There are as many different methodologies of comparing life insurance policies as there are generic types of coverage. Historically the traditional net cost method was widely utilized. Its methodology is quite simple, easy to understand, and even easy to calculate. The starting point is a specification of the duration of coverage to be evaluated. Often this was for either 10 years or 20 years of coverage. The actual mechanics of the evaluation involve taking all of the net premiums paid under the policy and adding them together, then subtracting the cash surrender value for the interim being considered and all dividends paid over that interval. One of the reasons this method is so easy to understand is that it does not take into account the time value of money. In other words, it ignores interest.

The final cost derived under net cost method can be considered the amount the insurance company retains. The main criticism of this methodology is that after 20 years the net cost is usually negative. That is, the cash value amounts at the end of the interval plus dividends paid over the interval exceed the aggregate of premiums paid. The implication is that the policyowner has received insurance free of charge. The serious shortcoming of using this methodology is that it gives equal weight to payment amounts that may be separated by 10 or 20 years. By doing so, it totally ignores the opportunity costs of earnings forgone because the funds were not invested in an investment account. (See table 5�2.)

The net cost method is not appropriate for comparing policies, whether they are the same type or different types. It is totally unacceptable under the state statutes and regulations for purposes of making replacement evaluations. In fact, under some state statutes insurance agents are prohibited from using the net cost method.

The logic of using interest-adjusted indexes is similar to that of the traditional net cost approach with the exception that interest-adjusted indexes explicitly take into account the time value of money. The National Association of Insurance Commissioners developed the interest-adjusted cost indexes and also derived model laws requiring their use. These statutes were drafted and adopted during the 1970s prior to the high interest and inflation rates experienced in the late 1970s and early 1980s. Almost every one of the statutes mandates that the rate of interest to be used is 5 percent annually.

Essentially the interest-adjusted method takes all payments for premiums and treats them as if they had been put into interest-bearing accounts to accumulate interest until the end of the interval for evaluation. In a like manner, all dividend payments are carried as if they are deposited in an interest-bearing account, and that account balance is calculated for the end of the interim of evaluation. After all premium payments and all dividend payments have been adjusted to the end of the comparison interval, the policy cash value and accumulation dividends are subtracted from the accumulated value of all the premiums paid.

The next step is to take that future net cost and divide it by the future value of an annuity due, based on the specified interest rate and the period of time being evaluated. At 5 percent interest the factor to use for a 10-year evaluation is 13.2068. Likewise the factor to divide into the future value amount over a 20-year interval, again assuming a 5 percent interest rate, is 34.7193. The result represents the level annual cost for the policy. This will still be an aggregate amount that must be converted to a per-thousand amount, which is accomplished by dividing the level annual cost amount by the number of thousands of dollars in the policy death benefit. (For example, the aggregate level annual cost for a $50,000 policy is 50 times greater than it would be for a $1,000 policy. We would therefore divide the level annual policy cost by 50 to determine the level annual cost per thousand dollars of coverage.)

These future values appear on most sales presentation materials utilized by insurance agents. For that reason there is usually no need to calculate them independently. The numbers presented will be based on the 5 percent mandated interest rate and the methodology described in the statutes. The same method-ology works for any other interest rate the evaluating party thinks is appropriate.

The future value factor for an annuity due can easily be derived on a financial calculator. Merely specify the number of periods in the evaluation interval (such as 10 or 20) on the N key, and enter the interest rate on the I key and the payment amount of $1.00 on the PMT key. Press the FV key to solve for the future value. The resulting factor is then divided into the net future value of the accumulated premium amounts in excess of the accumulated dividends and end-of-period cash value. If there are terminal dividends available at the end of the interval, they are subtracted from the accumulated premiums before dividing by the annuity due factor to determine the surrender cost index. (See table 5�3.)

