SOA Exam ALTAM Spring 2024, Question 5

Study guide: Exam ALTAM

You are the actuary for a small defined benefit pension plan. At the valuation on 1/1/2024 there are 5 members, all of whom retired at age 65 as detailed below. All benefits are paid in the form of a monthly annuity-due payable during the life of the member with payments guaranteed for 10 years following retirement (that is, up to the attainment of age 75).

Member	Exact Age as of 1/1/2024	Annual Pension (000s)
A	69	42.0
B	69	48.0
C	69	60.0
D	72	36.0
E	72	42.0
Total		228.0

The valuation assumptions are as follows:

Mortality follows the Standard Ultimate Mortality Model.
Deaths are assumed to be uniformly distributed between integer ages.
There are no expenses paid from the pension assets.
$i = 0.05$

Part a (1 point)

Show that $\ddot{a}^{(12)}_{\overline{72:\overline{3}|}} = 10.94$ to the nearest 0.01. You should calculate the value to the nearest 0.0001.

Part b (2 points)

Show that the Total Actuarial Liability (in 000s) for the accrued benefits at the valuation date is 2660 to the nearest 10. You should calculate the value to the nearest 1.

Part c (1 point)

Briefly explain why there is no Normal Cost for this plan.

Part d (4 points)

Three years later you are asked to perform a new valuation for the same pension plan. You are given the following information:

The valuation basis on 1/1/2027 is the same as the basis on 1/1/2024.
Member B died on 12/31/2026.
There have been no other changes in membership.
The plan was 100% funded as of 1/1/2024 (that is, the value of assets in the pension fund was exactly equal to liabilities at that time).
The plan assets earned a constant rate of return of 3% per year between 1/1/2024 and 1/1/2027.

(i) Show that the value of the plan assets (in 000s) on 1/1/2027 is 2190 to the nearest 10. You should calculate the value to the nearest 1.

(ii) Show that the Total Actuarial Liability (in 000s) for all members' accrued benefits on 1/1/2027 is 2020 to the nearest 10. You should calculate the value to the nearest 1.

(iii) Calculate the aggregate gain or loss on the plan between 1/1/2024 and 1/1/2027.

(iv) State with reasons whether the mortality experience of the plan generated a gain or loss between 1/1/2024 and 1/1/2027.

Part e (2 points)

The plan sponsor is considering purchasing annuities to provide the remaining benefits to the retired members. Briefly describe two advantages and two disadvantages to the sponsor of buying annuities at this time.

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