Question

Sachs Brands's 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 2007 and is expected to retire at the end of 2041 after 35 years' service. Her retirement is expected to span 18 years. Davenport's salary is $99,000 at the end of 2021 and the company's actuary projects her salary to be $325,000 at retirement. The actuary's discount rate is 9%. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Required:
2. Estimate by the projected benefits approach the amount of Davenport's annual retirement payments earned as of the end of 2021.
3. What is the company's projected benefit obligation at the end of 2021 with respect to Davenport? (Do not round intermediate calculations. Round your final answer to the nearest whole dollar.)
4. If no estimates are changed in the meantime, what will be the company's projected benefit obligation at the end of 2024 (three years later) with respect to Davenport? (Do not round intermediate calculations. Round your final answer to the nearest whole dollar.)

Answer 1

Req. 2 : Calculation of the amount of Davenport's annual retirement payments earned as of the end of 2021 by using the projected benefits approach:

Sachs Brand's defined benefit pension plan specifies annual retirement benefits = 1.6% × service years × final year's salary

=1.6%*15 years(From 2007 to 2021)*$99000

=$23760

Req. 3 : Calculation of company's projected benefit obligation at the end of 2021 with respect to Davenport :

Present Value of the retirement benefits a the end of 2021 = $208034*0.17843 =$37120

(present value of $1: n= 20, i= 9% (from PV of $1)

Working :

Present Value of the retirement annuity as of the retirement date i.e. end of 2041 =$23760*8.75562 =$208034

(present value of an ordinary annuity of $1: n= 18, i= 9% (from PVA of $1)

Req. 4 : Calculation of company's projected benefit obligation at the end of 2024 with respect to Davenport :

Present Value of the retirement benefits a the end of 2024 = $249640*0.23107 =$57684

(present value of $1: n= 17, i= 9% (from PV of $1)

Working :

1.6%*18 Years(From 2007 to 2024)*$99000 =$28512

Present Value of the retirement annuity as of the retirement date i.e. end of 2041 =$28512*8.75562 =$249640

(present value of an ordinary annuity of $1: n= 18, i= 9% (from PVA of $1)