Real Estate Mathematics and Formulas

Lee has to report his home office deprecation for the tax year. He has a 2,500 SF home and a 500 SF office area. Lee paid $280,000 for his home, and he figures the land portion carries about 25% of that value. If Lee depreciates on a 29-year basis, how much can he write off for his home office depreciation per year?

$1,076.92 First, Lee's depreciable basis, without the land, is $280,000 x 75%, or $210,000. The annual depreciation for the entire home is ($210,000 / 39 years), or $5,384.61. Second, his office is 20% of the house (500 SF / 2,500 SF). Therefore, Lee can take annual depreciation of ($5,84.61 x 20%), or $1,76.92.

The Keegans obtain a fixed-rate amortized 30-year loan for $280,000 @ 6.25% interest. If the monthly payments are $1,724, how much interest do the Keegans pay in the second month of the loan?

$1,456.94. In the first month they pay interest of ($280,000 x 6.25%) / 12, or $1,458. If their fixed payment is $1,724, they paid down the principal by $266 ($1,724 - 1,458). Now they must pay 6.25% interest on the new principal balance of $279,734. This equals (279,734 x .0625) / 12, or $1,456.94.

A homeowners residence has an assessed valuation of $140,000, and a market value of $170,000. The homestead exemption is $25,000. Tax rates for the property are 7 mills for schools, 3 mills for the city, 2 mills for the county; and 1 mill for the local community college. What is the homeowner's tax bill?

$1,495 First, always use the assessed valuation, not the market value. Subtract out the homestead exemption to derive the taxable value, or $140,000 minus 25,000 = $115,000. As a shortcut to calculating the tax bill, simply add up all the mills, multiply them times .001 to convert mills to decimals, then multiply this number times the taxable value. Thus (7 + 3 + 2 + 1) x .001 x $115,000 = $1,495.

A property has sold for $127,000. The listing agent agreement calls for a commission of 7%. The listing broker and selling broker agree to share the commission equally. What will the listing agent receive if the agent is scheduled to get a 40% share from his broker?

$1,778. First calculate the total commission, then the co-brokerage splits, then the agent-broker split. Thus: $127,000 x 7% = $8,890 total commission. ($8,890 x 50%) = $4,445 total listing broker share. ($4,445 x 40% = $1,778 agent's share.

Loan applicant Taylor has an annual gross income of $76,000. How much will a lender allow Taylor to pay for monthly housing expense to qualify for a loan if the lender uses an income ratio of 30%?

$1,900 Monthly income qualification is derived by multiplying monthly income by the income ratio. Thus (76,000 / 12) x .30 = $1,900. Remember to first derive the monthly income.

A property has a net income of $150,000, interest payments of $105,000, principal payments of $30,000, and annual cost recover of $7,000. The property's tax rate is 28%. What is the property's annual tax on income?

$10,640. The basic formula for tax liability is: Taxable income x Tax Rate = Tax Liability. Taxable Income is Net Operating Income - Income Expense - Cost Recovery Expense. Therefore, the annual tax is $150,000 (NOI) - $105,000 (interest expense) x 28% = $10,640. Note that the principal payment is not deductible in calculating taxable income.

Debra bought a home for $120,000, paying $24,000 down and taking a mortgage loan for $96,000. The following year she had a new roof put on at a cost of $5,000. What is Debra's adjusted basis in the house if she now sells the house for $150,000?

$125,000 The basic formula for adjusted basis is: Beginning Basis + Capital Improvements - Exclusions and Credits = Adjusted Basis. Debra's adjusted basis is therefore $120,000 + $5,000 = $125,000. The financing terms and subsequent selling price are not relevant.

The Uptons carry a $140,000 property insurance policy which covers 75% of the replacement cost of their insurable property, valued at $190,000. They have an 80% co-insurance requirement in the policy. If the family incurs a $150,000 loss, what if any amount will the Uptons recover?

$140,000. Use the formula: (Percent of insurable property value carried / 80% replacement cost) x claim = recovery. Thus, (75% / 80% x $150,000) = $140,625. However, the face value of the policy is the maximum they can receive, which is $140,000.

