Module 26 - Real Estate Math

Capitalization Rate

A property has a net operating income (NOI) OF $12,000 and a capitalization rate of 6%. What is the value of the asset? NOI/Capitalization % per year = Value of Asset $12,000/.06 = $200,000 1. The capitalization rate, often just called the cap rate, is the ratio of NOI to property asset value. So, for example, if a property was listed for $1,000,000 and generated an NOI of $100,000 then the cap rate would be $100,000/$1,000,000 or 10% Cap Rate = Annual NOI/Cost (or value)

Loan Financing Costs - Discount Points

1% of the loan amount. Prepaid interest. For every point a lender charges, their yield increases by 1/8 of 1%.

Setting Listing Price - What approach would you use to determine the value of:

1. A bank owned foreclosed residential property? Market Approach 2. New Construction? Cost Approach 3. A strip center with several tenants? Income Approach 4. A residential home? Market Approach

Assessed Value and Property Taxes

1. Assessment rate and property assessed value 2. Divide the assessment rate by 100 to convert to decimal 3. Assessed value of home is $200,000. The tax rate is 6% 4. What are the annual taxes? $200,000 x .06 = $12,000

1 Acre =

43,560 square feet

Property Management

A property has monthly gross effective income of $10,000 and annual operating expenses of $25,000. The property management fee is 5% of gross effective income and is included in the expense total. Operating expenses also include annual amounts for real estate taxes of $8,000 insurance of $4,200 and common area maintenance of $4,000. One tenant occupies 6,000 square feet which is 40% of the rentable space. They pay $3,800 in monthly base rent. a. What is the monthly property management fee? 10,000 x .05 = $500 b. What is the tenant's annual rent per square foot? 3800 x 12 = 45,600/6,000= $7.60/ square foot c. What is the monthly cash flow of the property? 10,000 x 12 = 120,000 - 25000 / 12 = $7,916.67

Volume

To calculate volume, multiply length by width by height

Area

to calculate area, multiply length by width

Capitalization Rate

used to calculate the rate of return on an investment

Biannual vs

Twice a year vs. every two years

Loan Financing Costs - Prepayment Penalties

Usually a percentage of the outstanding balance of the loan

Loan Financing Costs - Amortization

a. The buyer's interest rate is 4% for a 30-year term mortgage. The total loan is $200,000. What is the payment? To calculate the Principal and Interest payment, multiply the interest rate by the number of 1000s in the total loan $200,000 / 1000 = 200 x 4 = $800

Converting Percentages

a. converting % to fraction Ex. 25% = 25/100 = 1/4 b. Converting % to decimal. Drop the % sign and move the decimal 2 places to the left Ex. 25% = .25 c. Converting decimal to percent. Move the decimal two places to the right and add a percent sign Ex. .25 = 25%

Loan Financing Costs - Fees or Closing Costs

Includes commissions, title insurance, taxes, home warranties etc.

Property Area Calculations

1. Rectangle - Multiply length x width 2. Triangle - Multiply base by its height and divide by 2 a. A parcel of land measures 400' x400' square. How many acres are contained in this parcel? 400'x400'=160,000 160,000 square feet / 43,560 = 3.6731 b. A parcel is 7.5 acres. How many square feet are in the parcel? 7.5 x 43,560 = 326,700 square feet c. What's the area of a parcel with 1,500 feet of frontage and a depth of 300 feet? 1,500 feet x 300 feet = 450,000 d. The lot is 450,000 square feet with 1,500 feet of frontage. How deep is the lot? 450,000/1,500= 300 e. From question above, how many acres are in the parcel? 450,000/43,560=10.331

Commission and Compensation

1. The commission was $44,000. The commission rate was 8%. What was the sales price? 44,000/.08= $550,000 2. Your company charges a 5% commission. The seller netted $235,155 AFTER paying your company the 5% fee. What was your company's commission in dollars? 235,155/.95=247,531.58 sales price 247,531.58 x .05 = $12,376.58 3. Your company charges a 6% commission. The seller netted $188,000 AFTER paying your company the 6% fee. What was your company's commission in dollars? 188,000 / .94 = $200,000 sales price 200,000 x .06 = $12,000 4. The seller wants a net of $45,000 after paying off $123,125 first mortgage, $ a $7,555 second mortgage and closing costs of $2,567. The broker's commission is 5%. The property should sell for at least what amount to meet the seller's goals? $45,000+$123,125+$7,555+2,567 / .95 = $187,628.42

Investments

1. The potential gross income from an apartment building is $40,000 and there is an allowance for vacancy of 5%. The taxes are $2,500 per year annual maintenance is $4,000, and the repairs are $2,200/ year. What is the estimated value of the property with a desired capitalized rate of 13%? 40,000 x .95% = $38,000 2,500 + 4,000 + 2,200 = 8700 38,000 - 8700 = $29,300 / .13 = $225,385 2. What monthly net income is needed to return 15% on a property valued at $90,000? 90,000 x .15 = 13,500 annual net income/12 = $1,125 3. A residential investment property was purchased for $350,000. The land component was $50,000. It has a life of 27.5 years. a.What would be the annual depreciation amount? 350,000 - 50,000= 300,000/27.5 = $10,909.09 per year b. What is the adjusted basis if held for 10 years? 350,000-10,909.09/year x 10 years = $240,909.10 c. If sold at the end of year 10 what is the taxable gain? 320,000 (adjusted net) - 240,909.10 = 79,090.90 d. Assuming the asset appreciated 15% over the 10-year period, what is the ROI? (ignore taxes) 350,000 + 15% = $52,500

