Part $2($weight: $50\%)$

In May $2013,$ Rebecca Young completed her MBA and moved to Toronto for a new job in

investment banking. There, she rented a spacious, two$-$bedroom condominium for $$3,000$ per

month, which included parking but not utilities or cable television. In July $2014,$ the virtually

identical unit next door became available for sale with an asking price of $$620,000,$ and Young

believed she could purchase it for $$600,000.$ She realized she was facing the classic buy$-$versus$-$

rent decision. It was time for her to apply some of the analytical tools she had acquired in

business school $-$ including "time value of money" concepts $-$ to her personal life.

While Young really liked the condominium unit she was renting, as well as the condominium

building itself, she felt that it would be inadequate for her long$-$term needs, as she planned to

move to a house or even to a larger penthouse condominium within five to $10$ years $-$ even

sooner if her job continued to work out well.

Friends and family had given Young a variety of mixed opinions concerning the buy$-$versus$-$

rent debate, ranging from "you're throwing your money away on rent" to "it's better to keep

things as cheap and flexible as possible until you are ready to settle in for good." She realized

that both sides presented good arguments, but she wanted to analyze the buy$-$versus$-$rent

decision from a quantitative point of view in order to provide some context for the qualitative

considerations that would ultimately be a major part of her decision.

FINANCIAL DETAILS

If Young purchased the new condominium, she would pay monthly condo fees of $$1,055$ per

month, plus property taxes of $$300$ per month on the unit. Unlike when renting, she would

also be responsible for repairs and general maintenance, which she estimated would average

$$600$ per year.

If she decided to purchase the new unit, Young intended to provide a cash down payment of

$20$ per cent of the purchase price. There was also a local deed$-$transfer tax of approximately

$1\mathrm{.}5$ per cent of the purchase price, and a provincial deed$-$transfer tax of $1\mathrm{.}5$ per cent, both due

on the purchase date. $($For simplicity, Young planned to initially ignore any other tax

considerations throughout her analysis.$)$ Other closing fees were estimated to be around

$$2,000.$

In order to finance the remaining $80$ per cent of the purchase price, Young contacted several

lenders and found that she would be able to obtain a mortgage at a $4$ per cent "quoted" annual

rate$1$ that would be locked in for a $10-$year term and that she would amortize the mortgage

over $25$ years, with monthly payments. The money that Young was planning to use for her

down payment and closing costs was presently invested and was earning the same effective

monthly rate of return as she would be paying on her mortgage. Young assumed that if she

were to sell the condominium $-$ say, in the $8$ years $-$ she would pay $5$ per cent of the selling

price to realtor fees plus $$2,000$ in other closing fees.

Questions:

$1.$ a$.$ Mortgage calculation

i$.$ What is the amount Young will borrow$/$mortgage for her condo

ii$.$ The quoted rate on Young's mortgage is $4\%($compounded semiannually$).$ What is the

effective monthly rate on her mortgage?

iii. With monthly payments for $25$ years amortization, the effective monthly interest

rate and the total borrowing, what will Young's monthly mortgage payment be$?$

b$.$ Other costs to purchase condo

i$.$ What is the downpayment Young will make?

ii$.$ What are the other up$-$front costs required to purchase the condo?

iii. If Young forgoes the income on the initial cash downpayment and up$-$front costs,

how much will she lose in investment income each month $($opportunity cost$)?$

c$.$ In addition to the mortgage payment and the opportunity cost of lost investment income,

what

other costs will Young face on a monthly basis when owning her condo?

d$.$ What is the total monthly cost of owning the condo?

$2.$ What is the current cost of renting her condo?

$3.$ What is the present value of the additional cost of owning a condo $($at the

same interest rate as the mortgage$)$ till selling date?

$4.$ Potential selling scenarios of condo

a$.$ Mortgage remaining

i$.$ How much principal will be left on Young's mortgage at the end of:

$1.2$ years,

$2.5$ years and