The University of British Columbia Diploma Program in Urban Land Economics Sample Final Examination BUSI 121 FOUNDATIONS OF REAL ESTATE MATHEMATICS

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The Uiversity of British Colubia Diploa Progra i Urba Lad Ecooics Saple Fial Exaiatio BUSI 121 FOUNDATIONS OF REAL ESTATE MATHEMATICS Tie: Date: 3 Hours Saple Fial Exa Istructios This exaiatio

1 The Uiversity of British Colubia Diploa Progra i Urba Lad Ecooics Saple Fial Exaiatio BUSI 121 FOUNDATIONS OF REAL ESTATE MATHEMATICS Tie: Date: 3 Hours Saple Fial Exa Istructios This exaiatio cosists of two sectios: Part Oe: Writte Aswers 70% Part Two: Multiple Choice Questios 30% 100% This exaiatio cosists of twety-oe (21) pages. Please check to esure that you have a coplete exaiatio. No outside aterials are allowed other tha a had-held, cordless, silet calculator that is NOT alphaueric ad prograable. Part Oe (writte aswers) MUST be aswered i the appropriate booklet(s) provided. Where applicable, show all calculatios so that partial credit ca be awarded if your solutios erit it. Part Two (ultiple choice questios) MUST be aswered, i pecil, o the ultiple choice aswer sheet provided. Istructios o this procedure are cotaied withi the exaiatio. Aswers recorded i ay other aer will ot be cosidered. Please ote that forulae pages for your use are attached to the exaiatio. Aswer ALL Questios. IMPORTANT This exaiatio is the property of the UBC Real Estate Divisio Educatioal Testig Service. No part of this exaiatio is to be reoved fro this exaiatio roo. If ay portio of the exaiatio paper is issig fro the exa evelope, the exaiatio will ot be arked.

2 The Uiversity of British Colubia 2 BUSI 121 Saple Fial Exaiatio PART ONE Writte Aswers Record your aswers i the booklet(s) provided. Eter your studet uber i the box arked Studet Nuber. Where appropriate, show ALL calculatios required ad clearly LABEL ALL GRAPHS draw. Marks 1. George Parrot, the ower of Frieds Developet Co., is i eed of a iterest accruig costructio loa with progress advaces. George aticipates that he will eed to ake five draws o the loa as follows: Ed of Moth Aout 1 $110,000 2 $ 75,000 5 $ 21,000 8 $ 7, $ 3,000 4 The Fraser Bak of B.C. has agreed to George s schedule ad requires a retur of 2 = 12% o its costructio loas. How uch will the Frieds Developet Co. owe at the ed of the teth oth? 2. The followig represets the uber of bedroos i a populatio of five houses: 2, 1, 4, 3, 10 For this distributio: 1 (a) calculate the ea 1 (b) calculate the edia 1 (c) calculate the ode 2 (d) calculate the stadard deviatio 2 (e) calculate the variace 2 (f) calculate the coefficiet of variatio 3 (g) explai which easures of cetral tedecy ad dispersio are best ad why? Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

3 The Uiversity of British Colubia 3 BUSI 121 Saple Fial Exaiatio Marks 3. For a populatio of sigle faily dwellig uits, the stadard deviatio of the sales prices is $100, (a) Assuig a saple size of 25 are take fro this populatio, what is the stadard error of the ea? 2 (b) Calculate the saple size of the ea required if you wat to achieve a stadard error of the ea of o ore tha $10, The followig are the ages of all the sales persoel i a large real estate sales office: (a) Place this data ito 5 groups with appropriate rages. (Ex. Age 20-29) 2 (b) Costruct a frequecy distributio for this grouped data, showig both the absolute group frequecy ad the relative group frequecy. 2 (c) Costruct a histogra of the grouped data. Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

4 The Uiversity of British Colubia 4 BUSI 121 Saple Fial Exaiatio Marks 5. Cosider the followig hypothetical data regardig the average price of hoes i Caada over a eleve 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, $305, $309,000 4 (a) Calculate a three year ovig average o the sales price data. 2 (b) Why would a ovig average be preferable to usig the raw data to exaie log ter treds? 6. Jill has the opportuity to ivest i Whitewater, a recetly developed waterslide park i the suy Okaaga. The forecasted et 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, $ 950,000 2 (a) If Jill requires a retur of 9% per au, copouded aually, is this ivestet attractive at the askig price of $2,000,000? Show calculatios. Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

