Suppose that in a certain defined benefit pension plan (a) Employees work for 45

Question

Suppose that in a certain defined benefit pension plan (a) Employees work for 45 years earning wages that increase at a real rate of 2%. (b) They retire with a pension equal to 70% of their final salary. This pension increases at the rate of inflation minus 1%. (c) The pension is received for 18 years. (d) The pension fund’s income is invested in bonds which earn the inflation rate plus 1.5%. Estimate the percentage of an employee’s salary that must be contributed to the pension plan if it is to remain solvent. (Hint: Do all calculations in real rather than nominal dollars.)

Explanation / Answer

Typical defined benefits plan provides an employee with about 70% of final salary as a pension and includes indexation for inflation (Hull). The employees wages are constant in real terms. The pension is 0.70X. The real return earned is zero. The present value of the contributions made by one employee is 45XR where R=contribution rate as a percentage of the employees wages. The present value of benefits is 18 x.070x = 12.60x

Therefore the value of R to adequately fund the plan is 45xr = 12.60x

The total of the employer and employee contributions should be 0.280 or 28% of salary.

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