P a g e 1 REAL ESTATE MATH REVIEW Quick Reference... 2 Review Quiz 1... 4 Review Quiz 2... 5 Review Quiz 3... 6 Review Quiz 4... 9 Answer Key... 11
P a g e 2 QUICK REFERENCE INCOME APPROACH/CASH FLOW GI V E E N M C Gross income -Vacancy =Effective gross income -Expenses =Net operating income -Mortgage =Cash flow All numbers annual Value = NOI in top of T over cap rate EQUITY DIVIDEND RATE Also called rate of return on equity and cash on cash rate of return Use GiVEENMC Cash flow in top of T over equity (cash invested) SALES COMPARISON Subject does not change: has one column of bedrooms, bathrooms, fireplaces, etc. Comps have two columns: one of bedrooms, etc. and one of dollar amount adjustments Compare subject to each comp Add inferior items, subtract superior ones Baths: add up how much baths are worth in subject and then comp and compare Garages: take difference between garage worth in subject and comp Appreciation: percent for year * sales price divided by 12 * number months ago sold COST APPROACH Age and Life Age divided by Life = depreciation % New building depreciation % + land = value BALANCE AFTER PAYMENT Monthly payment - Monthly Interest - Loan amount or balance = owed after one payment INTEREST OVER LIFE OF LOAN Monthly payment * 12 * number of years in loan loan amount = interest over life Do NOT use interest rate NET TO SELLER Add everything up, put in top of T over inverse of commission (95%, not 5%) GROSS RENT MULTIPLIER Price divided by monthly rent A number (not percentage) usually between 100 and 200 or so PERCENTAGE PROFIT/LOSS Profit or loss in top of T over original price
P a g e 3 PRORATIONS Taxes: draw time line and ask who is getting stuck paying the whole tax bill? Before Sep 1: Buyer gets stuck credit buyer, debit seller their part of the year After Sep 1 paid: Seller was stuck credit seller, debit buyer their part of the year After Sep 1 unpaid: Neither is stuck, both pay their part at closing, two different debits Interim interest: buyer pays for rest of month plus one day Loan amount * rate divided by 360 * number of days Accrued interest: seller pays 1 st day of month through closing date Loan payoff amount * rate divided by 360 * number of days QUALIFYING A BUYER 28% side Housing expense (PITI) 36% side Recurring obligations (PITI + other recurring debt) Monthly income in bottom of T with PITI and recurring debt on top Solve both sides and determine what the question is asking INCREASE IN EQUITY Increase in equity in top of T with original equity in bottom Original equity = purchase price loan amount Increase in equity = increase in equity 1 + increase in equity 2 Increase in equity 1 = loan amount * decrease in loan % Increase in equity 2 = purchase price * increase in value % Often a large percentage: 100, 200, 300% IRV CIRCLE/MAGIC CIRCLE/ T Percentage always in the same place bottom left. Where are the other two numbers? Rule of thumb: Little number on top, big number on bottom. Commission on top, sales price on bottom. Net to seller on top, sales price on bottom. PITI on top, monthly income on bottom. NOI on top, value on bottom UNLESS you are dealing with two points in time in the same circle. Two points in time: New number on top, old number on bottom regardless of size. Purchase price on bottom, sold for on top Purchase price on bottom, profit at sale on top Purchase price on bottom, loss at sale on top Original equity on bottom, increase in equity on top
P a g e 4 REVIEW QUIZ 1 1. A parcel is in the shape of a triangle. There is 120' of road frontage and the depth is 230'. If the parcel sells at $16,000 per acre, what is the sales price of the parcel? 2. Closing is March 13. The assessed value of the property is $79,000 and the tax rate is $.73 per $100 of assessed value. What are the correct entries for unpaid taxes on the closing statement? 3. An apartment complex's annual income and expenses: gross income of $435,000, effective gross income of $405,000, operating expenses of $137,000 and mortgage payments of $216,000. Using a cap rate of 12% what is the estimated value? 4. Subject property: 1,800 square feet, 2 bedrooms, 1 ½ baths, 1 car garage, $10,000 of recent landscaping upgrades. Comparable property sold 3 months ago for $185,000, 1,950 square feet, 2 bedroom, 2 baths, 1 car garage, standard landscaping. Construction costs are $105 per square foot, $2,000 for ½ bath, $3,500 for full bath, 6% price appreciation in previous year. What is approximate value of subject property? 5. A buyer is getting an 80% loan for a property with a sales price of $787,500. They receive a loan offer for a 15- year loan at 4.65% with monthly principal and interest payments of $4,875.44 and a 1% loan origination fee. What is the amount of interest paid over the life of this loan? 6. A buyer has $75,000 in annual income. He is applying for a $220,000 mortgage, 30 year fixed rate at 4.5%. His mortgage will have monthly principal and interest payments of $1,100 with taxes and insurance totaling $125 per month. He owes monthly car payments of $269, monthly child support payments of $400 and averages credit card payments of $625 a month. Will he qualify under 28/36 ratios? 