I think the mathematical model for my policy is pretty darn good, but
there are factors I have to guess at, hopefully with some degree of
intelligence. Even if the model were perfect, there could well be
minor differences in what it calculates and what actually happens.

Let us examine the assumptions upon which the model is based, as well as some of the results.

Let us examine the assumptions upon which the model is based, as well as some of the results.

**Dividends earned are related to total cash value (TCV).**

This assumption underlies the very existence of the model. If there is no relationship between dividends and TCV, then both you and I have been wasting a lot of time. The policy illustrations exhibit such a relationship, and I will accept it as a given.

**Only part of each dividend is related to TCV.**

Based on analysis of my policy illustrations as well as actual policy history, about $160 of each dividend is return of premium. US tax code generally considers the entire dividend payment as a refund for overpayment of premium. So long as an annual dividend does not exceed the premium payments for that year, it is not taxable. Dividends are eventually expected to exceed premium payments, which supports point 1.

**More Acronyms**

PUA Paid-Up Additional Insurance OPP Optional PUA purchased

with out-of-pocket money

(dividends can yield PUA also)

**example from 2nd policy statement:**My policy illustration does not include OPP. For its 2nd policy year, the dividend equaled exactly $160. Since there was no cash value until the dividend was paid, I deduce this amount is "refund of premium".TCV at end of previous year: $938.10 PUA purchased previous year: -651.84 ------- TCV eligible to earn dividends: $286.26 The policy states that PUA are not eligible for dividends until the year after the PUA was purchased.

dividend: $169.85 rate 1: 169.85 / 286.26 = 59.33% rate 2: 169.85 / 938.10 = 18.11% rate 3: 9.85 / 286.26 = 3.44% Which rate seems most likely?

**Guaranteed Cash Value (GCV) accumulates without regard to TCV.**

While GCV makes up a major portion of TCV, its annual accumulation is a contractual guarantee, regardless of how much or how little TCV there may be in a given year. Even if I should obtain a loan or withdraw some of the TCV as income, so long as my premium payments are made, GCV will build up according to the scale defined in the policy.

**Linear Increase in Value (LIV) accumulates separately from dividends.**

This assumption is validated by every policy statement. For example, see the 3rd policy statement . Observe that the middle column of black numbers is a gain not documented in the dividends section of the official NYLIC Policy Summary (at the top of the example page). I.e., NYLIC does not consider this gain to be dividends. Hence, neither do I.

**LIV accumulates neither linearly nor at a compounded rate.**

It took me a long time to realize why it does not increase linearly. The goal of this increase is such that at policy maturity (age 100), the cash value associated with PUA is equal to its death benefit. Using basic algebra, this goal can be achieved in a straight-forward manner:

linearIncrease = (deathBenefit - cashValue) / (100 - age)

example (OPP):`(10,711 - 3957.82) / (100 - 47) = $127.42`

example (Div):`(3670 - 1217.97) / (100 - 47) = $46.26`

The above input numbers are from the OPP and Dividend lines of my 5th statement. The OPP calculation was $127.42. If I never bought any more OPP, its death benefit would remain at $10,711. And if $127.42 were added to the OPP cash value every year (from $3957.82), then at age 100 the death benefit and cash values would be equal.

The 6th statement shows that OPP cash value gained $121.89 (not $127.42), and that dividend cash value gained $44.51 (not $46.26). The numbers are in the linear ballpark, but there is certainly no home run. The same discrepancy occurs throughout all the statements.

The policy provides little insight. Here is a quote.

**Paragraph from OPP Rider**

**Values**The paid-up insurance under this rider has cash value and loan value, and is eligible for dividends. Cash values and net single premiums are based on the 1980 CSO Tables of Mortality (the male table if the insured is a male or the female table if the insured is a female). Continuous functions are used. Interest is compounded at 4%. During the policy year in which a payment is made under this rider, the cash value of paid-up insurance purchased by that payment will be limited to the amount of that payment.I wrote NYLIC and asked what this meant. I received an informative and personal reply. It explained that the Mortality Table applies a factor each year to the interest earned, and the result is an almost linear function.

Earlier I wished they would throw the darn mortality table away. After they use it to set the age-based cost of PUA, it seemed to serve little purpose except complicate the gain calculations. As I analyzed my policy, it became clear why they cannot do so. A policyholder can sell back PUA (this money can be used to help pay premiums, for example). But when part of the PUA is sold back, my straight-forward "linearIncrease" formula (above) falls apart.

Fred the Actuary seems to know what he is doing after all, even if his "linear" is not my "linear".

In my opinion, the rider should not say, "Interest is compounded at 4%." The way I (and probably most other non-actuaries) read it, there would be interest earned on interest. The PUA Cash Value Machine would not work if this were so. Within several years, cash value would exceed death benefit. The insurance policy would no longer be considered tax deferred. For that matter, it would not be a life insurance policy any more, either. What kind of policy pays you less if you die than if you live?

Note that paid up additions earn dividends as well as LIV. If dividends are kept within the policy, they**do**accumulate in a**compounded**manner. In this case everything works, because the dividends purchase more insurance, so both cash value and death benefit increase at the same time.

**Dividend PUA is cheaper than Optional PUA (OPP).**

Examine this data.6th Policy Year

(age 48)Price

PaidInsurance

BoughtCost

per $1000

Death BenefitOPP Death Benefit $616.92 $1,620 $380.81 Dividend Death Benefit $437.33 $1,275 $343.00 OPP Cost

from Male Chart

of OPP Riderage cost/$1000 --- ---------- 43 327 44 337 45 348 46 359 47 370 48 381 49 393

The chart is and has been accurate for my OPP purchases. Observe that dividend PUA is noticeably less expensive. So far it has tracked at about "3.5 years" cheaper.

I believe the reason for cheaper dividend PUA involves my "mortality class". The policy was issued for a healthy non-smoker, so dividend PUA benefits from this favorable risk classification. Extra insurance purchased via the OPP rider is bought at a "standard class of risk". NYLIC cannot know if I will start smoking (I won't!) or acquire a medical condition which will reduce my life expectancy. They need to account for policyholders who start building up a lot of OPP

*after*their health situation deteriorates.**Dividend PUA is Substantially Similar to OPP.**

The policy does not provide pricing information for dividend PUA. Nor does it state that the cash value associated with dividend PUA will both earn "interest" and be eligible for future dividends. This information concerning PUA is only mentioned as part of my OPP rider.However, the NYLIC annual policy summaries have so far illustrated that both PUA sub-accounts operate very much alike. Indeed, the nature of PUA almost forces parallel operation. The only difference observed so far is the previous point about dividend PUA being cheaper. Here I stated that the linear increase in value for PUA is guaranteed. The guarantee is explicit in the case of OPP PUA, but implicit in the case of dividend PUA.

**Comparisons between strategies are made at the policy anniversary.**

An instant in time is assumed where a given year's gains have been added to the policy (dividends, GCV, and LIV), but the premium and OPP payments for the next year have not been made. Equivalence is established with inflation and investments in T+I mutual funds, both of which have had the whole year to potentially gain in value.

Accesses since 24 June 2001

last modified 22 November 2010

© 2001 - 2010 by Rich Franzen

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