrap paper to use during the exam. Use it to list known variables and to work-out equations (use flow charts or pictures if possible). The most difficult math questions may require either multiplication or division after some preliminary adding or subtracting (basic algebra). 1. Nature of Real Estate Math: Math-related questions on the exam are most often presented as "story" problems. Story problems require that you solve equations by interpreting sometimes lengthy narratives. Unlike other topics on the exam, math answers are always certain and verifiable by plugging the correct choice into the proper equation.

Mortgage Calculations

Mortgages entail a variety of calculations and potential story problems relating to real property financing. 1. Down Payment/Amount to be Financed: In order to qualify the buyer for a loan, the lender requires the buyer to have a certain amount of money invested in the property. This amount, the down payment, is the difference between the amount the lender is willing to finance and the purchase price. Down Payment/Amount to be Financed: EXAMPLE: "The purchase price of John's house is $275,000. The lender is requiring John to put 10 percent down on the property. How much is John's the down payment and how much is the amount financed? Down payment: 10% x $275,000 = $27,500 Amount financed: 90% x $275,000 = $247,500

A developer owns four parcels of land. He plans to sell one parcel for construction of an office building. The building plans will require 2 acres, which will include the actual building, landscaping, and parking. What is the smallest parcel that would accommodate this construction?

Parcel C: 120 feet x 860 feet . Correct answer. •First calculate the area needed for the construction: -2 acres x 43,560 sq. ft/acre = 87,120 sq. ft. •Then calculate the square footage of each of the lots. -1. 83 x 950 = 78,850; This lot is too small. -2. 102 x 840 = 85,680; This lot is too small. -3. 120 x 860 =103,200; This lot is large enough. -4. 140 x 900 =126,000; This lot is large enough. •The question asks which is the smallest lot that would accommodate the construction. The answer is therefore Parcel C.

2. Interest Rates/Interest Amounts: Interest is the cost of borrowing money. A borrower's interest rate is stated in a note, and is expressed as an annual rate. EXAMPLE: "Sam bought a house for $335,000. He got an interest rate of 5.5%, on a 90% loan for 30 years. His monthly payment is $1,711.88. How much interest did Sam pay the lender in his first payment?"

Then, you must determine what the first month's interest would be: - Annual interest / 12 = Monthly interest.- $16,582.50 / 12 = $1,381.88 interest paid in first monthly payment.

Calculating for Transactions

Transaction calculations usually appear in questions about real estate closing or settlement. 1. Prorations: A proration is a proportionate distribution of certain expenses between the property buyer and seller at closing, such as homeowner's association dues, utilities, taxes, and rents. Borrower's monthly interest on his new loan is also prorated so that he will not be charged on the loan before the day of settlement. Unlessinstructed otherwise when doing proration problems, you can use a 360-day year (known as a banker's year) and a 30-day month. Proration: EXAMPLE: "A Seller paid the yearly county taxes of $720. Closing was held on October 10. How much should the seller be reimbursed for county taxes at closing?" Formula: (Annual county tax/360 days) x Number of days after closing = Reimbursed amount Solution: First, understand that the seller is being reimbursed for the days that the buyer will own the property, or all the days after closing: 20days (Oct.) + 30 days (Nov.) + 30 days (Dec.) = 80 days total. Next, calculate the reimbursement amount: ($720 / 360 days) x 80 days = $160. The seller will be reimbursed $160 at closing.

1. Nature of Property Tax Calculations: Property is taxed by local taxing authorities, based on a percentage of the assessed value, for the purpose of raising state operating revenue.

