Profile Facts: life annuity value

In actuarial science, the actuarial present value of a payment or series of payments which are random variables is the expected value of the present value of the payments, or equivalently, the present value of their expected values.

Actuarial present values are calculated for the payment or series of payments associated with life insurance and life annuities. In this case, the probability of a future payment is based on assumptions about the person's future mortality taking into account the person's age and an assumed life table, while the present value of those future assumed payments depend upon the interest rate (or rates) used to discount them for the passage of time.

The internal rate of return of a contract is the rate of return for which the actuarial present value of all cash flows is zero.

Life insurance

Let $T$ be the future lifetime random variable of an individual age x and $Z$ be the present value random variable of a whole life insurance benefit of 1 payable at the instant of death.

$\,Z=v^T=(1+i)^{-T}=e^{-\delta T}$

where i is the interest rate and δ is the equivalent force of interest.

To calculate the actuarial present value we need to calculate the expected value $\,E(Z)=E(v^T)$ of this random variable Z. For someone aged x this is denoted as $\,\overline{A}_x\!$ in actuarial notation. It can be calculated as

$\,\overline{A}_x\! = E(v^T) = \int_0^\infty v^t f_T(t)\,dt = \int_0^\infty v^t\,_tp_x\mu_{x+t}\,dt$

where $f T$ is the probability density function of T, $\,_tp_x\!$ is the probability of a life age $x$ $x + t$ and μ denotes force of mortality. surviving to age

The actuarial present value of an n-year term insurance policy can be found similarly by integrating from 0 to n.

The actuarial present value of an n year pure endowment insurance benefit of 1 payable after n years if alive, can be found as

$\,_nE_x = P(T>n)v^n = \,_np_xv^n.$

In practice the best information available about the random variable T is drawn from life tables, which give figures by year. The actuarial present value of a benefit of 1 payable at the birthday after death would be

$\,A_x = \sum_{k=0}^\infty v^{k+1} P(k<T<k+1) = \sum_{k=0}^\infty v^{k+1} \,_kp_xq_{x+k}$

where $\,q_x\!$ is the probability of death between the ages of $x$ and $x + 1$ .

In practice an insurance policy pays soon after death, which requires an adjustment of the formula.

Life annuity

The actuarial present value of a life annuity of 1 per year paid continuously can be found in two ways:

Aggregate payment technique (taking the expected value of the total present value):

This is similar to the method for a life insurance policy. This time the random variable Y is the total present value random variable of the life annuity of 1 per year paid continuously as long as the person is alive, and is given by:

$Y=a_{\overline{T|}} = \frac{1-(1+i)^{-T}}{\delta} = \frac{1-v^T}{\delta}.$

The expected value of Y is:

$\,\overline{a}_x = \int_0^\infty a_{\overline{t|}} f_T(t)\,dt = \int_0^\infty a_{\overline{t|}} \,_tp_x\mu_{x+t}\,dt$

Current payment technique (taking the total present value of the function of time representing the expected values of payments):

$\,\overline{a}_x =\int_0^\infty v^{t} (1-F_T(t))\,dt= \int_0^\infty v^{t} \,_tp_x\,dt\,$

where F(t) is the cumulative distribution function of the random variable T.

The equivalence follows also from integration by parts.

In practice life annuities are not paid continuously. If the payments are made at the end of each period the actuarial present value is given by

$a_x = \sum_{k=1}^\infty v^k (1-F_T(k)) = \sum_{k=1}^\infty v^k \,_kp_x.$

Keeping the total payment per year equal to 1, the longer the period, the smaller the present value is due to two effects:

The payments are made on average half a period later than in the continuous case.
There is no proportional payment for the time in the period of death, i.e. a "loss" of payment for on average half a period.

Conversely, for contracts costing an equal lumpsum and having the same internal rate of return, the longer the period between payments, the larger the total payment per year.

Life insurance as a function of the life annuity

The value of a life insurance can be derived from the value of a life annuity-due this way:

$\,A_x = 1-iv \ddot{a}_x$

This is also commonly written as:

$\,A_x = 1-d \ddot{a}_x$

The formula also works equally well in the continuous case. In the case where the annuity and life insurance are not whole life, one should replace the insurance with an n-year endowment insurance (which can be expressed as the sum of an n-year term insurance and an n-year pure endowment), and the annuity with an n-year annuity due.

See also

LendingTree ,

Disability ,

Asset-backed security ,

Lump-sum ,

Distortion (economics) ,

Life annuity ,

In actuarial science, the actuarial present value ... ,

Structured Settlements in the United States,

(source:wikipedia)

A structured settlement is a financial or insurance arrangement, including periodic payments, that a claimant accepts to resolve a personal injury tort claim or to compromise a statutory periodic payment obligation. Structured settlements were first utilized in Canada and the United States during the 1970s as an alternative to lump sum settlements. Structured settlements are now part of the statutory tort law of several common law countries including Australia, Canada, England and the United States. Structured settlements may include income tax and spendthrift requirements as well as benefits and are considered to be an asset backed security. Often the structured settlement will be created through the purchase of one or more annuities, which guarantee the future payments. Structured settlement payments are sometimes called “periodic payments” and when incorporated into a trial judgment is called a “periodic payment judgment." This is also called a coupon for a regular bond.

Structured Settlements in the United States

The United States has enacted structured settlement laws and regulations at both the federal and state levels. Federal structured settlement laws include sections of the (federal) Internal Revenue Code. State structured settlement laws include structured settlement protection statutes and periodic payment of judgment statutes. Medicaid and Medicare laws and regulations affect structured settlements. To preserve a claimant’s Medicare and Medicaid benefits, structured settlement payments may be incorporated into “Medicare Set Aside Arrangements” “Special Needs Trusts."

