Mortality Comparison

Mortality Comparison

August 4, 2000

Is there a difference between using an equation to calculate the present value of a cohort's benefit cost versus using life probability tables? Table 1 shows the results of two methods of calculating the present value of a $12,000 a year benefit. It shows a method which uses the formula below

which is referred to in TABLE 1 as the EQUATION. An iterative method was used to calculate the present value another way. This method first calculated the cost on a yearly basis. An iterative program was then used to calculate the present value of this irregular cash flow. When the small change in the starting balance was less than $1 and the final balance at age 113 was close to zero, the program was terminated. TABLE 2 refers to this method as ITERATIVE.

To further analyze the cash flow between male and females, since both have different life expectancies at age 65, the program was run three times, separately for male, separately for female and combined male and female.

The differences for all three calculations are found in TABLE 1. When only males were analyzed, the difference was 3.4%. When only females were analyzed, the difference was 3.4%. When the combined male and female population were combined, the difference increased to 5.6%.

Is this a significant difference between the two methods? Not really. Considering the time it takes to calculate the unique cash flows of each compared to using a simple formula. The Equation provides a good estimate of ones needs, this is more than adequate. In fact the results yield a higher present value which is a bit of a safety factor.

NOTE: Age 113 was the year being evaluated to. Going to age 120 would not change the present value due to the extreme low numbers of people living that long. The slight difference between this calculation and the previous calculation is due solely to using the exact quoted Life expectancy at age 65 instead of rounding to the whole number value.