a. Assessed Value: Value assigned to property by a local government as a basis for determining property taxes. Assessed values are usually a percentage of (thus, lower than) the market value. b. Tax Rate: Method of calculating the amount of tax owed to a taxing authority. Each taxing body arrives at its tax rate separately. The amount of money needed by each taxing district is divided by the total assessment for all real estate located within the jurisdiction in order to arrive at that district's percentage. In most states, the taxpayer is presented with one tax bill. b. Tax Rate (cont.): However, in some areas of the country, separate bills are prepared by each taxing district (school districts, water districts, and the like). Due dates for taxes are set by statute. Property tax rates are usually expressed as either a percentage (5%) or a specified amount per $100 of assessed value ($5 per $100). 1. Nature of Property Tax Calculations 2. Common Equations: Property Taxes/Assessed Value = Tax rate; Tax Rate x Assessed Value = Annual Taxes; Property Tax/Tax Rate = Assessed Value, as in "property with an annual tax of $5,600 and a tax rate of $5.60 per $100 has an assessed value of X." ($5.60/$100 = 0.056; $5,600 / ($5.60/$100) = $100,000). Tax Rate - EXAMPLE: "A property has an assessed value of $100,000 and the annual property taxes are $5,600. What is the tax rate?" Formula: Property Taxes / Assessed Value = Tax RateSolution: First, calculate the tax rate as follows: $5,600 / $100,000 = 0.056. Next, convert the tax rate into a percentage by multiplying it by 100, or moving the decimal two places to the right as follows: 100 x 0.056 = 5.6%. The tax rate is 5.6%. Property Tax - EXAMPLE: "A property has an assessed value of $100,000 and the tax rate is $5.60 per $100. What are the annual property taxes? " Formula: Tax Rate x Assessed Value = Annual TaxesSolution: First, determine the tax rate as follows: $5.60 / $100 = 0.056 Tax Rate. Next, multiply the tax rate by the assessed value to arrive at the solution as follows: 0.056 x $100,000 = $5,600. The annual property taxes are $5,600. Assessed Value - EXAMPLE: "A property has an annual property tax of $5,600 and the tax rate is $5.60 per $100. What is the assessed value?" Formula: Property Tax / Tax Rate = Assessed ValueSolution: First, determine the tax rate as follows: $5.60 / $100 = 0.056. Next, divide the property tax by the tax rate to arrive at the solution as follows: $5,600 / ($5.60 / $100) = $100,000. The assessed value is $100,000.

Area

a. Nature of Area: Area is a measure of space in a bounded shape, as in the square footage of carpet required for a square room. b. Units of Measure: The most difficult task of an area question is converting units of measure. However, most problems will identify the conversion factor, if any. Still, consider the following common conversions. i. Feet per Yard: 3 feet = 1 yard. ii. Feet per Acre: 1 acre = 43,560 square feet, or 208.71 feet by 208.71 feet. iii. Feet per Mile: 1 mile = 5,280 feet. iv. Yards per Acre: 1 acre = 4,840 square yards. v. Acres per Square Mile: 1 square mile = 640 acres. c. Common Equations: Length x Width = Area; Area/Length = Width, as in "if the area of a lot is 1,600 feet and the lot is 80 feet in length, what is the width of the lot?" (1,600/80 = 20 feet). Area - EXAMPLE: "A rectangular lot measures 80 feet by 20 feet. What is the area of the lot in square feet?" Formula: Length x Width = Area of a RectangleSolution: Multiply the length by width to arrive at the unit of measure as follows: 80 x 20 = 1,600. The area of the lot is 1,600 square feet. Area - EXAMPLE: "The area of a lot is 1,600 square feet. The lot is 80 feet in length. What is the width of the lot?" Formula: Area / Length = WidthSolution: Supply the missing variable by dividing as follows: 1,600 / 80 = 20. The width of the lot is 20 feet.

Comparative Market Analysis

a. Nature of CMAs: Also referred to as a competitive market analysis. An informal comparison of recently sold properties, used by real estate agents to recommend listing or offering prices. Good comparables should be similar in location, size, age, style, and amenities (adjustments may be necessary). b. Common Equations: Total Comparable Sales Prices / Total Number of Comparables = Average Selling Price, as in "Comp 1 sold for $275,000, Comp 2 sold for $325,000, and Comp 3 sold for $295,000. What is the best listing price for a home assuming the comps are reasonably similar?" ($275,000 + $325,000 + $295,000 = $895,000; $895,000/3 = $298,333.33). CMA - EXAMPLE: "Sue is providing a CMA for her client Betty. Sue found three homes that recently sold nearby that are similar. House A sold for $275,000, House B sold for $325,000, and House C sold for $295,000. What sales price should Sue advise Betty to seek, assuming the comparables are reasonably similar to Betty's house?" Formula: Total Comparable Sales Prices / Total Number of Comparables = Average Selling PriceSolution: First, add the sales price of each comparable as follows: $275,000 + $325,000 + $295,000 = $895,000. Next, divide the sum of all comparables by the total number of comparables to arrive at the solution as follows: $895,000 / 3 = $298,333.3333. Finally, round the final product as follows: $298,333.3333 = $298,333.33. Sue should advise Betty to seek a sales price of $298,333.33.

