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¬ve years of service. This is called cliff vesting”the participant is either
vested or not vested, with no partial vesting.
29-6 Pension Plan Management
Chapter 29

2. Three-to-seven-year rule. Under this rule, participants are partially
vested according to the number of years of service:

Years of Service Percent Vested

3 20%
4 40
5 60
6 80
7 100

Of course, employers may offer plans that vest pension rights more quickly
than mandated by these two vesting rules.

Portable means “capable of being carried,” and a portable pension plan is
one that an employee can carry from one employer to another. Portability is
extremely important in occupations such as construction, where workers
move from one employer to another fairly frequently. A de¬ned contribu-
tion plan is always portable, because the plan™s assets are held in the
employees™ names. However, for a de¬ned bene¬t plan to be portable, both
the old employer and the new employer would have to be part of the same
plan”it would simply not be feasible for an IBM employee to leave IBM
and go to work for Delta Airlines and take along a share of the IBM plan.
(Note, however, that if the employee™s rights under the IBM plan were
vested, then he or she could receive payments from both Delta and IBM
upon retirement.) Where job changes are frequent”as in trucking, con-
struction, and coal mining”union-administered plans are used to make
portability possible.
Note that cash balance plans are completely portable. Indeed, this fact,
combined with the increasing mobility of the U.S. work force, is one reason
for the rapid growth of cash balance plans. By adding portability to the
advantages of a traditional de¬ned bene¬t plan, it can better serve the retire-
ment needs of employees of all ages.

Under de¬ned contribution, pro¬t sharing, and cash balance plans, the com-
pany must make annual contributions. However, under a de¬ned bene¬t
plan the company promises to give employees pensions for some unknown
number of future years based on their unknown future salaries, and from
a fund whose future value is unknown, so its true costs are uncertain.
However, pension fund actuaries can estimate the present value of the
expected future bene¬ts under a de¬ned bene¬t plan, and this present value
constitutes a liability of the plan. The liability may be measured (1) by the
present value of all projected bene¬ts accrued by present workers, or (2) by
the present value of vested bene¬ts earned to date. The vested amount is
obviously smaller, and it represents the expected present value of the bene-
¬ts that would be paid to workers if the ¬rm went out of business today or
if all workers resigned today. The value of the fund™s assets is calculated as
their current market value. If the present value of all expected retirement
bene¬ts is equal to assets on hand, then the plan is said to be fully funded.
Key Terms and Concepts

If assets exceed the present value of bene¬ts, the plan is overfunded. If the
present value of bene¬ts exceeds assets, the plan is underfunded, and an
unfunded pension liability exists.

Actuarial Rate of Return
The discount rate used to determine the present value of future bene¬ts
under a de¬ned bene¬t plan is called the actuarial rate of return. Often, this
rate is the same as the assumed rate of return on the plan™s assets.
The actuarial rate of return is a critical element in pension plan manage-
ment. A higher assumed actuarial rate leads to lower current contribution
requirements because (1) the present value of bene¬ts will be lower and (2)
the plan™s assets will be assumed to earn more, hence to grow at a faster rate.
Since the actuarial rate is a forecast of the expected future rate of return on
the plan™s assets, there is a great deal of room for judgment. Some ¬rms base
their actuarial rate on recent plan performance, while others base the rate on
long-term historical returns on different asset classes and then apply these
historical returns to the plan™s current asset mix to get a weighted average.
If the estimates are unbiased, errors in actuarial rate assumptions should bal-
ance out over time. However, if a ¬rm purposely sets its actuarial rate too
high in order to hold down its contributions and thus raise its reported
income, its pension plan will build up a large unfunded de¬ciency.

