Download 8.1 Basic Principles of Retirement Planning

Chapter 8
Retirement Plans
START
EXIT
7-1
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
8.1
Basic Principles of Retirement Planning
8.2
Details of Retirement Plans
8.3
Assessing the Effect of Inflation
Chapter Summary
Chapter Exercises
7-2
8.1
Basic Principles of Retirement Planning
• Most retirement programs fall into one of two
categories: defined benefit plans and defined
contribution plans.
• A defined benefit (DB) plan is a retirement
program that provides a set income in
retirement, which may be calculated on the basis
of pre-retirement earnings, years worked,
retirement age, and/or the period of time for
which benefits are guaranteed to be paid.
7-3
8.1
Basic Principles of Retirement Planning
Example 8.1.1
• Problem
– A union retirement plan promises an income to union
members beginning at age 65 and continuing until
death. The formula states that retirees who have at
least 5 years of service will receive a monthly income
of $80 for each year of service, up to a maximum
monthly income of $2,000.
– Find the benefit that would be payable to a member
who retires at age 65 with (a) 4 years of service, (b)
10 years of service, and (c) 40 years of service.
7-4
8.1
Basic Principles of Retirement Planning
Example 8.1.1 Cont.
• Solution
– Since the formula requires a minimum of 5 years
of service, someone retiring with fewer than 5
years would not receive any benefit.
– For someone with 10 years of service, the
monthly benefit would be 10 x $80 = $800
– For someone with 40 years of service, the
monthly benefit would be $2,000. Even though
40 x $80 = $3,200, the maximum benefit is
$2,000.
7-5
8.1
Basic Principles of Retirement Planning
Example 8.1.2
• Problem
– The XYZ Corporation Pension Plan provides a
lifetime income to its employees on retirement at
age 65. The formula provides 2% for each year
of service of the average of the employee’s
earnings for the last 3 years on the job, up to a
maximum of 70%.
– Jen retired at 65 with 28 years of service. Her
earnings for the last 3 years were $37,650,
$39,525, and $40,187.
– What is her pension benefit?
7-6
8.1
Basic Principles of Retirement Planning
Example 8.1.2 Cont.
• Solution
– Jen is entitled to 28 x 2% = 56% of her final 3year average income
– Her 3-year average income is
($37,650 + $39,525 + $40,187)/3 =
$39,120.67
– So her annual pension benefit is
56% x $39,120.67 = $21,907.58 per year
7-7
8.1
Basic Principles of Retirement Planning
Example 8.1.3
• Problem
– The XYZ Corporation offers employees the choice to
retire as early as age 60 or as late as age 72. Those
retiring before age 65 have their calculated benefit
reduced by 2.5% for each year they retire prior to age
65; those retiring later have their benefit increased by
1.9% for each year beyond age 65 that they work.
– Brooke plans to retire this year at age 63. She has 19
years of service to the company and her last 3 years’
earnings were $48,000, $52,000, and $54,000.
– Kurt plans to retire this year at age 69. He has 37
years of service and his last 3 years’ earnings were
$41,500, $43,750, and $46,300.
7-8
8.1
Basic Principles of Retirement Planning
Example 8.1.3 Cont.
• Solution
– Brooke’s 19 years of service entitle her to
38% of benefits.
– Her final 3-year average salary is $51,333.33.
If she were 65, her annual benefits would be
$19,506.67.
– Because she is retiring 2 years early, she will
give up 2 x 2.5% = 5% of the benefit.
– So her annual benefits would be only
$19,506.67 x 95% = $18,531.34.
7-9
8.1
Basic Principles of Retirement Planning
Example 8.1.3 Cont.
• Solution
– Kurt’s 37 years of service would give him 74%,
except that the maximum is 70%.
– His final 3-year average salary is $43,850.
– If he were 65, his benefit would be $30,695 per
year.
– Retiring 4 years later means he will get an extra 4
x 1.9% = 7.6%.
– So he will get $30,695 x 107.6% = $33,027.82
per year.
7-10
8.1
Basic Principles of Retirement Planning
• Unlike defined benefit plans, defined contribution
(DC) plans do not provide a fixed, guaranteed
income in retirement.
