Question

In recent years, there has been a lot of media coverage about the funding status of pension plans for state employees. In many states, the amount of money invested in employee pension plans is far less than the amount estimated to pay employees the retirement benefits they have been promised. Basically, pension plans work by investing enough money while employees are working so that the money invested, plus the investment income it earns over the years, will be sufficient to pay the workers their retirement incomes once they have retired. There are many complicated assumptions, estimates, and calculations needed to determine how much money a state should invest in its pension fund each year. One of the most important assumptions is the rate of return the plan's investments will earn in the future. As you have seen in this chapter, the higher the rate of return used to calculate the present value of future cash flows, the lower the present value will be. To determine a pension plan's funded status, actuaries (1) estimate the future cash payments expected to be made to employees, (2) calculate the present value of those cash flows using an assumed rate of return (this present value is the gross liability of the fund), and (3) subtract the amount of money that has been invested from the gross liability calculated in step 2 (this amount is the funded status of the pension plan). Essentially, this is the same as calculating the net present value of an investment. If the plan has less money in its investments than the present value of its estimated future cash flows, it has a net liability and is considered to be underfunded by that amount. Many states' pension plans have assumed they will earn 7 percent or more on their investments, even though many experts think a more appropriate assumption would be 5.5 percent. As an example, the state of Virginia used an assumed rate of return of 7.5 percent in 2009 but reduced the rate to 7.0 percent in 2010. Actual investment returns can vary widely. In 2016, Virginia's actual return on its pension assets was only 3.8 percent, but in 2017 it was 14.0 percent. Virginia paid out approximately $4.2 billion in benefits to retirees in 2017. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) Required a. Assume Virginia's annual payments will continue to be $4.2 billion, and that retirees will receive benefits for 20 years on average. Using an assumed rate of return of 7 percent, calculate the liability of the state's pension plan. The liability is the present value of the future cash payments. (Be aware that the real-world calculation for a state's pension plan liability involves many more assumptions than just these two.) b. Assume the annual payments will continue to be $4.2 billion, and that retirees will receive benefits for 20 years on average. Using an assumed rate of return of 5 percent, calculate the liability of the state's pension plan.

Answer 1

Answer a.

The liability is calculated as follows using assumed rate of return @7%:

Year	Payout each year ($ in billion)	DF @ 7%	PV of future payouts ($ in billion)
1	4.2	0.934579439	3.925233645
2	4.2	0.873438728	3.668442659
3	4.2	0.816297877	3.428451083
4	4.2	0.762895212	3.204159891
5	4.2	0.712986179	2.994541954
6	4.2	0.666342224	2.79863734
7	4.2	0.622749742	2.615548916
8	4.2	0.582009105	2.444438239
9	4.2	0.543933743	2.284521719
10	4.2	0.508349292	2.135067027
11	4.2	0.475092796	1.995389745
12	4.2	0.444011959	1.864850229
13	4.2	0.414964448	1.742850681
14	4.2	0.387817241	1.628832412
15	4.2	0.36244602	1.522273282
16	4.2	0.338734598	1.422685311
17	4.2	0.31657439	1.32961244
18	4.2	0.295863916	1.242628449
19	4.2	0.276508333	1.161334999
20	4.2	0.258419003	1.085359812
		State pension plan liability	44.49485983

Answer b.

The liability is calculated as follows using assumed rate of return @5%:

Year	Payout each year ($ in billion)	DF @ 5%	PV of future payouts ($ in billion)
1	4.2	0.952380952	4
2	4.2	0.907029478	3.80952381
3	4.2	0.863837599	3.628117914
4	4.2	0.822702475	3.455350394
5	4.2	0.783526166	3.290809899
6	4.2	0.746215397	3.134104666
7	4.2	0.71068133	2.984861587
8	4.2	0.676839362	2.842725321
9	4.2	0.644608916	2.707357448
10	4.2	0.613913254	2.578435665
11	4.2	0.584679289	2.455653014
12	4.2	0.556837418	2.338717156
13	4.2	0.530321351	2.227349673
14	4.2	0.505067953	2.121285403
15	4.2	0.481017098	2.020271812
16	4.2	0.458111522	1.924068392
17	4.2	0.436296688	1.832446088
18	4.2	0.415520655	1.74518675
19	4.2	0.395733957	1.662082619
20	4.2	0.376889483	1.582935828
		State pension plan liability	52.34128344

Hence we see that if the rate of return is less, then we have a greater liability towards pension, as the contribution to pesion would need to be that much more so as to compensate for the lesser return that a pension fund is generating.