Question

PBO Calculations, Service Costs & Gains/Losses on PBO (Adapted from Chapter 17, P2-P5)
Sachs Brands defined benefit pension plan specifies annual retirement benefits equal to:
1.5% * Service Years * Final Year’s Salary
Payable at the end of each year. Trom Specht was hired by Sachs at the beginning of 2004 and
is expected to retire at the end of 2038, after 35 years’ of service. Her retirement is expected to
span 18 years. Specht’s salary is $120,000 at the end of 2020 and the company’s actuary
projects her salary to be $210,000 at retirement. The actuary’s discount rate is 8%.
Instructions:
1. What amount of retirement benefits has Specht earned at the end of 2019?
2. What is the Projected Benefit Obligation (PBO) at the end of 2019?
3. What is the service cost for 2020 with respect to Specht?
4. What is the interest cost for 2020 with respect to Specht?
5. What is the 2020 PBO for with respect to Specht?
At the beginning of 2021, the pension formula was amended to:
1.75% * Service Years * Final Year’s Salary
6. What is the company’s prior service cost at the beginning of 2021, with respect to
Specht?
7. How much of the prior service cost should be amortized during 2021 (remember that
the change was at the beginning of 2021)?
8. What is the service cost for 2021 with respect to Specht?
9. What is the interest cost for 2021 with respect to Specht?
10. What is the 2021 PBO for with respect to Specht?
At the end of 2021 (beginning of 2022), changing economic conditions caused the actuary to
reassess the applicable discount rate. It was decided that 7% is the appropriate rate.
11. What is the effect of this change in the discount rate?

Answer 1

The values provided in the question are as follows :-

Specht’s salary = $120,000

actuary projected salary = $210000

discount rate = 8%

The formula to calculate annual retirement benefits equal to:

1)

1.5% * 16 * $210000 = $ 50400

2)

1.5% * Service Years * Final Year’s Salary

1.5% * 17 * $210000 = $ 53550

$53550 * 9.3719 = $ 501865.245

(present value of an ordinary annuity of $1: n=18, i=8)

$501865.245 * 0.2502 = $1255667

(present value of $1: n=17, i=8%)

3)

service cost 2020 = $ 50400 * 9.3719 = $ 472344

$ 472344 * * 0.2502 = $ 118180.

4)

interest cost 2020 = $1255667 * 8% = $ 100453