• Instead, the employer contributes money to a
retirement account for each employee on the basis
of some set formula.
• The money is then invested and grows in value
during the employee’s working years.
• Sometimes the contributions to the plan are made
entirely by the employer. In most cases, though, the
employee is either permitted or required to
contribute money as well.
7-11
8.1
Basic Principles of Retirement Planning
Example 8.1.4
• Problem
– The company Jesse works for contributes 8% of each
employee’s annual earnings to a defined contribution plan,
provided that the employee contributes at least 3%. Jesse
makes $32,500 per year. How much will go into his
account this year if he contributes (a) nothing, (b) 3%, and
(c) 10% of his income?
• Solution
– If Jesse does not contribute anything, he is not qualified for
any employer’s contributions.
– If Jesse contributes 3%, his employer will contribute 8%.
Therefore, the total contribution would be 11% x $32,500 =
$3,575.
– If Jesse contributes 10%, his employer will contribute 8%.
Therefore the total contribution would be 18% x $32,500 =
$5,850.
7-12
8.1
Basic Principles of Retirement Planning
Example 8.1.5
• Problem
– XYZ Digital Devices has a defined contribution plan.
The company matches 75% of each employee’s
contributions up to a maximum of 10%.
– Hal earns $60,000. How much will be deposited to
this account this year if he contributes (a) nothing, (b)
5%, and (c) 15% of his earnings?
7-13
8.1
Basic Principles of Retirement Planning
Example 8.1.5 Cont.
• Solution
– If Hal contributes nothing, his company won’t
contribute anything either.
– If Hal contributes 5%, his portion would be 5% x
$60,000 = $3,000. His employer will contribute 75% x
$3,000 = $2,250. So the total contribution would be
$3,000 + $2,250 = $5,250
– If Hal contributes 15%, his portion would be 15% x
$60,000 = $9,000. His employer will contribute 75% x
(10% x $60,000) = $4,500. The total contribution
would be $9,000 + $4,500 = $13,500.
7-14
8.1
Basic Principles of Retirement Planning
• After you have accumulated a certain number of years of
service, you become vested in the plan, meaning that
any benefits earned will not be lost, regardless of
whether or not you continue working or even if the plan
is discontinued.
• How quickly someone attains this vesting is determined
by a vesting schedule.
• With cliff vesting, it is an all-or-nothing deal. After a
certain number of years of service, you become fully
vested in the plan; prior to that point, you have no vested
benefit and will receive no benefits from the plan if you
depart before that point.
• With step vesting, you may be entitled to a certain
percent of your benefits, depending on your years of
service when you leave.
7-15
8.1
Basic Principles of Retirement Planning
Example 8.1.6
• Problem
– Dave has just been laid off from his
job. He was covered by the
company’s defined benefit pension
plan, which provides a benefit of 2%
final year’s salary for each
completed year of service, beginning
at age 65.
– Dave earned $43,600 at this job in
the last year, and had completed 6
years of service.
– The pension plan uses the 7-year
20% vesting schedule. What is
Dave’s vested benefit?
Yrs of
Service
Completed
Vesting
Percent
< 3 years
0%
3-4 years
20%
4-5 years
40%
5-6 years
60%
6-7 years
80%
7+ years
100%
7-16
8.1
Basic Principles of Retirement Planning
Example 8.1.6 Cont.
• Solution
– Dave is entitled to 6 x 2% = 12% of
salary as a benefit.
– However, he has only 6 years of
service and so he eligible for only
80% of the benefits.
– Therefore, his vested benefit is
(12% x $43,600) x 80% = $4,185.60
per year, beginning at age 65.
Yrs of
Service
Completed
Vesting
Percent
< 3 years
0%
3-4 years
20%
4-5 years
40%
5-6 years
60%
6-7 years
80%
7+ years
100%
7-17
8.1
Basic Principles of Retirement Planning
Example 8.1.7
• Problem
– Kelly is leaving her job after
working there for 3 ½ years.
– She has contributed a total of
$5,722.16.
– The company contributed a total
of $4,810.33.
– Find her vested balance in this
plan.
