Chapter 28

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1. Award: 10.00 points Problems? Adjust credit for all students. George More is a participant in a defined contribution pension plan that offers a fixed-income fund and a common stock fund as investment choices. He is 40 years old and has an accumulation of $100,000 in each of the funds. He currently contributes $1,500 per year to each. He plans to retire at age 65, and his life expectancy is age 80. Required: a. Assuming a 3% per year real earnings rate for the fixed-income fund and 6% per year for common stocks, what will be George’s expected accumulation in each account at age 65? b. What will be the expected real retirement annuity from each account, assuming these same real earnings rates? c. If George wanted a retirement annuity of $30,000 per year from the fixed-income fund, by how much would he have to increase his annual contributions? Required A Required B Complete this question by entering your answers in the tabs below. Assuming a 3% per year real earnings rate for the fixed-income fund and 6% per year for common stocks, what will be George’s expected accumulation in each account at age 65? Note: Do not round time value factors and round your final answers to the nearest dollar amount. Required A Required B Required C $ $ Fixed income fund 264,067 Common stock fund 511,484 Explanation: a. George More’s expected accumulation is $775,551 ($264,067 + $511,484) at age 65: n i PV PMT FV Fixed income 25 3% $ 100,000 $1,500 FV = $264,067 Common stocks 25 6% $ 100,000 $1,500 FV = $511,484 b. Expected retirement annuity: n i PV FV FV Fixed income 15 3% $264,067 0 PMT = $22,120 Common stocks 15 6% $511,484 0 PMT = $52,664 c. To get a fixed-income annuity of $30,000 per year, his accumulation at age 65 would have to be: n i PMT FV PV Fixed income 15 3% $30,000 0 PV = $358,138 His annual contribution would have to be: n i PV FV PMT Fixed income 25 3% $100,000 −$358,138 PMT = $4,080 This is $2,580 more per year than the $1,500 current contribution. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 28: Investment Policy and the Framework of the CFA Institute > Chapter 28 Problems - Static References
1. Award: 10.00 points Problems? Adjust credit for all students. George More is a participant in a defined contribution pension plan that offers a fixed-income fund and a common stock fund as investment choices. He is 40 years old and has an accumulation of $100,000 in each of the funds. He currently contributes $1,500 per year to each. He plans to retire at age 65, and his life expectancy is age 80. Required: a. Assuming a 3% per year real earnings rate for the fixed-income fund and 6% per year for common stocks, what will be George’s expected accumulation in each account at age 65? b. What will be the expected real retirement annuity from each account, assuming these same real earnings rates? c. If George wanted a retirement annuity of $30,000 per year from the fixed-income fund, by how much would he have to increase his annual contributions? Required A Required C Complete this question by entering your answers in the tabs below. What will be the expected real retirement annuity from each account, assuming these same real earnings rates? Note: Do not round time value factors and round your final answers to the nearest dollar amount. Required A Required B Required C $ $ Fixed income fund 22,120 Common stock fund 52,664 Explanation: a. George More’s expected accumulation is $775,551 ($264,067 + $511,484) at age 65: n i PV PMT FV Fixed income 25 3% $ 100,000 $1,500 FV = $264,067 Common stocks 25 6% $ 100,000 $1,500 FV = $511,484 b. Expected retirement annuity: n i PV FV FV Fixed income 15 3% $264,067 0 PMT = $22,120 Common stocks 15 6% $511,484 0 PMT = $52,664 c. To get a fixed-income annuity of $30,000 per year, his accumulation at age 65 would have to be: n i PMT FV PV Fixed income 15 3% $30,000 0 PV = $358,138 His annual contribution would have to be: n i PV FV PMT Fixed income 25 3% $100,000 −$358,138 PMT = $4,080 This is $2,580 more per year than the $1,500 current contribution. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 28: Investment Policy and the Framework of the CFA Institute > Chapter 28 Problems - Static References
