Questions Answers to help you pass the

Questions & Answers to help you pass the Real Estate Appraisal Exams These Questions and Answers were taken from the above named book written by Jeffrey D. Fisher and Dennis S. Tosh These explanations have been compiled for the express use of the students of Rob Rooks of Cerritos College This Question and Answer book is recommended for students who are anticipating sitting for any of the following California Appraisal Examinations. Trainee – Residential – General Questions Robert. Rooks@Robert. Rooks. com rrooks@cerritos. edu Erookrob@gte. net (626)331 -7577 1

Mathematics Practice Final Exam Introduction To Appraisal Questions 32 and 33 are based on the following information: The Capitalization Rate that you have been working with is the Overall Capitalization Rate, or the Capitalization Rate for the Land for the Building. This is your first introduction to divided Capitalization Rates. One Capitalization Rate is attributed to the improvement and one capitalization rate to the land. The two capitalization Rates together would be the Overall Capitalization Rate. 2

Math Questions 32 and 33 Continued Construction Costs Improvements $5, 900, 000 $8, 600, 000$4, 300, 000 N. O. I. $1, 204, 000 $ 850, 000 Building Capitalization Rate = Land Capitalization Rate = l $ 650, 000 12% 10% The Authors multiplied the given improvement costs by 12%, the buildings Capitalization Rate and came up with the Buildings Contribution to the Net Operating Income. 3

Math Questions 32 and 33 Continued Improvement Values Building N. O. I. Total N. O. I. Less Building N. O. I. Difference Apartment $5, 900, 000 X 12% $ 708, 000 Office Retail/Commercial $8, 600, 000 $4, 300, 000 X 12% $1, 032, 000 $ 516, 000 $ 850, 000 $1, 204, 000 $ 650, 000 $ 708, 000 $ 142, 000 $1, 032, 000 $ 172, 000 $ 516, 000 $ 134, 000 This Difference $ 142, 000 $ 172, 000 $ 134, 000 is attributed to the land, or the investments earning by the land 4

Math Questions 32 and 33 Continued LAND VALUE Land Income/Land Capitalization Rate = Land Value Apartment Office Retail/Commercial $ 142, 000/10% $ 172, 000/10% $ 134, 000/10% = $1, 420, 000 = $1, 720, 000 = $1, 340, 000 IMPROVEMENT VALUE Building Income/Building Capitalization Rate = Improvement Apartment $ 708, 000/12% = $5, 900, 000 Office $1, 032, 000/12% = $8, 600, 000 Retail/Commercial $ 516, 000/12% = $4, 300, 000 5

Math Questions 32 and 33 Continued OVERALL VALUE FROM CAPITALIZATION RATES Improvement Values Land Values Apartment $5, 900, 000 $1, 420, 000 Office Retail/Commercial $ 8, 600, 000 $4, 300, 000 $ 1, 720, 000 $1, 340, 000 Overall Value $7, 320, 000 $10, 320, 000 $5, 640, 000 The Highest and Best use of the land would be the Office Building The Land Value of the Office Building would be $1, 720, 000 6

QUESTION 54 What is the indicated value of the property? You are using the “Cost Approach”. A house has a living area of 1, 900 Square Feet. An attached garage has a total area of 420 square feet. The building has an expected life of fifty years and an effective age of five years. The site or lot is worth $15, 000. If it costs $50 a square foot to reproduce the living area and $25 a square foot to replace the attached garage, what is the indicated value of the property? First realize that the land does not depreciate. The improvement has already depreciated five years. This would amount to 10%. Fifty years divided into 100 years would equal 2% a year depreciation. 5 times 2% = 10%. 7

QUESTION 54 Continued What is the indicated value of the property? You are using the “Cost Approach”. Step 1. Find the un-depreciated value of the or living area. dwelling Area X Square Foot Value = Un-depreciated Value 1900 Square Feet X $50 Per Square Foot = $95, 000 Step 2. Find the un-depreciated value of the Square Foot attached garage. 420 Area X Square Foot Value = Un-depreciated Value 420 Square Feet X $25 Per Square Foot = $10, 500 8

QUESTION 54 Continued What is the depreciated value of the improvements? Step 3. Find the depreciated value of the improvements. If the estimated life of the improvements is 50 years, the depreciation will be 2% a year or; 100%/50 Years = 2% Step 4. Five years effective age means the improvement has aged 5 years. Since it is losing 2% a year it has lost 10% of it’s original value. This can be approached two ways, or from either end. 90% of value left or 10% of value gone. 9

QUESTION 54 Continued What is the depreciated value of the improvements? Step 5. Find the depreciated value of the improvements. Dollar value of living space Dollar value of attached garage Value New of Improvements = $ 95, 000 = $ 10, 500 = $105, 500 Depreciated Value of Improvements Value New X Depreciation Factor $105, 500 X 90% = Remaining Value = $ 94, 950 10

QUESTION 54 Continued What is the depreciated value of the Property? Step 6. Find the depreciated value of the improvements. Dollar value of Subject = $ 94, 950 Land Value of Subject Land doesn’t depreciate so the original value in this exercise is the current value or $15, 000. ? Value of Depreciated Subject Depreciated Value Improvement + Land Value = Depreciated Value of Subject $94, 950 + $15, 000 = $109, 950 11

QUESTION 64 Using Present Value of Cash Flows to Find Value A property is projected to have a level Net Operating Income of $25, 000 per year for the next five years. The property value is projected to increase a total of 15% over the next 5 years. The appraiser determines that an appropriate discount rate is 12%. What is the value of the property? This question posses two problems; a. Find the Present Value of the property today. b. Find the Value in 5 years by multiplying the Present Value by 15% each year for 5 years. 12

QUESTION 64 Using Present Value of Cash Flows to Find Value Solving the first part means finding the value of 5 cash flows today. In other words if you were being paid $25, 000 annually, at the end of each year, what would each cash flow be worth today. You can also look at these annual cash flows as how much money would you have to put in a bank today at 12% interest to get $25, 000 at the end of Year 1, Year 2, Year 3, Year 4 and Year 5. The value of the money you would put in the bank today at 12% interest would be the value of the site. 13

QUESTION 64 Using Present Value of Cash Flows to Find Value Solving the first part means finding the value of 5 cash flows today. In other words if you were being paid $25, 000 annually, at the end of each year, what would each cash flow be worth today. End Year 1. 2. 3. 4. 5. Present Value $ 22, 321 $25, 000 $ 19, 930 $ 17, 795 $ 15, 888 $ 14, 186 $90, 120 Present Value $25, 000 14

