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

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 1.5 per cent of the

purchase price, and a provincial deed-transfer tax of 1.5 per cent, both due on the purchase date. (For

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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 rate1 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 next two to 10 years

— she would pay 5 per cent of the selling price to realtor fees plus $2,000 in other closing fees.

SCENARIO ANALYSIS

In order to complete a financial analysis of the buy-versus-rent decision, Young realized that her first task

would be to determine the required monthly mortgage payments. Next, she wanted to determine the

opportunity cost (on a monthly basis) of using the lump-sum required funds for the condominium

purchase rather than leaving those funds invested and earning the effective monthly rate, assumed to be

equivalent to the mortgage rate. She would then be able to determine additional monthly payments

required to buy the condominium compared to renting, including the opportunity cost.

Young wanted to consider what might happen if she chose to sell the condominium at a future date. She

was confident that any re-sell would not happen for at least two years, but it could certainly happen in five

or 10 years’ time. She needed to model the amount of the outstanding principal at various points in the

future — two, five or 10 years from now. She then wanted to determine the net future gain or loss after

two, five and 10 years under the following scenarios, which she had determined were possible after some

due diligence regarding future real-estate prices in the Toronto condo market: (a) The condo price

remains unchanged; (b) The condo price drops 10 per cent over the next two years, then increases back to

its purchase price by the end of five years, then increases by a total of 10 per cent from the original

purchase price by the end of 10 years; (c) The condo price increases annually by the annual rate of

inflation of 2 per cent per year over the next 10 years; and (d) The condo price increases annually by an

annual rate of 5 per cent per year over the next 10 years.

FINAL CONSIDERATIONS

Young realized she had a tough decision ahead of her, but she was well trained to make these types of

decisions. She also recognized that her decision would not be based on quantitative factors alone; it would

need to be based on any qualitative considerations as well. She knew she needed to act soon because

condominiums were selling fairly quickly, and she would need to arrange financing and contact a lawyer to

assist in any paperwork if she decided to buy

Requirements:

1. determine the required monthly payments for the mortgage.

2. determine the 'opportunity' cost, on a monthly basis, of using the required funds for closing (i.e., down payment plus all closing costs), rather than leaving those funds invested and earning the monthly effective rate determined in question (1).

3. determine the monthly additional paymentd required to buy versus rent ( include the monthly opportunity costs determined in question (2).