Commissions

a. Nature of Commissions: Many real estate agents are compensated by a commission, calculated as a percentage of the sales price. The rate of a broker's commission, and any fees he or she may charge, is always negotiable. It would be a violation of antitrust laws for multiple firms to agree upon or fix a commission rate. b. Common Equations: Sale Price x Commission Rate = Commission Amount; Commission Amount/Sales Price = Commission Rate, as in "what is the commission if the sales price is $120,000 and the commission rate is 6%?" (convert the percent to a decimal as in 6% = 0.06; sales price x commission rate as in $120,000 x 0.06 = $7,200). Commission - EXAMPLE: "The sales price is $120,000 and the commission rate is 6%. What commission is owed?" Formula: Sale Price x Commission Rate = Commission AmountSolution: First, convert the percentage into a decimal by dividing by 100, or moving the decimal two places to the left as follows: 6% = 0.06. Next, multiply the sale price by the commission rate to arrive at the solution as follows: $120,000 x 0.06 = $7,200. The commission owed was $7,200. Commission - EXAMPLE: "The sale price is $120,000 and the commission was $7,200. What was the commission rate?" Formula: Commission Amount / Sale Price = Commission RateSolution: First, divide the commission amount by the sales price: $7,200 / $120,000 = 0.06. Next, convert that figure into a percentage by multiplying by 100, or moving the decimal two places to the right as follows: 0.06 = 6%. The commission rate was 6%.

