Math 01 Flashcards
Jackie obtains a 60% LTV loan on her new $250,000 home with an annual interest rate of 5.5%. What is the first month’s interest payment?
$250,000 x 0.60 = $150,000 loan, $150,000 x 0.055 = $8,250, $8,250 ÷ 12 = $688
Laura obtains a new loan @ 67% of her home’s price of $300,000. The loan constant is 6.321. What is Laura’s monthly payment?
$300,000 ÷ 1000 = $300, $300 x 6.321 = $1,896, $1,896 x 0.67 = $1,270
Price / 1000 = A
A X Constant = B
B X Rate = Monthly Payment
Jerry recently obtained an 75% loan on his $410,000 home, and he had to pay $5,600 for points. How many points did he pay?
$410,000 x 0.75 = $307,500, $5,600 ÷ $307,500 = 0.018 = 1.8 points
A borrower obtained a 70% loan for $600,000. What was the price of the home (to the nearest thousand)?
Loan / Rate = Price
$600,000 / 0.70 = $857,142.86
The loan officer at 2nd National Bank tells Lana she can afford a monthly payment of $1,900 on her new home loan. Assuming this is an interest-only loan, and the principal balance is $410,000, what interest rate is Lana getting?
$1,900 x 12 = $22,800, $22,800 ÷ $410,000 = 0.0556
A home buyer pays $1,800 / month for the interest-only loan on his new house. The loan’s interest rate is 6%. If he obtained a 80% loan, what was the purchase price?
$1,800 x 12 = $21,600, $21,600 ÷ 0.06 = $360,000, $360,000 ÷ 0.80 = $450,000
If you owe $14,000 on a new loan and pay $880 of interest for the year, your interest rate is?
.063 = 6.3%
A loan applicant has an annual gross income of $76,000. How much will a lender allow the applicant to pay for monthly housing expense to qualify for a loan if the lender uses an income ratio of 30%?
1900
(Gross Income / 12) x Income Ratio = Monthly Housing Expense
Formula: AGI / 12 = MGI
MGI X Income Ratio = Monthly Housing Expense
A loan applicant has an annual gross income of $42,000. How much will a lender allow the applicant to pay for monthly housing expense to qualify for a loan if the lender uses an income ratio of 32%?
1120
Formula: Monthly Principal and Interest (PI) payment = Income ratio X Monthly gross income
The Browns obtain a fixed-rate amortized 30-year loan for $310,000 @ 6% interest. If the monthly payments are $1,815, how much interest do the Browns pay in the first month of the loan?
1550
(Loan x Rate) / 12
Formula: Step 1: Principal X Interest Rate = Annual Interest
Step 2: Annual Interest / 12 months = 1 month’s Interest
A lender determines that a homebuyer can afford to borrow $160,000 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?
200,000
A home buyer pays $1,800 / month for the interest-only loan on his new house. The loan’s interest rate is 6%. If he obtained a 80% loan, what was the purchase price?
Annual Interest / Rate = Loan Amount
Loan Amount / LTV = Price
450000
A lender uses a 39% debt ratio. A borrower earns $40,000 / year and has monthly non-housing debt payments of $700. What housing payment can she afford?
Monthly Principal and Interest (PI) payment = Income ratio X Monthly gross income
$1300
Christy has monthly loan payments of $1,200. Her loan is for $210,000 @ 6.1% interest. How much of her first payment goes towards principal?
Annual Interest / 12 - Monthly Payment
$132.50
The loan officer at 2nd National Bank tells Lana she can afford a monthly payment of $1,900 on her new home loan. Assuming this is an interest-only loan, and the principal balance is $410,000, what interest rate is Lana getting?
Monthly Payment X 12 = Annual Interest
Annual Interest / Principal Balance = Interest Rate
.0556
A borrower has a $770,000 interest-only loan @ 5.5% interest. What are the monthly interest payments?
Loan Amount X Rate = Annual Interest
Annual Interest / 12 = Monthly Interest Payment
$3529
A property sells for $180,000 one year after it was purchased. If the annual appreciation rate is 10%, how much did the original buyer pay for it?
