Refunds, risks, and time value of money: A case of insurance policy analysis

Some important aspects to consider when deciding about insurance purchases

After a generic intro, a few key factors of policy alternative evaluations will be scrutinized, using the example of a 25 year old healthy woman who is concerned about suffering some critical illness in the future. First, we’ll see some meaningful charts about the probabilities of need occurrence in various time frames, followed by some basic premium/policy alternatives. Next, time value of money (TVM) based calculations will be done to realistically compare costs and benefits, or various cost alternatives. Internal rate or return (IRR) calculations and related probability estimates will show that Return of Premium (ROP) riders can be quite wasteful additions to critical illness insurance (CI) plans. There will be arguments for one ten-year-term (T10) policy the unique ROP feature of which appears to be a much better buy than ROPs in general. Similar conclusions will be drawn from analysis of unfolding (accumulating) total cost calculations, even after considering the potential of repeated term policy renewals: ROPs are usually not worthwhile (with the possible exception of the above-mentioned, not widely known T10 policy), and preference for either the best term or level-cost-to-age-75 (T75) policies can be argued for, depending on rather subjective factors.

The post’s main focus is not information on CI insurance needs or the comprehensive description, analysis, or comparison of CI policies. Readers interested in those can find lots of relevant information on this site and elsewhere. Here, we are more concerned about generic lessons regarding evaluation of needs and solution alternatives, including dispelling of some myths, demonstration of the importance of circumspect analysis, and of time value of money calculations.

The post is quite long to read; you may want to just lean back instead and watch the slide show summary of it. Enjoy!



  • Background fundamentals: a tune-in exercise
  • Why buy it at all: Mary’s case
  • T10 or T75?
  • ROP or not?
  • Would term policy renewal help a lot?
  • What did we learn?

    An audio slideshow summary will appear here soon!


    Tune-in exercise

    What would be the sensible choice if someone offered you a raffle ticket for $3, where a third of all tickets are going to win $20 each? It’s a no-brainer, right? Probabilistically speaking, each ticket has a 33.33% chance to win the $20 prize, therefore the expected value of the prize money a ticket will buy is 0.3333 times $20, that is $6.67. Under these conditions, and as long as this expected value is higher than the purchase price, buying tickets is a good or even excellent investment. Using the above amounts and likelihood, it would be such even if the prizes were paid in a few years, not immediately. (But would you find the offer attractive if the prizes were paid in 10 years? How about 20 years?)

    This simplistic exercise appears to contain the main factors to be considered when dealing with many important financial decisions, including buying insurance, in real life: what/how much is to pay, what/how much is to get, what are the chances, and what are the temporal parameters? Sensible, meaningful calculations can be done using them. Still, let’s consider an additional one, because it will change the character of how we approach issues. First, let’s assume that the prizes are paid immediately, and you can buy as many tickets as you want. How much of your money would you spend on it, how many tickets would you buy?

    Unless you are against having too much money, you’d be smart to invest all you have in this raffle, … and then even more. I mean, it would be rational to recycle all the prize money you collected back into the raffle, … as long as the gold laying goose behind the scenes has not snuffed out. Sooner or later it necessarily would, … just ask Bernie Madoff, Earl Jones (or study a bit the ecological status of the Earth). Lets’ put aside now our legitimate concerns regarding the sustainability of this raffle for the promoters/financiers though. They’d be overwhelmed with the storm of ticket-purchasers right now anyways, … would not have time to worry about the future. Let’s say that, to simplify things, they would add three zeros to both the price and the prize: a new $3,000 ticket would still have the same 33.33% probability of winning, but now the prize would be $20,000. Who and how would be affected, if at all?

    Your friendly neighbor, Mike the Millionaire, would not mind the change; by playing at this new, higher level, he could even increase the pace of moving ahead toward new riches (and toward that inevitable collapse of the offering, … but we decided to put that concern aside for this exercise). If, however, you’d have much less – let’s say only $9,000 – at your disposal, it would be time to start thinking seriously. Yes, every third ticket is a winner, and any winning ticket is a very significant boost to your wealth, … but this “every third” is valid ‘on average’, for long sequences of events only. To see what the chances are that you will draw three losing tickets in a row – that would wipe you out completely -, you first have to look at the same old probability with a fresh eye. A one-in-three (33.33%) chance for winning means a two-in-three (66.66%) chance for losing. To get the probability of losing three times in a row, you have to calculate 2/3 times 2/3 times 2/3 = 8/27 = 0.296. In other words, there is a 29.6% chance that instead of winning, you’d lose everything. The relative magnitude of the stakes (price and prize) to your assets brought in a pair of new factors to consider: the rather objective factor of what you have, and the subjective factor of what kind of likelihood of a huge loss you’re willing to suffer. We can call this combination of subjective and objective components together as risk tolerance or financial resilience. Adding this factor to the previous list of price, prize, chance, and time factors lifts the decision making dilemma from the domain of dry but precise mathematics over to the domain of human lives, with much less precise and much less clearly calculable decisions and solutions.


