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 2010 and is expected to retire at the end of 2044 after 35 years' service. Her retirement is expected to span 18 years. Davenport's salary is $94,000 at the end of 2024 and the company's actuary projects her salary to be $300,000 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.) At the beginning of 2025, the pension formula was amended to: 1.75% × Service years × Final year's salary The amendment was made retroactive to apply the increased benefits to prior service years.

Required: 1. What is the company's prior service cost at the beginning of 2025 with respect to Davenport after the amendment described above? 2. Since the amendment occurred at the beginning of 2025, amortization of the prior service cost begins in 2025. What is the prior service cost amortization that would be included in pension expense? 3. What is the service cost for 2025 with respect to Davenport? 4. What is the interest cost for 2025 with respect to Davenport? 5. Calculate pension expense for 2025 with respect to Davenport, assuming plan assets attributable to her of $220,000 and a rate of return (actual and expected) of 10%. (For all requirements, do not round intermediate calculations. Round your final answers to the nearest whole dollar.)

1 answer

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

  1. Expected Return: \[ \text{Expected Return} = \text{Plan Assets} \times \text{Expected Return Rate} = 220,000 \times 10% = 22,000 \]

  2. 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:

  1. Prior Service Cost: $15,750
  2. Prior Service Cost Amortization: $875
  3. Service Cost for 2025: $5,250
  4. Interest Cost for 2025: $3,488
  5. Pension Expense for 2025: -$13,387