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:
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||
|
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
|
||
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(18 years = 2010 to 2028)
|
|
|
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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.