A lender determines that a homebuyer can afford to borrow $130,000 on a mortgage loan. The lender requires an %80 loan-to-value ratio. How much can the borrower pay for a property and still qualify for this loan amount?

$162,500 Use the formula: Price x LTV Ratio = Loan. The plug in the figures and calculate: Price x .80 = $130,000. Therefore, Price = $130,000 / .80 = $162,500.

Emily has an interest-only home equity loan at an annual interest rate of 5.3%. If her monthly payment is $790, how much is the loan's principal balance (to the nearest $1,000)?

$179,000 The equation for the loan amount is (annual interest divided by the interest rate) = loan amount. Thus, ($790 x 12) / .053 = $178,868 or $179,000 rounded.

A property is being appraised by the cost approach. The appraiser estimates that the land is worth $40,000 and the replacement cost of the improvements is $175,000. Total depreciation from all causes is $27,000. What is the indicated value of the property?

$188,000 Cost Approach formula: Land + (Cost of Improvements + Capital Additions - Depreciation) = value. Thus, you have $40,000 + ($175,000 - 27,000), or $188,000.

A rental home has a monthly gross income of $1,100. A suitable gross income multiplier derived from market data is 14.7. What estimated sale price (to the nearest $1,000) is indicated?

$194,000 Use the formula: GIM = Price / Annual income. To solve for price convert the formula to Price = GIM x Annual Income. Thus, ($1,100 x 12) equals $13,200 annual income. ($13,200 x 14.7 GIM) = $194,040, or $194,000 rounded.

An investor paid $80,000 for a lot and $600,000 to have an apartment building constructed on it. He has depreciated the property for the past 10 years on a 39-year straight-line schedule. If he sells the property this year and realizes $780,000, what is his capital gain?

$253,846 Total depreciation on this property = ($600,000 / 39 years) x 10 years, or $153,846. His adjusted basis is therefore ($680,000 original price minus $153,846 depreciation taken), or $526,154. The gain is then ($780,000 minus $526,154), or $253,846.

A homeowner bought a house five years ago for $250,000. Since then, the homeowner has spent #2,000 to build a screened porch and has added a central air-conditioning system at a cost of $5,000. What is the homeowner's adjusted basis is the house is sold today?

$257,000 Adjusted basis = beginning basis ($250,000) + capital improvements ($2,000 + $5,000) minus depreciation (0) = adjusted basis ($257,000).

A homeowner sold her house and had net proceeds of $265,000. Her adjusted basis in the home was $231,000. She immediately bought another house for $301,000. What was her capital gain?

$34,000 Capital gain = amount realized (net sales proceeds, $265,000) -adjusted basis ($231,000) = (34,000).

Maria plans to mulch the flower area around her house. The house measures 40' x 30' and she figures she'll mulch an area 8' in width to form a big rectangle all around the perimeter. She also figures 4" of depth should be sufficient. If a landspacer quotes Maria that mulch costs $20 / cubic yard, how much will she spend?

$340 First figure the area to be mulched. If the home is 40 x 30, the flower area adds 8' to each side of the house. Thus the outside perimeter of the flowered area is (40 + 8 + 8), or 46' by 56'. The area of the flowered area is (46' by 56') minus the house area of 1,200 SF. Thus the flowered area is 1,376 SF. Second, figure the volume of the mulch: 1,376 SF x 4" = 459 cubic feet. Since there are 27 cubic feet in a cubic yard, she will need 459 / 27 cubic yards, or 17. Thus she will spend $340.

Lots in the South Hyde subdivision are selling for approximately $.50 / SF. The Grandersons want to build a 2,500 SF home on a 1.5 ace lot. The custom builder can build the home for $135 / SF. What will the completed property cost the Grandersons?

$370,170 The land costs $.50 x 43,560 SF/ac. x 1.5 ac, or $32,670. The home will cost $135 / SF . 2,500, or $337,500. The total property will cost $370,170.

If gross income on a property is $75,000, net income is $30,000 and the cap rate is 8%, the value of the property using the income capitalization method is

$375,000 Value = Income / Cap rate. Thus, V = $30,000 / .08 = $375,000.