    Mary’s case

    The exercise shown in the rest of this posting assumes that a healthy 25 years old woman, Mary, is in the midst of deciding if she will buy a critical illness insurance policy or not, and if she does, what kind. The analysis will be less than comprehensive in two respects: it will not consider all the available kinds of policies, and it will not consider all the at least potentially important factors and features. Still, elaborating a bit on those major factors referred to in the first four paragraphs, but now with specific real life quantities, will probably be informative in the sense that it will help readers to form or improve on their decision making framework for similar situations.

    Mary is single, childless, and has quite a good job, with group life and disability insurance from her employer. Therefore, she’s not interested in life insurance and individual income protection (disability) plans. However, she’s heard a lot about the dangers of getting stricken by some life-threatening illnesses (‘critical conditions’ would be a more precise term, especially for a young person, since these policies cover some situations as well that are more likely caused by accidents than illnesses), and she even knows people personally who suffered financially because of such disruptions in their life. She remembers vaguely references to statistics stating that more than every third people will get cancer in their lifetime, and she knows that cardiovascular diseases or diabetes as well affect many people even before they get really old. She has learned that a significant part of health care costs in dire situations is sometimes not covered by provincial health care plans, … so she wants to look into the main issues of buying critical illness insurance coverage. While there are several other versions available, she is looking first at only a few T10 (ten year term, where premiums are guaranteed to stay constant for ten years, then increase in a step-like fashion for consecutive ten year periods) and T75 (level premium until age 75) policies. She wants to see how costly and how worthwhile they’re.

    Her secondary objective – in case she decides that she wants to purchase – is to understand what she heard from a friend about policies on which the buyer allegedly never loses money. If they are unlucky and do get hit by a serious illness that is covered, then they get a large cheque soon after the diagnosis; if however they will never need to claim a benefit, then at age 75 (or even earlier) they’ll get back all (or almost all) they money they paid into the policy, … giving a good boost to their retirement funds. This ‘not loosing in either way’ variant has a certain appeal to Mary, even though she fears that there might be some catch connected to them, or that they might be simply too expensive for her.

    She needs and wants exploration, calculations, and understanding. She has learned the basics of critical insurance, and understands the principles of insurance in general, so she’s aware that her current good insurability is of value not to be taken as granted to remain, even though she conducts a healthy lifestyle. What she needs is quantification, then many specific features /details; here we will deal mainly with the quantification part.

    Her chances

    First, let’s see some statistics about the likelihood of suffering from a life threatening critical illness/condition at various ages.

    Mary’s very first reaction to this chart is some mixture of fear and disbelief. More than 40% chance of getting a life threatening illness or injury? It’s not really a consolation to see that her brother and boyfriend have much worse chances. How could the chances of a young person like her be worse than of people of her parents’ age? She’s stronger and healthier than her mom, and it’s the same with most of her friends. After the first shock though, being a smart lady, she looks carefully again at the title of the chart, and realizes that what is at play here is very similar to what she’s learned about life expectancy statistics: old people, on average, have higher life expectancy than young ones. For example, a 25 years old female’s life expectancy is about 83-84 years, but her 75 year old grandma’s is about 4 years more. The 25 year old granddaughter has a 3% chance to live to age 100, but the grandma has a 5% chance for that.

    The explanation is simple: the old, by virtue of being already old, have done what the young can only hope for: they survived the decades that separate them from the young. Some of their old class-mates dropped out during the intervening decades, but those are not part of the life expectancy forecast for the (now senior) survivors. On the other hand, those (not yet identifiable) few from the 25 year age cohort who will drop out prematurely, are part of the forecast, pulling the life expectancy figure down. Another aspect to note is that these statistical tables themselves are not static. When the now 75 old grandma was 25, her life expectancy was much less than 83-84 years. Longevity and health improved a lot in the last century or so, resulting in well advancing life expectancies. As for the future continuation of this trend, we can only guess. There can be arguments for both hope (science, technology, better life conditions, etc.) and deep concerns (obesity, unhealthy lifestyle, worse life conditions, etc.), … so it’s probably the best to rely on the currently valid statistics.

