The Dow Jones Industrial Average (INDEX: ^DJI) fell seven points to end the day at 13,164. But the chief investment officer of AllianceBernstein, Seth Masters, is thinking much bigger things for the index. He recently wrote a the case for the Dow to hit 20,000.

The Dow
Currently, the market -- as represented by the S&P 500 index -- trades at a P/E ratio of roughly 12.5, far below its historical average since 1970 of 17.5. That's a reflection of investors' uncertainty about the world economy. And investors have good reasons to be worried. For example, economic bellwethers Alcoa (NYSE: AA) and Freeport-McMoRan (NYSE: FCX) recently posted bad results because of China's slowest growth in the past three years.

Others are concerned that companies won't be able to maintain their current all-time high margins. IBM (NYSE: IBM) and Home Depot recently reported their highest gross margins in 20 years, and IBM did it in the face of falling revenues. Lately, similar to Dow tech components Hewlett-Packard and Cisco, IBM has taken steps to "boost productivity" while reducing its workforce. Whether this "workforce rebalancing," as Big Blue calls it, will prove sustainable is a critical question when predicting future performance.

Masters, however, takes a look at several scenarios for the economy going forward.

Scenario

Earnings Growth

Annualized Return

P/E Ratio

Years to  Dow 20,000

Current earnings, normal growth, below-average P/E 6% 9% 15 5
Current earnings, normal growth, above-average P/E 6% -- 20 0
Lower margins, normal growth, average P/E 6% 5% 17.5 10
Lower margins, lower growth, average P/E 2% 4% 17.5 20

Let's review the projections in each of his scenarios.

Current earnings, normal growth, below-average P/E
In the first scenario Masters lays out, if the market maintains its current earnings and normal growth, and the P/E ratio rises halfway to its historical average, the market will take five years to reach Dow 20,000. Over that timeframe, investors would be rewarded with a 9% annualized return.

Current earnings, normal growth, above-average P/E
In the second scenario, if the market were to immediately take off to a P/E ratio of 20, the Dow would be at 20,000, a 50% gain in a single day! If only we were so lucky.

This is extremely unlikely, as the Dow's current low P/E ratio of 12.5 shows investors don't believe the economy will be able to maintain earnings or growth at these levels, and there's no reason to think they will change their minds by such a huge degree any time soon.

Lower margins, normal growth, average P/E
In the third scenario, the market returns to normalized margins. Currently, businesses' margins are at an all-time high of 9.5%. The average for companies' margins over the long term is 6.75%. Comparatively, workers' wages versus GDP are at an all-time low. While some would say this time is different (the famous last words of many investors before losing their money), these things tend to revert to the average over the long run. Therefore, you can make a good case that corporate margins will be lower in the future.

Masters' third scenario also assumes normal growth and a normal P/E ratio. Under this scenario it will take the Dow 10 years to hit 20,000 for an annualized return of 5%.

Lower margins, lower growth, average P/E
In Masters' fourth and final scenario, if the market returns to normalized margins (lower earnings), lower growth, and a normal P/E ratio, it will take the Dow 20 years to hit 20,000 for an annualized return of 4%.

So what I'm getting at?

Foolish bottom line
In all cases, the annualized return is at least double what bonds currently offer. For long-term investors you'd be a fool (lowercase "f") to invest in bonds at such low rates.

The market can go anywhere in the short term, which is why watching the market every day is exciting but also gut-wrenching and stressful. Forget the Dow, and focus on companies that will crush it over the next 10, 20, and 30 years and invest for the long term. If you're looking for long-term investing ideas, The Motley Fool has created a brand-new free report: "3 American Companies Set to Dominate the World." Get access to the report and find out the name of these legendary companies. The report is free, but it won't be forever, so check it out today.