Valuing Different Types of Single Premium Immediate Annuities (SPIA) and Single Premium Deferred Annuities (SPDA).

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This article was first posted November 1, 2009.

Back in July, Retire Early looked at the high costs embedded in Single Premium Immediate Annuities (SPIA) in an article that examined the expected present discounted value (EPDV) of a standard, single-life immediate annuity. Several readers asked how to expand that to valuing a life annuity with a guaranty period, or a period certain annuity that lacked a life-contingent benefit. We'll also consider the single premium deferred annuities (SPDA) that are the basis for longevity insurance, a little-known product now being pushed by the financial services industry. You can download an updated copy of Retire Early's spreadsheet, click here.

Period-Certain Single Premium Immediate Annuities

A period-certain annuity is an insurance contract that provides a series of payments for a fixed term, say ten annual payments over ten years. The number of payments received does not depend on your life expectancy. If you die in year five, your heirs still receive payments 6 through 10.

The are two different types of period certain annuities; CD-type annuities and fixed annuities. The major difference between the two is that CD-type annuities guarantee the interest rate for the full term of the annuity while fixed annuities may only guarantee the rate for part of the term.

The expected present discounted value (EPDV) of this type of annuity is a simple present value of an annuity calculation that you can do with Excel's present value function.

Single Premium Immediate Annuities with a guaranty period

To overcome customer objections that "they don't want to buy an annuity and then die the next week and get nothing", insurance companies offer single premium immediate annuities with a guarantee period. These products pay the annual benefit to the annuitant's heirs if he or she dies before the end of the guarantee period. Valuing this type of annuity is simply the sum of a period certain annuity that covers the guarantee period and a deferred annuity that covers the risk that the annuitant is still alive after the end of the guarantee period.

Single Premium Deferred Annuities

Single premium deferred annuities (SPDA) are unusual in that you pay a lump sum of money today, but typically wait 20 or 30 years before you start collecting any benefits. You can get a relatively large annual benefit for the premium paid since the insurance company has a long time to invest the premium. Also, very few people live long enough to collect any significant benefit. For example, the 2004 Social Security mortality table predicts that less than one-third of 55-year-old males are expected to live to age 85.

Of course, there's always the risk that the insurance company won't be around in 20 or 30 years when the benefit is scheduled to commence, and inflation is a concern. If prices grew at 3% per year for the next 30 years, a $1,000/month benefit today would buy only $412 worth of goods when the benefit starts. If inflation was 5%, the adjusted future value drops to $231/month.

The table below shows the expected present discounted values (EPDV) for a Met Life longevity insurance product.

Comparison of the Expected Present Discounted Value (EPDV) of a nominal Single Premium Deferred Annuity (benefit begins at age 85) with quotes from insurer . Based on the Social Security mortality table and an interest rate of 4.00%
.		----- $12,000 annual benefit -----
.		EPDV ($)		Insurer's Quote	Money's Worth Ratio (MWR)
Age/Sex	Years Deferred	General Population	Annuitants Note (1)	Met Life	General Population	Annuitants
55 male	30	$6,324	$11,719	$7,996	0.79	1.47
60 male	25	$8,061	$14,593	$10,694	0.75	1.36
65 male	20	$10,532	$18,397	$14,529	0.72	1.27
55 female	30	$10,571	$16,701	$10,132	1.04	1.65
60 female	25	$13,233	$20,611	$13,439	0.98	1.53
65 female	20	$16,843	$25,648	$18,126	0.93	1.41
(Note (1) New Evidence on the Money's Worth of Individual Annuities, Olivia S. Mitchell, James M. Poterba, Mark J. Warshawsky and Jeffrey R. Brown, December 1999, American Economic Review. -- The information from Table 2 in Mitchell's article on the relative mortality between the general population and annuitants was used to adjust the 2004 Social Security mortality table for adverse selection. The adjustment places the median annuitant in the 66th percentile of the mortality distribution for the general population as described by the 2004 Social Security table. This translates to almost a 5-year spread for adverse selection for a 55-year-old and 3 years for a 70-year-old.

As expected, the table above shows that single premium deferred annuities (SPDA) tend to have poor value for people of average mortality. However, they can be a good deal (i.e., MWRs well in excess of 1.00) for individuals in good health who believe their longevity lies at the far end of the mortality curve.

Resources for further information

A new strategy to guarantee retirement income using TIPS and longevity insurance, by Shankar, S Gowri.

Best to reject annuities that feature an inflation rider , by Lynn O'Shaughnessy.

The Principal Financial Group annuity quotes a listing of their current annuity payouts.

Berkshire Hathaway annuity quotes online calculator gives you an immediate quote.

Immediateannuities.com annuity quotes online calculator gives you an immediate quote on both period certain and life annuities.

Forbes magazine Guaranteeing Lifetime Income.

The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program, Jeffrey R. Brown, Olivia S. Mitchell and James M. Poterba, 1998, The Wharton School.

Assessing Investment and Longevity Risks within Immediate Annuities, Daniel Bauer, Frederik Weber, 2007, Munich School of Management.

Immediate Annuity Pricing in the Presence of Unobserved Heterogeneity , Kim G. Balls, 2004, Managing Retirement Assets Symposium - Society of Actuaries

IS ADVERSE SELECTION IN THE ANNUITY MARKET A BIG PROBLEM? , Anthony Webb, 2006, Boston College, Center for Retirement Research

Annuities Markets Around the World: Money’s Worth and Risk Intermediation, Estelle James and Xue Song, October 2001, American Economic Association.

Hewitt Associates - 401(k) index some interesting information on how people allocate their retirement acounts.

Lifetime Financial Advice: Human Capital, Asset Allocation and Insurance, by R.G. Ibbotson, M.A. Milevsky, P. Chen and K.X.Zhu

Social Security Handbook -- information on your Social Security benefits.