Test 10: Real Estate Math

$.023 / SF

5/6ths of an acre = (5 x 43,560 SF) / 6, or 36,300 SF. Her commission was (.06 x $28,000) x .50, or $840. $840 / 36,300 SF = $.023 / SF.

$370,170

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

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.

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.

6

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.

1,376 SF

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) by (30+8+8), or 46’ by 56’. The area of the flowered area is (46’ x 56’) minus the house area of 1,200 SF. This is 1,376 SF.

40 acres

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

10 acres

This key to this question is to recall that a section has 640 acres. Theresa’s property only is a ¼ of a ¼ of a ¼ 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.

$38,955

Their fixed rent is (1,800 SF x $1.40/SF) x 12 months, or $30,240. The percentage rent is ($41,500 x .0175) x 12, or $8,715. Total rent is ($30,240 + 8,715), or $38,955.

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%

29 %.

Appreciation as a per cent can be estimated by (1) subtracting the estimated current market value from the price originally paid (239,000 – 185,000 = 54,000) and (2) dividing the result by the original price (54,000 / 185,000 = . 29 or 29%).

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.

$206,000.

Remember the formula V = I / R where V is value, I is annual income, and R is the cap rate. Variations of this are: R = I / V in solving for the cap rate, and I = V x R in solving for income. Here, first identify net income by subtracting out vacancy and expenses. Then divide by the capitalization rate. Thus, ($30,000 – 1,500 – 10,000) / 9% = $205,555, or $206,000 rounded.

$375,000.

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

$13,600.

First derive the annual depreciation which is the cost divided by the economic life. Then multiply annual depreciation times the number of years to identify total depreciation. Remember to subtract depreciation from the original cost if the question asks for the ending value. Thus, ($16,000 / 20 years x 3 years) = $2,400 total depreciation. The ending value is $16,000 –2,400, or $13,600.

$1,077

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 ($5,384.61 x 20%), or $1,076.92.

$376,000.

Cost Approach formula: Land + (Cost of Improvements + Capital Additions – Depreciation) = Value. Thus you have $80,000 + ($350,000 – 54,000), or $376,000.

$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 the land, only the cost of the 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 – 50,000), or $475,000.

125.

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

$582,000

Use the formula: GIM = Price / Annual Income. To solve for price convert the formula to Price = GIM x Annual Income. Thus, ($3,300 x 12) equals $39,600 annual income. ($39,600 x 14.7 GIM) = $582,100, or $582,000 rounded.

$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.

$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.

4.82%.

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

$1,456.95

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 $1,456.95.

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.

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.

$4,875.

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

$162,500

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

$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.

$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.

$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 – 153,846 depreciation taken), or $526,154. The gain is then ($780,000 – 526,154), or $253,846.

$257,000.

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

$34,000.

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

$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.

$15,000 overpriced.

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).

Yes, since he will yield 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%.

$1,680.

Annual gross operating income ($1,650 x 12 = $19,800) – annual operating expenses ($600 x 12 = $7,200) = annual net operating income ( $12,600); annual net operating income ($12,600) – cost recovery expense ($7,000) = taxable income ($5,600); taxable income ($5,600) x tax rate (30%) = tax liability ($1,680).

$10,640

The basic formula for tax liability is: Taxable Income x Tax Rate = Tax Liability. Taxable Income is Net Operating Income – Interest Expense – Cost Recovery Expense. Therefore, the annual tax is $150,000 (NOI) – $105,000 (Interest Expense) – $7,000 (Cost Recovery Expense) x 28% = $10,640. Note that the principal payment is not deductible in calculating taxable income.

31.4%

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

$1,000,000,000.

The mill rate = (tax requirement / the tax base). A mill is one one-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.

$1,495

First, always use the assessed valuation, not the market value. Subtract out the homestead exemption to derive taxable value, or $140,000 – 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.

2.13%

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

$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.

$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 credit to the buyer and debit to the seller for $785.34.

The daily tax expense, first, is ($3,150 / 365) or $8.63. Since the buyer will pay the taxes after closing, the seller must pay the buyer his or her portion of the tax bill at closing, which is the 91 days from the beginning of the year through closing. Therefore, credit the buyer and debit the seller ($8.63 x 91), or $785.34.

$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.

Credit buyer $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.

$86,372

First calculate the transfer tax: ($322,600 / 500) = 645.2 units 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.

$5,848.

Be careful here. Since the net price is $5,000, the taking price (TP) minus the commission must equal the net price. In other words, the net price is 90% of the taking price. Since TP x 90% = Net, TP = Net / 90%. So the taking price is $5,556 ($5,000 / .9). Apply the same logic to deriving the asking price: the taking price is 95% of the list price, therefore the list price = (taking price / 95%), or $5,848. Now work backwards to prove your answer: (5,848 x 95% margin x .90 net of commission) = $5,000

$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

$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.