Homebuyer Janet pays $1,600 / month for the interest-only loan on her new house. The loan's interest rate is 6.75%. If she obtained a 75% loan, what was the purchase price?

$379,259 First, the annual interest paid is $1,600 x 12, or $19,200. The interest rate is 6.75%. Using the formula (Loan = Interest/Rate), the loan amount is $19,200 / 6.75%, or $284,444. As this is 75% of the price, the price is $284,444 / .75), or $379,259

Mack is buying Roy's house for $500,000. Mack's loan amount is $325,000. He has agreed to pay 1.5 points at closing. How much will Mack pay for points?

$4,875 $325,000 x .015 = $4,875. Remember, one point = 1% of the loan amount.

the Wildes have purchased a $740,000 home. The land is worth 25%, and the insure the improvements @ 75% of their replacement value. If the Wildes suffer damage estimated at $500,000, and they have an 80% co-insurance clause, what will their recovery be from the policy?

$468,750 Use the formula: (Percent of insurable property value carried / 80% replacement cost) x claim = recovery, where the insurable property value variable excludes the land value and is valued at replacement cost. Here, the insurable portion of the property is ($740,000 - 25% land value, or $555,000. The Wildes are carrying insurance to cover 75% of the replacement cost of the entire property. Their recovery amount is therefore (75% / 80%) x $500,000, or $468,750.

An apartment owner paid $500,000 for her complex 5 years ago. An appraiser at that time valued the land @ $100,000, but land as appreciated 25% over this period. The investor has used a 40-year straight-line depreciation method to depreciate the property. What is its current value using the cost approach?

$475,000 Use the same Cost Approach formula: Land + (Cost of Improvements + Capital Additions - Depreciation) = Value. The land is worth (100,000 x 125%), or $125,000. Remember, you cannot depreciate land, only the cost of improvements. Therefore, annual depreciation is ($400,000 / 40), or $10,000. Total depreciation is ($10,000 x 5 years), or $50,000. Thus the value is ($125,000 + 400,000 minus 50,000), or $475,000.

Chad owns a small retail property that he inherited from his father. There are no mortgages or interest expenses connected with the property. Chad takes an annual cost recover expense of $7,000. The property has a monthly gross income of $1,650 and monthly operating expenses of $600. Chad's taxable income from this property will be taxed at a rate of 30%. What is the tax liability for the year?

$5,940 INCORRECT!

Alexis is buying Jack's house. The closing date (day belongs to the seller) of the sale transaction is September 1 (day 244 of the year). Her loan has a monthly payment of $577.84 with $525 going to interest in the first month. At closing, Alexis must pre-pay interest for the period of Sept. 2-Sept. 30. Use the 365-day method for prorating. What is her prepaid interest amount?

$507.50 If the buyer pays $525 interest for 30 days, the daily expense is ($525 / 30), or $17.50. If there are 29 days of pre-paid expense, the buyer's charge is ($17.50 x 29), or $507.50.

Kevin, who works for selling broker Paul, sells a house listed by listing broker Adams. The house sells for $325,000. The co-brokerage split between Paul and Adams is 50-50. Kevin is on a 65% commission schedule with Paul. If the total commission rate is 6.5%, what is Kevin's commission?

$6,866 Figure the total commission, then the co-brokerage splits, then the broker-agent splits. Thus, ($325,000 x 6.5%) = $21,125. ($21,125 x 50%) = $10,563. ($10,563 x .65) = $6,866.

A sale transaction on rental property closes on December 16. The landlord received the December rent of $1,380 on December 1. Assuming the closing date is the buyer's and that the 365-day method is used for prorating, which of the following entries would appear on the settlement statement?

$712.26 For the monthly proration using the 365-day method, solve first for the daily rent amount: ($1,380 / 31), or $44.52. Since the landlord received the rent and owes the buyer portions of the rent, the buyer will be credited. The owed amount is for the 16th through the 31st, or 16 days, since the closing day belongs to the buyer. Therefore, credit the buyer and debit the seller ($44.52 x 16), or $712.26

Amy obtains a 75% LTV loan on her new $200,000 home with an annual interest rate of 6%. What is the first month's interest payment?

