In assignments involving taxation, appraisers are required to opine a single number – a point estimate – of fair market value. Revenue Ruling 59-60 defines fair market value as “the price at which…” (Italics added). Taxpayers must enter one value number on their returns to calculate their tax liabilities.
In most cases, however, value is uncertain. It could be expressed as a reasonable range (from X to Y), but there is no law, guidance, or agreement on how wide the reasonable range should be. Statistics allow us to estimate the confidence we have in a given range (e.g. “95% of the time the value will be between X and Y”), but the techniques and the associated confidence levels are also uncertain. Moreover, they rest on assumptions and information which are also uncertain, limited, and imperfect.
None of this is news, but it is easy to lose sight of the fundamental uncertainty associated with (fair market) value for many reasons:
It is obvious.
We can often amass large quantities of data to develop and support our findings.
We can use many theoretically correct techniques to do so.
The second and third points are the crux of this post. I have elected to discuss them only with respect to the Income Approach, but you can extend my argument to the Market and Asset Approaches with a little bit of thought. My conclusion is that these data and techniques:
- Do not reduce the uncertainty of the value estimate, and may increase it.
- Can be misleading in that they create an illusion of precision.
- Can be difficult to explain in lay language.
- Create a great deal of additional, unnecessary work and expense for us.
My favorite example is mid-year discounting. Assume a 20% discount rate for five forecast annual cash flows of $1 (no terminal value). Most of us discount each year’s $1 cash flow at multiplicative factors (year 1 at 1.2, year 2 at 1.44, etc.). This assumes the $1 is received at the END of the year. But cash flow really arrives throughout the year. The mid-year convention assumes cash flows are received at the middle of the year (a rough approximation to being received ratably throughout the year). To do this, the first year’s cash flow is discounted at 1.2 to the 0.5th power (=1.09), the second at 1.2 to the 1.5th power, and so forth. If you do the math, the difference in values is 0.65%. In other words, the end of year convention understates cash flow by 0.65%.
Come on, man!
Are you so confident in your cash flow forecast and discount rate that a 0.65% difference means anything?
- Are you going to show exponents, let alone non-integer exponents, in your appraisal report?
- Most businesses I value pay out most of their bonus or dividend distributions at yearend (or later) anyhow, so the mid-year convention may be wrong to start with!
Here are three more examples along this line:
Specifying discount and capitalization rates with decimal points (e.g. 20.06% or 20.1% instead of 20%). You included a company-specific risk premium component that has a range of at least a few whole percentage points. This swamps the 0.06% or 0.1%!
Developing an “expected equity risk premium” from historical data. There was a bubble of discussion about this several years ago, and it is addressed in the Ibbotson book, but the bottom line was that the indicated adjustment was on the order of 1%. My rebuttal is the same: other uncertainties in the buildup swamp this.
In capitalizing benefits, using next year’s as opposed to this year’s benefits (usually multiplying this year’s by 1 plus a growth rate). Particularly now, when growth rates are low and uncertainties are high, this adjustment is built on a foundation of sand. Besides, market multiples are based on TRAILING benefits (sales, earnings, etc.).
My favorite example of a procedure that creates tons of extra work and adds little precision is the development of excessively detailed financial forecasts. Here I am referring to forecasting (for example) every line item component of operating expenses individually rather than aggregating them either into one total or breaking them out into major items and “all other”. If total operating expenses are on the order of $100,000, why would you waste time forecasting $500 items?
Now I am really getting going! Do you build regression models with limited (e.g. 5 years of) historical data to predict financial performance? Just as with the Direct Market Data Method, a sample size of five (years or guidelines) is not sufficient for statistical confidence. Please don’t tell me that you are building a model based on 20 quarters or 60 months of historical data either; now you will have to seasonally adjust each quarter or month. What independent variables are you going to use? How will you predict them? Is it safe to assume the future will be like the past? (Regression analysis is built on that.)
Long-time readers of my blog know that I hate WACC. Why use it (and go through the iterative process) if you can develop explicit annual assumptions about the projected levels of debt, which you can almost always do, and thus project cash flow to equity directly?
Finally, when valuing minority interests, why adjust benefits to control and then apply a lack of control discount? First of all, you should end up in the same place, making this exercise totally circular and a waste of time. Secondly, if you do so, you run into huge problems when the ratio of control to minority benefits is so large (i.e. control benefits $100, minority benefits $20) that enormous lack of control discounts are warranted by case facts but not supported by (public market) data.
My bottom line is simple. In the Income Approach, I spend my time substantiating reasonable and simple forecasts and discount rate buildups. I do not use these theoretically correct but, in practice, quite useless bells and whistles.