Saturday, ABC World News aired an investment snippet on how Americans should prepare for retirement. The feature lasted just under a minute and a half.

Consequently, there was no time to explain the numbers. Such are mass communications, and you will find no protest from me. This column skips plenty of details itself. However, I do have enough room to explore the segment's most dramatic claim: That somebody who begins investing at age 23 can retire with $1 million by investing $14 daily into a "low-cost S&P 500 fund."

ABC's report assumes that future stock market returns are known. This supposition is clearly false, but necessary. A 90-second report cannot explain the assumptions that underlie the calculations, including how wealth projections vary with market forecasts. By the time the caveats are over, so is the dispatch.

Thus, this column.

**Making it real**

My first task was to reverse-engineer the calculation: What rate of return would create that $1,000,000? The ABC report did not specify whether the $14 must also be saved on weekends and holidays, as opposed to only the days in which the stock markets are open. Initially, I tested the latter: 250 investments of $14 each year, for a total of $3,500 annually. Could $1 million be generated in that fashion, or would it need a 365-day schedule?

(My spreadsheet assumes a constant rate of return for stocks. Of course, that will not occur in real life. However, as the model generates a so-called geometric rate of return--as opposed to arithmetic--it can be reasonably compared with historic stock market results, which are also quoted in such terms.)

The answer is "perhaps." The required rate of return to achieve the $1 million nest egg is 7.6% annually, which at first glance seems reasonable. But inflation has not been considered, and it must be, otherwise that $1 million figure is illusory. After all, who can say what $1 million can buy in 2060? To be useful, the retirement goal must be expressed in *today's* dollars.

And making 7.6% annually, in real terms, is a tall order. True, that is about what the S&P 500 has gained over the past 42 years. But that was a favourable stretch. The prior 42-year period generated 6.4% per year, and the one before that 5.6%. What's more, as the academic researchers point out, the U.S. enjoyed the best of all possible worlds. It has been the single high-performing stock market of the past century. In all other countries, the results have been worse.

So while accruing a real $1 million by investing $14 per trading day is possible, it is not probable. The more-realistic path would be to set aside that $14 (which, by the way, would be $14 only in year 1, as the investment amount would need to adjust for inflation to reach the $1 million goal in real terms) each calendar day. The spreadsheet informs me that switching to the 365-day schedule lowers the required rate of return to 6.3%. That remains optimistic, but not foolishly so.

**Sensitivity testing**

Of course, as previously stated, actual stock market results will vary. Cutting the real-return assumption by a single percentage point, to 5.3%, slashes the after-inflation nest egg for the 365-day strategy by almost a fourth, to $767,000. Drop another percentage point, to 4.3%, and the retirement amount dips to $590,000. As Jack Bogle taught, and ABC correctly reiterates, the investment math works only if the investment fees are modest. Over such a long time period, a little extra cost can cause a lot of extra damage.

Conversely, bumping the real return to 7.3% boosts the retirement total to $1.33 million. Pushing it to 8.3% yields almost $1.8 million. Finding something that grows even faster than the S&P 500 is a profitable endeavour! Unfortunately, although advice abounds for earning above-market returns -- such as investing in value-style stocks, or emerging markets, or leveraged funds -- those outcomes are far from certain.

**The generation gap**

ABC's investment advice contained a second item: the importance of time. The earlier contributions begin, the fewer dollars must be invested. Obviously, that is correct. The report then stated that, to stockpile that same $1 million, those who began at age 40 would need to stash away $42 per day--thrice as much as the 23-year old! That counsel is less obvious.

It's also not entirely accurate, as the relationship between the two hypothetical investors depends on the stock market's performance. If equities thrive, then the 23-year old will enjoy extra benefit from being early. Conversely, if stocks are sluggish, then the older investor will pay a lower penalty for waiting. He need not invest as heavily to catch up. (Relatively speaking, that is. In absolute returns, both parties must save more, because the stock market will give them less assistance.)

The break-even point is 5.5%. Above that rate of return, the older investor must invest more than $42 per day to keep pace with the youngster. In fact, should real stock returns hit the unlikely level of 9.4%, the 40-year old novice will need to contribute 5 times as much money as the younger buyer, rather than the 3 times cited in ABC's story. However, cut those stock market returns to a disappointing 2% per year, and the 40-year-old need invest only at double the youngster's level.

**Conclusion**

Stock market performance is nowhere near as certain as portrayed by ABC's report. In addition, the network's example assumes a 100% stock allocation until age 65 -- a tactic few investors will follow. Thus, the story's results should be interpreted loosely. But as a general illustration of the results of long-term investing, as well as an indication of the benefits of starting early, the segment is broadly accurate.