ARE 142 Practice Questions and Solutions _3 _11-10-2009_

ARE 142 Practice Questions and Solutions _3 _11-10-2009_ -...

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Unformatted text preview: ARE 142 Practice Problem # 3 1. You are ready to buy a home and have found two different houses that you like. Both are located in Sacramento. You have saved up $25,000 for a down payment. House A fits nicely in your price range. It is $200,000. It is a little smaller than you would like and a little farther from your job than you would like. Assume your annual homeowner's insurance policy for this house would be $650 and you would want to save 1% of the home's value for maintenance and repairs. House B is your dream first home. It has a great location and floor plan, but it costs $225,000. . Assume your annual homeowner's insurance policy for this house would be $700 and you would want to save 1% of the home's value for maintenance and repairs. Answer the following questions for each of the potential houses. A. What percentage of the purchase price is your down payment? B. Assume that you could get a 30year fixed rate loan for 80% of the home's value at an annual interest rate of 5.5%. What would your monthly payments (principal + interest) be for this loan? C. Assume that you would finance the remaining portion of your purchase with a second 30year fixed rate loan at an annual interest rate 7%. How much would the monthly payments be? D. How much would you pay in property taxes per month? E. What would your monthly insurance costs be? F. What would your monthly maintenance expenditures be? G. What would your total monthly costs be? H. On average, how much would you save in taxes per month during your first year in the home? Assume your marginal tax rate is 25% and you itemize your deductions. Assume your interest payments for the year for both loans are: $9,791.38 for house A and $11,233.05 for house B. What is your aftertax monthly costs (Actual monthly costs savings in taxes) How much more does House B cost per month? House A ($200,000) House B ($225,000) 2. Three years ago, you bought a house for $500,000 with a 30 year fixed loan at an interest rate of 7%. Your monthly payments for principal and interest are: $3,326.51. Interest rates have fallen to 6%, and you are considering refinancing your loan (taking out a new loan and paying off your original loan). You still have $483,634.82 in outstanding principal that you owe on your original loan. a. If you took out a new 30 year fixed rate loan at 6%, what would your monthly payments be for principal and interest if you took 30 years to pay off the new loan? b. What if you took out that new loan, but increased your payments every month so you could pay the loan off in 27 years instead of 30 (it is difficult to find a bank that will give you a 27 year loan)? c. Compared to what you are paying with your current loan, how much do you save in your monthly mortgage payment if you use the plan described in part b? d. A lot of your savings is actually saved interest (ultimately the principal you are paying is same with both options). So, the tax break you were receiving for your interest goes down. Assume you are in a 25% tax bracket, itemize your deductions, and that all the reduction in your mortgage payment comes from reduced interest. How much more will you be paying in tax after you refinance? e. What are your aftertax savings? (To compute your aftertax savings, subtract your answer in d from your answer in c. ) f. After one year, how much will you have saved? g. Refinancing is not free. To refinance, it would cost you $2,500 in closing costs for lender's fees, an appraisal, title fees, and title insurance. If you are planning to stay in your house for at least 3 more years, is it worth refinancing? 3. You have been out of school for a few years and your gross income is now $5,000 per month. You have no other longterm debt. a. What is the maximum PITI you are likely to qualify for based on your ability to pay ratio? b. Would the bank be likely to give you a 30year fixed loan of $250,000 to buy your dream house in California if the current interest rate is 5%? (Assume the bank is willing to give you a loan with a 0% down payment.) c. How much would the bank be willing to lend you? Assume that the house you want costs 250,000, is in California, and that the annual insurance premium would be $600. Retirement Accounts 4. You have decided to contribute $5000 a year into your company's 401K, each year for the next 40 years. (You make 40 contributions. The first one starts at the end of the end of year 1 and the last one at the end of year 40). You expect to earn 8% return on your investment. a. How much will you have accumulated 40 years from now (at n=40)? b. If you want to take annual, equal distributions (withdrawals) from