Yrs of
Service
Completed
Vesting
Percent
< 3 years
0%
3-4 years
20%
4-5 years
40%
5-6 years
60%
6-7 years
80%
7+ years
100%
7-18
8.1
Basic Principles of Retirement Planning
Example 8.1.7 Cont.
• Solution
– She is eligible for 20% of
employer’s contribution, so that
portion is 20% x $4,810.33 =
$962.07.
– Her own contribution is always
fully vested so she will keep
$5,722.16 + $962.07 = $6,684.23
Yrs of
Service
Completed
Vesting
Percent
< 3 years
0%
3-4 years
20%
4-5 years
40%
5-6 years
60%
6-7 years
80%
7+ years
100%
7-19
Section 8.1 Exercises
Problem 1: Defined Benefit Plans
Problem 2: Defined Contribution Plans
Problem 3: Vesting
7-20
Problem 1
• Pacifica International has a defined benefit
pension plan. On retirement at age 65, the
plan provides 1.75% of the 3-year final average
salary for each year of service, up to a
maximum of 60%.
• Dave has 25 years of service and his 3-year
final average salary is $48,734.
• Calculate his pension benefit.
CHECK YOUR ANSWER
7-21
Solution 1
• Pacifica International has a defined benefit pension plan.
On retirement at age 65, the plan provides 1.75% of the
3-year final average salary for each year of service, up to
a maximum of 60%.
• Dave has 25 years of service and his 3-year final
average salary is $48,734.
• Calculate his pension benefit.
• Dave qualifies for 1.75% x 25 = 43.75%
• 43.75% x $48,734 = $21,321.13
BACK TO GAME BOARD
7-22
Problem 2
• Fischer’s Bakery offers its employees a defined
contribution retirement plan with 40% matching
up to 10% of salary. If Rhonda’s annual salary
is $39,400, how much will be deposited to her
account if she contributes 5% of her salary?
CHECK YOUR ANSWER
7-23
Solution 2
• Fischer’s Bakery offers its employees a defined
contribution retirement plan with 40% matching
up to 10% of salary. If Rhonda’s annual salary
is $39,400, how much will be deposited to her
account if she contributes 5% of her salary?
• Rhonda’s Contribution: $39,400 x 5% = $1,970
• Employer’s Contribution: $1,970 x 40% = $788
• Total Contribution = $1,970 + $788 = $2,758
BACK TO GAME BOARD
7-24
Problem 3
• Sally has $23,498 in her defined
contribution plan at work. Of that
balance, $15,264 comes from her
employer.
• The plan uses the 7-year step
vesting schedule.
• How much of her balance would
Sally keep if she has 6 ½% years
of service?
Yrs of
Service
Completed
Vesting
Percent
< 3 years
0%
3-4 years
20%
4-5 years
40%
5-6 years
60%
6-7 years
80%
7+ years
100%
CHECK YOUR ANSWER
7-25
Solution 3
• Sally has $23,498 in her defined contribution
plan at work. Of that balance, $15,264 comes
from her employer.
• The plan uses the 7-year step vesting schedule.
• How much of her balance would Sally keep if
she has 6 ½% years of service?
• Her own contribution is $23,498 -- $15,264 =
$8,234 and she keeps the full amount.
• However, she will be able to keep only 80% of
employer’s contribution so that comes to
80% x $15,264 = $12,211.20
BACK TO GAME BOARD
7-26
8.2
Details of Retirement Plans
• An individual retirement account (IRA) is a special
type of account that can be set up by an individual
through almost any bank, brokerage firm, credit union,
or other financial institution.
• The purpose of an IRA is to allow an individual to save
for retirement, and the tax laws offer significant tax
advantages to encourage people to set up and
contribute to these sorts of accounts.
• There are limits, however, to how much an individual
can contribute to an IRA in any one year.
• An IRA is not a type of investment in itself; it’s a type
of account that can contain almost any sort of
investment within it.
• Also, money invested in an IRA can’t usually be
withdrawn until its owner reaches age 59 ½.
7-27
8.2
Details of Retirement Plans
• Roth IRAs are a special type of IRA. They get their
name from the late Senator William Roth of
Delaware, who championed their creation.
• Contributions to a Roth IRA are not tax deductible
but, like ordinary IRAs, their investment growth is
not taxed while the money is in the account.
