Joint-and-Survivor Pension Election at Retirement
A married couple, both age 65, is choosing how to take the husband's defined-benefit pension. The single-life annuity is $60,000 per year, paid monthly for as long as the husband lives. The joint-and-two-thirds option pays $52,000 per year while both are alive and two-thirds of that amount to the survivor after the first death. The plan's actuarial assumptions are 4% annual interest and the following annuity factors: male age 65, a_65 = 12.8; female age 65, a_65 = 14.6; joint-and-last-survivor factor for both alive, a_65:65 = 10.5. The husband has recently been diagnosed with a condition that reduces his expected remaining lifetime by roughly four years; the plan's standard table does not reflect this. The wife is in excellent health and has no pension of her own. The couple has two adult children and a modest bequest motive. They ask whether the joint option is worth the $8,000 annual reduction and how the husband's health changes the comparison. Ignore taxes and COLAs.
1. Using the provided annuity factors, compute the expected present value of each option under standard mortality. Which is larger?
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Single-life option: EPV = 60,000 x a_65(male) = 60,000 x 12.8 = 768,000.
For the joint-and-two-thirds option, the factor is the joint annuity while both are alive plus two-thirds of each single-life annuity while exactly one is alive. Since a_male_only = a_male - a_joint = 12.8 - 10.5 = 2.3, a_female_only = a_female - a_joint = 14.6 - 10.5 = 4.1, the joint-and-two-thirds factor is a_J2/3 = 10.5 + (2/3)(2.3 + 4.1) = 10.5 + (2/3)(6.4) = 10.5 + 4.2667 = 14.7667. EPV = 52,000 x 14.7667 = 767,868.
Under standard mortality the two options are essentially equal in EPV: about 768,000 for the single life and about 767,900 for the joint-and-two-thirds. The $8,000 annual reduction is almost exactly the actuarial price of the survivor protection. The decision therefore cannot be made on EPV alone; it depends on risk preferences, health and bequest motives.
2. Recompute the comparison if the husband's impaired health reduces his single-life annuity factor to 10.8 and the joint factor to 9.6 because the joint annuity also depends on his survival while both are alive. Keep the wife's factor at 14.6. What is the new EPV difference?
Read the worked answer
Single-life EPV becomes 60,000 x 10.8 = 648,000.
For the joint option, use a_joint = 9.6, a_male = 10.8 and a_female = 14.6. Then a_male_only = 10.8 - 9.6 = 1.2, a_female_only = 14.6 - 9.6 = 5.0. a_J2/3 = 9.6 + (2/3)(1.2 + 5.0) = 9.6 + (2/3)(6.2) = 9.6 + 4.1333 = 13.7333. EPV = 52,000 x 13.7333 = 714,133.
Now the joint option exceeds the single-life option by 714,133 - 648,000 = 66,133. The impaired health lowers the value of both options, but it lowers the single-life option much more because that option ends at the husband's death. The joint option retains substantial value through the wife's survivor benefit. On actuarial grounds alone, the joint option is now clearly preferable.
3. Discuss the couple's decision, including the survivor's longevity risk, the bequest motive, and interest-rate sensitivity.
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The wife has no pension of her own and is in excellent health, so the joint option provides valuable longevity insurance. If the husband dies first, the survivor benefit of two-thirds of 52,000, or 34,667 per year, continues for her lifetime. The single-life option provides no survivor income, so the couple would need to self-insure that risk.
The bequest motive pulls the other way: the single-life option pays 8,000 more per year while the husband is alive, which could fund savings or life insurance. But the husband's medical condition may make him uninsurable, and the couple's modest bequest motive may not justify giving up the survivor floor. A common compromise is to take the joint option and use some of the survivor security as intended.
Interest-rate sensitivity matters because the joint option has a longer expected duration: it lasts until the second death. If interest rates fall, the EPV of the joint option rises more than the single-life EPV, making the joint option relatively more attractive. If rates rise, the single-life option becomes relatively more attractive. The couple should also recognize that electing the joint option when the husband's health is impaired is actuarially favorable, but the plan may pool that risk across all retirees.