Josit Ltd. initiated a
one-person pension plan in January 2005 that promises the employee a pension on
retirement according to the following formula: pension benefit = 2.5% of final
salary per year of service after the plan initiation. The employee began
employment with Josit early in 2002 at age 33, and expects to retire at the end
of 2028, the year in which he turns 60. His life expectancy at that time is 21
years. Assume that this employee earned an annual salary of $40,000 when he
joined Josit, that his salary was expected to increase at a rate of 4% per year,
and that this remains a reasonable assumption to date. Josit considers a
discount rate of 6% to be appropriate.
Instructions
(a) What is the employee’s
expected final salary?
(b) What amount of current
service cost should Josit recognize in 2010 relative to this
plan?
(c) What is the amount of
the accrued benefit obligation at December 31, 2010?
(a) The employee’s expected
final salary in 2028 would be calculated as follows:
$40,000 X
(1.04)26 = $110,899
(in 27 years there would
be 26 raises)
(b) Step 1:Calculate
annual pension benefit on retirement from working in 2010:
Annual pension benefits
on retirement
= 2.5% X $110,899 X 1
year
= $2,772 per year of
retirement
Step 2:Discount
the present value of the annuity of $2,772 for 21 years at 6% to December 31,
2028.
Present value of an annuity of $2,772
discounted at 6% for 21 periods:
|
($2,772 X
11.76408) = |
$32,610 |
|
Using a financial
calculator: |
| |
|
PV |
$ ? |
Yields $32,610 |
|
I |
6% |
|
|
N |
21 |
|
|
PMT |
$ (2,772) |
|
|
FV |
$ 0 |
|
|
Type
|
0 |
|
|
Excel formula:
=PV(rate,nper,pmt,fv,type) |
Step 3: Discount the present value
of the annuity in 2028 to its present value at 2010:
|
Present value of
$32,610 discounted at 6% for 18 years | ||
|
($32,610 X .35034)
= $11,425 |
| |
|
(18 years = 2010
to 2028) |
|
|
|
Using a financial
calculator: |
| |
|
PV |
$ ? |
Yields $11,425 |
|
I |
6% |
|
|
N |
18 |
|
|
PMT |
$ 0 |
|
|
FV |
$ (32,610 )
|
|
|
Type
|
0 |
|
|
Excel formula:
=PV(rate,nper,pmt,fv,type) |
The current service cost
relative to this plan for 2010 would
be $11,425.
(c) Pension
benefits earned to December 31, 2010
= 2.5% X $110,899 X 6
years = $16,635 per year of retirement.
Present value at December 31, 2028 of an
annuity of $16,635 discounted at 6% for 21
periods:
|
($16,633 X 11.76408) = |
$195,676 |
|
Using a financial
calculator: |
| |
|
PV |
$ ? |
Yields $195,676 |
|
I |
6% |
|
|
N |
21
|
|
|
PMT |
$ (16,633) |
|
|
FV |
$ 0 |
|
|
Type
|
0 |
|
|
Excel formula:
=PV(rate,nper,pmt,fv,type) |
The accrued benefit obligation represents the
present value of this amount discounted at 6% for 18 years:
|
Present value of
$195,676 discounted at 6% for 18 years | |
|
($195,676 X
.35034) = $68,558 |
|
|
Using a financial
calculator: |
| |
|
PV |
$ ? |
Yields $68,558 |
|
I |
6% |
|
|
N |
18
|
|
|
PMT |
$ 0 |
|
|
FV |
$ (195,676 )
|
|
|
Type
|
0 |
|
|
Excel formula:
=PV(rate,nper,pmt,fv,type) |
The accrued benefit obligation at December 31, 2010 would be $68,558.
Queensland Importers provides the following pension plan information:
Fair value of pension plan
assets, Jan. 1, 2011 ……………….. $1,418,750
Fair value of pension plan
assets, Dec. 31, 2011 ……………… 1,596,875
Contributions to the plan in
2011 ……………………………… 212,500
Benefits paid retirees in
2011 ………………………………….. 218,750
Instructions
Calculate the actual return
on the plan assets for 2011.
Calculation of Actual Return
on Plan Assets
Fair value of plan assets at
12/31/11 $1,596,875
Fair value of plan assets at
1/1/11 1,418,750
Increase in fair value of
plan assets 178,125
Deduct: Contributions to
plan during 2011 $212,500
Less: benefits paid
during 2011 218,750 6,250
Actual return on plan assets
for 2011 $ 184,375
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