• Roth IRAs have a unique advantage, though,
because their investment growth is not taxed when
money is withdrawn from the account either.
• In other words, all of the investment growth from a
Roth IRA is income tax free, not just income tax
deferred.
7-28
8.2
Details of Retirement Plans
Example 8.2.1
• Problem
– Sarah has $3,000 that she wants to invest in an IRA. She
expects that this money will earn 9% and does not expect to
withdraw the money from her IRA for another 40 years.
– Assuming that she will pay a 30% rate for combined state and
federal income taxes, how much will she have after taxes if she
invests in (a) a Roth IRA or (b) a traditional IRA.
• Solution
– Compounded at 9% for 40 years, her $3,000 would grow to:
FV = PV(1 + i)n
FV = $3,000(1 + 0.09)40 = $94,228.26
No taxes will be owed when she withdraws her money from a
Roth IRA
– Her money would grow to the same amount in a traditional IRA.
However, paying 30% in income taxes would leave her with 70%
x $94,228.26 = $65,959.78.
7-29
8.2
Details of Retirement Plans
• 401(k)s are a type of retirement account offered as a
benefit by employers. Workers contribute to their 401(k)
accounts by payroll deductions and money contributed is
not included in taxable income.
• As in a traditional IRA, the money grows tax-deferred,
and is subject to income tax when it is withdrawn from
the plan.
• When a company sets up a 401(k) plan for its
employees, it generally selects a plan administrator such
as a bank, insurance company, or mutual fund company.
• Employees control how their money is invested by
choosing from a selection of mutual funds.
• In many, though not all, cases the employer offers some
matching of the employee’s contributions.
7-30
8.2
Details of Retirement Plans
Example 8.2.2
• Problem
– Shannon makes $26,735 annually working for BB Chemical
Corp. The company offers a 401(k) plan with 75% matching
up to 6% of her salary. How much in total would Shannon
have deposited to her 401(k) each year if she decides to
contribute (a) 4% or (b) 10%.
• Solution
– 4% of her annual salary is 4% x $26,735 = $1,069.40
– The company will match 75% of this amount or
75% x $1,069.40 = $802.05
– In total, this makes $1,069.40 + $802.05 = $1,871.45
– 10% of her annual salary is $2,673.50
– The company will match 75%(6% x $26,735) = $1,203.08
– In total, this makes $2,673.50 + $1,203.08 = $3,876.58
7-31
8.2
Details of Retirement Plans
Example 8.2.3
• Problem
– Curt is 24 years old and just started a new job which offers a 401(k)
plan. He will be making $31,000 per year.
– Looking to the future, Curt is wondering what percent of his salary he
should contribute to the 401(k) if he wants to have $750,000 in this
account when he reaches age 65.
– He is paid biweekly, his company does not offer any matching, and
he expects that his investments can earn 10%.
4126
• Solution
1 0.1 1
FV = PMTsn/i
s4126| 1 0% 
26
26
 
0.1
26
 15,305.5773419
$750,000 = PMT x 15,305.57734
PMT = $49.00

Curt’s biweekly pay will be $31,000/26 = $1,192.31. A $49 contribution
amounts to $49.00/$1,192.31 = 4.11%
7-32
Section 8.2 Exercises
Problem 1:
Traditional and
Roth IRAs
Problem 2:
401(k) Plan
Projections
7-33
Problem 1
• Suppose Misty deposits $2,000 into a Roth IRA
which earns an average rate of 9% for the next
30 years. What is the future value of this
deposit?
CHECK YOUR ANSWER
7-34
Solution 1
• Suppose Misty deposits $2,000 into a
Roth IRA which earns an average rate of
9% for the next 30 years. What is the
future value of this deposit?
• FV = PV(1 + i)n
FV = $2,000(1 + 9%)30
FV = $26,535.36
BACK TO GAME BOARD
7-35
Problem 2
• Jess’ company offers a 401(k) plan with no
employer match. She would like to have
$500,000 in her account in 30 years. Her
annual salary is $48,000. She believes her
investments can earn 7%.
• How much should she be depositing with each
paycheck if she gets paid monthly?
