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%. (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 2018.
3. What is the company's projected benefit obligation at the end of 2018 with respect to Davenport? (Do not round intermediate calculations. Round your final answer to 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 2021 (three years later) with respect to Davenport? (Do not round intermediate calculations. Round your final answer to nearest whole dollar.)

Answer 1

Answer 2	Year completed [beginning of 2004 to end of 2018 = 15 years]
	Annual retirement payments (90000*15*1.6%)		$               21,600
Answer 3	Annual retirement payments (90000*15*1.6%)		$               21,600
	Multiply: Present value of annuity table of $1: n=18, i=7%		10.05909
	Present value of annuity		$             217,276
	Multiply: Present value table of $1: n=20, i=7%		0.25842
	Pojected benefit obligation at the end of 2018		$               56,149
Answer 4	Year completed [beginning of 2004 to end of 2021 = 18 years]
	Annual retirement payments (90000*18*1.6%)		$               25,920
	Multiply: Present value of annuity table of $1: n=18, i=7%		10.05909
	Present value of annuity		$             260,732
	Multiply: Present value table of $1: n=17, i=7%		0.31657
	Pojected benefit obligation at the end of 2021		$               82,540

Year	PV factor @7%	Remarks
1	0.93458	= 1 / 1.07
2	0.87344	= 0.93458 / 1.07
3	0.81630	= 0.87344 / 1.07
4	0.76290	= 0.8163 / 1.07
5	0.71299	= 0.7629 / 1.07
6	0.66634	= 0.71299 / 1.07
7	0.62275	= 0.66634 / 1.07
8	0.58201	= 0.62275 / 1.07
9	0.54393	= 0.58201 / 1.07
10	0.50835	= 0.54393 / 1.07
11	0.47509	= 0.50835 / 1.07
12	0.44401	= 0.47509 / 1.07
13	0.41496	= 0.44401 / 1.07
14	0.38782	= 0.41496 / 1.07
15	0.36245	= 0.38782 / 1.07
16	0.33873	= 0.36245 / 1.07
17	0.31657	= 0.33873 / 1.07
18	0.29586	= 0.31657 / 1.07
Total	10.05909
18	0.29586
19	0.27651	= 0.29586 / 1.07
20	0.25842	= 0.27651 / 1.07