In May 2013 , Rebecca Young completed her MBA and moved to Toronto for a new job

Question

In May 2013 , Rebecca Young completed her MBA and moved to Toronto for a new job in investment banking. There, she rent ed a spacious , two -bedroom condominium for $3,000 per month, which included parking but not utilities or cable television. In July 2014, the virtuall y identical unit next door became available for sale with an asking price of $620,000, and Young believed she could purch ase 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 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 g ood.” She realized that both sides presented good arguments, but she wanted to analyze th e 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 r esponsible 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. (For For the exclusive use of A. Figares, 2017. This document is authorized for use only by Alex Figares in 2017. Page 2 9B14N024 simplicity, Young plann ed 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 4 per cent “quoted” annual rate 1 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 effecti ve monthly rate, assumed to be equivalent to the mortgage rate. She would then be able to determine additional mont hly 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 fu ture 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 af ter some due diligence regarding future real -estate prices in the Toronto condo market: (a) The co ndo price remains unchanged; (b) The condo price drops 10 per cent over the next tw o 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 ann ual 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 You ng 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 qua ntitative factors alone ; it would need to be based on any qualitative consideration s 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

Questions:

1. Determine required monthly mortgage payments.

2. Determine opportunity cost (on a monthly basis) of using the lump sum to purchase the condominium rather than leaving the funds invested at the present rate of return.

3. Determine additional required monthly payments required to buy the condominium compared to renting, including the opportunity cost.

4. What decision should Rebecca make? Include and identify any qualitative factors in your analysis.

a. Determine outstanding principal balance on mortgage loan at the end of year 5

b. Determine the net future gain or loss (after 5 years) if the condominium price remains unchanged

c. Determine the net future gain or loss if the condominium price drops 7% over the next two years, then increases back to the purchase price by the end of five years, then increases by a total of 7% of the original purchase price at the end of ten years.

d. Determine the net future gain or loss if the condominium price increases annually by the annual rate of inflation (assume 5% per year) over the next ten years.

e. Determine the net future gain or loss if the condominium price increases annually by an annual rate of 8% per year over the next ten years.

Explanation / Answer

1) Total Purchase price = $600,000. Down payment Young would make = 20% of the price = $120,000. Thus, total loan amount = Purchase price - Down payment = $600K - $120K = $480,000.

Annual rate on the mortgage = 4%, to determine monthly payments, we need effective monthly interest rate on the mortgage. Effective Monhtly rate = (1+Annual rate)^(1/# of months) - 1 = (1+4%)^1/12 - 1= 0.327%

Ammortization period = 25 years = 300 months (25*12)

Amount to be paid as installement is given by the = p*r*(1+r)^n/((1+r)^n-1)

Thus, Monthly installments = $480,000*0.327%*(1+0.327%)^300/((1+0.327%)^300-1) = $2514.70

2. Opportunity cost = The lost benifit one could have recieved but lost them by going for an alternate option (Young is taking away her investments to fund her down payment, she could have had returns from the investment, if she had not opted for the Buy option)

Total Down payment = Young's present investment = $120,000 (from 1 above)

Present rate of return on investment = Effective monthly interest rate on the mortgage = 0.327% (from 1 above)

Total amortization period = 25 years = 300 months.

Young's investments in the next 30 months could've grown by 0.327% per month. Total Value could've been = 120,000*(1+0.327%)^300 = $319,900.36,

Lost opportunity or Opportunity cost = $319,900.36-$120,000 = $199,900.36

Average Monthly Opportunity cost = $666.33

3. Expenses if rented are rent to be paid monthly = $3000

Expenses if Young brought the condo = Monthly mortgage + Monthly condo fee + Property taxes + repair costs + Opportunity cost

= $2514.70 (from 1) + $1055 + $300 + $600/12 + $666.33 (from 2) = $4586

Additional cost per month = $4586 - $3000 = $1586

4a) Outstanding principal balance at the end of 5 years = (5*12 = 60 months), We will try to solve this by each month (Beginning balance, Interest per month, principal repaid per month, end of of month balance, an excel for 60 months would give end of 5 year outstanding)

Solving for Balances;

Beginning Balance = $480K,

Monthly Installment = $2514.70 (From 1),

Interest = Beginning Balance*Effective monthly rate of Interest = $480K*0.327% = $1571.40,

Principal = Monthly Repayment - Interest = $2514.70 - $1571.40 = $943.31

Ending Balance = Beginning Balance - Principal = $480K - $9431 = $479.056.69.

Calculation for first 5 months and 60th month below

Thus, outstanding at end of 5 years = $417,572.86

4b) House value remains unchanged after 5 years, thus Condo value = $600,000

Outstanding Mortgage = $417,572.86

Future value of Money paid at the start date (FV after 5 years) = FV(Down payment + Loan deed transfer tax + Provincial dead transfer tax + other fee), future value at an effective monthly interest rate of 0.327%

FV ($120K + 1.5% $600K + 1.5% $600K + $2K) = FV($140K) = $140K*(1+0.327%)^60 = $170,331.41

Thus total Cost = $417,572.86 + $170,331.41 = $587,904.27

Gain/ Loss = $600K - $587,904.27 = $12,095.73

Years Beginning of year balance Installments interest Prinicpal End of Year Balance 1 $480,000.00 $2,514.70 $1,571.40 $943.31 $479,056.69 2 $479,056.69 $2,514.70 $1,568.31 $946.40 $478,110.30 3 $478,110.30 $2,514.70 $1,565.21 $949.49 $477,160.80 4 $477,160.80 $2,514.70 $1,562.10 $952.60 $476,208.20 5 $476,208.20 $2,514.70 $1,558.98 $955.72 $475,252.48 60 $418,716.80 $2,514.70 $1,370.77 $1,143.93 $417,572.86

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