THE BUY vs$.$ RENT DECISION

In May $2013,$ Rebecca Young completed her MBA and moved to Toronto for her new job in investment banking. There, she rented a spacious $2-$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 Ms$.$ Young believes that she can purchase it for $$600,000.$ She realized that she was facing a 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, in her personal life.

While Ms$.$ Young really liked the condominium unit she was renting, as well as the condominium building itself, she felt that it maybe inadequate for her long term needs, as she planned to move a house or even to a larger penthouse condominium in the next $5-10$ years, or even sooner if her job continued to work out well.

Friends and family have given Ms$.$ Young a variety of mixed opinions concerning the buy$-$versus$-$rent debate, ranging from "you're throwing your money away on rent" or "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 the 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 Ms$.$ 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, Ms$.$ Young intended to provide a cash down payment of $20\%$ of the purchase price. There was also a local deed$-$transfer tax of approximately $1\mathrm{.}5\%$ of the purchase price, and a provincial deed$-$transfer tax of $1\mathrm{.}5\%,$ both due on the purchase date. $($For simplicity, Ms$.$ Young planned to initially ignore any other tax considerations throughout her analysis.$)$ Other closing fees were estimated to be around $$2,000.$

SCENARIO ANALYSIS

In order to complete a financial analysis of the buy$-$versus$-$rent decision, Ms$.$ Young realized that her first task would be to determine the required monthly mortgage payments. Next, she wanted to determine the opportunity costs $($on a monthly basis$)$ of using the lump$-$sum required funds for the condominium purchase rather than keaving those funds invested and earning the effective monthly rate, assumed to be equivalent to the mortgage rates. She would then be able to determine the additional monthly payments required to buy the condominium compared to renting, including the opportunity cost.

Ms$.$ Young wanted to consider what might happen if she decided to sell the condominium at a future date. She was confident that any resell would not happen for at least two years, but could certainly happen in the next $5$ or $10$ years' time. She needed to model the amount of the oustanding principal at various points in the future $--2$ years, $5$ years, or $10$ years from now. She then wanted to determine the net future loss or gain after $2$ years, $5$ years, or $10$ years under the following scenarios, which she had determined were possible after some due diligence regarding the future real estate prices in the Toronto Condo Market:

$($a$)$ the condo price remains unchanged

$($b$)$ the condo price drops $10\%$ over the next $2$ years, and then increases back to the purchase price by end of $5$ years, and then increases by $10\%$ from the original purchase price at the end of $10$ years

$($c$)$ the condo price increases annually by the annual rate of inflation at $2\%$ per year over the next $10$ years

$($d$)$ the condo price increases annually by an annual rate of $5\%$ per year over the next $10$ years

FINAL CONSIDERATIONS

Ms$.$ Young realized that she had a tough decision ahead of her, but she was well traiined 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.

Given the above Mini$-$Case Study $(4-$page Info Data$),$ please answer the following $6$ questions by stating the formula used, step by step computations, and final answer. You can also use a table $/$ illustration for comparison purposes and analysis. In addition, kindly identify the Group Members who were assigned or voluntered to answer each question:

$1.$ Determine the required monthly payments for the mortgage.

$2.$ Determine the "opportunity" costs, on a monthly basis, of using the r