Pension Mathematics: Defined Benefit Plan Valuation
Value defined benefit pension plans using actuarial cost methods for Exam LTAM.
Benefit Formulas
Defined benefit (DB) pension plans promise retirement income based on salary and service. A typical formula might be 1.5% times years of service times final average salary. Valuing these benefits requires projecting future salaries using a salary scale s_x (the ratio of salary at age x to salary at some reference age), estimating the probability of surviving to retirement in the multiple decrement environment (considering death, withdrawal, disability, and retirement), and discounting projected benefits at the valuation interest rate.
Actuarial Liability
The actuarial liability (AL) represents the present value of benefits attributed to past service. The calculation depends on the actuarial cost method used. The projected unit credit method attributes to past service the benefit based on projected final salary times past service years. The entry age normal method attributes a level cost to each year from entry to retirement. The normal cost (NC) is the portion of the present value of benefits attributed to the current year of service. The unfunded actuarial liability equals AL minus plan assets. Exam LTAM tests valuation under multiple methods.