16th February 2014
Benefit Illustrations (Part 1) (Reply to Queries)
1) Just a month ago I received a Mail from Shri.K.K.Bijumon, Chief Manager, Bilaspur, and I have reproduced below the relevant sections of that Mail.
Recently, LIC has launched 6 new products, as per the revised guidelines of IRDA. While studying these plans in detail, it is seen that LIC is projecting a shockingly low Bonus in its benefit illustrations. As a lay man, I am not in a position to understand the reason why LIC thinks itself incapable of paying reasonable Bonuses in future. It is my earnest request to you to kindly share your thoughts and wisdom in this matter, as you have done every time there was a demand to understand the nuances of product structuring in simple, lay man’s language.
2) From what I understand, LIC should be in a position to improve its capability to pay increased Bonuses in future, even when its returns from investment continue to be at the levels they are now. This I say, because of the following factors:1) Service Tax (currently at 3.09%), which was borne by LIC hitherto, has been loaded to the premium and the customer has to bear the burden hence forth. 2) LIC will be using the new Mortality Tables in deciding the premium rates in these new plans. It is a known fact that Mortality rates have improved drastically in the past 5 decades.
3) Minimum Sum Assured is increased from Rs.50,000 to Rs.1,00,000 in new plans, reducing the need for cross-subsidisation 4) Maximum Maturity age has been reduced to 65 years from 75 years. Maximum age at entry is reduced from 65 years to 55 years. Minimum term has been increased from 5 years to 10 years. These steps may aid LIC in limiting higher incidences of mortality. 5) Introduction of TPA medical under high Sum Assured cases may have a positive impact on selection of lives. 6) In spite of all the above factors, LIC has increased the premium rates under most ages and has reduced rebates for Mode and high Sum Assured in these new products which are launched.. 7) Commission rates and DO credit are kept at the same level, except under Money Back type policies. In spite of the above factors which, we think, should enable LIC to pay better Bonuses in future, the Benefit Illustrations under the new plans show a completely different picture
3) The Mail was precise and clearly summarised the doubts lingering in the minds of the Field Force, who have to explain to their clients the changes that have taken place. Since the issues raised will be of interest to almost everyone in the field, I thought that I should give my views on these issues at the earliest opportunity. I am not aware of the details of the discussions that might have taken place in the actuarial department before the finalisation of the new products and so, will adopt a simple common sense approach to answer these queries. No actuarial knowledge is required to understand my replies.
(Query 1) Service Tax (currently at 3.09%), which was borne by LIC
hitherto, has been loaded to the premium and the customer has to
bear the burden hence forth. Will not this shifting of service tax burden to the policyholders result in higher profits and enable the Corporation to pay higher bonus? Reply 4) Left to itself, LIC might not have imposed this burden on the policyholders, and would have liked to bear the burden itself. It appears however, that it was not given any option on this issue.
5) The imposition of service tax would create two groups of policyholders. Those, on whose behalf, service tax is being paid by the Corporation and those, from whom service tax is being collected along with each premium. The average expense per policy, in the case of the first group, will naturally be higher than that in the second group. This differential treatment will raise an important question in the case of with profit policies. Will the bonus rates under the second group of policies be higher than the corresponding rates under the first group? I am sure that this question will be nagging the minds of many in the field force. I will try to answer this query. ♦ Consider two policies with the same plan, term and mode and, taken at the same time. The sum assured under one is Rs.100,000 and that under the second is Rs.150,000. The renewal expense say, Rs.400 per policy, will be the same under both the policies. The expense per 1,000 sum assured under the first policy will be (400/100 = 4) and that under the second will be (400/150 = 2.7), significantly lower than that under the first policy. But, the bonus rates under both are the same. ♦ Next consider two policies with the same plan, term, mode and sum assured. Under the first, premiums are received always in time and there are no other transactions like, address change, policy alterations, change of nomination, -- etc. till maturity. Under the second, premiums are always received late
and that too only after a reminder is sent and there are also many other transactions, atleast one per year. The servicing cost under the first will be substantially lower than that under the second. Still, the bonus rates under both will be the same. ♦ While determining bonus rates, the actuary works out a broad and equitable average. Only where it is possible to differentiate between two groups of policies and, there is significant number of policies under each group, differential bonus rates will be adopted. For example, during the first few decades, the bonus rates did not depend on policy terms, since the proportion of short term policies was not quite significant. Till a few years ago, the rates of final additional bonus did not depend on the sum assured under a policy, since the proportion of higher sum assured policies was not very significant. ♦ In the case of service tax, there is ofcourse a clear distinction between the two groups of policies. One group paying service tax and the other, for whom the tax is being paid by the Corporation. And, the number of policies under each group will also be quite large. At the same time, one more fact has to be considered. The bonus rate under a group of policies depends on the Surplus emerging under that group. Tax takes away 14.1625% of the surplus. Out of the post tax surplus, 5% goes towards Government’s share of surplus. Only the balance surplus can be distributed as bonus. As per the latest amendment to the LIC Act, out of the post tax surplus, 10% will go as Government’s share. This amendment is applicable only to the new policies being issued and not to the policies issued before this amendment. So, in the case of new policies, the balance surplus available for distribution as bonus will get reduced. ♦ The difference in treatment between the old and new policies in respect of service tax will not impact, in my view, the rates of reversionary bonus. It may impact only the Final Additional Bonus (i.e. Terminal Bonus). That is,
the impact of this differential treatment will be known only after a minimum period of 10 years. What other developments will take place in the coming years? None can predict. The actuary has got to take into consideration all the developments that have taken place before determining these rates. But, one can be confident that the decision of the actuary, whoever he/she may be at that point of time, will be perfectly fair.