Depreciation

a. Nature of Depreciation: The decrease in value of an asset. For appraisal purposes, depreciation refers to a loss in actual property value due to any natural or economic cause. However, for tax purposes, depreciation is an allowable expense deduction that can be taken even if the property in question increases in value. The purpose of the depreciation tax deduction is to allow investors to recover the cost of their investment over a certain period of time. A tax deduction for depreciation is only allowed for income-producing property, and not for personal residences. The useful life of an income producing property is the period of time that it is expected to remain economically profitable to its owner. The amount of permissible depreciation is directly related to the expected useful life of the improvement. The shorter the useful life, the greater the annual deduction. b. Common Equations: Cost x Annual Depreciation Rate = Annual Depreciation; Annual Depreciation / Annual Depreciation Rate = Cost; Annual Depreciation / Cost = Annual Depreciation Rate; Annual Depreciation Rate x Number of Years = Current Value as a Percent; Cost x Current Value as a Percent = Current Value; Current Value / Current Value as a Percent = Cost; Current Value / Cost = Current Value as a Percent, "What is the accumulated depreciation after 5 years on a 6-unit apartment building purchased for $500,000, where the land was valued at $100,000 and the property depreciated at 3% a year?" ($500,000 - $100,000 = $400,000; 3% = 0.03; $400,000 x 0.03 = $12,000; $12,000 x 5 = $60,000). Depreciation - EXAMPLE: "A 6-unit apartment building was purchased for $500,000. The land was valued at $100,000. The property depreciated at 3% a year. What is the accumulated depreciation after 5 years?" Formula: (Purchase Price - Land Value) x Yearly Depreciation x Years = Accumulated DepreciationSolution: First, isolate the value by subtracting the purchase price from the land value as follows: $500,000 - $100,000 = $400,000. Next, convert the depreciation rate into a decimal by dividing by 100, or moving the decimal two places to the left as follows: 3% = 0.03. Now, determine the annual depreciation by multiplying the value by the depreciation rate as follows: $400,000 x 0.03 = $12,000. Depreciation - EXAMPLE: "A 6-unit apartment building was purchased for $500,000. The land was valued at $100,000. The property depreciated at 3% a year. What is the accumulated depreciation after 5 years?" Formula: (Purchase Price - Land Value) x Yearly Depreciation x Years = Accumulated DepreciationSolution (cont.): Finally, determine the cumulative depreciation by multiplying the annual depreciation by 5 as follows: $12,000 x 5 = $60,000. The accumulated depreciation after 5 years is $60,000. Depreciation - EXAMPLE: "Jerry purchased a home six years ago for $125,000. Unfortunately for Jerry, the City built a dump next door. What is the home worth today assuming a depreciation rate of 3.5%?" Formulas: Cost x Annual Depreciation Rate = Annual Depreciation; Annual Depreciation / Annual Depreciation Rate = Cost; Annual Depreciation / Cost = Annual Depreciation Rate; Annual Depreciation Rate x Number of Years = Current Value as a Percent; Cost x Current Value as a Percent = Current Value; Current Value / Current Value as a Percent = Cost; Current Value / Cost = Current Value as a Percent. Depreciation - EXAMPLE: "Jerry purchased a home six years ago for $125,000. Unfortunately for Jerry, the City built a dump next door. What is the home worth today assuming a depreciation rate of 3.5%?" Solutions: First, determine the accumulated depreciation rate over 6 years by multiplying the depreciation rate by the number of years as follows: 3.5% x 6 = 21%. Now, determine the percentage of current value by subtracting 100% of the cost from the accumulated depreciation rate as follows: 100% - 21% = 79%. Next, convert the percentage of current value to a decimal by dividing by 100, or moving the decimal two places to the left as follows: 79% = 0.79 . Depreciation - EXAMPLE: "Jerry purchased a home six years ago for $125,000. Unfortunately for Jerry, the City built a dump next door. What is the home worth today assuming a depreciation rate of 3.5%?" Solutions (cont.): Finally, determine the current value by multiplying the initial purchase price by the percentage of current value to arrive at the solution as follows: $125,000 x 0.79 = $98,750. Today, the home is worth $98,750.

Equity

a. Nature of Equity: Cash value of property after deducting all debts, including any mortgage indebtedness. b. Common Equations: Down Payment + (Original Loan Amount - Current Loan Amount) + Appreciation = Equity, as in "A buyer who made a $20,000 down payment, borrowed $80,000 to purchase the property, and has $70,000 left on the loan has what amount of equity?" ($80,000 - $70,000 = $10,000; $10,000 + $20,000 = $30,000). Equity - EXAMPLE: "A buyer made a down payment of $20,000 and borrowed $80,000. The buyer paid down the loan to $70,000. How much equity does the owner have in the property?" Formula: Down Payment + (Original Loan Amount - Current Loan Amount) = EquitySolution: First, subtract the original loan amount from the current loan amount as follows: $80,000 - $70,000 = $10,000. Next, add the down payment to the previous figure to arrive at the solution as follows: $20,000 + $10,000 = $30,000. The owner has $30,000 in equity in the prop

Gross Rent Multipliers

a. Nature of Gross Rent Multipliers: Ratio between the sales price of a property and its gross rental income, used to estimate property value. The GRM is also known as Gross Income Multiplier. A GRM is a less accurate means of estimating the rate of return than a capitalization rate because a GRM relies on less data. In order to develop a GRM, an appraiser must obtain comparable rental rates and analyze the strengths and weaknesses of each to develop a multiplier that adequately reflects the income-generating ability of the subject property. This ratio is applied to the estimated income for the subject property in order to find an indication of value by the Income Approach. Note that gross rent multipliers provide only a rough estimate—gross rent multipliers do not account for variations in vacancies, uncollectible rents, property taxes, and other factors. b. Common Equations: Sales Price / Gross Rent = GRM, as in "What is the estimated value of property with a market rent of $700 per month and a GRM of 121.11? ($700 x 121.11 = $84,777).

