FNCE 623 : Financial Management
Assignment 1
Buy or rent decision
Done by:
Sameen Raian
MBA
University Canada West(UCW)
Submission Deadline: 12 May 2021
Introduction:
Case Summary:
Rebecca Young is an investment banker in Toronto. She is living in a rented condominium, but
recently, her next-door condo. has been up for sale. Now, she is in a dilemma whether she should
continue to live in her rented condo or buy a new condo. To take this decision, she needs to consider
many quantitative as well as qualitative aspects.
Purpose of the case study:
The purpose of this study is to help Rebecca to reach a decision regarding buying or renting the
condominium.
Steps of the financial analysis:
To reach the buy or rent decision, the following tasks need to be completed:

First, Rebecca should calculate the monthly mortgage payment that is required, if she plans
on buying the condominium. (Cleary & Foerster, 2014)

Second, she should calculate the opportunity cost of using her saved funds to buy the condo
instead of keeping those funds invested and earning monthly, at a rate equivalent to the
mortgage rate. (Cleary & Foerster, 2014)

Then, she needs to compare the cost-benefit analysis of the additional monthly payments
that is required to buy the condo to the cost of renting along with the opportunity cost.
(Cleary & Foerster, 2014)

Lastly, she needs consider the different scenarios that might occur in the future if she
decides to sell the condo. (Cleary & Foerster, 2014)
Taking all these analyses into account, Rebecca will be able to reach an informed and good
decision.
Findings and Analysis:
Some financial details to keep in mind:

The price of the condominium for sale is $600,000.

Rebecca will require to pay 20% down payment which is $120,000, if she decides to buy

The rest of the amount, which is $4480,000 will be taken as loan from bank at 4% annual
interest for 25 years.

If Rebecca decides to buy, she will have to disinvest her funds to pay for down payment
and other closing costs. She earns 4% interest from her investments annually.

She might sell the condo. in 2-10 years. We will consider scenarios if the condo. is sold in
year 2, 5 and 10.
The first thing to consider in order to help Rebecca to take a decision is to calculate the monthly
payments. For this, we considered the monthly payment for both the buy and rent decision. The
monthly rent of Rebecca is $3000. If she continues to live in her rented apartment, she will have
to spend $3000 for the purpose of living. On the other hand, from Appendix 2, we find that if
Rebecca buys the apartment, she will have to pay $3938.62 monthly including the condo. Fees,
taxes, maintenance fees and mortgage payments. In this case, Rebecca’s expense will increase by
$938.62 monthly if she decides to buy the apartment. If we look at only the monthly increase in
Rebecca’s expense, it will appear that it is better to stay in the rented condo. but there are many
other aspects to consider before taking the final decision.
In this case, the cost of buying is more than the cost of renting.
Next, we will consider the opportunity cost of buying the apartment. In Appendix 3, we find that
there are 3 different opportunity costs if Rebecca decides to buy the condo.

As we know that Rebecca has to pay 20% down payment along with closing costs to buy
the condo., we find the lumpsum amount to be $140,000. If this amount is kept invested in
the bank, Rebecca will earn $462 monthly at 4% annual interest.

If $140,000 is invested in the bank instead of paying for the condo, then in 2,5 and 10 years,
the future value of this amount will reach $151,424 , $170,331 and $207,234 respectively.
So, the future value of the opportunity cost is $11,424, $30,331 and $67,234(Appendix 3)

Again, the monthly additional $938.62 that Rebecca has to pay as condo fees is also an
opportunity cost. The future value of this additional cost in 2, 5, and 10 years is $23,411.89,
$62,229.55 and $138,211.61. (Appendix 3)

Considering all these, the total opportunity cost in year 2, 5, and 10 is $34,835.89
$92,560.55, and $205,445.61. (Appendix 3)
In this case also, the opportunity cost of buying the condo is greater than that of renting.
Now, we have to consider the given scenarios in the case study to find out whether it will be
beneficial for Rebecca to sell the condo under the mentioned circumstances.