6) At this stage, it is necessary to comment on the imposition of service tax on life insurance premium. To provide minimum financial security to families in case of untimely death of the bread winner is the responsibility of a welfare Government. The Government has similar responsibility to provide minimum sustenance to elderly persons having no or very little income. In an economically weak country, when the government is not able to fulfill these basic responsibilities, it should atleast help people, through proper incentives, to make their own arrangements in this regard. Life insurance and pension policies are important vehicles that provide security against premature death and longevity (i.e. old age). Imposition of service tax on such vehicles only exposes the complete lack of understanding of Social Security needs.
(Query 2) LIC will be using the new Mortality Tables in deciding the
premium rates in these new plans. It is a known fact that Mortality rates have improved drastically in the past 5 decades. Will not this improvement in Mortality experience result in higher profits and enable the Corporation to pay higher bonus? Reply 7) Use of a lighter mortality table will result in reduction of premium rates and the use of a heavier mortality table will result in increase of premium rates.
Continuing to use old and heavier mortality tables, even after improvement in mortality rates, would lead to overcharging of premiums and hence, higher profits. On the other hand, use of a new and lighter mortality table for determining premium rates would only result in reduction of premium rates but will not increase profitability. If at all, it would only reduce profitability.
Monitoring Mortality Experience 8) To continuously monitor the mortality experience, the LIC calculates a ratio, known as the (A/E) ratio, each year. A, stands for Actual and E, for expected. That is, the ratio of Actual Strain due to death claims to the Expected Strain due to death claims.
9) What is meant by Death Strain? Under each policy, out of the premium collected and the investment income earned, provision has to be made for agency commission and other administrative expenses and also for the premium required to provide the risk cover. The balance available is set aside as reserve. This statement is ofcourse an over simplification of what really takes place and the actual process will be dealt with in detail, in a separate article on Cash flow and Preparation of Benefit Illustration. When a claim arises, the sum assured and vested bonus, if any, have to be paid. Invariably, the amount payable as death claim will be higher than the reserve being held under the policy. The difference between the two is known as the “Death Strain”. This strain will be quite high if the claim arises in early durations and will gradually decrease as the duration increases. For example, if the claim arises immediately after the commencement of risk, the strain would be very high and, if the claim arises just before maturity, it would be very low. In the case of pure term assurance policies, the death strain will be almost uniform throughout the policy term.
10) Each year, the actuarial department calculates, on the basis of the mortality table used in the last valuation, the amount of strain to be expected (E) during
the year. From the actual claims incurred during the year, the actual strain experienced (A) will also be determined. In the case of LIC of India, the ratio (A/E) has remained almost steady between 85% and 90%, for many years. What does this imply?
11) Whenever a switchover is made to a lighter mortality table, the Expected Strain (i.e. E) will decrease. In the ratio (A/E), if the denominator decreases, it would result in an increase in the ratio. If the ratio (A/E) still remains constant between 85% and 90%, it means that A too has decreased correspondingly, indicating improvement in claim experience. The ratio (A/E) remaining constant can also be interpreted in another way. The inherent mortality rate is not uniform throughout the country. It varies from region to region and also between different strata of the society, with affluent people having lighter mortality. As the business expands and a few crore new policies are added each year, people with inherently higher mortality rates come under the fold of insurance. At the same time, for the country as a whole, the overall mortality rates are gradually decreasing. Due to the impact of the two opposing forces, the overall mortality experience of the Corporation is remaining steady.