5 The Uiversity of British Colubia 5 BUSI 121 Saple Fial Exaiatio Marks (b) Assue Jill purchases the waterslide park for $1,750,000 ad she wishes to ear 1 = 9% per au o her ivestet. For this ivestet: 2 (i) Deterie the profitability idex. 2 (ii) Deterie the preset value ratio. 2 (iii) Assuig that she purchases the waterslide park for $1,750,000, calculate the iteral rate of retur o Jill s ivestet. 7. Theo wats to purchase Pavel s house. Three years ago, whe Pavel purchased the property, he arraged a ortgage of $850,000. The ortgage is writte with a 5 year ter ad a 25 year aortizatio period. The loa has payets of $6, per oth. At the ed of the 5 year th ter Pavel will owe $783, Pavel has ust paid the 36 payet of the loa. Theo offers Pavel $1,000,000 for the property, cosistig of the assuptio of the $813, book value of the ortgage, plus a dowpayet of $186, The curret rate o coparable 2 year ortgages is 6.5% per au, copouded sei-aually. 4 (a) What is the arket value of Theo s offer? 3 (b) All other thigs beig equal, would the arket value of Theo s offer be higher or lower if the origial loa had bee fully aortized. Explai. (Note: o recalculatio is required) 8. Matt Stai is cosiderig ivestig i his old fried Charles Sith s ew restaurat, the U.K. Grill. I retur for a $35,000 ivestet today, Charles has proised to pay back Matt the followig cash flows at the ed of each of the ext five years: Year Cash Flows 1 $5,000 2 $8,000 3 $7,500 4 $9,000 5 $9,750 Charles isists this ivestet offers a excellet retur. Matt, havig received bad advice fro Charles i the past, has doe his hoework this tie, ad has foud out that the arket discout rate for siilar ivestets is 12% per au, copouded aually. Calculate the followig retur easures for Matt s ivestet, assuig Matt does receive the cash flows described above: Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

6 The Uiversity of British Colubia 6 BUSI 121 Saple Fial Exaiatio Marks 2 (a) Net Preset Value (NPV) 2 (b) Iteral Rate of Retur (IRR) 2 (c) Preset Value Ratio 2 (d) Iteral Rate of Retur (IRR) if Matt is able to reivest the yearly cash flows at 8% per au, copouded aually. 2 (e) Based o these retur easures, briefly outlie your opiio whether Matt should ivest or ot? 9. Stellar Fiacig has arraged a loa i the aout of $250,000, writte at a iterest rate of 8.75% per au, copouded sei- aually. The loa calls for othly payets, a five year ter, ad a aortizatio period of twety-five years. You have bee asked by the borrower to help explai the iterest cosequeces of this fiacig arrageet. Specifically, you ust calculate: 2 (a) th The pricipal ad iterest portios of the 12 payet. 2 (b) How uch iterest ad pricipal will be paid durig the ter of the loa. 2 (c) th How uch iterest will be paid durig the 5 year. 1 (d) The outstadig balace at the ed of the ter of the loa. 10. Mr. Brow has approached Ms. Jae, a ortgage broker, about a ortgage loa for the purchase of a ew house. Ms. Jae has agreed to arrage a loa with a face value of $130,000, at a iterest rate of 9.5% per au, copouded sei-aually, with a 25 year aortizatio ad a 5 year ter. The loa will be repaid with quarterly payets rouded up to the ext higher dollar. Icluded i the face value of the loa are a $4,000 coissio for Ms. Jae ad survey ad legal fees totallig $2, (a) What is the cost of the fuds advaced to Mr. Brow, expressed as a effective aual rate? 2 (b) If a ortgage ivestor cae alog ad purchased Mr. Brow s ortgage for a aout greater tha the outstadig balace, would this be a discouted ortgage or a boused ortgage? Explai the differece betwee the two. END OF PART ONE Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

7 The Uiversity of British Colubia 7 BUSI 121 Saple Fial Exaiatio MULTIPLE CHOICE ANSWER SHEET INSTRUCTIONS Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

8 The Uiversity of British Colubia 8 BUSI 121 Saple Fial Exaiatio PART TWO Multiple Choice Questios 1 ark each Record your aswers o the ultiple choice aswer sheet provided. Aswers recorded i ay other aer will NOT be cosidered. Each questio has oly ONE correct aswer. The ext THREE (3) QUESTIONS are based o the followig iforatio: Frak Noad recetly iherited a sall fortue. He has several ivestet optios ad is aalyzig the to deterie which has the highest retur. His optios are as follows: Ivestet Aout to ivest Ter Aout received (today) (years) (at ter ed) A $500,000 1 $600,000 B $480,000 2 $542,000 C $490,000 3 $550, The effective aual rate ( ) eared o Ivestet A is: 1 (1) 20% (2) 20.36% (3) % (4) 8.3% 2. The sei-aual periodic rate (i ) eared o Ivestet B is: sa (1) % (2) % (3) % (4) % 3. The weekly periodic rate (i ) eared o Ivestet C is: w (1) % (2) % (3) % (4) % Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

