Selecting the discount rate for the valuation of retirement obligations according to international accounting standards is increasingly in the focus of employers, actuaries, auditors, stock exchange regulators, and the German financial reporting enforcement panel, the Deutsche Prüfstelle für Rechnungslegung. The standards are mainly IAS19, but may also be the relevant US GAAP standards such as FAS87 and FAS106.

One reason for this change in attitude was the introduction of the so-called SORIE-option under IAS 19 that essentially leads to full balance sheet recognition of the portion of the obligation that is not funded by plan assets or the amount of overfunding, if any. Another reason is that US GAAP now requires the recognition of the funded status on the balance sheet.

While in the past employers have often determined the discount rate in relation to other companies of comparable size or in the same industry, auditors and stock exchange regulators nowadays demand that the discount rate reflect the structure of the underlying obligations and be set by a transparent process.

However, some parties tend to view the guidance given in the standards on how the liability valuation ought to be conceptually considered (denoted below as ‘theoretically correct’ or ‘cash flow matching’ method) as a compulsory approach to be followed in practice. Such demands are predominantly voiced in the US where sometimes the provision of expected benefit payments for the next 80-100 years is requested. Proponents justify this by saying that this is now required by the relevant standards1. We do not consider this to be correct, the more so, as the relevant FASB staff position (FSP on Statement 158)2 refers to ‘guidance’ in this context as an abstract process that should lead the reporting entity to proper sources on the basis of which a discount rate is chosen.

The ‘theoretically correct’ method may have its methodical advantages: discussion is then only about the ‘right’ choice of yield curve so that, given different discount rates, the obligation may be valued without consulting an actuary. However, projecting the future cash flow implies extra work that should not be underestimated.

In connection with the revision of FAS132 in 2003, the FASB refrained from requiring the full cash-flow profile, arguing that the expected future benefit payments for the following 10 years are easier to obtain. Indeed, most actuarial advisers in Germany will be able to project the cash flows needed for the ‘theoretically correct’ method. However, these are not usually part of standard DBO calculations and therefore must be derived in additional computations leading to extra costs. That extra cost does not usually justify the additional information gained.

With this background, the accounting working group established by the German Actuarial Association’s committee for employee benefits has taken up the issue of selection of the discount rate on the basis of a given yield curve. A subgroup has discussed practical methods that will typically lead to appropriate results. These methods are described in this article.

The yield curve has been almost flat in recent months (to April 2007), the duration-dependent differences in the discount rate amounted to 25-50bps. In light of this, the relevance of a practical method to select a discount rate that accurately reflects the underlying liability structure does not have such a high priority as in the past. However, it is to be expected that interest rates and the steepness of the yield curve will increase again. Therefore, actuaries should be able to demonstrate that they choose discount rates consistently on the basis of appropriate methods.


Starting point

The ‘theoretically correct’ selection of the discount rate for an actuarial valuation of employee benefit obligations according to IAS19 and FAS87, respectively, would have to be done as follows:

q A projection of the future cash flows of the liabilities accrued as at the balance sheet date is done taking into account all other relevant assumptions. These cash flows are then discounted using the yield curve as at each future date to determine the actuarial present value; and

q The single (‘substitute’) rate to be disclosed is that rate that leads to the same present value.

However, such a method is not always practical as the following constraints apply:

q The valuations are typically performed before the balance sheet date, reworking them on changed assumptions is done only reluctantly;

q The valuation software produces present values but typically not the associated cash flows underlying the DBO computations; and

q The valuations are usually performed under time pressure and are often complex and multifaceted.

The computation of a present value based on a vector of discount rates is also conceivable without an explicit cash flow projection. However, such an approach is typically not feasible with the software currently used by actuaries. Also, a single discount rate cannot be dispensed with as it is to be used for determining the current service cost, past service cost and curtailment/settlement effects. Thus, besides a valuation based on a vector of discount rates additional computations using a single rate would have to be made anyway.

Usually, employers are not prepared to pay for the extra work if their auditor does not object to the use of a single discount rate if this is selected according to a rational, practical method.


Practical method

The aim is to develop a method that allows the derivation of a single discount rate while at the same time meeting all of the following conditions:

q The method must be practicable;

q The method must be transparent to a third party (eg reporting entity, auditor), that is, it must rely on objective facts and be applicable consistently over time;

q The method must suitably take into account the circumstances as at the balance sheet date; and

q The method must yield a discount rate that is derived from the underlying liability being valued, ie take into account the structure of the population and the duration of the obligations.

The following should be borne in mind:

q In order to justify the single (substitute) discount rate, an appropriate, objective, transparent and consistently applied approach is required. The standards do not require the expected cash flows to be determined and then discounted using the yield curve in order to show that the substitute discount rate disclosed leads to the same result;

q The valuation results are estimates. In this respect, the apparent accuracy of the result is always relative. The accuracy and objectivity of the method, its consistent application and the correct application of its principles3 explicitly more important than numerical accuracy.

