From the very beginning of my stock market journey, I have believed that valuation matters.

But sometimes, the view is expressed that valuation does not matter to the long-term investor, because 20 years from now, you won't care whether you paid a few dollars more for a stock. It will be worth so much more than your original price, and it will be delivering such a greater dividend return, that your original purchase price will have become irrelevant.

I got wondering if this is true. Let's create a hypothesis and then test it.

Here is the hypothesis:

*I want to own company A. It is a high quality Dividend Champion with a current yield of 4%. Its dividend growth rate over the past 10 years has been 10% per year, and its earnings have been growing at the same rate. Unfortunately, A is currently trading for 25% more than what I consider to be fair value. But I intend to hold A for at least 10 years, reinvesting its dividends along the way. So I decide to buy company A. In 10 years I won't care what I paid.*

OK. Now we need to test the hypothesis. We need some presumptions to do that. Keep in mind that these are all hypothetical, but they are reasonable, and they do let us create a model to test the hypothesis.

The test model, of course, is theoretical. Some of the presumptions are impossible to know in a real-life situation. But we do not need exact real-world values for any particular stock. We are just trying to test the hypothesis that valuation does not matter for long-term holders.

So here are what I think are reasonable presumptions for this thought experiment.

1. I presume that I can reasonably estimate A's fair value. My estimate is that its fair value is $20. At its market price of $25, it is 25% overvalued.

2. With a current yield of 4%, A will pay $1.00 in dividends per share in Year Note: If the stock were fairly valued ($20), that would not change the *dividend amount*. The payout would still be $1.00 in Year 1. What would be different is its *yield*. At a fair price of $20, A's yield would be 5%.

3. The company has been growing it earnings 10% per year, and it will continue to do so.

4. The board of directors will increase the dividend each year in line with the company's earnings growth. So A's dividend increase rate will also be 10% per year for 10 years.

5. The stock market's opinion on valuation will stay the same throughout the scenario. The market likes this stock. At the time of purchase, A is 25% overvalued with a P/E ratio of 25. At the end of 10 years, it will still be overvalued with a P/E of 25.

6. Because the P/E ratio will stay the same, the stock's price change each year will be in line with its earnings growth: 10% per year.

7. For convenience in calculations, the full year's dividends are paid in one installment in late December each year and reinvested. The stock's price stays constant all year until it jumps 10% on the last day of each year (which determines the price for the following year).

8. We invest $1,000 at the beginning of Year 1.

9. We collect the full year's dividend in Year 1 and all subsequent years.

10. We hold the stock for 10 years, with no further money added from outside.

11. We ignore taxes and any frictional costs of reinvesting dividends.

That gives us all that we need to test the hypothesis.

The first scenario represents buying the stock at its overvalued price of $25.

Year # | P/E Ratio | Price $ | Shares Bought Initially # | Dividend per Share $ | Dividend Received for Shares Owned $ | Shares Bought with Dividend # | Shares Held at End of Year # | Annual Increase in Earnings % |

1 | 25 | 25 | 40 | 1.00 | 40 | 1.6 | 41.6 | 10 |

2 | 25 | 27.50 | 1.10 | 45.76 | 1.66 | 43.26 | 10 | |

3 | 25 | 30.25 | 1.21 | 52.34 | 1.73 | 44.99 | 10 | |

4 | 25 | 33.28 | 1.33 | 59.84 | 1.80 | 46.79 | 10 | |

5 | 25 | 36.60 | 1.46 | 68.31 | 1.87 | 48.66 | 10 | |

6 | 25 | 40.26 | 1.61 | 78.34 | 1.95 | 50.61 | 10 | |

7 | 25 | 44.29 | 1.77 | 89.58 | 2.02 | 52.63 | 10 | |

8 | 25 | 48.72 | 1.95 | 102.63 | 2.11 | 54.74 | 10 | |

9 | 25 | 53.59 | 2.14 | 117.14 | 2.19 | 56.93 | 10 | |

10 | 25 | 58.95 | 2.36 | 134.35 | 2.28 | 59.21 | 10 | |

| $788.29 | 19.21 | 59.21 |

So what do we have at the end of 10 years?