The Employee Retirement Income Security Act of 1974 (ERISA) is the basic
federal law governing the structure and administration of corporate pension
plans. ERISA requires that companies fully fund their de¬ned bene¬t pen-
sion plans, although it gives them up to 30 years to make up for under-
funding of past service bene¬ts. For example, if a company agreed in 2003
to double payments to all employees who retire in the future, it would imme-
diately have a large unfunded liability. If the company had to come up with
the money to fully fund its plan, it would probably not be able to offer the
improved bene¬ts. The phased adjustment period is obviously important in
such a situation.
In addition, ERISA has several other provisions that affect the manage-
ment of de¬ned bene¬t plans. First, ERISA mandates that pension funds be
managed according to the “prudent man” rule, which focuses on diversi¬-
cation as the cornerstone of portfolio management. This has resulted in
pension funds diversifying into such investments as real estate, international
stocks and bonds, LBOs, and venture capital. Second, ERISA sets the manda-
tory vesting requirements discussed earlier to prevent situations whereby
long-term employees are ¬red or laid off just before their bene¬ts are vested.
Finally, ERISA established the Pension Bene¬t Guarantee Corporation
(PBGC), which we discuss next.

The Pension Bene¬t Guarantee Corporation (PBGC) was established by
ERISA to insure corporate de¬ned bene¬t pension funds. The PBGC, which
is an agency within the U.S. Department of Labor, steps in and takes over
payments to retirees of bankrupt companies with underfunded pension plans.
Currently, the PBGC is paying (or will pay when they retire) bene¬ts to some
624,000 retirees from 2,975 companies, including Pan American Airlines,
Eastern Airlines, Allis-Chalmers, Republic Steel, and LTV Corporation.
29-8 Pension Plan Management
Chapter 29

Funds for the PBGC come from premiums paid by sponsors of de¬ned
bene¬t plans. Currently, the premium is $19 per participant per year, plus an
additional fee of $9 per $1,000 of unfunded liabilities. However, the ulti-
mate backers of the PBGC are the taxpayers. Just a few years ago, the PBGC
was grossly underfunded, with known obligations exceeding assets by some
$3 billion. At that time, pundits were predicting that the only thing that
would save the PBGC was a large government bailout. However, by 1997,
increased collections from sponsoring corporations, coupled with high
investment returns and a decline in large bankruptcies, resulted in a PBGC
surplus of about $900 million, its ¬rst ever.
To help control costs, the PBGC does not cover company-promised health
insurance for retirees. Further, PBGC payments to retirees are capped at
about $42,954 (in 2002 dollars) per year, which for some highly paid work-
ers is much less than their plan originally promised. Finally, the PBGC does
not guarantee pensions that are to be paid by annuities purchased by plans
from insurance companies. This feature is important, because in the 1980s,
many companies terminated overfunded de¬ned bene¬t plans, used a por-
tion of the plan™s assets to purchase insurance contracts to cover promised
bene¬t payments, and then recovered the excess assets for the stockholders.

Contributions to the Plan
Actuaries calculate annually how much a company must pay into its de¬ned
bene¬t fund in order to keep it fully funded (or to move it toward full fund-
ing). These contributions are a tax-deductible expense, just as are wages.
Obviously, if a company agrees to an increase in bene¬ts, this increases its
required contribution and consequently lowers its reported pro¬ts and cash
¬‚ow to stockholders. Also, if pension bene¬ts are tied to wages, then any
wage increase will also require an increase in payments to the pension plan.
Payments also depend on the investment performance of the pension fund”
if the fund™s managers do a good job of investing its assets, then required
annual contributions will be reduced, and vice versa if the fund™s investment
performance is poor.
During the 1990s, as a result of the greatest bull market in history, many
corporations™ pension plans were overfunded to such an extent that they did
not have to make any annual contributions. Indeed, many ¬rms received
earnings credits. For example, in 1999 GE reported pension income of $1.38
billion, which was almost 5 percent of its operating income; its fund earned
that much more than the cost of the bene¬ts it provided to retirees during
the year and the cost of funding the additional future bene¬ts that it
promised during the year.3 However, since the tech crash and recession of
2001 and 2002, pension plans have faired less well. In 2001 GM lost $4.4
billion on its pension assets, and as a result of these losses and plan payouts,
its plan went from being overfunded by $1.7 billion in 2000 to being under-
funded by $9 billion at the end of 2001.