1. Award: 10.00 points Problems? Adjust credit for all students. George More is a participant in a defined contribution pension plan that offers a fixed-income fund and a common stock fund as investment choices. He is 40 years old and has an accumulation of $100,000 in each of the funds. He currently contributes $1,500 per year to each. He plans to retire at age 65, and his life expectancy is age 80. Required: a. Assuming a 3% per year real earnings rate for the fixed-income fund and 6% per year for common stocks, what will be George’s expected accumulation in each account at age 65? b. What will be the expected real retirement annuity from each account, assuming these same real earnings rates? c. If George wanted a retirement annuity of $30,000 per year from the fixed-income fund, by how much would he have to increase his annual contributions? Required B Required C Complete this question by entering your answers in the tabs below. If George wanted a retirement annuity of $30,000 per year from the fixed-income fund, by how much would he have to increase his annual contributions? Note: Do not round time value factors and round your final answer to the nearest dollar amount. Required A Required B Required C $ Increase his annual contributions by 2,580 Explanation: a. George More’s expected accumulation is $775,551 ($264,067 + $511,484) at age 65: n i PV PMT FV Fixed income 25 3% $ 100,000 $1,500 FV = $264,067 Common stocks 25 6% $ 100,000 $1,500 FV = $511,484 b. Expected retirement annuity: n i PV FV FV Fixed income 15 3% $264,067 0 PMT = $22,120 Common stocks 15 6% $511,484 0 PMT = $52,664 c. To get a fixed-income annuity of $30,000 per year, his accumulation at age 65 would have to be: n i PMT FV PV Fixed income 15 3% $30,000 0 PV = $358,138 His annual contribution would have to be: n i PV FV PMT Fixed income 25 3% $100,000 −$358,138 PMT = $4,080 This is $2,580 more per year than the $1,500 current contribution. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 28: Investment Policy and the Framework of the CFA Institute > Chapter 28 Problems - Static References
2. Award: 10.00 points Problems? Adjust credit for all students. The difference between a Roth IRA and a traditional IRA is that in a Roth IRA taxes are paid on the income that is contributed, but the withdrawals at retirement are tax-free. In a traditional IRA, however, the contributions reduce your taxable income, but the withdrawals at retirement are taxable. Assume you plan to devote $5,000 to retirement savings in each year. You will retire in 30 years and expect to live for an additional 20 years after retirement. Required: a. Assume the before-tax interest rate is 5%. What will be your after-tax 20-year retirement consumption stream if you choose to save in a traditional IRA? Assume your tax rate is fixed at 30%. b. What will be your 20-year retirement consumption stream if you choose to save in a Roth IRA? c. Which provides better expected results if you expect your tax rate on wage as well as all investment income to decrease from 30% today to 25% at retirement? Required A Required B Complete this question by entering your answers in the tabs below. Assume the before-tax interest rate is 5%. What will be your after-tax 20-year retirement consumption stream if you choose to save in a traditional IRA? Assume your tax rate is fixed at 30%. Note: Round your answers to 2 decimal place. Required A Required B Required C $ 20-year consumption stream (assuming monthly payouts) 1,534.63 Explanation: a. Using the financial calculator, first calculate future value, before taxes: n = 30 P ÷ y = 1 i ÷ y = 5 PV = 0 PMT = −$5,000 (Cash outflow into the retirement account) CPT FV = $332,194,24 Therefore, after-tax wealth = $332,194.24 × (1 − 0.3) = $232,535.97 Calculate the 20-year consumption stream of $1,534.63 (assuming monthly payouts): n = 20 × 12 = 240 P ÷ y = 12 i ÷ y = 5 PV = −$232,535.97 (purchase retirement stream) FV = 0 CPT PMT = $1,534.63 b. Using the financial calculator, first calculate future value, before taxes: n = 30 P ÷ y = 1 i ÷ y = 5 PV = 0 PMT = −$5,000 × (1 − 0.3) = −3,500 (after-tax contributions) CPT FV = −232,535.97 Therefore, after-tax wealth = $232,535.97 (since taxes were already taken out) Calculate the 20-year consumption stream (assuming monthly payouts): n = 20 × 12 = 240 P ÷ y = 12 i ÷ y = 5 PV = –$232,535.97 (purchase retirement stream) FV = 0 CPT PMT = $1,534.63 With unchanging tax rates, the Traditional IRA and the Roth IRA are equivalent. c. If you tax rate decreases to 25% upon retirement the Roth IRA still provides a monthly consumption stream of $1,534.63. However, the Traditional IRA now provides (using the financial calculator): n = 30 P ÷ y = 1 i ÷ y = 5 PV = 0 PMT = −$5,000 (cash outflow into the retirement account) CPT FV = $332,194.24 Therefore, after-tax wealth = $332,194.24 × (1 − 0.25) = $249,145.68
Calculate the 20-year consumption stream (assuming monthly payouts): n = 20 × 12 = 240 P ÷ y = 12 i ÷ y = 5 PV = −$249,145.68 (purchase retirement stream) FV = 0 CPT PMT = $1,644.25 If taxes are expected to fall, the Traditional IRA provides a larger consumption stream. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 28: Investment Policy and the Framework of the CFA Institute > Chapter 28 Problems - Static References
2. Award: 10.00 points Problems? Adjust credit for all students. The difference between a Roth IRA and a traditional IRA is that in a Roth IRA taxes are paid on the income that is contributed, but the withdrawals at retirement are tax-free. In a traditional IRA, however, the contributions reduce your taxable income, but the withdrawals at retirement are taxable. Assume you plan to devote $5,000 to retirement savings in each year. You will retire in 30 years and expect to live for an additional 20 years after retirement. Required: a. Assume the before-tax interest rate is 5%. What will be your after-tax 20-year retirement consumption stream if you choose to save in a traditional IRA? Assume your tax rate is fixed at 30%. b. What will be your 20-year retirement consumption stream if you choose to save in a Roth IRA? c. Which provides better expected results if you expect your tax rate on wage as well as all investment income to decrease from 30% today to 25% at retirement? Required A Required C Complete this question by entering your answers in the tabs below. What will be your 20-year retirement consumption stream if you choose to save in a Roth IRA? Note: Round your answers to 2 decimal place. Required A Required B Required C $ 20-year consumption stream (assuming monthly payouts) 1,534.63 Explanation: a. Using the financial calculator, first calculate future value, before taxes: n = 30 P ÷ y = 1 i ÷ y = 5 PV = 0 PMT = −$5,000 (Cash outflow into the retirement account) CPT FV = $332,194,24 Therefore, after-tax wealth = $332,194.24 × (1 − 0.3) = $232,535.97 Calculate the 20-year consumption stream of $1,534.63 (assuming monthly payouts): n = 20 × 12 = 240 P ÷ y = 12 i ÷ y = 5 PV = −$232,535.97 (purchase retirement stream) FV = 0 CPT PMT = $1,534.63 b. Using the financial calculator, first calculate future value, before taxes: n = 30 P ÷ y = 1 i ÷ y = 5 PV = 0 PMT = −$5,000 × (1 − 0.3) = −3,500 (after-tax contributions) CPT FV = −232,535.97 Therefore, after-tax wealth = $232,535.97 (since taxes were already taken out) Calculate the 20-year consumption stream (assuming monthly payouts): n = 20 × 12 = 240 P ÷ y = 12 i ÷ y = 5 PV = –$232,535.97 (purchase retirement stream) FV = 0 CPT PMT = $1,534.63 With unchanging tax rates, the Traditional IRA and the Roth IRA are equivalent. c. If you tax rate decreases to 25% upon retirement the Roth IRA still provides a monthly consumption stream of $1,534.63. However, the Traditional IRA now provides (using the financial calculator): n = 30 P ÷ y = 1 i ÷ y = 5 PV = 0 PMT = −$5,000 (cash outflow into the retirement account) CPT FV = $332,194.24 Therefore, after-tax wealth = $332,194.24 × (1 − 0.25) = $249,145.68
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