###### Study Notes for CFA® Level II – Eco ...

Reading 6: Currency Exchange Rates: Understanding Equilibrium Value -a. Calculate and interpret the... **Read More**

The pension obligation is measured as the present value of future benefits that the employees earn for services provided to date under both IFRS and US GAAP. It is denoted as the present value of defined benefit obligation (PVDBO) under IFRS and projected benefit obligation (PBO) under US GAAP.

Here are the three ways of measuring pension obligation:

PBO is the actuarial present value at the assumed discount rate of all future pension benefits earned to date, based on expected future salary increases. It measures the obligation of the company on a going concern assumption.

ABO is the actuarial present value of benefits (whether vested or non-vested) earned to date based on current salary levels, ignoring future salary increases. The accumulated benefit obligation differs from the projected benefit obligation in that it makes no assumption about future salary levels.

VBO is the actuarial present value of vested benefits.

We can link those three measures mathematically as:

$$ VBO < ABO < PBO $$

We use the following formula:

$$\begin{align*} \text{PBO} & \text{ at the end of the year} \\ & \text{= PBO at the beginning of the year} \\ & \text{+ Current service cost}\\ & \text{+ Interest cost}\\ & \text{+ / (-) Actuarial gains / (losses) }\\ & \text{+ Plan amendments}\\ & \text{- Benefits paid} \\ \end{align*}$$

Where:

**PBO at the beginning of the year** is the closing obligation at the end of the previous year or the present value of benefits earned in prior years. Mathematically,

$$\text{PBO at the beginning of the year}=\frac{\text{Benefits earned in prior years}}{(1+\text{Discount date})^{\text{Years until retirement}}}$$

**Current service cost** refers to the increase in the present value of a defined benefit obligation as a result of employee service in the current period.

**Interest cost** is the increase in the present value of the defined benefit obligation due to the passage of time:

$$ \text{Interest cost} = \text{Opening pension obligation} × \text{Discount rate} $$

**Vesting** is a provision in pension plans where an employee gains rights to future benefits only after meeting specific criteria, such as a pre-specified number of years of service. Fluctuations of estimates and assumptions about future salary increases, the discount rate, and the expected change in vesting cause changes in the present value of the defined benefit obligation. If the change in the pension obligation is **positive**, it is an **actuarial loss**, and an adverse change in the pension obligation is an **actuarial gain**.

ABC Company sets up a DB pension plan. A newly employed personnel has a salary of £90,000 in the coming year. Let’s assume that he has 10 years of service before retiring. The assumed discount rate is 10%, and the assumed compensation increase is 6% per annum.

For simplicity in this calculation, we make further assumptions:

- No changes in actuarial assumptions.
- The company awards its employees all compensation increases on the first day of the service year.
- No additional adjustments are made to reflect the possibility that the employee may leave the company at an earlier date.

What is the closing benefit obligation in Year 1?

The steps for calculation of closing defined benefit pension obligation for this employee for the first year are as follows:

Breaking down the information given, we have:

$$\begin{array}{l|c} \textbf{Current salary }& \text{ £90,000}\\ \text{Years to retirement}&\hline10\\ \text{Annual compensation increase}&\hline6\%\\ \text{Discount rate}&\hline10\%\\ \end{array}$$

$$\begin{align*}&=\text{Current Salary} ×[(1+\text{Annual compensation increase})^{\text{Years to retirement}-1}]\\&=\text{£90,000}×1.06^{9}\\&=\text{£152,053}\end{align*}$$

At the end of Year 2, assuming the actual increase in employee’s salary was 6%, the final year’s estimated salary is:

$$\begin{align*}=£95,400 × [(1.06)^{8}] = £152,053, \text{same result as above.}\end{align*}$$

Where,

$$\begin{align*}=95,400=\text{Year 2 salary}= £90,000×1.06\end{align*}$$

If ABC Company pays the benefit as a lump sum upon retirement, then a lump sum pension benefit equal to 4%, i.e. (10%-6%) of the employee’s final salary for each year of service after the commencement date.

The lump-sum payable on retirement is given by:

$$\begin{align*}&=\left( \text{Final salary}\times \text{Benefit formula}\right) \times \text{Years of service}\\&=\text{£152,053} \times 0.04 \times 10 \\&=\text{£60,821}\end{align*}$$

$$\begin{align*}\text{Annual benefit (unit credit) per service year}&=\frac{\text{Value at retirement}}{\text{Years of service}}\\&=\frac{\text{£60,821}}{10}\\&=\text{£6,082}\end{align*}$$

$$\begin{array}{l|r} \textbf{Year}&1\\ \hline \text{Estimated annual}&{}\\ \text{to:}&{}\\ \hline \text{Prior year}&\text{£0.00}\\ \hline \text{Current year}&\text{£6,082}\\ \hline \text{Total benefits}&\text{£6,082}\\ \text{earned}&{}\\ \hline \text{Opening obligation}&\text{£0.00}\\ \hline \text{Current service}&\text{£14,341}\\ \hline \text{costs}&{}\\ \hline \text{Closing obligation}&\text{£14,341}\\ \end{array}$$

