TIME VALUE OF MONEY: THE BUY VERSUS RENT DECISION
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 $700,000.
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. (Forsimplicity, 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 5.50% APR
semi-annual compounding 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.
SOLUTION:
To analyze the buy-versus-rent decision, Rebecca Young needs to consider several financial factors. Let's
break down the key points and calculations she needs to make:
Monthly Mortgage Payments: Rebecca plans to make a 20% down payment on the purchase price of
$700,000. Therefore, her down payment would be $140,000. The remaining amount to be financed is
$560,000. She will amortize this mortgage over 25 years with monthly payments.
To calculate the monthly mortgage payments, Rebecca needs to use the mortgage rate of 5.50% APR
semi-annual compounding. First, she needs to convert this rate to a monthly rate. Assuming monthly
compounding, the monthly interest rate would be (1 + 0.055/2)^(1/6) - 1. She can use this monthly rate
to calculate her monthly mortgage payments using a loan amortization formula.
Opportunity Cost of Lump-Sum Funds: Rebecca needs to determine the opportunity cost of using her
lump-sum funds for the condominium purchase rather than leaving them invested. She mentioned that
her invested funds are earning the same effective monthly rate of return as she would be paying on her
mortgage. Therefore, she can consider the monthly return on her invested funds as the opportunity cost.
Additional Costs of Buying the Condominium: In addition to the mortgage payments, Rebecca needs to
consider other costs associated with buying the condominium. These include monthly condo fees of
$1,055, property taxes of $300 per month, estimated repairs and maintenance costs of $600 per year,
local and provincial deed-transfer taxes, and other closing fees.
Modeling Future Scenarios: Rebecca wants to analyze the potential net gain or loss if she decides to sell
the condominium in the future. She needs to model the outstanding principal at different time points (2,
5, and 10 years) and consider different scenarios for the condo price:
a) No change in condo price. b) 10% price drop over the next two years, followed by an increase back to
the purchase price by the end of five years, and then a total 10% increase from the original purchase
price by the end of 10 years. c) Annual increase in condo price based on the annual rate of inflation of
2% over the next 10 years. d) Annual increase in condo price based on an annual rate of 5% over the
next 10 years.
For each scenario, Rebecca needs to calculate the net future gain or loss, taking into account realtor fees
and other closing fees.
By analyzing these factors, Rebecca will be able to compare the financial implications of buying versus
renting the condominium and make an informed decision based on quantitative considerations.
Solution:
The two options with Rebecca Young and variables associated with them are tabulated hereunder:
Option I : Renting two-bedroom condominium
Monthly Rental - $3000
Option II: buying identical condominium
Purchase Price - $700000
Monthly condo fees of $1000 per month plus
property tax $300 per month plus Annual repair
and maintenance of $600
Cash down payment of 20%, LOCAL DEED
TRANSFER TAX 1.5%, PROVISIONAL TRANSFER
TAX 1.5% both at purchase date. Closing fees
$2000.
Financing of 80% by mortgarte at 5.5% APR with
semi-annual compounding locked in for 10-year
term. Amortize in 25 years.
Sale Considerations:
Realtor fees 5% plus $2000 closing fees
Opportunity cost of down payment sum at 5.5%
To find out:
1. Monthly mortgage payments = 5.5% APR with semi annual compounding of 560000 per year
calculated in attached excel sheet as $22727 per month.
2. Opportunity cost on monthly basis of suing the lump-sum – 20% of 700000 = 140000
3. Additional payment per month on purchase compared to renting - $22727-$3000 - $19727
4. What will be the value for selling at a future date in 2, 5 or 10 years by calculating outstanding
principal under following cenario to calculate net cash flow at the sale date
a. No change in condo price
b. Condo price drop 10% for 2 years, then increase to purchase price at end of 5 years and
then increase 10% of purchase price at end of 10 years.
c. Condo price increase annually by inflation of 2% over 10 years
d. Condo price increases annually by 5% per year over 10 years.