Having studied Roger Grabowski’s article cited in a previous post, reread the SBBI book, the Duff & Phelps publications, and other literature, I have some additional suggestions about the Rate of Return Paradox.
Above all, remember that we are trying to ESTIMATE the cost of equity capital for a subject private business. We CANNOT MEASURE it directly or precisely by observation or any other method, because it is forward looking. We are going to apply a discount rate (the cost of equity capital) to future cash flows, which are unknown, and the value of the subject business’s equity is also unknown.
We use HISTORICAL data from the public markets – stock prices, dividends, and computed rates of return – as data on which to form our estimates. (Duff & Phelps and SBBI use the same basic data, information from the Center for Research on Securities Prices or CRSP). This gives us one of the unknowns – stock price – but it comes with two costs.
First, we have the problem of assuming that the future will be like the past. It won’t be, but we hope that, by using very long-term time series (going back to the 1920’s), we capture enough historical trends and volatility to be comfortable. That is arguable, but the famous graph on page 22 of the 2008 SBBI book shows that stocks have historically earned greater long-term returns than other securities. From this we assume that, in the future, this relationship will continue to hold, so this data will be a reasonable proxy, or substitute, for the cost of equity capital that we are trying to estimate.
Second, we know our subject company is not the same as the stock market as a whole in terms of its risk / return characteristics. We thus assume that we can adjust for that with good analysis, which means we break up the long-term stock market return into a number of parts and try to understand how the parts relate to our subject company. The problem is that when we do so, we have to estimate the value of each of the parts. None of those estimates is perfect, each one is a source of potential error, they are all based on the same underlying data (with a great deal of sophisticated statistical processing and adjustments) and it is definitely illogical to assume that the errors will cancel out.
Current build-up methodology breaks the cost of equity capital into parts: the risk-free rate, the equity premium, the industry premium, the size premium, and the company-specific risk premium. Focusing just on the first two, note that the equity risk premium is the total return on stocks minus the risk-free rate. These three time series are as of the same date and based on the same historical time series. As of the end of 2008, the SBBI risk-free rate (20-year Treasurys) was 3.0% and the long-horizon equity risk premium (based on historical data) was 6.5%, As of the date of this post, 20-year Treasurys are yielding (call it) 4%. The stock market is also up for the year. In theory, if we are valuing a business as of today, you would use the 4% risk-free rate AND an equity risk premium updated through today. It would not be correct to use the current 4% risk-free rate and the 12/31/08 6.5% equity risk premium, because they are reflective of different dates and historical periods. Granted, this error might be small, but if interest rates continue to rise this year (and most people think they will), this error will become larger.
Likewise with the industry and size premium components and the company-specific risk premium (particularly if you use the Butler Pinkerton Model) – in theory they should be updated as of the valuation date. But most of us do not have access to this data, so we must be aware of the errors we are introducing by using out-of-date numbers. Remember, we are ESTIMATING the cost of capital. Our estimate will not be perfect. That does not allow us to make conscious estimation errors, in fact, it requires that we acknowledge them and try to compensate as best we can (which unfortunately creates even more error).
Do not get lost in the details of the parsed data. Remember, we are ESTIMATING a future cost of private equity capital from historical rates of return on public equity capital. All estimates are subject to uncertainty. The future will not be like the past, public and private capital markets are fundamentally different, and our dividing the data into parts and estimating them creates additional errors.
In the end, the only way to achieve more comfort with all of this is to go back to basic common sense. One way to do that is to put the CRSP-based data aside, and think of the problem of estimating the cost of equity capital in a different way. I do it along these lines. For a going concern private business, the cost of equity capital should be no lower than the cost of mezzanine money (subordinated debt with equity kickers like warrants), which is normally around 20%. It should be no higher than that for a startup – at least 40%. (The 20% and 40% are arguable.) Both of these numbers are after-tax to the company but pretax to the investor (that is, before income taxes on dividends and capital gains taxes on appreciation). This gives us a reasonable range for the cost of equity capital.
Now, I have been doing this for 25 years and I think I can distinguish whether a business is very low risk (20%), about average (30%), high risk (40%) based on my economic, industry, company and financial analyses. In other words, I can tell between white, gray and black. Maybe I can even distinguish a low-to-average (25%) or average-to-high (35%) risk level. That would be light or dark gray. I do not ever think I can do better than that. This exercise gives me a reasonability test of my build-up of the cost of equity capital. If the exercise and build-up are off by more than 5%, then I review all of my assumptions and analysis until they converge. When they do, I at least have some comfort that I am in the realm of what is reasonable.