by William L. Hezzelwood
- This paper is intended to address a need in the financial community: the lack of adequate analytical information to enable life insurance policy owners and their advisers to make informed policy management decisions.
- This paper presents three hypothetical questions that life insurance policy owners often face, but are ill-equipped to answer; it then shows how analytical techniques can be applied in answering them.
- This paper illustrates how the familiar concept of internal rate of return also can be used to guide life insurance policy decisions.
- The paper includes actuarial formulas used to calculate the numbers presented in the hypothetical cases.
William L. Hezzelwood is a member of FPA, a fellow of the Society of Actuaries, and a member of the American Academy of Actuaries. He is an independent consulting actuary. His firm, Actuarial Analytics, is based in San Clemente, California. (Email HERE)
The techniques presented in this paper can be helpful when a client is considering a change to their life insurance policy death benefits. These types of changes are usually made without any quantitative cost-benefit analysis. Such an analysis is often viewed as an insurmountable obstacle because it requires that one first obtain an estimate of the client’s future mortality risks, which may be beyond the skill set of some planners. However, by partnering with a consulting actuary this data can be developed, and by using the techniques presented here, it may be possible to offer better recommendations to clients.
Life insurance used to be simple. Clients paid a guaranteed schedule of premiums in return for a guaranteed death benefit, some guaranteed cash values, and a stream of non-guaranteed (but very stable) dividends that could be used to reduce premiums or buy more insurance. After the purchase, there was little someone needed to think about other than whether to continue paying the premiums. If a client decided to let the policy lapse, he or she would receive one of the guaranteed nonforfeiture options. How simple it was.
Then came the idea of universal life (UL) insurance, and the wave of product innovation has yet to let up. Remember the phrase, “The last life insurance policy you’ll ever need to buy”? That phrase revealed both a naïve belief in the power of the new UL product and a serious underestimation of the life insurance industry’s ability to innovate. Many of the UL policies sold in the early 1980s were eventually replaced by more competitive UL, variable universal life (VUL), or indexed UL policies.
Innovations have resulted in products that are more cost effective and more adaptable to the needs of consumers, but their flexibility requires greater attention to the ongoing management of each contract. Combine this new product flexibility with the turbulent economic times in which clients live and it is apparent that financial planners have serious need of a better way for people to make smarter decisions about their life insurance.
As examples, here are some questions financial planners and their clients (policy owners) may need to face, but may be ill-equipped to answer:
- Your client is 65 years old. His $350,000 life insurance policy will lapse at age 91 if he pays no more premiums. If the client wants his coverage to continue to age 100 he will need to pay an additional $43,464 immediately. At this stage of his life, is that a smart way to use his retirement savings?
- Your client’s estate is less than $5 million, and the recent change in estate taxes means that his heirs will not have to worry about federal estate taxes, so he may no longer need the life insurance policy originally purchased for that purpose. Should he cash it out or keep it as an investment?
- Your client’s life insurance policy has an increasing death benefit (equal to the face amount plus the cash value). He likes the idea of his policy’s death benefit increasing over time, but the policy looks like it is in danger of lapsing. Should he change his policy’s death benefit to be equal to the face amount?
To answer these questions, one must be able to put a value on changes to the future death benefits provided by the policy. Unfortunately, few people know how to do that. The two big questions are: (1) What is the value of the change in death benefits? and (2) Is it worth the cost in terms of either additional premiums or reduced account values?
Keep in mind that any of these transactions mentioned in the examples could cause a policy to violate the Internal Revenue Code definition of life insurance or cause the policy to become a modified endowment contract. Either outcome could cause adverse tax results; however, these considerations are beyond the scope of this discussion. Instead, the analysis will focus on finding a way to measure the financial impact of these kinds of policy transactions aside from any such considerations.
Measuring the Change in Benefits
To evaluate the cost/benefit implications of policy changes, it is essential to start with a set of before-and-after policy illustrations. These illustrations should be based on realistic or conservative assumptions about the policy’s nonguaranteed features. The “before” illustration should project the future premiums, account values, and death benefits on the policy as-is. The “after” illustration should project the policy reflecting any proposed changes in premiums, benefits, loans, or withdrawals that are being contemplated. Financial planners and their clients usually review these illustrations and make a decision based more on instinct than anything else. Here are two common comments on the value of changes to death benefits.
Comment 1: “The change in death benefits is worth exactly what the company is charging for it. The company sets the price.”
