Real world examples are complicated. However, to help you understand, in a simplified manner, the general workings of the Actuary in determining the DBO, we ignore decrements (mortality, attrition) and only allow for a benefit to be paid on a retirement date.
Let’s say that a company pays an End of Service Benefit (“EOSB”) upon normal retirement age of 60 years. The benefit is defined as one monthly salary per every year of service (eg 20 years’ work will give 20 months’ salary as a one-off lump sum payment).
Our assumptions are as follows:
- Salaries will grow at 5% for each future year
- Interest/asset return rate is 4% per annum, based on quality bonds, 20-year term
- Guaranteed employment to retirement
- Death is not allowed!
The personal details of the one single employee is as follows:
- Age at Joining Company: 30
- Age at Valuation Date (Now): 40
- Current Monthly Salary is: 5,000
- Normal Retirement Age: 60
- This means Past service is 40 – 30 = 10 years
- This means Future service is 60 – 40 = 20 years (see interest rate assumption)
- This means Total service is 60 – 30 = 30 years (10 + 20)
According to IAS 19, the International Accounting Standards for Employee Benefits, the actuarial funding cost or valuation method to be used is the Projected Unit Credit (PUC) Method.
The simplified calculation stages are as follows:
- Projected Final Salary = Current Salary * (1 + Salary Escalation) ^ (Future Service)
- = Current Salary * (1 + 5%) ^ (60 – 40)
- = 5,000 * (1.05) ^ 20
- = 13,266 at retirement
- Retirement Benefit = Projected Final Salary * Total years service
- = 13,266 * (60 – 30)
- = 13,266 * 30
- = 397,980 as a lump sum
- Projected (all service) Gratuity Amount = 397,980 undiscounted
- Projected gratuity benefit accrued up to age 40
- = Projected Final Salary * Past Service
- = 13,266 * 10
- = 132,660 as the undiscounted DBO
- DBO = 132,660 * (1 + interest rate) ^ (- future service)
- = 132,660 * (1.04) ^ (-20)
- = 60,544 after discounting, reflected in FS
- Unit normal service cost = Projected Gratuity Amount / Total service
- = 397,980 / 30
- = 13,266 per annum undiscounted
- Normal Service Cost = 13,266 * (1.04) ^ (-20)
- = 6,054 Normal or Current Service Cost
This valuation assumes that there will be no service termination or other decrements. However, in real life situations, the actuarial valuation exercise will also consider decrements such as terminations, early retirements, disability, death etc.
The computation gets complicated; the actuary is professionally trained to deal with these mathematical intricacies and probabilities of various exit states.