    Having refreshed all this information, Mary realizes that for her, instead of getting scared by the over 40% chance of having a critical illness before age 75, right now, it’s more important to look at the slope of that blue curve. Its relative flatness in the near future suggests that she has a rather low chance of being hit with a critical illness in the next about two decades; the steeper curve after about age 45 shows that that’s when such mishaps become more frequent. She was looking for some statistics that would show what her chances are for shorter time horizons, let’s say the next one or two decades. She couldn’t find one, so she asked me to crunch the numbers shown in the first chart. Here is what we got:

    Looking at this chart was, first, certainly a small relief for Mary: she can, to some extent, put her worries on hold for now, the chances are much smaller than in the previous chart. Also, she feels that it’s more fair to present the data this way. In the first chart, she had higher percentages than her mom because the chart referred to the next 50 years of Mary’s life, but only to the next 25 years of her 50 year old mom. Here, we’re looking ahead 10 or 20 years at every age. Mary’s second reaction was that, especially if we consider that last factor on the list we built in the introductory section, the magnitude and its relative size to her assets (the ‘real life, not purely mathematical factor’), then she’d probably be much safer financially if she had insurance protection. Those rather low probabilities for the next 10 or 20 years (1.32% and 4.41%, respectively) are still not negligible, even though she notices also that the statistics used here refers to smokers and non-smokers lumped together. Being a non-smoker, she knows that her chances are better than indicated by these percentages. Still, she could quite easily get into deep trouble financially, having not been able to accumulate any serious assets, if a critical condition does occur.


    Term (T10) or level cost (T75) policy?

    Maybe the best would be, she thought, to buy some low-cost term policy, because there are so many other destinations for every dollar she can spend. She doesn’t want to get overwhelmed with all the versions of available CI policies at once, so she wanted to see some comparison of the two most typical types, T10 and T75 policies. She knows that the average size of critical illness policies bought is around $100,000. It seems to be a lot of money, … obviously, in a crunch, even a fraction of that would matter. She also knows, however, how inflation erodes the real value of money on the long run; for example, assuming 3% inflation, the purchasing power of that $100K would shrink to $57K in 20 years. Therefore, she wants to look first at $200K policies; if she finds the premium just too much at the end, she can go lower for the final decision.

    Looking at some premium calculations

    Here are the annual premiums for three of the best T75 policies:
    Company A: CAD1,009 — that is, total premiums paid by age 75 is: 50yrs times $1.009/yr = $50,450
    Company B: CAD955 — that is, total premiums paid by age 75 is: 50yrs times $955/yr = $47,750
    Company C: CAD970 — that is, total premiums paid by age 75 is: 50yrs times $970/yr = $48,500

    Here is the premium for a well-priced T10 policy:

    Company D:
    in 1st 10 years – CAD536
    in 2nd 10 years – CAD1,018
    in 3rd 10 years – CAD1,906
    in 4th 10 years – CAD3,606
    in 5th 10 years – CAD8,612
    In other words, the total of premiums paid by age 75 is $156,780. Unfortunately, too often, many ‘experts’ and unsuspecting customers stop right here. For them, there doesn’t appear to be anything to further scrutinize, the long term advantage of T75 policies over the term policy seems to be so obvious, … more than three times more premium required by age 75, correct? The customer is better off with the level premium policy (and so is the agent, because the immediate commission on the higher starter premium T75 policy is higher), right? But no, jumping onto such firm conclusion would be a bit prematurely at this stage.

    The common practice of showing the disadvantage of term policies this way can be criticized on at least two counts:
    – First, adding up annual premiums this way, without considering the time value of money (TVM), is completely inadequate; the value of one dollar is significantly different from the value of one dollar years from now (or years back in the past)
    – Second, the basic rule with term policies is that at the end of each period, before the premium would go up to the next guaranteed level for the next term, there is a new shopping around to be done. It will hopefully lead to significantly better premiums than the old guaranteed ones. There is some uncertainty involved, of course, and some potential other disadvantages of changing policies (new contestability period, perhaps new transitory periods during which the protection is somewhat restricted, etc.), still, if there is no problem with insurability (and it’s a significant if, that’s why it’s always important to look at the guaranteed renewal premiums, … because one may get stuck with them if one loses insurability!), then the total of premiums paid for consecutive term policies can be much lower than the guaranteed amount was according to the original term policy. (As we’ll see later, this argument can be much weaker in reality than it sounds to be.)

