Problem 1 Emma Li graduated fromand found a great job she loves. She currently r

Question

Problem 1 Emma Li graduated fromand found a great job she loves. She currently rents a beautiful one bedroom plus den apartment at Fallingbrook Road for $2,000 per month (parking included, but not utilities) A very similar apartment in her building is on the market for $545,000. In 10 years Emma is planning to move to a house, but at this point in her life she is facing a classic buy versus rent decision If Emma were to buy the apartment, she would face condo fees of $550 monthly (utilities not included) and, in addition to that, property taxes of $300 per month. There are also closing fees and land transfer taxes (provincial and city) associated with the condo purchase. Emma's lawyer will arrange for land transfer taxes to be paid when the deed to the new home is transferred in her name (on closing day). The land transfer taxes for the apartment Emma is considering are $14,750. Emma estimates other closing fees to be around $1,000 Emma would pay down payment due at closing, equal to the 20% of the property value. The rest 80% would be financed with a mortgage. Emma is considering a 25 year mortgage at an interest rate of 6.10% compounded semiannually. This rate is fixed for 10 years.

Explanation / Answer

Present Value (PV) of Cash Flow: (Cash Flow)/((1+i)^N) i=Discount Rate N=Year of Cash Flow b) Amont Needed for closing,if Emma decides to buy Down Payment $109,000 (0.2*545000) Land transfer taxes $14,750 Closing fees $1,000 Total amount of Payment $124,750 Annual interest on this amount $7,610 (124750*0.061` Monthly interest $634 (7610/12) Opportunity cost (Monthly basis) $634 .(c) Monthly Cassh flow: Monthly Mortgage interest rate =(6.1/12)% Amount of Mortgage Loan=(545000-109000) $436,000 Number of months of mortgate 300 (25*12) Monthly mortgage payment $2,835.87 (Using PMT function of excel with Rate=(6.1/12)%,Nper=300, PV=-436000) Condo fees per month $550 Property taxes per month $300 Total Monthly cash flow $3,685.87 Monthly additional cash flow for buying $1,685.87 (3685.87-2000) Additional amount to be paid monthly , if Emma decides tobuy $1,685.87 Present Value of additional cash flow for 120months $151,167.11 (Using PV function of excel with Rate=(6.1/12)%,Nper=120, Pmt=-1685.87) Total Present value of buying instead of renting for 10years $275,917 (124750+151167) (d) LOAN BALANCE AFTER 10 YEARS Future Value of monthly mortgage payments after 10 years(120months) $467,270.66 (Using FV function of excel with Rate=(6.1/12)%,Nper=120, Pmt=-2835.87) Future Value of Loan after 10years(120months) $801,189.15 (Using FV function of excel with Rate=(6.1/12)%,Nper=120, PV=-436000) LOAN BALANCE AFTER 10 YEARS $333,918.49 (801189.15-467270.66) Total amount paid in 10 years $340,304.40 (2835.87*120) Amount of Principal paid $102,081.51 (436000-333918.49) Amount of interest paid $238,222.89 (340304.40-102081.51) (e) Assume Net Selling Price of the apartment after 10year= X Additional amount to be paid monthly , if Emma decides tobuy $1,685.87 Present Value of additional cash flow for 120months $151,167.11 (Using PV function of excel with Rate=(6.1/12)%,Nper=120, Pmt=-1685.87) Total Present value of buying instead of renting for 10years $275,917 (124750+151167) Net cashInflow after 10years (X-333918) Discount at annual rate of 6.1%(compounded monthly) for 120 months Present Value of Cash inflow after 10years=(X-333918)/((1+(6.1/1200))^120) Present Value of Cash inflow=(X-333918)/1.83759 If Price of condo remains same after 10 years X=545000 Present Value of Cash Inflow $ 114,868.93 (545000-333918)/1.83759 PRESENT VALUE OF CASH INFLOW IS LESS THAN PRESENT VALUE OF TOTAL COST RECOMMENDED:RENTING If Price of condo increased by 5% after 10 years X= 572250 (545000*1.05) Present Value of Cash Inflow $ 129,698.14 (572250-333918)/1.83759 PRESENT VALUE OF CASH INFLOW IS LESS THAN PRESENT VALUE OF TOTAL COST RECOMMENDED:RENTING For Break Even: (X-333918)/1.83759=275917 X-333918=275917*1.83759= $507,022.52 X=507022+333918= $840,941 If the Net Value of the apartment is above $840941 She should buy otherwise it will be economical to rent

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