As at the year-end the required yield curve (assumed in the following to be compliant with the standard) is to be derived from corporate bonds of AA rating. Although there is some scope for discussion, the auditor must be convinced that the method of setting the discount rate meets the above characteristics.


Appropriate method

Several methods have emerged which usually lead to appropriate results. However, these methods are not suitable in all conceivable situations. The actuary should therefore be aware of their limitations and should not apply the methods without due consideration.

1. Duration method

This is the most common method and it works as follows:

In a first step the duration of the underlying population(s) is determined. This may be done by, for example, performing two computations of present values on the basis of the same population with marginally differing discount rates close to the presumed ‘correct’ discount rate. The discount rate sensitivity derived form this is an approximate measure for the (Macaulay) duration at the presumed ‘correct’ discount rate.

The final step consists of reading off the yield curve the substitute discount rate corresponding to the duration obtained in the first step.

This method has the major advantage that the results allow us to estimate effects that changes in the discount rate will have on the valuation result.

For mixed populations or populations consisting of actives and deferred vesteds only (durations of more than 15 years) this method usually leads to appropriate discount rates. However, for populations consisting of retirees only this method leads to discount rates that tend to be slightly too low. Based on the current flat yield curve, the resulting error in the present value is of the order of 1-2%.

In order to adjust for this effect in the situation of a typically shaped yield curve for retiree populations it may be considered to:

q Derive the discount rate for durations that are generally increased by two to three years; or

q Compute the duration based on a discount rate of 0% and use this to read a corresponding discount rate off the yield curve.

The duration in respect of a 0% discount rate reflects the cash flow-weighted mean payment year.


2. Modified duration method

Again, in a first step, the duration of the underlying population(s) is determined.

In a second step typical cash flow profiles (‘model cash flows’) of benefit schemes (eg annuity payments for populations consisting of actives only, retirees only and mixed populations) are taken and modified so that they have the same duration as the population of the reporting entity.

Finally, in a third step based on the duration-adjusted model cash flows thus derived (eg using a solver function) the substitute discount rate is determined according to the ‘theoretically correct’ method.

The actual cash flow profile of the liabilities being valued will usually be similar to the duration-adjusted model cash flow. The resulting discount rate will therefore typically differ only marginally from the discount rate obtained using the ‘theoretically correct’ method.

The setting of the discount rate based on this method will only indirectly depend on the underlying liabilities. In individual circumstances it may therefore be tedious to convince employers and auditors that the method yields appropriate results.


3. Modified theoretically correct method

This method is similar to the modified duration method. Instead of a duration-adjusted model cash flow, the method is based on a model cash flow that is derived from the underlying liabilities being valued.

In a first step, the relevant future cash flows of the underlying population(s) are projected forward. The actuary will not produce such a forecast every year but only every three to five years so that the latest projection will be used as a model cash flow for the following years.

This, of course, assumes that the population does not undergo material changes between two forecasts.

In a second and final step the substitute discount rate is determined according to the ‘theoretically correct method’ based on the cash flow projection.

This method leads to a ‘theoretically correct’ discount rate at the balance sheet date immediately following the performing of a projection. In the following years the model cash flow should still be representative of the population unless major changes have impacted the benefits or the population structure. It should be feasible to convey to employers and auditors that this method yields appropriate results.


1Cf. FAS 87.44A concerning the (theoretical) determination of the discount rate, see appendix

Cf. FAS 87.44A concerning the (theoretical) determination of the discount rate, see appendix

2The purpose of this guidance in paragraphs 44 and 44A of Statement 87 is to direct the employer to the proper sources for selecting assumed discount rates

The purpose of this guidance in paragraphs 44 and 44A of Statement 87 is to direct the employer to the proper sources for selecting assumed discount rates

3Cf. FAS 87.10

Cf. FAS 87.10


Extract of FAS87 Par. 44A:

“Pursuant to paragraph 44, an employer may look to rates of return on high-quality fixed-income investments in determining assumed discount rates. The objective of selecting assumed discount rates using that method is to measure the single amount that, if invested at the measurement date in a portfolio of high-quality debt instruments, would provide the necessary future cash flows to pay the pension benefits when due. Notionally, that single amount, the projected benefit obligation, would equal the current market value of a portfolio of high-quality zero coupon bonds whose maturity dates and amounts would be the same as the timing and amount of the expected future benefit payments….”

Udo Bauer, Raimund Rhiel, Friedemann Lucius and Alf Gohdes are members of the accounting policies working group of the German Association of Pension Actuaries