# Factors and assumptions that affect the present value calculation of a pension

The factors that affect the present value of a pension include the following: a) the number of years between the present and the time you begin receiving benefits; b) the age at which you begin receiving benefits; c) long-term interest rates, particularly the 30-year US Treasury Rate; d) the dollar value of the monthly benefit you will receive; e) any cost of living adjustments (COLA’s) in your pension, and f) assumptions about mortality.

Before I go through these different factors, I should note that there are two key principles for understanding the present value of a pension. Both have to do with “discounting”, which makes the present value of your pension much lower than the sum of the benefits that you might receive in the future.

The first of these ideas for understanding present value is the principle of “time value of money”. This is simply the idea that money you have in the *present* time is worth more than the same amount of money in the *future*. It is much better to have $1,000 now than it is to have $1,000 in 20 years. This is because money you have in the present can earn interest over time, so that it will grow. Another way to think about this is in terms of inflation—because of inflation, $1,000 will be worth less in 20 years than it is today. When inflation is high, interest rates tend to be high, and when inflation rates are low, interest rates tend to be low. Present value calculations “discount” the value of the benefits that you are likely to receive because they are in the future.

The second idea for understanding present value of pensions is mortality: a person might die before they receive a lot of benefits. Actuarial present value calculators, such as the one on this site, use mortality tables that indicate how likely people are, on average, to survive from year to year. Because there is a chance, each year, that a person might not survive and collect more pension benefits, the value of promised future benefits is lower than the value of actually having the equivalent amount of cash in hand.

The central effect of these two ideas—time value of money and mortality–is that the “present value” of the money you will receive in the future is *less* than the actual dollar amount you will receive in the future. So if you are projected to receive, say, $240,000 of pension benefits ($1,000/month over 20 years of retirement), the *present* value of that pension will be considerably less than $240,000.

## How each of the factors that you input affects the present value of a pension

Before considering each of these factors individually, a baseline example can help illustrate the effect of changing individual input factors:

The baseline example is a 45 year old who plans to retire at age 65 with a projected monthly benefit of $1000. This person uses the 2018 Applicable Mortality Table and enters a current 30-year Treasury rate of 2.83.

The present value of this example person’s pension is $101,841.

a) If the number of years between the present and the time you begin receiving benefits is higher, then the present value of your pension will be lower. There are two reasons for this. First, the present value discounts the value of the pension by the 30-year Treasury rate that you enter for each year that you wait before you start collecting. Second, there is a chance that you might not survive until the time that you begin collecting benefits.

If our example person were 55 instead of 45, the present value of their pension would be $135,971 rather than $101,841. If the person were 35 instead of 45, the present value of their pension would sink to $76,776.

b) The age at which you begin receiving benefits affects the present value of the pension because it is related to how many years you are likely to survive and collect more benefits. If you begin collecting a particular monthly benefit at age 55, the present value of that pension is higher than if you begin to collect that particular monthly benefit at age 65. To use an extreme example, think about making a promise to a person to pay them $1000/month for life. That is not a big (expensive) promise to make to a 105-year-old person, who is unlikely to survive many months to collect the benefit. In contrast, it is a very expensive promise to make to a 45-year-old, who is likely to collect the monthly payment for decades. The “present value” is the technical term for what a person might think of “the expense of the promise to pay a person a certain monthly benefit for life.”

If our example person projected a retirement age of 60 (rather than 65), the present value of the pension increases from $101,841 to $137,463. If instead, the person projects a retirement age of 70, rather than 65, the present value sinks from $101,841 to $71,960.

c) Lower long-term interest rates make the present value of a pension higher, and higher long-term interest rates make the present value of the pension lower. This is easiest to understand if you think about interest rates as correlated with inflation. If inflation is high, then payments of, say, $1000, will not be worth so much in today’s dollars in 10 years. If inflation is low, future payments of $1000 will not drop as much in value in those 10 years.

If the long-term interest rate were 2.33% rather than 2.83%, the present value would rise from $101,841 to $118,339. If interest rates rose to 3.38%, the present value would sink to $87,835.

d) If you have a higher monthly benefit at retirement, the pension is worth more in the present, and if you have a lower monthly benefit at retirement, then the present value is lower.

If the projected monthly benefit is $1500/month rather than $1000, the present value rises from $101,841 to $152,762. With a projected monthly benefit of $500, the present value drops to $50,921.

e) Cost of living adjustments increase the present value of a pension because they increase the take home amount of future monthly pension benefits. A simple way of thinking of this is that they can mitigate the effects of inflation on your pension. The most advantageous COLA’s—those that guarantee a compounding percentage increase on the entire pension benefit each year—could, in principle, overcome the effects of interest rate discounting if the COLA percentage were higher than the 30-year Treasury rate.

A compounding COLA of 1% would raise the present value of our example pension from $101,841 to $114,197. A compounding COLA of 2% would raise the present value to $127,999. A compounding COLA of 4% (uncommonly high for pensions these days) would raise the present value to $166,239.

A fixed COLA of $100/year would increase the present value of our example pension from $101,841 to $111,218. A fixed annual COLA of $250 would increase it to $125,224.

f) Nobody knows how long a given person will survive, but researchers collect data on what percent of a large population survives each year. They assemble this into mortality tables, which suggest how likely a person is to survive from one year to the next, given the mortality rates in that population. Women, on average, live longer than men, so the present values of women’s pensions will be higher than the present values of men’s pensions. People also live longer now, on average, than they did in the past, which makes present values based on current mortality tables higher than present values based on older tables.

Our example person used the unisex 2018 Applicable Table. If this person is female and uses the 2018 Female Combined Funding mortality table, the present value of the pension rises from $101,841 to $106,619. If the example person is male and uses the 2018 Male Combined Funding mortality table, the present value sinks from $101,841 to $97,475. If this male were to use the GAM83 chart, from 1983, when people did not live as long as they do today, the present value would calculate as $76,897.