Question

State Retirement Funding

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)

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

B) Suppose that instead of 7.5% the assets earn 5% per year. By how much is the pension under-funded assuming the 2% COLA adjustment continues.

C) At a 5% growth rate what total annual payments can the original asset balance support for 22 years with no inflation adjustment? i.e., the same amount each year.

D) Given the initial balance of $635,244,352.26 and assuming a 2% COLA increase ever year, what initial payment can be made to beneficiaries?

Answer 1

Answer Part (A) of Question:

Create an amortization table that shows the pension is fully funded:

Year (from today)	Opening Balance of Retirement Fund	Income on Funds @7.5%	Payout	Closing Balance of Retirement Fund
1	635,244,352	47,643,326	-51,000,000	631,887,679
2	631,887,679	47,391,576	-52,020,000	627,259,255
3	627,259,255	47,044,444	-53,060,400	621,243,299
4	621,243,299	46,593,247	-54,121,608	613,714,938
5	613,714,938	46,028,620	-55,204,040	604,539,518
6	604,539,518	45,340,464	-56,308,121	593,571,861
7	593,571,861	44,517,890	-57,434,283	580,655,467
8	580,655,467	43,549,160	-58,582,969	565,621,658
9	565,621,658	42,421,624	-59,754,628	548,288,654
10	548,288,654	41,121,649	-60,949,721	528,460,582
11	528,460,582	39,634,544	-62,168,715	505,926,411
12	505,926,411	37,944,481	-63,412,090	480,458,802
13	480,458,802	36,034,410	-64,680,332	451,812,880
14	451,812,880	33,885,966	-65,973,938	419,724,908
15	419,724,908	31,479,368	-67,293,417	383,910,859
16	383,910,859	28,793,314	-68,639,285	344,064,889
17	344,064,889	25,804,867	-70,012,071	299,857,684
18	299,857,684	22,489,326	-71,412,312	250,934,698
19	250,934,698	18,820,102	-72,840,559	196,914,242
20	196,914,242	14,768,568	-74,297,370	137,385,440
21	137,385,440	10,303,908	-75,783,317	71,906,031
22	71,906,031	5,392,952	-77,298,984	-0

Answer Part (B) of Question

Suppose that instead of 7.5% the assets earn 5% per year. By how much is the pension under-funded assuming the 2% COLA adjustment continues:

Effective Rate will be =[(1+5%)/(1+2%)]-1= 1.05/1.02-1= 0.029411765

PV =PV(0.029411765,22,-50000000,0,0)=  801,561,983

If Growth rate is 5%, Pension fund is under funded by $  166,317,631 ( 801,561,983 -  635,244,352)

Answer to Part (C) of the Question

At a 5% growth rate what total annual payments can the original asset balance support for 22 years with no inflation adjustment? i.e., the same amount each year.

Fixed amount of payout will be Rs  48,259,836.49.

Year (from today)	Opening Balance of Retirement Fund	Income on Funds @5%	Payout (fixed)	Closing Balance of Retirement Fund
1	635,244,352	31,762,218	(48,259,836.49)	618,746,733
2	618,746,733	30,937,337	(48,259,836.49)	601,424,234
3	601,424,234	30,071,212	(48,259,836.49)	583,235,609
4	583,235,609	29,161,780	(48,259,836.49)	564,137,553
5	564,137,553	28,206,878	(48,259,836.49)	544,084,594
6	544,084,594	27,204,230	(48,259,836.49)	523,028,987
7	523,028,987	26,151,449	(48,259,836.49)	500,920,600
8	500,920,600	25,046,030	(48,259,836.49)	477,706,793
9	477,706,793	23,885,340	(48,259,836.49)	453,332,297
10	453,332,297	22,666,615	(48,259,836.49)	427,739,075
11	427,739,075	21,386,954	(48,259,836.49)	400,866,192
12	400,866,192	20,043,310	(48,259,836.49)	372,649,665
13	372,649,665	18,632,483	(48,259,836.49)	343,022,312
14	343,022,312	17,151,116	(48,259,836.49)	311,913,591
15	311,913,591	15,595,680	(48,259,836.49)	279,249,434
16	279,249,434	13,962,472	(48,259,836.49)	244,952,069
17	244,952,069	12,247,603	(48,259,836.49)	208,939,836
18	208,939,836	10,446,992	(48,259,836.49)	171,126,992
19	171,126,992	8,556,350	(48,259,836.49)	131,423,505
20	131,423,505	6,571,175	(48,259,836.49)	89,734,844
21	89,734,844	4,486,742	(48,259,836.49)	45,961,749
22	45,961,749	2,298,087	(48,259,836.49)	0

Answer to Part D of the Question

Given the initial balance of $635,244,352.26 and assuming a 2% COLA increase ever year, what initial payment can be made to beneficiaries?

though Question is not clear about the growth rate, we presume to take 5% as growth rate, as 7.5% is already considered in part A of the question.

Initial amount of payout will be $  39,625,404 which is 79% of 50,000,000.

Year (from today)	Opening Balance of Retirement Fund	Income on Funds @5%	Payout @7.5% Growth	Payout @5% Growth	Decrease in Payout	Closing Balance of Retirement Fund
				-39,625,404
1	635,244,352	31,762,218	-51,000,000	-40,417,912	79%	626,588,658
2	626,588,658	31,329,433	-52,020,000	-41,226,271	79%	616,691,820
3	616,691,820	30,834,591	-53,060,400	-42,050,796	79%	605,475,615
4	605,475,615	30,273,781	-54,121,608	-42,891,812	79%	592,857,584
5	592,857,584	29,642,879	-55,204,040	-43,749,648	79%	578,750,815
6	578,750,815	28,937,541	-56,308,121	-44,624,641	79%	563,063,714
7	563,063,714	28,153,186	-57,434,283	-45,517,134	79%	545,699,766
8	545,699,766	27,284,988	-58,582,969	-46,427,477	79%	526,557,278
9	526,557,278	26,327,864	-59,754,628	-47,356,026	79%	505,529,115
10	505,529,115	25,276,456	-60,949,721	-48,303,147	79%	482,502,425
11	482,502,425	24,125,121	-62,168,715	-49,269,210	79%	457,358,336
12	457,358,336	22,867,917	-63,412,090	-50,254,594	79%	429,971,659
13	429,971,659	21,498,583	-64,680,332	-51,259,686	79%	400,210,557
14	400,210,557	20,010,528	-65,973,938	-52,284,879	79%	367,936,205
15	367,936,205	18,396,810	-67,293,417	-53,330,577	79%	333,002,438
16	333,002,438	16,650,122	-68,639,285	-54,397,189	79%	295,255,372
17	295,255,372	14,762,769	-70,012,071	-55,485,132	79%	254,533,008
18	254,533,008	12,726,650	-71,412,312	-56,594,835	79%	210,664,823
19	210,664,823	10,533,241	-72,840,559	-57,726,732	79%	163,471,333
20	163,471,333	8,173,567	-74,297,370	-58,881,266	79%	112,763,633
21	112,763,633	5,638,182	-75,783,317	-60,058,892	79%	58,342,923
22	58,342,923	2,917,146	-77,298,984	-61,260,069	79%	0