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).

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

Present salary as at the beginning of 2021 = $100,000

Expected salary increase per year = 3%

Years upto retirement = 35 years

Salary at retirement = $100,000 * (1+ 3%)^{^35}

= $281,386.25

Annual retirement benefits between end of 2055 and 2080 = 1.5% * Years of service * Salary at retirement

= 1.5% * 35 * $281,386.25

= $147,727.78

This annual retirement benefit of $147,727.78 will be received for each of the 25 years from end of 2055 to end of 2080 (like and annuity).

Given the rate of return 8%, calculating the present value of these retirement benefit payments as on retirement date as follows:

PVIFA (Present value interest factor of an annuity) of $1 @ 8% for 25 years = 10.6748 (from the PV tables available online)

Present value of retirement benefits at the end of 2055 = $147,727.78 * 10.6748

= $1,576,964.49

Now, to calculate the present value of this retirement benefits lumpsum as at the end of 2021, we need to discount the amount as above @ 8% rate given for 24 years (24 years because we require the present value as at the end of 2021 and not the beginning of 2021, which gives us 24 years )

PVIF (Present value interest factor) of $1 @ 8% for 24 years = 0.1577

Present value of retirement benefit lumpsum as at the end of 2021 = $1,576,964.49 * 0.1577

= $248,687.30

Hence, the PBO under the DBP for the employer as the end of 2021 will be $248,687.30