12) So, the surplus emerging from continuously improving mortality experience has always remained quite moderate.
13) This answers also the Fifth Query, viz.” Introduction of TPA medical under high Sum Assured cases may have a positive impact on selection of lives and should result in increase in bonus rates”. When the claim experience improves, it does not get reflected immediately in reversionary bonus rates. Its impact would be felt only in the Final Additional Bonus.
(Query 3) In spite of reduction in mortality rates why have the
premiums increased? Reply 14) The extent of impact of reduction in mortality rates can differ from plan to plan. It would be quite high under Term Assurance and may be quite insignificant in the case of short term Endowment Assurance for younger ages. Again, it would be quite significant under double cover or triple cover long term Assurances. Let us first see the scale of reduction in mortality rates. The Table below compares the earlier Mortality Table [LIC (1994 – 96)] with the latest one, Indian Assured Lives Mortality [IALM (2006 -08)], at quinquennial ages.
TABLE I (1) Age
(2) LIC(1994–96)
(3) IALM(2006-08)
(4) (3) as % of (2)
10
0.0003800
0.0004400
116%
15
0.0007700
0.0006400
80%
20
0.0009986
0.0008880
89%
30
0.0011704
0.0010560
90%
40
0.0020528
0.0018030
88%
50
0.0052440
0.0049460
94%
60
0.0130733
0.0115340
88%
70
0.0362944
0.0258550
71%
80
0.1043314
0.0605580
58%
15) So, between the ages 20 and 60, the reduction in mortality rates is about 10%. What will be the impact on premium rates due to a reduction of 10% in mortality rates? Consider the Table given below.
16) Non-Par Endowment Plan, Age at entry is 30, Policy and Premium terms 20 years. Administrative Expenses have not been taken into account and only Commission Expenses have been considered. For a change, the mortality table used is that pertaining to the U.K. Assured Lives, for the period 1967–1970. This is lighter than the Indian Assured Lives Mortality (IALM) for the period 2006–2008. TABLE II Premium per 1000, No Extra Mortality
Extra Mortality
Revised Premium
Percentage Increase/Decrease in Premium
27.93
+10%
28.02
+ 0.32%
27.93
+20%
28.12
+ 0.68%
27.93
−10%
27.83
− 0.36%
27.93
−20%
27.74
−0.68%
It can be seen from the Table that, the change in premium rates in respect of Endowment Assurance, due to a reduction of 10% in mortality rates, is negligible.
17) Let us next consider a term assurance plan for 20 years for age at entry 30. In this case, the administrative and commission expenses have together been taken as 30% of the premium. As given in TABLE III, in the case of term assurance, increase or decrease in mortality rates will have significant impact on premium rates. In the case of Endowment type of assurances, the impact of increase or decrease in mortality rates will not be very significant.
TABLE III Premium per 1000, No Extra Mortality
Extra Mortality
Revised Premium
Percentage Increase/Decrease in Premium
2.66
+10%
2.92
+ 9.8%
2.66
+20%
3.18
+ 19.5%
2.66
−10%
2.39
− 10.2%
2.66
−20%
2.13
−19.9%
18) When the expenses increase, the corresponding increase in premium rates will be higher than the decrease in premium rates due to any reduction in mortality rates. Over the past 8 years, under the impact of inflation, expense per policy has more than doubled. This can be the reason for the increase in premium rates, in spite of the use of lighter mortality Table.
(Query 4) Minimum Sum Assured is increased from Rs.50,000 to
Rs.1,00,000 in new plans, reducing the need for cross-subsidisation Reply 19) It has to be remembered that, under the impact of inflation, the operational expenses, excluding agency commission, are continuously increasing. The total operational expense in 2012–2013 was more than 15 times that in 1992–1993, 20 years earlier. A major portion of this increase in expenses is in respect of policy servicing. During the same period of two decades, the increase in the total number of policies was just more than five times.
20) The expenses, other than agency commission, can be divided into two parts. One part is the expenses relating to first year of the policy, viz. marketing,
underwriting, and policy issue. This is known as First Year Expenses. The second part is the expenses relating to policy servicing. This is known as the Renewal Expenses. The total First Year Expense, divided by the number of new policies issued, gives the Per Policy Expense for first year and, the total Renewal Expense, divided by the total number of policies, gives the Per Policy Expense for renewal. While per policy expense for the first year has gone up three times over the two decades, the per policy expense for renewal has gone up by about 5 times.
Let us see how this affects the premium rates and
profitability.
