The theoretical basis for the loading formula is the same as that for computing net premiums. The present value of income must equal the present value of payments. Specifically, the present value of policy expenses, margins for contingencies, and anticipated dividends should be divided by the present value of an appropriate life annuity due.

A key difference lies in the certainty of the two sets of present values. The contract specifies benefits with certainty. Policy expenses, on the other hand, are estimates at best. They are found only after a painstaking analysis of operating costs and the probable future trend of such costs. Allocating costs to the various policies and ages of issue also presents one of the actuary�s most difficult tasks�and one that cannot be accomplished with complete equity.

Cost studies usually precede adoption of a loading formula. Expenses are reduced to a unit basis and allocated among the various policy plans and ages at issue. Each unit expense rate is expressed either as a percentage of the premium, an amount per $1,000 of face value, or an amount per policy. While the first of these types is straightforward, the latter two require sophisticated cost studies to achieve valid rates.

To calculate the present value of these expenses, the time of their occurrence must be known. One must know whether the expenses occur at the inception of the contract, at periodic intervals after that, or only upon the occurrence of some particular event in the future. A typical formula might contain values for the following elements:

Under the first bulleted item expenses incurred only at time of issue include first-year commissions, agency expense allowances, and other acquisition costs. First-year commissions to the soliciting agent vary widely among companies and, to a lesser extent, among policy plans of the same company. A typical first-year commission on an ordinary life policy issued at age 32 might be 55 percent or more of gross premium. Additional expenses, including inspection reports, medical exam, administration, reserve establishment, and the override commission to the general agent or agency might also amount to as much as 55 percent of gross premium. Thus the total of all the expenses incurred at the time of issue may be substantially more than 110 percent of the first year�s premium.

These costs are paid by the company during the first policy year while the policyowner pays only a level gross premium plus perhaps a modest policy fee. Consequently these first-year expenses must be amortized over the entire premium-paying period of the policy. To do this the actuary finds the level percentage of the gross premium that amortizes this first-year expense. If premiums are payable throughout the insured�s lifetime and first-year expenses equal 110 percent of the premium, the actuary divides 110 percent by the present value of a whole life annuity due of $1 as of age 32. Based on the previously determined value of $16.49, a level 6.67 percent (1.10 � 16.49) of each premium payment is available to amortize the acquisition expenses.

Items of expense here include renewal commissions to the soliciting agent and agency expense allowances. Recent compensation agreements show many patterns of renewal commissions. Some provide a minimum commission or service fee throughout the life of the policy. For a simple illustration, assume a renewal commission of 5 percent payable for 9 years. Since these commissions will be paid only if the policy�s premiums are paid, the actuary discounts for the probability that the insured dies or the policyowner lapses or surrenders the policy. Discounts also could apply for termination of the agent without vested rights to the renewal commissions. In practice, however, companies do not discount these expenses for termination of the policy or the agent. With a discount for mortality only, based on the 1980 CSO Male Table and 5.5 percent interest, the present value at issue of the 5 percent renewal commissions is 33.97 percent of the annual gross premium. This must also be spread over the entire premium-paying period of the policy, here assumed to be the lifetime of the insured. The percentage of the annual premium necessary to amortize these commissions is obtained by dividing 33.97 percent by 16.49, which yields 2.06 percent.

State premium taxes are the only significant item of expense that occurs every year, including the first. These taxes vary somewhat among states, but they average about 2 percent. No computation of present value is required since the tax applies equally to each year. It adds 2 percent to the loading formula.

Table 17-1 summarizes the assumptions and calculations for our illustration. Beside the type of expense or loading factor are two major columns. The first column shows the expense rates assumed; the second shows what must be added to the annual net premiums to recover expenses. Each of these major columns is subdivided into three subcolumns, one for each type of expense: percent of gross premium, per policy, and per $1,000 of insurance.

The previous discussion explains how the actuary finds the amount that must be added to the premium to recover the assumed expenses�but just for the percent-of-gross-premium expenses. Similar calculations are made for per-policy and per-$1,000 expenses.

We must introduce one more increment�premium additions�to handle settlement costs at the policy�s maturity. Premium additions to pay expenses at death are calculated in the same way as finding the present value of the death benefit, as explained earlier. To find the amount to add to the annual premium, divide this present value by the appropriate annuity-due factor.

The lower right-hand corner of table 17-1 displays the results. The expenses expressed as a percentage of the gross premium total 10.76 percent. Those expressed as an amount per $1,000 are $0.31 per $1,000. Those expressed as an amount per policy are $36.25. If no other factors were considered, this would be the loading formula. Other factors must be considered, however.

