Saturday, November 10, 2007

Fair Value Data

See Also: Fair Value for an updated discussion.

Each stock analysis contains a link to a detailed analytical PDF. In this PDF is a section titled Fair Value Data (located in the top left section of the 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. The Closing Price is as of the date shown in the Fair Value Data title. A Star is added if the closing price is less than the "Fair Value Buy 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). 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.

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. Includes the assumptions used for the calculation. 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.

Avg. 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. 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.

Graham Number:
Price calculated by taking the square root of 22.5 times the tangible book value per share times EPS (lower of trailing twelve months or average last 3 years). Benjamin Graham, Warren Buffett's mentor and the father of value investing, developed rules for the defensively 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 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.

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.

Mid-2 Price:
Of the four fair value calculations, "Avg. High Yield Price", "20-Year DCF Price", "Avg. P/E Price" and "Graham Number", the highest and lowest fair values are excluded and the remaining two calculations are averaged to calculate the Mid-2 price.

NPV MMA Price:
Price is price where NPV MMA value equals the NPV MMA target. The basis of NPV MMA value calculation is a hypothetical $1,000 investment in the subject stock and a Money Market Account (MMA) earning a 20 year average rate (I use a 20 year Treasury as a proxy). The value calculated is the net present value (NPV) of the difference between the dividend earnings of this investment and the interest income from the MMA over 20 years. Other assumptions include: 1.) dividends grow at a historically calculated rate, 2.) dividends are reinvested, 3.) share price appreciation is not considered, 4.) interest income is reinvested in the MMA. The NPV MMA target is determined based on the number of consecutive years of dividend increases. The formula is: Target = Base - (Years x Increment) + Minimum where Base=3,000, Increment=100, Minimum=500. Thus 0 years of dividend growth yields a $3,500 target and 30 years of growth yields a $500 target.

Fair Value Buy Price:
Historically, I have conservatively taken the lower of the NPV MMA Price or Mid-2 Price as the stock's fair value. This made sense when the markets were don. However, as the market recovered and companies histories include some very lean times, the pendulum has swung to the other extreme where very few companies were trading below my conservative calculation of fair value (in most cases driven by the Mid-2 value).

I have added to my model the ability to calibrate the Fair Value calculation based on where we are within the market cycle. Below are the various options:

Option: 1 = The lower of the Mid-2 price or the NPV MMA price.
Option: 2 = Lesser of the Mid-2 price or NPV MMA price + lower of 10% increase or 25% of the difference between Mid-2 price and NPV MMA price.
Option: 3 = same as Opt: 2 except + lower of 20% increase or 50% of the difference.
Option: 4 = same as Opt: 2 except + lower of 30% increase or 75% of the difference.
Option: 5 = The higher of the Mid-2 price or the NPV MMA price.
Option: 6 = Weighted: 25% Mid-2 price + 75% NPV MMA price.

The option used is disclosed on the back of the analytical PDF.

Full Disclosure: See a list of all my income holdings here.

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