However, the important point is that the increase in the equity beta measured by the risk premium is exactly offset by a lower debt factor as the firm gears up leaving the asset beta unaffected. The premium represents the difference between the all-equity beta and debt beta multiplied by the debt-equity ratio. This equation reveals that the equity beta in a geared company equals the equity beta for an all-share company in the same class of business risk, plus a premium for systemic financial risk. If we now rearrange terms, divide through by VE and solve for bEG, the mathematical relationship between the geared and ungeared equity betas can be expressed as follows: To illustrate the MM relationship between the beta factors of all-equity and geared companies with the same systemic business risk, let us begin with the following equation using our familiar notation in a tax less world. However, because these assumptions also underpin much else in finance (including the CAPM) for the moment we shall accept them. You will recall from your studies that MM's capital theory (like their dividend irrelevancy hypothesis) depends on perfect market assumptions. The asset beta (equity beta) of an unlevered company can be used to evaluate projects in the same risk class without considering their finance.
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