Alternatively, to be consistent with an M & M world, we can assume that the return to unlevered equity is constant and use the value of p in year 2 to calculate the value of the unlevered equity at the end of year 0 and thus, indirectly determine the value of the levered equity at the end of year 0.

Table 2a: Value of levered equity, with e1 = 20% Year 0 1 2 Value of debt 1,100.

3, and from this we can deduce that the value of the levered equity at the end of year 0 is $2,022.

In Table 2b, the value of the levered equity at the end of year 0 is based on valuation in an M & M world with a constant return to unlevered equity.

The different values for the levered equity implies that the debt-equity ratios will be different at the end of year 0.

Although the debt-equity ratio changes, with the assumption of a constant return to unlevered equity, the return to levered equity adjusts to maintain a constant WACC.

If one were to find the single WACC of the FCF with the assumption of constant return to levered equity equal to 20%, we see that the value is 16.

If the return to levered equity is held constant, and the return to unlevered equity is allowed to change, then the correct value is $2,083.

If we violate the assumptions of an M & M world, and use a constant value for the return to levered equity (at the same time, assuming a constant return to unlevered equity), the calculations will overstates the value of the levered equity at the end of year 0 by 3 percent, relative to the correct value under the assumption that the return to unlevered equity is constant.

We will assume that p, the return to unlevered equity is constant, and estimate the magnitude of the error in assuming that the return to levered equity is also constant.

Table 4 shows the relationship between the return to levered equity in year 1 and various parameters, namely, the value of the levered equity at the end of year 0, the percentage of debt at the end of year 0, the debt-equity ratio at the end of year 0 and the WACC for year 1.

3 An analyst, using a constant return to levered equity of 20% for year 1 and year 2 will obtain a value of $2,083.

The following table summarizes the values for the cash flow to the levered equity holders for the different values of the WACC.