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Calculating the real cost of income annuities

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As the market for single premium immediate and deferred income annuities heats up, a calculation you can use to compare competing products and estimate embedded costs is called the Money’s Worth Ratio. The concept was developed in a 1999 analysis by Olivia Mitchell, James Poterra, Mark Warshawsky and Jeffrey Brown, which you can find here: 

A less academic explanation is offered by the website Retire Early: 

In essence: “You can estimate the costs embedded in a single premium immediate annuity by comparing the premium quote you get from the insurance agent to the expected present discounted value (EPDV) of an immediate life annuity. … Economists define the ratio between the EPDV and the premium quote as the Money’s Worth Ratio.”  

To determine EPDV, you will need: 

  • The current yield on 10-year U.S. Treasuries, which is used as the discount rate in the present value calculation.

  • The client’s life expectancy taken from the most current Social Security Actuarial Life Table, which is here: 

Example: You quote an SPIA rate of $550 per month ($6,600 per year) for a 65-year-old male with a life expectancy of 17.57 years, according to the Social Security Actuarial Life Table. The premium is $100,000. Using a discount rate of 2.4% (for the 10-year Treasury yield), the present value of this payment stream over 17.57 years is $93,715. 

MWR is the $93,715 present value divided by the $100,000 single premium = 93.7%. The embedded costs in the SPIA are $6,285 – 6.3% of the premium paid. 

In Excel, the formula is: =PV(2.4%,17.57,-6600). 

Note that the embedded cost is fixed (guaranteed) at the time the SPIA is purchased. To do a similar calculation for a DIA, you can add together the present values of each future year of payout, to life expectancy. 

The cost of an SPIA or DIA has three main components: 

  • Mortality risk.

  • Insurance company administration and profit.

  • Survivorship bias, which occurs to the degree that the annuitant pool has a greater life expectancy than the general population (as measured by the Social Security table).


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