### Deriving a Forward-Looking Equity Market Risk Premium

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It is always better to use a forward-looking value that reflects the current market conditions. But the standard methods for calculating equity risk premiums rely on historical estimates—and therefore are backward looking. These approaches produce a type of average that may not reflect expectations of future returns at a particular moment in time (e.g., when volatility is high). This article describes a method of estimating a forward-looking equity risk premium based on prospective market multiples—in particular, the ratio of enterprise value to EBIT (earnings before interest and taxes). The example below is only an illustration, because forecasts are outdated by the time they make it to press. The numbers are based loosely on estimates from around mid-2009.

**USING DIVIDENDS TO COMPUTE THE EQUITY RISK PREMIUM**

The method for calculating the equity risk premium that is described in most textbooks involves the DDM (dividend discount model). This method relies on analysts’ consensus forecasts for S&P 500 company earnings for the next five years, which are used to estimate dividends. After five years, the formula for a growing perpetuity is used to value all subsequent dividends.

The calculation might be as follows: assume that (1) earnings grow at 11% for the next five years; (2) the current prospective P/E (price-earnings) ratio for 2009 is 13.3x; (3) the current payout ratio is 36%, rising linearly over five years to the long-run average of 50%; and (4) dividends will grow at a long-run constant rate of 5.7% from year six onwards. The final assumption is justified by arguing that the company will be reinvesting 50% of its earnings at the cost of equity and by taking into account the long-run estimated inflation rate of 2.5%.

Given the above assumptions, it is possible to calculate the discount rate that produces a present value of future dividends that is equal to the current level of the index. This is the expected average return on equity, from which an estimated equity risk premium can be derived (see Table 1).

Table 1: Comparison of the Dividend Discount and EV/EBIT Method.

Estimates for S&P 500 Dividend Discount Method EV/EBIT Method Cost of equity 8.84% 10.30% Equity risk premium 4.75% 6.07%

There are several assumptions in this calculation—in particular, the long-run dividend growth rate assumption, by which a small change can lead to a large change in valuation. The DDM method is very sensitive to the assumption about long-run growth. This problem of sensitivity can also affect the WACC (weighted average cost of capital) equity valuation method as the same formula is used to value the cash flows in the terminal value period. However, an alternative method using EV/EBIT (enterprise value/earnings before interest and taxes) multiples avoids many of the above assumptions (including the long-run growth rate assumption), although it involves others that are less sensitive.

**USING THE EV/EBIT MULTIPLE FOR THE S&P 500 **

The multiples-based method starts with a prospective EV/EBIT multiple (which is assumed to be 9.1x) and then derives a forecast cash flow for 2009, which is inserted into a perpetuity formula. In this simple illustration, only the FCF (free cash flow) for 2009 is used. A more sophisticated calculation would use forecasts for the next five years and then a terminal value calculation (as in the dividend example above).

The problem of estimating the growth rate in the terminal value period can be avoided completely if it is assumed that growth is zero. This corresponds to a steady-state scenario in which the company is simply standing still, maintaining its productive capacity at a constant level.

Of course most companies expand, but this will only add value if the company can earn more on its new investment than its cost of capital. Investing at a return equal to the cost of capital is a zero NPV (net present value) project, so will add no value. This is likely to be true for most large companies. While some companies may have a competitive advantage that leads to above-average returns, this will be for a limited period and certainly not forever. So, the steady-state assumption is realistic—particularly for a group of large companies.

A further assumption needs to be made: for a company to maintain the steady state, it needs to replace its plant, etc. What is needed here is maintenance capex (capital expenditure) as opposed to organic or expansionary capex. It is not correct to assume that maintenance capex is equal to depreciation for the simple reason that depreciation is based on historic costs that will understate replacement costs in an inflationary environment. So, to calculate the replacement cost, an adjustment needs to be made to depreciation to reflect the impact of inflation.

For S&P 500 companies, depreciation is about 15% of EBIT on average. For a 10-year asset life (assuming inflation averaging 2.5% over that period), the additional cost of replacement at current prices would amount to around 3% of current EBIT. This allows the net cash flow to be calculated as EBIT less tax and less the additional cost of replacing equipment not covered by depreciation (i.e., the extra 3% of EBIT). Tax is a complicated computation and a simple rate of 38% has been applied here—but more sophistication can be introduced.

So the current enterprise value is equal to the adjusted cash flow divided by WACC. This allows WACC to be computed, and then the cost of equity. To estimate the cost of equity, an assumption about capital structure is needed. A split of 23% debt and 77% equity is assumed, and cost of debt is taken as 7%. This produces an average WACC for S&P 500 companies of 8.97%, which, given the capital structure assumptions, converts into a cost of equity of 10.3%.

To compute the equity risk premium, we need the average beta for the S&P 500 (around 1.1) and the risk-free rate (around 3.62%). The estimates produced by the different methods can now be compared (see Table 1).

A more sophisticated calculation can be attempted. The important point is that the multiples method involves fewer assumptions, particularly since it excludes the highly sensitive growth rate assumption in the terminal value period.

This method can be extended to sectors or individual companies where the steady-state assumption is valid, and if an estimate of the equity risk premium (from the S&P 500) is available, a forward-looking beta can be obtained.

**–Paul H. Richards, CFA, FSIP, is a former investment banker and a visiting lecturer at Cranfield School of Management. He also teaches courses on finance for Euromoney. The views expressed are personal and not those of the institutions with which he is associated.**

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