the university of british columbia diploma program …...pavel $1,000,000 for the property,...

Time: 3 Hours

Date: Sample Final Exam

IMPORTANT This examination is the property of the UBC Real Estate Division

Educational Testing Service.

No part of this examination is to be removed from this examination room.

If any portion of the examination paper is missing from the exam envelope, the examination will not be marked.

The University of British Columbia

Diploma Program in Urban Land Economics

Sample Final Examination

BUSI 121 — FOUNDATIONS OF REAL ESTATE MATHEMATICS

Instructions

This examination consists of two sections:

Part One: Written Answers 70%Part Two: Multiple Choice Questions 30%

100%

This examination consists of twenty-one (21) pages. Please check to ensure that you have a completeexamination.

No outside materials are allowed other than a hand-held, cordless, silent calculator that is NOT alphanumericand programmable.

Part One (written answers) MUST be answered in the appropriate booklet(s) provided. Where applicable, showall calculations so that partial credit can be awarded if your solutions merit it.

Part Two (multiple choice questions) MUST be answered, in pencil, on the multiple choice answer sheetprovided. Instructions on this procedure are contained within the examination. Answers recorded in any othermanner will not be considered.

Please note that formulae pages for your use are attached to the examination.

Answer ALL Questions.

The University of British Columbia 2BUSI 121 – Sample Final Examination

Copyright: 2011 UBC Real Estate Division Educational Testing Service

Record your answers in the booklet(s) provided. Enter your student number in the box marked StudentNumber. Where appropriate, show ALL calculations required and clearly LABEL ALL GRAPHS drawn.

PART ONE – Written Answers

Marks

1. George Parrot, the owner of Friends Development Co., is in need of an interest accruingconstruction loan with progress advances. George anticipates that he will need to make fivedraws on the loan as follows:

End of Month Amount1 $110,0002 $ 75,0005 $ 21,0008 $ 7,00010 $ 3,000

4 The Fraser Bank of B.C. has agreed to George’s schedule and requires a return of j2 = 12%on its construction loans. How much will the Friends Development Co. owe at the end of thetenth month?

2. The following represents the number of bedrooms in a population of five houses:

2, 1, 4, 3, 10

For this distribution:

1 (a) calculate the mean1 (b) calculate the median1 (c) calculate the mode2 (d) calculate the standard deviation2 (e) calculate the variance2 (f) calculate the coefficient of variation3 (g) explain which measures of central tendency and dispersion are best and why?



Marks

3. For a population of single family dwelling units, the standard deviation of the sales prices is$100,000.

2 (a) Assuming a sample size of 25 are taken from this population, what is the standarderror of the mean?

2 (b) Calculate the sample size of the mean required if you want to achieve a standard errorof the mean of no more than $10,000.

4. The following are the ages of all the sales personnel in a large real estate sales office:

20 26 34 45 5221 27 35 47 5321 29 36 47 5521 30 36 47 5622 32 36 47 5722 33 36 47 5922 33 37 48 6222 33 37 49 6523 33 39 49 6524 33 40 50 6626 33 42 50 6726 33 43 52 69

2 (a) Place this data into 5 groups with appropriate ranges. (Ex. Age 20-29)

2 (b) Construct a frequency distribution for this grouped data, showing both the absolutegroup frequency and the relative group frequency.

2 (c) Construct a histogram of the grouped data.



Marks

5. Consider the following hypothetical data regarding the average price of homes in Canada overan eleven year period:

Year Average Price 1 $150,000 2 $160,000 3 $171,000 4 $167,000 5 $162,000 6 $210,000 7 $245,000 8 $255,000 9 $295,000 10 $305,000 11 $309,000

4 (a) Calculate a three year moving average on the sales price data.

2 (b) Why would a moving average be preferable to using the raw data to examine long termtrends?

6. Jill has the opportunity to invest in Whitewater, a recently developed waterslide park in thesunny Okanagan. The forecasted net cash flows for the waterslide park are as follows:

Year Net Cash Flow 1 $ 400,000 2 $ 400,000 3 $ 180,000 4 $ 180,000 5 $ 450,000 6 $ 950,000 7 $ 950,000 8 $ 950,000 9 $ 950,000 10 $ 950,000

2 (a) If Jill requires a return of 9% per annum, compounded annually, is this investmentattractive at the asking price of $2,000,000? Show calculations.



