Question

Lasting Inc. has a defined benefit pension plan. One of its employees has vested benefits under the plan. During the current year, the employee earned an annual retirement benefit of $1,500. The employee has just reached the age of 45. Annual retirement payments will begin on the day the employee retires at the age of 65 and based on standard mortality tables the employee's life expectancy is 80, meaning the payments are expected to continue for 16 years after retirement. The implicit interest rates under the plan is 9%.

a. What will be the present value of the pension obligation at the time of the employee's retirement?

b. How much would the company have to contribute today in order to pay the pension benefits earned this year (the payments will begin in 20 years)?

TABLE 2 Present Value of $1 $1 PV = (1 + i)" wi 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 7.0% 8.0% 9.0% 0.0% 11.0% 12.0% 20.0% 10.99010 0.98522 0.98039 0.97561 0.97087 0.96618 0.96154 0.95694 0.95238 0.94787 0.94340 0.93458 0.92593 0.91743 0.909090 .90090 0.89286 0.83333 2 0.98030 0.97066 0.96117 0.95181 0.94260 0.93351 0.92456 0.91573 0.90703 0.89845 0.89000 0.87344 0.85734 0.84168 0.82645 0.81162 0.79719 0.69444 3 0.97059 0.95632 0.94232 0.92860 0.91514 0.90194 0.88900 0.87630 0.86384 0.85161 0.83962 0.81630 0.79383 0.77218 0.75131 0.73119 0.71178 0.57870 4 0.96098 0.94218 0.92385 0.90595 0.88849 0.87144 0.85480 0.83856 0.82270 0.80722 0.79209 0.76290 0.73503 0.70843 0.68301 0.65873 0.63552 0.48225 5 0.95147 0.92826 0.90573 0.88385 0.86261 0.84197 0.82193 0.80245 0.78353 0.76513 0.74726 0.71299 0.68058 0.64993 0.62092 0.59345 0.56743 0.40188 6 0.94205 0.91454 0.88797 0.86230 0.83748 0.81350 0.79031 0.76790 0.74622 0.72525 0.70496 0.66634 0.63017 0.59627 0.56447 0.53464 0.50663 0.33490 7 0.93272 0.90103 0.87056 0.84127 0.81309 0.78599 0.75992 0.73483 0.71068 0.68744 0.66506 0.62275 0.58349 0.54703 0.51316 0.48166 0.45235 0.27908 8 0.92348 0.88771 0.85349 0.82075 0.78941 0.75941 0.73069 0.70319 0.67684 0.65160 0.62741 0.58201 0.54027 0.50187 0.46651 0.43393 0.40388 0.23257 9 0.91434 0.87459 0.83676 0.80073 0.76642 0.73373 0.70259 0.67290 0.64461 0.61763 0.59190 0.54393 0.50025 0.46043 0.42410 0.39092 0.36061 0.19381 10 0.90529 0.86167 0.82035 0.78120 0.74409 0.70892 0.67556 0.64393 0.61391 0.58543 0.55839 0.50835 0.46319 0.42241 0.38554 0.35218 0.32197 0.16151 11 0.89632 0.84893 0.80426 0.76214 0.72242 12 0.88745 0.83639 0.78849 0.74356 0.70138 13 0.87866 0.82403 0.77303 0.72542 0.68095 14 0.86996 0.81185 0.75788 0.70773 0.66112 15 0.86135 0.79985 0.74301 0.69047 0.64186 0.68495 0.64958 0.66178 0.62460 0.63940 0.60057 0.61778 0.57748 0.59689 0.55526 0.61620 0.58468 0.55491 0.52679 0.47509 0.42888 0.38753 0.35049 0.31728 0.28748 0.58966 0.55684 0.52598 0.49697 0.44401 0.39711 0.35553 