Income Properties

a. Nature of Income Properties: Many income property problems deal with return on investment, and use net operating income (NOI) or capitalization rates. b. Common Equations: Annual Gross Income - Vacancies and Credit Losses = Annual Effective Gross Income; Annual Effective Gross Income - Annual Operating Expenses = Annual NOI; Annual NOI / Annual Rate of Return = Value; Value x Annual Rate of Return = Annual NOI; Annual NOI / Value = Annual Rate of Return, as in "What is the annual rent of a percentage lease at $1,000 per month plus 5% of gross sales where the tenant's annual gross sales were $350,000? ($1,000 x 12 = $12,000; $350,000 x 0.05 = $17,500; $12,000 + $17,500 = $29,500). Income Properties - EXAMPLE: "In a percentage lease, the rent charged is $1,000 per month plus 5% of gross sales. The tenant's annual gross sales were $350,000. What is the total annual rent based on a percentage lease?" Formula: (Rent Per Month x 12 Months) + (Gross Sales x 0.05) = Annual RentSolution: First, determine the base annual rent by multiplying the monthly rent by 12 months as follows: $1,000 x 12 = $12,000. Next, determine the landlord's share of the annual gross sales by multiplying the tenant's annual gross sales by 12 months as follows: $350,000 x 0.05 = $17,500. Finally, add the base rent to the Landlord's share of the tenant's gross sales to arrive at the solution as follows: $12,000 + $17,500 = $29,500. The total annual rent of this percentage lease is $29,500. Income Properties- EXAMPLE: "Determine the estimated value of an office building that produces $156,000 of gross income. Assume annual expenses of $43,000 and a 7% capitalization rate." Formulas: Annual Gross Income - Vacancies and Credit Losses = Annual Effective Gross Income; Annual Effective Gross Income - Annual Operating Expenses = Annual NOI; Annual NOI / Annual Rate of Return = Value; Value x Annual Rate of Return = Annual NOI; Annual NOI / Value = Annual Rate of Return Income Properties- EXAMPLE: "Determine the estimated value of an office building that produces $156,000 of gross income. Assume annual expenses of $43,000 and a 7% capitalization rate." Solution: First, determine the annual NOI by subtracting the building's gross income from the building's annual expenses as follows: $156,000 - $43,000 = $113,000. Next, convert the capitalization rate percentage into a decimal by dividing by 100, or moving the decimal two places to the left as follows: 7% = 0.07. Finally, divide the annual NOI by the capitalization rate to arrive at the solution as follows: $113,000 / 0.07 = $1,614,285.71. The estimated value of the office building is $1,614,285.71.

Loan-to-value Ratios (LTV)

a. Nature of LTVs: Ratio between a mortgage loan amount and the sales price or appraised value of real estate, whichever is lower. Lenders analyze LTV and establish maximum ratios in order to reduce the risk that a borrower will default on his loan. The higher the LTV, the lower the down payment because the lender is lending a greater amount of the purchase price. Conversely, the lower the LTV, the higher the down payment because the lender lends a lesser amount of the purchase price. Higher LTV means a greater risk for the lender because, as lenders theorize, the more equity one has in a home (created by the down payment), the less likely one will default. b. Common Equations: Loan Amount/Property Value = LTV; Property Value x LTV = Loan Amount, as in "property valued at $80,000 financed by a loan of $60,000 has an LTV of X" (loan value divided by property value = LTV, or $60,000/$80,000 = 0.75 or 75%). Loan-to-Value Ratios LTV - EXAMPLE: "A property is valued at $80,000 and has a loan amount of $60,000. What is the loan-to-value ratio?" Formula: Loan Amount / Property Value = Loan-to-Value RatioSolution: First, divide the loan amount by the property value as follows: $60,000 / $80,000 = 0.75. Next, convert your solution into a percentage by multiplying by 100 or moving the decimal two places to the right to arrive at the solution as follows: 0.75 = 75%. The LTV ratio is 75%. LTV - EXAMPLE: "A property valued at $80,000 has a loan-to-value ratio of 75%. What is the loan amount?" Formula: Property Value x Loan-to-Value Ratio = Loan AmountSolution: First, convert the LTV ratio into a decimal by dividing it by 100, or moving the decimal two places to the left as follows: 75% = 0.75. Next, multiply the property value by the LTV to arrive at the solution as follows: $80,000 x 0.75 = $60,000. The loan amount was $60,000.

