Using wind up liability to validate actuarially determined liability

We often come across clients (and auditors) who want to understand how to validate the high-level movement in the actuarial liabilities during the inter-valuation period or how to perform high level checks on the overall size of the liability to ensure they understand the liability and its drivers.

In such cases, we suggest our clients 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.

As a general rule, the actuarial liability tends to be in a reasonable range of the wind-up liability. However, where the actuarial liability is significantly lower or higher than the wind up liability (say less than 80%), the company may want to analyze and understand the reasons for same to ensure they feel comfortable with the overall liability figures.

There could be many (company specific) reasons which may result in a significantly lower or higher actuarial liability compared to the wind-up liability such as high attrition, difference between salary growth rate and discount rate etc. Whilst these differences may justly result in a significantly different actuarial liability, it is essential that the company is aware of and understands the reason for these differences to gain a better control on their actuarially valued liabilities.

What is wind-up liability?

Wind-up liability (also referred to as 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 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.