This is fundamentally true, because what the company charges is what the change in death benefit is worth to the insurance company. Their charge is the amount they need (together with earned investment income) to cover taxes, expenses, and profit and still have enough to pay for the change in death benefits. The insurance company bases this on their assessment of a client’s chance of dying. That assessment was made (unless evidence of insurability is required for an increase in benefits) at the time the policy was purchased. It is very unlikely that the insurance company’s price would be the same as the value that a client would put on the change in death benefit today.
Comment 2: “The change in death benefit is worth what it would cost the client to purchase equivalent coverage on the open market.”
Unfortunately, this is not a very good answer either. The required pattern of death benefit changes might not even be purchasable on the open market. Alternatively, a client might get about the same result by exchanging the existing policy for a new one and rolling into the new policy the current policy’s net cash value plus or minus the amount necessary to accomplish their goal. The “amount necessary” would be a relatively good measure of the value of the change in benefits, but it still does not measure the value to the client. Such an exchange might require new evidence of insurability, so the client would have to go through the full underwriting process, and they might not be willing or able to do that.
Here is an example of an alternative, analytical approach that measures directly the value of the change in death benefit from a client’s perspective.
Comment 3: “The value of the change in death benefits is the sum of the present values of all future years’ changes in expected death benefit payout (measured from the client’s point of view), discounted at the rate that the client could otherwise earn on their money.”
This direct approach is more theoretically appealing and, as will be shown, it gives planners the ability to do other useful calculations. A reasonable formula for calculating this present value is:
n is the number of years over which the measurement is to be calculated,
t is the policy duration being summed (t=1 is the first year, etc.),
x is the client’s age at the beginning of the measurement period,
ΔDB t is the change in death benefit in year t,
i is the interest rate to be used for discounting,
t-1px is the probability that the client age x will live to age x+t–1 , and
qx+t-1 is the probability that the client, having lived to age x+t–1 , will die
in the next year.
As long as this present value is greater than the present value of the change in cost, the client could feel good about making the change. This provides a bridge to the second part of this methodology; namely, how to measure the change in cost?
Measuring the Change in Cost
The change in cost is the present value of the change in future annual outlays reduced by the present value of the change in cash value at the end of the measurement period. Assuming that all outlays occur at the start of each year, the formula for this can be written as:
ΔOutlay t is the change in outlay each year and is presumed to occur at the start of each year. If the premiums are paid more frequently, the annual equivalents should be used,
ΔCSVn is the change in cash value at the end of the measurement period,
npx is the probability that the individual will survive n years.
The problem with this method is it requires that your client be able to estimate year by year probabilities of survival and death. Most people don’t have a personal mortality table for use in calculating these probabilities. Fortunately, it is possible to develop this information at a reasonable cost. There are consulting actuaries who can develop mortality rates for any given client based on the individual’s health history, occupation, avocation, and other lifestyle characteristics. With a set of mortality rates developed for an individual client, it is possible to perform the calculations described previously. Some planners may wonder if there are standard mortality tables they can use. The short answer is “no,” but additional explanation is provided later in this paper.
Other Useful Calculations
This method gives planners the ability to do some other useful calculations. For example, if someone solves for the value of i that makes the Present Value of Change in Benefits equal to the Present Value of Change in Cost, that value of i is the expected Internal Rate of Return (IRR) on the transaction. This can be compared to the yield available on alternative uses capital.
Another calculation planners may find helpful is the distribution of IRRs. This distribution allows an adviser to say, for example, “Mrs. Client, your expected return on this transaction is X percent, and there is a 90 percent chance that your actual return will be between Y percent and Z percent.”
But how can this be used to answer the three questions posed at the beginning of this paper? The following discussion looks at this issue in detail, and although the examples are hypothetical, they use values from an actual universal life product.
Should Client Pay to Keep Policy in Force?
Your client, now age 65, bought a $350,000 policy 12 years ago at age 53 as a standard nonsmoker. He elected to have a level death benefit. His premiums were scheduled to cease at age 65, but declining interest rates have caused his policy’s cash value to be much lower than originally illustrated, and his policy is now expected to lapse at age 91. If he makes a lump sum payment of $43,464 now his coverage will continue to age 100. Is this a good deal? What yield is he getting on his payment of $43,464?
In this example, the additional $43,464 will provide no additional benefit if the client happens to die before age 91, but will provide a $350,000 payment if he dies between the ages 91 and 99. Assume that no information about the client’s health is available other than that he received a favorable underwriting decision when he purchased his policy 12 years ago. Also assume that the client can earn an after-tax rate of 4 percent on his money.
