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Time Value of Money: Buy v/s Rent Decision REBECCA YOUNG CASE

Situation — Rebecca Young, a fresh MBA graduate is faced with a

dilemma of whether to buy or continue to stay in a rented two bedroom apartment after moving to Toronto. — She wants to take a decision based on both qualitative and quantitative factors such as comparing both the rent and buy decision based on time value of money (concepts which she learnt in MBA ).

Financial Details Scenario 1: Buy Price = $600,000 Down payment = 20% of $600,000 $ 120,000 Remaining Payment to be made = $480,000

— Other One time payments : Local deed transfer = 1.5% Provincial deed transfer = 1.5% Closing fees = $2000 Total one time payment/lumpsum payment= down payment + one time charges +Closing fees =20+1.5+1.5 = 23% of 600,000 = 138,000+2000= $140,000 We will look at the calculations now.

Calculation Now to raise the remaining amount ie $480000, Rebecca plans to take a loan as per below details: PV = $480,000 Repayment is to be done in 25 years with EMIs k= 4% pa n=25 years *12 = 300 First we will need to calculate effective monthly rate to find out the EMIs.

K=4%pa Effective monthly rate = (1+k/m)^m – 1 = (1+0.04/12)^1/12 -1 = 0.0033 =0.33 % Now PV = 480000 N=300 , k= 0.0033 Using Formula PV= A[(1+k)^n -1]/k(1+k)^n A= 2524 Lets prepare Loan Amortization schedule. •

Microsoft Office Excel Worksheet

FV of loan = 2524*300 =$757,200 Lumpsum( $ 140,000) paid by Rebecca is currently invested in earning 0.33% monthly rate interested for a period of 25 yrs or 300 months FV= PV(1+k)^n =140,000 (1+0.0033)^300 = 376,159.2 Therefore total FV in case of buy decision = 1,133,359.2

Scenario 1 : Rent If Rebecca decides to rent the condo Monthly rent = $3000 FV of condo if assuming she had invested the amount for 25 years at 0.33% monthly rate FV= A [(1+k)^n – 1]/k = 3000[(1+0.0033)^300 – 1] /0.0033 = $1,533,501

Conclusion — Therefore from previous slides , its clear that

Rebecca should buy the condo as it is cheaper.

Purchasing the condominium — Monthly Rent = $1055 — Property Tax = $300 — Repairs and maintenance = $600 per year

=600/12 = $50 per month Therefore total monthly effective rent = 1055+300+50 =$1405 P

Possible Scenarios Case 1 : condo price remains unchanged Selling Price = 600000 Realtor Fees = 5% of 600,000+2000 =320,000

Case 2 : condo price drops 10% over the next 2 years, then increases back to its purchase price by the end of 5 years, then increases by a total of 10% from the original purchase price by the end of 10 years Lets take a look at the board !

Case 3 : condo price increases annually by the annual rate of inflation of 2% pa over the next 10 years Lets take a look at the board !

Case 4 : condo price increases annually by an annual rate of 5%pa over the next 10 years Lets take a look at the board !