- Annual dividends increased from $40 in Year 1 to $134.35 in Year 10. That is a total increase of 236% and a CAGR of 14.4% per year. This is the combined result of first the company's annual 10% increase in the dividend, and second the impact of reinvesting the dividend each year. Note that the number of years used to calculate the CAGR is 9 years, since we did not receive and reinvest the first dividend until the end of Year 1.
- The value of the portfolio has grown from $1000 to $3490. That is a total increase of 249% and a CAGR of 13.3% per year. The increase is the combined result of the 10% annual growth in share price each year and the increase in the number of shares owned as the result of dividend reinvestment. Note that the number of years used to calculate this CAGR is 10 years, since the $1000 was invested on Day 1 of Year 1.
- The number of shares owned has increased from 40 shares initially purchased to 59.21 at the end of 10 years.

If we look under the hood, we see that all these results were the result of a few key drivers:

- The company increased its earnings at 10% per year.
- The P/E ratio stayed (overvalued) at 25 for the full 10 years.
- The company increased its dividend to match its earnings growth every year. (That is equivalent to saying that the company kept its payout ratio constant.)
- The dividends were reinvested every year into the same stock, thus compounding the investor's results beyond the company's results. The company grew 10% per year, as did its price and dividend. But our investor's dividends increased 14.4% per year and the paper value of the holding increased 13.3% per year.

Was it a good decision to buy the stock? In one obvious sense it was, because the results are fabulous by almost any standard. The annual dividend and total return of A more than tripled over 10 years. I would take that result any time.

But that wasn't the question. The question is whether valuation matters. We paid 25% "too much" for the stock. So to see whether valuation matters, we need to compare that scenario to others. The most obvious alternative is a base case where the only thing different is that we buy the stock at fair value. We hold all the other factors the same, because we want to isolate the impact of valuation.

So in our presumptions for the second scenario, everything stays the same except:

1. We buy the stock at $20 per share, which we have determined is its fair price.

2. At its fair price, its P/E ratio is 20 instead of 25 paid in the preceding scenario.

3. At its fair price, A's yield is 5%, not 4%. Same dividend, but different price means different yield.

Let's run the numbers. Note that the "Dividend per Share" column is identical to the earlier scenario. The company's dividend is not determined by how many shares you own or what you paid for them. The board of directors determines the dividend.

So for Scenario 2, we invest $1000 at $20 per share and see what happens.

Year # | P/E Ratio % | Price $ | Shares Bought Initially # | Dividend per Share $ | Dividend Received for Shares Owned $ | Shares Bought with Dividend # | Shares Held at End of Year # | Annual Increase in Earnings % |

1 | 20 | 20 | 50 | 1.00 | 50 | 2.5 | 52.5 | 10 |

2 | 20 | 22.00 | 1.10 | 57.75 | 2.63 | 55.13 | 10 | |

3 | 20 | 24.20 | 1.21 | 66.71 | 2.76 | 57.89 | 10 | |

4 | 20 | 26.62 | 1.33 | 76.99 | 2.89 | 60.78 | 10 | |

5 | 20 | 29.28 | 1.46 | 88.74 | 3.03 | 63.81 | 10 | |

6 | 20 | 32.21 | 1.61 | 102.73 | 3.19 | 67.00 | 10 | |

7 | 20 | 35.43 | 1.77 | 118.59 | 3.35 | 70.35 | 10 | |

8 | 20 | 38.97 | 1.95 | 137.18 | 3.52 | 73.87 | 10 | |

9 | 20 | 42.87 | 2.14 | 158.08 | 3.69 | 77.56 | 10 | |

10 | 20 | 47.16 | 2.36 | 183.03 | 3.88 | 81.44 | 10 | |

| $1039.80 | 31.44 | 81.44 |

What does this investor end up with?

- His annual dividends increased from $50 in Year 1 to $183.03 in Year 10. That is a total increase of 266% and a CAGR of 15.5% per year.
- The value of his portfolio has grown from $1000 to $3841. That is a total increase of 284% and a CAGR of 14.4% per year.
- The number of shares owned has increased from 50 shares initially purchased to 81.44 shares.

