Philadelphia Reflections

The Accordion Principle

If you will tell me the average investment return and the amount you invest in an escrow account, I can easily tell you how much money you will have at any future age. You can't do that very well, so we are going to show some rough guesses. It is simple to tell you the amount you will have if you live an average life expectancy, it's just hard to say what the life expectancy will be in the coming century. Next, you will have to tell me what kind of healthcare you want to cover, at today's rates, and at today's rate of inflation. Future projections are just guesses, however. The simplest kind of question would be what kind of health care do you want to cover, covering what ages, paying for it at the time of your death, at average life expectancy. In parentheses after each amount you would need, is the amount that would have to be deposited at birth to reach that particular goal at the death after 6.5% interest compounded. To stay on the safe side, the following costs are based on fractions of $ 350,000-lifetime calculation, rather than actual figures, and are therefore possible on the high side. For example,

Last year of life:$48,000 ($165 at birth, once)
Last two years of life:$56,000 ($193 at birth)
Last three years of life:$64,200 ($221)
All 18 years of Medicare:$187,000 ($646)

All of Medicare, paying no premiums(13%):$162,000 ($559)
All of Medicare, refunding payroll deductions(38%):$118,000 ($107)

First year of life (grandchild):$10,000 ($34)
First 21 years of life (grandchild):$28,000 ($96)

First and last years of life: $58,000 ($200)
All of Medicare plus all of childhood: $ 146,000 ($504)

Note: All "data" above are approximations of relative amounts. The last year of life contains hospice, etc, and the first year reflects obstetrical costs. Some cost offsets cannot be readily calculated for individual years from public sources. In fact, one of the implicit reasons for suggesting first-and-last year funding is to separate those costs which can be reduced through eliminating the disease by research, from the two extremes of life, where that is less likely.

Other things can be calculated, but the math gets a little beyond my pay grade. After all, if you reimburse the cost of the last year of life, the costs for the other 18 years of Medicare will be reduced. To calculate that, you would have to know how many Medicare recipients there are at various ages, and whether certain age groups have special costs. If you reimburse all of Medicare costs, the resulting cost for all of Medicare should be zero, so you are allowed to deduct all present funding sources, but only in that one instance. But there are lots of complicated data, like how much do we owe the Chinese Government for Treasury bonds to cover previous deficits, and do you want to include these servicing costs in the cost of Medicare? Do you actually want to do this, or are you just shopping? This is a quick shopping guide.

The accordion principle should be clear enough. If someone finds a cure for cancer, we could probably afford to reimburse two or three more years at the end of life. In all probability, a system like this would start with the last year and add other portions of the program if surpluses appeared. To do this sort of thing in an orderly manner, it would be desirable to start searching immediately for portions of all healthcare programs to peel off at pre-calculated rates. Not everything would be as simple to calculate as the average cost of a particular year of life. Cures for the remaining dozen major diseases are probably inevitable, but the timing and cost of those cures are impossible to judge in advance. The extraordinary extra costs of being born and dying do the bear investigation but are not relevant to this immediate discussion.

So we start with an average balance at age 84, after a lifetime of depositing $50 a year and investing @ 6.5%, of nearly $300,000. What would you like to fund with that? The answer I would give is the healthcare costs of the first and last years of life. They would phase in gradually, and give the greatest impact for the money. And the deliberate use of approximate numbers is intended to imply only that a relatively small amount of investment will buy a whole lot of healthcare if you go about it in this general way. Plenty of people can supply more precise calculations, but nobody is likely to come closer to the final answer than this.

Reducing This Process to a Formula? This approach reduces to: accumulating a sum of money in an escrow fund starting at birth and reaching a peak at death; then re-distributing the accumulation to repay a series of other funds which have actually financed the medical care. By making reasonable assumptions about the ingredients of this process, we can approximate its limits. We chose 6.5% as an interest rate. It was a stretch perhaps but allows simple calculation by the reader. If you take the trouble to divide the amount required by the (single-premium) deposit at birth, you will see the ratio is always 289. But this only applied to this longevity of age 90 At age 80 it would have been 154, and at age 100 it will be 543. That is, if longevity continues to increase, we can expect the multiplier to increase returns toward $543 per dollar invested at birth. The consequence is, as longevity increases by ten years we can provide more money for the same investment. In this case, we choose to represent it as $250 per year bonus for the elderly during their Medicare years. More likely, it should serve as a margin for error in these distant uncertainties. And it certainly illustrates how spending from the fund should be as delayed as possible, to achieve maximum returns.

Selecting Pieces of the Transfer Process. We show in the table what the average balance should look like within the escrow fund. It essentially transfers $70,000 to a fund with a lifetime duration for compounding, instead of using the actual age of the decedent, and it reaches for the maximum possible interest income; the graph shows the lifetime balance of the fund at various stages of life. Theoretically, it could be used for any healthcare purpose, but the reality is that distant events are more efficiently served. Although transfers between generations may seem bizarre, they seem to be the most rewarding way to pre-fund the health costs of newborns. For practical purposes, this is often the only it can be done, at all.

Originally published: Sunday, November 08, 2015; most-recently modified: Thursday, June 06, 2019