21) Premium rates are always given for Rs.1,000 sum assured. So, if per policy expenses are, • F for first year and • R for renewal, these have to be expressed as expenses per 1000 sum assured. If the average sum assured under a policy is Rs.100,000 and the First Year expense per policy is = F, First Year expense for One Rupee sum assured will be = (F / 100000) So, First Year expense for Rs.1000 sum assured will be = 1000 x (F / 100000) = (F / 100) Similarly, the Renewal expense for Rs.1000 sum assured will be = (R / 100)
22) The amount Renewal Expense in respect of a policy is independent of the sum assured under the policy. If the average sum assured were Rs.150,000/, the expenses per Rs.1000 sum assured would have been, (F/150) for first year and (R/150) for renewal, resulting in reduction in Required Premium Rates. But, the premium rates being charged will not be revised just because of increase in average sum assured and so, the difference between the Premium Charged and the Actual Premium Required will result in higher profits and hence higher
bonus. When expenses increase, the Required Premium will also increase and so, the difference between the Premium Charged and Required Premium will decrease, resulting in decrease in profits and hence, decrease in bonus rates. When expenses increase under the impact of inflation, if the average sum assured increases in step with increase in expenses, the adverse effects of inflation will get neutralised to a very great extent.
23) At the time of issue of a new policy, the expense provision in the premium charged may be quite adequate to meet the actual expenses. But, within a few years, when expenses increase under the impact of inflation, the provision for expenses in the premium charged will become inadequate and the deficit will have to be financed by new polices with higher sum assured, and Cross Subsidisation will commence. So, cross subsidsation cannot be avoided and the effort should be to keep the number of policies requiring to be subsidised as low as possible.
(Query 5) Maximum Maturity age has been reduced to 65 years
from 75 years. Maximum age at entry is reduced from 65 years to 55 years. Minimum term has been increased from 5 years to 10 years. These steps may aid LIC in limiting higher incidences of mortality. 24) Decreasing maximum ages at entry and maturity will not in any way impact profitability. If at all, the profitability may get marginally reduced. This may look like a paradox. Let us analyse the reasons.
25) At higher ages, there may be more death claims. It will not however result in reduction in profitability. While determining premium rates, the mortality rate at each age is taken into consideration. The expected number of death claims will depend on the mortality rate. As long as the actual number of death
claims does not exceed the expected number of death claims, there will not be any loss. Consider a hypothetical example.
26) Hundred thousand persons, all aged 30, take life insurance at the same time. As per the Indian Assured Lives Mortality Table (2006–2008) (Ultimate), the mortality rates are, At Age 30 – 0.001056, Age 31 – 0.001084, Age 32 – 0.001119, Age 33 – 0.001164, Age 34 – 0.001218, Age 35 – 0.001282, … etc.
27) During the first year, the Expected Number of death claims among the 100,000 policies issued will be (100,000 x Mortality Rate at age 30) = 100,000 x 0.001056 = 105.6 = 106 approximately The balance number of policies = 100,000 – 106 = 99,894 Expected number of death claims in the second year will be = 99,894 x Mortality Rate at age 31 = 99,894 x 0.001084 = 108.285 = 108 approximately
28) If the policies are all without profit policies and the sum assured under each policy is Rs.100,000/=, the total expected outgo in respect of death claims during the first year will be, (106 x 100000) = Rs.1,06,00,000/= Similarly, the total expected outgo in respect of death claims during the second year will be, (108 x 100000) = Rs.1,08,00,000/=
29) If the age at entry of the 100,000 persons were 50, instead of 30, Expected number of death claims during the first year would have been, = 100,000 x 0.004946 = 495 approximately (i.e. more than 4 times that at age 30) The balance number of policies = 100,000 – 495 = 99,505
Expected number of death claims during the second year = (99,505 x 0.005483) = 546 approximately (i.e. 5 times the number at age 31) The total expected outgo in respect of death claims during the first year will be, (495 x 100000) = Rs.4,95,00,000/= Similarly, the total expected outgo in respect of death claims during the second year will be, (546 x 100000) = Rs.5,46,00,000/= However, this fact has been taken into account while determining the premium to be charged and, as long as the actual number of death claims is not greater than the number expected, there will not be any loss.
30) It was stated earlier that, “Decreasing maximum ages at entry and maturity will not in any way impact profitability. If at all, the profitability may get marginally reduced. This may look like a paradox”. Let us analyse it further. It was also seen earlier that the (Actual to Expected Ratio), i.e. (A/E) ratio has remained steady between 85% and 90%. Let us assume that the actual mortality rates experienced were 90% of the rates given.
