Abrams Valuation Group, Inc.

Uniquely Applying Original Valuation Theory

I wrote the majority of How to Value Your Business and Increase its Potential in 2002, and it printed in August 2004. By the time it printed, it was already a little bit out of date. The purpose of this section is to provide you numbers that are current as of the printing of the book.

Once every year-usually in April or May-Ibbotson Associates prints its SBBI yearbook, and I perform a regression analysis (a statistical technique) to update the numbers in Table 5.4, which also affect Tables 6.1, 7.1, and 7.2. This is an explanation of the updated valuation tables.

**Table 5.4 Updated to 12/31/03: Discount Rates According to Firm Value**

There are two changes reflected in this table:

1) A new regression equation, which results from updating my analysis for the new SBBI data; and

2) Incorporating new academic evidence that affects adjustments to the table.

Let's start with item (1). The new regression equation for data from 1938-2003, and the new regression equation-which you do not have to understand in order to use this-is equation [1] below:

[1] r = .4218 - [.012425537 × ln(FMV) ], where r is the discount rate, ln is the natural logarithm, and FMV is the fair market value of the company. Cell D48 is the regression constant (i.e., the y-intercept), and D49 is the x-coefficient to the log size variable.

Column A is a list of various firm values. Note that it is missing the $35.4 million amount that appeared in the original Table 5.4 in the book, as it serves no purpose here. Column B, labeled "Historical Returns", shows the result of using the regression equation without further adjustment. For example, the natural logarithm of $10 billion (A5) is 23.02585. Multiplying this by the x-coefficient of -0.012425537 (B48) equals -0.286. Adding this to 0.422 (D48) equals 0.136 (B4).

In column C, we subtract the 2% adjustment (D22). Footnote [2] discusses academic research that there is reason to forecast future rates of return to be somewhat less than historical rates of return. From the body of literature cited, I made my own professional judgment to use the 2% downward adjustment from the Lettau, Ludvigson, and Wachter article. My main reason for this is that they have a compelling macroeconomic explanation behind their adjustment. My secondary reason for selecting the 2% adjustment is that it is intermediate between the Ibbotson & Chen 1% adjustment and the Fama & French 4% adjustment.

Thus, column C is 2% less than column B. Column D is column C rounded off to the nearest percent. Column D is my updated set of numbers that I feel readers should be using.

**Table 6.1 Updated to 12/31/03**

My updated Table 6.1, column B uses the discount rates from Table 5.4, column D.

**Table 7.1 (Updated to 12/31/03): Sample DCF Valuation**

This table, like the one in the book, has the ability to perform the consistency check, i.e., to make sure that the discount rate assumed to begin with and the discount rate implied by the valuation itself, automatically for FMVs between $310,000 and $190 million. It is identical to Table 7.1 in the book, except that this spreadsheet incorporates the updates mentioned above, i.e., incorporating stock market data through 2003 and the 2% downward adjustment. If your FMV is outside of that range, it will be necessary to use Table 7.1 Version 2, a professional version of the DCF spreadsheet, which I will describe further below.

You will need to insert your assumptions in row 6 and in cells B19 and B21. Do not insert your own discount rate in B20. This is a complicated formula, and if you insert your own, it will destroy the automatic feature of the spreadsheet.

Table 7.2 is identical to 7.1, except that it does not have row 6 filled in.

**Table 7.1 Version 2**

This is a professional version of the spreadsheet. You will need to insert your assumptions in row 6 and in cells B19, B20, and B21. The essential difference between this and Table 7.1 is that this spreadsheet does not automatically calculate the right discount rate for you. Instead, you will have to insert your best estimate in B20.

When all of the other assumptions are filled in properly, you will have a tentative present value of cash flows in B17. We now jump to the Discount Rate Calculations in rows 38 and below. Cell B38 is a repeat of B17. B39 is the natural logarithm of B38. B40 is the x-coefficient of -0.0124 mentioned above. In B41, we multiply B39 × B40, which equals -0.1654. We then add the regression constant of 0.4218 (B42, as mentioned earlier in this commentary), to total 25.6% (B43). We subtract the 2% (B44) adjustment for the Lettau, Ludvigson, and Wachter research, which leaves us with a discount rate of 23.6% (B45), which we round to 24% (B46). This result is consistent with our assumption in B20, and we can stop.

If B46 were 25% instead of 24%, then we would insert 25% in B20, and hopefully B46 would also calculate to 25%. I have never seen more than one additional iteration required to achieve consistency in the discount rate assumed and the discount rate implied by the FMV that we calculate. However, if that occurred, you would keep repeating the procedure of inputting the new discount rate calculated in B46 into B20 until you achieve consistency between the two cells. When you do, then the present value in B17 is your marketable minority FMV, and you may decide to make adjustments to the level of value, as discussed in Chapter 8.

The last table is a five-year version of the same.

[Last updated 7/23/04]

Available File Downloads | Size |
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Table 7.1 Version 2: 5 Yr Cash Flow | 104.5 KB |