9 The Uiversity of British Colubia 9 BUSI 121 Saple Fial Exaiatio th 4. A house purchase closes o October 12. Fuds will be advaced o that date such that, with iterest st accrued, $223,500 will be owig o Noveber 1. The iterest rate to be charged o the loa will be 8.75% per au, copouded othly. What aout will be advaced to the borrower o October th 12? It is ot a leap year. (1) $ 222, (2) $ 222, (3) $ 222, (4) $ 222, The ext TWO (2) QUESTIONS relate to the followig iforatio: Fracie ad Balfour Shufflebotto have foud a hoe that they siply ust ow. However, i order to purchase the hoe, they ust obtai fiacig. 5. The Shufflebottos ca oly afford to pay $1,500 per oth. If the loa has a aortizatio period ad ter of 15 years ad a arket rate of = 12.55%, what is the axiu they ca borrow? 1 (1) $ 125, (2) $ 143, (3) $ 123, (4) $ 121, The Shufflebottos have foud a lower iterest rate at a differet fiacial istitutio. If the rate is 1 = 12.45%, ad payets are still $1,500 per oth over a 15 year aortizatio period, what is the axiu loa the Shufflebottos ca obtai? (1) $126, (2) $124, (3) $122, (4) $144, Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

10 The Uiversity of British Colubia 10 BUSI 121 Saple Fial Exaiatio The ext THREE (3) QUESTIONS are based o the followig iforatio: The followig table outlies fiacial iforatio with respect to coercial leases. I each istace, lease payets are ade i advace. Periodic Payet Payet Lease Preset Value Noial Rate Frequecy Lease Ter (i advace) A $200, aually 25 years $16, B = 12% othly 25 years $ C $150, = 18% quarterly 25 years The oial rate per au, with sei-aual copoudig, for Lease A is: (1) % (2) % (3) % (4) % 8. The preset value of Lease B is: (1) $ 85, (2) $ 86, (3) $ 86, (4) $ 87, The required payet for Lease C is: (1) $ 6, (2) $ 6, (3) $ 6, (4) $ 6, You have ust wo a lottery that will pay you $10,000 at the ed of each year, forever. If iterest rates are = 9%, what is the preset value of your wiigs? 1 (1) $ 111, (2) $1,000, (3) $ 109, (4) ipossible to calculate, due to isufficiet data Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

11 The Uiversity of British Colubia 11 BUSI 121 Saple Fial Exaiatio The ext THREE (3) QUESTIONS are based o the followig four graphs: (A) (B) (C) (D) 11. The equatio for the lie x - 2y = -4 correspods to which graph? (1) A (2) B (3) C (4) D 12. The equatio for the lie 5x - 2y = -10 correspods to which graph? (1) A (2) B (3) C (4) D Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

12 The Uiversity of British Colubia 12 BUSI 121 Saple Fial Exaiatio 13. The equatio for the lie x - y = 1 correspods to which graph? (1) A (2) B (3) C (4) D The ext TWO (2) QUESTIONS are based o the followig etes ad bouds descriptio of a property: ove 22 feet 45E to the east (N45EE) to the southwest corer of the property; ove 80 feet due east (N90EE) to the southeast corer of the property; ove 92.4 feet 30E to the ortheast (N30EE) to the ortheast corer of the property; ove feet due west (S90EW) to the orthwest corer of the property; ove 80 feet due south to the southwest corer of the property, to close or "boud" the property. 14. Which of the followig shapes best approxiates the shape of this property? A. B. C. D. (1) A (2) B (3) C (4) D Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

13 The Uiversity of British Colubia 13 BUSI 121 Saple Fial Exaiatio 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 ext TWO (2) QUESTIONS are based o the followig iforatio: The followig are hypothetical data for residetial real estate sales activity: Year Sales 1 12, , , , , What is the percetage icrease i housig prices fro year 3 to year 5? (1) 10.3% (2) 9.3% (3) 5.3% (4) 5% 17. Fill i the blaks. The percetage chage betwee year 1 ad 2 is A tha betwee year 4 ad 5, ad the absolute chage betwee year 1 ad 2 is B tha betwee year 4 ad 5. (1) A = Larger, B = Larger (2) A = Saller, B = Saller (3) A = Saller, B = Larger (4) A = Larger, B = Saller 18. A $40,000 loa at 14% per au, copouded othly, is to be advaced o Septeber 18th. The first othly payet is due Noveber 1st. The iterest adustet charge o October 1st will be: (1) $ (2) $ (3) $ (4) $ Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