7. A building's lot is worth $145,000. The 20 year old building with 3,250 square feet will take $118 per square foot to replace. The economic life of the building is 40 years and the effective age is 12 years. What is the estimated value of the property? 8. An apartment complex has 56 units that rent for $975 a month. For the past year 2 units per month were vacant. Additionally, $2,925 in rent due was not collected for the year. Annual management fees were 6% of effective gross income, property taxes were $32,000, utilities were $44,000, maintenance costs were $29,000, debt service was $205,000 and other expenses were $86,000. What was the before tax cash flow? 9. If a property recently sold for $115,000 and its monthly rental income was $850, what is the gross rent multiplier? 10. A seller wants to net $135,000 after paying off a mortgage of $376,000, $4,700 in expenses and a 6% commission to the broker. What must the sales price be? 11. Closing is July 22. Annual homeowner's dues of $1,500 have been paid for the calendar year. What are the correct entries for homeowner's dues on the closing statement? 12. What are the annual taxes on a property located within the city, with an assessed value of $335,000, if the county tax rate is $0.56 and the city tax rate is $0.62? 13. An apartment complex's annual income and expenses: gross income of $435,000, effective gross income of $405,000, operating expenses of $137,000 including reserves of $12,000 and mortgage payments of $216,000. If an investor buys the property for $2,000,000 with a $400,000 down payment, what would be the rate of return on equity?
P a g e 5 REVIEW QUIZ 2 1. A buyer bought a house for $85,000 and sold it for $125,000. What is the percentage profit? 2. Closing is November 6 and real estate taxes of $1,575 have not been paid. What are the correct entries for the closing statement? 3. A 50 unit apartment complex has: vacancy rate of 5%, operating expenses of $233,000 and mortgage payments of $177,000. If all units rent for the same amount, what must each unit rent for in order to have cash flow of $137,200? 4. A subject property has 1,600 square feet. Comparable 1 has 1,700 square feet and sold for $185,000. Comparable 2 has 1,675 square feet and sold for $183,000. Comparable 3 has 1,540 square feet and sold for $177,000. Using a price of $82 per square foot what is the range of the estimated selling price of the house? 5. A property sells for $145,000 in a co-brokered transaction. The seller has agreed to pay the listing firm a 6% commission. The listing firm has agreed to equally split the commission with the selling firm. What is the buyer s broker commission payment if they receive 70% of the selling firm s commission? 6. A buyer's monthly PITI payment will be $875 with monthly recurring debt of $435. What is the minimum monthly income the buyer needs to qualify for the loan using 28/36 ratios? 7. A building's lot is worth $112,000. The 15 year old building with 3,875 square feet will take $114 per square foot to replace. The economic life of the building is 40 years and the effective age is 10 years. What is the estimated value of the property? 8. 45 apartments rent for $625 each and have an 8% vacancy rate. If expenses are 42% of gross income, what is the value applying a 10.5% cap rate? 9. What would be the interim interest entry on a September 19 th closing for a new 6.25% 30-year loan for $145,000? 10. A subject property has 1,800 square feet, 3 bedrooms and 2 baths. Comparable 1 has 1,900 square feet, 3 bedrooms, 2 baths and sold for $190,000. Comparable 2 has 1,900 square feet, 3 bedrooms, 3 baths and sold for $198,000. Comparable 3 has 1,700 square feet, 3 bedrooms, 2 baths and sold for $175,000. Based on this information what is the best estimate of value for the subject property? 11. A seller wants to net $75,000 after paying off a mortgage of $210,000, $3,500 in expenses and a 6% commission to the broker. What must the sales price be? 12. An apartment complex's annual income and expenses: property taxes of $18,000, gross income of $325,000, vacancy and collection of 5%, other operating expenses of $111,000 and debt service of $115,000. What is the before-tax cash flow? 13. A buyer is purchasing a home for $325,000 that will close on February 16. They paid $600 for an appraisal at the time of loan application and will receive a mortgage loan for $260,000 with a 4.25% interest rate and will pay interim interest. $900 hazard insurance premium is due at closing. Real property taxes are $3,500 and will be paid later in the year. Escrow deposits required at closing of 2 months real property taxes and 2 months hazard insurance premium. The buyer must pay additional closing costs of $4,200. How much will the buyer owe at closing?