Most life insurance policies are long-term contracts with premiums that cannot be changed after issue. Many unforeseen developments may occur, however, before the company discharges its contractual obligations. Possible developments unfavorable to the company include epidemics, heavy investment losses, lower-than-anticipated interest rates, adverse tax legislation, and unexpected increases in operating expenses. A specific increment to the loading enables the company to accumulate funds to meet such contingencies if and when they arise. Since overcharges in a participating policy can be returned through the dividend formula, the company usually allows a generous amount for contingencies. An addition of 3 percent of the gross premium would be reasonable.

Mutual companies also usually load the premium intentionally to create surplus from which dividends can be paid. To provide these anticipated

dividends, the company adds safety margins to the mortality and interest assumptions. The extent to which the expense-loading formula is used to create dividends depends on managerial viewpoints. The company decides where it wants to be along the spectrum between high-premium, large-dividend companies and low-premium, small-dividend companies. If management leans in the former direction, the addition to the loading formula will be large; if it favors the latter approach, the increment will be at a minimum level. The example in table 17-1 includes a loading for contingencies of 3 percent of the premium plus $.50 per $1,000 of the policy�s face amount and a loading for dividends that consists of 2.40 percent of gross premium plus $3 per policy plus $1.25 per $1,000 of face amount.

Before a formula is adopted, the company tests it at various pivotal issue ages, such as 15, 25, 35, 45, and 55. These tests show whether realistic assumptions about mortality, interest earnings, expenses, and cancellations produce a workable set of gross premiums. The premiums "work" if the group of policies is anticipated to develop sufficient assets to provide the surrender values promised under the contract, to meet the reserve requirements imposed by law or adopted by the company, to support a reasonable dividend scale, and to provide the desired addition to the company�s surplus. Gross premiums are also compared to those of competing companies to see whether they meet the competition. Of course these two objectives are often in conflict.

Adequacy tests for loading, as well as other aspects of product pricing, use asset share calculations. To understand the asset share, first think of a block of identical policies all issued on the same day and on different lives. As time passes, the assets accumulated for these policies could be measured and the share belonging to each allocated. This stream of actual asset shares would be of interest only historically. For them to be of value at the time of pricing, the actuary projects (forecasts) asset shares based on a set of actuarial assumptions. These assumptions may range from simple to complex. In the extreme, if one assumes no expenses other than benefits and no terminations other than for death or maturity, asset shares would equal the net level premium reserves described in chapter 16. For pricing purposes, however, the assumptions also include expenses and rates of termination.

The asset share calculation traces the share from the end of one policy year to the end of the next. Assumptions reflect the timing of the payment of premiums, expenses, and benefits. For premiums and expenses paid at the beginning of the year and benefits at the end of the year, the actuary would perform the following steps:

To test the adequacy of participating premiums, the actuary compares the asset shares year by year to the policy surrender values and reserve. In a policy�s early years, the asset shares are less than the surrender values because of the insurer�s high first-year expenses. Therefore a loss occurs any time a policy terminates in the early years. When the asset share is larger than the surrender value but less than the reserve, the insurance company experiences a gain if the policy lapses, but it experiences a loss if the policy matures then as a death claim. At later durations the asset shares usually exceed the reserve, and the policy contributes to surplus when it is surrendered or matures. If, in the opinion of management, too many years pass before these crossover points are reached, then the loading should be increased. The converse would be true if the crossovers are too early.

The percentages and factors in table 17-1 were set for a policy issued to a male aged 32. Similar elements would be developed for other issue ages. In the process of adjusting the loading to balance the various factors involved, such as competitive considerations, the percentage and constant factors will be modified and may lose all linkage to the cost studies on which they were initially based. Frequently the only logic supporting the percentage and constant factors that evolve is that they represent the only combination that will produce a satisfactory result at all ages of issue.

In that spirit, we simplify our example here by adopting the following loading factors:

Percent-of-gross-premium expenses 16%

Constant expenses per $1,000 $  2.00

Per-policy expenses $42.00

Let us apply these factors to find the gross premium for a $100,000 ordinary life policy issued to a 32-year-old male. Recall that the net premium for benefits for this policy is $8.51. Thus 84 percent of the gross premium (that is, 100 percent minus 16 percent for percent-of-gross-premium expenses) must provide 100 x $8.51 for benefits and (100 x $2.00) + $42.00 for expenses. That is, 84 percent of the gross premium must be $851 + $200 + $42, or $1,093. Therefore the gross premium is $1,093 � .84, or $1,301 to the nearest dollar.

This procedure for gross premiums is not followed by all mutual companies. Some mutual companies calculate their gross premiums using a process similar to the one that follows for nonparticipating premiums.