Since November 2000, shares of Paychex (Nasdaq: PAYX) have declined nearly 50%, from $61 to $31, while earnings growth fell a near-equal 44%, from 36% growth to projected 20% growth for the company's 2002 just started.

If history teaches us anything time and again, it's that share prices, in the intermediate and long-term, rise and fall with earnings creation.

That said, does a 50% price decline now make Paychex's stock worth purchasing? When we looked at its price to free cash flow last week we concluded that the stock looked fairly yet still aggressively priced. Today we'll run a discounted cash flow (DCF) model on Paychex to gain more perspective on the share price.

In the past, we've run DCF models on companies like Pepsi, Pfizer and Johnson & Johnson. Aside from putting prices on the stocks, these columns help lay out how to run the model that we're about to run. (Anyone can do this.)

We've always run our models with a 15% to 15.5% discount rate, because Drip Port's goal is to achieve 15.5% long-term returns. Our past models have told us that Pfizer (NYSE: PFE) was a good value at $32, and that we should be cautious to pay more than $38 for Pepsi (NYSE: PEP). (Although that was before the Quaker Oats (NYSE: OAT) acquisition -- we'll need to run a new model.) (By the way, we slowly began to build a position in Pepsi despite its $44 price, partly because we believed its results could top expectations, and they have.)

The models also told us that we should aggressively buy Johnson & Johnson (NYSE: JNJ) when it falls below $44 without good reason. This meant that we should buy like crazy when it gets chopped to something like $36, as it did in early 2000, when we bought with the fervor of children on the first day of summer.

I've been pleased so far with how our models have guided us on these companies. Paychex is a younger, quickly growing and less predictable company, so we need to be aware that it presents more uncertainties, whatever the following numbers show.

Paychex's price looks good
As you start a discounted cash flow model, first you need to determine your discount rate. The rate you use is usually equal to your desired long-term return. In our case, it's 15.5%. We then determine the company's free cash flow. We saw last week that Paychex had $259.7 million in 2001 free cash flow, up 20%. We subtract from this the $26.4 million that Paychex received in tax benefits from the exercise of stock options. This leaves us $233.3 million in free cash flow the most recent year. We start from there and assume this number can grow 20% annually for now, which Paychex guidance indicates.

You can also estimate a company's long-term rate of growth by using a return on equity (ROE) average and dividend payout ratio. For example, Paychex's return on equity has averaged 38%. Its dividend payout ratio was recently 48.5% of earnings. So, if we calculate 1 minus the dividend payout ratio, multiplied by ROE, we can approximate the company's future rate of growth. Doing so, we get 1 - 0.485 X 38 = 19.57%.

Coincidence? Not usually. This is indeed the rate of growth that we can currently hope for from Paychex. We'll round it up to 20% because it's more likely in my mind that Paychex will top these new growth estimates than fail to achieve them. Now let's start discounting (to present value) the company's future free cash flows, discounting by our 15.5% discount rate, and starting from $233.3 million in last year's free cash flow, plus 20%.

Year  Free Cash Flow   Growth   Discounted Value* 
       (millions)       Rate       (millions)
---   --------------  -------    ---------------
 1       $279.9         20%         $242.3
 2       $335.9          "          $251.8
 3       $403.1          "          $261.6
 4       $483.7          "          $271.8
 5       $580.5          "          $282.4
 6       $685.0         18%         $288.5
 7       $801.4         17%         $292.3
 8       $937.7         17%         $296.0
 9     $1,087.7         16%         $297.3
10     $1,250.9         15%         $296.1
11     $1,438.5          "          $294.7
12     $1,654.3          "          $293.5
13     $1,902.4          "          $292.2
14     $2,187.8          "          $291.0
15     $2,516.0          "          $289.7
Fifteen year value                  $4.24 billion

*at 15.5%

If the company were to stop operating in 15 years, after achieving the growth outlined above, it would create current value of $4.24 billion. But Paychex shouldn't disappear in 2016, so we now need to add a continuing valuation factor. If we assume that Paychex can grow 13% in year 16 (and from there forward), we get another $2.843 billion in year 16 value.

To find the company's continuing value, we divide that year 16 value by the difference between our discount rate and our assumed growth rate (0.155 - 0.13, which equals 0.025). After dividing $2.84 billion by 0.025, we arrive at a monstrous number that we discount at 15.5% from year 16 (so to the 16th power) to reach $11.33 billion in continuing value. We add this continuing value to our 15-year total value above. $11.33 billion plus $4.24 billion = $15.57 billion. Divide that by Paychex's 377 million diluted shares outstanding and we arrive at $41.29 per share.

Thus, we shouldn't pay more than $41.29 per share if we want 15.5% annualized returns and if we believe Paychex will perform close to the expectations above, with a 13% terminal growth rate (high, but not impossible). If we assume a 12% terminal growth rate rather than 13%, we get $8.02 billion in continuing value + $4.24 billion = $12.26 billion / 377 million shares = $32.5 per share. Today's price is about $32 per share. Theoretically, we could buy at this price and hope for 15.5% returns if Paychex grows as outlined above and then 12% terminally.

DCF models are of course not infallible
We assume at least 20% annual growth for the first five years because that was our goal in our high-growth study, and, for now anyway, that looks like the amount of growth Paychex can achieve at least the next few years. Our assumptions above are still clearly aggressive, though not impossible. Many things would need to go in Paychex's favor to achieve these numbers, including interest rates rising and the economy being favorable again for new small businesses.

In conclusion, the stock's 50% decline this year, to about $31, does appear to put it it at an attractive value for long-minded investors who believe the business will continue growing well.

-Jeff Fischer, TMF Jeff on the discussion boards

Jeff Fischer owns the stocks in the Drip Port and others, as shown in his profile, but not Paychex. The Fool has a full disclosure policy.