When an actuary values your gratuity or leave encashment obligation, they apply a discount rate to convert projected future cashflows into a present value. Both AS 15 and Ind AS 19 require this discount rate to be derived from government bond yields — specifically, bonds whose term is consistent with the term of the obligation being valued. To apply this requirement correctly, the actuary must first determine what the "term of the obligation" actually is.
Where the Requirement Originates
Under AS 15, Para 78 states that the discount rate must be determined by reference to market yields at the balance sheet date on government bonds whose term is consistent with the estimated term of the obligation. Ind AS 19, Para 83, carries an equivalent requirement, additionally permitting reference to high-quality corporate bond yields where a deep market exists — though in India, the absence of a deep corporate bond market means government securities remain the reference.
The source of government bond yields used in India is FBIL (Financial Benchmarks India Pvt. Ltd.), authorised by the Reserve Bank of India for valuation of Government Securities since 31 March 2018, having taken over from FIMMDA. The CCIL (Clearing Corporation of India Limited) zero-coupon yield curves are also widely used, particularly by firms that rely on NSE-traded bond data.
Macaulay Duration — The Standard Measure
The term of obligation is measured using Macaulay Duration, which is the weighted average time until cashflows are received, expressed in years. The weights are the present values of individual cashflows relative to the total present value of all cashflows.
CFₖ = Amount of the k-th projected cashflow
tₖ = Time (in years) when the k-th cashflow is paid
PV(CFₖ) = Present value of that cashflow at the discount rate
PV(All CFs) = Present value of the defined benefit obligation (DBO)
Macaulay Duration is measured in years and represents the weighted average maturity of the liability's cashflow stream. A higher duration means the obligation's cashflows are, on average, further in the future — which matters because longer-dated bond yields are typically different from shorter-dated yields, and the shape of the yield curve varies over time.
Modified Duration — A Related but Distinct Concept
Modified Duration is a different measure — it captures the sensitivity of the obligation's present value to changes in the discount rate. Specifically, it measures the percentage change in the present value of the obligation for a one percentage point change in the discount rate.
PV = Present value of all projected cashflows (the DBO)
i = Discount rate (interest rate)
∂PV/∂i = Rate of change of PV with respect to the discount rate
Numerically, Macaulay Duration and Modified Duration are close in value for typical employee benefit obligations (they differ by a factor of 1/(1+i), which is small when i is small). Conceptually, however, they are distinct: Macaulay Duration is a time measure; Modified Duration is a price sensitivity measure. For the purpose of selecting a discount rate under AS 15 or Ind AS 19, Macaulay Duration is the relevant concept — you are matching the maturity of a bond to the weighted average maturity of the obligation's cashflows.
In the Context of Employee Benefits
For post-employment benefit plans, the "cashflows" in the duration formula are the projected benefit payments — the amounts expected to be paid to employees at each future date, modelled using the plan's benefit formula and the actuarial assumptions (salary escalation, attrition, mortality, retirement age). These cashflows extend many years into the future, particularly for young or mid-career employee populations.
The present value referenced in the formula is the Defined Benefit Obligation (DBO) as at the valuation date. The discount rate used in the discounting is the same rate being informed by the duration exercise — which means, in practice, the duration is solved iteratively or the actuary uses a reasonable initial estimate of the discount rate to compute the duration and then selects the matching bond yield.
| Measure | What It Means | Unit | Used For |
|---|---|---|---|
| Macaulay Duration | Weighted average time to cashflows | Years | Selecting the discount rate |
| Modified Duration | % change in DBO per 1% change in discount rate | Dimensionless | Sensitivity analysis |
Common Misconceptions
Duration is not the same as average future service
The term of obligation is not equal to the average number of years until each employee retires. Average future service is a simple arithmetic mean and ignores the time value of money and the shape of the benefit cashflow curve. Duration properly weights each cashflow by its present value, which may produce a materially different result, particularly for plans where large lump-sum payments occur at retirement.
Duration is not the average age of the workforce
Some companies mistakenly derive a duration estimate from average employee age. This is not supported by the accounting standards and will typically produce an incorrect discount rate. The duration must be computed from the projected cashflows of the specific benefit being valued.
Practical Implication: Choosing the Right Bond Yield
Once the duration is established — say, 11 years — the actuary looks up the government bond yield at the 11-year maturity on the FBIL or CCIL yield curve as at the balance sheet date. This is the discount rate to be used for the valuation. If the yield curve is not flat (and it rarely is), using a 10-year bond yield when the duration is 14 years can meaningfully understate the discount rate and overstate the liability — or vice versa.
This is why the discount rate is not a generic "market rate" — it is a specifically computed rate tied to the measured duration of the specific obligation being valued.
What Should You Do?
- Ask your actuary to disclose the duration of the obligation (in years) as part of the standard valuation report. This is a required disclosure under Ind AS 19 and best practice under AS 15.
- Verify that the discount rate used is consistent with the government bond yield at the reported duration — particularly in years where the yield curve is steeply sloped.
- Where the duration changes significantly year-on-year (due to workforce changes, benefit amendments, or assumption changes), understand the impact on the discount rate — this is a legitimate source of actuarial gains or losses.