Determining the payment cost index is similar to calculating the surrender cost index except that there is no recognition of the end-of-period cash value. Under this index calculation, dividends over the internal and terminable dividends at the end of the interval are the only items subtracted from the accumulated premium amounts. This gives a future value of net premiums that is then divided by the annuity due factor for the appropriate period and appropriate interest rate. Future values contained in agents� sales materials are usually based on either a 10- or 20-year interval and a 5 percent annual interest rate. (See table 5�4.)^*

A simple example of a fictitious policy is presented in table 5�5^*. In the example there are $15 premiums per year over a 10-year interval and dividends of $0.00 the first year and $1.00 the second year, increasing by $1.00 each year until they reach $9.00 in the 10th policy year. The accumulation at 5 percent of all premiums paid is $198.10; the accumulation of all dividends is $54.14. Subtracting the accumulated value of dividends from the accumulated value of premiums yields a future value of net premiums equal to $143.97. Subtracting the cash value at the end of 10 years ($120) from that amount yields a future value of net cost equal to $23.97. This future net cost is then divided by the future value of an annuity due for 10 years, or 13.2068, which yields a surrender cost index of $1.814676. In the same table we can see that by ignoring the cash value, the payment cost index becomes $10.90.

Calculations under interest-adjusted indexes can be done by hand, but they are easier and quicker when done on a computer or financial calculator. Index values are sensitive to the interval being evaluated and the insured�s age of issue for the policies being compared.

These cost indexes are an acceptable means of comparing similar policies. Usually the policy with the smaller numerical values for surrender cost and payment cost indexes is preferable to policies with higher index values. The method is not acceptable, however, for comparing dissimilar policies�for example, a term policy with a whole life policy. It is also not well suited for evaluating policy replacements.

The cash accumulation comparison method is much more complex than the net cost method and requires a computer to make the calculations. A significant amount of data must be entered into the computer program in order to calculate the results accurately. One of the strengths of this method is that it is acceptable to compare permanent insurance policies with term policies. It can also be used for evaluation of replacement proposals.

The technique is simply to accumulate the premium differences between the policies being compared, while holding the death benefits of both policies constant and equal. For example, to compare a cash value contract with a term contract, set the death benefits equal at the beginning of the period, and use the premium amount for the whole life policy to determine the amount to deposit into a side fund to accumulate at interest. The calculation is basically a buy-term-and-invest-the-difference approach to comparing the policies. At the end of the interval being evaluated the side fund accumulation amount can be compared to the cash value in the whole life or other form of cash value insurance policy. The

policy with the greater accumulation at the end of the comparison interval is considered the preferable of the two contracts. (See tables 5�6 to 5�10.)

As noted before, this comparison method really requires a computer in order to be efficient. Not only does the difference in premium have to be allocated to a side fund and accumulated interest but there is also a necessary adjustment of the amount at risk. The side fund accumulated with the term policy acts much like the cash value in the whole life policy, and the amount of term coverage being purchased has to be adjusted so that when it is added to the side fund it will exactly equal the death benefit under the permanent policy to which it is being compared. Using a computer, once a spreadsheet has been built with all of the logic to make the necessary comparisons, it is just a matter of plugging in new values for premiums, cash values, and accumulation account amounts.

The equal outlay method is somewhat similar to the cash accumulation method. Again, the same amount of premium dollars is expended, on the one hand for a cash value contract and on the other for a term policy. The amount by

which the cash value contract premiums exceed the term premiums is deposited into a side fund, and the difference in premium amounts is accumulated at specified interest rates. Then the death benefit of the term insurance plus the accumulated side fund amounts are compared with the death benefit under the cash value contract in which dividends, if any, have been used to purchase paid-

benefit amount and the value of those paid-up additions. Under this type of comparison the policy producing the greater death benefit is considered the preferable contract. (See tables 5�11 to 5�15.)

Both this method and the cash accumulation method are very sensitive to the interest rate chosen for purposes of the side fund accumulation. Manipulating the interest rate can skew the comparison results. The higher the interest rate used, the more the equal outlay method will tend to favor the lower-premium policy with the side fund combination.

There are three other comparison methods that all utilize an assumed cost of coverage to isolate an interest rate for comparison purposes. One of the problems of comparing any life insurance policies is that there are degrees of freedom in the parameters involved. We cannot make a single-factor comparison without choosing assumptions for the other factors and doing so in a way that those factors are also comparable. In other words, if we want to calculate a policy�s internal cost of insurance, we have to make some assumptions about interest rates; if we want to calculate interest rates, we have to make some assumptions about the cost of insurance.