your account for the following 35 years (starting at n=41) and your annual interest rate is now 5%, how much can you withdraw each year? c. Assume the tax brackets are as in Table 1 (on next page) when you withdraw your money and that you take the standard deduction ($5700) and have one exemption of $3,650 but no adjustments. What is your aftertax distribution each year? d. Assume that when you take your distributions, all the money is taxed at 25%. What would your distribution be? 5. This question is similar to the last one, except the focus is on a Roth IRA. For each of the next 40 years, you have decided to save $5000 of your pretax earnings for retirement in a Roth IRA. a. Assume your marginal tax rate is 25%. How much will you have accumulated 40 years from now? b. If you want to take annual, equal distributions (withdrawals) from your account for the following 35 years (starting at n=41) and your annual interest rate is now 5%, how much can you withdraw each year? c. Assume the tax brackets are as in Table 1 below when you withdraw your money and that you take the standard deduction (5700) and have one exemption of $3,650 but no adjustments. What is your aftertax distribution each year? 6. Try to replicate Sethi's figure on page 79. One thing he does is assume that payments are made at the beginning of each year instead of the end. The trickiest (and I think inappropriate) thing he does is with the regular taxable account. If you can replicate this figure and explain how you did it, I'll enter your name in the drawing to win a Starbucks gift card. Since no one took me up on my offer last time, I'll give out 3 cards this time. Table 1 2009 Tax Brackets If Taxable Income is: Over $0 $8,350 $33,950 $82,250 $171,550 $372,950 Your Tax Is: But not over $8,350 $33,950 $82,250 $171,550 $372,950 No limit 10% of amount over $0 15% of amount over $8,350 + $835 25% of amount over $33,950 + $4,675 28% of amount over $82,250 + $16,750 33% of amount over $171,550 + $41,754 35% of amount over $372,950 + $108,216 A. What percentage of the purchase price is your down payment? B. Assume that you could get a 30year fixed rate loan for 80% of the home's value at an annual interest rate of 5.5%. What would your monthly payments (principal + interest) be for this loan? Use: SOLUTIONS: House A ($200,000) 25,000/200,000= .125 Amount of loan: .8*200,000=160,000 PV=160,000 i=.055/12 n=30x12 Solve for PMT Monthly pmt=$908.46 Amount of loan= (200,000160,00025,000) =15,000 PV=15,000 i=.07/12 n=30x12 Solve for PMT Monthly pmt=99.80 .01*200000=166.67 650/12=54.17 .01*200000=166.67 908.46 Loan 1 P&I 99.80 Loan 2 P&I 167.67 Prop Taxes 54.17 Insurance 166.67 Maintenance 1395.77 Total Annual tax savings for interest= .25*9791.38= 2447.85. Monthly savings =2447.85/12 =203.99 Prop tax savings: .25*166.67= 41.67 Total=203.99+41.67 =245.66 1395.77245.66= 1150.11 House B ($225,000) 25,000/225,000=.11 Amount of loan: 180,000 .8*225,000=180,000 PV=180,000 i=.055/12 n=30x12 Solve for PMT Monthly pmt=$1022.02 Amount of loan= (225,000180,00025,000) =20,000 PV=20,000 i=.07/12 n=30x12 Solve for PMT Monthly pmt=133.06 .01*225,000=187.50 700/12=58.33 .01*225,000=187.50 1022.02 133.06 187.5 58.33 187.5 1588.41 Total Monthly int savings: 234.02 Prop tax savings 46.88 Total=280.9 C. Assume that you would finance the remaining portion of your purchase with a second 30year fixed rate loan at an annual interest rate 7%. How much would the monthly payments be? Use: D. How much would you pay in property taxes per month? E. What are your monthly insurance costs? F. What would your monthly maintenance expenditures be? G. What would your total monthly costs be? H. On average, how much would you save in taxes per month during your first year in the home? Assume your marginal tax rate is 25% and you itemize your deductions. Assume your interest payments for the year for both loans are: $9,791.38 for house A and $11,233.05 for house B. What is your aftertax monthly costs (Actual monthly costs savings in taxes) 1588.41280.90= 1307.51 Even though house B costs $25,000 more, it would cost only $157.40 more per month (1307.511150.11) SOLUTIONS: 2. Three years ago, you bought a house for $500,000 with a 30 year fixed loan at an interest rate of 7%. Your monthly payments for principal and interest are: $3,326.51. Interest rates have fallen to 6%, and you are considering refinancing your loan (taking out a new loan and paying off your original loan). You still have $483,634.82 in outstanding principal that you owe on your original loan. a. If you took out a new 30 year fixed rate loan at 6%, what would your monthly payments be for principal and interest if you took 30 years to pay off the new loan? $2,899.64 Use: PV=$483,634.82 i=.06/12 n=30 b. What if you took out that new loan, but increased your payments every month