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1 Case Study Students Name Institutional Affiliation Course Title Professor’s Name Date
2 Case Study To analyze and advise Rebecca Young on Toronto apartment rental or purchase; Calculation of Monthly Mortgage Payment: Purchase Price = $700,000 Mortgage Rate = 7% APR Mortgage Term = 10 years (converted to 20 semi-annual periods) M=P (1+r)n−1r(1+r)n Where: M = Monthly Mortgage Payment P = Principal Loan Amount (80% of the purchase price) r = Monthly Interest Rate (Annual Rate divided by 12) n = Total Number of Payments (20 for a 10-year term) Let's calculate the monthly mortgage payment: Principal Loan Amount (P) = 80% of the purchase price = $700,000 * 0.80 = $560,000. Monthly Interest Rate (r): Annual Rate = 7% Semi-annual compounding, so we need to calculate the semi-annual rate: 7% / 2 = 3.5% per semi-annual period. Monthly rate = (1 + 0.035)^(1/6) - 1 = 0.02798 (approximately). Total Number of Payments (n) = 10 years * 2 (for semi-annual payments) = 20 payments.
3 Now, plug these values into the formula: M = $560,000 \cdot \frac{0.02798(1 + 0.02798)^{20}}{(1 + 0.02798)^{20} - 1} M ≈ $5,005.98 per month So, Rebecca's monthly mortgage payment would be approximately $5,005.98. Calculation of Principal Outstanding on Mortgage After 2 Years, 5 Years, and 10 Years: We can use an amortization schedule to determine mortgage principle after 2, 5, and 10 years. Mortgage payments reduce principle. Using the formula to calculate the principal outstanding at any point in time: Pt=P(1−(1+r)−n)/r Where: P_t = Principal Outstanding after t periods (in our case, 2, 5, or 10 years) P = Initial Principal Loan Amount ($560,000) r = Monthly Interest Rate (0.02798) n = Total Number of Payments (20) Now, let's calculate the principal outstanding for each time period: After 2 years: P_2 = $560,000 * (1 - (1 + 0.02798)^(-2*20))/0.02798 P_2 ≈ $525,168.35 After 5 years: P_5 = $560,000 * (1 - (1 + 0.02798)^(-5*20))/0.02798
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4 P_5 ≈ $479,930.63 After 10 years: P_10 = $560,000 * (1 - (1 + 0.02798)^(-10*20))/0.02798 P_10 ≈ $381,367.36 So, the principal outstanding on the mortgage after 2 years is approximately $525,168.35, after 5 years is approximately $479,930.63, and after 10 years is approximately $381,367.36. Calculation of Opportunity Costs: Consider the alternative investment opportunity to assess the opportunity cost of spending the required cash for closure (down payment and closing charges) instead of leaving the money invested at the monthly rate. Rebecca's opportunity cost is the return she could have made investing. Rebecca said her investments earned the same effective monthly rate of return as her mortgage. Since the mortgage monthly rate is 0.02798, we'll suppose her alternative investment earns the same. Let's compute monthly opportunity cost. Using the the formula for compound interest: A=P(1+r)n Where: A = Future Value P = Principal Amount (initial investment) r = Monthly Interest Rate (0.02798)
5 n = Number of Months For this estimate, Rebecca's down payment and closing fees are unknown, but let's assume $200,000. She would have invested this money if not for the condo. Now, let's calculate the opportunity cost for 2, 5, and 10 years: After 2 years: A_2 = $200,000 * (1 + 0.02798)^24 A_2 ≈ $232,081.14 After 5 years: A_5 = $200,000 * (1 + 0.02798)^60 A_5 ≈ $268,884.23 After 10 years: A_10 = $200,000 * (1 + 0.02798)^120 A_10 ≈ $343,469.47 Now that we have the future values of her investments after 2, 5, and 10 years, we can calculate the opportunity cost by subtracting the initial investment from these values: Opportunity Cost after 2 years: $232,081.14 - $200,000 = $32,081.14 Opportunity Cost after 5 years: $268,884.23 - $200,000 = $68,884.23 Opportunity Cost after 10 years: $343,469.47 - $200,000 = $143,469.47 Scenario Analysis:
6 Rebecca wants to know what would happen if she sold the condo in 2, 5, or 10 years under four scenarios: (a) Condo prices remain steady. (b) The condo price declines 10% over the next two years, returns to its purchase price after five years, and rises 10% more by 10 years. (c) Over 10 years, condo prices rise 2% annually due to inflation. (d) The condo price rises 5% annually for 10 years. Let's analyze each scenario: Scenario (a): Condo Price Remains Unchanged: After 2 years: Condo Price: $700,000 Principal Outstanding: $525,168.35 Realtor Fees (5%): $35,000 Other Closing Fees: $2,000 Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees Net Gain/Loss = $700,000 - $525,168.35 - $35,000 - $2,000 = $137,831.65 After 5 years: Net Gain/Loss = $700,000 - $479,930.63 - $35,000 - $2,000 = $183,069.37 After 10 years: Net Gain/Loss = $700,000 - $381,367.36 - $35,000 - $2,000 = $281,632.64 Scenario (b): Condo Price Drops 10% in 2 Years, Recovers, and Grows 10%: After 2 years: Condo Price: $700,000 - 10% = $630,000
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7 Principal Outstanding: $525,168.35 Realtor Fees (5%): $31,500 Other Closing Fees: $2,000 Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees Net Gain/Loss = $630,000 - $525,168.35 - $31,500 - $2,000 = $71,331.65 After 5 years: Condo Price: $700,000 Net Gain/Loss = $700,000 - $479,930.63 - $35,000 - $2,000 = $183,069.37 After 10 years: Condo Price: $700,000 + 10% = $770,000 Net Gain/Loss = $770,000 - $381,367.36 - $38,500 - $2,000 = $348,132.64 Scenario (c): Condo Price Increases by 2% Annually: In this scenario, the condo price increases by 2% per year. We'll calculate the future condo price for each time period: After 2 years: $700,000 * (1 + 0.02)^2 = $744,800 After 5 years: $700,000 * (1 + 0.02)^5 = $735,696 After 10 years: $700,000 * (1 + 0.02)^10 = $718,161.97 After 2 years: Condo Price: $744,800 Principal Outstanding: $525,168.35 Realtor Fees (5%): $37,240
8 Other Closing Fees: $2,000 Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees Net Gain/Loss = $744,800 - $525,168.35 - $37,240 - $2,000 = $180,391.65 After 5 years: Net Gain/Loss = $735,696 - $479,930.63 - $36,784.80 - $2,000 = $216,880.57 After 10 years: Net Gain/Loss = $718,161.97 - $381,367.36 - $35,908.10 - $2,000 = $298,886.51 Scenario (d): Condo Price Increases by 5% Annually: In this scenario, the condo price increases by 5% per year. We'll calculate the future condo price for each time period: After 2 years: $700,000 * (1 + 0.05)^2 = $770,000 After 5 years: $700,000 * (1 + 0.05)^5 = $862,737.50 After 10 years: $700,000 * (1 + 0.05)^10 = $1,221,386.25 After 2 years: Condo Price: $770,000 Principal Outstanding: $525,168.35 Realtor Fees (5%): $38,500 Other Closing Fees: $2,000 Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees Net Gain/Loss = $770,000 - $525,168.35 - $38,500 - $2,000 = $204,331.65
9 After 5 years: Net Gain/Loss = $862,737.50 - $479,930.63 - $43,136.88 - $2,000 = $337,669.99 After 10 years: Net Gain/Loss = $1,221,386.25 - $381,367.36 - $61,069.31 - $2,000 = $776,949.58 Let's examine Rebecca's decision's quality. She wants to relocate to a house or penthouse in 5–10 years. This means her apartment purchase should match her long-term aims and lifestyle. Qualitative Considerations: Long-Term Goals: Rebecca wants to move to a house or penthouse condo in five to ten years, so buying an apartment may not be the best option. Condominium ownership may include restrictions and prices that could prevent her from moving. Flexible: Renting lets Rebecca change her living arrangement as her work and life change. For those with changing home demands, renting may be best. Real estate market uncertainty: The analysis scenarios show condo ownership benefits and losses. However, the real estate market is uncertain, and many factors can affect prices. Rebecca must examine her risk tolerance and market changes' influence on her finances. Lifestyle:
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10 Rebecca should consider whether condo living fits her lifestyle. Condo upkeep and association costs may effect her lifestyle and finances. Our recommendation for Rebecca Young is based on financial analysis and qualitative factors. Rebecca might rent a Toronto condo instead of buying. Her monthly mortgage payments, property taxes, condo fees, and prospective maintenance charges could strain her financially, especially considering her long-term aim of relocating to a house or penthouse condo within five to 10 years. Renting allows her to adjust her living environment as her profession and requirements change. Renting also decreases her real estate market risk due to market uncertainties and price swings.