QUESTION 64 Using Present Value of Cash Flows to Find Value You can solve this problem with any Financial Calculator. Using the Hewlett Packard 17 B II you would set the problem up as follows; Payments Each Year = 1 N I%YR PV PMT FV 5 12 90, 119 -25, 000 OTHER 0 You would set the payments per year to 1, then put 5 in N, 12 in I%YR, finally – 25, 000 in PMT and then you would simply press PV and you would have the answer 90, 119. 15

QUESTION 64 Now You Have The Present Value The Second Part is Find The Future Value You have solved the first part of the problem two different ways, there at least three more that we could pursue. We only need one and your one will be the Calculator or Computer. Present Value $ 90, 119 Multiplier 15% Time 5 Yrs. Future Value ? 16

QUESTION 64 Now You Have The Present Value The Second Part is Find The Future Value You could use a calculator, as you will in business, if you used the 17 BII you would set the payments per year at 12 payments per year. N I%YR PV PMT FV 5 15 -90, 119 0 0 N I%YR PV PMT FV 5 15 -90, 119 0 OTHER 181, 261. 50 17

QUESTION 64 Now You Have The Present Value The Second Part is Find The Future Value Mathematically a future value of any amount of money earning an annual compound interest of 15% would be (1+i)n which in this case would be (1+. 15)5 this means (1. 15) times itself 5 times, or simply stated; 1. 15 X 1. 15 = 2. 0114 This 2. 0114 times any number would be its’ value if you multiplied it by 15% for 5 years; $90, 119 X 2. 0114 = $181, 265. 36 18

QUESTION 65 A property is leased as follows: Years 1 – 5, $10, 000 per year Years 6 – 10 $15, 000 per year Using a 10% discount rate, what is the present value of the lease payments assuming they are paid at the end of the year? 19

QUESTION 65 Continued The question is similar to question the amount of money that would be necessary in an interest bearing bank account at the beginning of the period to achieve $10, 000 at the end of each of the years and then $15, 000 at the end of each of the years. The formula for the present value of the year five cash flow of $10, 000 would be; 1 (1+i)n 1 1. 6105 = 1 (1+. 10)5 = 1 1. 105 = 0. 6209 20

QUESTION 65 Continued This means that any number multiplied by 0. 6209 will that number five years before, multiplied by 10% annually. Present Value of First 5 Year Cash Flows Cash Flow Year 1 = $ 9, 091 Cash Flow Year 2 = $ 8, 264 Cash Flow Year 3 = $ 7, 513 Cash Flow Year 4 = $ 6, 830 Cash Flow Year 5 = $ 6, 209 Present Value = $ 37, 907 21

QUESTION 65 Continued The second part of the question is exactly the same as the first part of the question. The amount of money at the end of each period is $15, 000 and the time periods are different. The capitalization rate is still 10%. Present Value of First 5 Year Cash Flows Cash Flow Year 6 Cash Flow Year 7 Cash Flow Year 8 Cash Flow Year 9 Cash Flow Year 10 = = = $ $ $ 8, 467 7, 697 6, 998 6, 361 5, 783 Present Value = $ 35, 306 22

QUESTION 65 Continued The Present Value of the lease payments are these discounted values added together. Present Value 1 st 5 Years Present Value 2 nd 5 Years Present Value of these Cash Flows = = = $ 37, 907 $ 35, 306 $ 73, 213 23

Question 16 General Exam A Real Property Tax Problem The annual property tax on a property that you are appraising is $756. The County Tax Assessors Office assesses land at 60% of market value. The tax rate is $1. 80 per $100 of value (18 mills). What is the estimated market value of the land? A mill is 0. 001 so $1. 80 X one mill (0. 001) = 18 Mills Taxes by Mills = Total Assessed Value $756 0. 018 = $42, 000 60% = $70, 000 The Fair Market Value of the parcel is $70, 000 24

Question 16 Exam A 2 nd Solution Real Property Tax Problem The annual property tax on a property that you are appraising is $756. The County Tax Assessors Office assesses land at 60% of market value. The tax rate is $1. 80 per $100 of value (18 mills). What is the estimated market value of the land? You could divide the taxes by the tax rate per $100 of value and come up with $42, 000. Then divide $42, 000 by 60% and you would come up with a fair market value of $70, 000 Taxes Cost per $100 = $756 $1. 80 = 42. 00 x 100 = $42, 000 60% = $70, 000 Total Assessed Value 25

Question 17 General Exam A Acreage Problem A parcel of land 440 feet by 792 feet contains how many acres? This question tests two things. 1. Can you figure the square footage of a property. 2. Do you know how many square feet are in an acre? 1 st figure the square footage in the parcel. 440 X 792 348, 480 = 348, 480 Square Feet 43, 456 Square Feet = 8 Acres The answers are given to you and 8 Acres is one of the answers. 26

Question 40 General Exam A Front Foot Problem A lot on a commercially zoned street contains 105, 000 square feet and has a depth of 300 feet. Commercial land in the area is currently selling for $400 per front foot. What is the indicated value of the lot? Since you know the total square feet and the lot depth you can figure the front footage by dividing the total square footage by the depth of the lot. 105, 000 Sq. Ft. 300 Feet Deep = Lot Width 105, 000 Sq. Ft. 300 Ft. Deep = 305 Ft. Wide The Land Cost is $400 per front foot 305 Front Feet x $400 per Front Ft. = $140, 000 27

Question 54 General Exam A Acreage Cost Problem A lot measures 600 feet by 800 feet. What is the total land value if the land is worth $15, 000 per acre? First you would figure the square footage in the parcel. Width X Depth = Square Feet 600 x 800 = 480, 000 Square Feet 480, 000 Sq. Ft. ÷ 43, 560 Sq. Ft. / Acre = 11. 019284 $15, 000 x 11. 019284 = $165, 289. 26 The problem gives an answer of $165, 300. That’s the closest. Select that answer. 28

Question 55 General Exam A Office Building Value – Cost Approach An office building has a leasable area of 45, 000 square feet. Its current reproduction cost is $65 per square foot. The building is on one acre of land. Comparable land costs $17 per square foot. Because the building is poorly designed the building suffers a loss of $40, 000 in functional obsolescence. What is the total cost of the property using the cost approach? Here you would figure the replacement cost new at $65 per square foot, add the value of the one acre of land or 43, 560 x $17 per square foot. Add the building and acreage together and subtract the $40, 000 of functional obsolescence. 29