    To quantitatively assess these two factors, the TVM effect and the likelihood of keeping insurability (and therefore the ability to get new term polices at regular intervals), we have to do calculations with somewhat imprecise assumptions. There is no carved-in-stone way of determining, e.g., how large the discount factor to be used for making justice with money paid or received at different times (so that we can really add them up) should be. Similarly, there are no precise data for keeping insurability for even the average person, … but we can make some sensible estimates and guesses. For Mary’s analysis, this is how it went:

    Time-value of money considerations:

    Long term inflation rate is about 3% per year. Therefore, it is reasonable to consider at least as much as that for the discount factor. One can argue even that if one invests money in virtually no-risk investments, one can get one or two percentage point higher rates on average than inflation, … so maybe applying a little bit higher discount rate is warranted as well. Again, there is no precise or widely agreed upon rate to be used, … but this factor should definitely not be 0%, the one implicitly assumed when today’s money is simply added to money from future years. In our calculations, three versions (3%, 4%, and 5%) of discount rate assumptions were used for serious consideration.

    Discounted total premiums paid by age 75:

    .. at 0% discount rate at 3% discount rate at 4% discount rate at 5% discount rate
    Company A – T75 $50,450 $26,740 $22,542 $19,341
    Company B – T75 $47,750 $25,309 $21,336 $18,306
    Company C – T75 $48,500 $25,706 $21,671 $18,594
    Company D – T10 $156,780 $58,886 $42,170 $31,920

    If you prefer it visually, here it is:

    Calculating the TVM didn’t make the cost-disadvantage of the term policy disappear, but it made it look much smaller. Furthermore, if we also consider that there is a good chance that insurability will be kept at least for a while, therefore a new, lower cost term policy can be bought at renewal time/s/, then the cost difference will shrink even further. (How much is that ‘good chance’ for remaining insurability? I don’t know, but a 60 to 70% estimate is probably conservative enough. How much is the real value of buying anew at renewal times? Let’s look at that later.) How about future scenarios when the insurance will not be kept (for whatever reason, … death, a critical illness benefit payment, or simply financial inability to pay for it, etc.) for the whole period considered here, that is up to age 75? In all those scenarios, the advantage of the level-premium plan over the term policy way will be smaller, … it might even disappear completely. You cannot see it from the chart above, but you will from the next ones.

    It will be instructive to look at charts showing the Present (discounted) Value (PV) of all premiums paid during shorter periods of time as well, not just until age 75. It will be even more meaningful if we look in the same charts also at the PV of the contracted benefit amount. Again, we’ll look at 3%, 4%, and 5% discount rate variants, and using the numbers for Company A (T75) and Company D (T10).

    There are two interesting cross-over points in each chart. Before the light blue line crosses the dark blue one (at around Yr29 to Yr32), the term policy costs less, and after that the T75 level cost policy costs less. Then there is the other cross-over (or pair of cross-overs, when 5% discount rate is used), before which the red benefit line is over the cost line/s/, … but after which point it’s below the cost line. What does it mean? Nothing else that if a critical illness happens after this point in time, the value of the benefit received will be lower than the value of all the premiums paid for the policy during the years (provided that the discount rate used is realistic/acceptable, … but I claim it is). Looking at it with a ‘pure’ mindset of a mathematician or an investor, we can say that in these situations the insurance policy turned out to be not a good investment. It’s important to understand that the mindset recommended for insurance is different. We can refer back to our oversimplified introductory exercise with the raffle tickets, where we soon realized that magnitude of costs and losses and the ability to handle unlucky outcomes (subjective/objective risk tolerance or financial resilience) are additional important considerations when making insurance decisions. If one bought an insurance policy purely with an investor’s mindset then one should start praying immediately for getting a critical illness (or dying when thinking about life insurance) as soon as possible. If /s/he (or rather the heirs, in case of a life policy) can collect the insurance benefit after paying for the first premium, why would they want to wait till they have to pay the second one as well? It’s nonsense not to see the difference between the logics to be used, and it’s dishonest to pretend that there are policies where the buyer cannot lose money, … because the benefit received will always be higher than the premiums paid, or because even if there will be no benefit payment (due to no covered condition occurring) there will be no ‘loss’ since all (or almost all) the money paid during the years will be refunded, guaranteed. Unfortunately, these claims are often made. Let’s see how the first claim shows, simply by forgetting to consider the time value of money:

    As we have seen, this approach distorts the relative costs of the T10 vs the T75 policies (by bringing the cross-over point a few years earlier than when PVs are calculated), … but it even more distorts the reality of the cost/benefit comparison.


