### Accounting

# How To Compute Amortization In Pension Accounting?

Following on my previous post [accounting for pension], this post specifically provides ways to compute amortization both “**Unrecognized Prior Service Cost**” and “**Unrecognized Gain or Loss**” in pension accounting.

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**How To Compute Amortization Of Unrecognized Prior Service Cost?**

**A company may decide to give pension benefits retroactively to employees who performed services prior to the initiation of the pension plan**. For example: if the pension plan was created in 20X5, it may give pension credits to employees for their services prior to 20X5. Thus when these employees retire, say, in 20X9, they will be entitled to benefits both for services performed from 20X5 to 20X9 and for services performed before 20X5. These are called “**prior service costs**”.

Similarly, **a company may decide to make retroactive amendments to its pension plan which increases the amount of benefits to be paid**. These are also called “**prior service costs**“. The question is: **Should these prior service costs be recognized entirely in the year they are adopted?** **Or** **should they be recognized gradually (amortized) over several years?**

**The accounting profession decided in favor of the latter option**. Thus **these costs must be amortized over the remaining service life of these employees**. This can be done in two ways: either via “**straight-line amortization**” or **by assigning to each remaining year of service an amortization fraction**.

**EXAMPLE**: Company ABC has prior service costs of $60,000. It has four employees who are entitled to benefits for these prior services, with remaining expected service periods as follows:

Employee Remaining Years

1 5

2 1

3 2

4 4

**12** total service years

**If we use straight-line amortization**, we divide the $60,000 by the average number of years remaining. **The average is determined by dividing the total remaining years (12) by the number of employees** (4), yielding 3. We thus have: $60,000/3 = $20,000 per year

**EXAMPLE**: Let’s use the same information as in the previous example but **assume each year is assigned its own amortization fraction**. The fractions are computed as follows:

Year 1: 4/12 × $60,000 = $20,000

Year 2: 3/12 × $60,000 = $15,000

Year 3: 2/12 × $60,000 = $10,000

Year 4: 2/12 × $60,000 = $10,000

Year 5: 1/12 × $60,000 = $5,000

**If the employees are going to retire according to a fixed pattern, a method similar to the sum-of-the-years-digits method of depreciation can be used**. Each year receives its own amortization fraction. The numerator is the number of employees who worked this year; **the denominator** (which represents the total service period) **is determined under the following formula**:

Denominator= [(n x (n + 1))/2] xd

** d** represents the decrease in employees each year, n represents the number of physical years remaining from the point the prior service costs are created until the last of the employees affected by these service costs retires.

**EXAMPLE**: On January 1, 20X5, Company DEF amends its pension plan, resulting in prior service costs of $100,000. This amendment affects 100 employees. Twenty of these employees are expected to retire each year; thus by the end of 5 years, they will all be gone. Accordingly, d = 20 and n = 5. The denominator is:

[(n x (n + 1)/2) x

d= [(5(6))/2] x 20 = 30/2 x 20 = 300

**The yearly computations are**:

Year 1: 100/300 × $100,000 = $33,333

Year 2: 80/300 × $100,000 = $27,667

Year 3: 60/300 × $100,000 = $20,000

Year 4:40/300 × $100,000 = $13,000 (rounded)

Year 5:20/300 × $100,000 = $6,667 (rounded)

**How To Compute Amortization Of Unrecognized Gains Or Losses?**

**I Mentioned earlier that one of the five components of pension expense is the return on pension fund assets, and that the expected return, rather than the actual return, is to be used**. Thus **if the actual return was** $10,000 but **the expected return was only** $7,000, **the difference of** $3,000 **is unrecognized and deferred as a gain to future periods** **to be amortized gradually over those periods**. Conversely, **if the actual return was** $7,000 **and the expected return was** $10,000, **the difference of** $3,000 **is an unrecognized and deferred loss**.

There is one additional gain or loss that is currently unrecognized and deferred to future periods: a change in the PBO due to changes in actuarial estimates.

As mentioned earlier, **pension accounting relies heavily on estimates made by actuaries:**

**If the actuaries revise their estimates and increase the PBO**, the difference is a**loss****If they decrease it**, the difference is a**gain**

**These losses or gains are unrecognized and deferred to later periods**.

**How should both of these gains and losses be amortized?**

**The FASB has stated they should be amortized only if they accumulate to a value greater than the** “**corridor amount**” **and only the excess above this value should be amortized**. The procedure is as follows:

- Compare the PBO at the beginning of the year to the market value of the pension fund at that time and choose the larger figure.
- Take 10% of this figure. This is the corridor amount.
- Compare the unrecognized gain or loss at beginning of year to the corridor amount. If it is greater than the corridor amount, amortize the excess over the average remaining service years.

**EXAMPLE**: During 20X7, Company N had an expected rate of return of 10% on its beginning pension fund balance of $100,000. The actual return was 9%. Thus the difference of $1,000 is an unrecognized loss. Also during 20X7, the company actuaries revised the PBO downward by $15,000. **This is a gain**. **We thus have a net unrecognized pension gain** of $14,000 ($15,000 ? $1,000) **which is to be deferred to future periods**.

**EXAMPLE**: Let’s use the same information given in the preceding example involving Company N. At the beginning of 20X8, the pension fund had a balance of $125,000 and the PBO was $135,000. Thus the corridor amount is $13,500 (10% of $135,000), and the excess above the corridor is $500 ($14,000 ? $13,500). If the average remaining service period is 10 years, the amortization of the unrecognized gain is $50 ($500/10). Thus the amount still unrecognized is $13,950 ($14,000 ? $50).

EXAMPLE: Let’s continue with Company XYZ and go to 20X9. At the beginning of 20X9, the pension fund had a balance of $127,000 and the PBO balance was $123,000. The corridor is therefore 10% of $127,000 = $12,700. During 20X8, Company N had a new unrecognized net pension gain of $1,000. The balance of the unrecognized amount would be determined as follows, at January 1, 20X9:

- Balance at January 1, 20X8 $14,000
- Amortized during 20X8 (50)
- New net gain 1,000
- Balance, January 1, 20X9 $14,950

**We now compare this balance to the corridor** of $12,700, **resulting in an excess of** $2,250. **Dividing this by the average service life of 10 years results in amortization of** **$225**.