Question 55 General Exam A – Page 2 Office Building Value – Cost Approach Cost of Building 45, 000 Square Feet X $65 per Sq. Ft. = $2, 925, 000 Adjust the building cost for Functional Obsolescence $2, 925, 000 - $40, 000 = $2, 885, 000 Building Value One Acre at $17 Per Square Foot 43, 560 Sq. Ft. X = Land Cost $17/sq. ft. = $740, 520 Building Value Using Cost Approach Building Replacement Cost $2, 885, 000 + Land = Total Value + $740, 520 = $3, 625, 520 30

Question 58 General Exam A Capitalization Problem Which of the following estimates would result in a capitalization rate of 20%? A. B. C. D. Potential Gross Income $100, 000; value $500, 000. Effective gross income $100, 000; value $500, 000. Net Operating Income $100, 000; value $500, 000. Cash Flow $100, 000; value $500, 000 This is not really a mathematical problem. The only answer that is possible is C. This is because all Capitalization Rates are calculated using the NET OPERATING INCOME. 31

Question 59 General Exam A Gross Rent to Break Even An office building has 10, 000 square feet of net leasable space. The owner has an annual mortgage payment of $75, 000 and operating expenses of $25, 000. If the owner wants a before tax cash flow of $50, 000, what should the gross rent per square foot be on a monthly basis. Add up the expenses of operation, plus the loan payments, plus the cash flow and divide that sum by 10, 000 square feet. Expenses Loan Payments Cash Flow Potential Gross Income $25, 000 + $75, 000 + $50, 000 = $150, 000 ÷ 10, 000 Sq. Ft. $15 Per Sq. Ft. /Year ÷ 12 Mo. = = $15 Per Square Foot/Year $1. 25 Per Square Foot 32

Question 63 General Exam A Capitalization Rate Problem Which of the following estimates will result in a Capitalization Rate of 10%? a. b. c. d. Value $500, 000; gross income $50, 000 effective gross income $500, 000 Net Operating Income $50, 000 cash flow $50, 000 The answer to this problem has to be C. The answer C is the only answer that contains the Net Operating Income. The Net Operating Income is an inherent part of the Capitalization Rate. Without the NOI you can’t have a proper Capitalization rate. 33

Question 68 – General Exam A Basis Point Problem If interest rates were 8 percent but they rose by 50 basis points, what would the new rate be? a. b. c. d. 8. 5 percent 12. 0 percent 13. 0 percent 58. 0 percent A basis point is 1 ÷ 100 or 1% (0. 01). If 100 basis points equal 1% then 50 basis points would be ½% or 0. 005. Consequently the answer. A is the answer 8 per cent plus 50 basis points or ½% would be 8. 5% or 81/2%. 34

Question 70 – General Exam A Coverage Ratio A property has an NOI of $10, 000, interest payments of $8, 000 and a principal payment of $1, 000. What is the debt coverage ratio? a. 0. 80 b. 0. 90 c. 1. 11 d. 1. 25 C Debt coverage ratio equals Net Operating Income divided by the mortgage payment. In this problem the $10, 000 NOI would be divided by the total loan payment $9, 000. $10, 000 ÷ $9, 000 = 1. 11. The Debt Coverage Ratio is 1. 11. 35

Question 71 – General Exam A Overall Capitalization Rates Given the following information: Building Capitalization Rate: Land value as a percent of total value 0. 11 0. 09 35 percent What is the overall capitalization rate by using the band of investment approach? Since land is 35% of value we can take 35% of the land cap rate of 0. 09 a. 0. 097 0. 35 x 0. 09 = 0. 03150 If the land is 35% the b. 0. 100 improvement is 65% c. 0. 103 0. 65 x 0. 11 = 0. 71500 Overall Capitalization Rate 0. 10300 d. 0. 110 36

Reserves Question 73 General Test A A small restaurant contains an oven and a freezer. Each cost $900 and both have a useful life of 10 years. Carpeting for the restaurant costs $3, 500. The carpeting has a useful life of 7 years. What annual reserve for replacement would be appropriate for these items? A. B. C. D. 590 607 $680 $500 Oven Freezer Carpet = $ 900 ÷ 10 Years = $ 90 a Year = $ 900 ÷ 10 Year Life = $ 90 a Year = $3, 500 ÷ 7 Year Life = $500 a Year Annual Reserve for Replacement $680 a Year 37

Capitalization Question 74 General Test A Given the following information, what is the building capitalization rate for the subject property? Land Value Net Operating Income Land Capitalization Rate Overall Capitalization Rage a. b. c. d. 10. 9% 9. 30% 8. 40% 8. 80% = = $60, 000 $25, 000 8% 9% b is the answer see next slide. 38

Answer Question 74 Since the land value is $60, 000 and the Land Capitalization Rate RL is 8% we would have $60, 000 x 9% = $4, 800 That means that $4, 800 of the NOI has been used for land. The Overall Capitalization Rate (RO) is 9% we know the buildings value is $25, 000/9% = $277, 778. n used for land. If the total value is $277, 778 and the land value is $60, 000 then the buildings value is $277, 778 - $60, 000 = $217, 778. The NOI is $25, 000 and $4, 800 of that belongs to the land so $25, 000 - $4, 800 = $20, 200 the NOI for the building. Building NOI ÷ Building Value = Building Cap Rate $20, 200 ÷ $217, 778 = 9. 2755% Rounded the Buildings Cap Rate is 9. 3% the answer is B 39

Question 75 General Test A Overall Capitalization Rates If a property has a net income ratio of. 75 and a gross income multiplier of 9, what is the indicated overall capitalization rate? a. b. c. d. 2. 78 6. 75 8. 33 12. 00 The answer is c. Having a net income ratio of 75% means that vacancy and expenses are 25%. If the building had a $100, 000 PGI then the NOI would be $75, 000. The gross multiplier tells us the buildings value is $900, 000. $75, 000 divided by $900, 000 = 8. 3333% 40

Question 76 General Test A Equity Dividend Rate If a property has an overall capitalization rate of 0. 095 and a mortgage at a 75 percent loan to value ratio and a mortgage constant of. 11, what is the equity dividend rate? a. b. c. d. 0. 05 0. 06 0. 07 0. 09 The equity dividend rate is the same as Cash on Cash, or Cash Flow divided by the owners equity. Also called equity capitalization rate. Before tax cash flow on the equity investment. 41

