pension modes except German and U.K.

A modified cash refund annuity is a payment form typically used by contributory pension plans, in which a plan participant’s contributions (typically with interest) are due to his/her beneficiary(ies) in the event he/she dies before receiving all of the contributions in the form of annuity payments. In ProVal, this guaranteed amount is entered for inactive participants as a database field containing the guaranteed amount at the Valuation Date or as a Benefit Formula Component for active participants.

The liability in any decrement year is the sum of two liabilities:

1. The liability arising from the annuity payment, contingent on the member’s survival.

2. The liability arising from the payment of any remaining cash refund, contingent on the member’s death.

The guaranteed amount will increase during the deferral period, if any, in accordance with the rates specified for the Modified Cash Refund Annuities category of the Interest & Crediting Rates topic of the Valuation Assumptions Command. Once annuity payments commence, interest is no longer applied to the guaranteed amount and the “remaining cash refund” is calculated by subtracting cumulative annuity payments from the initial guaranteed amount, determined as of:

• the benefit commencement date, for active participants,

• the benefit commencement date, for inactive participants with benefit payments deferred as of the valuation date and

• the valuation date, for inactive participants in receipt of benefit payments on the valuation date.

Cumulative annuity payments are calculated by summing the following two items:

1. Cumulative annuity payments in prior decrement years.

2. Annuity payments in the current decrement year, adjusted for an approximate UDD (uniform distribution of death) assumption.

Note that if the payment form is temporary, the cash refund will expire at the end of the temporary period, regardless of whether any cash refund amount remains when annuity payments stop. In addition, the liability arising from the payment of the cash refund upon member death is always valued assuming the refund is paid at the end of the year of death, regardless of the payment timing selected under Plan Attributes.

The present value can be represented formulaically as the present value of the single life annuity plus the present value of the guaranteed amount. The formula below breaks the present value of the guaranteed amount into the part attributable to any deferral period and the part attributable to commencement of the annuity.

Where:

x = age on valuation date,

r = age when benefit commences,

w = age when probability of death becomes 100%,

t = number of years from valuation date,

Adj = payment frequency adjustment (see Present Values: benefits payable (m)thly for details)

Annuity_t = annuity payable at time t,

Guarantee = amount, as of the valuation date for inactive participants or the date of decrement for active participants, guaranteed to be paid,

Guarantee_r = amount guaranteed to be paid as determined at the date the annuity commences,

i_s = interest rate applied during the deferral period at time s, and

Adj_mcr = payment form adjustment for guaranteed amount, for beginning of period annuity payments and for end of period annuity payments, where m is the number of annuity payments made during the year.

Example

A 62 year-old retiree has an annual single life annuity of $1,000, with a cash refund amount of $8,500 on the valuation date. With payments assumed monthly at the beginning of period and an interest discount of 8%, the liability would be developed as follows:

 

The cumulative annuity payments of $2,541.67 at age 64 are calculated by summing (a) $1,000 paid at ages 62 and 63, and (b) $1,000 payable at age 64, adjusted by a factor of 13/24. This total is subtracted from $8,500 to arrive at the remaining cash refund.