With this information a planner can apply the above formulas and calculate that if the client makes the required $43,464 payment, the present value of the changes in his death benefits from age 91 to age 100 will be $28,812 (see Table 1, panel A). This can be easily compared to the change in cost, which is the required $43,464 payment because it is due now and no discounting is required. Because the value of the benefits is much less than the cost, the client may decide to not make the additional payment.
However, the expected IRR on the transaction is 2.53 percent. This IRR may seem low, but remember that the return is provided through tax-free life insurance proceeds. With this information in hand, both client and planner can make a more informed decision.
Here is how the distribution of IRRs looks. There will be no additional death benefit provided by the additional payment if death occurs either before age 91 or after age 99. The probability of that happening is 74 percent, so there is a 74 percent chance that the actual IRR on the $43,464 investment will be zero. However, there is a 26 percent chance of dying in the 91 to 99 age range, and in that case, the actual IRR will be between 8.27 percent and 6.46 percent, depending on the specific year of death. This will give the client some idea of the potential variability of his rate of return depending on the actual age of death.
Should Client Cash Out?
Assume that the policy is the same one used in the previous example and that no additional information is available regarding the client’s health. Also, continue to assume that he can earn 4 percent after tax. Instead of making the lump sum additional premium payment, the client is considering cashing out the policy. The current cash value is $91,671. If he surrenders the policy for this cash value, he will no longer have the $350,000 death benefit from age 65 to age 91.
As illustrated in Table 1, panel B, the present value of the expected cash flows from the policy’s death benefits is $132,872. This is substantially greater than the $91,671 cash value, so the client would be well-advised to keep the policy in force.
If the client does decide to keep the policy, Table 1, panel B also shows that the expected IRR will be 6.79 percent. Again, this return is provided by tax free life insurance proceeds. This would compare very favorably to any taxable investment with a comparable risk profile.
Now suppose the client recently had a medical exam and was given a clean bill of health. How would that change his expectations? With this information it would be reasonable to expect him to experience somewhat lower mortality rates in the early years, but eventually the effect of this will wear off and his mortality will become similar to that in the first example. This will cause the present value of the death benefits between age 65 to age 91 to fall. Instead of being worth $132,872, the benefits would be worth $120,030 and the expected IRR decreases to 5.82 percent.
Alternatively, suppose a client developed high blood pressure since the original policy was issued. This would increase the value of the death benefits to $170,390 and increase the IRR to 9.38 percent, making the argument for keeping the policy in force much more compelling.
Should Client Reduce Death Benefit?
Now assume that the client is a 65-year-old male nonsmoker who, 20 years ago at age 45, bought a policy with a $1 million face amount and a death benefit equal to the sum of the face amount and the cash value. (The expected mortality rates for this example are slightly higher than in the first two examples, because the insured was underwritten 20 years prior rather than 12 years.) The original premium, payable for 20 years, was projected to keep the policy in force to age 100, but declining credited interest rates have made that unlikely. Current projections show the policy lapsing at age 92. The current cash value is $403,468 and the death benefit is $1,403,468. A comparable projection shows that if he reduces the face amount to $961,168 and changes to a level death benefit the coverage will stay in force to age 100. In this situation, the question is, “Which pattern of death benefits provides the greater value?”
As shown in Table 2, if no change is made to the policy, the death benefits will continue to grow as long as the cash value increases, but the cash value actually peaks at age 74 and thereafter declines to zero at age 92, at which time the policy lapses. The present value of the varying death benefit is calculated to be $560,221.
Alternatively, if the death benefit is reduced to $961,168 and changed to a level benefit it will stay in force to age 100 with no residual cash value at that time, but the present value of the death benefits will be reduced to $453,864. Although the policy might lapse sooner without making a change, it does provide a greater expected return to the policy owner.
An IRR analysis shows that the current pattern of death benefits provides an expected rate of return of 6.55 percent on the initial cash value, whereas the expected rate of return provided by the modified death benefits is 4.75 percent.
With these data, the policy owner is now in a position to decide if he would rather accept a smaller (yet reasonable) rate of return in exchange for having the death benefits last longer.