    The Return of Premium (ROP) feature

    If one relies on this above chart, one can say that if there will be a critical illness before age 75, she will get back much more than what was paid into the policy, … and then comes the second distortion: if there was no benefit paid (insured remained healthy to age 75) then all the money will be refunded, … provided she bought a Return of Premium Rider (ROP) at the beginning. There is an extra charge for this privilege, of course, … but even that extra charge will be paid back, so there is no way to lose. There are serious efforts made by the industry and many agents to sell this ROP privilege, and many customers are really very much attracted to the idea of getting everything back. It’s because they just cannot psychologically handle the prospect of paying insurance premiums without getting back at least as much as they sunk into a plan. They want to believe so much – deep in their heart – that they wouldn’t actually use the policy anyway, that this ROP thing is perhaps the only way to get them over the resistance against still considering it as possible. In other words, there are lots of emotions, efforts, and manipulations involved. Here, let’s look simply at the rationality of buying an ROP rider. For this purpose, we can really put on our ‘investor’s hat’. With that hat on, talking about the profitability of the ROP cost does make sense, unlike it did when thinking about premiums paid for protection or risk management.

    First, let’s have a look at the costs of these riders for the policies we’ve seen above.
    Company A: $191.71 — premium refund at age 75: $60,035.50
    Company B: $264 — premium refund at age 75: $48,760
    Company C: $147 — premium refund at age 75: $55,100

    In case you had wondered before why do I keep talking about the three T75 policies, why not I just pick the one (Company B) with the lowest premiums, here you can see the reason. While this particular policy has a slight premium advantage over the other two, that is more than compensated by the lower ROP premiums of those for someone who wants to buy the ROP. The annual internal rate of returns (IRR) on the ROP-cost_as_investment for these policies are: 6.05%, 4.47%, and 6.57%, respectively. These returns are not that bad, or could be seen even as good long term returns, since they’re guaranteed and tax-free, one might say, … again, too early. They’re much less attractive if one considers also that they’re guaranteed, PROVIDED the policy remains in force and all the premiums are paid in time before age 75. If, however, there was a benefit paid or if the policy was canceled before age 75, then there will be no premium refund. (In fact, I’m not telling the full truth here because at least with some of these policies, there is a partial premium refund somewhat earlier as well, in case the policy is canceled, … but I don’t want to over complicate the analysis by going into all details. The IRR would not be better with those potential partial refunds either.) Because this will happen to more than half of all policies, the IRR for the average policy should be seen as not more than perhaps half of what are listed above, that is slightly more than 3% only even for the best one. It’s not terrible perhaps, but I wouldn’t be to enthusiastic about it either.

    ROP for term policies?

    Well, how about the ROP for T10 policies, you may ask. A first response to that is that adding an ROP to a term policy kind of beats the purpose (or one of the purposes) of having the term policy in the first place. As you will remember, a fundamental consideration (and hope) with term policy purchases is that there will be new term policies bought at renewal times, … which means there will be a cancellation of the old policy, rendering all the ROP premiums paid before completely useless. What was said in the previous paragraph about the not too high chance of keeping the policy in force up to age 75, and of the resulting potential of extra premium payment without any refund, could be repeated here. This is the brief answer that can be given generally. However, this particular T10 policy from Company D, a not widely known but financially strong mutual insurer, is a unique one. Under some conditions that can be easily created, the owner can buy an unusual ROP, similar only to some ROP available with some high-end disability policies. This ROP gives back 75% of all premiums paid after consecutive 10 year periods. This is significant because there is no need here for waiting very long (that might lead to losing of the refund opportunity) to get some money back, and no need for policy termination either. Since the chance for Mary to have a critical illness in the next 10 years is quite low, she can reasonably expect that it’s very likely she will get a refund after 10 years if she buys the ROP. In the second decade, her chances for a critical illness are somewhat higher, but it’s still rather small, … meaning that she will still have a decent chance for getting the refund. The likelihood of getting a refund is further deteriorating as she ages, of course, but with this refund-at-10 year-intervals method the chances of actually benefiting from the ROP rider is much higher than with the typical ones. Just imagine, for example, that she will get a critical illness at age 70. With the typical rider, she will have paid the ROP premium for 45 years, and she won’t see any benefit from it, … because the insurance benefit received will have been bought not by the ROP rider but the base policy. With the ROP on this special T10 policy, on the other hand, she would have had premium refunds four times before, at age 35, 45, 55, and 65, … and would ‘waste’ only ROP premiums paid for the last 5 years.

