Moore, Ellrich & Neal P.A

In constructing the cost of equity capital, Duff & Phelps currently recommends that investors/valuation analysts use a 5.5% equity risk premium and a 4% normalized risk-free rate (i.e. a total cost of equity capital of 9.5%). The normalized risk free rate, which is based upon a long-term average rate, is used in place of the spot yield during those months in which Duff & Phelps believes the risk-free rate is artificially low (however that is determined). In my opinion, while the Duff & Phelps methodology develops an appropriate base cost of capital that is consistent with other metrics that I commonly rely upon, the concept of “normalizing” the risk free rate is problematic for two reasons. First, normalizing the risk free rate creates an “artificial” rate of return that is not available for investors to actually purchase. Second, normalizing the risk-free rate distorts the composition of investor’s future expectations of returns relative to other models. These issues are further discussed below:

Normalizing Risk-Free Rate – An Artificial Return

When we construct the cost of equity capital, we must remember that what we are constructing is an opportunity cost; that is, the cost of equity capital represents the minimum required rate of return that investors require given competing alternatives in the marketplace. One of those competing alternatives is the risk-free rate of interest, which theoretically compensates for inflation plus a real return for the use of funds over the investment holding period. When Duff & Phelps normalizes this rate to 4% vs. the roughly 2.5% actually available to investors, they create an artificial and unavailable rate of return in the marketplace. This violates an assumption of the cost of capital, which is an opportunity cost of funds. Since investors cannot actually earn 4% in the marketplace, it should not form the basis of the base cost of capital, as 4% is not the true opportunity cost of funds.

Misrepresents the Composition of Returns

The second issue with the Duff & Phelps methodology is that the method misrepresents the composition of total returns. For example, under the Duff & Phelps methodology only 5.5% of the total 9.5% expected return on the market is attributable to equity risk (i.e. the equity risk premium) with the remaining amount attributable to the “normalized” risk free rate of 4% (i.e. inflation and real interest). However, other forward looking models (such as Damadoran’s ERP calculator or my supply-side estimate), which are based upon actual rates available in the marketplace, indicate that approximately 7-7.5% of the total 9-10% rate of return on the market is attributable to equity risk, with the remaining attributable to the risk free rate. Therefore, the Duff & Phelps model, in my opinion, understates the amount of equity risk that investors are actually pricing in the market.

This has important implications when estimating the cost of equity using the capital asset pricing model. For example, using Damodarans forward looking calculator (reformulated to the 20 year treasury) we discover that the total expected return on the S&P 500 is approximately 9.91%, composed 7.34% of equity risk and 2.57% of risk free rate (as of December 31, 2011). Duff & Phelps predicts a 9.5% total return on the market, composed of 5.5% equity risk and 4% of normalized risk-free rate. Therefore, if a company had a beta of 2.0x, one would compute a cost of equity capital using the capital asset pricing model as follows:

Damodaran = 2.57% + 7.34%*2 = 17.25%

Duff & Phelps = 4% + 5.5%*2 = 15.00%

As one can see, even though the total expected market return on both methods is comparable (i.e. 9.97% vs 9.50%), the cost of capital using the implied ERP from Damodaran is 2.25% higher than the cost of capital obtained using the Duff & Phelps “normalized” ERP/risk-free rate estimate. This differential is entirely related to the composition of returns assumed by the models. Again, the Duff & Phelps model presumes that investors require a much smaller fraction of the total expected return to compensate for equity risk, while other forward looking models indicate that a much larger fraction of the total return is attributable to equity risk.

In my opinion, the forward looking models provide a better indication of the true compensation demanded by market participants for bearing the risk of equities. Furthermore, these models are more consistent with the definition of “fair market value’ because they utilize the actual spot yield on treasuries as of the valuation date, as opposed to an artificial and unavailable risk-free rate of interest (as used in the Duff & Phelps model).

- Joshua B. Angell, Valuation Analyst at Moore, Ellrich & Neal, P.A.