31) If the age at entry is 30, the actual number of death claims in the first year will only be, 90% of (100,000 x 0.001056) = 95.04 = 95 approximately The actual amount of death claim paid will only be, Rs.95,00,000 The surplus arising in the first year in respect of death claims will be, Expected amount of death claims to be paid – Actual amount of death claims paid = Rs.106,00,000 – Rs.95,00,000 = Rs.11,00,000/=
32) If the age at entry is 50, the actual number of death claims in the first year will only be, 90% of (100,000 x 0.004946) = 445.14 = 445 approximately The actual amount of death claim paid will only be, Rs.445,00,000
The surplus arising in the first year in respect of death claims will be, Expected amount of death claims to be paid – Actual amount of death claims paid = Rs.495,00,000 – Rs.445,00,000 = Rs.50,00,000/= So, in terms of absolute amounts, the surplus arising in respect of death claims can be higher at higher ages.
33) One more factor has also to be considered. Suppose an insurer adopts the Mortality Table, IALM (2006 – 2008) for determining premium rates. The insurer cannot be 100% certain that the mortality rates experienced in future will never exceed the rates given in the Table. Adverse situations can always arise and the actual experience may prove to be higher than that expected. To guard against such eventualities, the general practice is to build in a margin by rating up the mortality rate at each age by about, say 10%. So, At age 30, the assumed rate of mortality will be, (110% of 0.001056 = 0.0011616) At age 50, the assumed rate of mortality will be, (110% of 0.004946 = 0.0054406) This rating up of mortality rates, while determining premium rates, will also result in the emergence of additional surplus in the case of death claims.
34) So, higher ages at maturity need never be a matter of concern. Whole life policies are standing examples. The only concern regarding higher ages at entry can be the moral hazard, arising from the absence of insurable interest. What is the need for life insurance in the case of a retired person, having no earned income? If at all there is any need, it may be quite limited.
35) Next comes the question, “Why have Maximum ages at entry and maturity been decreased and minimum term increased?”
These steps have been taken only to comply with the new conditions imposed by the IRDA. As per the latest Product Regulations, the Risk Cover under a policy should not be less than 10 times the annual premium, excluding extra premiums and rider premiums.
36) In a short term policy, say for a term of 9 years, under a with profit plan, 10 times the annual premium will certainly be higher than sum assured. Similarly, under higher ages at entry too, this condition will not be satisfied. Till now, under most of the plans, the sum assured payable on death has been the same as the sum assured payable on maturity. One way to satisfy the newly imposed condition is to increase the sum assured payable on death to 1.25 times the sum assured payable on maturity. This has been done in the case of New Money Back and New Jeevan Anand plans. Under the Endowment Plan, since this condition is getting automatically satisfied for most of the terms and ages at entry, this step has not been taken and instead, shorter terms and higher entry ages have been avoided. I am sure that the Corporation will be soon bringing out a separate Endowment Plan, with higher risk cover, for shorter terms and higher ages at entry. One may ask as to why the new plan could not have been introduced immediately.
37) Till a decade ago, before the opening of the insurance sector, introducing a new Plan of Insurance used to be quite simple. The actuarial department designed the new plan in consultation with the marketing department, determined the premium rates, laid down the underwriting requirements and placed the Note before the board for approval. Once the Note was approved, the new plan, giving all the required details, was filed with the Department of Insurance, Ministry of Finance, for approval. It was a case of “File and Proceed”. That is, the insurer could proceed with marketing the plan once it was filed. It was the responsibility of the Chief Actuary of the organisation to ensure that there were no mistakes in the plan design, premium rates and policy
conditions. If the Department of Insurance found any deficiency in the plan design or errors in premium rates, it could ask the insurer to suspend the marketing of the product till the deficiencies and errors were rectified. Such a situation however, never arose.
38) Things changed after the constitution of the IRDA. Elaborate procedures have now been prescribed and there is a manifold increase in the number of documents to be completed for filing the new product. The system of File & Proceed has been replaced by File & Wait and, the new plan cannot be introduced in the market without getting the written approval of the Regulator. Number of queries to be answered and clarifications to be given before getting the approval, has also increased. All these have resulted in increased work load for the actuarial department. Two decades ago, when I was the Chief Actuary of the LIC, only one officer (actuary) used to look after product development. Now, a separate section, with a number of actuaries, is struggling to cope with the manifold increase in work load. The only Plus Point is the “Increased job opportunities for actuaries and actuarial students”.
39) When a significant change is being made in the Product Regulations, resulting in a major revision of product structure and premium rates, it is logical to expect the new regulation to come into effect from the commencement of a financial year. But the effective date of the new Product Regulation was kept as 1st January 2014 and the life insurance companies were given six months, from 1st July to 31st December, 2013, to revise their products. This was not a big problem for the new companies. In the case of LIC it was however, different.
