To solve these pension-related questions for Angela Davenport under Sachs Brands's defined benefit pension plan, we will break down each requirement step by step.
Requirement 1: Prior Service Cost at the Beginning of 2025
Old Plan Formula:
- Retirement Benefit = \(1.6% \times \text{Service Years} \times \text{Final Year's Salary}\)
New Plan Formula:
- Retirement Benefit = \(1.75% \times \text{Service Years} \times \text{Final Year's Salary}\)
Service Years and Final Year’s Salary:
- Service Years = 35 years (from end of 2010 to end of 2044)
- Final Year’s Salary = $300,000 (projected)
Calculate the benefits under both the old and the new plan:
Old Plan Benefit Calculation: \[ \text{Old Benefit} = 1.6% \times 35 \times 300,000 = 0.016 \times 35 \times 300,000 = 168,000 \]
New Plan Benefit Calculation: \[ \text{New Benefit} = 1.75% \times 35 \times 300,000 = 0.0175 \times 35 \times 300,000 = 183,750 \]
Prior Service Cost: \[ \text{Prior Service Cost} = \text{New Benefit} - \text{Old Benefit} = 183,750 - 168,000 = 15,750 \]
Answer Requirement 1:
Prior Service Cost = $15,750
Requirement 2: Prior Service Cost Amortization in 2025
The prior service cost of $15,750 will be amortized over the average remaining service life of employees. Since Angela is retiring in 2044, and she is expected to retire at the end of her 35 years of service, she has no remaining service life as of 2025. Thus, for this calculation, we will consider her full remaining service life to be 18 years at the point of retirement.
For amortization, the formula is: \[ \text{Annual Amortization} = \frac{\text{Prior Service Cost}}{\text{Remaining Service Life}} = \frac{15,750}{18} \approx 875.00 \]
Answer Requirement 2:
Prior Service Cost Amortization = $875
Requirement 3: Service Cost for 2025
Calculate the Service Cost for 2025: Using the new plan formula: \[ \text{Service Cost} = 1.75% \times 1 \times 300,000 = 0.0175 \times 300,000 = 5,250 \]
Answer Requirement 3:
Service Cost for 2025 = $5,250
Requirement 4: Interest Cost for 2025
The interest cost for 2025 is calculated using the projected benefit obligation (PBO) as of the beginning of the year (2025). After the amendment, we refer back to the updated retirement benefit ($183,750) as of the retirement date (2044).
Interest Cost Calculation: Total Interest Cost = PBO at beginning of 2025 × Discount Rate \[ \begin{align*} \text{PBO} & = \text{New Benefit} \times \text{PV Factor} \ & = 183,750 \times \text{PV Factor}(9%, 18 \text{ years}) \ \end{align*} \]
To find the present value factor (PV factor) for 9%, 18 years: Using the present value of $1 table, the PV factor for 9% and 18 years is approximately 0.211.
Calculation: \[ \text{PBO} \approx 183,750 \times 0.211 \approx 38,749.96 \ \]
Now calculate the interest cost: \[ \text{Interest Cost} = 38,749.96 \times 9% = 3,487.50 \]
Answer Requirement 4:
Interest Cost for 2025 = $3,488 (rounded)
Requirement 5: Pension Expense for 2025
Pension Expense = Service Cost + Interest Cost + Prior Service Cost Amortization - Expected Return on Plan Assets
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Expected Return: \[ \text{Expected Return} = \text{Plan Assets} \times \text{Expected Return Rate} = 220,000 \times 10% = 22,000 \]
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Total Pension Expense: \[ \text{Pension Expense} = Service Cost + Interest Cost + Amortization - Expected Return \] \[ = 5,250 + 3,488 + 875 - 22,000 = 8,613 - 22,000 = -13,387 \]
Answer Requirement 5:
Pension Expense for 2025 = -$13,387 (Indicates a gain in pension expense due to expected high return on assets)
In summary, the answers to the requirements are as follows:
- Prior Service Cost: $15,750
- Prior Service Cost Amortization: $875
- Service Cost for 2025: $5,250
- Interest Cost for 2025: $3,488
- Pension Expense for 2025: -$13,387
1 answer