so you could pay the loan off in 27 years instead of 30 (it is difficult to find a bank that will give you a 27 year loan)? $3,017.81 Use: PV=$483,634.82 i=.06/12 n=27 c. Compared to what you are paying with your current loan, how much do you save in your monthly mortgage payment if you use the plan described in part b? 3326.513017.81=308.70 d. A lot of your savings is actually saved interest (ultimately the principal you are paying is same with both options). So, the tax break you were receiving for your interest goes down. Assume you are in a 25% tax bracket, itemize your deductions, and that all the reduction in your mortgage payment comes from reduced interest. How much more will you be paying in tax after you refinance? 0.25*308.70=77.17 e. What are your aftertax savings? (To compute your aftertax savings, subtract your answer in d from your answer in c. ) 308.7077.17=231.52 f. After one year, how much will you have saved? 231.52*12 =$2,778.30 g. Refinancing is not free. To refinance, it would cost you $2,500 in closing costs for lender's fees, an appraisal, title fees, and title insurance. If you are planning to stay in your house for at least 3 more years, is it worth refinancing? Yes, you make up your costs within the first year. SOLUTIONS: 3. You have been out of school for a few years and your gross income is now $5,000 per month. You have no other longterm debt. a. What is the maximum PITI you are likely to qualify for based on your ability to pay ratio? PITI/5000=.28 So, PITI=1400. b. Would the bank be likely to give you a 30year fixed loan of $250,000 to buy your dream house in California if the current interest rate is 5%? (Assume the bank is willing to give you a loan with a 0% down payment.) The monthly payment for principal and interest on a 30 year 5% loan of 250,000 is 1342.05. In California, you have to pay 1% of sales price in property tax every year, which is $2500 per year, or 208.33 per month. That brings your PITI up to $1550.39 and you haven't yet added on your insurance premiums. This exceeds your answer to part a, so the bank would not likely loan you the money. c. How much would the bank be willing to lend you? Assume that the house you want costs 250,000, is in California, and that the annual insurance premium would be $600. In part 3a, we found that the bank would allow a PITI of $1400. Property taxes would be 208.33/mo and insurance $50/mo. That leaves ($1400208.3350)=$1142 left to spend on principal and interest. Solve for PV when you know PMT. Use PMT=1141.67, i=.05/12, n=30. The bank would lend you $212,672.13. You would need a down payment of (250,000212,672)=37,328 (plus additional fees to cover the closing costs). Retirement Accounts 4. You have decided to contribute $5000 a year into your company's 401K, each year for the next 40 years. (You make 40 contributions. The first one starts at the end of the end of year 1 and the last one at the end of year 40). You expect to earn 8% return on your investment. a. How much will you have accumulated 40 years from now (at n=40)? 1,295,283. Use: PMT=5000, i=.08, n=40 b. If you want to take annual, equal distributions (withdrawals) from your account for the following 35 years (starting at n=41) and your annual interest rate is now 5%, how much can you withdraw each year? $79,105.12 Use: PV=1,295,283 i=.05, n=35 SOLUTIONS: c. Assume the tax brackets are as in Table 1 (on next page) when you withdraw your money and that you take the standard deduction ($5700) and have one exemption of $3,650 but no adjustments. What is your aftertax distribution each year? Taxable income=79105.1257003650=69755.12 Tax= 4675 + .25x(69,755.1233,950)=13626.28 After tax distribution=79,105.12 13,626.28=65,479. d. Assume that when you take your distributions, all the money is taxed at 25%. What would your distribution be? $59,328 = 79105.12 .25*(79,105.12) 5. This question is similar to the last one, except the focus is on a Roth IRA. For each of the next 40 years, you have decided to save $5000 of your pretax earnings for retirement in a Roth IRA. a. Assume your marginal tax rate is 25%. How much will you have accumulated 40 years from now? $971,462 (Us the same formula in 4a, PMT=.75*5000 (you have to pay 25% in tax now) b. If you want to take annual, equal distributions (withdrawals) from your account for the following 35 years (starting at n=41) and your annual interest rate is now 5%, how much can you withdraw each year? $59,328 (Use formula in 4b, but now PV=971,462. c. Assume the tax brackets are as in Table 1 below when you withdraw your money and that you take the standard deduction (5700) and have one exemption of $3,650 but no adjustments. What is your after tax distribution each year? $59,328 (you don't pay tax on a distribution from a roth) ...
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