40) The number of products to be revised was many. Further, till September 30th the actuarial department is always fully occupied with the annual valuation. So, the actuarial department effectively had only three full months to revise all the products. As in the case of product filing, there is also manifold increase in
the number of returns to be filed in the case of annual valuations. Further, in the case of LIC of India, with a portfolio of thirty crore policies, spread over more than 2,500 Branches, the work relating to collection and processing of data is a major exercise and the department could not spare any additional time or man power to the product development work. It goes to the credit of the Field Force in rising to the occasion and maximising the business, before the end of December.
41) Finally, what is the reason behind the new stipulation that, “The Risk Cover under a policy should not be less than 10 times the annual premium, excluding extra premiums and rider premiums?” This may always remain as a Question Mark and we may never know the reason.
42) I received also the following query from Shri.M.Shyam, Asst.Secretary, Marketing Research Cell, Southern zone. “In the case of the plan New Jeevan Anand, there is wide variation in returns shown in the two scenarios given in the Sales Illustration and the field force wants to know the reason for the same, since they have to explain it to their customers, who may wonder whether it is a mistake’.
43) To fully explain the reasons one may have to explain the process by which the Sales Illustrations are prepared. I will take up this task in Two separate articles. The process does not involve more than Plus-2 level algebra and can be followed by anyone having aptitude for mathematics. In other words, by anyone not having aversion for, or fear of algebra. For the present, I will just demonstrate that there is no mistake in the illustration. This demonstration will also involve some elementary level algebra.
44) Everyone would have studied compound interest in the VII or VIII Standard. Let us therefore start with this simple concept.
If the rate of interest is i, an amount A will become, ♦ A(1 + i) at the end of one year, ♦ A(1 + i)2 at the end of two years, ♦ A(1 + i)3 at the end of three years, ♦ … And, ♦ A(1 + i)20 at the end of 20 years. So, if i = 4% (i.e. 0.04), the premium P, paid at the beginning of first year will accumulate to P (1.04)20 at the end of 20th year.
45) In the 20 year Jeevan Anand policy, the premium P will be paid at the beginning of each year for 20 years. If the rate of interest is i, the • Accumulated amount, at the end of 20th year, of the premium paid at the beginning of first year, will be P(1 + i)20 • Accumulated amount, at the end of 20th year, of the premium paid at the beginning of second year, will be P(1 + i)19 ♦
Accumulated amount, at the end of 20th year, of the premium paid at the beginning of third year, will be P(1 + i)18
• --------------------------------• Accumulated amount, at the end of 20th year, of the premium paid at the beginning of twentieth year, will be P(1 + i)1 46) So, the Total Accumulated amount, at the end of 20th year, of the premiums paid at the beginning of 1st, 2nd, 3rd, … and 20th years will be, P [(1 + i)20 + (1 + i)19 + (1 + i)18 + ----- + (1 + i)1 ] Or, writing in the Reverse Order, P [(1 + i)1 + (1 + i)2 + (1 + i)3 + ----- + (1 + i)20 ] ----- (I) It may be seen that,
♦ Each term within the bracket is obtained by multiplying the previous term by (1 + i). (This is called the Common Ratio) ♦ There are 20 terms and, ♦ The first term is (1 + i), There is a simple formula in algebra to find the Sum, of the terms given within brackets [ ]. It is, First Term x [{(Common Ratio)
number of terms
– 1}/ (Common Ratio – 1)]
So, the value of (I) is equal to, P (1 + i) [(1 + i)20 − 1] / [(1 + i) – 1] = P (1 + i) [{(1 + i)20 − 1} / i ] ------ (II)
47) Let us consider some simple examples. Ex.1) Find the sum of 1 + 2 + 22 + 23 + -------------- + 239 ♦ Each term is obtained by multiplying the previous term by 2.
So, the
Common Ratio is 2. ♦ There are 40 terms and, ♦ The first term is 1.
Sum = First Term x [(Common Ratio)Number of terms – 1] / (Common Ratio – 1) 1 x (240 − 1) / (2 – 1) = 1 x (1,099,511,627,776 – 1) / 1 = 1,099,511,627,775
Ex.2) Find the sum of 9 + 27 + 81 + 243 + 729 + 2187 + 6561 + 19683 + 59049 + 177147 ♦ Each term is obtained by multiplying the previous term by 3. So, the Common Ratio is 3. ♦ First term is 9 and ♦ The number of terms is 10. Sum = 9 x (310 – 1) / (3 – 1) = 9 x (59048) / 2 = 265,716
48) Now consider the Benefit Illustration under the New Jeevan Anand Plan. Age at entry 40 and Term 20 Sum Assured Rs. 100,000 Mode Yearly, Annual Premium Rs. 6,060 (approximately) So, Rs. 6,060 will be paid at the beginning of each year for 20 years. What will be the accumulated amount of all the premiums, net of expenses, as at the end of the premium paying period, i.e. 20 years?
