Actuarial equivalence is the concept that different forms of distributions (e.g. various types of annuities or a one-time lump sum payout), with different payment amounts and/or different times of payment, have the same actuarial present value.

Traditional defined benefit pension plans provide a retiree an annuity benefit where the payment amount is calculated by the plan's formula and is payable as an annuity in the normal form commencing at the normal retirement age. Plans typically offer a variety of optional forms of annuity, and early or deferred commencement -- and this necessitates an actuarial equivalence calculation in order to determine the optional payment amount. A lump sum option is often available, and this necessitates an actuarial equivalence calculation as well.

Other pension plans, including defined contribution plans, provide a retiree a cash amount that is determined by the plan's formula or from an accumulated account balance, that may optionally be converted to an actuarially equivalent annuity benefit.

General formula

Actuarial equivalence is based on the premise that one form of payment has the same present value as another form of payment. The determination is based on form of payment and timing of payments, and assumptions as to interest and mortality, and perhaps future rates of inflation if the benefit is subject to cost-of-living increases.

An actuarial equivalent factor is calculated by this general formula, where  is the normal form of payment and  is the optional form of payment:

When the actuarial equivalent factor has been determined, then  is calculated as

Excel functions

Click here to see the various Excel functions to handle actuarial equivalence functions.