Retiree

Study guides: Exam CP-321, Exam RET-101

A retiree is a former employee who has left active service and is receiving, or is entitled to, benefits from a plan sponsor's retirement plan or post-retirement welfare plan — a pension, retiree health coverage, retiree life insurance. In a valuation a retiree's benefit is fully accrued: no more service is earned, so the obligation is simply the expected present value of the benefits still to be paid.

$\text{Obligation}_x = \sum_{t \geq 0} v^{t}\, {}_{t}p_{x}\, B_{x+t}$

$B_{x+t} = s\; c_{x+t}\,(1+h)^{t}$

$x$ is the retiree's age, ${}_tp_x$ the probability of surviving $t$ years (mortality), $v$ the discount factor at the discount rate, and $B_{x+t}$ the benefit expected at age $x+t$ . For a pension, $B$ is the annuity payment (with any indexation); for retiree health, $c_{x+t}$ is the per capita claims cost at that age, $h$ the health care cost trend, and $s$ the share the plan pays after retiree contributions and any government program.
Because a retiree earns no further service, the retiree's whole obligation is accrued liability: under IAS 19 the defined benefit obligation equals the full expected present value, and there is no current service cost — the same split as accrued liability and normal cost for an active member.
Risks a retiree faces (RET-101): outliving savings (longevity), inflation eroding fixed income, investment and interest rate risk on savings and annuity purchase, rising health and long-term care costs, the death of a spouse, cognitive decline, and the sponsor reducing or ending a benefit.
Plan design moves those risks: a life annuity form pools longevity, indexation absorbs inflation, joint-and-survivor forms protect the spouse, and retiree health design (caps on the employer subsidy, defined-dollar accounts, a pre-65 bridge) decides how much health cost risk stays with the sponsor and how much passes to the retiree.

Retiree Health Obligation for a Pre-65 Bridge A retiree aged $62$ is covered by an employer plan until $65$ , when a government plan takes over. The per capita claims cost at $62$ is $\$9{,}000$ , rising $4\%$ a year with age; health care trend is $6\%$ ; the retiree pays $30\%$ of cost. Survival: ${}_1p_{62} = 0.99$ , ${}_1p_{63} = 0.985$ . Discount at $4\%$ ; costs are paid at the start of each year. Compute the employer's obligation.
Answer Employer cost each year is $0.70 \times 9{,}000 \times (1.04)^t (1.06)^t$ :
 $\begin{align*} B_{62} &= 0.70 \times 9{,}000 \\ &= 6{,}300.00 \\ B_{63} &= 0.70 \times 9{,}921.60 \\ &= 6{,}945.12 \\ B_{64} &= 0.70 \times 10{,}937.57 \\ &= 7{,}656.30 \end{align*}$ 
 $\begin{align*} \text{Obligation} &= 6{,}300 + 0.99\,v\,(6{,}945.12) \\ &\quad + 0.97515\,v^{2}(7{,}656.30) \\ &= 6{,}300.00 + 6{,}611.22 + 6{,}902.77 \\ &= 19{,}813.99 \end{align*}$ 
The employer's obligation is about $\$19{,}814$ . Aging and trend together grow the cost $10.2\%$ a year, more than the discount rate pulls it back — which is why trend is the assumption retiree health valuations argue about most.

Longevity Risk in a Drawdown vs. an Annuity A $65$ -year-old retiree has $\$500{,}000$ and plans to withdraw $\$35{,}000$ at the start of each year while the balance earns $4\%$ . An insurer quotes an annuity-due factor of $14.2$ at $65$ . How long does the drawdown last, and what life income would the annuity buy?
Answer The drawdown runs out when $35{,}000\,\ddot{a}_{\overline{n}|} = 500{,}000$ :
 $\begin{align*} \ddot{a}_{\overline{n}|} &= 500{,}000 / 35{,}000 \\ &= 14.2857 \\ 1 - v^{n} &= 14.2857 \times 0.03846 \\ &= 0.5495 \\ n &= -\ln(0.4505) / \ln(1.04) \\ &= 20.3 \end{align*}$ 
 $\begin{align*} \text{Annuity income} &= 500{,}000 / 14.2 \\ &= 35{,}211 \end{align*}$ 
The drawdown is exhausted a little after age $85$ ; the annuity pays slightly more, for life. The retiree who self-insures bears the whole tail of the survival curve, while the annuity pools it — the core RET-101 argument for annuity forms in plan design, against which the retiree gives up liquidity and any bequest.

How it appears on the exam

RET-101 (Participant Risks): written answers that identify the risks a retiree faces and say which plan design features (annuity form, indexation, survivor benefits, retiree medical) manage each, or where a sponsor's goals contradict them.

CP-321 (Retiree Group Benefits): a retiree health valuation — per capita costs by age, trend, contributions, survival and discount — to give the obligation, often with a change in design (a cap, a bridge ending at 65) to evaluate.

CP-321 also asks, in writing, for design proposals that manage retirees' risks and for advice to a sponsor choosing retiree health design elements.

Exam traps

Charging service cost on a retiree: a retiree accrues no further service, so the whole value is accrued obligation; a positive retiree "service cost" is the giveaway.

Applying trend without aging (or the reverse): $c_{x+t}(1+h)^t$ needs both; dropping aging understates a retiree health obligation materially.

Forgetting retiree contributions or the government plan offset: the plan's share $s$ applies to gross cost, not the other way round.

Treating a lump sum as protection against longevity: a drawdown that lasts to life expectancy leaves roughly half of retirees outliving it.