# Using wind up liability to validate actuarially determined liability

May 30th, 2018

We come across many clients who question us on the size of actuarial liability. We also come across many clients who question us on the movement in actuarial liability during the year. Finally, we also come across many new clients who are not sure of how their previous liabilities were calculated and hence the movement in the liability in the current year.

In most of such cases, we request them to **consider the size of ‘accrued’ or ‘wind-up’ or ‘discontinuance’ liability** (hereinafter referred to as the ‘wind-up liability’) **and relate it to the actuarial liability**. The wind up liability can be easily calculated by the Company from the data provided for actuarial valuation and it provides a good insight into the size of the actuarial liability. Also, the movement in wind up liability can help in understanding the movement in actuarially determined liability.

It is for the above reasons that we at KPAC include wind up liability and comparison of wind up liability with actuarially determined liability in our actuarial valuation reports. And it is for the above reasons that we encourage our clients to question us in case the actuarial liability is significantly lower or higher than the wind up liability. For example, if the actuarial liability is less than 80% of the wind up liability, the Company (as well as the auditor) must **ask, know, understand and be comfortable with the reason for the same**.

**In case the actuarial liability is significantly lower compared to the wind up liability, it could be an indication of weak assumptions or incorrect determination of liability.** Similarly, in case the actuarial liability is significantly higher compared to the wind up liability, it could be an indication of overly strong assumptions.

In this article, we explore in detail what wind up liability is and how it can be used to gain better control on your actuarially valued liabilities.

### What is wind up liability or discontinuance liability or accrued liability?

Wind up liability or discontinuance liability or accrued liability is the amount that would be payable to the employees if all the obligations were to be **settled immediately**. It is typically calculated ignoring the vesting criteria.

For example, in case of gratuity benefit, consider an employee with 10 years of past service and a basic salary of Rs. 100,000 per month. The wind up liability for this employee would be Rs. 576,923, which is simply calculated as Rs. 100,000 * 10 (years) * 15 / 26.

Similarly, in case the above employee had, say, 22 days of outstanding leaves to his credit, then the wind up liability for this employee for leave encashment would be Rs. 73,333, which is simply calculated as Rs. 100,000 * 22 (leave days) / 30 (days in a month).

It should be noted that the wind up liability, when being used to validate actuarial liability, is typically calculated ignoring the vesting criteria, if any. This is because actuarial liability is calculated in respect of employees who haven’t completed the vesting criteria as well (e.g. 5 years in case of gratuity). The actuarial liability does allow, through use of attrition rates, for the possibility that employees may leave before they meet the vesting criteria. Thus, putting a value of zero as wind up liability for employees who have not completed the vesting criteria will make the comparison of actuarial liability inconsistent.

### Simple worked example – earned leave encashment valuation

Consider a company with 100 employees. Consider the valuation inputs and results for this entity in the table below:

As can be seen from the above table, the accrued or wind up liability for 100 employees is Rs. 23,293,287. The actuarial valuation results are given based on discount rate of 8% per annum, attrition rate of 10% per annum (for all ages) and four different salary growth rate assumptions i.e. 7% p.a., 8% p.a., 9% p.a. and 10% p.a.

As one can notice from the above table, **when the salary growth rate is equal to discount rate** (i.e. both are 8% p.a.), **the actuarial liability is extremely close to the accrued or wind up liability** (in fact, the ratio of actuarial liability to wind up liability is 100%).

In the scenario where the salary growth rate is more than the discount rate, the actuarial liability is more than the wind up liability. The extent to which it is higher depends up on the duration of the liability. For example, when the salary growth rate is higher than discount rate by 1% per annum (i.e. salary growth rate is 9% p.a.), the actuarial liability is about 8% higher compared to wind up liability. Similarly, when the salary growth rate is higher than discount rate by 2% per annum (i.e. salary growth rate is 10% p.a.), the actuarial liability is about 16% higher compared to wind up liability. As you shall be able to notice, in both cases, the increase in liability for 1% change in salary growth rate depends on the duration of liability.

Thus, if one knows the salary growth rate, discount rate and the duration (which can be approximately inferred based on the assumed attrition rate), the range of actuarial liability can be easily determined. This can be used to validate actuarial valuation results.

Let us now consider an example of gratuity liability.

### Simple worked example – gratuity valuation

Consider a company with 100 employees with average past service of about 4 years. Consider the valuation inputs and results for this entity in the table below:

As can be seen from above table, the wind up liability for 100 employees is Rs. 80,32,725. The actuarial valuation results are given based on discount rate of 8% per annum, attrition rate of 10% per annum (for all ages) and four different salary growth rate assumptions i.e. 7% p.a., 8% p.a., 9% p.a. and 10% p.a.

As one can notice from the above table, **when the salary growth rate is equal to discount rate, the actuarial liability is 10% lower than accrued liability**. Whilst the actuarial liability should have been close to the wind up liability (given that the salary growth rate and discount rate are equal), it is lower to reflect that fact that the average past service of employees is 4 years and that there is a 10% probability (basis the chosen attrition rate of 10% per annum) that the employees will not satisfy the vesting condition and hence the gratuity benefit will not be payable.

Thus, in case of gratuity, if one knows the salary growth rate, discount rate, average past service (which can be estimated from the data) and the duration (which can by approximately inferred based on the assumed attrition rate), the range of actuarial liability can be easily determined. Again, this can be used to validate actuarial valuation results.

### How can wind up liability help?

Thus, as can be noticed from above examples, the wind up liability can be used to validate the actuarial liability. Typically, the actuarial liability will be higher than wind up liability if the salary growth rate is greater than discount rate and vice versa.

The extent to which the actuarial liability is higher or lower than the wind up liability depends on the following:

- Difference between the salary growth rate and the duration of liability. If the salary growth rate is lower than discount rate by, say, 1% and the duration is 10 years, then one would expect the actuarial liability to be around 90% of the wind up liability (ignoring other factors);
- Attrition Rate, which affects the probability of people completing the vesting criteria (e.g. 5 years in case of gratuity) and hence can result in the actuarial liability being lower than the wind up liability.
- Leave availment rate: In leave encashment valuations, in case a leave availment rate is used, then the ratio may be higher than that implied by the relationship between salary growth rate and discount rate. This is because projected leave availments are valued on gross salary and the accrued liability for leave is typically calculated on encashment salary (which is basic salary in most organizations). Thus, typically, higher the rate of assumed leave availment in the valuation, higher will be the actuarial liability compared to wind up liability.

Please note that the above three points are not exhaustive as there are other aspects (e.g. limit on gratuity benefit) which can impact the relationship between actuarial liability and wind up liability. However, the above three points are the key points impacting the relationship between actuarial liability and wind up liability.

### Concluding Thoughts

Considering wind up liability can be of great use in validating actuarial liabilities. In particular, one must understand if there is large difference in the actuarial liability and the wind up liability. In case the actuarial liability is significantly lower compared to the wind up liability, it could be an indication of weak assumptions or incorrect valuation. Similarly, in case the actuarial liability is significantly higher compared to the wind up liability, it could be an indication of overly strong assumptions. In either case, the organization must be comfortable with the gap between the wind up liability and the actuarial liability.

I thank you for reading this note and welcome any comments or recommendations or observations you may have on the subject. You can direct those to the email address mentioned below.

**Khushwant Pahwa, **FIAI, FIA, B Com (H)

Founder and Consulting Actuary

**KPAC (Actuaries and Consultants)**

k.pahwa@kpac.co.in

www.kpac.co.in