In Jan $2019,$ Missy Grant moved to Uptown Dallas for a new job in a commercial real estate investment firm. There, she rented a spacious, two$-$bedroom condominium for $$2,000$ per month, which included parking but not utilities or cable television. In July $2019,$ the virtually identical unit next door became available for sale with an asking price of $$620,000,$ and Grant 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 like $$time value of money$$ concepts she had acquired in business school to her personal life. While she 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 within five to $10$ years $$ even sooner if her job continued to work out well. Friends and family had given her a variety of mixed opinions concerning the buy$-$versus$-$rent debate, ranging from $$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.

FINANCIAL DETAILS

If Grant 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 $$600$ per year. If she decided to purchase the new unit, Grant intended to provide a cash down payment of $20$ per cent of the purchase price. There was also a local deed$-$transfer tax of approximately $1\mathrm{.}5$ per cent of the purchase price, and a provincial deed$-$transfer tax of $1\mathrm{.}5$ per cent, both due on the purchase date. $($For simplicity, ignore any other tax considerations throughout her analysis.$).$ Other closing fees were estimated to be around $$2,000.$

In order to finance the remaining $80$ per cent of the purchase price, Grant contacted several lenders and found that she would be able to obtain a mortgage at a $7\mathrm{.}5$ per cent $$quoted$$ annual rate that would be fixed rate fully amortized mortgage over $25$ years, with monthly payments. The money that Grant was planning to use for her down payment and closing costs was presently invested and was earning the same rate of return as she would be paying on her mortgage.

Grant assumed that if she were to sell the condominium $$ say, in the next two to three years $$ 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, Grant 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 rate of return, 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. Grant 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 a year, but it could certainly happen in $2$ or $3-$years$$ time. She needed to model the amount of the outstanding principal at various points in the future $$ two or three years from now.

She then wanted to determine the net future gain or loss after two, and three years under the following scenarios, which she had determined were possible after some due diligence regarding future real$-$estate prices in the Dallas condo market:

$($a$)$ The condo price remains unchanged;

$($b$)$ The condo price drops $10$ per cent over the next $2$ years, then increases back to its purchase price by the end of three years

$($c$)$ The condo price increases annually by the annual rate of inflation of $2$ per cent per year over the next $10$ years;

FINAL CONSIDERATIONS

Grant 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. Answer using Excel Functions, show work.