Equity Dividend Rate page 2 If a property has an overall capitalization rate of 0. 095 and a mortgage at a 75 percent loan to value ratio and a mortgage constant of. 11, what is the equity dividend rate? Create an example. A million dollar property with a 75% loan $750, 000 at 11% interest, and an Overall Capitalization Rate of 9. 5% (RO) What is the Equity Dividend Rate (RE) Since the loan is 75% and that equals $750, 000, your equity is 25% or $250, 000. The Overall Rate is 9. 5% or $1, 000 x 9. 5% = $95, 000. The loan is using [$750, 000 x 11% = $82, 500 (which is the loan payment). To find the Equity Dividend Rate you subtract the loan payments from the Net Operating Income and divide the difference by the Equity. $95, 000 - $82, 500 = $12, 500 that is the RE or $12, 500/$250, 000 = 5%. The answer 42 is a.

Question 77 General Test A Highest & Best Use Problem The appraiser collects the following information for a proposed new building, which is proposed to be the highest and best use. Net Operating Income: Land Capitalization Rate: Building Value (based on cost): A. B. C. D. $150, 000 9% 11% $1, 100, 000 $1, 221, 000 $1, 250, 000 $1, 422, 222 $1, 500, 000 43

Question 77 General Test A Highest & Best Use Problem 1. First figure out how much of the NOI will go to the building. The building has an 11% Capitalization Rate and the value of the building is $1, 100, 000. Building Rate = $1, 100, 000 x 11% = $121, 000 2. Second, figure how much NOI is left for the land. NOI – RB = Land Capitalization Rate. $150, 000 - $121, 000 = $29, 000 3. Third, figure the value of the land. Land Income divided by land capitalization rate (RL) = Land Value $29, 000 ÷ 9% = $322, 222 4. Add the land the building together. Building Value + Land Value = Total Value $1, 100, 000 + $322, 222 = $1, 422, 222 44 C = The Answer

Question 79 General Test A Annuity Due Problem What is the present value (PV) of an annuity of $100 pre year for the next five years? Use a 10% discount rate. A. B. C. D. $379. 08 $450. 00 $550. 00 $772. 17 There are three ways to solve the problem; 1. Using formulas. 2. A Financial Calculator 3. Tables 45

Annuity Due Using Formula page 2 Year Present 1. $ 91 2. $ 83 3. $ 75 4. $ 68 5. $ 62 Total $379 Discount Rate 1 (1+i)1 1 (1+i)2 1 (1+i)3 1 (1+i)4 1 (1+i)5 Future Value $100 $100 $500 46

Annuity Due Problem page 3 Any financial calculator will solve the problem. Here I am using the HP 17 BII N I%Yr 5 10 PV PMT FV OTHER ? -100 0 OTHER 5 10 379. 08 -100 0 OTHER Most problems that you have to solve will be done on one of the financial calculators. When you are doing them on a regular basis they are simplicity itself. When you haven’t done the calculation for a time you’ll have to practice a little. Keep your notes. 47

Annuity Due Problem page 4 Tables are the oldest method used by appraisers and real estate brokers. If you look on Page 250 in Appendix B – in column 5 at year 5 you will see the number 3. 790787 That number is the multiplier for an annuity due. In this example you have an annuity due problem. Your annuity is coming in at the end of annual intervals, you simply take the annual cash flow, the $100 and multiply the $100 by the indicated multiplier 3. 790787. You will come up with the present value of an annuity due. $500 x 3. 790787 The Answer is A = $379. 08 48

Question 80 General Test A Another Annuity Due Problem A discount rate of 10% applied to $100 sum that will be received at the end of one year results in a Present Value of? All three methods will work. The problem is exactly the same as problem 79 except this problem is for one year. A. B. C. D. $90. 90 $100 $110 The answer is $90. 91 = A 1 1 1 (1+i)n = (1+. 10)1 = 1. 10 = 90. 91 49

Question 82 General Test A Financial Management Rate of Return Problem (FMRR) An investment requires $10, 000 negative cash flows for the first three years, then offers $8, 500 in cash flows for years 4 through 10, or 7 years of $8, 500. Using a “safe rate? Of 5%, the negative cash flows have a present value of $27, 232. If the positive cash flows are reinvested at 10%, the cash flows will have a future value of $80, 641. What is the FMRR? My first and last impression of this problems is that it is not a FMRR problem at all. The cash flows may have been handled incorrectly. Regardless, the author reduces this to a calculator problem. 50

Question 82 General Test A Financial Management Rate of Return Problem (FMRR) Using an HP 17 BII we would have the following: N I%YR PV PMT FV 10 ? -27, 232 0 80, 641 10 137. 608077 -27, 232 0 80, 641 Note that because the returns are monthly you get 137. 608077. This you divide by 12 and you come out with 11. 467340 One safe conclusion you can come to with calculators is that you have gotten the accurate answer to something. It may not be the answer to what you think but it is the answer to something. 51

Question 84 General Test A Operating Statement The following income statement is provided to the appraiser by the owner: Potential Gross Income Vacancy Factor Effective Gross Income Utilities Property Taxes Management Fee Maintenance Expenses Total Expenses Net Operating Income Interest Depreciation Allowance Income Taxes Sub-Total Net Cash Flow Not Given $10, 000 ($ ($ ($ 1, 500) 1, 000) 500) 2, 000) 5, 000) ($ ($ 2, 000) 1, 000) 9, 000) ($ 5, 000) $ 5, 000 ($ 9, 000) $1, 000 52

Question 84 General Test A continued What is the Net Operating Income The question is what is the Net Operating Income (NOI). I have already figured that for you because I use a slightly different cash flow line. This question is meant to make you identify the costs that are catalogued as expenses. In this problem that would be: Utilities ($1, 500) Property Taxes ($1, 000) Management fee ($ 500) Maintenance fee ($ 2, 000) TOTAL EXPENSES ($ 5, 000) Net Operating Income is Potential Gross Income less vacancy factor, less expenses. We only have expenses, starting with the Effective Gross Income so, $10, 000 – $ 5, 000 = $5, 000 the answer is D. 53