Where:

$$\text{The benefit attributed to prior years} = \text{Annual unit credit}\times\text {Years of prior service}$$

$$\text{The benefit attributed to current year} = \text{Annual unit credit based on benefit formula} = \text{Final year’s estimated salary}\times \text{Benefit formula}$$

$$\text{Opening obligation}=\frac{\text{Benefits earned in prior years}}{1+\text{Discount rate}^{\text{Years until retirement}}}$$

$$\text{Interest cost}=\text{Opening obligation}\times\text{Discount rate}$$

$$\text{Current service costs}=\frac{\text{Benefit per service year}}{(1+\text{Discount rate})^{\text{Years until retirement}}}$$

$$\text{Closing Obligation}=\frac{\text{Total benefits earned}}{(1+\text{Discount rate})^{\text{Years until retirement}}}$$

$$ \text{Fair value of plan assets at the year-end = Fair value of plan assets at the year start + Actual returns on assets + Employer contributions – Benefits paid} $$

As discussed in the previous learning outcome, it is a requirement under both IFRS and US GAAP for companies to report the funded status on their balance sheets.

$$ \text{Funded status = Fair value of the plan assets – PV of the Defined benefit obligation} $$

Overfunding results from a positive funded status while underfunding is due to negative funded status.

Net pension liability is an amount equal to the net underfunded pension obligation, and net pension asset is an asset equal to the overfund pension obligation.

When a company has a surplus, the amount of assets that it reports is the lower of the overfund and the asset ceiling.

The **asset ceiling** refers to the present value of future economic benefits, such as refunds from the plan or reductions of future contributions.

Company XYZ has a present value of defined benefit obligation of £5,000, and the fair value of the pension plan assets is £8,830. The company has available future refunds and reductions in future contributions with a present value of £2000.

Another Company PWF has a present value of defined benefit obligation of £3,350, and the fair value of the pension plan assets is £1,500.

The amount that each company would report as a pension asset or liability on its balance sheet is *closest *to:

**Company XYZ**

$$\begin{array}{l|l} \text{The present value of the defined benefit }&\text{£5,000}\\ \text{obligation}&{}\\ \hline \text{The fair value of plan assets}&\text{£8,830}\\ \hline \text{Net pension assets}&\text{£3,830}\\ \end{array}$$

Company XYZ’s pension plan has an overfund of £3,830, which is the amount by which the fair value of the plan’s assets exceed the defined benefit obligation (£8,830 − £5,000).

Recall that when a company has an overfund in a defined benefit plan, it reports an asset amount, which is the lower of the overfund and the asset ceiling. In this case, the asset ceiling is £2,000, so the amount of company XYZ’s reported net pension asset would be limited to £2,000.

**Company PWF**

$$\begin{array}{l|l} \text{The present value of the defined benefit}&\text{£3,350}\\ \text{obligation}&{}\\ \hline \text{The fair value of plan assets}&\text{£1,500}\\ \hline \text{Net pension liability}&\text{£1,850}\\ \end{array}$$

PWF Company would report the full underfunded status of its pension plan, which is a net pension liability of £1,850.

## Question

ABC Company sets up a DB pension plan. A newly employed personnel has a salary of £90,000 in the coming year. Let’s assume that he has 10 years of service before retiring. The assumed discount rate is 10%, and the assumed compensation increase is 6% per annum.

For simplicity in this calculation, assume the following:

- No changes in actuarial assumptions.
- The company awards its employees all compensation increases on the first day of the service year.
- No additional adjustments are made to reflect the possibility that the employee may leave the company at an earlier date.
What are the interest cost and the current service costs for year 2?

A. Interest cost = £284 and current service costs = £13,037.

B. Interest cost = £1,840 and current service costs = £6,837.

C. Interest cost = £2,500 and current service costs = £2,586.

## Solution

The correct answer is A.To calculate the interest cover, we first need to compute the opening PBO for year 2.

$$\begin{align*}\text{Opening PBO for year 2}&=\frac{\text{Benefits earned in year 1}}{(1+\text{Discount rate})^{\text{Years until retirement}}}\\&=\frac{6,082}{(1.10)^{8}}\\&=\text{£2,837}\end{align*}$$

$$\begin{align*}\text{Interest cost}&=\text{Opening pension obligation}\times\text{Discount rate}\\&=\text{£2,837}\times0.10\\&=\text{£284}\end{align*}$$

$$\begin{align*}\text{Current service costs}&=\frac{\text{Benefit per service year}}{(1+\text{Discount rate})^\text{Years until retirement}}\\&=\frac{6,082}{(1.10)^{8}}\\&=\text{£13,037}\end{align*}$$

Reading 10: Employment Compensation: Post-Employment and Share-Based

LOS 10 (b) *E**xplain and calculate measures of a defined benefit pension obligation (i.e., the present value of the defined benefit obligation (PVDBO) and projected benefit obligation (PBO) and net pension liability (or asset)*