$750 The loan amount is $200,000 x .75, or $150,000. The first month interest equals ($150,000 x 6%) / 12 months, or $750.

Calculate how many acres are in the Southeastern 1/4 of the Western 1/2 of the Eastern 1/2 Section 9.

First, remember that a section contains 640 acres. The area in question is a fourth of a half of half of the total section. So divide 640 by (4 x 2 x 2). that's 16 and 640/16 = 40 acres.

A lender offers the Greys two alternative loan packages for their $60,000 home equity application. One option is an interest-only loan for 5 years @ 6.5% interest with no points. The second, a 6.25% interest-only loan for 5 years with 1 point to be paid at closing. Which loan will cost the Greys less total interest and by how much?

The second option, by 150 The first option's interest total is (6.5% x $60,000) x 5 years, or $19,500. The second option will charge ($6.25% x $60,000) x 5 years, plus $600, or a total of $19,350. The 2nd option is $150 cheaper.

Yard of Pizza has a percentage lease on its $1,800 SF space in Lincoln Shops. The terms are $1,40 / SF / month rent plus 1.75% of the store's gross income. If monthly sales averaged $41,500 last year, how much annual rent did Yard of Pizza pay last year

Their fixed rent is (1.800 SF x $1.40/SF) x 12 months, or $30,240. The percentage rate is ($41,500 x .0175) x 12, or $8,715. Total rent is ($30,240+ 8,715), or $38,955

A certain investor wants an 11% return on investment from any real estate investment. A property priced at $360,000 has gross income of $60,000 and expenses of $22,000. Approximately how much too hgih or too low is the price of this property for the investor to obtain her desired return exactly?

Use the same formula V = I/R where V is the price and R is the rate of return. Then plug in the numbers to solve for V. The NOI of this property is ($60,000 - $22,000), or $38,000. The return is 11%. Therefore, the value to get this return must be $38,000 / .11, or $345,455. Since the price is $360,000, the price exceeds the amount needed for an 11% return by approximately $15,000 ($360,000 - $345,455 = $14,545.)

A school district's tax rate is 10 mills. The school district's required revenue from taxes is $10,000,000. What is the tax base of the area?

$1,000,000,000 The mill rate = (tax requirement / the tax base.) A mill is one onth-thousandth of a dollar ($.001). To solve for the tax base, reconfigure this formula to be: Base = Tax Requirement / Mill Rate. Thus the base = $10,000,000/ .010, or $1,000,000,000.

A home sells for $322,600 in Primm County. Here, transfer taxes are set at $1.00 $500 of the sale price. Title insurance runs $450, and the attorney costs $550. The agent's commission is 7%, and the mortgage balance is $210,000. Annual real estate taxes are estimated to be $4,000, half of which will have to be charged to the seller. If the seller pays all of these expenses, what will she net at closing?

$86,372. First calculate the transfer tax: ($322,600 / 500) = 645.2 unites of $500. Round this up to 646, then multiply times $1.00 to get $646 transfer tax cost. Next figure the commission @ ($322,600 x .07), or $22,582. Next, the seller's real estate tax proration charge will be $2,000. Then, add up the expenses: ($646 transfer tax + $450 title + $550 attorney + $22,582 commission + 210,000 loan payoff + 2,000 tax proration) = $236,228. Subtracting this from the sale price = $86,372.

Jose recently obtained a 90% loan on his $410,000 home and he had to pay $6,150 for points. How many points did he pay?

1.67 points A discount point is one percent of the loan amount. Jose's loan is ($410,000 x 90%), or $369,000. If he paid $6,150, he paid 1.67% of the loan amount ($6,150 / 369,000, or 1.67 points.

Homeowner Savannah owns the Southeastern 1/4 of the Southwestern 1/4 of the Northwestern 1/4 of Section 4. How many acres is that property?