The comparative interest rate method is really a modification of the cash accumulation method, whereby we are calculating the interest rate that would make a term insurance policy side fund exactly equal to the difference between the available cash value policy death benefit and the term insurance death benefit. The comparative interest rate method looks for the interest rate that would make the buy-term-and-invest-the-difference comparison exactly equivalent in the death benefits provided. To make that calculation both the outlays for premiums and side funds and the death benefit levels must be held equal. This method is often referred to as the Linton yield method, named for actuary Albert Linton, who first published the approach in the early 1900s. (See table 5�16.)* Its primary drawback is the complexity of the calculation, which requires not only a computer program to accurately calculate the interest rate desired but also a large amount of policy information that must be entered into the program before it can be run.

Another caution with using software for this type of comparison is that each comparison should use the same assumed term premium rates to derive the interest rate. Otherwise there will have been manipulation (intentional or unintentional) of the interest rates derived by the calculations. The policy generating the highest comparative interest rate is assumed to be the preferable policy when making comparisons by this method.

Joseph Belth, a retired professor of insurance and publisher of the Insurance Forum newsletter, has developed more cost comparison approaches than any other scholar known to this author. This chapter presents two of his many different policy comparison approaches. (See table 5�17.) He is quick to point out that there is no perfect comparison method because the wide range of objectives that insurance policies address requires that different levels of priority be placed on the death benefits and cash values in different situations. Each methodology puts its primary emphasis on the elements considered to be the highest priorities for that particular approach.

Under the Belth yearly rate of return approach only one year of the policy is considered in making an individual calculation. Such a calculation can be made for each and every year of coverage over the given interval. The objective is to identify the benefits provided by the policy during that year (the end-of-year cash value plus the dividends paid during the year and the net death benefit for the policy year) and the investments in the policy necessary to derive those benefits (a combination of the beginning-of-the-year cash value and the premium paid for that year of the policy). The yearly rate of return formula divides the sum of the benefits by the sum of the investments and then subtracts the number 1 from that amount. This process is repeated for each year over the comparison interval. The policy with the highest rates of yearly return in the largest number of years over the observation interval is considered the preferable policy. The calculation under the Belth yearly rate of return method depends on a realistic assumed term rate, not a manipulated rate that is intentionally much too high or low that it skews the results. This method does not necessarily make it easy to identify a predominant policy. The highest yearly rate of return may change back and forth among the policies being compared.

Under the Belth yearly price approach we must assume an investment or interest rate and thereby calculate the cost of protection. Again, the calculations are made one year at a time for each of the years in the comparison interval (usually 10 or 20 years as in most other comparison methods). Using this methodology, the beginning cash value plus the current premium are accumulated at the assumed rate of interest to derive a year-end surrender value. After computing the theoretical end-of-year value from the beginning cash value and the premium plus interest, we subtract the actual end-of-year cash value plus dividends paid during the year. This is the difference assumed to have been available to pay mortality charges.

The next step is to divide the difference between theoretical year-end values and actual year-end values plus dividends by the amount at risk per $1,000 of coverage. The actual formula looks quite formidable, but when its terms are defined, it is really quite simple and straightforward.

After making a yearly price-of-protection calculation for each policy being compared for each year in the comparison interval, it is then a matter of identifying the policy with the lowest cost of protection for the largest number of years over that interval. In most cases that policy would be the preferable one of those under consideration. The benchmark prices derived by Professor Belth (see table 5�18 below) are based on United States population data, rather than on insured lives data, and represent a relatively high cost of providing death benefits only; there is no allowance for company overhead or operations.

In most cases term rates for standard-issue policies to people in good health will be below these benchmark prices, which are only a crude yardstick and should not be used as the criterion for automatically rejecting a policy. These benchmark prices would have no validity at all for evaluating rates on policies issued or proposed to persons in poor health who are charged associated higher premiums. Such premiums might legitimately be multiples of the benchmark prices.

Both Belth methods of policy comparison are appropriately used for comparing similar and dissimilar policies. With some modification these methods are even appropriate for comparing replacement evaluations. Part of their attractiveness is their simplicity and their ability to be calculated without the need of a computer. Calculations are actually simple enough they can be done by hand; nevertheless, the process can be expedited with a good calculator or a computer.