P a g e 6 REVIEW QUIZ 3 1. A buyer is receiving an 80% loan for a $192,000 property. She is considering two loan offers. One is a 15 year mortgage with monthly principal and interest payments of $1,195. Another loan offer is for a 30 year mortgage with principal and interest payments of $801. What is the difference in the total amount of interest charged over the life of these loans if both are offered at 4.75%? 2. What is the gross rent multiplier for a rental house which recently sold for $230,000 and that generates monthly rental income of $1,800? 3. Homeowner s dues of $45 per month are paid annually for each calendar year and were paid by the seller in January. How would the entries for prorated homeowners dues appear on the closing statement for a closing on May 16? 4. A property sells for $265,000 in a co-brokered transaction. The seller has agreed to pay a 5% commission. The listing firm has agreed to pay a 3% commission to the selling firm. How much commission will the listing firm retain? 5. A buyer wants to receive a mortgage for $120,000. The monthly PITI payments would be $608. The buyer s car payment and credit card payment total $450 a month. What is the minimum monthly income needed for the buyer to qualify for the mortgage using ratios of 28% and 36%? 6. A property located in the city has an assessed tax value of $495,000 and was recently appraised for $545,000. The tax rate is $0.37 per hundred in the city and $0.89 per hundred in the county. What is the total annual property tax? 7. A buyer has an annual income of $96,000 and is applying for a mortgage loan with monthly principal and interest payments of $1,475 and taxes and insurance of $275. What is the buyer s maximum allowable monthly recurring non-housing expense using loan qualifying ratios of 28% and 36%? 8. A seller wants to receive $60,000 from the sale of a property. The current mortgage of $90,000, the brokerage commission of 7%, and $4,800 of other expenses must be paid at closing. What must the sales price be to meet the seller s goal? 9. A buyer obtained a 15 year 80% loan at 4.5% for a property costing $185,000. How much interest will be paid over the life of the loan if the monthly principal and interest payments are $1,132? 10. Using the subject and comparable properties shown below, what is the most appropriate estimate of value for the subject property? Subject Comp #1 - $222,000 Comp #2 - $215,000 Comp #3 - $205,000 2100 sq ft 2200 sq ft 2200 sq ft 2000 sq ft 3 Bedrooms 3 Bedrooms 3 Bedrooms 3 Bedrooms 2 Baths 2 Baths 1 Bath 2 Baths
P a g e 7 11. A rental property has 30 units that rent for $950 per month. In the previous year, an average of 2 units per month were vacant. Additionally, $1,900 in rent due was not collected in the past year. Annual expenses are: Management $24,000 Property taxes $20,000 Utilities $30,000 Maintenance $15,000 Other expenses $45,000 Mortgage $115,000 What is the before-tax cash flow? 12. A broker is performing a comparative market analysis on a 2800 square foot house. Comparable 1 has 2700 square feet and sold for $319,000. Comparable 2 has 2900 square feet and sold for $335,000. Comparable 3 has 2750 square feet and sold for $325,000. If $121 is an appropriate price per square foot for adjustments, what is the range for the probable sales price of the subject house? 13. A licensee is preparing a comparative market analysis for a possible listing. The house is 9 years old, fibercement siding, 2200 square feet, 3 bedrooms, 2 baths, 1-car garage with bonus room, and a recent kitchen upgrade worth $15,000. A similar house sold 3 months ago for $235,000. That house is 8 years old, fibercement siding with 2350 square feet, 3 bedrooms, 2 baths, 2-car garage with no upgrades. Construction costs for similar houses are $130 per square foot, $12,000 for a 1-car garage, and $18,000 for a 2-car garage. Price appreciation has been 4% during the previous year. Based on this information, what is the probable sales price of the house to be listed? 14. A parcel of land costs $14,000 per acre. What is the total cost if the parcel measures 650 feet wide by 900 feet deep? 15. A house was purchased for $145,000 cash and sold several years later for a net amount of $188,500. What was the percentage profit on the sale? 16. An investor in interested in a rental property. The purchase price is $750,000 with a down payment of $187,500. The mortgage payment will be $2,850 a month. For the previous year, annual income and expenses were: gross income of $145,000, effective gross income of $137,750, operating expenses of $75,000 including reserves of $5,000. What would be the investor s rate of return on equity? 17. The estimated replacement cost of a 7,000 square foot, 30-year old building is $150 per square foot, the economic life of the building is 50 years, and the effective age of the building is 20 years. The buildings lot is valued at $285,000. Based on this information, what is the estimate of the property s value?