10 acres The key to this question is to recall that a section has 640 acres. Savannah's property only is a 1/4 of a 1/4 of a 1/4 of the entire section. Multiply 4 x 4 x 4 which equals 64. Savannah owns 1/64 of the section. Divide 640 by 64 and you get the answer of 10 acres.

Ivan owned a 1/4 acre lot. He wanted to construct a 120' x 80' tennis court on the lot. What approximate percentage of the lot will be left over, if any, when he has completed construction?

12% The lot measures 43,560 / 4, or 10,890 SF. The tennis court will take up 9,600 SF, leaving 1,290 SF. This amount is 11.8% of the total lot area.

An apartment building that recently sold for $400,000 had monthly gross rent receipts of $3,200. what is its monthly gross rent multiplier?

125 Use the formula: GRM = Price / Monthly Rent. Thus, $400,000 / $3,200 = 125

The village of Goodsprings has an annual budget requirement of $8,000,000 to be funded by property taxes. Assessed valuations are $400,000,000, and exemptions total $25,000,000. What must the tax rate be to finance the budget?

2.13% The rate = budget / tax base. Thus, $8,000,000 / (400,000,000 - 25,000,000) = 2.13%

An investor bought 4 oversized lots in order to subdivide. He paid $70,000 for the lots. After subdividing, the investor was able to sell each lot for $23,000. Excluding commissions and closing costs, what per cent profit did the investor realize?

31.4% The formula for profit % is (profit / initial investment). The profit made was ($23,000 x 4) minus 70,000 initial investment, or $22,000. dividing this by the amount invested derives a profit percent of 31.4%.

The loan officer at Sixth Fourth Bank tells Amanda she can afford a monthly payment of $1,000 on her new home loan. Assuming this is an interest-only loan, and the principal balance is $249,000, what interest rate is Amanda getting?

4.82% The equation for the interest rate is (annual payment / loan amount) = interest rate. Thus ($1,000 x 12) / $249,000 = 4.82%.

A developer wants to develop a 16-acre subdivision. He figures that the streets and common area will take up about 30% of this overall area. If the minimum lot size is to be 12,000 SF, how many lots can the developer have on his property?

40 The total area available for lots is 11/2 acres (16 acres x 70% for houses), or 487,872 SF (11.2 x 43,560). Dividing this area by 12,000 SF / lot = 40.66. Thus he can have a 40-lot subdivision.

A home appreciated 2 2/3% in one year, then 5 1/5% the next year, then 7 1/4% the third year. What was the average appreciation over the 3-year period expressed as a decimal?

5.04% First, convert to decimals: 2 2/3% = 2.67%; 5 1/5% = 5.2%; 7 1/4% = 7.25%. Thus total appreciation = (2.67% + 5.2% + 7.25%), or 15.12%. Divide by 3 to derive the average: 15.12% / 3 = 5.04%

A homeowner wants to insulate the new recreation room in her basement. She has been told that 3' of insulation would do the job. The walls are 9' high and respectively measure 13', 13', 18', and 18' in length. How many rolls will she need if each roll measures 3' X 2' X 50'?

6 Rolls First, the requirement = 2(13' x 9') + 2(18' x 9') = 558 SF. Each roll is 2' x 50', or 100 SF. Thus she will need 6 rolls.

An office building investor sees a listing of an office building which is priced at $2 million. He loves the property, but he knows he needs to make a return of at least 8% to satisfy his partners. If the building is 25,000 SF, rents for $10/SF per year, has 5% vacancy, and annual expenses of $70,000, should he buy it? What is his return?

8.375% Use the same formula R = I / V where V is the $2 million price, and R is the cap rate or rate of return. To identify income: (25,000 SF x $10/SF) = $250,000 gross income, minus 5% vacancy (.05 x $250,000), or $12,500, minus expenses of $70,000 = $167,500 net income. ($250,000 - $12,500 - 70,000) Now divide net income of $167,500 by $2,000,000 to derive the return of 8.375%

Seller Frank receives an offer of $290,000 on a property he listed at $308,000. How much is the offer as a percent of the listing price?

94% To find the percent of listing price the offer is, divide the offer by the listing price. In this question the offer is $290,000 and the listing price is $308,000.