Settlement and Closing Costs

A. A house is sold for $100,000 with the buyer to pay 20% down and 2 points in loan discount fees. The purchaser's other closing costs totaled $650. How much money should the buyers bring to closing? first, the points are charged only on the loan amount. Find loan amount. 100,000 x.20=$20,000 $100,000-20,000 = $80,000 loan amount $80,000 x .02 = $1600 $1600+650+20,000= $22,250 to closing B. A home sold for $42,500 and the seller paid 7% commission. The seller's net was 15% greater than the purchase cost. What did the seller pay for the property to the nearest dollar? 42,500 x .93 = 39,525 / 1.15 = $34,370 C. A property sold for $150,000 with a down payment of $30,000. The new mortgage has a 5% interest rate with the monthly PI constant of $644 for 30 years. How much interest will be paid in the first year of the loan? 150,000-30,000=120,000 x .05 = $6,000 D. The Smith's are closing the sale on their home on April 10. The 12% interest on their mortgage is paid in arrears. The outstanding balance after the April 1 payment is $57,500. What entry will be made for interest at Smith's settlement? (Use banker's year 360 days) 57,500 x .12 = 6,900 /360 = 19.17 per day x 10 days = $191.70 E. Original Purchase price of the property was $342,750. The loan to value was 90%. The seller sold the property and grossed $382,423 after a 5% commission. 1. What was the down payment? 342,750 x.10=34,275 2. What's the sale price? 382,750 x .95 = $363,612.5 3. What was the cash needed by the buyer in (b) if there is a loan to value of 80%, a loan origination fee of 1% and title insurance fee of $800? $402,550.53 x .80 = $322,040.42 322,040.42 x .01 = $3,220.40 402,550.53 x .20 = 80,510.11+3,220.40 +800= $84,530.51.

Proportion

A. Most real estate involves 3 basic variable algebraic equations usually shown as (A) X (B) = (C) B. The calculations are usually for a particular context for a certain purpose, such as: 1. Sales price x commission % = commission dollars 2. Loan amount x interest rate % per year = interest dollars per year 3. front footage x depth footage =area in square feet often then converted to acres C. Some problems have a different starting point. We have (C) and (B) and want to determine (A). Manipulating equations is easy if you use a quick mental tool called the Memory Circle, "T" Bar. It looks like this: C A B All this means is: (A) x (B) = (C) or (C) / (A) = (B) or (C) / (B) = A D. Percentages can be listed different ways. It is short hand notation or a ratio or proportion. 5.25% is a quick way of showing 5.25/100 or .0525/1.00

Loan Financing Costs - Interest Rates

A. The buyer borrowed $100,000 at 4% interest over 30 years. The monthly payment is $477.00; how much is the first year's interest? $100,000 x .04 = $4,000 B. Using the information above, how much is the first month's interest? 4,000/12 = $333.33 C. What is the loan balance after the first payment? 477 - 333.33 = 143.67 principal paid 100,000-143.67 = $98,856.33 remaining

Loan Financing Costs - Loan to Value Ratio (LTV)

A. The buyer wants to buy a $150,000 home with $20,000 down. What is the loan to value ratio? 150,000-20,000 = 130,000 / 150000 = 87% B. The buyer is putting 20% down on the $150,000 sales price. How much is the down payment? 150,000 x .20 = $30,000 C. The home sold for $300,000 and the buyers have $40,000 available for a down payment. What is the Loan to value ratio? 300,000-40,000 = 260,000/300,000 = 87%

Comparative Market Analysis (CMA)

CIA - Comparative is Inferior, Add CBS - Comparative is Better, Subtract Ex. Comparable Sales Price = $325,000 -It has 1 full bath more than the subject. Assume value of $10,000 - It has one less garage bay. Assume value is $18,000 - Using this information, what is the subject property's price? Adjustments: $325,000-$10,000+$18,000=$333,000

Home Equity

Current fair market value of the property minus the amount owed on the property Ex. The current loan balance on a home is $140,000. The home's value is $200,000. What is the equity in the home? $200,000-$140,000=$60,000 Does the equity change if there's a secondary loan of $20,000? Yes, $60,000-$20,000=$40,000

Gross rent multiplier and Gross income Multiplier

Gross rent multiplier = price/Potential Gross Income Another example: price = potential gross income x gross rent multiplier Example: A retail income property has the following data: Gross monthly revenues - $83,400 Purchase Price - $7,500,000 Annual expenses of $270,000 includes RE taxes Annual reserve for capital improvements of $30,000 A capitalization rate of 6% An economic life of 80 years Loan balance- $5,400,000 Monthly PI - $38,582.94 Interest Rate: 5% Annual RE Taxes 1. What is the gross rent multiplier? 7,500,000/83,400=64.75 2. What is the gross income multiplier? 83,400x12= 1,00,800 5,400,000/1,00,800= 5.4 3.Using the current loan amount what is the owner's equity? 7,500,000-5,400,000=2,100,000 4. If the tax rate is $1.25 per $100 of assessed value what is the assessed value? 75000/.0125= 60 million assessed value

Real Estate Equation chart

Page 262-3 in yellow book for reference

Sample Question:

The commission paid to the broker company was $12,000 and the commission rate was 6% A. What was the sales price? Sales Price (A) x Comission % (B) = Commission Rate (C) C/B=A $12,000 / .06 = Sales Price

Interest

The cost of borrowing money

Return of Investment

The key is to understand that the same math applies but both profit and loss are a percent of initial cost Cost of Asset (A) X Profit % (B) = Profit Dollars (C) $200,000 x .06 = $12,000 Note: The sales price is Cost PLUS Profit or $212,000, which is 1.06 x cost. But a sale at a loss is a bit different $200,000 x .06 = $12,000 (loss) Note: The sales price is cost LESS loss or $188,000, which is .94 x cost