Case Study $-$II

Time Value of Money

Harvard Business Case Study Modified by Seth Soman.

Ellie Drees, from Norwich university completed her undergraduate degree in Business

Management, $2022,$ with a concentration in Financial Economics and moved to Toronto for a

new job as a financial analyst. In Toronto she is renting a two$-$bedroom condominium for $$4,500$

per month, which included parking but not utilities or cable television. In July $2023,$ the virtually

identical unit next door became available for sale with an asking price of $$1,250,000,$ and Ellie

believed she could purchase it for $$1,200,000.$ She realized she was facing the classic buyversus$-$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 Ellie 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 Ellie 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 to provide some context for the qualitative considerations that would

ultimately be a major part of her decision.

Financial Details of Purchasing the Condominium

Cash Down payment $20\%$ of the purchase price

Closing fees $$12,000$

Loan $($annual rate$1,$ locked for $10$yrs$)5\mathrm{.}25\%$

Length of the loan $25$ years

Condo Fees $$2,000/$month

Property tax $$500/$month

Repairs and General maintenance $$750/$year

Financial Details of Selling the Condominium

Selling cost $5\%$ of the selling price

Closing fees $$12,000$

The money that Ellie 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. Ellie assumed that if she were to sell the condominium $$ say, in the next two to

$10$ years $$ she would pay $5$ per cent of the selling price to realtor fees plus $$12,000$ in other

closing fees.

Ellie 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, assuming the condo price increase

annually at a rate of $7\mathrm{.}5\%$ per year over the next $10$ years.

Questions

$1.$ Describe the problem using a timeline.

$2.$ Analyze the buying and renting decision, at various points in the future $(2,5,$ or $10$ years$)$

completing all relevant cash flows.

$3.$ Provide your recommendations