49) Premiums Received The accumulated value of these premiums, at the end of 20 years will be, as per result (II) of Sec. 6,060 (1 + i) [{(1 + i)20 − 1} / i]
At 4% interest, the value of the above will be,
6,060 (1.04) [{(1.04)20 − 1} /0.04] 6,060 (1.04) [(2.191123143 – 1) /0.04] 187,673 ------ (A1)
At 8% interest, the value of the above will be,
6,060 (1.08) [{(1.08)20 − 1} /0.08] 6,060 (1.08) [(4.660957144 – 1) /0.08] 299,503 ------ (A2)
Outgo in respect of Commission and Marketing Expenses 50)
In the first year of the policy, Commission (with Service Tax) and
Marketing Expenses, including expenses in respect of development officers, will be about 55% of first year premium.
In the second and third years,
commission (with service tax) will be about 8.5% and, in subsequent years, about 5.6%. The First year expenses on commission and marketing, on accumulating upto the end of 20 years, at interest rate i, will become, (55% of 6,060) x (1 + i)20 Similarly, second year expense on commission will accumulate to, (8.5% of 6,060) x (1 + i)19 Third year expense on commission will accumulate to, (8.5% of 6,060) x (1 + i)18 ---- etc.
52)
Finding the value of each of the 20 terms and adding them up, the
accumulated value of expenses on commission and marketing can be found. This will however be a tedious process. Instead, one can take this value to be approximately equal to about 10% of the accumulated value of premiums. i.e. [10% of 187,673] = 18,767 at 4% ------ (B1) [10% of 299,503] = 29,950 at 8% ------ (B2)
Outgo in respect of Operating Expenses 53)
Assume that operating expenses will be Rs.400 per year and will be
incurred at the beginning of each year. The operating expenses can be treated as Negative Premium.
Premiums come in and Expenses go out.
The
accumulated value of these expenses, as at the end of 20 years, at rate of interest
i, will be, as in the case of accumulation of Premiums, That is, 400 (1 + i) [{(1 + i)20 − 1} / i]
At 4% interest, the value of the above will be, 400 (1.04) [{(1.04)20 − 1} / 0.04 ]
400 (1.04) [(2.191123143 – 1) /0.04] = 11,556
54) The operating Expenses will not however remain constant throughout the term but, will increase each year under the impact of inflation. For example, if the inflation is 3%, the expenses will be, 400 in the first year, 400(1.03) = 412 in the second year, 412(1.03) = 424 in the third year --- etc. How to find the accumulated value of all these expenses, as at the end of 20 years? Here, the formula will be a little more complicated and can be approximately calculated as given below. 55) If i is the rate of interest and f is the rate of inflation, take the rate of interest net of inflation, as j, where j = (i – f) In the given case, i = 4% and f = 3%. So, j = 4% – 3% = 1%. Or, 0.01 What will happen if the rate of inflation is higher than rate of interest? It would make the formula more complicated and let us not take it up for the present.
56) The accumulated value of expenses, with inflation, will be given by the formula, [400(1 + f)20] (1 + j) [{(1 + j)20 − 1} / j]
The value at 4% will be, = [400 (1.03)20] [(1.01)[{1.0120 – 1}/ 0.01]] = 400 (1.8061)(22.2392) = 16,066
------ (C1)
This is an approximate value and the correct value will be, 16,017. So, the approximation is good enough
The value at 8% will be,
= [400 (1.03)20] [(1.05)[{1.0520 – 1}/ 0.05]] = 25,083
------ (C2)
When the interest rate is 8%, the interest rate net of inflation will be 8% – 3% = 5%
i.e. 0.05
57) However, the first year operational expenses will always be higher than operational expenses in subsequent years. Let the additional expenses in the first year be, Rs.500. The accumulated value of this additional expense, as at the end of 20 years, will be At 4% [500 (1.04)20] = 1,096
------ (D1)
At 8% [500 (1.08)20] = 2,330
------ (D2)
58) So, the available mount at the end of 20 years will be, Accumulated Value of Premiums − Accumulated Value of Commission and Marketing Expenses – Accumulated Value of Operating Expenses
At 4%, = A1 – B1 – (C1 + D1) = 187,673 – 18,767 – (16,066 + 1,096) = 151,744 ------ (E1)
At 8%, = A2 – B2 – (C2 + D2) = 299,503 – 29,950 – (25,083 + 2,330) = 242,140 ------ (E2)
59) Since a Non-Par whole life policy will continue after the end of premium paying term (i.e. after age 60), we have to deduct from (E), we have to deduct from the amount in (E) the single premium required for a Non-Par Whole Life
policy, for a sum assured of Rs.100,000 corresponding to age at entry 60. From the Agents’ Manual of LIC, the Single Premium for age at entry 60, for a sum assured of Rs.1,000 is found to be Rs.358. Since no commission and marketing expenses or underwriting and other expenses are involved when a Jeevan Anand policy continues as a whole life policy after the end of premium paying term, for the sake of simplicity, let us take the single premium required as a round amount of Rs.300. The Single Premium required for a sum assured of Rs.100,000 will then be, Rs.30,000. (Though the amount of single premium required may be higher at 4% and, lesser at 8%, let us take Rs.30,000 as the single premium required in both cases).
