Question

You are hired as a junior manager at a state-owned institution at the beginning of 2021 with a salary of $100,000. You must choose between two retirement plans in the first week of your employment. This choice cannot be reversed. The two alternatives are:

• the state’s defined benefit plan (DBP): under which you will receive annual retirement benefits determined by the following formula: 1.5% * years of service * salary at retirement.
• a defined contribution plan (DCP): under which the institution will contribute each year an amount equal to 8% of your salary to your retirement fund.

You assume that salaries will rise by 3% a year, the interest rate and return of retirement assets will roughly match the market index return of 8%, you will retire after 35 years (end of 2055), and receive retirement payment for the subsequent 25 years (between the end of 2055 and the end of 2080).

1.) What is the amount of PBO under the DBP for your employer at the end of 2021? Hint: present value at the end of 2021

Answer 1

Estimated Final Salary after 35 Years (end of 2055)= Annual Salary at the beginning of 2021* (1+annual rate of increase)^Years to Retirement = $100,000* (1+3%)^35 => $281,386

Estimated annual payment (end of year) for each of the 25 years (between the end of 2055 and the end of 2080)  = (Estimated final salary × Benefit formula) × Years of service = ($281,386 × 0.015) × 35 => $147,728

Value at the end of Year 35 (retirement date) of the estimated future payments = PV of $147,728 for 25 years at 8 percent = $1,576,963

Annual unit credit (i.e. Benefits earned by the employee for each year) = Value at retirement date/Years of service = $1,576,963/35 = $45,056

Total Benefits earned at the end of 2021= Annual Unit Credit * Years of Service Completed => $45,056*1 => $45,056

PBO at end of 2021= Present Value of Total Benefits earned at the end of 2021

=Total Benefits earned at the end of 2021/ (1+ interest Rate )^Years to Retirement

= $45,056/(1+8%)^34

= $3,291