Percentages

a. Nature of Percentages: A percentage is a specified part of 100, as in a commission rate or a minimum down payment. b. Converting Numbers: Most percentage problems require that students convert numbers in decimal form to a percentage, and percentages into decimal form, before multiplying or dividing. i. Convert a Percentage to a Decimal: Move the decimal two places to the left, or divide by 100, as in 1% = 1/100 = 0.01. ii. Convert a Decimal to a Percentage: Move the decimal two places to the right, or multiply by 100, as in 0.01 x 100 = 1%. c. Converting Text: The use of the word "of" in a percentage story problem is often an indication to multiply, as in "what is 16% of 1,000?" (0.16 x 1,000 = 160). However, sometimes you must work backwards by dividing, as in "what percent of 1,000 is 160?" (P x 1,000 = 160; 160/1,000 = 0.16 = 16%). Converting - EXAMPLE: "How much down payment does a buyer owe if she agrees to pay $80,000 for a house and wants to make a mortgage down payment of 25%?Formula: House Cost x Percentage = Down paymentSolution: First, convert the percentage into a decimal by dividing by 100 as follows: 25 / 100 = 0.25. A quicker way to convert a percentage into a decimal is to move the decimal two places to the left, as follows: 25% = 0.25. Next, multiply the House Cost by the percentage (in decimal form) to arrive at the solution as follows: $80,000 x 0.25 = $20,000. The buyer's down payment is $20,000. Percentages Converting - EXAMPLE: "If a buyer makes a mortgage down payment of $20,000 on a house that costs $80,000, what percentage of the house price is the down payment?" Formula: Down Payment / House Cost = Down Payment PercentageSolution: First, divide the Down Payment by the House Cost as follows: $20,000 / $80,000 = 0.25. Next, convert the answer into a percentage by multiplying by 100, or moving the decimal two places to the right to arrive at the solution as follows: 0.25 x 100 = 25%. The down payment is 25% of the house price.

Discount Points

a. Nature of Points: Additional fees paid to the lender by the borrower in order to reduce the interest rate of his mortgage (below market interest rates). Discount points are paid in a lump sum at the time of closing. Generally, the borrower pays 1% of the loan amount per point and he may reduce his interest rate by 1% by purchasing eight points (0.125% per point). b. Common Equations: Loan Amount x Number of Points = Point Dollar Amount; Point Dollar Amount/Loan Amount = Number of Points, as in "for a $50,000 loan the lender requires 2.5 points, which cost X" (convert the percent to a decimal or 2.5% = 0.025; loan amount x number of points = point dollar amount, or $50,000 x 0.025 = $1,250). Discount Points Discount Points - EXAMPLE: "For a loan amount of $50,000, the lender requires payment of 2.5 points. One point is equal to one percent of the loan, and must be converted as such for use in calculating the point dollar amount. How much would the borrower pay in points?" Formula: Loan Amount x Number of Points = Point Dollar AmountSolution: First, because each point is equal to one percent of the loan, convert 2.5% into a decimal by dividing by 100, or moving the decimal two places to the left as follows: 2.5% = 0.025. Next, multiply the loan amount by the points (in decimal format) to arrive at the solution as follows: $50,000 x 0.025 = $1,250. The borrower would pay $1,250 in points. Discount Points - EXAMPLE: "One point is equal to one percent of the loan. For a loan amount of $50,000, the borrower pays $1,250 in points. What number of points did the borrower pay?" Formula: Point Dollar Amount / Loan Amount = Number of PointsSolution: First, determine the number of points by dividing the point dollar amount by the loan amount as follows: $1,250 / $50,000 = 0.025. Next, convert the solution into a percentage by multiplying by 100, or moving the decimal two places to the right to arrive at the solution as follows: 0.025 = 2.5%. The borrower paid 2.5 points.