CHECK YOUR ANSWER
7-36
Solution 2
• Jess’ company offers a 401(k) plan with no employer match. She
would like to have $500,000 in her account in 30 years. Her annual
salary is $48,000. She believes her investments can earn 7%.
• How much should she be depositing with each paycheck if she gets
paid monthly?
• FV = PMTsn/i
(1  i )  1 1  
sn|i 


i
n


0.07 360
12
0.07
12
1
 1,219.970996
$500,000 = PMT x 1,219.970996
PMT = $409.85
BACK TO GAME BOARD
7-37
8.3
Assessing the Effect of Inflation
Example 8.3.1
• Problem
– Loosely speaking, inflation is the tendency of prices to
rise over time.
– Suppose that a lawnmower costs $189.95 today and that
you expect lawnmower prices to rise at a 4% effective
rate in the future. If your assumption is correct, how
much would this mower cost 20 years from now?
• Solution
– FV = PV(1 + i)n
FV = $189.95(1 + 4%)20 = $416.20
7-38
8.3
Assessing the Effect of Inflation
Example 8.3.2
• Problem
– Suppose you want to have $1,000,000 in your 401(k)
account in 40 years. How much do you need to deposit
into this account each week to achieve your goal if you
expect to earn 9% on your investments?
– Also assume that your goal is not $1,000,000 in actual
dollars but instead in today’s dollars.
7-39
8.3
Assessing the Effect of Inflation
Example 8.3.2
• Solution
– Our first step is to figure out what the actual goal is. Of course,
since we can’t know what inflation will be over the next 40 years,
there is now way to know this for sure. We will assume a 3.5%
inflation rate.
FV = PV(1 + i)n
FV = $1,000,000(1 + 3.5%)40 = $3,959,259.72
– So the goal is to actually have $3,959,259.72
FV = PMTsn/i
2080
(1 i) 1


i
n
sn / i
0.09
1

 52 
1
 
0.09
52
 20502.1701556
$3,959,259.72 = PMT x 20502.1701556
PMT = $193.11
7-40
Problem 1 (Projecting Future Dollar Amounts)
• In 2005, Gena was quoted a price of $24,583 for a large
array of solar panels for her home. An industry expert
was predicting that prices for solar arrays would drop at
a roughly 10% annual rate for the next 10 years. If this
prediction is correct, how much would this array cost in
2015?
7-41
41
Solution 1
• In 2005, Gena was quoted a price of $24,583 for a large
array of solar panels for her home. An industry expert was
predicting that prices for solar arrays would drop at a
roughly 10% annual rate for the next 10 years. If this
prediction is correct, how much would this array cost in
2015?
• FV = PV(1 + i)n
FV = $24,583(1 – 0.1)10 = $8,571.56
7-42
42
Chapter 8 Summary
•
•
•
•
•
•
•
Defined Benefit Plans
Defined Contribution Plans
Vesting
IRAs
Roth IRAs
401(k)s
Projections with Inflation
7-43
Chapter 8 Exercises
Section 8.1
Section 8.2
Section 8.3
$100
$100
$100
$200
$200
$200
EXIT
7-44
Section 7.1 -- $100
• The Reynolds Enterprises, Inc. provides a lifetime income to its
employees on retirement at age 65. The formula provides 1.5%
for each year of service of the average of the employee’s
earnings for the last 3 years of service, up to a maximum of 75%.
• However, employees can retire as early as 60 or as late as 70.
Those retiring before age 65 have their calculated benefit
reduced by 1.5% for each year they retire prior to age 65. Those
retiring later have their benefit increased by 1.5% for each year
beyond age 65.
• Linda plans to retire this year at age 67. She has 30 years of
service and her average salary for the last 3 years was $49,371.
• What is her pension benefit?
CHECK YOUR ANSWER
7-45
Section 7.1 -- $100
•
•
•
•
•
•
The Reynolds Enterprises, Inc. provides a lifetime income to its employees
on retirement at age 65. The formula provides 1.5% for each year of
service of the average of the employee’s earnings for the last 3 years of
service, up to a maximum of 75%.
