Question

A state retirement plan has been frozen. It is considered fully-funded, with $635,244,352.26 of assets on hand and makes payouts to 1,000 recipients. It assumes it will earn 7.5% per year on these assets. The most recent total payout was $50,000,000. Next year it will be $51,000,000, which includes a 2% COLA increase in benefits. This payout amount is scheduled to increase by 2% per year for inflation. All interest earned and payments occur at the end of the year. For this cohort of retirees the final payment will be made in exactly22 years from today. The fund balance at that time will be zero.

The effective rate for annuities like this is RATE = [(1+growth)/(1+Inflation)]-1=0.0539216.

The PV was calculated as =PV(RATE,22,-50000000,0,0).

Create an amortization table that shows the pension is fully-funded.

Answer 1

payout every year present value year $51,000,000 $47,441,860.47 1+growth rate 1+inflation rat 1.075 $52,020,000.00 $45,014,602.49 1.02 $53,060,400.00 $42,711,529.80 $40,526,288.74 inflation rate 0.02 3 $54,121,608.00 4 $55,204,040.16 $38,452,850.71 growth rate 0.075 $56,308,120.96 $57,434,283.38 $36,485,495.56 $34,618,795.79 effective rate 0.0539216 $58,582,969.05 $59,754,628.43 $32,847,601.59 8. $50,000,000 $31,167,026.62 payout $60,949,721.00 $29,572,434.56 $28,059,426.28 $26,623,827.73 10 laibility value $635,244,173.91 $62,168,715.42 11 $63,412,089.73 12 $64,680,331.52 $25,261,678.40 $23,969,220.44 $22,742,888.23 22 13 years $65,973,938.15 $67,293,416.92 $68,639,285.25 14 15 $21,579,298.60 $20,475,241.46 16 $70,012,070.96 $71,412,312.38 17 $19,427,670.97 $18,433,697.10 18 $72,840,558.63 19 $74,297,369.80 $75,783,317.19 $17,490,577.72 $16,595,710.95 20 21 $77,298,983.54 $15,746,628.06 $635,244,352.26 22 total liabilities B.

in above case pension are fully funded = total asset - total liability = $635244352.26 - $635244352.26 = 0

payout will  increase at 2% every year so payout in n year = $50000000 * (1.02)*ⁿ

present value of pay out = payout in n year / (1+R)ⁿ where R = growth rate = 0.075

Total present value of all payout = total liabilities = $ 635244352.26 = total asset so pension account is fully funded