    When I calculated the IRR for this special T10 policy, I got the following results:

    In the original post: Corrective addendum, on May 2, 2011:
    in the 1st decade: 10%

    in the 2nd decade: 14%

    in the 3rd decade: 15%

    in the 4th decade: 15%

    in the 5th decade: 15%

    - - - - 5.42%

    - - - - 6.50%

    - - - - 8.87%

    - - - - 7.91%

    - - - - 6.02%

    It’s good nobody noticed it before I did it myself : the IRR calculations shown in the original post – while technically correct – can be criticized because of the following. If we want to measure the profitability of the ROP_fee_as_investment, then it would make sense to use the lowest available premium_without_ROP as the non_investment portion of total premiums for all the companies, instead of using the various base premiums for the various IRR calculations. When done this way, the IRR numbers for the T75 policies changed a bit (from 6.05% to 5.31% for Company A, and from 6.57% to 6.29% for Company C, … but there was no change for Company B because their base premium – the lowest on the whole market – was already used in the original calculation). The change was more dramatic for the T10 policy from Company D, as you can see in column 2 on the left. The difference is because while the T75 policies were from the top of the base premium ranking of all insurance companies offering this kind of product, the base premium of the T10 from Company D was only #7 lowest on the corresponding ranked list of dozens of policies available on the market.

    I could just quietly change these percentages in the post, since nobody complained about or criticized them. Instead, I decided to add this correction note because from this glitch it may be easier to understand why circumspection and patience is important with these things. Without them, even with best intentions, it’s too easy make small (or not so small) mistakes.

    The conclusions to be drawn should be a bit modified as well, of course: the lower annual returns give less credence to arguments for ROP, especially on the T10 policy. The lower percentages are not as attractive any more as they were, but still respectable, I think, especially for the early decades when there is a very high probability that the refund will actually be achieved. I don’t see the need to change anything in the previous paragraphs and did cross over only three modifiers now in the next paragraph due to these lower percentages. The ROP-on-T75 (or the ROP-on-T10-policies-in-general) arguments were rather weak even before, and now the ROP-on-this-particular-T10 argument is less compelling as well, … that’s all that happened.

    These are the annual growth rates that the extra_ROP_costs_as_investments achieve, provided the policy is in force at the end of these decades. These are much more attractive numbers than the ones before. Included in the calculation is the cost of creating the necessary precondition mentioned above: It’s simply buying a $400 per month disability-from-accident plan, which has value in itself, but let’s not even include that benefit value in this evaluation. A further advantage is that there are other coverages that can be added for which the 75% refund would also apply. Going into details about those would derail our train of thought here, so let’s stay with the CI coverage only now. This ROP is a very strong feature; on the other hand, not all the costs are fully guaranteed and shown unequivocally in this policy’s illustration, … but fortunately the most fundamental component (the cost of the critical illness protection itself) is. In other words, even if one is very cautious, there is no reason to deduct much from these very attractive internal return rate numbers above.

    These are the annual growth rates that the extra_ROP_costs_as_investments achieve, provided the policy is in force at the end of these decades. These are much more attractive numbers than the ones before. Included in the calculation is the cost of creating the necessary precondition mentioned above: It’s simply buying a $400 per month disability-from-accident plan, which has value in itself, but let’s not even include that benefit value in this evaluation. A further advantage is that there are other coverages that can be added for which the 75% refund would also apply. Going into details about those would derail our train of thought here, so let’s stay with the CI coverage only now. This ROP is a very strong feature; on the other hand, not all the costs are fully guaranteed and shown unequivocally in this policy’s illustration, … but fortunately the most fundamental component (the cost of the critical illness protection itself) is. In other words, even if one is very cautious, there is no reason to deduct much from these very attractive internal return rate numbers above.

    Total cost accumulation of policy alternatives

    Though looking at the ‘should or shouldn’t I add an ROP rider to my policy’ dilemma rationally requires an investor’s mindset and calculations (of IRR), the issue most likely will emerge and be perceived a bit differently. Namely, since it’s not a separate investment opportunity but a potential add-on to the protection plan, one will buy it if it’s perceived as a likely way of cost-saving on the long run. It’s costs not returns or growth that is the focus of attention. I did some calculations of this type, charting the accumulating costs of four policy versions: One of them is the T75 policy without ROP from Company B, because their base premium was the lowest in our sample of three. The ‘T75 with ROP rider’ version is from Company C, because – as you may remember – their ROP was the most lucrative of the three T75 policies. From Company D, both the ‘without ROP’ and the ‘with ROP’ versions are charted. Let’s look first at the way it’s done by most advisors or agents.

