Last week I posted a Stock Analysis on PAYX including a link to a PDF containing a detailed analysis. In this article, I will explore the section titled **Fair Value Data** (located in the top left section of the above linked PDF). This section provides metrics to help you to determine if the investment is trading at a premium, discount or if it is fairly priced. Below is a description of each item in the **Fair Value Data** section from page 2 of the detailed analysis:

Closing Price:

Recent closing price. A Star is added if the closing price is less than the average of "Avg. High Yield Price", "20-Year DCF Price" and "Avg. P/E Price"; or less than the "Graham Number". A Star is deducted if the closing price is 5% greater than the "Mid-2 Fair Value" high price.Avg. High Yield Price:

Price calculated by dividing current dividend per share by the average high dividend yield for each of the last 5-years (dividend per share divided by the year's low share price).20-Year DCF Price:

Price calculated by taking the Net Present Value (NPV) of the next 20 years of dividends and the estimated value of the stock at the end of 20 years. Below are the assumptions used for this company:Discount rate:15.0%EPS growth rate:17.1%Div. growth rate:18.5%Calculated NPV:$68.14Avg. P/E Price:

Price calculated by multiplying the EPS (trailing twelve months) times the minimum of: 1.) 5-year average of high and low P/Es or 2.) Last years high P/E.Graham Number:

Price calculated by taking the square root of 22.5 times the tangible book value per share times EPS (trailing twelve months). Benjamin Graham, Warren Buffett's mentor and the father of value investing, developed rules for the defensivly screening stocks. This formula uses his principles to calculate the "maximum" price one should pay for the stock. He believed - as a rule of thumb - the product of P/E ratio and price-to-book should not be more than 22.5 (P/E ratio of 15 x price-to-book value of 1.5). The 15 P/E was was a result of Graham wanting his portfolio to have a yield equal yield to that of a AA bond (back then around 7.5%). The inverse of this yield is 1 divided by 7.5%. That works out to 13.3; he rounded up to 15.Mid-2 Fair Value:

Range of fair values with the low-end equal to minimun of the four fair value calculations above, and the high-end is equal to the average excluding the highest and lowest fair value calculations. The discount or premium is calculated using the high-end of the range.

The

**Closing Price**is as of the date shown in the

**Fair Value Data**title.

The

**Avg. High Yield Price**is calculated by dividing current dividend per share by the average high dividend yield. For example, say a stock has a 5-year average yield of 2.5% and its current annual dividend is $1.00 per share, then the calculated fair value is $40.00 per share ($1.00 / .025). If the closing price is less than $40.00 then the stock is selling at a discount based on the

**Avg. High Yield Price**.

The value of any investment can be estimated using a discounted cash flow (DCF) model. That is what the

**20-Year DCF Price**is based on. The historical inputs to this model are: annual earnings per share (EPS), annual dividend per share and price earnings (P/E) ratio.

In addition, the following future assumptions are entered into the model: discount rate, EPS growth rate and dividend growth rate. My model defaults to the following values based on historical data. EPS growth rate: the minimun of the historical 5- or 10-year growth rate; dividend growth rate: as described in my earlier post, Dividend Analytical Data. My target discount rate is 15%. The model assumes the stock is sold at the end of 20 years. The assumptions used for any given stock analysis are shown in the

**20-Year DCF Price**section on page 2, along with the calculated net present value (NPV). Needless to say, this is the most complicated fair value calculation of those presented and these two paragraphs can't begin to do it justice.

The

**Avg. P/E Price**price is a fairly straight forward calculation. It is calculated by multiplying the trailing 12-months (TTM) EPS times the stocks P/E. For example, if the TTM EPS for a company was $3.80 and it had a P/E of 12, then the calculated fair value is $45.60 per share ($3.80 x 12). If the closing price is less than $45.60 then the stock is selling at a discount based on the

**Avg. P/E Price**.

The

**Graham Number**is calcculated by taking the square root of 22.5 x tangible book value per share x TTM EPS. For example, if the TTM EPS for a company was $6.80 and it had a tangible book value per share of $12.50, then the calculated fair value is $43.73 per share (square root[$6.80 x 22.5 x 12.50]). If the closing price is less than $43.73 then the stock is selling at a discount based on the

**Graham Number**. Since the

**Graham Number**tends to be the most conservative value, the stock is awarded a fair value Star if it is trading below it.

The

**Mid-2 Fair Value**(shown on pg. 2 of the linked analysis) sets a range of fair values, with the low-end of the range equal to the lowest of the four calculations described above. The ranges high-end is equal to the average of the remaining values after excluding the highest and lowest values. The discount or premium shown throughout the document is calculated using the high-end of the range.

What do you consider when determining the fair value of a stock?

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Anonymous// March 29, 2008 at 10:20 AMI have been reading your blog for the last 2 - 3 months. I am a pretty new investor and the information presented is awesome. Gives an insight on what other investors do and gives me a great starting point for my research. Thanks

Anonymous// March 29, 2008 at 7:07 PMGuppy: Thank you for reading my blog and your kind words!

Best Wishes,

D4L

Anonymous// January 15, 2009 at 11:19 PMHow do you calculate Tangible Book Value, is it just Book value with Goodwill subtracted from total assets?

Anonymous// January 17, 2009 at 12:59 PMAnon: I actually pull Tangible Book Value from a S&P report. It is calculated by taking total assets less all intangibles (including goodwill).

Best Wishes,

D4L