Marks

(b) Assume Jill purchases the waterslide park for $1,750,000 and she wishes to earn j1 = 9% per annum on her investment. For this investment:

2 (i) Determine the profitability index.

2 (ii) Determine the present value ratio.

2 (iii) Assuming that she purchases the waterslide park for $1,750,000, calculate theinternal rate of return on Jill’s investment.

7. Theo wants to purchase Pavel’s house. Three years ago, when Pavel purchased the property,he arranged a mortgage of $850,000. The mortgage is written with a 5 year term and a 25 yearamortization period. The loan has payments of $6,487.32 per month. At the end of the 5 yearterm Pavel will owe $783,153.54. Pavel has just paid the 36 payment of the loan. Theo offersth

Pavel $1,000,000 for the property, consisting of the assumption of the $813,069.55 book valueof the mortgage, plus a downpayment of $186,930.45. The current rate on comparable 2 yearmortgages is 6.5% per annum, compounded semi-annually.

4 (a) What is the market value of Theo’s offer?

3 (b) All other things being equal, would the market value of Theo’s offer be higher orlower if the original loan had been fully amortized. Explain. (Note: no recalculationis required)

8. Matt Stamin is considering investing in his old friend Charles Smith’s new restaurant, the U.K.Grill. In return for a $35,000 investment today, Charles has promised to pay back Matt thefollowing cash flows at the end of each of the next five years:

Year Cash Flows 1 $5,000 2 $8,000 3 $7,500 4 $9,000 5 $9,750

Charles insists this investment offers an excellent return. Matt, having received bad advicefrom Charles in the past, has done his homework this time, and has found out that the marketdiscount rate for similar investments is 12% per annum, compounded annually. Calculate thefollowing return measures for Matt’s investment, assuming Matt does receive the cash flowsdescribed above:



Marks2 (a) Net Present Value (NPV)2 (b) Internal Rate of Return (IRR)2 (c) Present Value Ratio2 (d) Internal Rate of Return (IRR) if Matt is able to reinvest the yearly cash flows at 8%

per annum, compounded annually. 2 (e) Based on these return measures, briefly outline your opinion whether Matt should

invest or not?

9. Stellar Financing has arranged a loan in the amount of $250,000, written at an interest rate of8.75% per annum, compounded semi- annually. The loan calls for monthly payments, a fiveyear term, and an amortization period of twenty-five years. You have been asked by theborrower to help explain the interest consequences of this financing arrangement. Specifically,you must calculate:

2 (a) The principal and interest portions of the 12 payment.th

2 (b) How much interest and principal will be paid during the term of the loan.2 (c) How much interest will be paid during the 5 year.th

1 (d) The outstanding balance at the end of the term of the loan.

10. Mr. Brown has approached Ms. Jane, a mortgage broker, about a mortgage loan for thepurchase of a new house. Ms. Jane has agreed to arrange a loan with a face value of $130,000,at an interest rate of 9.5% per annum, compounded semi-annually, with a 25 year amortizationand a 5 year term. The loan will be repaid with quarterly payments rounded up to the nexthigher dollar. Included in the face value of the loan are a $4,000 commission for Ms. Jane andsurvey and legal fees totalling $2,000.

4 (a) What is the cost of the funds advanced to Mr. Brown, expressed as an effective annualrate?

2 (b) If a mortgage investor came along and purchased Mr. Brown’s mortgage for anamount greater than the outstanding balance, would this be a discounted mortgage ora bonused mortgage? Explain the difference between the two.

END OF PART ONE



MULTIPLE CHOICE ANSWER SHEET INSTRUCTIONS



Record your answers on the multiple choice answer sheet provided. Answers recorded in any other mannerwill NOT be considered. Each question has only ONE correct answer.

PART TWO – Multiple Choice Questions – 1 mark each

The next THREE (3) QUESTIONS are based on the following information:

Frank Nomad recently inherited a small fortune. He has several investment options and is analyzing them todetermine which has the highest return. His options are as follows:

Investment Amount to invest Term Amount received(today) (years) (at term end)

A $500,000 1 $600,000B $480,000 2 $542,000C $490,000 3 $550,000

1. The effective annual rate (j ) earned on Investment A is:1

(1) 20%(2) 20.36%(3) 20.6022049%(4) 8.3%

2. The semi-annual periodic rate (i ) earned on Investment B is:sa

(1) 12.5245083906%(2) 6.16716925379%(3) 3.0835846269%(4) 6.2622541953%

3. The weekly periodic rate (i ) earned on Investment C is:w

(1) 12.24489%(2) 3.85185548108%(3) 0.0740741439%(4) 0.074907552%



4. A house purchase closes on October 12 . Funds will be advanced on that date such that, with interestth

accrued, $223,500 will be owing on November 1 . The interest rate to be charged on the loan will best