The selling price is 110% of the purchase price. Therefore, the purchase price is the selling price divided by 1.1 (110%). $180,000 / 1.1 = $163,636.
A homeowner paid $185,000 for a house three years ago. The house sells today for $239,000. By what percent has the property appreciated?
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%.
An office building has $300,000 net income and sold for $4,800,000. What was the rate of return?
Rate = ($300,000 NOI ÷ $4,800,000 price) = 6.25%
An office building has $400,000 net income and a cap rate of 8.25%. What is its value?
Value = ($400,000 ÷ 8.25%) = $4,848,485
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?
Equity = $300,000 value - $80,000 debt = $220,000
Yvonne bought a home in Biltmore Estates 3 years ago for $250,000. She obtained an 80% loan. Over the past three years, the total appreciation rate has been 18%, and she has paid down her loan by $4,000. What is Yvonne’s equity after this period?
Equity = Market value – loan balance. Her loan was .8 x $250,000, or $200,000. Her initial equity was 20% x $250,000, or $50,000. The home has appreciated 18%, or (.18 x $250,000), or 45,000. Plus she has paid down her loan $4,000. Her equity is therefore ($295,000 market value – 196,000 loan), or $99,000.
Using the terms Potential Gross Income, Vacancy, Other Income, Operating Expenses, and Gross Operating Income, express the equation for Net Operating Income.
(Potential Gross Income - Vacancy) + Other Income = Gross Operating Income
Gross Operating Income - Operating Expenses = Net Operating Income (NOI)
Describe the difference between NOI and cash flow.
Cash flow is net operating income minus debt service. If there is no loan the two are the same.
An apartment building was purchased for $500,000, with the land value estimated to be $100,000. The owner added a $100,000 parking lot. The property was depreciated on a 40-year schedule (for present purposes!). Three years later the property sold for $700,000, and selling costs were $50,000. What was the capital gain?
Tip: work example backwards from last formula to first formula.
depreciable basis = $500,000 purchase price + 100,000 parking lot - 100,000 land = $500,000
total depreciation = ($500,000 ÷ 40 years) x 3 years = $37,500
adjusted basis = $500,000 purchase price + 100,000 parking lot - 37,500 total depreciation = $562,500
amount realized = $700,000 sale price - 50,000 selling costs = $650,000
capital gain = $650,000 amount realized - 562,500 adjusted basis = $87,500
An office building has NOI of $200,000, an annual reserve expense of $20,000, interest expense of $130,000 and annual depreciation of $50,000. Assuming a 28% tax bracket, what is its income tax liability?
Tax liability = ($200,000 + $20,000 - $130,000 - $50,000) x 28% = $11,200
An investor sold a property for $3 million and incurred $300,000 in selling costs. He originally paid $2.4 million 3 years ago and has depreciation expense totaling $150,000. What was his capital gain?
Capital gain = Take the purchase price ($2.4 million) - depreciation ($150,000) which equals the adjusted basis ($2.25 million). Amount realized = selling price ($3 million) - selling cost ($300,000) which equals $2.7 million. Finally, you take the amount realized ($2.7 million) - adjusted basis ($2.25 million) which equals capital gain ($450,000).
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?
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.
An investor pays $300,000 for a property, $50,000 of which is land, puts $50,000 capital improvements into it, and borrows $250,000 to finance the property. What is the property’s depreciable basis?
$300,000 cost minus $50,000 land plus $50,000 capital improvements, or $300,000. The loan is irrelevant.
A principal residence is bought for $180,000. A new porch is added, costing $7,000. Five years later the home sells for $220,000, and the closing costs $18,000. What is the homeowner’s capital gain?
Gain = amount realized ($220,000 - $18,000) - adjusted basis ($180,000 + $7,000) = $15,000.
An income property has a net income of $20,000, interest expense of $12,000, cost recovery (depreciation) of $3,000, and a tax rate of 28%. What is its income tax liability?
