Sachs Brands\' defined benefit pension plan specifies annual retirement benefits
ID: 2529074 • Letter: S
Question
Sachs Brands' defined benefit pension plan specifies annual retirement benefits equal to: 1.3% × 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 $96,000 at the end of 2018 and the company's actuary projects her salary to be $310,000 at retirement. The actuary's discount rate is 6%.
At the beginning of 2019, changing economic conditions caused the actuary to reassess the applicable discount rate. It was decided that 7% is the appropriate rate. (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:
Calculate the effect of the change in the assumed discount rate on the PBO at the beginning of 2019 with respect to Davenport. (Do not round intermediate calculations. Round your final answer to nearest whole dollar.)
Explanation / Answer
The company’s obligation for the year 2018 is the present value of net obligation at the year 2038. The pension withdrawals are in annual installments, thus the company calculates the present value of 18 pension installments and thereafter the company shows the present value of obligation at 2018.
Plan Benefit Obligation = 310000 * 15yers *1.3%= $60450
Present value of PBO at previous rate @ 6%
($60450 * P.V. of annuity @6% for 18 years) * P.v.@ 6% for 20th Year
=(60450* 10.8276) * 0.3118
= $2,04,082
Present value of PBO at revised rate @ 7%
($60450 * P.V. of annuity @7% for 18 years) * P.v.@ 7% for 20th Year
= (60450 * 10.5909) * 0.25842
= $1,57,138
There will be a gain of ( $204082 - $157138) = $46,944 on PBO due to change in the assumed discount rate.
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