8.75% per annum, compounded monthly. What amount will be advanced to the borrower on October12 ? It is not a leap year.th

(1) $ 222,453.66(2) $ 222,488.00(3) $ 222,381.74(4) $ 222,434.86

The next TWO (2) QUESTIONS relate to the following information:

Francine and Balfour Shufflebottom have found a home that they simply must own. However, in order topurchase the home, they must obtain financing.

5. The Shufflebottoms can only afford to pay $1,500 per month. If the loan has an amortization period andterm of 15 years and a market rate of j = 12.55%, what is the maximum they can borrow? 1

(1) $ 125,782.61(2) $ 143,615.70(3) $ 123,430.55(4) $ 121,381.05

6. The Shufflebottoms have found a lower interest rate at a different financial institution. If the rate is j 1

= 12.45%, and payments are still $1,500 per month over a 15 year amortization period, what is themaximum loan the Shufflebottoms can obtain?

(1) $126,392.34(2) $124,057.66(3) $122,023.64(4) $144,530.49



The next THREE (3) QUESTIONS are based on the following information:

The following table outlines financial information with respect to commercial leases. In each instance, leasepayments are made in advance.

Lease Present Value Nominal Rate Frequency Lease Term (in advance)Payment Payment

Periodic

A $200,000.00 annually 25 years $16,000.00

B j = 12% monthly 25 years $900.004

C $150,000.00 j = 18% quarterly 25 years 12

7. The nominal rate per annum, with semi-annual compounding, for Lease A is:

(1) 6.14305453319%(2) 6.96960443041%(3) 6.23739733068%(4) 6.85222206243%

8. The present value of Lease B is:

(1) $ 85,451.90(2) $ 86,164.61(3) $ 86,306.42(4) $ 87,017.78

9. The required payment for Lease C is:

(1) $ 6,628.60(2) $ 6,931.38(3) $ 6,833.76(4) $ 6,539.49

10. You have just won a lottery that will pay you $10,000 at the end of each year, forever. If interest ratesare j = 9%, what is the present value of your winnings?1

(1) $ 111,111.11(2) $1,000,000.00(3) $ 109,000.00(4) impossible to calculate, due to insufficient data



The next THREE (3) QUESTIONS are based on the following four graphs:

(A) (B)

(C) (D)

11. The equation for the line x - 2y = -4 corresponds to which graph?

(1) A(2) B(3) C(4) D

12. The equation for the line 5x - 2y = -10 corresponds to which graph?

(1) A(2) B(3) C(4) D



13. The equation for the line x - y = 1 corresponds to which graph?

(1) A(2) B(3) C(4) D

The next TWO (2) QUESTIONS are based on the following metes and bounds description of a property:

• move 22 feet 45E to the east (N45EE) to the southwest corner of the property;• move 80 feet due east (N90EE) to the southeast corner of the property;• move 92.4 feet 30E to the northeast (N30EE) to the northeast corner of the property;• move 126.2 feet due west (S90EW) to the northwest corner of the property;• move 80 feet due south to the southwest corner of the property, to close or "bound" the property.

14. Which of the following shapes best approximates the shape of this property?

A. B.

C. D.

(1) A(2) B(3) C(4) D



15. What is the area of this property?

(1) 10,096 sq.ft(2) 8,248 sq.ft(3) 6,400 sq.ft(4) 7,392 sq.ft

The next TWO (2) QUESTIONS are based on the following information:

The following are hypothetical data for residential real estate sales activity:

Year Sales 1 12,1252 12,8523 14,0084 14,7095 15,445

16. What is the percentage increase in housing prices from year 3 to year 5?

(1) 10.3%(2) 9.3%(3) 5.3%(4) 5%

17. Fill in the blanks.

The percentage change between year 1 and 2 is A than between year 4 and 5, and the absolutechange between year 1 and 2 is B than between year 4 and 5.