P a g e 8 18. An apartment complex has annual income and expenses of: Gross Income $925,000 Effective Gross Income $880,000 Operating Expenses $450,000 Debt Service $310,000 Using a capitalization rate of 9%, what is the estimated value of the complex rounded to the nearest thousand? 19. What is the gross rent multiplier for a residential quadplex which recently sold for $660,000 and that generates monthly rental income of $1,200 per unit? 20. An apartment building has 10 units that rent for $950 per month and 5 units that rent for $1200 per month. Vacancy and collection for the previous year was 3% of gross income. Operating expenses are $95,000 per year. Using a capitalization rate of 9%, what is the estimated value of the property rounded to the nearest thousand? 21. A buyer is approved for a $168,000, 30-year mortgage at 4.5%. How much interim interest will the buyer owe at a March 12 closing? 22. The assessed value of a property is $125,000. The local ad valorem tax rate is $0.94 per $100 of assessed value. What are the correct prorated tax entries on the closing statement for a May 13 closing date? 23. A property manager is estimating an operating budget for a 65 unit apartment complex. Annual property taxes are $60,000, other operating expenses are $215,000 and mortgage payments are $155,000 a year. Vacancy and collection average 3% of gross income. If all units rent for the same amount what must each unit rent for, rounded to the nearest dollar, in order to have a before-tax cash flow of $175,000? 24. A buyer purchased a home for $235,000 and paid $5,000 in closing costs. The buyer paid both $375 for an appraisal and $65 for a credit report at the time of loan application. The buyer received an 80% loan at 4.25% with a closing on June 30. Annual property taxes of $1675 were unpaid on the closing date. Property insurance of $850 was paid outside of closing. The buyer owed interim interest on the new loan and escrow deposits for 2 months property taxes and 2 months property insurance premium. How much money did the buyer bring to closing? 25. The principal balance on a mortgage is $191,600. The mortgage is 30 years at 4.25% interest. Monthly principal and interest payments are $984. What is the principal balance on the loan after the next monthly payment?
P a g e 9 REVIEW QUIZ 4 1. The payment on a mortgage is $1,646.73 for 30 years at 4 ½ %. How much interest will be paid over the life of the loan if the loan amount is $325,000? 2. An investor lost 12% of her real estate investment. How much did she pay for the property if the dollar loss was $21,000? 3. What is the monthly payment of a $150,000 loan, with a loan factor of 6.54, annual taxes of $1,234, and annual insurance premium of $870? 4. What will be the effective yield to a lender for a loan of $375,000, 30 years, 4.5% interest, 2 points charged? 5. What is the Loan to Value (LTV) for a $275,000 loan, purchase price of $350,000, appraisal of $343,750? 6. What are the annual taxes on a property assessed at $345,000 at a tax rate of 15 mills? 7. A building contains floor space of 200' x 150' and the ceiling is 12' high. How many cubic yards of air space must be heated and cooled in the building? 8. Closing on a rental house is March 9. The rent of $1,350 a month has been paid. What are the correct entries for rent on the closing statement? 9. A developer is purchasing 250 acres of land. He wants each lot to be 150' x 185'. Streets will take up 9 % of the land. How many lots can be developed on this tract? 10. What is the principal amount of a loan with an interest rate of 7.5% if the interest paid over a 3 month period is $600? 11. How much was invested in a lot that sold for $420,000 and gave the owner 40% profit? 12. A lot is sold with a 9% commission to the agent. The owner must net $30,000 after paying off a $14,000 loan on the property and $1,500 in expenses. How much must the lot sell for? 13. A house was purchased for $325,000 with a 10% down payment. The mortgage has been reduced by 14% and the property value has increased by 11%. What is the percent of equity increase? 14. How much will be owed after the first payment on a $290,000 loan at 4.5% for 30 years with a monthly payment of $1,469.39? 15. Buyers make $175,000 per year. They owe $1,200 per month for car payments and credit card payments. What is the maximum PITI they can qualify for? 16. A subject house has 1,600 square feet and a large lot worth $12,000 more than the comparable. The subject has 2 baths and no fireplace. The comparable sold 4 months ago for $165,000 with 1,675 square feet, 1.5 baths and a fireplace. Costs are $100 per square foot for construction, ½ bath $2,000, full bath $3,500, fireplace $4,000 and appreciation of 5% a year. What is the approximate value of the subject?