Question 85 General Test A continued Internal Rate of Return An income producing property requires a $10, 000 investment. The property promises a $1, 000 annual return for five years, then resale proceeds of $15, 000. What is the Internal Rate of Return (IRR) (nearest percent)? A. B. C. D. 10 percent 14 percent 15 percent 17 percent 54

Question 85 General Test A continued IRR Solution HP 17 II There are several methods of solving this problem. There at least two ways to solve the problem on the HP 17 II N 5 I%YR PV FV -10, 000 $15, 000 ? PMT Then solve for interest rate N I%YR PV 5 17. 112390 -10, 000 PMT $1, 000 FV $15, 000 The Answer then is 17% Which is the answer D 55

Question 85 General Test A continued IRR Using IRR Function 56

Question 85 General Test A continued IRR Using Tables 57

Question 86 General Test A continued Mean, Median, Mode and Range Questions 86 thorough 89 are based on the following data collected by an appraiser in regard to office space and the annual rent paid on a square foot basis. Office Building 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Rent Per Square Foot $12 $17 $14 $15 $16 $17 $18 $16 58

Question 86 General Test A continued What Is The Mean? A. B. C. D. $15. 70 $16. 50 59

Answer Question 86 General Test A What is The Mean Answer Remember the mean and the average are the same thing. Here you simply add the numbers and divide by the number of numbers that you have added. $12 $16 + $17 + $14 + $15 + $17 + $18 = $157 ÷ 10 = $15. 70 + $15 + $16 The answer is B 60

Question & Answer Question 87 General Test A What is The Median? The Median is the “Middle Most Number” that is not the average or Mean. What if you added 1, 000 and 200, the mean or average would be 500, 100. Averages can be like having one foot in a bucket of ice water and the other foot in a blast furnace. The Median is the middle most number. $12 $17 $14 $15 $16 $17 $18 $16 The middle most number is $16 The answer to 87 is C 61

Answer Question 88 General Test A What is The Mode? The Modes the Number that occurs the most number of times. This is what we look for in comparables. $12 $17 $14 $15 $16 $17 $18 $16 $17 is the square foot rent for three of the rents in these comparables and a $17 is the most recurring number. $17 is the Mode and the answer is D 62

Answer Question 89 General Test A What is The Range? The Range in a set of numbers ordered sequentially from the lowest to the highest. Range of Value – in an appraisal report, the confidence interval in which the final estimate of a property’s value may lie. The numbers range from a low of $12 to a high of $18 so the range is the interval from the highest to the lowest is $6 or simply $18 – $12 = $6 63

Answer Question 90 General Test A Ratio of Value for Rent A tenant has signed a lese in which the rent is based on the appraised value of the property. During the first year the property is appraised for $400, 000 and the rent is $36, 000. If during the second year the property increases in value to $40, 000, what is the annual rent for the second year? A. $36, 000 B. $36, 600 C. $39, 600 D. $44, 000 64

Answer Question 90 General Test A - Answer Ratio of Value for Rent One easy solution here is to establish a capitalization rate between the current and current value. Then apply that capitalization rate to the new value and find the new rent. Current Rent divided by Current Value Capitalization Rate $36, 000 New Value x $400, 000 = 9% x $440, 000 = Annual Rent Capitalization Rate x 9% = New Rent = $39, 600 The answer then is C $39, 600 65

Question 92 General Test A Square Foot Rent Problem A commercial building leases for $3, 000 per month. If the building’s dimensions are 60 feet by 80 feet, what is the annual rent per square foot? A. $. 63 B. $ 1. 00 C. $ 7. 50 D. $12. 00 66

Answer Question 92 General Test A Square Foot Rent Problem A good first step is to figure the square footage of the building: Width in feet X Depth in feet = Square Footage 60 X 80 = 4, 800 Sq. Ft. Since the problem gives you the monthly rent but asks for an annual result a good second step would be to convert the monthly rent of $3, 000 per month to an annual rent: Monthly Rent X 12 Months = Annual Rent $3, 000 X 12 = $36, 000 Annual Rent ÷ Square Feet $36, 000 ÷ 4, 800 = Annual Rent Per Sq. Ft. = $7. 50 Per Square Foot The Answer is C $7. 50 Per Square Foot Per Year 67

Question 50 General Test B Square Foot Value A lot measuring 130 feet by 200 feet recently sold for $71, 500. What was the selling price per square foot? A. $2. 75 B. $5. 50 C. $275 D. $550 68

Question 50 General Test B Square Foot Value Logic of Problem 50. Square Footage = 130 ft. x 200 ft. = Selling Price 26, 000 sq. ft. Continued 26, 000 Sq. Ft. = $71, 500 $2. 75 Sq. Ft. $71, 500 The Answer is A $2. 75 Per Square Foot 69

Question 53 General Test B Depreciation Amount You are appraising a warehouse using the cost approach to value. The effective age of the building is 15 years. The remaining economic life is 45 years. What is the total depreciation taken. A. 25 percent B. 33. 3 percent C. 66. 7 percent D. 75 percent 70

Question 53 General Test B continued Depreciation Amount Solution The effective age tells you 15 years are gone. The remaining 45 years tells you that the total was 60 years. 15 Years + 45 Years = 60 Years. Since 15 years have been taken the answer is; 25% or 15 ÷ 60 = 25% A is the answer 25% 71

Question 54 General Test B Living Area & Cost A house has a living area of 1900 sq. ft. An attached garage has a total area of 420 square feet. The building has an effective age of five years. The lot is worth $15, 000. It cost $50 per square foot to reproduce the living area and; and $25 per square foot to reproduce the garage. What is the indicated value of the property? 72

Question 54 General Test B Answer Living Area & Cost 1900 Sq. Ft. x $50 = $ 95, 000 for House 420 Sq. Ft. x $25 = $ 10, 500 for Garage Total Value New = $105, 500 Expected Life 50 Years Depreciation a year = 100% ÷ 50 Years= 2% a Year 5 Years x 2% a Year = 10% Used Reproduced Value x 10% = $10, 550 Depreciated Reproduce value $105, 500 – Depreciation $10, 550 = $94, 950 Present Value of Improvements. $ 15, 000 Value of Land $109, 950 = Present Value. Answer is C 73

Question 56 General Test B Gross Income Multiplier A warehouse as a Market Value of $3, 000. It generates an annual gross income of $500, 000. Annual operating expenses are also $500, 000. What is the Gross Income Multiplier? A. 4 Times Gross B. 5 Times Gross C. 6 Times Gross D. 6. 5 Times Gross 74