Scenario A- The condo. price remains unchanged: In this scenario, there will be no price
appreciation of the condo over the years. We have to find out whether selling the condo.
will be worth for Rebecca under this scenario. The selling price of the condo will be
$600,000. From Appendix 5, we find the costs related to selling including the closing costs
and realtor fees. From the gained amount, Rebecca will also pay off the outstanding loan
amount that we found from Appendix 4. From Appendix 5,we find that the net proceeds
that Rebecca will get if she decides to sell the condo in year 2, 5 and 10 ,even if there is no
price change of the condo are $111,299.67, $149,927.37 and $225,525.40.

Scenario B- Condo price drops 10% over next 2 years, increases back to original price
by the end of 5 years, increases by 10% at the end of 10 years: The same method of
calculation is applied in this scenario. From Appendix 5, we see that the price of the condo
in year 2 is $540,000, in year 5 is $600,000 and in year 10 is $660,000. The outstanding
balance and the additional selling costs are subtracted from the selling price and Rebecca
is expected to receive net profit of $54,299.67, $149,927.37 and $282,525.40 in year 2, 5
and 10 respectively.

Scenario C- Condo price increases by 2% inflation over 10 years: The inflation rate is
adjusted with the original price of the condo and we find the appreciated value after 2, 5
and 10 years. We calculate the net proceeds in the same way by subtracting the costs and
loan payoffs from the selling price.

