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ILLUSTRATIVE DIVIDEND COMPUTATION

This section illustrates the principles explained earlier in this chapter through a hypothetical dividend calculation. Details of computing the 10th-year dividend of a $100,000 ordinary life policy issued to a male aged 32 are shown in table 20.1.

 

 

TABLE 20-1
Illustrative Dividend Calculation
$100,000 Ordinary Life Policy Issued to Male Aged 32
Reserve Basis: Full Net Level Premium Reserves, 1980 CSO Male Table, and 5.5% Interest

(1)

Gross premium: $12.51 x 100 + $50 policy fee

$1,301

(2)

Net level premium: 100 x 8.51

851

(3)

Loading: (1) � (2)

450

(4)

Mortality contribution to 10th-year dividend

 
 

(a) 9th-year terminal reserve

7,653

 

(b) 10th-year terminal reserve

8,671

 

(c) Tabular cost of insurance: {[100,000 � 4(b)]/1,000} x 3.29

301

 

(d) Mortality charge: 0.695 x 4(c)

209

 

(e) Return of tabular mortality: 4(c) � 4(d)

92

(5)

Interest contribution: (0.0625 � 0.055) x [(2) + 4(a)]

64

(6)

Loading contribution

 
 

(a) Expense charge: .115 x (1) + 35.00 + 20.00

205

 

(b) Return of loading: (3) � 6(a)

245

(7)

Total dividend for the 10th year: 4(e) + (5) + 6(b)

401

 

 

The steps in the calculation are as follows: The gross premium for the policy in this example is $12.51 per $1,000, plus a policy fee of $50. This premium is the net level premium ($8.51 per $1,000), computed using mortality from the 1980 CSO Male Table and 5.5 percent interest, plus loading. The loading�developed in table 17-1 of chapter 17 and used in this example�is 16 percent of the gross premium, plus $2 per $1,000, plus the policy fee of $50.

The mortality contribution to the 10th-year dividend is the tabular cost of insurance minus the actual mortality charge for the 10th year. The tabular charge in this example is the net amount at risk, multiplied by the 1980 CSO Male Table rate at age 41, 3.29 per 1,000, which yields $301. The actual mortality charge is the percentage of actual to expected mortality for age 41 multiplied by the tabular cost of insurance. The rate of mortality used in the calculation of an actual dividend varies by attained age and reflects the company�s own mortality experience during recent years. In this illustration, the percentage was taken from the scale used in the construction of table 20-2. If we assume the actual rate of mortality at age 32 is 65 percent of the 1980 CSO Male Table rate and that the percentage increases by one-half point for each year of attained age, the assumed actual rate of mortality at age 41 would be 69.5 percent of the rate reflected in the table. The mortality saving at attained age 41 is 30.5 percent of the tabular rate. Therefore the mortality charge would be $209, which, deducted from $301, gives a mortality saving for the year of $92.

The interest contribution at all durations is calculated by multiplying the initial reserve for the year in question and the net level premium by the difference between the assumed rate of interest and the so-called dividend rate of interest. While the latter will bear a close relationship to the actual rate of interest the company earned in recent years, it might deviate in either direction in any particular year. In the illustration the dividend rate of 6.25 percent produces an excess interest factor of 0.75 percent when compared to the assumed rate of 5.5 percent. Applying this factor to the sum of the initial reserve of $7,653 produces an excess interest contribution of $64 for the year.

The loading in our example is 16 percent of the gross premium, $2.00 per $1,000 of insurance, and a per-policy expense of $42. Of this, 2.4 percent of the gross premium, $1.25 per $1,000 of insurance, and $3.00 per policy were included intentionally to provide future dividends. The difference between actual expenses and the policy�s loading for our $100,000 example policy provides a savings of $245. This amount is available for dividend distribution, a portion of which may well have been included in the loading formula for that specific purpose. The assumptions described in this dividend illustration result in a total dividend of $401�that is, $92 from mortality savings plus $64 from excess interest, plus $245 from expense savings.

Table 20-2 shows how dividends might be determined for the first 20 years of an ordinary life policy issued to a 32-year-old male. The following experience factors have been chosen arbitrarily:

 

 

Note that the rates used in the dividend computation represent actual experience of the company. They will always differ from the assumptions that were used to compute premiums, reserves, and surrender values.

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