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RYERSON UNIVERSITY REM 400 Real Estate Finance Graded Assignment One Due Date: 26 October 2015 Instructions: Solve each of the four problems which appear below. You may submit your answers either in hard copy form or as file via email (sent to my email address on your syllabus.) Please write or print out your solutions, without accompanying derivations, on one sheet of paper. Your solutions must be legibly stated, in black ink or black font colour, using the notation we are using in the course.1 Circle each of the numerical values composing each of your solutions to the problems in any color of ink (except black) if you are submitting your answers in hard copy, and, if electronically, indicate the final numerical answer in boldface or by some other appropriate means. On subsequent, separate pages in your submission (or an attached Excel file if you are submitting electronically and used spreadsheets for calculations)you have the option, if you wish, of showing your work in deriving your solutions, but you are not required to do so. Your grade for this assignment will, consequently, be awarded solely on the basis of your numerical solutions and not on any derivations you might submit.2 Stated numerical solutions should be rounded to basis points (4 decimal points), or to 2 decimal points if you explictly express your solution as a percentage.3 Remember that, for the purposes of this assignment, all mortgages will be considered \"riskless\" (meaning in finance jargon that the mortgagor will default on none of the component coupon payments in his mortgage.) If you submit your solutions in hard copy form, answers must be printed from a word-processing program (if not handwritten) and all hard copy submissions must be stapled together (unstapled answer sheets will be be left ungraded until you remember to staple them.) If you have solved the problems in a group, you must nevertheless submit an individual set of answers, but in addition you must list all other members of your group directly below your name. No assignments submitted after the midterm exam on 26 October will be accepted, regardless of reason. 1. If, in today's respective markets for one-month, three-month and six-month mortgage coupon payments, trading determines a market price of ninety-nine and one-half ($99.50) dollars per one hundred dollars of coupon payment receivable in one month, ninety-eight and one-fourth ($98.25) dollars today per one hundred dollars ($100.00) of coupon payment receivable in three months, and ninety-seven and onefourth ($97.25) dollars per one hundred dollars ($100.00) of coupon payment receivable in six months. a. Calculate the respective net and gross values of the current market rates of interest and discount on these one- , three- and six-month coupon payments. b. Using English only, state the definitions of the respective market values of the interest rate and the discount rate, in the case of the six-month coupon. c. Using English only, state, for this same six-month coupon, which respective cash flow is being valued and which is being used to measure this value (ie, the unit of measure) in the calculation of its market interest rate. 1 A 2 S in ce y ou r gr ad e w ill d ep en d on ly on th e b asis of y ou r d er iv ation s w n ote, on a d iffer en t top ic, th at it w ill b e p osted after th e m id ter m 3 Mean in g, if y ou ar e cr u n ch in g n u m b er s b y h an d , y ou sh ou ld car r y ou t y ou r actu al calcu lation s to fi v e d ecim al p oin ts. com p r eh en siv e list of su ch n otation is p osted in th e n otes fold er on ou r D2L cou r se site. on y ou r d esign ated ill n ot b e en ter tain w ou ld b eh oov e y ou ex am on 26 Octob fi n al an sw er s, ap p eals to r aise th e aw ar d ed scor e on an y giv en p r ob lem ed (as it w ou ld n ot b e b y y ou r su p er v isor in an y job situ ation . P lease to sav e a cop y of y ou r w or k to com p ar e w ith th e an sw er sh eet, w h ich er . d. Do the same for the market discount rate determined by this same six-month coupon. 