Net Operating Income (NOI) $20,000 - interest expense $12,000 - cost recovery expense $3,000 = taxable income $5,000 x tax rate (28%) = tax liability $1,400
An investment property generates a cash flow of $50,000 and appraises for $700,000. What is the owner’s return on investment?
ROI = $50,000 ÷ 700,000 = 7.14%
An investment property generates a cash flow of $200,000. The owner has $450,000 equity in the property. What is the owner’s return on equity?
ROE= $200,000 ÷ 450,000 = 44%
A property’s return on equity ratio is 28% and generates a cash flow of $70,000. How much equity does the owner have (to the nearest hundred)?
250,000
An office building has NOI of $110,000, interest expense of $47,000 and annual depreciation of $16,000. Assuming a 28% tax bracket, what is its income tax liability?
13,160
A home that was purchased for $440,000 with a $320,000 loan is now worth $530,000. The current loan balance is $280,000. What is the homeowner’s equity?
250,000
An apartment complex generates $335,000 in effective rental income and $2,500 in other income. The same complex has $144,000 in operating expenses and $116,000 in debt service payments. What is the pre-tax cash flow of the complex?
77,500
An office building sells for $979,000 at a cap rate of 8.3%. What is its NOI?
81,257
A property has a net income of $40,000, interest payments of $17,000, and annual cost recovery of $9,000. The property’s tax rate is 25%. What is the property’s annual tax liability?
3500
Marcos Pizza has a percentage lease on its 1,500 SF space in the Ashwood Center. The terms are $1.25 / SF / month rent plus 2% of the store’s gross income. If monthly sales averaged $35,000 last year, how much annual rent did Marcos Pizza pay last year?
Their fixed rent is (1,500 SF x $1.25/SF) x 12 months, or $22,500. The percentage rent is ($35,000 x .02) x 12, or $8,400. Total rent is ($22,500 + $8,400), or $30,900.
A tax rate on a house with a $300,000 taxable value is 11 mills per thousand dollars of assessed valuation. What is the tax?
Tax = ($300,000 ÷ 1,000) x 11 mills = $3,300
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?
The rate = budget / tax base. Thus, $20,000,000 / ( $400,000,000 – $25,000,000) = 5.33%
A $300,000 property sells at a 7% commission with a 50-50 co-brokerage split and a 60% agent split with her broker. What are total, co-brokerage, agent’s, and broker’s commissions?
Total commission = $300,000 x .07 = $21,000
Co-brokerage splits = $300,000 x .07 x .50 = $10,500
Agent split = $10,500 x .60 = $6,300
Agent’s broker’s split = $10,500 - 6,300 = $4,200
A home seller wants to net $50,000. The commission is 7%, the loan payoff is $150,000, and closing costs are $4,000. What must the minimum contract price be?
Add up the desired seller’s net, the loan payoff and the closing cost: $50,000 + 150,000 + $4,000 = $204,000 seller’s gross profit
Since the seller has agreed to a 7% sales commission, that means he will get to keep 93%, which is 0.93 as a decimal.
Divide seller’s gross profit by seller’s %: $204,000 ÷ .93 = $219,354.83
So, the very minimum amount that the seller can list his house at and still cover his expenses and make his desired profit is $219,354.83.
A homeseller wants to net $75,000. The commission is 9%, the loan payoff is $450,000, and closing costs are $36,000. What must the price be (to the nearest $100)?
Desired Net + Closing / (1 - Commission) = Sale Price
$75,000 + $450,000 + $36,000 = $561,000
$561,000 / (1 - .09) = 616,483.51
A town has a tax base of $88,000,000 and a total assessed valuation of $99,000,000. What is the total amount of the town’s tax exemptions?
11,000,000
Rusty sells his home for $330,000. He must pay a 6% brokerage fee which will be split evenly between the selling broker and listing broker. He will also incur $5,000 in other closing costs and pay off a $225,000 mortgage balance. How much can Rusty expect to receive at closing?
80,200
