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: http://business.illinois.edu/ormir/AER%20December%201999.pdf
A less academic explanation is offered by the website Retire Early: http://www.retireearlyhomepage.com/annuity_costs.html
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: http://www.ssa.gov/oact/STATS/table4c6.html
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:
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).