Real Estate Math Problems

Question 1

An office building rents for $600,000, has expenses of $400,000, and cash flow of $100,000. The prevailing gross rent multiplier is 8. Using the GRM, what is the value of the building?

Answer 1

p. 321
Searching for property value in this equation.

Annual Gross Rents X Gross Rent Multiplier (GRM) = Property Value

So, According to given formula

Gross Rent = $600,000

Gross Rent Multiplier (GRM) = 8

Building Value = Gross Rents X Gross Rent Multiplier (GRM)

Building Value = $600,000 X 8

Building Value = $4,800,000

Question 2

A borrower earns $3000/month and makes credit card and car not payments of $500. A conventional lender requires a 27% income ration. What monthly amount for housing expenses will the lender allow this person to have in order to qualify for a conventional mortgage loan?

Answer 2

$3000 x 12 (months) = $36,000 salary

$36,000 - 27% maximum= $9720/year of debt

$9720/12 months= $810

Question 3

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

Answer 3

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

Question 4

A lender is charging 2.75 points on a $240,000 loan. How much must the borrower pay for points?

Answer 4

$240,000 x 2.75%= $6600

Question 5

An office building has $300,000 net income and sold for $4,800,000. What was the rate of return?

Answer 5

Rate = ($300,000 NOI ÷ $4,800,000 price) = 6.25%

Question 6

An office building has $400,000 net income and a cap rate of 8.25%. What is its value?

Answer 6

Value = ($400,000 ÷ 8.25%) = $4,848,485

Question 7

A home that was purchased for $150,000 with a $100,000 loan is now worth $300,000. The current loan balance is $80,000. What is the homeowner’s equity?

Answer 7

Current value $300k minus loan balance $80k

$300,000 value - $80,000 debt = Equity $220,000

Question 8

A $250,000 interest-only loan carries a 7% rate. Monthly payments are…

Answer 8

$250k x 7%= $17,500

$17500/12 months= $1458

Question 9

An office building has potential income of $500,000 and vacancy of $10%. Its cash paid bills total $300,000, and annual depreciation is $5000. Payments on the loan total $100,000. What is the property’s pre-tax cash flow?

Answer 9

Subtract annual rental income- vacancy
$500k-10%= $450k
$450k is my Effective Gross Income (EGI)

Subtract my operating expenses
$300k bills
$450k-$300k= $150k
$150k is my NOI Net Operating Income

Subtract the value of the debt service from my NOI
$150k-$100k= $50,000 Pre-tax value

Question 10

A property is purchased for $200,000. Improvements account for 75% of the value. Given a 39 year depreciation term, what is the annual depreciation expense?

Answer 10

$200,000 x 75% = $150,000

$150,000/39= $3846

Question 11

An income property is bought for $500,000. Gross income is $100,000 and net operating income is $60,000. Cash flow is $10,000. What is the return on Investment (ROI)?

Answer 11

Net Operating Income / Cost of Investment x 100

$60k/$500k= 0.12 x 100= 12%

Question 12

The village of Parrish has an annual budget requirement of $20,000,000 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?

Answer 12

Municipality budget ÷ total assessed valuation = tax rate

$20,000,000/ ($400,000,000-$25,000,000)
$20,000,000 / $375,000,000 = .0533333

.053 x 100 = 5.33%

Question 13

A canal dredging project is to cost $100,000. There are 40 properties along the canal, and 40 across the street from the canal. The total canal footage to be dredged is 2500 feet. How much will the assessment be for 150-foot property on the canal?

Answer 13

$100,000 / 2500 = 40

40 X 150 = $6000

Question 14

Similar properties to Joe’s property that are in the area have an average gross rent multiplier of 13 Joe’s property brings in $1000 a month what is the estimated value of his property

Answer 14

$156k

When you see monthly always x12 to get the annual then multiply the GRM

Notice small number= annual

Question 15

Sharon owned an income property with an adjusted cost basis of $1.5 million in a fair market value of 2 million. She exchanged the property for another income property which is the fair market for 2.1 million both parties have no loans. what will the new basis be?

1mil 2mil 2.1 mil 1.5mil

Answer 15

1.5mil

Cost basis of Old property is the cost basis of the new property.

Cost basis isn’t a math problem

Question 16

Individual borrowed $7000 on a straight note at 9% interest. If the total interest paid on a new it was $945, what was the term of this loan?

20 months 16 months 12 months or 18 months

Answer 16

18

7000 x 9% = 630
630/12 = 52.5
52.5 x 18 months= $945

Question 17

GIM formula

Answer 17

Yearly gross income

Question 18

If a man has 6 acres of land and deeds 3/4 of it to a son and the remainder to a nephew, how many square feet of land does the nephew acquire?
261,360
196,020
65,340
43,560

Answer 18

65,340

Question 19

How many cubic feet of space is there in a warehouse that is 610 feet wide by 140 feet deep and has an 18 foot ceiling?
85,400
1,537,200
35
2,520

Answer 19

1,537,200