    What can be concluded from this chart? It shows that while the T10 policy (especially if bought without the ROP rider) does have a small cost advantage for about 25 to 30 years, it becomes much more expensive later, … so it’s not a good buy on the long run. Also, it shows that with the ROP rider on the T75 policy, the buyer may get back, at age 75, all the money paid into the policy, … no cost if lucky, while with the T10 policy, even if she is going to be lucky and collects the refunds five times, the final total cost will be quite substantial, over $60,000. The choice appears to be obvious, … unless one remembers the TVM aspect (completely disregarded in the above chart), and the probabilities related to actually getting refund/s at various ages from these policies (as discussed a few paragraphs up). Let’s see how the chart changes if we do consider the time value of money:

    Assuming a modest 3% discount rate is enough to dispel myths of ‘free if you stay healthy’ insurance, and it shows the T10 policy as much more competitive than before. It now appears to have a bigger relative cost advantage lasting for a longer time than before. Though if kept until age 75, the cost advantage of the T75 is still considerable, the ‘with ROP’ variant will stay competitive up to the end of (even though not always during) the fourth decade. Let’s see how these things are affected by making a bit higher discount rate assumptions.

    Basically, it tells us the same things, only a bit more so.

    Applying a 5% discount rate assumption shows the T10 policy, and especially its ‘with ROP’ version probably a better choice than the T75 policies. Yes, if kept until age 75, the T75 policies’ cost is still lower, … but there is a not negligible chance that the policy will not be kept until age 75. Mary might claim a benefit payment, or she might die, or she might cancel the policy before that. The chart, with even more emphasis than the previous two, demonstrates why there is no obvious choice to be made, despite what is suggested by the chart (and ‘experts’) disregarding the time value of money. If you could tell in which year you are to suffer a critical illness, then it would be easy to pick which policy variant is the most advantageous. (But then why wouldn’t you postpone buying until right before the crisis, … and so you could get rich immediately, right?) Since the ‘if’ and ‘when’ are unknowable in advance, there is always an element of luck and subjectivity remaining.

    Assuming a 5% discount rate is perhaps already a stretch (I feel more comfortable with 4%), but to show you how easy it would be to manipulate an unsuspecting audience into believing that there is an unequivocal choice that is without doubt the best, this time the T10 policy with the ROP rider, let’s look at the chart where a 6% discount rate is used.

    Don’t worry, most likely nobody will try to manipulate you in this direction. The danger of being misled, but in the other direction, may come from honest ignorance (either of product choice or of the time value of money concept), or as a consequence of incentives. Distorting the picture so that the term policy would look better than it is in reality is in nobody’s interest.


    What if the term policy will be renewed?

    Let’s do a demonstration of the real value of the renewability feature for Mary. For that, we select the best term policy available on the market for the present (initial premiums), then assume that (i) she will be able to buy at the end of each of the next four decades a new term policy, (ii) at the prices of what would be the lowest premium for 35, 45, 55, and 65 year old females today. These are quite optimistic assumptions, far from being guaranteed to happen. In the next chart, in addition to the lowest premium T10 (without ROP) available today, you can see how the accumulating cost would differ from this extremely optimistic ‘always renew at today’s prices’ scenario, or from the ‘without ROP’ version of the already familiar T10 policy from Company D.

    The outcome may have a cooling effect on the inflated optimism expressed by the ‘repeated renewal’ assumption: even if everything turns out to be the best, the potential cost saving is moderate. This is not a summary opinion on the importance of the renewability factor in general, but at least a reminder that it shouldn’t be taken as universally present. In Mary’s case, with the examined kind of policy, it turned out to be not a major cost saving opportunity. On the other hand, we found a repetition of what we already saw with the T75 policies: adding or not a feature (here, the ROP rider) can significantly change the competitive position and ranking of policies. I mean, if she does want a T10 but without ROP, then Company D is not a strong contender; but if she wants a T10 with ROP, Company D is the only serious one, … because the others’ ROPs are of different – qualitatively inferior – kind).

    Instead of looking at this chart at different discount rates, let’s move immediately to another where we drop the uncompetitive ‘without-ROP’ version of the T10 from Co. D, but include the already examined ‘with-ROP’ version of it, together with the ‘without-ROP’ version of the lowest cost T75. (As we’ve discovered, there is no point in including any other T10 or T75 ‘with-ROP’ policies, … there is too high a chance that they’d be a waste of premium dollars.)

