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 6 percent or more on their investments, even though many experts think a more appropriate assumption would be 4.5 percent. As an example, the state of Virginia used an assumed rate of return of 6.5 percent in 2009 but reduced the rate to 6.0 percent in 2010. Actual investment returns can vary widely. In 2016, Virginia's actual return on its pension assets was only 2.1 percent, but in 2017 it was 12.3 percent. Virginia paid out approximately $3.9 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 $3.9 billion, and that retirees will receive benefits for 20 years on average. Using an assumed rate of return of 6 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 $3.9 billion, and that retirees will receive benefits for 20 years on average. Using an assumed rate of return of 4 percent, calculate the liability of the state's pension plan. (For all requirements, enter your answers in dollars not in billions.) Gross Pension Liability a b. TABLE 1 PRESENT VALUE OF $1 n 4% 5% 6% 7% 8% 9% 10% 12% 14% 16% 20% 1 0.961538 0.952381 0.943396 0.934579 0.92526 0.917431 0.909091 0.892857 0.877193 0.862069 0.833333 2 0.924556 0.907029 0.889996 0.873439 0.857339 0.841680 0.826446 0.797194 0.769468 0.743163 0.694444 3 0.888996 0.863838 0.839619 0.816298 0.793832 0.772183 0.751315 0.711780 0.674972 0.640658 0.578704 4 0.854804 0.822702 0.792094 0.762895 0.735030 0.708425 0.683013 0.635518 0.592080 0.552291 0.482253 5 0.821927 0.783526 0.747258 0.712986 0.680583 0.649931 0.620921 0.567427 0.519369 0.476113 0.401878 6 0.790315 0.746215 0.704961 0.666342 0.630170 0.596267 0.564474 0.506631 0.455587 0.410442 0.334898 7 0.759918 0.710681 0.665057 0.622750 0.583490 0.547034 0.513158 0.452349 0.399637 0.353830 0.279082 8 0.730690 0.676839 0.627412 0.582009 0.540269 0.501866 0.466507 0.403883 0.350559 0.305025 0.232568 9 0.702587 0.644609 0.591898 0.543934 0.500249 0.460428 0.424098 0.360610 0.307508 0.262953 0.193807 10 0.675564 0.613913 0.558395 0.508349 0.463193 0.422411 0.385543 0.321973 0.269744 0.226684 0.161506 11 0.649581 0.584679 0.526788 0.475093 0.428883 0.387533 0.350494 0.287476 0.236617 0.195417 0.134588 12 0.624597 0.556837 0.496969 0.444012 0.397114 0.355535 0.318631 0.256675 0.207559 0.168463 0.112157 13 0.600574 0.530321 0.468839 0.414964 0.367698 0.326179 0.289664 0.229174 0.182069 0.145227 0.093464 14 0.577475 0.505068 0.442301 0.387817 0.340461 0.299246 0.263331 0.204620 0.159710 0.125195 0.077887 15 0.555265 0.481017 0.417265 0.362446 0.315242 0.274538 0.239392 0.182696 0.140096 0.107927 0.064905 16 0.533908 0.458112 0.393646 0.338735 0.291890 0.251870 0.217629 0.163122 0.122892 0.093041 0.054088 17 0.513373 0.436297 0.371364 0.316574 0.270269 0.231073 0.197845 0.145644 0.107800 0.080207 0.045073 18 0.493628 0.415521 0.350344 0.295864 0.250249 0.211994 0.179859 0.130040 0.094561 0.069144 0.037561 19 0.474642 0.395734 0.330513 0.276508 0.231712 0.194490 0.163508 0.116107 0.082948 0.059607 0.031301 20 0.456387 0.376889 0.311805 0.258419 0.214548 0.178431 0.148644 0.103667 0.072762 0.051385 0.026084 600 VOU AWNA TABLE 2 PRESENT VALUE OF AN ANNUITY OF $1 n 4% 5% 6% 7% 0.961538 0.952381 0.943396 0.934579 1.886095 1.859410 1.833393 1.808018 2.775091 2.723248 2.673012 2.624316 3.629895 3.545951 3.465106 3.387211 4.451822 4.329477 4.212364 4.100197 5.242137 5.075692 4.917324 4.766540 6.002055 5.786373 5.582381 5.389289 6.732745 6.463213 6.209794 5.971299 7.435332 7.107822 6.801692 6.515232 10 8.110896 7.721735 7.360087 7.023582 11 8.760477 8.306414 7.886875 7.498674 9.385074 8.863252 8.383844 7.942686 9.985648 9.393573 8.852683 8.357651 14 10.563123 9.898641 9.294984 8.745468 15 11.118387 10.379658 9.712249 9.107914 16 11.652296 10.837770 10.105895 9.446649 17 12.165669 11.274066 10.477260 9.763223 18 12.659297 11.689587 10.827603 10.059087 19 13.133939 12.085321 11.158116 10.335595 20 13.590326 12.462210 11.469921 10.594014 | 123456789wHAB899 8% 0.925926 1.783265 2.577097 3.312127 3.992710 4.622880 5.206370 5.746639 6.246888 6.710081 7.138964 7.536078 7.903776 8.244237 8.559479 8.851369 9.121638 9.371887 9.603599 9.818147 9% 0.917431 1.759111 2.531295 3.239720 3.889651 4.485919 5.032953 5.534819 5.995247 6.417658 6.805191 7.160725 7.486904 7.786150 8.060688 8.312558 8.543631 8.755625 8.905115 9.128546 10% 0.909091 1.735537 2.486852 3.169865 3.790787 4.355261 4.868419 5.334926 5.759024 6.144567 6.495061 6.813692 7.103356 7.366687 7.606080 7.823709 8.021553 8.201412 8.364920 8.513564 12% 0.892857 1.690051 2.401831 3.037349 3.604776 4.111407 4.563757 4.967640 5.328250 5.650223 5.937699 6.194374 6.423548 6.628168 6.810864 6.973986 7.119630 7.249670 7.365777 7.469444 14% 0.877193 1.646661 2.321632 2.913712 3.433081 3.888668 4.288305 4.638864 4.946372 5.216116 5.452733 5.660292 5.842362 6.002072 6.142168 6.265060 6.372859 6.467420 6.550369 6.623131 16% 0.862069 1.605232 2.245890 2.798181 3.274294 3.684736 4.038565 4.343591 4.606544 4.833227 5.028644 5.197107 5.342334 5.467529 5.575456 5.668497 5.748704 5.817848 5.877455 5.928841 20% 0.833333 1.527778 2.106481 2.588735 2.990612 3.325510 3.604592 3.837160 4.030967 4.192472 4.327060 4.439217 4.532681 4.610567 4.675473 4.729561 4.774634 4.812195 4.843496 4.869580