14 The Uiversity of British Colubia 14 BUSI 121 Saple Fial Exaiatio 19. Suppose a ortgage leder has a portfolio of ivestets which cotais the followig ortgage loas at the followig iterest rates: Value of Loas Iterest Rate ($ illios) (%) What is the weighted ea iterest rate for this portfolio? (1) 12.83% (2) 10% (3) 14.5% (4) 11.35% 20. A ivestor plas to purchase a existig leasehold iterest i a icoe-producig property ad expects to receive icoe i accordace with the followig schedule: Ed of Moth Cash Flow 6 $17, $19, $19, $19, Give that the ivestor deads a iiu yield o ivestet of 15% per au, copouded othly, his axiu bid price should be: (1) $ 64, (2) $ 67, (3) $ 66, (4) $ 66, A ivestor coteplates the purchase of a icoe producig property where aual payets of $15, are expected for a period of 20 years. The first payet is to be received i 5 years tie. The preset value of the ivestet, calculated at = 12%, is: 1 (1) $ 79, (2) $ 112, (3) $ 63, (4) $ 71, Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

15 The Uiversity of British Colubia 15 BUSI 121 Saple Fial Exaiatio The ext TWO (2) QUESTIONS relate to the followig equatio for the price of a house: PRICE=20, ,000ROOMS + 10,000BATHROOMS 22. A icrease i the uber of bathroos fro 1 to 3 would icrease the sale price by: (1) $10,000 (2) $30,000 (3) $20,000 (4) $15, A house with 4 roos ad 2 bathroos would sell for: (1) $20,000 less tha a house with 2 roos ad 3 bathroos. (2) $30,000 less tha house with 6 roos ad 4 bathroos. (3) The sae as a house with 3 roos ad 3 bathroos. (4) $5,000 less tha a house with 3 roos ad 4 bathroos. 24. Real estate appraisers ofte use the sale prices of 3 or 4 coparable properties i order to deterie the ost likely sales price of the property they are appraisig. The choice of coparable properties by the appraiser is a exaple of what kid of saple? (1) rado saple (2) coveiece saple (3) udget saple (4) cluster saple 25. Mutual fud aagers that are tactical asset allocators buy stocks whe the arket is i a dowtur ad sell the whe the arket is o the uptur. These aagers believe that the stock arket exhibits what kid of fluctuatios? (1) Seasoal variatio (2) Secular tred (3) Cyclical variatio (4) Irregular variatio THE NEXT TWO (2) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A loa i the aout of $216, bears iterest at 18% per au copouded othly, ot i advace. Payets are ade othly. The loa has a 20 year aortizatio period ad ter. Payets are rouded up to the ext higher dollar. 26. The othly payets are: (1) $ 3,228 (2) $ 3,227 (3) $ 3,333 (4) $ 3,334 Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

16 The Uiversity of British Colubia 16 BUSI 121 Saple Fial Exaiatio 27. The outstadig balace after 120 payets is: (1) $ 188, (2) $ 186, (3) $ 184, (4) $ 182, The ter of a boused ortgage is icreased fro 5 years up to 15 years (while keepig the aortizatio period at 20 years). This eas the effective rate charged to the borrower o fuds advaced: (1) does ot chage. (2) icreases. (3) decreases. (4) chages but the chage caot be deteried with the iforatio give. THE NEXT TWO (2) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Susy has decided to purchase her ow rollerblade shop i Kitsilao. She has bee advaced a iterest oly loa of $215,500 by the Bak of Kara. The iterest rate is 13.5% per au, copouded quarterly, with aual payets (ot i advace). The ter of the loa is 7 years. 29. What is her yearly iterest payet (rouded up to the ext higher dollar)? (1) $ 28,772 (2) $ 29,093 (3) $ 30,599 (4) $ 30, Now assue that Susy's loa is iterest accruig istead of iterest oly. How uch would Susy owe at the ed of the 7 years? (1) $ 537, (2) $ 545, (3) $ 246, (4) $ 246, END OF PART TWO Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