Structured settlements have been endorsed by many of the nation's largest disability rights organizations, including the American Association of People with Disabilities and the National Organization on Disability.

In April 2009, financial writer Suze Orman wrote in a column that structured settlements "provide ongoing income and reduce the risk of blowing a Lump sum through poor financial choices." In response to a reader's question, she added that financial security can be improved "if you use the structured payouts wisely.",

Structured Settlements Definitions,

A definition of “structured settlement” can be found in Internal Revenue Code Section 5891(c)(1) (26 U.S.C. § 5891(c)(1)), which states that a structured settlement is an "arrangement" that meets the following requirements:

* A structured settlement must be established by:

o A suit or agreement for periodic payment of damages excludable from gross income under Internal Revenue Code Section 104(a)(2) (26 U.S.C. § 104(a)(2)); or

o An agreement for the periodic payment of compensation under any workers’ compensation law excludable under Internal Revenue Code Section 104(a)(1) (26 U.S.C. § 104(a)(1)); and

* The periodic payments must be of the character described in subparagraphs (A) and (B) of Internal Revenue Code Section 130(c)(2) (26 U.S.C. § 130(c)(2))) and must be payable by a person who:

o Is a party to the suit or agreement or to a workers' compensation claim; or

o By a person who has assumed the liability for such periodic payments under a qualified assignment in accordance with Internal Revenue Code Section 130 (26 U.S.C. § 130).

It is important to note that the language immediately prior to Internal Revenue Code Section 5891(c)(1) states that the definition that appears there is "for the purposes of this section". Internal Revenue Code Section 5891 entitled "Structured Settlement Factoring Transactions" deals with the excise tax imposed on the "factoring discount" (see IRC 5891(c)(4)), when there is a purchase of structured settlement payment rights and the exceptions to the excise tax. A number of structured settlement industry commentators have been observed attempting to broaden the express language that appears in the Internal Revenue Code.,

Structured Settlements Legal Structure,

The typical structured settlement arises and is structured as follows: An injured party (the claimant) settles a tort suit with the defendant (or its insurance carrier) pursuant to a settlement agreement that provides that, in exchange for the claimant's securing the dismissal of the lawsuit, the defendant (or, more commonly, its insurer) agrees to make a series of periodic payments over time. The defendant, or the property/casualty insurance company, thus finds itself with a long-term payment obligation to the claimant. To fund this obligation, the property/casualty insurer generally takes one of two typical approaches: It either purchases an annuity from a life insurance company (an arrangement called a "buy and hold" case) or it assigns (or, more properly, delegates) its periodic payment obligation to a third party ("assigned case") which in turn purchases a "qualified funding asset" to finance the assigned periodic payment obligation. Pursuant to IRC 130(d) a "qualified funding asset" may be an annuity or an obligation of the United States government.

In an unassigned case, the defendant or property/casualty insurer retains the periodic payment obligation and funds it by purchasing an annuity from a life insurance company, thereby offsetting its obligation with a matching asset. The payment stream purchased under the annuity matches exactly, in timing and amounts, the periodic payments agreed to in the settlement agreement. The defendant or property/casualty company owns the annuity and names the claimant as the payee under the annuity, thereby directing the annuity issuer to send payments directly to the claimant. If any of the periodic payments are life-contingent (i.e., the obligation to make a payment is contingent on someone continuing to be alive), then the claimant (or whoever is determined to be the measuring life) is named as the annuitant or measuring life under the annuity.

In an assigned case, the defendant or property/casualty company does not wish to retain the long-term periodic payment obligation on its books. Accordingly, the defendant or property/casualty insurer transfers the obligation, through a legal device called a qualified assignment, to a third party. The third party, called an assignment company, will require the defendant or property/casualty company to pay it an amount sufficient to enable it to buy an annuity that will fund its newly accepted periodic payment obligation. If the claimant consents to the transfer of the periodic payment obligation (either in the settlement agreement or, failing that, in a special form of qualified assignment known as a qualified assignment and release), the defendant and/or its property/casualty company has no further liability to make the periodic payments. This method of substituting the obligor is desirable for defendants or property/casualty companies that do not want to retain the periodic payment obligation on their books. A qualified assignment is also advantageous for the claimant as it will not have to rely on the continued credit of the defendant or property/casualty company as a general creditor. Typically, an assignment company is an affiliate of the life insurance company from which the annuity is purchased.

An assignment is said to be "qualified" if it satisfies the criteria set forth in Internal Revenue Code Section 130 . Qualification of the assignment is important to assignment companies because without it the amount they receive to induce them to accept periodic payment obligations would be considered income for federal income tax purposes. If an assignment qualifies under Section 130, however, the amount received is excluded from the income of the assignment company. This provision of the tax code was enacted to encourage assigned cases; without it, assignment companies would owe federal income taxes but would typically have no source from which to make the payments.,

Structured Settlements Appears In,

* JG Wentworth is the largest buyer of structured settlements in the US. The company is best known for the "Opera" commercial that appeared in early 2010 on most cable channels in the continental United States. J.G. Wentworth's commercials are often considered to be over the top and many parodies have been born from it ever since.,

Profile Facts

Tuesday, October 26

Life annuity value

Life insurance

Life annuity

Life insurance as a function of the life annuity

Structured Settlements in the United States