However, employees can retire as early as 60 or as late as 70. Those
retiring before age 65 have their calculated benefit reduced by 1.5% for
each year they retire prior to age 65. Those retiring later have their benefit
increased by 1.5% for each year beyond age 65. Linda plans to retire this
year at age 67. She has 30 years of service and her average salary for the
last 3 years was $49,371.
30 x 1.5% = 45%
45% x $49,371 = $22,216.95
2 x 1.5% = 3%
$22,216.95 x 103% = $22,883.46
BACK TO GAME BOARD
7-46
Section 7.1 -- $200
• Fabrics Galore, Inc. contributes 5% of
each employee’s annual earnings to a
defined contribution plan. In addition,
employees can contribute up to 20% of
their annual pay.
• Shalonda makes $52,397 per year. How
much will go into her account this year if
she contributes 10%?
CHECK YOUR ANSWER
7-47
Section 7.1 -- $200
• Fabrics Galore, Inc. contributes 5% of each employee’s
annual earnings to a defined contribution plan. In
addition, employees can contribute up to 20% of their
annual pay.
• Shalonda makes $52,397 per year. How much will go
into her account this year if she contributes 10%?
• 5% x $52,397 = $2,619.85
• 10% x $52,397 = $5,239.70
• Total Contributions = $7,869.55
BACK TO GAME BOARD
7-48
Section 7.2 -- $100
• Jasmine would like to invest last year’s income
tax refund, $1,849, in an IRA. She expects that
this money will earn 8% for the next 35 years.
• Assuming that Jasmine will pay a 32% combined
state and federal income taxes, how much will
she have after taxes?
CHECK YOUR ANSWER
7-49
Section 7.2 -- $100
• Jasmine would like to invest last year’s income tax
refund, $1,849, in an IRA. She expects that this money
will earn 8% for the next 35 years.
• Assuming that Jasmine will pay a 32% combined state
and federal income taxes, how much will she have after
taxes?
• FV = PV(1 +i)n
FV = $1,849(1 + 8%)35
FV = $27,338.10
Taxes = 32% x $27,338.10 = $8,748.19
Therefore, Jasmine will have a total of
$27,338.10 -- $8,748.19 = $18,589.91
BACK TO GAME BOARD
7-50
Section 7.2 -- $200
• Gerard makes $82,400 annually working for
Chesapeake Bay Accounting Services. The
company offers a 401(k) plan with 70% matching
up to 10% of salary. How much would be
deposited to Gerard’s account if he contributes
5%?
CHECK YOUR ANSWER
7-51
Section 7.2 -- $200
• Gerard makes $82,400 annually working for
Chesapeake Bay Accounting Services. The
company offers a 401(k) plan with 70% matching
up to 10% of salary. How much would be
deposited to Gerard’s account if he contributes
5%?
• $82,400 x 5% = $4,120
• $4,120 x 70% = $2,884
• Total = $4,120 + $2,884 = $7,004
BACK TO GAME BOARD
7-52
Section 7.3 -- $100
• Suppose a refrigerator costs $1,200 today and
you suspect the prices will rise at 3.5% effective
rate in the future. How much would an
equivalent refrigerator cost in 10 years?
CHECK YOUR ANSWER
7-53
Section 7.3 -- $100
• Suppose a refrigerator costs $1,200 today and
you suspect the prices will rise at 3.5% effective
rate in the future. How much would an
equivalent refrigerator cost in 10 years?
• FV = PV(1 + i)n
FV = $1,200(1 + 3.5%)10 = $1,692.72
BACK TO GAME BOARD
7-54
Section 7.3 -- $200
• Jennifer would like to have $500,000 in her
401(k) account in 30 years. How much would
she really need to deposit into this account over
the period of 30 years if her goal is not $500,000
in actual dollars but instead $500,000 in today’s
dollars (expected inflation rate is 3.5%).
CHECK YOUR ANSWER
7-55
Section 7.3 -- $200
• Jennifer would like to have $500,000 in her 401(k)
account in 30 years. How much would she really
need to deposit into this account over the period
of 30 years if her goal is not $500,000 in actual
dollars but instead $500,000 in today’s dollars
(expected inflation rate is 3.5%).
• FV = PV(1 + i)n
FV = $500,000(1 + 3.5%)30 = $1,403,396.85
BACK TO GAME BOARD
7-56