    Basically, we arrived at the end of the quantitative exploration: Mary can pick her choice based on these charts. There are, of course, other kinds of CI policies available as well that she can explore: T20, T100 (permanent), coverage-until-75-but-premium-payment-finishing-earlier versions, etc. There are policies where CI coverage is somehow connected with life, disability, or long-term-care coverage. She will be better prepared for her final decision if she explores all these variants at least a little bit as well but, for the sake of brevity, here we’ll not follow her further in that journey: we assume that she will make her choice from the range of alternatives shown so far. If she wants to lock-in everything so that by age 75 she’d have the lowest cost paid, she should go for the T75. If she does, she shouldn’t fall though to the temptation of trying to ensure (by paying extra for an ROP rider) that she ‘will get all her money back’, … it’s a false promise, as we’ve seen. If, on the other hand, she wants to ensure that she pays less in the next thirty-some years than she’d for the level-premium T75, then she should opt for the T10, … without ROP if she’s less risk tolerant, and with ROP if she can handle more uncertainty perhaps. There is no objective measure of telling in advance which choice will be the best. She could consider the following things, some of which we’ve seen:

      the rather law probability that she’ll suffer a critical illness soon, … but its accelerating increase from her mid-forties onward
      the discount rate assumption she feels most comfortable about
      the challenges questioning the reality of ‘shop-around_at_renewal’ hopes, including influence on insurability by many factors (health history of parents and siblings included), and that there might be a disappearance of the (now internationally unique) guaranteed premium CI policies in Canada by then
      the shrinking of the magnitude of the whole issue as time passes, and the dynamics of the cost-benefit comparison at various discount factor assumptions

    To help this very last consideration, and the related decision on how much coverage she should buy now, here are the main choices again, but this time shown together with the real value of the potential benefit amounts at various policy ages.

    Any of these charts depicts a more-or-less realistic unfolding relationship between costs and benefits, or between various cost alternatives, … unlike the next one, which – once again – is built on the senseless lumping together of dollars from various years, as practiced by many sales people.


    What did we learn?

    Here is a list of some of the things readers may learn, or at lest refresh memory about, from the above demonstration of scrutiny of insurance alternatives:

  • Quantitative analysis of costs and benefits, and comparison of a range of alternatives is important for sensible decision making. It can be time consuming, and will not necessarily tell us what exactly the best choice is, but at the minimum it can deter us from making serious mistakes.
  • For quantitative analysis, the main factors are: cash flow projections (cash-out & cash-in, timed), probability estimates, reasonable discount rate, and risk tolerance or financial resilience
  • Doing time value of money calculations is vital; if a sales person/advisor/’expert’ talks about evaluation of future costs and benefits without willing/able to take into account TVM, it’s enough reason to cut off further conversation. There is no generally agreed upon discount rate for TVM calculations; 3 to 5% is probably a good range to work with
  • When dealing with statistical probabilities of future health problems, it makes sense to differentiate between various life stages, and quantify them to the best of our abilities.
  • Insurance policy costs and returns cannot be sensibly evaluated with a pure investor’s mindset; the logic of insurance, its ‘Raison d’etre’ (reason for existence), or arguments for having it are different. When evaluating ROP options, however, it’s sensible to approach the issue with the mindset of an investor
  • ROP riders on CI policies are generally oversold; buyers should look at both TVM calculations and chances that the ROP benefit will be paid at all when deciding about them
  • The ‘there is no free lunch‘ principle is valid in the area of insurance protection plans; if you’re going to remain lucky for long enough, you’ll pay more for a policy – in real terms – than you may get back from it. (Tax-sheltered investing in some life insurance policies is – or can be – a different creature, for a minority of people, but we’re not dealing with that here&now.)
  • Insurability, in terms of having or not having an opportunity to buy insurance in the first place, is a serious matter. The real financial value of future insurability (for shopping around to find lower cost policies later, at renewal times) should be checked out on a case by case basis; it’s not as general and huge as often imagined
  • Sometimes attractive products and other benefits are available from insurers (often mutuals) disregarded by most financial service providers; the unique ROP feature shown here is a good example. Relying on size and wide public awareness of companies can be misleading.
  • Considering incentives and motivations of people offering advice and selling any kind of financial solution is a healhty habit. Assuming conflict of interest is prudent; nevertheless, open communication and cooperation is the only way to go through search and analysis that can lead to understanding, informed decisions, and optimal outcome. ‘Trust but verify’ principle and dealing patiently and honestly with inherent contradictions and complexities are useful guides.
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