The Financial Accounting Standards Board (FASB), together with the SEC,
establishes the rules under which a ¬rm reports its ¬nancial condition to
stockholders. FASB Statement 87, “Employers™ Accounting for Pension

William Persek Jr., “Hidden Asset: For Many Companies, Pension Plans Are Bolstering Pro¬ts,” Barron™s, May 29,
2000, 22.
Pension Fund Mathematics: Defined Benefit Plans

Plans,” and Statement 35, “Accounting and Reporting by De¬ned Bene¬t
Plans,” provide guidance for reporting pension costs, assets, and liabilities.
The reporting of de¬ned contribution plans is relatively straightforward”
the annual contribution is shown on the income statement, and a note to the
¬nancial statements explains the entry. However, reporting for de¬ned ben-
e¬t plans is much more complex. Basically, a ¬rm with a de¬ned bene¬t plan
must report in its annual report the plan™s overall funding status; the annual
pension expense; a full description of the pension plan, including the
employee groups covered, type of bene¬t formula, funding policy, and types
of assets held; the actuarial discount rate used, and any justi¬ed difference
between this rate and the rates used to project the bene¬t obligation or to
project the return on the plan™s assets; and the amounts and types of securi-
ties issued by the employer and/or related parties that are held by the plan.4

Define the following terms:
Self-Test Question
(1) Vested; nonvested; deferred vesting
(2) Portability
(3) Fully funded; overfunded; underfunded
(4) Actuarial rate of return
(6) PBGC
(7) Plan contributions

Pension Fund Mathematics:
Defined Benefit Plans
It is clear that the calculation of the present value of expected future bene-
¬ts is of primary importance for de¬ned bene¬t pension plans. This calcula-
tion determines both the required contribution to the fund for the year and
the reported unfunded liability or surplus. Thus, it is essential that ¬nan-
cial managers understand the basic mathematics that underly the bene¬ts
To illustrate the process, let us begin with the following assumptions:
1. A ¬rm has only one employee, age 40, who will retire 25 years from
now, at age 65, will die at age 80, and hence will live for 15 years after
retirement. There is no uncertainty about these facts.
2. The ¬rm has promised a bene¬t of $10,000 at the end of each year fol-
lowing retirement until death. For accounting purposes, 1/25 of this
$10,000 payment will be vested each year the employee works for the
3. No uncertainty regarding the contribution stream exists; that is, the
company will de¬nitely make the required payments, in equal annual
installments over the next 25 years, in order to build up the fund to the
level needed to make the payments of $10,000 per year during the
employee™s 15-year retirement life.
4. The pension fund will earn 8 percent on its assets; this rate is also
known with certainty.

FASB Statement 87 is very complex, hence we cannot discuss its provisions in detail in this text.
29-10 Pension Plan Management
Chapter 29

The problem is to ¬nd (1) the present value of the future bene¬ts and
(2) the company™s required annual contributions. We ¬nd these values as
Step 1. Find the present value (at retirement) of a 15-year regular annuity
of $10,000 per year. Using a ¬nancial calculator, enter PMT
10000 [or 10000], n 15, and i 8; then solve for PV
Step 2. Find the set of equal annual cash contributions required to accu-
mulate $85,594.79 over 25 years. Using a ¬nancial calculator,
enter FV 85594.79 [or 85594.79], n 25, and i 8; then
solve for PMT $1,170.83. Thus, the company must contribute
$1,170.83 per year to satisfy its pension requirements. If it makes
these payments each year, it will be able to report a fully funded
A graphical representation of the contributions, bene¬ts, and fund value
is presented in Figure 29-1. The “Value of Fund” line is drawn continuously,
although in reality it would be a step function. Note also that setting up a
pension plan for this worker requires analysis over a 40-year horizon.
The rate of return assumed makes a substantial difference in the annual
contribution. If we had assumed a return of 9 percent rather than 8 percent,
the annual contributions would have dropped from $1,170.83 to $951.67.
Thus, annual contributions would have fallen by 18.7 percent from only a
one percentage point change in the assumed investment rate. Conversely, if
we had assumed a 7 percent return, the annual contributions would have
increased to $1,440.01, a 23 percent increase. Assumptions about how long
the worker will live, years before retirement, and, if the payment is based on
salary, annual raises will have similarly large effects on the required annual

Pension Fund Cash Flows and Value under Certainty
Figure 29-1
Value of Fund = Annual Contributions
+ Investment Returns
“ Benefit Payments


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