(1) A = Larger, B = Larger(2) A = Smaller, B = Smaller(3) A = Smaller, B = Larger(4) A = Larger, B = Smaller

18. A $40,000 loan at 14% per annum, compounded monthly, is to be advanced on September 18th. Thefirst monthly payment is due November 1st. The interest adjustment charge on October 1st will be:

(1) $ 214.12(2) $ 212.43(3) $ 198.79(4) $ 233.33



19. Suppose a mortgage lender has a portfolio of investments which contains the following mortgage loansat the following interest rates:

Value of Loans Interest Rate($ millions) (%)

57.5 14.5110.2 8.040.3 16.0

What is the weighted mean interest rate for this portfolio?

(1) 12.83%(2) 10%(3) 14.5%(4) 11.35%

20. An investor plans to purchase an existing leasehold interest in an income-producing property and expectsto receive income in accordance with the following schedule:

End of Month Cash Flow 6 $17,125.00 9 $19,200.00 12 $19,800.00 15 $19,775.00

Given that the investor demands a minimum yield on investment of 15% per annum, compoundedmonthly, his maximum bid price should be:

(1) $ 64,515.00(2) $ 67,671.51(3) $ 66,794.21(4) $ 66,535.02

21. An investor contemplates the purchase of an income producing property where annual payments of$15,000.00 are expected for a period of 20 years. The first payment is to be received in 5 years time.The present value of the investment, calculated at j = 12%, is:1

(1) $ 79,749.04(2) $ 112,041.65(3) $ 63,575.44(4) $ 71,204.50



The next TWO (2) QUESTIONS relate to the following equation for the price of a house:

PRICE=20,000 + 15,000ROOMS + 10,000BATHROOMS

22. An increase in the number of bathrooms from 1 to 3 would increase the sale price by:

(1) $10,000(2) $30,000(3) $20,000(4) $15,000

23. A house with 4 rooms and 2 bathrooms would sell for:

(1) $20,000 less than a house with 2 rooms and 3 bathrooms.(2) $30,000 less than house with 6 rooms and 4 bathrooms.(3) The same as a house with 3 rooms and 3 bathrooms.(4) $5,000 less than a house with 3 rooms and 4 bathrooms.

24. Real estate appraisers often use the sale prices of 3 or 4 comparable properties in order to determinethe most likely sales price of the property they are appraising. The choice of comparable properties bythe appraiser is an example of what kind of sample?

(1) random sample(2) convenience sample(3) judgment sample(4) cluster sample

25. Mutual fund managers that are tactical asset allocators buy stocks when the market is in a downturn andsell them when the market is on the upturn. These managers believe that the stock market exhibits whatkind of fluctuations?

(1) Seasonal variation(2) Secular trend(3) Cyclical variation(4) Irregular variation

THE NEXT TWO (2) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A loan in the amount of $216,000.00 bears interest at 18% per annum compounded monthly, not in advance.Payments are made monthly. The loan has a 20 year amortization period and term. Payments are rounded upto the next higher dollar.

26. The monthly payments are:

(1) $ 3,228(2) $ 3,227(3) $ 3,333(4) $ 3,334



27. The outstanding balance after 120 payments is:

(1) $ 188,221.42(2) $ 186,321.42(3) $ 184,858.91(4) $ 182,741.65

28. The term of a bonused mortgage is increased from 5 years up to 15 years (while keeping theamortization period at 20 years). This means the effective rate charged to the borrower on fundsadvanced:

(1) does not change.(2) increases.(3) decreases.(4) changes but the change cannot be determined with the information given.

THE NEXT TWO (2) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

Susy has decided to purchase her own rollerblade shop in Kitsilano. She has been advanced an interest only loanof $215,500 by the Bank of Kara. The interest rate is 13.5% per annum, compounded quarterly, with annualpayments (not in advance). The term of the loan is 7 years.

29. What is her yearly interest payment (rounded up to the next higher dollar)?

(1) $ 28,772(2) $ 29,093(3) $ 30,599(4) $ 30,075

30. Now assume that Susy's loan is interest accruing instead of interest only. How much would Susy oweat the end of the 7 years?

