Question

The following information relates to the defined benefit pension plan of the Kraemerica Company. Only a single employee is covered by the plan. That employee has worked for Kraemerica since 1-1-2014 and she has earned pension benefits since 1-1-2014. Additional informa­tion is provided below.

                  1)   Benefit formula: Upon retirement and upon reaching age 65, the employee will receive a pension payment annually (payments to be made as long as employee lives).  

                       The first check will be issued one year after retirement.  

                        The annual payment will be for 3% of employee’s highest annual salary multiplied by the number of years of service.  

                        His salary has increased each year and is expected to increase each year in the future.

                  2)   Expected Retirement Date: December 31, 2022 - he will reach age 65 at this time; first pension check is expected to be issued 12-31-2023

                  3)   Expected Date of Death: January 1, 2030 (last (7th) pension check is expected to be issued 12-31-2029)

                  4)   Actuary’s Discount Rate (Settlement Rate): 6% per year

                  5)   Actual Annual Salary for 2016: $60,000

                  6)   Expected Annual Salary for 2022: $70,000

What is the projected benefit obligation (PBO) as of 12-31-2016 ?

Answer 1

Projected Benefit Obligation is based on the maximum annual salary drawn by an individual during his service. Since his annual salary always increases( as per note 1 in the question), we can conclude that the individual draws the maximum annual salary in 2022, which is $70,000.

Lets draw a timeline for the events that happen.

• Jan 2014--> T=0 - Today
• December 2022 -> T= 8 years - He retires
• Devember 2023 -> T=9 years - First check is drawn
• December 2029 -> T= 15 years - Final check is drawn.

We have to calculate the PBO at the end of 2016, which is T=3

As per the pension formula, he earns 3% of the max salary drawn from T=9 years to T=15years. So, if he works for 1 year from T=0 to T=1, he earns 3% of 70,000 = $2,100. But he works for 3 years from T=0 to T=3. So, he shall receive 3(the number of years he worked)*3%*$70,000 = $6,300 as payment from T=9 to T=15 years.

Now, we have to calculate the Present value of all these payments of 7 payments of $6,300 from T=9 to T =15. You can calculate the Present Value of these payments by using a financial calculator using the following variables :

N = 7 years

I/Y = 6%

FV = 0

Payment per period = $6,300

Calculate PV, Once You plug these variables, you obtain a Present Value of $35,169. Alternatively, you can use the Excel Formula "PV" and enter "Rate" as 6%, " NPer" as 7(since there are 7 payments), "PMT" as $6,300(the annual payment), "FV" as 0, "Type" as 0.

Please note that this is the PBO at T=8, since the payments begin from T=9. To calculate the PBO at the T=3, you will have to discount it by 5 periods.

So, the PBO at the end of 2016 or T=3, is

=

PBO at the end of 2016 is therefore $26,280.325