Question 56 General Test B Gross Multiplier Logic & Answer The logic is the fact that the Annual Gross Rent Multiplier is found by dividing the buildings value by the Gross Scheduled Income. In this problem they gave you the price of the building and the Gross Scheduled Income. All you have to do is divide $3, 000 by $500, 000 6 Times Gross $3, 000 The answer is C 6 Times Gross 75

Question 59 General Test B Capitalization Rate to Value The net operating income of $60, 000 of a property capitalized at a rate of 14% indicates a value of The value indicated by capitalizing a net operating income of $30, 000 at a 7% is. A. less than B. equal to C. greater than D. exactly twice 76

Question 59 General Test B Capitalization Rate Solution The questions is this; How does $60, 000 divided by 14% relate to $30, 000 divided by 7%? $428, 571. 43 14% $60, 000 $428, 571. 43 7% $30, 000 The answer is that they are the same. So you would pick answer B or equal to 77

Question 59 General Test B Capitalization Rate to Value The net operating income of $60, 000 of a property capitalized at a rate of 14% indicates a value of $428, 571 The value indicated by capitalizing a net operating income of $30, 000 at a 7% is $428, 571. A. less than B. equal to C. greater than D. exactly twice Answer is B Equal to 78

Question 61 General Test B Value Due to Loan Discount A property sold for $145, 000 with $30, 000 down and the balance in the form of a purchase money mortgage (seller financing) at 8% interest for 15 years with monthly payments. Shortly after the sale of the property the seller sold the mortgage for $105, 000. The sale price reflected to current mortgage rates. What does this indicate about the cash equivalent of the selling price? Loans are discounted and sold in secondary markets. In this problem the seller has carried the 1 st Trust Deed, or Mortgage, and immediately after escrow closes he sells the loan for less than the face amount. In this case the loan is $115, 000 and the seller sells it for a $10, 000 discount, or $105, 000. That is the hear of the question and the answer. 79

Question 61 General Test B Continued Value Due to Loan Discount Sales Price Cash Down Payment Loan Carried by Seller $145, 000 ($ 30, 000) $115, 000 The seller sells the loan for Face Amount of Loan Discount for Sale $105, 000 $115, 000 $ 10, 000 Purchase Price of Home Less Discount on Loan Adjusted Value of Home $145, 000 ($ 10, 000) $135, 000 The answer is D or $135, 000 80

Question 62 General Test B Capitalization Rate Problem A property has a gross income multiplier of 9 and a net income ratio of. 75. What does this indicate for the overall capitalization rate? 1 st, know that the Overall Capitalization Rate is the Capitalization Rate for the Improvement and for the Land or RB + RL = RO this is the capitalization rate that we usually use. 2 nd, the gross rent multiplier will give us the buildings value. We don’t have a Potential Gross Income (PGI). 3 rd, the Net Income Ratio simply means that the building has a cash flow of 75% of its PGI. 81

Question 62 General Test B Answer Capitalization Problem B 62 The overall rate is equal to the net income ratio divided by the gross income multiplier. Or, 0. 75/9 = 8. 33% You won’t remember it that way for awhile but you can create a model. You have a building with $100, 000 PGI, the multiplier is 9 so the buildings value is $900, 000. The Net Operating Income is PGI X. 75 = NOI, or $100, 000 X 75% = $75, 000. Then $75, 000/$900, 000 = 8. 33% 82

Question 63 General Test B Debt Service Problem What is the annual debt service on a $75, 000 loan with a monthly payments over 20 years at a nominal annual rate of 13%? Nominal Rate is the stated rate in a note. Note that the problem asks for the annual rate. If we look in the back of our text on the 13% interest chart, (p. 253) in the 6 th column PAYMENT TO AMORTIZE $1. Follow that line down to 20 years and you will find 0. 142354. That means it will take 14. 2354¢ for each dollar to amortize that dollar in 20 years. We then multiply 75, 000 dollars by 0. 142354 and we come up with $10, 676. 55, our annual payment. Our answer is D illustrated as $10, 676 83

Calculator Answer to Problem 63 B The HP 17 B II will look like this; N I%YR PV PMT 20 156 75, 000 ? Make sure calculator is set for end mode. N I%YR PV PMT 20 156 75, 000 10, 676. 53 You could solve the problem using the formula which you can get from a set of Six Functions of One Dollar. You will solve most of your problems using a calculator of some kind. 84

Question 64 General Test B Yield Capitalization Problem 64 B A property is projected to have a level NOI of $25, 000 per year for the next five years. The property value is projected to increase a total of 15% over the five years. The appraiser determines that a 12% discount rate is appropriate. What is the value of the property? Present Future Year Value Multiplier Value 1. $22, 321. 43 0. 8929 $25, 000 2. $19, 929. 85 0. 7972 $25, 000 3. $17, 794. 51 0. 7118 $25, 000 4. $15, 887. 95 0. 6355 $25, 000 5. $14, 185. 67 0. 5674 $25, 000 $90, 119. 41 Value of five cash flows 85

Question 64 General Test B Yield Capitalization Problem 64 B Information is missing from this question. If the present value of the property is $90, 119 and the author and everyone agrees on that. If the property increased in value 15% over the 5 years it would be worth; $90, 119 X 1. 15 = $103, 636 If on the other hand the property increased 15% annually from $90, 119 we would have; $90, 119 X (1. 15)5 = $181, 261 I need to talk to the author and find out what he was trying to say. 86

Question 65 General Test B Yield Capitalization Problem 66 B A property is leased as follows: Years 1 – 5 $10, 000 per year Years 6 – 10 $15, 000 per year Using a 10% discount rate, what is the present value of the lease payments? Each year would be different. We can get the numbers A property is leased as follows: Years 1 – 5 $10, 000 per year Years 6 – 10 $15, 000 per year Using a 10% discount rate, what is the present value of the lease payments? 87

Question 65 General Test B Yield Capitalization Problem 66 B This problem has to do with discounting each cash flow and adding all of the present values together to arrive at a value. Year 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Present Value $ 9, 091 $ 8, 264 $ 7, 513 $ 6, 830 $ 6, 209 $ 8, 467 $ 7, 698 $ 6, 997 $ 6, 361 $ 5, 782 Future Value $10, 000 $10, 000 $15, 000 $15, 000 Multiplier 0. 9091 0. 8264 0. 7513 0. 6830 0. 6209 0. 5645 0. 5132 0. 4665 0. 4241 0. 3855 $73, 211 Value of five cash flows 88