0.31863 0.28584 0.25668 0.56427 0.53032 0.49856 0.46884 0.41496 0.36770 0.32618 0.28966 0.25751 0.22917 0.53997 0.50507 0.47257 0.44230 0.38782 0.34046 0.29925 0.26333 0.23199 0.20462 0.51672 0.48102 0.44793 0.41727 0.36245 0.31524 0.27454 0.23939 0.20900 0.18270 0.13459 0.11216 0.09346 0.07789 0.06491 16 0.85282 0.78803 0.72845 0.67362 0.62317 0.57671 0.53391 0.49447 0.45811 0.42458 0.39365 0.33873 0.29189 0.25187 0.21763 0.18829 0.16312 0.05409 17 0.84438 0.77639 0.71416 0.65720 0.60502 0.55720 0.51337 0.47318 0.43630 0.40245 0.37136 0.31657 0.27027 0.23107 0.19784 0.16963 0.14564 0.04507 18 0.83602 0.76491 0.70016 0.64117 0.58739 0.53836 0.49363 0.45280 0.41552 0.38147 0.35034 0.29586 0.25025 0.21199 0.17986 0.15282 0.13004 0.03756 19 0.82774 0.75361 0.68643 0.62553 0.57029 0.52016 0.47464 0.43330 0.39573 0.36158 0.33051 0.27651 0.23171 0.19449 0.16351 0.13768 0.11611 0.03130 20 0.81954 0.74247 0.67297 0.61027 0.55368 0.50257 0.45639 0.41464 0.37689 0.34273 0.31180 0.25842 0.21455 0.17843 0.14864 0.12403 0.10367 0.02608 21 0.81143 0.73150 0.65978 0.59539 0.53755 0.48557 0.43883 0.39679 0.35894 0.32486 0.29416 0.24151 0.19866 0.16370 0.13513 0.11174 0.09256 0.02174 24 0.78757 0.69954 0.62172 0.55288 0.49193 0.43796 0.39012 0.34770 0.31007 0.27666 0.24698 0.19715 0.15770 0.12640 0.10153 0.08170 0.06588 0.01258 25 0.77977 0.68921 0.609530.53939 0.47761 0.42315 0.37512 0.33273 0.29530 0.26223 0.23300 0.18425 0.14602 0.11597 0.09230 0.07361 0.05882 0.01048 28 0.75684 0.65910 0.57437 0.50088 0.43708 0.38165 0.33348 0.29157 0.25509 0.22332 0.19563 0.15040 0.11591 0.08955 0.06934 0.05382 0.04187 0.00607 29 0.74934 0.64936 0.56311 0.48866 0.42435 0.36875 0.32065 0.27902 0.24295 0.21168 0.18456 0.14056 0.10733 0.08215 0.06304 0.04849 0.03738 0.00506 30 31 40 0.74192 0.63976 0.73458 0.63031 0.67165 0.55126 0.55207 0.47674 0.41199 0.54125 0.46511 0.39999 0.45289 0.37243 0.30656 0.35628 0.34423 0.25257 0.30832 0.26700 0.29646 0.25550 0.20829 0.17193 0.23138 0.20064 0.17411 0.13137 0.09938 0.07537 0.05731 0.22036 0.19018 0.16425 0.12277 0.09202 0.06915 0.05210 0.14205 0.11746 0.09722 0.06678 0.04603 0.03184 0.02209 0.04368 0.03338 0.00421 0.03935 0.02980 0.00351 0.01538 0.01075 0.00068

Answer 1

a) The Present value of 16 annual installments of $1500 at the time of retirement is

PV = 1500 + 1500/1.09 + ... +1500/1.09^15

This is an Annuity due of $1500 (1st installment at beginning of period) for 16 years at 9%

So, PV   = 1500 * PV of annuity due (16 years, 9%)

=1500 * 9.06069 (from table 6)

= $13591.04

b) To pay the pension benefits, the amount the company has to pay today is equal to the present value of the amount calculated above i.e.$13591.04

So, amount required = 13591.04/1.09^20 = 13591.04 * PV factor (20 years, 9%)

=13591.04 *0.17843 (from Table 2)

= $2425.05