Exercise 4 - Renting vs. buying a house: You are faced with the decision to purc
ID: 2519077 • Letter: E
Question
Exercise 4 - Renting vs. buying a house: You are faced with the decision to purchase a new home that will serve you for the next 30 years, or rent a similar home. The home you are interested in costs $1 million. Annual real estate taxes are S9,600. Alternatively, monthly rental payments are S3,500 with no additional fees. In addition, you have $250,000 in cash which you saved. This implies you will need a $750,000 mortgage. The mortgage will be paid monthly, at the end of every month over a period of 30 years. Interest is compounded monthly. Annual interest rate is 3% annually Below is a table showing various factors that may have a financial impact: Rental option Will be invested in a fund generating 8% expected returns annually. The interest is compounded annual Description S250,000 savings Purchase option Would be used for down | payment on the house. S9,600 annual real estate taxes N/A. Included in the rent Paid in monthly installments at the end ofe You are getting S750,000, which you will be You will need to make monthly payments, at the end of every month, for 30 years. Interest rate is 3% (annually). You will need to calculate the monthly payment. month. S750,000 mortgage N/A. paying immediately Present value multipliers (in case you are not using financial calculator or excel) n-360, i-0.25% n-360, i-0.5% n-12, i-0.25% n-12, i-0.5% 237.189 166.792 11.807 11.619 S3,500 rent expense House value appreciation Broker fee You need to pay S3,500 at the N/A. end of every month for 30 years N/A 3% annually. Compounding is on an annual basis 4% of the fair value of the house at the time of sale (after 30 N/A earsExplanation / Answer
1. Number of Months in 30 Years = 12 months x 30 years = 360 months
Monthly Compound Interest Rate = 3% / 12 = 0.25%
Monthly Mortgage Payment = Mortage Amount / Present Value Multiplier (where n = 360, i = 0.25%)
= $750,000 / 237.189 = $3,162.0353
2. Monthly Payment on Real Estate Taxes = $9,600 / 12 Months = $800
3. Total Monthly Payment = $3,162.0353 + $800 = $3,962.0353
4. Present Value of Monthly Savings under the Rental Option = $3,962.0353 - $3,500 = $462.0353
Total Future Value of Monthly Savings under the Rental Option
= Present Value of Monthly Savings x Future Value Multiplier (where n = 360, i = 4/12 or 0.33%)
= $462.0353 x 694.049 = $320,675
5. Future Value of Savings = Present Value of Savings x (1 + Interest Rate)^Number of Years
= $250,000 x (1.08)^30 = $2,515,664
6. Future Value of Total Savings under the Rental Option = $2,515,664 + $320,675 = $2,836,339
7. Future Value of House = $1,000,000 x 1.03^30 = $2,427,262
8. Net Consideration on Sale of the House in 30 Years after Commission = $2,427,262 x 0.96 = $2,330,172
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