17 The Uiversity of British Colubia 17 BUSI 121 Saple Fial Exaiatio Forulae BUSI Foudatios of Real Estate Math Matheatical Forula Fiacial Notatio 1. Iterest Rate (1 + i o) = (1 + i q) 2 1 Coversio = (1 + i ) = (1 + i ) 2. Preset Value of a Lup Su PV = FV (1 + i) - = FV (1 % i) 3. Future Value of a Lup Su FV = PV (1 + i) sa a 12 4 Preset Value of a 1&(1%i) 4. PV = Pt &() PV = Pt aú, i%á Ordiary Siple Auity i PV ' Pt % Preset Value of a 5. Siple Auity Due Pt 1&(1%i)&(&1) PV = Pt + Pt aú-1, i%á i Future Value of a (1%i) &1 6. FV = Pt FV = Pt sú, i%á Ordiary Siple Auity i 7. Sikig Fud Pt = FV 1 Pt = FV (1%i) &1 i 1 sú, i%á Pt = FV (1%i) &1 i Equatio 8.14 APR = (100 x C) (T x P) Equatio 9.3 Preset Value Ratio = Equatio 9.4 Profitability Idex = Preset Value of Net Cash Flows Cost Preset Value of Positive Cash Flows Preset Value of Negative Cash Flows Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

18 The Uiversity of British Colubia 18 BUSI 121 Saple Fial Exaiatio Equatio 10.1 Equatio 10.2 Y = X + b A = L W Equatio 10.3 c 2 = a 2 % b 2 Equatio 10.4 A = ½ B H Equatio 10.5 A = Br 2 Equatio 11.1 Equatio 11.2 TOTAL = X + X + X + X X i ' X 1 % X 2 % X 3 %... % X Equatio 11.3 Percetage chage = 100 Fial value & Base value Base value Equatio 12.1 X i Equatio 12.2 µ ' X i Equatio 12.3 µ ' f i X i Equatio 12.4 f i X i ' f 1 X 1 % f 2 X 2 % f 3 X 3 %... % f X Equatio 12.5 f i ' Equatio 12.6 µ ' f i (X i ) Equatio 12.7 µ ' w i X i w i Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

19 The Uiversity of British Colubia 19 BUSI 121 Saple Fial Exaiatio Equatio 12.8 µ ' f i M i Equatio 12.9 F ' (X i &µ) 2 Equatio F ' 1 ( X 2 i & µ 2 ) Equatio F 2 ' (X i & µ) 2 Equatio σ 2 ' 1 ( X 2 i & µ 2 ) Equatio Coefficiet of variatio = F µ (100) Equatio 13.1 r ' [ X 2 i X i Y i & ( & ( X i ) 2 ][ X i )( Y 2 i Y i ) & ( Y i ) 2 ] Equatio 13.2 Y i ' a % bx i Equatio 13.3 S ' (Y i & Ŷ i ) 2 Equatio 13.4 â ' Y i & ˆb X i Equatio 13.5 ˆb ' X i Y i & X i Y i X 2 i & ( X i ) 2 Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

20 The Uiversity of British Colubia 20 BUSI 121 Saple Fial Exaiatio Equatio 13.6 S YX ' Y 2 i & ˆb X i Y i & â Y i & 2 Equatio 13.7 S YX ' (1 & r 2 )F 2 y & 2 Equatio 13.8 Y i ' a % bx i % cz i Equatio 14.1 I ' X t X t& (100) Equatio 14.2 PI ' P P o (100) Equatio 14.3 PI ' P i Q i o P i o Q i o (100) Equatio 14.4 PI ' P i Q i P i o Q i (100) Equatio 14.5 QI ' Q Q o (100) Equatio 14.6 QI ' Q i P i o Q i o P i o (100) Equatio 14.7 QI ' Q i P i Q i o P i (100) Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

21 The Uiversity of British Colubia 21 BUSI 121 Saple Fial Exaiatio Equatio 14.8 VI ' P i Q i P i o Q i o (100) Equatio 15.1 F x ' F END OF EXAMINATION Exaiatio Results The UBC Real Estate Divisio kows that exaiatio results are iportat ad tries to get grades back to studets as soo as possible. You ca expect to receive your results withi six weeks of the date the exaiatio was writte. Oce your exaiatio has bee graded, your results will be posted i your Course History/Exa Results ad a results letter will be set to you i the ail. Please ote that exaiatio results will be withheld util all outstadig fees are paid. No results are provided i perso, by telephoe or by eail. Copyright: 2011 UBC Real Estate Divisio Educatioal Testig Service

The self-assessment will test the following six major areas, relevant to studies in the Real Estate Division's credit-based courses:

The self-assessment will test the following six major areas, relevant to studies in the Real Estate Division's credit-based courses: Math Self-Assessmet This self-assessmet tool has bee created to assist studets review their ow math kowledge ad idetify areas where they may require more assistace. We hope that studets will complete this