TABLE 1
SUMMARY OF CALCULATION

METHODOLOGY

EQUATION ITERATIVE DIFFERENCE

MALE $135,840 $131,227 3.4%

FEMALE $159,648 $154,245 3.4%

BOTH $152,039 $143,504 5.6%

TABLE 2
ASSUMPTIONS

CURRENT LIFE EXPECTANCY @ 65 17.778

EQUIVALENT AGE TO LIVE TO 82.778

RATE OF RETURN 6.9%

INFLATION 3.3%

EFFECTIVE RATE 3.5%

BENEFIT AMOUNT $12,000

AGE EVALUATED 113

BALANCE AT AGE EVALUATED $9

TABLE 3
SUPPORTING CALCULATION

AGE LIFE EXPECTANCY BOTH AVERAGE PRESENT VALUE $143,504

65 15.28 19.03 17.78 LAST INCREMENTAL VALUE $1

STARTING BALANCE $23,001,659,886

AGE MALES FEMALES BENEFIT COST PER YEAR INTEREST BALANCE

65 74,797 85,489 $12,000 $1,923,432,000 $1,587,114,532 $22,665,342,418

66 73,027 84,322 $12,396 $1,950,498,204 $1,563,908,627 $22,278,752,841

67 71,128 83,056 $12,805 $1,974,336,605 $1,537,233,946 $21,841,650,182

68 69,116 81,698 $13,228 $1,994,912,582 $1,507,073,863 $21,353,811,463

69 67,015 80,258 $13,664 $2,012,359,952 $1,473,412,991 $20,814,864,502

70 64,838 78,741 $14,115 $2,026,626,783 $1,436,225,651 $20,224,463,370

71 62,583 77,139 $14,581 $2,037,267,086 $1,395,487,972 $19,582,684,256

72 60,238 75,440 $15,062 $2,043,586,052 $1,351,205,214 $18,890,303,418

73 57,800 73,634 $15,559 $2,044,991,671 $1,303,430,936 $18,148,742,684

74 55,262 71,710 $16,073 $2,040,760,784 $1,252,263,245 $17,360,245,145

75 52,621 69,660 $16,603 $2,030,221,595 $1,197,856,915 $16,527,880,465

76 49,879 67,470 $17,151 $2,012,631,084 $1,140,423,752 $15,655,673,133

77 47,041 65,133 $17,717 $1,987,363,507 $1,080,241,446 $14,748,551,072

78 44,118 62,650 $18,301 $1,954,008,881 $1,017,650,024 $13,812,192,214

79 41,120 60,026 $18,905 $1,912,205,046 $953,041,263 $12,853,028,432

80 38,065 57,263 $19,529 $1,861,686,504 $886,858,962 $11,878,200,889

81 34,971 54,359 $20,174 $1,802,120,074 $819,595,861 $10,895,676,677

82 31,862 51,312 $20,839 $1,733,302,247 $751,801,691 $9,914,176,121

83 28,768 48,131 $21,527 $1,655,418,200 $684,078,152 $8,942,836,073

84 25,718 44,832 $22,238 $1,568,860,660 $617,055,689 $7,991,031,102

85 22,745 41,433 $22,971 $1,474,259,230 $551,381,146 $7,068,153,019

86 19,882 37,956 $23,729 $1,372,464,958 $487,702,558 $6,183,390,618

87 17,159 34,432 $24,513 $1,264,626,463 $426,653,953 $5,345,418,108

88 14,607 30,894 $25,321 $1,152,151,481 $368,833,849 $4,562,100,476

89 12,249 27,384 $26,157 $1,036,682,840 $314,784,933 $3,840,202,569

90 10,107 23,947 $27,020 $920,147,426 $264,973,977 $3,185,029,120

91 8,197 20,632 $27,912 $804,672,545 $219,767,009 $2,600,123,584

92 6,524 17,490 $28,833 $692,395,814 $179,408,527 $2,087,136,298

93 5,091 14,565 $29,784 $585,444,044 $144,012,405 $1,645,704,659

94 3,888 11,898 $30,767 $485,693,922 $113,553,621 $1,273,564,358

95 2,903 9,518 $31,783 $394,773,010 $87,875,941 $966,667,289

96 2,118 7,451 $32,832 $314,164,977 $66,700,043 $719,202,355

97 1,508 5,704 $33,915 $244,594,819 $49,624,962 $524,232,499

98 1,049 4,270 $35,034 $186,346,760 $36,172,042 $374,057,781

99 712 3,125 $36,190 $138,862,179 $25,809,987 $261,005,589

100 472 2,236 $37,385 $101,237,441 $18,009,386 $177,777,533

101 304 1,562 $38,618 $72,061,693 $12,266,650 $117,982,490

102 191 1,063 $39,893 $50,025,413 $8,140,792 $76,097,870

103 117 703 $41,209 $33,791,488 $5,250,753 $47,557,135

104 69 451 $42,569 $22,135,897 $3,281,442 $28,702,680

105 39 279 $43,974 $13,983,672 $1,980,485 $16,699,493

106 21 167 $45,425 $8,539,890 $1,152,265 $9,311,868

107 11 95 $46,924 $4,973,941 $642,519 $4,980,446

108 6 52 $48,472 $2,811,403 $343,651 $2,512,694

109 3 27 $50,072 $1,502,162 $173,376 $1,183,908

110 1 13 $51,724 $724,142 $81,690 $541,456

111 1 6 $53,431 $374,019 $37,360 $204,797

112 0 3 $55,195 $165,584 $14,131 $53,344

113 0 1 $57,016 $57,016 $3,681 $9

114 0 0 $58,898 $0 $1 $9

115 0 0 $60,841 $0 $1 $10

116 0 0 $62,849 $0 $1 $10

117 0 0 $64,923 $0 $1 $11

118 0 0 $67,065 $0 $1 $12

119 0 0 $69,279 $0 $1 $13

120 0 0 $71,565 $0 $1 $14

TABLE 1 SUMMARY OF CALCULATION
	METHODOLOGY
	EQUATION	ITERATIVE	DIFFERENCE
MALE	$135,840	$131,227	3.4%
FEMALE	$159,648	$154,245	3.4%
BOTH	$152,039	$143,504	5.6%

TABLE 2 ASSUMPTIONS
CURRENT LIFE EXPECTANCY @ 65	17.778
EQUIVALENT AGE TO LIVE TO	82.778
RATE OF RETURN	6.9%
INFLATION	3.3%
EFFECTIVE RATE	3.5%
BENEFIT AMOUNT	$12,000
AGE EVALUATED	113
BALANCE AT AGE EVALUATED	$9

