# What is annuities

**Payout Rates and Returns on Income Annuities** Forbes Thursday, August 27, 2015

Wade Pfau

The pricing of an income annuity is typically described using either the monthly income amount it generates, or as the annual payout rate of the income received as a percentage of the premium amount. For example, an annuity might offer $416.67 per month on a $100,000 premium. For 12 months, that sums to $5,000, which is 5% of the initial premium amount. In this case, the annuity payout rate is 5%. I generally describe annuity pricing by annual payout rate.

With income annuities, these amounts are what the annuitant receives. There are no additional fees to be paid. Annuities are not free, though occasionally a financial service professional might mischaracterize them as such. But the point is that there are no additional fees extracted from the quoted payout rate. Any fees served to internally lower the payout rate before it was presented to you. The nature of these fees is generally low, and you could think of income annuities as the term life insurance of the annuity world. Both offer the lowest cost and are the easiest-to-understand versions in their respective categories.

Expressing annuity characteristics through the payout rate is useful because it has a more direct comparison to withdrawal rates from investment portfolios. A withdrawal rate is how much you withdraw as a percentage of remaining assets, and the payout rate is how much you receive as a percentage of the annuitized amount. Both numbers are comparable (though portfolio withdrawal rate discussions generally assume inflation adjustments by default).

It is important to recognize that the payout rate is not a return on the annuity, which may create some confusion. I have seen explanations which may suggest something along the lines of: You can earn 1% by holding a CD and 5% from an income annuity, so the income annuity is 5x more powerful than the CD. The problem is that the 1% number for the CD only represents its interest payments. The principal value is returned at maturity.

Meanwhile, a 5% payout from an annuity includes interest and principal payments (as well as mortality credits). Principal is being spent as well, and so the comparison to the 1% from the CD is neither fair nor meaningful. The annuity does have a return, but it is less straightforward to calculate.

To know the annuity return, it is necessary to know how long the annuitant will live and receive payments. Or, at least, returns can only be calculated by assuming how long income payments will be received. I generally do not speak about the returns from annuities, because for a life-contingent annuity you will not know your overall return until you know how long you have lived. The longer you live, the higher the return from the annuity. For life-only annuities, returns will be very low early on as relatively little income has been received relative to the principal purchase amount. Eventually, the return will exceed the payout rate.

Calculating an annuity return is done by determining its internal rate of return (IRR). The IRR is a mathematical calculation which looks at the inflows and outflows of money over time and calculates an investment return that would be needed to precisely allow the inflows to grow and match the outflows.

For example, suppose you put $1,000 into the bank today. In each subsequent year on the anniversary of this bank contribution, you withdraw $150 from your bank account. You

are able to keep this up until your ninth withdrawal, at which point your bank account balance falls to zero. What interest rate would you need to earn from the bank account to make this stream of nine $150 withdrawals work out as planned? This is an internal rate of return calculation, and it is the same process used with an annuity.

Setting up the calculation in Excel, I get an answer of 6.46%.

Time Period Cash Flow 0 -$1,000 1 $150 2 $150 3 $150 4 $150 5 $150 6 $150 7 $150 8 $150 9 $150 Internal Rate of Return: 6.46%

Perhaps internal rate of return can be understood more clearly by working in the reverse direction. Suppose I put $1,000 in the bank and it earns an annual interest rate of 6.46%. On each anniversary of my deposit, I withdraw $150 from the account. The account balance grows with interest but shrinks with withdrawals. When I take out the $150 withdrawal in year nine, the account balance has fallen to $0, as expected.

The table below illustrates why the internal rate of return is 6.46%.

Investment Return: 6.46% Time Period Cash Flow Account Balance 0 $1,000 $1,065 1 -$150 $974 2 -$150 $877 3 -$150 $774 4 -$150 $664 5 -$150 $547 6 -$150 $423 7 -$150 $291 8 -$150 $150 9 -$150 $0

To understand the distinction between the payout rate and the return on an annuity, we can consider a very simple annuity example which makes one annual payment each year rather than monthly payments. For a premium of $100, a payment of $6.73 is received immediately, and on each anniversary date of the contract an additional payment of $6.73 is received for as long as the annuitant lives.

The actual return starts out negative, and then it crosses from negative to positive with the payment received 14 years later at age 79. The point at which the return goes positive is intuitive, because with payments starting at 65, the age 79 payment is the 15th received, and the 15th payment pushes the total amount of income received to $100.95 (15 x 6.73), which surpasses the initial $100 premium. We have entered the range of positive returns.

With the age 83 payment, the return exceeds 2.5%, which was the assumed return on the underlying assets. Age 84 represents the median life expectancy for a 65-year old male, and with this payment the return increases to 3.38%. The annuitant has a more than 50% chance that the return on the annuity will exceed the 2.5% return on fixed income, because the annuitant is also receiving mortality credits which are amortized over the life of the annuitant. If the annuitant lives to 95, the return grows to 5.94%, and continues to rise.

Eventually, the return will grow to exceed the initial payout rate. Growth happens sooner when interest rates are higher. With our 2.5% interest rate, the return does not exceed the payout rate until age 107, making that the age where it would be correct to say that the payout rate is the same as the return. The most interesting aspect of this analysis is that even before life expectancy, the return from an income annuity exceeds the return from holding a portfolio of bonds without any mortality credits.

Figure 1**: Mechanics of a Single-Premium Immediate Annuity

Payout Rate and Internal Rate of Return by Age of Death for Purchase at Age 65

Source: news.yahoo.comCategory: Credit

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