In the examples presented in this paper the hypothetical clients are male nonsmokers who have been previously examined and underwritten for a life insurance policy. To develop estimates of their future mortality, one should use mortality rates derived from experience studies of insured lives. The Society of Actuaries has published many such tables. The examples presented in this paper are based on the 2008 Valuation Basic Tables (VBTs). For purposes of analysis, rates from the 2008 VBT were used without modification, but in actual practice it would be better to make adjustments to reflect mortality improvement that has occurred since 2008. Other refinements also could be made to reflect the client’s vocational and avocational risks, other lifestyle factors, and any medical issues that have developed since the insured was last underwritten.
If the choice of mortality rates did not make a significant difference in the calculated results, standard published tables might be suitable. As this paper shows, however, the assumed level of mortality can make a material difference in the result. For example, in the second example, the client was considering surrendering his policy for the cash value of $91,671. The analysis showed that the true underlying value of those death benefits could be anywhere between $120,000 for a more healthy client and $170,000 (or even higher) for a less healthy one.
Expected versus Actual IRRs
Financial planners are familiar with the concept of IRR, but a full understanding of the concepts presented here requires an appreciation of the difference between actual IRR and expected IRR where uncertainty of the return is involved.
For example, suppose you loan someone $100 and they promise to repay you $110 at the end of a year. Assuming they are trustworthy and you regard their promise as a solid one, your expected IRR on this transaction is 10 percent, because the interest rate at which the present value of the repayment is equal to the original loan is, in fact, 10 percent. Mathematically, $110/(1+i) = $100 only when i = 10 percent. At the end of the year, after you have received your $110 payment, you can say that your actual IRR on the transaction was 10 percent.
Now, suppose your $100 loan gets you a promise to repay either $120 if a year-end coin flip comes up heads, or only $100 if the coin flip comes up tails. The expected IRR is still 10 percent because you have a 50/50 chance of getting a return of either zero or 20 percent. Mathematically, ½ × zero + ½ × 20 percent = 10 percent. At the end of the year, however, you will realize an actual IRR of either zero or 20 percent. It is impossible to have an actual IRR of 10 percent even though that was the expected IRR at the start of the year.
This is the nature of the calculations presented here. Rather than dealing with a relatively certain stream of future payments, this paper has applied probabilities of survival and death to calculate the expected future cash flows from the life insurance policies. It is those expected cash flows that are used in the IRR calculation.
How does one go about finding an actuary to help with this kind of work? What follows is a brief introduction to building a working relationship with an actuary.
The cost of hiring a consulting actuary to perform a mortality risk analysis will vary significantly depending on the complexity and unique characteristics of each client, however, typical costs range from $1,000 to $3,000 for an actuary to provide a planner with a set of mortality and survival rates tailored to an individual client. The cost of actuary services, in the end, may provide a higher return than attempting to do it yourself. Many data sources can be used to assist in developing these rates, and the analysis requires experienced judgment.
The second step, which includes running specific financial calculations, can be done by any competent financial planning professional; however, the consulting actuary could perform this function as well.
Actuaries are often asked if a similar analysis can be conducted on a second-to-die policy. It can, although it doubles the effort on the mortality risk analysis and makes the financial calculations a bit more complex. Considering the cost of the mortality analysis and the financial analysis, planners may find that this kind of actuarial analysis does not make a great deal of sense where the amount of insurance is less than $500,000 (double that for second-to-die policies).
Whether someone works in a large firm or as a sole practitioner, the insights provided by this type of analysis can provide valuable information when advising more substantial clients. Financial planners who wish to contact a consulting actuary should look at the online membership directories of the Society of Actuaries (www.soa.org) and of the Conference of Consulting Actuaries (www.ccactuaries.org).
The purpose of this paper is to address a pervasive need in the financial community; namely, the lack of adequate analytical information to enable life insurance policy owners and their advisers to make informed policy management decisions. As illustrated, there can be great value in performing this kind of analysis. The key is to first obtain a reasonable estimate of the client’s expected future mortality. Armed with these details, and the results of an in-depth analysis of the changes being considered, the policy owner and his or her planner will be on much firmer ground when faced with complex policy change decisions.
Hezzelwood, William L. “Managing Life Insurance Policies: An Analytical Approach Built on Standard Actuarial Techniques.” Journal of Financial Planning 26 (10): 60–66.
- The half-year adjustment in the exponent is an approximate adjustment to account for the fact that death benefits are paid, on average, in the middle of the year.
- To be precise, this formula should include an element to address any increase in income taxes that might be due on surrender. For simplicity, this adjustment has been omitted. Alternatively, note that the increase in cash value at the end of the measuring period could have been included as an additive element to the formula for the Present Value of Change in Benefits.