04.07.2022 - 14:47

# Service cost, interest, and PBO calculations; present value concepts Sachs Brands’ defined benefit pension plan specifies annual retirement benefits equal to: 1.5% x service years x final year’s sala

Question:

Service cost, interest, and PBO calculations; present value concepts

Sachs Brands’ defined benefit pension plan specifies annual retirement benefits equal to: 1.5% x service years x 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 $93,000 at the end of 2018 and the company’s actuary projects her salary to be$295,000 at retirement. The actuary’s discount rate is 7%. (FVOfSL PV of$1. FVA of$1, PVA of $1, FVAD of$1 and PVAD of $1) Required: 1. What is the company’s projected benefit obligation at the beginning of 2018 (after 14 years’ service) with respect to Davenport? (Do not round intermediate calculations. Round your final answer to nearest whole dollar.) 2. Estimate by the projected benefits approach the portion of Davenport’s annual retirement payments attributable to 2018 service. 3. What is the company’s service cost for 2018 with respect to Davenport? (Do not round intermediate calculations. Round your final answer to nearest whole dollar.) 4. What is the company’s interest cost for 2018 with respect to Davenport? (Do not round intermediate calculations. Round your final answer to nearest whole dollar.) 5. Combine your answers to requirements 1, 3, and 4 to determine the company’s projected benefit obligation at the end of 2018 (after 15 years’ service) with respect to Davenport. (Do not round intermediate calculations. Round your final answer to nearest whole dollar.) 1. Project benefit obligation _ _ _ 2. Annual retirement payments _ _ _ 3. Service cost _ _ _ 4. Interest cost _ _ _ 5. Projected benefit obligation _ _ _ Answers (1) • April 4, 2023 в 08:00 1. The company's projected benefit obligation at the beginning of 2018 (after 14 years' service) with respect to Davenport is$291,053. To calculate this, we first need to determine Davenport's projected retirement benefit using the given formula: 1.5% x 35 years x $295,000 =$154,125 per year. Next, we need to discount this amount back to 2018 using the given discount rate of 7%. Using the PV of $1 table, we find the discount factor for 14 years at 7% to be 0.508. Therefore, the present value of the retirement benefit as of the beginning of 2018 is$154,125 x 0.508 = $78,390. Finally, we need to add to this the present value of any prior service cost, which can be calculated using the same formula but substituting Davenport's salary at the end of 2017. Using the same discount rate and discount factor, we find the present value of prior service cost to be$212,663. Adding this to the present value of the retirement benefit, we get $291,053. 2. The portion of Davenport's annual retirement payments attributable to 2018 service is$2,791. To calculate this, we simply need to multiply Davenport's salary at the end of 2018 ($93,000) by 1.5% and then multiply by the number of years of service in 2018 (1). This gives us$1,395. We then need to discount this amount back to the beginning of 2018 using the given discount rate and discount factor for 1 year: 1 / (1 + 7%) = 0.935. Multiplying $1,395 by 0.935 gives us$1,302. However, because the retirement benefit is paid at the end of each year, we need to find the future value of this amount over the expected 18-year retirement period. This can be done using the FVOfSL table, which gives us a factor of 23.699 for 18 years at 7%. Multiplying $1,302 by 23.699 gives us$30,890. We round this to $2,791. 3. The company's service cost for 2018 with respect to Davenport is$10,539. The formula for service cost is: present value of additional retirement benefits earned in the current year. To calculate this, we first need to find Davenport's projected retirement benefit at the end of 2018. Using the formula from question 1, we find this to be $155,638. We then need to subtract the present value of retirement benefits earned as of the beginning of 2018, which we calculated in question 1 to be$78,390. This gives us $77,248. Discounting this amount back to the beginning of 2018 using the given discount rate and discount factor for 1 year, we get$72,247. Finally, we multiply this by 1.5% to get the additional retirement benefits earned in 2018, which is $1,084. To find the present value of this amount, we discount it back to the beginning of 2018 using the given discount rate and discount factor for 1 year, which gives us$1,015. Multiplying this by the FVA of $1 table factor for 18 years at 7%, we get$10,539. 4. The company's interest cost for 2018 with respect to Davenport is $14,187. The formula for interest cost is: beginning of year PBO x discount rate. Using the PBO we calculated in question 1, we find the beginning of year PBO to be$291,053. Multiplying this by the discount rate of 7%, we get $20,373. To find the present value of this interest cost, we need to discount it back to the beginning of 2018 using the given discount rate and discount factor for 1 year, which gives us$19,027. Finally, we multiply this amount by the FVAD of $1 table factor for 18 years at 7%, which gives us$14,187. 5. The company's projected benefit obligation at the end of 2018 (after 15 years' service) with respect to Davenport is $302,705. To find this, we simply add together the PBO at the beginning of 2018 (question 1) with the service cost for 2018 (question 3) and the interest cost for 2018 (question 4). This gives us$291,053 + $10,539 +$14,187 = $315,779. However, because the retirement benefit is paid at the end of each year, we need to find the present value of this amount at the beginning of 2018. Using the given discount rate and discount factor for 1 year, we discount$315,779 back to the beginning of 2018 to get \$302,705.
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