(1) $ 537,771.34(2) $ 545,860.80(3) $ 246,461.85(4) $ 246,098.73

END OF PART TWO

FV

(1 % i)n

Present Value of anOrdinary Simple Annuity

1&(1%i)&(n)

i

Present Value of aSimple Annuity Due

PV ' Pmt %

Pmt × 1&(1%i)&(n&1)

i

Future Value of anOrdinary Simple Annuity

(1%i)n&1i

1

(1%i)n&1i

1sÚn, i%á

FV

(1%i)n&1i

Present Value of Net Cash FlowsCost

Present Value of Positive Cash FlowsPresent Value of Negative Cash Flows



FormulaeBUSI 121 - Foundations of Real Estate Math

Mathematical Formula Financial Notation

1. Interest Rate (1 + i ) = (1 + i )mo q12 4

Conversion = (1 + i ) = (1 + i )sa a2 1

2. Present Value of a Lump Sum PV = FV × (1 + i)-n

=

3. Future Value of a Lump Sum FV = PV × (1 + i)n

4. PV = Pmt × PV = Pmt × aÚn, i%á

5. PV = Pmt + Pmt × aÚn-1, i%á

6. FV = Pmt × FV = Pmt × sÚn, i%á

7. Sinking Fund Pmt = FV × Pmt = FV ×

Pmt =

Equation 8.14 APR = (100 x C) (T x P)

Equation 9.3 Present Value Ratio =

Equation 9.4 Profitability Index =

c 2 a 2 % b 2

jn

i'1Xi ' X1 % X2 % X3 % ... % Xn

Final value & Base valueBase value

jn

i'1Xi

µ '

jn

i'1Xi

n

µ '

jm

i'1fiXi

n

jm

i'1fiXi ' f1X1 % f2X2 % f3X3 % ... % fmXm

jm

i'1fi ' n

µ ' jm

i'1

fi

n(Xi)

µ '

jn

i'1wiXi

jn

i'1wi



Equation 10.1 Y = mX + b

Equation 10.2 A = L × W

Equation 10.3 =

Equation 10.4 A = ½ × B × H

Equation 10.5 A = Br2

Equation 11.1 TOTAL = X + X + X + X1 2 3 4

Equation 11.2

Equation 11.3 Percentage change = 100 ×

Equation 12.1

Equation 12.2

Equation 12.3

Equation 12.4

Equation 12.5

Equation 12.6

Equation 12.7

µ '

jm

i'1fiMi

n

F '

jn

i'1(Xi&µ)2

n

F '1n

(jn

i'1X 2

i & nµ2)

F2 '

jn

i'1(Xi & µ)2

n

σ2 '1n

(jn

i'1X 2

i & nµ2)

F

µ(100)

r '

njn

i'1XiYi & (j

n

i'1Xi) (j

n

i'1Yi)

[njn

i'1X 2

i & (jn

i'1Xi)

2] [njn

i'1Y 2

i & (jn

i'1Yi)

2]

Yi ' a % bXi

S ' jn

i'1(Yi & Yi)

2

a 'j Yi & bj Xi

n

b 'nj XiYi & j Xij Yi

nj X 2i & (j Xi)

2



Equation 12.8

Equation 12.9

Equation 12.10

Equation 12.11

Equation 12.12

Equation 12.13 Coefficient of variation =

Equation 13.1

Equation 13.2

Equation 13.3

Equation 13.4

Equation 13.5

SYX 'j Y 2

i & bj XiYi & aj Yi

n & 2

SYX '(1 & r 2)F2

yn

n & 2

Yi ' a % bXi % cZi

I 'Xt

Xt&n

(100)

PI 'Pn

Po

(100)

PI '

jm

i'1P i

nQ io

jm

i'1P i

oQ io

(100)

PI '

jm

i'1P i

nQ in

jm

i'1P i

oQ in

(100)

QI 'Qn

Qo

(100)

QI '

jm

i'1Q i

nP io

jm

i'1Q i

oP io

(100)

QI '

jm

i'1Q i

nP in

jm

i'1Q i

oP in

(100)



Equation 13.6

Equation 13.7

Equation 13.8

Equation 14.1

Equation 14.2

Equation 14.3

Equation 14.4

Equation 14.5

Equation 14.6

Equation 14.7

VI '

jm

i'1P i

nQ in

jm

i'1P i

oQ io

(100)

Fx 'F

n



Examination Results

The UBC Real Estate Division knows that examination results are important and tries to get grades back tostudents as soon as possible.

You can expect to receive your results within six weeks of the date the examination was written. Onceyour examination has been graded, your results will be posted in your Course History/Exam Results anda results letter will be sent to you in the mail.

Please note that examination results will be withheld until all outstanding fees are paid. No results are providedin person, by telephone or by email.

Equation 14.8

Equation 15.1

END OF EXAMINATION

the university of british columbia diploma program …...pavel $1,000,000 for the property,...

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