Question 67 General Test B Capitalization Spread for Value The subject property’s net income is $15, 000 per year. Comparable investments sold as follows: Comparable 1. 2. 3. 4. Net Income $14, 000 $13, 500 $14, 500 Sales Price $120, 000 $147, 400 $122, 700 $152, 600 All of the above sales are recent. Comparables 2 and 4 are the most similar to the subject. Using direct capitalization with an overall rate, what is the BEST estimate of the value of the subject property? 89

Question 67 General Test B continued Page 2 Capitalization Spread for Value When you look at this problem you see the Net Operating Income and the Sales Price. This should ring a bell that you are looking for the Overall Capitalization Rate (1 st year, building and land) Let’s construct Capitalization Rates, in this case RO for each of the buildings and keep in mind that the writer of the problem says numbers 2 and 4 are the most comparable. Comparable 1. 2. 3. 4. Net Income Sales Price $14, 000 $13, 500 $14, 500 $120, 000 $147, 400 $122, 700 $152, 600 RO 11. 67% 9. 49% 11. 00% 9. 50% 90

Question 67 General Test B continued Page 3 How Did We Do That? How did we do that. To get a capitalization rate, we simply divide the Net Operating Income by the Selling Price. The questions tells us that comparables 2 and 4 are the most similar. Their Overall Capitalization Rate is approximately 9. 5%. We can proceed with that for an estimate. If we divide the given Net Operating Income of $15, 000 by 9. 5% we come up with a value of $157, 894. 74. The answers are as follows: A. B. C. D. $125, 000 $137, 000 $143, 000 $158, 000 We would select answer D. $158, 000 91

Question 70 General Test B Land Residual Techniques Given the following information what is the indicated land value (using the land residual techniques)? n Building Value Net Operating Income Building Capitalization Rate Land Capitalization Rate $600, 000 $ 88, 000 11% 9% When you first look at this it’s enough to make you stay with the appraisal of homes only. Really it is quite simple. You have to work enough of them to make them simple. 92

Question 70 General Test B -- continued Land Residual Techniques – page 2 You have a building value given, $600, 000 you been given a Net Operating Income, (overall) $ 88, 000 a building capitalization rate and 11% a land capitalization rate 9% 1. Figure the NOI for the building. Building Value X Building Cap. Rate = Bldg. NOI $600, 000 X 11% = $66, 000 2. Subtract the buildings Net Operating Income from the NOI and you will have the land NOI. Net Operating Income - Building NOI = Land NOI $88, 000 $66, 000 = $22, 000 3. Divide the Land NOI by the Land Cap Rate and find land value. $22, 000 ÷ 9% = $244, 444. 44 – The answer is D 93

Question 70 General Test B -- continued Land Value Estimates – page 3 You are asked for the indicated land value. You came up with $244, 444 using the Land Residual Technique. The answers that were given to you are: A. B. C. D. $ 22, 000 $309, 091 $377, 778 $244, 444 Your conclusion should be answer D. $244, 444 94

Question 71 General Test B -- Prelude Debt Coverage Ratios Debt coverage ratios are used by lenders more than investors and realtors. The Debt Coverage Ratio (DCR) is the Net Operating Income divided by the Loan or Mortgage. Lenders will give you a minimum DCR. For example; The Net Operating Income is $120, 000 and the Loan Payments, principle and interest, are $100, 000 the DCR is: $120, 000 ÷ $100, 000 = 1. 20 This method views the valuation problem from the point of view of the lender only. 95

Question 71 General Test B -- Prelude Debt Coverage Ratio Formula This is a method of developing the overall capitalization rate by multiplying the debt coverage ratio by the mortgage capitalization rate and the loan-to-value ratio for the property: RO = DCR X RM X M Example of Estimation of Overall Capitalization Rate: You can purchase a property and get a 75% loan. The loan has a 30 year term with monthly payments at 7% interest (the mortgage capitalization rate would be 10. 7859% – the annual payments divided by the total loan) The lender requires a debt coverage ratio of 1. 2. You can estimate the Overall Capitalization Rate as follows: RO = 1. 2 X 0. 107859 X 0. 75 = 0. 10470 96

Question 71 General Test B Debt Coverage Ratios If the Overall Capitalization Rate is 10%, the annual mortgage constant is 11%, and the mortgage ratio is 70%, what is the indicated debt coverage ratio? Your text gives the answer as: RO 10% = M = 70% X X RM 11% Your text gives the answer as: 10% = 0. 077 10% ÷ 0. 077 Debt Coverage Ratio (DCR) X = = X X DCR DCR 1. 298701 1. 30 Answer D 97

Question 72 General Test B Overall Capitalization Rate What is the overall capitalization rate of a property with a land-to-value ratio of. 1, land capitalization rate of. 09, and building capitalization rate of. 12? A. 9. 3% B. 10. 5% C. 11. 7% D. 12. 0% 98

Question 72 General Test B – page 2 Overall Capitalization Rates These are nasty questions that are rarely used. Still, should you ever need the answer. What your trying to do is figure out the Overall Capitalization Rate RO from the Land Capitalization Rate RL and the Building Capitalization Rate RB. One key here is they tell you the land is 10% of the value. If you multiply the Land Capitalization Rate by 10% and add that to the Building Capitalization Rate multiplied by 90% you will come up with 11. 7%, which is the answer. (0. 1 X 9%) + (0. 9 X 12%) = Overall Capitalization Rate 0. 0009 + 0. 010800 = 0. 117 or 11. 7% 99

Question 74 and 75 General Test B Yield Capitalization A property is projected to have the following cash flows: Year 1 $ 5, 000 Year 2 $ 7, 000 Year 3 $ 9, 000 Year 4 $ 9, 000 Year 5 $110, 000 The cash flow in year 5 includes the reversion. Return of investment normally from the sale of the property. 100

Question 74 and 75 General Test B Present Value of Cash Flows Question 74. What is the present value of the cash flows using a 10% discount rate? A. $ 85, 896 B. $ 91, 541 C. $ 92, 224 D. $102, 273 101