60) Deducting this amount from the accumulated amounts given in (E1) and (E2), the balance amount available at the end of premium paying term will be, At 4%, 151,744 – 30,000 = Rs.121,744/ = Sum Assured + 21,744 At 8%, 242,140 – 30,000 = Rs.212,140/ = Sum Assured + 112,140 Where sum Assured = 100,000 So, the Non-guaranteed benefits are, At 4%, Rs.21,744 At 8%, Rs.112,140
61) Death Claims, Tax and Shareholder’s Share In the working so far, it may be noted that no provision was made for death claim payments over the 20 year period and also for tax and shareholder’s share of surplus. These were omitted since it is difficult to arrive at approximate values for them by simple methods. If provision for them is also made, the amount available at the end of the premium paying term will be quite near the amount shown in the Benefit Illustration corresponding to yields of 4% and 8% on investments.
62) How to find the bonus rate corresponding to the Non-guaranteed benefit? Bonus @ 1 per thousand sum assured will give 100 per year for 100,000 sum assured. The bonus for 20 years will then be, 2,000. The bonus rate will be equal to the non guaranteed benefit, divided by 2000.
63) One may wonder as to why Investment Income has not been added. It has not been added directly; but has been added indirectly. For example, Total amount of premiums paid in 20 years is 20 x 6,060 = 121,200 Accumulated Value of the premiums (at 4%) = 187,673 So, the interest income (at 4%) = 187,673 – 121,200 = 66,473 The interest income (at 8%) = 299,503 – 121,200 = 178,303 The big jump in interest income, when the rate of interest moves up, can be seen This is the main reason for the big jump in bonus rates when the interest increases from 4% to 8%. --------------------- x ----------------------------- x -------------------------- x
The Impact of High Sum Assured 64) What will be the impact of high sum assured on the Non-guaranteed benefits? In the above example, take the sum assured to be 5,00,000 instead of 1,00,000. The annual premium will be, 5 x 6060 = 30,300. Take the yield on investments to be 8%. ♦ The accumulated value of premiums, as given in (A2) will become, (5 x 299503) = 1,497,515 ♦ The accumulated value of Commission & Marketing expenses, as given in (B2) will become, 10% of 1,497,515 = 149,752
♦ The operating expenses will be the same, whether the sum assured is 100,000 or 500,000. There may be some marginal increase in additional first year expenses. Ignoring this marginal increase, the accumulated value of operating expense (at 8%) will be, (25,083 + 2,330) = 27,413 So, the amount available at the end of 20 years (at 8%) will be, = 1,497,515 – 149,752 – 27,413 = 1,320,350 = 500,000 + 820,000 = Sum assured + 820,000 The Non-guaranteed benefit becomes 812,000 for a sum assured of 500,000. That is, (812,000 / 5) = 162,400 per 100,000 sum assured, It was, 112,140 when the sum assured was only 100,000.
65)
As the average sum assured increases, the accumulated value of
operational expenses will not increase and so, the Non-guaranteed benefit and hence, the bonus rate, will increase.
66) By splitting policies, just for showing spurious increase in number of policies, the average sum assured per policy is decreased. This decreases the Non-guaranteed benefits, and hence results in decrease of bonus rates. Consequently, the policyholder is put to loss. But, the ultimate losers will be the agent and the organisation, since the decrease in bonus rates will make the Corporation’s products uncompetitive. The Management should look into this issue and take appropriate corrective steps.
16th February 2014
(R.Ramakrishnan) (Actuary)
