First, what you are doing is taking a net present value of a discounted cash flow, dividing it up into pieces and then population.
You cannot do this.
Say there is a discount rate of 8% and you owe $100 per year for 20 years. That's a NPV of about $980.
Then you say, $980 divided by 20 years is only $49! It's nothing. You just turned an obligation of $100 per year into $49 per year.
See, the pensions, when they say they have a shortfall of X, what they mean is that if they got X today, and invested it with their expected rate of return, in the future they would have what they need to pay out their obligations. They are not saying that their obligations are X when they are added together across time without discounting.
Second, in the case of pension funds, the discount rate is how much they think they can earn with the money. The pension industry has different assumed rates of return, but the most consistent one I've heard is 8%, which in today's world of secular low rates is insane. There is a whole world here of pension funds reaching for yield as risk free instruments drop to very low rates, and this is by far a much bigger impact on pensions than anything else and something not talked about when people cheer low interest rates. This is causing pension funds to be in shortfall all across the world.
There is also the issue that some pension plans contain provisions for health insurance, which is also hard to predict.
So I'm not saying I have the right number, but without knowing their discount rate or future obligations, you are not going to be able to get a good number.
Japan has a completely different pension system which is extremely conservative.
It's a two tier system, the first government funded, and of course the Japanese government is in enormous debt, but not because of pensions. The government funded pension is like welfare, it's very small, is fixed in amount for everyone, and funded by contributions. It would be what social security is if the amount was tiny -- say $200 per month -- and fixed for everyone regardless of how much they pay in, even though everyone pays in a bit less than 1% of their salary. It is a system not dependent on positive rates of return.
The second system is the main source of pensions for people and is employer/employee funded. It is also quite austere -- you pay in 18% of your income in year 1 and that amount increases by 0.25% each year. Of course only half is deducted from your paycheck, the rest from the employer, but it is effectively taken out of the worker's paycheck.
What you get when you retire is ~0.55% of your total lifetime wages each year. This amount is fixed in nominal terms -- there is no inflation, cost of living adjustment, etc. You get this fixed amount every year. That means that by design the system is solvent because even if nothing is invested and the money earns 0%, if you work for 30 years and never get a raise, you will have paid in an average of ~22% of your lifetime wages which will fund 32 years of retirement pension after 30 years of working. But a normal person will get raises, and as they get raises over time, they earn more later in life when their percentage contribution goes up, so pensions are well funded even for a population with long lifespans and low interest rates. Then of course people have private savings in addition to pensions.
Needless to say, Americans would riot if you told them they need to increase their social security contribution from 15% to 18%, with no cap, and that this amount goes up every year, and then what they get would be only 0.55% of their lifetime earnings with no COLA. That means someone earning the median per-capita income of about 31K for 40 years of work would get $570 per month in social security benefits after paying in an average of $594 per month over 40 years. But again, our system is designed for people who die younger and work in an economy with decent rates of return.
But if we adopted a Japanese style system, social security would be permanently in the black regardless of interest rates.
So does that mean the average retired Japanese person is living on less than $1k per month?? How are they doing that? Isn't Japan pretty Urban and the cities relatively expensive to live in?
You would be surprised at how low wages are in Japan and how frugal people are to save to supplement their employer pensions. You would also be surprised at how many poor people there are in Japan. The stereotypical wealthy Japanese salaryman has pretty low salaries by American standards. There are also homeless people in Tokyo who sleep quietly in the streets and then clean up after themselves, disappearing completely from sight so you wouldn't know there was an encampment there. There was one famous case of an older person starving in Japan. He had a very touching diary where he wrote he dreamed of eating just one rice ball. He went to the unemployment office but they turned him down.(source: https://asiancorrespondent.com/2012/02/starving-to-death-in-...)
In Japan 2/3 of the average person's retirement income is pension benefits and 1/3 is savings, so Japanese augment their frugal pensions by saving a lot. Even so, 1 in 6 Japanese live in poverty, and 1 in 5 seniors live in poverty, suggesting that the low pensions play a role and that some Japanese are suffering because of this (https://www.japantimes.co.jp/news/2019/06/04/business/financ...)
Private consumption in Japan, as a share of GDP, is about 10% less than in the U.S. E.g. they consume about 57% of GDP and we consume about 67% of GDP. This includes consumption of fixed capital. If you back that out, the median Japanese household is just much more frugal than the median US household, and it's not all increased out of pocket healthcare spending (source: https://www.bls.gov/opub/btn/volume-6/how-do-united-states-c...). They really are more frugal and more risk averse than US households.
In the U.S. 9% of seniors live in poverty compared to 13% of the population (and 18% of children). Social Security not only does a fantastic job of keeping seniors out of poverty, but for many seniors who lived in poverty before the age of 65, the receipt of social security benefits lifts them out of poverty in their old age.
Thus, social security is much more than a pension program, it's actually a significant transfer that causes seniors to have lower poverty rates than working-age Americans.
You cannot do this.
Say there is a discount rate of 8% and you owe $100 per year for 20 years. That's a NPV of about $980.
Then you say, $980 divided by 20 years is only $49! It's nothing. You just turned an obligation of $100 per year into $49 per year.
See, the pensions, when they say they have a shortfall of X, what they mean is that if they got X today, and invested it with their expected rate of return, in the future they would have what they need to pay out their obligations. They are not saying that their obligations are X when they are added together across time without discounting.
Second, in the case of pension funds, the discount rate is how much they think they can earn with the money. The pension industry has different assumed rates of return, but the most consistent one I've heard is 8%, which in today's world of secular low rates is insane. There is a whole world here of pension funds reaching for yield as risk free instruments drop to very low rates, and this is by far a much bigger impact on pensions than anything else and something not talked about when people cheer low interest rates. This is causing pension funds to be in shortfall all across the world.
There is also the issue that some pension plans contain provisions for health insurance, which is also hard to predict.
So I'm not saying I have the right number, but without knowing their discount rate or future obligations, you are not going to be able to get a good number.