Qualifying Buyers

a. Nature of Qualifying Buyers: Licensees may estimate monthly mortgage costs in order to determine the monthly payments for prospective purchasers. A loan repayment factor, also known as an amortization factor, can assist in determining the monthly principal and interest payment. Loan repayment factors are usually represented by some dollar amount per thousand (such as $5.00 per 1,000). b. Common Equations: Loan Amount / $1,000 x Loan Payment Factor = Monthly PI, as in "What is the monthly principal and interest payment on a $250,000 loan with a repayment factor of $7.50 per $1,000?" ($250,000 / $1,000 = 250; 250 x $7.50 = $1,875.00). Loan Repayment - EXAMPLE: "Assuming a loan repayment factor of $7.50 per $1,000, what is the monthly principal and interest payment on a $250,000 loan?" Formula: Solution: Loan Amount/ $1,000 x Loan Payment Factor = Monthly PI, Monthly PI / Loan Payment Factor = Loan Amount. First, determine the total number of $1,000 units in the loan amount by dividing the loan amount by $1,000 as follows: $250,000 / $1,000 = 250. Next, multiply the total units by the loan repayment factor to arrive at the solution as follows: 250 x $7.50 = $1,875.00. The monthly principal and interest payment on a $250,000 loan is $1,875.

Sales Proceeds (profits)

a. Nature of Sales Proceeds: Sales proceeds are the amount of money received from selling a home. Net proceeds are the amount of money received from selling a home after deducting expenses, such as commissions and closing costs (seller's profit). b. Common Equations: Sales Price - Purchase Price - (Sale Price x Commission Rate) = Profit, as in "What is the profit from property purchased for $120,000 and sold for $200,000 with a 6% commission?" (convert the percent to a decimal as in 6% = 0.06; $200,000 x 0.06 = $12,000; $200,000 - $120,000 - $12,000 = $68,000). Profit - EXAMPLE: "A property was purchased for $120,000 and sold for $200,000 with a 6% commission. What was the seller's profit on the property?" Formula: Sale Price - Purchase Price - (Sale Price x Commission Rate) = ProfitSolution: First, convert the commission rate from a percentage into a decimal by dividing by 100, or moving the decimal two places to the left as follows: 6% = 0.06. Next, determine the commission earned by multiplying the sale price by the commission rate as follows: $200,000 x 0.06 = $12,000. Next, subtract the sale price from the purchase price and the commission earned to arrive at the solution as follows: $200,000 - $120,000 - $12,000 = $68,000. The seller's profit on the property was $68,000. Sales Proceeds (Profit) Profit - EXAMPLE: "A property was purchased for $120,000 and sold for $200,000 with a 6% commission. What was the percent profit on the property?" Formula: Sale Price - Purchase Price - (Sale Price x Commission Rate) = ProfitSolution: First, convert the commission percentage into a decimal by dividing by 100, or moving the decimal two places to the left as follows: 6% = 0.06. Next, calculate the commission earned by multiplying the sale price by the commission rate as follows: $200,000 x 0.06 = $12,000. Now, determine the profit by subtracting the sale price from the purchase price and the commission earned as follows: $200,000 - $120,000 - $12,000 = $68,000. Next, determine the percentage of profit by dividing the profit by the purchase price as follows: $68,000 / $120,000 = 0.56666. Profit - EXAMPLE: "A property was purchased for $120,000 and sold for $200,000 with a 6% commission. What was the percent profit on the property?" Formula: Sale Price - Purchase Price - (Sale Price x Commission Rate) = ProfitSolution (cont.): Next, convert the solution into a percentage by multiplying by 100, or moving the decimal two places to the right as follows: 0.56666 = 56.6666%. Finally, round the percentage to the nearest 100th, or second decimal place. The rule of thumb is that if the number is 5 or more, round up; and if the number is four or less, round down as follows: 56.6666% = 56.67%. The percent of profit on the property was 56.67%.