2. Consider again these same three markets with today's market values of their respective prices. A mortgage lender has just originated a twenty year, interest-only Canadian mortgage with a balance of $500, 000.00 and an announced annual mortgage coupon rate, , of 6%. He offers to sell either you or your classmate, today, a security composed of a single three-month coupon plus a single six-month coupon, each of which could be traded on an individual basis in these markets.1 a. What should you offer to pay for this security today? b. What would your classmate offer to pay for this same security if he used the announced annual coupon rate of 6% to calculate its present discounted value?2 c. To whom would the lender sell the security? d. If your classmate buys the security at the price he calculates for its present discounted value, how much does he gain or lose (in dollars today) relative to what he would have paid by using the market prices in the three coupon markets above? e. Since you can trade in today's markets for one-month and three-month coupons, you decide you can make an arbitrage profit from your classmate's purchase by offering to trade each of the onemonth and three-month coupon payments composing the security he now owns. Assuming you and he limit your trading to just one coupon of each maturity, determine (i) how much of a profit you could make and (ii) whether you buy or sell the one-month coupon you trade with him and, analogously, whether you buy or sell the three-month coupon you trade with him. 3. Three mortgage-based securities are up for auction today, in riskless, arbitrage-free markets, by bond traders in Toronto. The first is a single one-year $5000.00 mortgage coupon and the second a single $7000.00 two-year mortgage coupon payment, each sold off of interest-only Canadian residential mortgages of twenty years maturity. The third security consists of two coupon payments, with the first coupon paying in one year and the second in two years, each being taken from an interest-only Canadian residential mortgage. This mortgage is also of twenty years maturity and has an announced annual coupon rate of 8.00% and an initial balance B0 of $1, 000, 000.00.3 Unfortunately, no one has yet bid for the second security, and consequently it does not yet have a market price, nor can corresponding market interest rate for two-year coupons be directly observed. Your supervisor, who is known as someone whose trading acuity cannot be underestimated, wishes however to bid on this second security and assigns you to estimate its market (no-arbitrage) price so he should know what to bid for it. Assuming the first security (the single one-year coupon) sells today for $98.80 per one hundred dollars of face value and the third security is selling today for $12, 824.5541, then based on these observed sales, infer the following: a. the respective market rates of interest and discount b. the current market (no-arbitrage) price of the second security 4. You've just been appointed senior mortgage loan officer at the Wawa (Ontario) brach of the Royal Bank. A Ms. K. Wynne, who is a potential mortgagor, comes to you seeking a $750, 000 fixed-rate mortgage loan, to be originated today, in order to purchase a local home currently listed for $1, 000, 000.00. Based on her credit record and this collateral, you offer her an announced mortgage rate of = 5%, fixed over 1 Restatin g th is for clar ity , th e secu r ity con sists of on e on e-m on th cou p on an d on e th r ee-m on th cou p on . 2 Y ou m igh t w ish to con su lt th e d ocu m en t, \"A cou r se w eb site. 3 Recall fr om class th at an in ter est-on ly tw en ty -y ear C an ad ian m or tgage featu r es eq u al m on th ly cou p on p ay m en ts calcu lated fr om th e actu al m on th ly cou p on r ate, , cor r esp on d in g to its an n ou n ced an n u al r ate, on th e in itial b alan ce B0 . T h e in itial b alan ce, in su ch a m or tgage, r em ain s th e u n p aid b alan ce ov er all $240 m on th s m atu r ity . N ote on C an ad ian 2 v . A m er ican Mor tgage Rates,\" p osted ear lier on th e the life of the loan and her choice of maturity and amortization schedule. She contemplates a maturity of either twenty or twenty-five years and either an interest-only mortgage or a constant-amortization mortgage with a zero terminal balance. Prior to deciding, she asks you to show her a sample of the respective monthly interest and amortization portions of the coupon payment, as well as the total monthly coupon payment itself, for each of the four combinations of maturity and amortization type from which she must decide. She also wants to know the initial balance of each mortgage if she could renew it on the same terms exactly six years from now, once she has paid all required coupon payments at the end of the fifth year of their respective maturities. Assuming the sample payments she wishes to see are those she would pay in the thirtieth month of her mortgage, calculate those variables for: 4 a. the mortgage with a 20 year maturity and interest-only amortization b. the mortgage with a 25 year maturity and interest-only amortization c. the mortgage with a 20 year maturity and constant monthly amortization d. the mortgage with a 25 year maturity and interest-only amortization 4 T h at is, calcu late th e in ter est, am or tization an d total cou p on p ay m en ts ow ed in th e th ir tieth an d six tieth m on th s of th e m or tgage. 3