P a g e 10 17. An office building has 37,000 square feet. The rental rate is $13 a foot plus $2 a foot for common maintenance with a 15% vacancy rate. Depreciation is 10% a year and the management fee is 12% of effective gross. Insurance, taxes, maintenance and utilities are 33% of gross income. Estimate the value using an 11% cap rate. 18. A real estate company and a broker split commissions 60% to the broker and 40% to the company. If the broker's share of the commission was $3,570, and the sale price was $85,000, what was the commission rate? 19. This month's interest payment is $585.70. If the buyer secured a 90 % loan at an 8.75 % annual rate of interest, what was the sales price? 20. Estimated sales price for an apartment complex is $860,000 with a capitalization rate of 12%. If vacancy and expenses are 40% of gross income, what is the property's estimated gross annual income? 21. A retail business leased a space in a strip mall with a percentage lease and agreed to pay $425 monthly fixed rent and 6 percent on all sales over $175,000. This year, the total rent paid was $9,321. What were the gross sales? 22. A survey description reads The N ½ of the SE ¼ of the SW ¼ of Section 32, Township 12 North, Range 3 West of the tenth Principal Meridian. What is the acreage of the parcel? 23. The market value of a property is $65,000 and is assessed for 45 percent of its value. If the owner s semiannual tax bill was $511.88, what was the tax rate per $100? 24. An owner of a quadplex has one unit that rents for $450 a month, one unit that rents for $475 a month, and two units that rent for $500 a month. The vacancy rate is 4 percent, and the monthly expenses average $350. If the rate of return on the property is 10 percent, what is the estimated value? 25. An investor purchased two parcels of land. One that is one mile square and another that measures 650 x 650. At a cost of $1,500 an acre, how much did she pay for the property?
P a g e 11 ANSWER KEY REVIEW QUIZ 1 1. $5,069 2. Debit seller $116.94, credit buyer $116.94 3. $2,233,333 4. $180,525 REVIEW QUIZ 2 1. 47% 2. Debit seller $1,338.75, debit buyer $236.25 3. $960 4. $176,800-$181,920 REVIEW QUIZ 3 1. $73,260 2. 127.78 3. $336 debit buyer, $336 credit seller 4. $5,300 5. $2,939 6. $6,237 7. $1,130 8. $166,452 REVIEW QUIZ 4 1. $267,823 2. $175,000 3. $1,156.33 4. 4 ¾ % 5. 80% 6. $5,175 7. 13,333 8. Debit seller $945, credit buyer $945 5. $247,579 6. No 7. $413,450 8. $195,143 9. 135.3 5. $3,045 6. $3,639 7. $443,313 8. $1,607,143 9. Debit buyer $302.08 9. $55,760 10. $213,500 11. $68,300 12. $322,900 - $331,100 13. $226,850 14. $188,017 15. 30% 16. 15.23% 17. $915,000 9. 357 10. $32,000 11. $300,000 12. $50,000 13. 236% 14. $289,618.11 15. $4,050 16. $169,750 17. $2,109,000 10. $548,617 11. Debit buyer $658.33, credit seller $658.33 12. $3,953 13. 13% 10. $182,500 11. $306,915 12. $64,750 13. $70,846.53 18. $4,778,000 19. 137.5 20. $949,000 21. $399 22. $434.10 debit seller, $434.10 credit buyer 23. $800 24. $51,606 25. $191,294.58 18. 7% 19. $89,250 20. $172,000 21. $245,350 22. 20 23. $3.50 24. $179,760 25. $974,549