Refer
to the example of HTSM Corp. in Appendix 19A and assume it is now 2010, two
years after the defined pension plan was initiated. In December 2010, HTSM’s
actuary provided the company with an actuarial revaluation of the plan. The
actuary’s assumptions included the following changes:
Estimated
final salary on retirement ………………. $145,000
Current
settlement/discount rate ………………………….7%
Instructions
(a)
Calculate the accrued benefit obligation (ABO) at December 31, 2010, and the
amount of any actuarial gain or loss.
(b)
Based on the revised assumptions at the end of the year, determine what
percentage increase or decrease there would be in the ABO for:
1.
a 1% increase in the discount rate.
2.
a 1% decrease in the discount rate.
(c)
Determine the effect of the actuarial revaluation on the plan’s funded status
at December 31, 2010, and on pension expense for 2010 and for 2011.
(d)
Based on the revised assumptions, recalculate the past service cost that was
incurred by the company in 2012.
(a)
|
|
|
Amounts using original assumptions
|
|
Amounts using revised assumptions
|
|
Pension benefits earned to December 31, 2012
|
|
$9,000
1
|
|
$8,700 2
|
|
PV of annuity at Dec. 31, 2044
|
|
75,455 3
|
|
69,101 4
|
|
ABO at Dec. 31, 2012
|
|
11,692 5
|
|
7,929 6
|
1 2% X $150,000 X 3 years = $9,000
2 2% X $145,000 X 3 years = $8,700
3 $9,000 X PV factor (6%, 12 years) = $9,000 X
8.38384
(Table A- 4) = $75,455
4 $8,700 X PV factor (7%, 12 years) = $69,101
Since
the tables do not include 7%, the calculation was
done
using a financial calculator:
|
PV
|
$
?
|
Yields $69,101
|
|
I
|
7%
|
|
|
N
|
12
|
|
|
PMT
|
$ (8,700)
|
|
|
FV
|
$ 0
|
|
|
Type
|
0
|
5 $75,454 X PV factor (6%, 32 years) = $75,454 X
0.15496
(Table A-2) =
$11,692
6 $69,101 X PV factor (7%, 32 years) = $7,929
|
PV
|
$
?
|
Yields $7,929
|
|
I
|
7%
|
|
|
N
|
32
|
|
|
PMT
|
$ 0
|
|
|
FV
|
$
(69,101)
|
|
|
Type
|
0
|
The calculations could also be done using Excel:
|
Excel formula:
=PV(rate,nper,pmt,fv,type)
|
The ABO at December 31, 2012, using the revised
assumptions would be $7,929. This represents an actuarial gain of $3,763
($11,692 – $7,929) since the revised ABO is lower than the ABO calculated under
the original assumptions.
(b)
|
|
|
6% discount rate
|
|
8% discount rate
|
|
Pension benefits earned to December 31, 2012
|
|
$8,700
|
|
$8,700
|
|
PV of annuity at Dec. 31, 2044
|
|
72,939 1
|
|
65,564 2
|
|
ABO at Dec. 31, 2012
|
|
11,303 3
|
|
5,586 4
|
|
ABO at Dec. 31, 2012 using 7%
|
|
(7,929 )
|
|
(7,929 )
|
|
Change in ABO
|
|
$ 3,374
|
|
$(2,343 )
|
|
Percentage change
|
43% increase
|
30% decrease
|
||
1 $8,700 X PV factor (6%, 12 years) = $8,700 X
8.38384
(Table A- 4) = $72,939
2 $8,700 X PV factor (8%, 12 years) = $8,700 X
7.53608
(Table A-4) =
$65,564
3 $72,939 X PV factor (6%, 32 years) = $72,939 X
0.15496
(Table A-2) =
$11,303
4 $65,564 X PV factor (8%, 32 years) = $65,564 X
0.08520
(Table A-2) =
$5,586
(c) Assuming the plan was 100% funded previously
(ABO = Fund assets), the decrease in ABO would make the plan overfunded by
$11,692 - $7,929 = $3,763.
Pension expense for 2012 would not be
affected if the defer and amortization method is used since the change took
place at December 31, 2012. The amortization of the actuarial gain is based on
beginning-of-year balances, and since the actuarial gain took place at the end
of the year, there would be no amortization in 2012. In 2013, the actuarial
gain would be amortized based on the excess of the gain over 10% of the greater
of ABO and plan assets at January 1, 2013 (i.e. the corridor approach). This
excess, if any, would be amortized over the employee’s average remaining
service period of 31 years. Any amortization of the actuarial gain would be
included as a reduction of 2013 pension expense.
If the immediate recognition method were
used, the actuarial gain of $3,763 would reduce the 2012 pension expense by
$3,763 as it is immediately recognized.
(d)
|
|
|
Before credit for prior service
|
|
After credit for prior service
|
|
Pension benefits earned to December 31, 2014
|
|
$14,500
1
|
|
$31,900 2
|
|
PV of pension earned at
Dec.
31, 2044
|
|
115,169 3
|
|
253,372 4
|
|
ABO at Dec. 31, 2014
|
|
15,129 5
|
|
33,285 6
|
|
ABO, at Dec. 31/14 after prior
service
recognized
|
|
|
|
$33,285
|
|
ABO, at Dec. 31/14 before
service
recognized
|
|
|
|
( 15,129)
|
|
Past service cost incurred
|
|
|
|
$18,156
|
1 2% X $145,000 X 5 years = $14,500
2 2% X $145,000 X 11* years = $31,900
* 11 years =
6 years past service cost before 2010 plus 5
years from
2010 to 2014.
3 $14,500 X PV factor (7%, 12 years) = $115,169
Since
the tables do not include 7%, the calculation was
done
using a financial calculator:
|
PV
|
$
?
|
Yields
$115,169
|
|
I
|
7%
|
|
|
N
|
12
|
|
|
PMT
|
$ (14,500)
|
|
|
FV
|
$ 0
|
|
|
Type
|
0
|
4 $31,900 X PV factor (7%, 12 years) = $253,372
|
PV
|
$
?
|
Yields $253,372
|
|
I
|
7%
|
|
|
N
|
12
|
|
|
PMT
|
$ (31,900)
|
|
|
FV
|
$ 0
|
|
|
Type
|
0
|
5 $115,169 X PV factor (7%, 30 years) = $15,129
|
PV
|
$
?
|
Yields $15,129
|
|
I
|
7%
|
|
|
N
|
30
|
|
|
PMT
|
$ 0
|
|
|
FV
|
$
(115,169)
|
|
|
Type
|
0
|
6 $253,372 X PV factor (7%, 30 years) = $33,285
|
PV
|
$
?
|
Yields $33,285
|
|
I
|
7%
|
|
|
N
|
30
|
|
|
PMT
|
$ 0
|
|
|
FV
|
$
(253,372)
|
|
|
Type
|
0
|