Scenario D- Condo price increases by annual rate of 5% over 10 years: Here, the
annual appreciation rate is adjusted and in the same way of calculation, we find the net
proceeds to be $169,724.67, $307,407.86 and $583,995.34 in year 2, 5 and 10 from
Appendix 5.
From the above scenarios, we can conclude that, it is beneficial for Rebecca if she wants
to sell the condo at a later period. If she sells the condo, she can payoff her outstanding
loan and in every scenario, she has profit which is greater than the opportunity cost.
Qualitative factors to consider: Apart from the financial analysis, Rebecca also needs to
consider some subjective factors before taking the decision of buying or renting. Rebecca
should consider whether the new condo will satisfy her needs, if it has enough space and
matches her style, how convenient the condo is, whether she features she wants in her home
is available or not, whether she likes the surrounding area and neighborhood.
(MASTROENI, 2021). Rebecca mentions that she already likes her condominium
building. So, it is evident that she likes the surrounding area and facilities. (Cleary &
Foerster, 2014)
Decision and conclusion:
In the case, it is mentioned that Rebecca felt that her rented condo would be inadequate for
her future needs. The condo which she plans to buy is identical to the one she is living in.
It means that the new condo will also be inadequate for Rebecca’s long-term needs. So,
there is a huge possibility that Rebecca might sell the condo in the future. From the
calculations we found that whenever she decides to sell, she will gain from the sale. On the
other hand, if she continues to live in the rented condo, after a few years she will definitely
move, and all her monthly rent will become sunk cost. Therefore, it is beneficial for
Rebecca to buy the condo. No matter how many years Rebecca lives in her rented condo,
she will not get the ownership. But, if she buys the condo, it will be her own and she can
decide to sell it later with huge profit or rent it and move to a bigger place. The rent from
er owned condo will add to her income.
Therefore, I would recommend Rebecca that, though the buying option is costly, it is
beneficial to buy the condo.
References
Cleary, S., & Foerster, S. (2014). Time value of money: The buy versus rent decision. Ivey Publishing.
MASTROENI, T. (2021, February 10). The 10 Most Important Factors for Buying Your Dream Home.
Retrieved from My Move: https://www.mymove.com/buying-selling/guides/most-importantfactors-for-buying-your-dream-home/
Appendix
Appendix 1
Buy
Purchase price
Downpayment (20% of price)
Mortgage Principal
Annual Interest rate
Number of years
Monthly mortgage payment
$ 600,000.00
$ 120,000.00
$ 480,000.00
$
0.04
$
25.00
$ 2,533.62
Appendix 2
Buy
Monthly condo fees
Monthly taxes
Monthly repairs( $600/12)
Monthly mortgage payment
Total monthly payment
$ 1,055.00
$ 300.00
$ 50.00
$ 2,533.62
$ 3,938.62
Appendix 3
Opportunity cost for buying
Purchase price
Downpayment (20%)
Closing fees
Local deed transfer tax (1.5%)
Provincial deed transfer tax (1.5%)
Monthly Interest rate (4%/12)
Monthly opportunity cost
$ 600,000.00
$ 120,000.00
$2,000
$ 9,000.00
$ 9,000.00
0.33%
$462
Total opportunity cost if the funds are used to buy the condo:
Total closing cost to buy the condo
FV of the closing costs if kept in the bank
Opportunity cost of the FV
Monthly cashflow to buy (mortgage payment)
Monthly vashflow to rent (rent)
Monthly additional opportunity cost
FV of monthly additional opportunity cost
2 years
$ 140,000.00
$ 151,424.00
$ 11,424.00
$
$
$
5 years
$ 140,000.00
$ 170,331.00
$ 30,331.00
10 years
$ 140,000.00
$ 207,234.00
$ 67,234.00
3,938.62
3,000.00
938.62
2 years
5 years
10 years
$ 23,411.89 $ 62,229.55 $ 138,211.61
FV of total opportunity cost for buying (additional monthly payment+ closing cost)
Total opportunity cost for buying
2 years
5 years
10 years
$ 34,835.89 $ 92,560.55 $ 205,445.61
Appendix 4
Ammortizaion table
Principal borrowed
No. of periods (25*12)
Interest rate (4%/12)
Payment (monthly)
Months
$ 480,000.00
300
0.00333
$2,532.56
Beginning principalMonthly PMT
1 $
480,000.00
$2,532.56
2 $
479,065.84
$2,532.56
3 $
478,128.58
$2,532.56
Interest Principal Outstanding principal
$ 1,598.40 $ 934.16 $
479,065.84
$ 1,595.29 $937.27
$478,128.58
$ 1,592.17 $940.39
$477,188.19
24 $
457,708.72
$2,532.56 $ 1,524.17 $1,008.39
$456,700.33
60 $
419,209.22
$2,532.56 $ 1,395.97 $1,136.59
$418,072.63
120 $
343,862.09
$2,532.56 $ 1,145.06 $1,387.50
$342,474.60
(Full calculation shown in excel file)
Appendix 5
Scenario A: if the price of the condo remains unchanged
Year 2
Selling price of the
condo.
Realor fees (5%)
Closing fees
Outstanding principal
Net proceeds
$ 600,000.00
$ 30,000.00
$ 2,000.00
$ 456,700.33
$ 111,299.67
Year 5
$ 600,000.00
$ 30,000.00
$ 2,000.00
$ 418,072.63
$ 149,927.37
Year 10
$ 600,000.00
$ 30,000.00
$ 2,000.00
$ 342,474.60
$ 225,525.40
Scenario B: if the price of the condo goes down by 10%, back to original, then goes up by 10%
Year 2
Selling price of the
condo.
Realor fees (5%)
Closing fees
Outstanding principal
Net proceeds
$ 540,000.00
$ 27,000.00
$ 2,000.00
$ 456,700.33
$ 54,299.67
Year 5
$ 600,000.00
$ 30,000.00
$ 2,000.00
$ 418,072.63
$ 149,927.37
Year 10
$ 660,000.00
$ 33,000.00
$ 2,000.00
$ 342,474.60
$ 282,525.40
Scenario C: if the price of the condo increases by 2% inflation annually
Year 2
Selling price of the
condo. PV*(1.02)^n
Realor fees (5%)
Closing fees
Outstanding principal
Net proceeds
$ 624,240.00
$ 31,212.00
$ 2,000.00
$ 456,700.33
$ 134,327.67
Year 5
$ 662,448.48
$ 33,122.42
$ 2,000.00
$ 418,072.63
$ 209,253.42
Year 10
$ 731,396.65
$ 36,569.83
$ 2,000.00
$ 342,474.60
$ 350,352.22
Scenario D: if the price of the condo increases by 5% inflation annually
Year 2
Selling price of the
condo. PV*(1.05)^n
Realor fees (5%)
Closing fees
Outstanding principal
Net proceeds
$ 661,500.00
$ 33,075.00
$ 2,000.00
$ 456,700.33
$ 169,724.67
Year 5
$ 765,768.94
$ 38,288.45
$ 2,000.00
$ 418,072.63
$ 307,407.86
Year 10
$ 977,336.78
$ 48,866.84
$ 2,000.00
$ 342,474.60
$ 583,995.34