TABLE 3 SUPPORTING CALCULATION
AGE	LIFE EXPECTANCY		BOTH	AVERAGE PRESENT VALUE		$143,504
65	15.28	19.03	17.78	LAST INCREMENTAL VALUE		$1
				STARTING BALANCE		$23,001,659,886
AGE	MALES	FEMALES	BENEFIT	COST PER YEAR	INTEREST	BALANCE
65	74,797	85,489	$12,000	$1,923,432,000	$1,587,114,532	$22,665,342,418
66	73,027	84,322	$12,396	$1,950,498,204	$1,563,908,627	$22,278,752,841
67	71,128	83,056	$12,805	$1,974,336,605	$1,537,233,946	$21,841,650,182
68	69,116	81,698	$13,228	$1,994,912,582	$1,507,073,863	$21,353,811,463
69	67,015	80,258	$13,664	$2,012,359,952	$1,473,412,991	$20,814,864,502
70	64,838	78,741	$14,115	$2,026,626,783	$1,436,225,651	$20,224,463,370
71	62,583	77,139	$14,581	$2,037,267,086	$1,395,487,972	$19,582,684,256
72	60,238	75,440	$15,062	$2,043,586,052	$1,351,205,214	$18,890,303,418
73	57,800	73,634	$15,559	$2,044,991,671	$1,303,430,936	$18,148,742,684
74	55,262	71,710	$16,073	$2,040,760,784	$1,252,263,245	$17,360,245,145
75	52,621	69,660	$16,603	$2,030,221,595	$1,197,856,915	$16,527,880,465
76	49,879	67,470	$17,151	$2,012,631,084	$1,140,423,752	$15,655,673,133
77	47,041	65,133	$17,717	$1,987,363,507	$1,080,241,446	$14,748,551,072
78	44,118	62,650	$18,301	$1,954,008,881	$1,017,650,024	$13,812,192,214
79	41,120	60,026	$18,905	$1,912,205,046	$953,041,263	$12,853,028,432
80	38,065	57,263	$19,529	$1,861,686,504	$886,858,962	$11,878,200,889
81	34,971	54,359	$20,174	$1,802,120,074	$819,595,861	$10,895,676,677
82	31,862	51,312	$20,839	$1,733,302,247	$751,801,691	$9,914,176,121
83	28,768	48,131	$21,527	$1,655,418,200	$684,078,152	$8,942,836,073
84	25,718	44,832	$22,238	$1,568,860,660	$617,055,689	$7,991,031,102
85	22,745	41,433	$22,971	$1,474,259,230	$551,381,146	$7,068,153,019
86	19,882	37,956	$23,729	$1,372,464,958	$487,702,558	$6,183,390,618
87	17,159	34,432	$24,513	$1,264,626,463	$426,653,953	$5,345,418,108
88	14,607	30,894	$25,321	$1,152,151,481	$368,833,849	$4,562,100,476
89	12,249	27,384	$26,157	$1,036,682,840	$314,784,933	$3,840,202,569
90	10,107	23,947	$27,020	$920,147,426	$264,973,977	$3,185,029,120
91	8,197	20,632	$27,912	$804,672,545	$219,767,009	$2,600,123,584
92	6,524	17,490	$28,833	$692,395,814	$179,408,527	$2,087,136,298
93	5,091	14,565	$29,784	$585,444,044	$144,012,405	$1,645,704,659
94	3,888	11,898	$30,767	$485,693,922	$113,553,621	$1,273,564,358
95	2,903	9,518	$31,783	$394,773,010	$87,875,941	$966,667,289
96	2,118	7,451	$32,832	$314,164,977	$66,700,043	$719,202,355
97	1,508	5,704	$33,915	$244,594,819	$49,624,962	$524,232,499
98	1,049	4,270	$35,034	$186,346,760	$36,172,042	$374,057,781
99	712	3,125	$36,190	$138,862,179	$25,809,987	$261,005,589
100	472	2,236	$37,385	$101,237,441	$18,009,386	$177,777,533
101	304	1,562	$38,618	$72,061,693	$12,266,650	$117,982,490
102	191	1,063	$39,893	$50,025,413	$8,140,792	$76,097,870
103	117	703	$41,209	$33,791,488	$5,250,753	$47,557,135
104	69	451	$42,569	$22,135,897	$3,281,442	$28,702,680
105	39	279	$43,974	$13,983,672	$1,980,485	$16,699,493
106	21	167	$45,425	$8,539,890	$1,152,265	$9,311,868
107	11	95	$46,924	$4,973,941	$642,519	$4,980,446
108	6	52	$48,472	$2,811,403	$343,651	$2,512,694
109	3	27	$50,072	$1,502,162	$173,376	$1,183,908
110	1	13	$51,724	$724,142	$81,690	$541,456
111	1	6	$53,431	$374,019	$37,360	$204,797
112	0	3	$55,195	$165,584	$14,131	$53,344
113	0	1	$57,016	$57,016	$3,681	$9
114	0	0	$58,898	$0	$1	$9
115	0	0	$60,841	$0	$1	$10
116	0	0	$62,849	$0	$1	$10
117	0	0	$64,923	$0	$1	$11
118	0	0	$67,065	$0	$1	$12
119	0	0	$69,279	$0	$1	$13
120	0	0	$71,565	$0	$1	$14