Question

Sachs Brands’ defined benefit pension plan specifies annual retirement benefits equal to: 1.6% × service years × final year’s salary, payable at the end of each year. Angela Davenport was hired by Sachs at the beginning of 2004 and is expected to retire at the end of 2038 after 35 years’ service. Her retirement is expected to span 18 years. Davenport’s salary is $90,000 at the end of 2018 and the company’s actuary projects her salary to be $240,000 at retirement. The actuary’s discount rate is 7%.

a)  Estimate by the accumulated benefits approach the amount of Davenport’s annual retirement payments earned as of the end of 2018.

b)What is the company's accumulated benefit obligation at the end of 2018 with respect to Davenport?

c)If no estimates are changed in the meantime, what will be the accumulated benefit obligation at the end of 2021 (three years later) when Davenport’s salary is $100,000?

Answer 1

a) Annual retirement payments earned as on the end of 2018 = 1.6% * service years * final year's salary

= 1.6% x 15 x $90,000 = $21,600

b) Company's accumulated benefit obligation at the end of 2018:-

The present value of the retirement annuity as of the retirement date (end of 2038) is:

$21,600 x 10.05909* = $217,276

* Present value of an ordinary annuity of $1: n = 18, i = 7%

The ABO is the present value of the retirement benefits at the end of 2018:

$217,276 x .25842* = $56,148

* Present value of $1: n = 20, i = 7%

c) If no estimates are changed, the accumulated benefit obligation at the end of 2021 (three years later) when Davenport’s salary is $100,000 should be computed as follows:-

1.6% x 18 x $100,000 = $28,800

$28,800 x 10.05909* = $289,702

$289,702 x 0.31657** = $91,711

*    Present value of an ordinary annuity of $1: n = 18, i = 7%

** Present value of $1: n = 17, i = 7%