Question 74 and 75 General Test B Answer to Question 74 1 1 Value end year 1 cash flow = = 0. 909091 (1+i)n (1. 10)1 1 1 Value end year 2 cash flow = = 0. 826446 2 (1+i)n (1. 10) 1 1 = = 0. 751315 n 3 (1+i) (1. 10) 1 1 Value end year 4 cash flow = = 0. 683013 n 4 (1+i) (1. 10) 1 1 Value end year 5 cash flow = = 0. 620921 n 5 (1+i) (1. 10) Value end year 3 cash flow These multipliers will adjust any amount of money to present value in the years indicated. 102

Question 74 and 75 General Test B Answer to Question 74 Continued Year Present Value Future Value Multiplier 1. 2. 3. 4. $ $ 4, 545. 45 5, 785. 12 6, 761. 83 6, 147. 12 0. 909091 0. 826446 0. 751315 0. 683013 $ $ 5. $ 68, 301. 36 0. 620921 $110, 000 Totals $ 91, 540. 88 The answer is B $91, 541 5, 000 7, 000 9, 000 103

What is A $100, 000 Investor’s Net Present Value? Question 75 asks us Assume the property is purchased by an investor for $100, 000. What is the investor’s net present value? Net Present Value (NPV) = The discounted value of all future cash flows minus the initial cash outlay. The answer is the total cash flows in the last problem, or $91, 541 less the initial investment of $100, 000 the NPV is -$8, 459 The answer is C 104

Question 78 General Test B Present Value of Cash Flows A landlord leases property for five years. The rent of $9, 000, payable at the beginning of each period, constitutes an annuity in advance. What is the present value using a 10% discount? The HP 17 BII will handle the problem nicely but you have adjust the periods and mode. Payments a year 1, Begin Mode. N I/%YR PV PMT 5 10 ? -9, 000 5 10 37, 528. 79 FV -9, 000 The answer is B $37, 529 105

Question 79 General Test B Basis Points 79. Mortgage loan interest rates are 12. 75 percent this week. They were 12. 25 percent last week. What is the increase in basis points? Basis points can be confusing. 100 basis points equals 1%. An easy way to figure basis points is to eliminate the percentage parts of numbers. In this example you would subtract 1225 from 1275 and the answer would be 50 and that is basis points. If the rate went from 12% to 6% you would subtract 600 from 1200 and come up with 600 basis points. Knowing that 100 basis points equals 1% you will have no problems. Remembering that over a long period of time is difficult. 106

Question 84 General Test B Internal Rate of Return The internal Rate of Return is an attempt to accurately measure irregular cash flows. It assumes that any positive cash flows are reinvested at the same rate and any negative cash flows are borrowed at the same rate. 84. Jones sells land for $20, 000 that he bought four years earlier for $10, 000. There were no carrying charges or transaction costs. What was Jones’s IRR (nearest percent)? A. B. C. D. 17% 19% 25% 100% The answer is B - 19% 107

Question 84 General Test B Internal Rate of Return Continued Using the HP 17 BII calculator we would tune it to one year periods. N I/%YR PV 4 4 ? 18. 920712 -10, 000 PMT FV 0 0 20, 000 We would use the 19% for the IRR In these problems End and Begin Modes don’t register. Only with payments and annuities. 108

Question 85 General Test B Cash Flow Models & Questions Operating expenses: Maintenance Insurance Property Taxes Management Utilities Total Expenses $20, 000 5, 000 10, 000 15, 000 $60, 000 Debt service: Interest Principal Total Loan Payments Income Taxes $18, 000 $ 2, 000 $20, 000 $ 5, 000 109

Question 85 General Test B Part 2 What is the Net Operating Income The Net Operating Income will always be the same. The scheduled income, less vacancy losses, less expenses of operation, but not any payments or taxes. Potential Gross Income Vacancy Factor (none noted) Effective Gross Income Expenses of Operation Net Operating Income A. B. C. D. $20, 000 $22, 000 $40, 000 $50, 000 $100, 000 ($ -0 - ) $100, 000 ($ 60, 000) $ 40, 000 The answer should be C 110

Question 86 & 87 General Test B Mean & Median Questions Parcel Sales Price 1. 2. 3. 4. 5. 6. 7. $80, 000 $81, 300 $81, 600 $82, 500 $84, 000 $86, 800 111

Question 86 & 87 General Test B Mean & Median Questions What is the mean selling price of the sample? A. B. C. D. $81, 300 $82, 886 $83, 666 $84, 000 The mean is the average. We simply add all of the numbers up and divide by the number that we added. This is the Average and the Mean. 112

Question 86 & 87 General Test B Solution For Average or Mean Add the following 1. 2. 3. 4. 5. 6. 7. $80, 000 $81, 300 $81, 600 $82, 500 $84, 000 $86, 800 $580, 200 Find the Median $580, 200 ÷ 7 = $82, 885. 71 Founded to $82, 886 Which is B The answer is B 113

Question 86 & 87 General Test B The middle figure in a numerically ordered set of data having an equal number of values lying above and below the middle figure; a measure of the central figure of data. The median is not affected by extreme numbers. What is the Median Selling Price of the Sample? 1. 2. 3. 4. 5. 6. 7. $80, 000 $81, 300 $81, 600 $82, 500 $84, 000 $86, 800 $82, 500 would be the middle sales price. 114

What is the Mode of The Sample? A. B. C. D. D. $80, 000 $82, 500 $82, 886 $84, 000 The mode is the value that occurs the most number of times. This is terribly important to us when we are trying to find suitable comparables. The comparables of similar properties that occur the most number of times usually indicates the Market Value of our subject property. In this example the number that occurred the most number of times is $84, 000, which occurred twice. 115

Question 90 General Test B Average Rent Problem A single story office building 100 feet by 80 feet rents for $18 per square foot per year. If a tenant agrees to sign a four year leas, no rent is due for the first six months. Under these conditions, what is the average rent paid per month over the full term of the lease. A. B. C. D. $ 3, 000 $10, 500 $12, 000 $42, 000 116

Question 90 General Test B continued Average Rent Problem 1 st notice that the rent is annual. 2 nd figure the square feet 100 x 80 = 8, 000 square feet 3 rd figure the annual rent 8, 000 sq. ft. x $18 per sq. ft. = $144, 00 per year 4 th determine the monthly rent $144, 000/12 Months = $12, 000 per month. 5 th estimate the number of months the new tenant will pay rent. 4 Years x 12 Monhts per year – 6 months = 42 Months 6 th 42 months x $12, 000 per month = $504, 000 7 th $504, 000 ÷ 48 Months = $10, 500 average rent per month The answer then is B, or $10, 500 per month, Average rent. 117

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