Transfer tax/ conveyance tax/ revenue stamps

a. Nature of Transfer Taxes: Fees (also known as excise taxes or revenue stamps) charged to grantors and grantees by local jurisdictions for the privilege of buying or selling real estate in that jurisdiction. Transfer taxes are generally paid by the seller, grantor, or lessor, and are due when the deed is recorded. Transfer taxes are generally paid by purchasing a stamp from the official in charge of recording deeds. This stamp is affixed to the deed as evidence that the tax was paid in full. Transfer taxes are usually based on the sales price of the property (such as $3.00 tax per $1,000 of sales price). Commonly exempted transfers include: mortgages, correction deeds, and transfers between husband and wife, or parent and child. b. Common Equations: (Sale Price x State Tax) + (Sale Price x County Tax) = Total Transfer Tax, as in "How much is the transfer tax on a property that sells for $150,000 under a local transfer tax rate of $1 per $1,000, and a state transfer tax rate of $0.50 per $1,000 based on the sales price?" (convert the tax rate to a decimal as in $1 per $1,000 = 0.001; $0.50 per $1,000 = 0.0005; $150,000 x 0.001 = $150; $150,000 x 0.0005 = $75; $150 + $75 = $225). Transfer Tax - EXAMPLE: "A property sold for $150,000. The state transfer tax is $1 per $1,000 based on the sales price, and the county transfer tax was $0.50 per $1,000 based on the sales price. How much was the total transfer tax for the sale?" Formula: (Sale Price x State Tax) + (Sale Price x County Tax) = Total Transfer TaxSolution: First, convert the state tax rate by dividing $1 by $1,000, or moving the decimal three places to the left as follows: $1 per $1,000 = 0.001. Next, convert the county transfer by dividing $0.50 by $1,000, or moving the decimal three places to the left as follows: $0.50 per $1,000 = 0.0005. Now calculate the state transfer tax by multiplying the sales price by the state tax rate as follows: $150,000 x 0.001 = $150. Transfer Tax - EXAMPLE: "A property sold for $150,000. The state transfer tax is $1 per $1,000 based on the sales price, and the county transfer tax was $0.50 per $1,000 based on the sales price. How much was the total transfer tax for the sale?" Formula: (Sale Price x State Tax) + (Sale Price x County Tax) = Total Transfer TaxSolution (cont.): Next, calculate the county transfer tax by multiplying the sales price by the county transfer tax rate as follows: $150,000 x 0.0005 = $75. Finally, add the state transfer tax to the county transfer tax to arrive at the solution as follows: $150 + $75 = $225. The total transfer tax for the sale was $225.

Volume

a. Nature of Volume: Volume is a measure of three-dimensional space that an object of a specific shape occupies. b. Units of Measure: Consider the following common conversions: iii. Cubic Yard: 27 ft3 iv. Cubic Mile: 5,451,776,000 yd3 = 3,379,200 acre-feet i. Cubic Inch: 16.387064 cm3 ii. Cubic Foot: 1,728 in3 c. Common Equations: Length x Width x Height = Volume of a cube.

Real estate taxes for the fiscal year are paid on June 30th. If the annual property taxes are $2,580 and a property sells and closes on April 15th, what is the settlement sheet entry for the proration of taxes?

credit to buyer $2042.50 . Correct answer. The buyer will get a credit since taxes for the year have NOT been paid. When the bill comes, the buyer will be in possession of the property and will have to pay the full amount, though he has only lived there for 2-1/2 months (1/2 Apr, May, and June). The seller is DEBITED (charged) and the buyer is CREDITED for the previous months. -Monthly Taxes = $2,580/ 12 = $215 -Buyer's Total Taxes = $215 x 2.5 = $537.50 -Reimbursement = $2,580 - $537.50 = $2,042.50 credit to the buyer The seller would have a debit for the same amount, but that is NOT one of your choices.

Jimmie the Gent is interested in property valued at $450,000. Jimmie will qualify for a $375,000 loan. However, Jimmie refuses to purchase if his LTV would fall under 80%. Is Jimmie likely to purchase the property?

yes, the LTV is within Jimmie's range . Correct answer. - First, determine the LTV on property valued at $450,000 on a $375,000 loan as follows: $375,000/$450,000 = 0.83 or 83%. - Now, compare Jimmie's minimum LTV with the LTV in question.