Let's look at the two scenarios in table form for easy comparison.

Scenario 1 - Overvalued | Scenario 2 - Fairly Valued | |

Fair value per share | $20 | $20 |

Actual price paid | $25 | $20 |

Initial Portfolio Value | $1000 | $1000 |

Holding period | 10 years | 10 years |

P/E (stays constant for 10 years) | 25 | 20 |

Company's EPS growth rate | 10% per year | 10% per year |

Company's dividend growth rate | 10% per year | 10% per year |

Company's share price growth rate | 10% per year | 10% per year |

Dividends reinvested? | Yes | Yes |

Shares Purchased Initially | 40 | 50 (25% more) |

Shares Owned after 10 Years | 59.21 | 81.44 (38% more) |

Year 1 Dividends Received | $40 | $50 (25% more) |

Year 10 Dividends Received | $134.35 | $183.03 (36% more) |

Total Dividends Received | $788.29 | $1039.80 (32% more) |

Dividend CAGR | 14.4% per year | 15.5% per year (7.6% more) |

Final Portfolio Value | $3490 | $3841 (10% more) |

Portfolio Value CAGR | 13.3% per year | 14.4% per year (8.3% more) |

It is hard to avoid the conclusion that valuation matters. On every metric, the stock bought at fair value delivered more than the stock purchased at an overvalued price. Not only that, the performance gap widens with each passing year.

Let's acknowledge that this model is entirely theoretical. In the real world, you may never find two stocks - or a single stock at two different points in time - that present the exact characteristics that I used to test the hypothesis.

One important presumption was that I can actually ascertain fair value. Valuation is part math and part judgement. No matter what method you use (here's mine), or whose valuation you believe, remember that every valuation is an appraisal, meaning that it has subjective elements. Beyond the inherent subjectivity, every valuation method looks forward, so it must use presumptions about things like earnings growth, dividend policies, business sustainability, and the like. Nobody knows the future, and many plug-in numbers are no more than reasonable guesses.

Nevertheless, I think that the principles illustrated here are valid, and that investment choices similar to the two scenarios herein are presented daily to investors.

I would like to wrap things up with a couple of real examples. Neither fits the model exactly, but they are directionally similar. Both companies are Dividend Champions.

The first - corresponding to Scenario 1 - is Automatic Data Processing (NASDAQ:ADP). Its P/E is above 28, and its high price contributes to a relatively low yield of 2.4%. Morningstar rates it as overvalued at 2 stars. On this graph, it appears to be wildly overvalued, currently trading above even its normal high P/E ratio of 25.5.

In contrast, representing Scenario 2, is Emerson Electric (NYSE:EMR). It is available at a P/E of 17.5, yield of 3.5%, and Morningstar rating of 4 stars.

Here is a tale of the tape for these two stocks.

ADP - Overvalued Example | EMR - Fair Value Example | |

Industry | Business Services | Industrial Equipment |

Morningstar Stock Type | Cyclical | Cyclical |

Dividend increase Streak | 41 years | 59 years |

Yield | 2.4% | 3.5% (46% more) |

Most Recent Increase | 8.4% | 1.1% (poor) |

10-year DGR | 9.9% per year | 8.4% per year (15% less) |

P/E | 28.2 | 17.5 |

Morningstar Star Rating | 2 stars - Overvalued | 4 stars - Undervalued |

Recent Price / Morningstar Fair Price | 1.1 | 0.9 |

Morningstar Moat | Wide | Wide |

S&P Credit Rating | AA | A |

Of course, there is far more to due diligence than this. Please do not interpret anything herein as a recommendation to do anything. Always perform your own due diligence on anything that you invest in.

There other scenarios that could be run. For example, Scenario 1 could have the P/E value return to fair value over time. Scenario 2 could have the P/E value fall or rise over time, or oscillate . Either scenario could make different presumptions about growth rates in earnings or the dividend payout rate. Scenarios could have new (outside) money coming in regularly.

But in my opinion, the scenarios herein support the idea that valuation matters, even over the long haul.

**Disclosure:** I am/we are long EMR.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.