Chapter 28
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Johns Hopkins University *
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180.367
Subject
Finance
Date
Jan 9, 2024
Type
Pages
30
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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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- ou annually invest $1,500 in an individual retirement account (IRA) starting at the age of 30 and make the contributions for 15 years. Your twin sister does the same starting at age 40 and makes the contributions for 20 years. Both of you earn 7 percent annually on your investment. What amounts will you and your sister have at age 60? Use Appendix A and Appendix C to answer the question. Round your answers to the nearest dollar.Amount on your account: $ Amount on your sister's account: $ Who has the larger amount at age 60?-Select-You haveYour sister hasItem 3 the larger amount.arrow_forwardQ)A civil engineer planning for her retirement places 11% of her salary each year into a high-technology stock fund. If her salary this year (end of year 1) is $200,000 and she expects her salary to increase by 4% each year, what will be th future worth of her retirement fund after 14 years provided it earns 8% per year? Explain it correctly typed or handwriting. Not solve in excel works.arrow_forwardGail Trevino expects to receive a $590,000 cash benefit when she retires eight years from today. Ms. Trevino’s employer has offered an early retirement incentive by agreeing to pay her $363,000 today if she agrees to retire immediately. Ms. Trevino desires to earn a rate of return of 8 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) Required a. Calculate the present value of the $590,000 future cash benefit. Assuming that the retirement benefit is the only consideration in making the retirement decision, should Ms. Trevino accept her employer’s offer? (Round your final answer to the nearest whole dollar value.) present value ?arrow_forward
- You annually invest $1,000 in an individual retirement account (IRA) starting at the age of 30 and make the contributions for 10 years. Your twin sister does the same starting at age 45 and makes the contributions for 20 years. Both of you earn 6 percent annually on your investment. What amounts will you and your sister have at age 65? Use Appendix A and Appendix C to answer the question. Round your answers to the nearest dollar.Amount on your account: $ Amount on your sister's account: $ Who has the larger amount at age 65?-Select-You haveYour sister hasItem 3 the larger amount.arrow_forwardMunabhaiarrow_forwardGail Trevino expects to receive a $580,000 cash benefit when she retires seven years from today. Ms. Trevino’s employer has offered an early retirement incentive by agreeing to pay her $354,000 today if she agrees to retire immediately. Ms. Trevino desires to earn a rate of return of 8 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) Required a. Calculate the present value of the $580,000 future cash benefit. Assuming that the retirement benefit is the only consideration in making the retirement decision, should Ms. Trevino accept her employer’s offer? (Round your final answer to the nearest whole dollar value.)arrow_forward
- Subject: accountingarrow_forwardPlease help me. Thankyou.arrow_forwardA self-employed person deposits $2,000 annually in a retirement account (called a Keogh or H.R. 10 plan) that earns 9 percent. Use Appendix A and Appendix C to answer the questions. Round your answers to the nearest dollar. How much will be in the account when the individual retires at the age of 65 if the savings program starts when the person is age 50?$ How much additional money will be in the account if the saver defers retirement until age 70 and continues the contributions?$ How much additional money will be in the account if the saver discontinues the contributions at age 65 but does not retire until age 70?$arrow_forward
- (Pension Funding) You have been hired as a benefit consultant by Jean Honore, the owner of Attic Angels. She wants to establish a retirement plan for herself and her three employees. Jean has provided the following information. The retirement plan is to be based upon annual salary for the last year before retirement and is to provide 50% of Jean’s last-year annualsalary and 40% of the last-year annual salary for each employee. The plan will make annual payments at the beginning of each year for 20 years from the date of retirement. Jean wishes to fund the plan by making 15 annual deposits beginning January 1, 2017. Invested funds will earn 12% compounded annually. Information about plan participants as of January 1, 2017, is as follows. Jean Honore, owner: Current annual salary of $48,000; estimated retirement date January 1, 2042.Colin Davis, flower arranger: Current annual salary of $36,000; estimated retirement date January 1, 2047.Anita Baker, sales clerk: Current annual salary of…arrow_forwardCan I please get the solution by using excelarrow_forward1. Bill has an emergency fund already set aside, so he can use his $400,000 of savings for retiremenr. How much can he withdraw on a monthly basis to supplement his retirement annuity if his investments return 5 percent annually and he expects to live 30 years? 2. Ignoring his Social Secuirty benefit, is the amount determined in question 1 sufficient to meet his current monthly expenses (keep in mind that he will receive a pension of $2,800 per month)? If not, how long will his retirement last if his current expenses remain the same? What if his expenses are reduced to $4,500 per month?arrow_forward
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