Unlevering and Relevering  Beta

It may be recalled that the beta of a portfolio formed by combining two assets is the weighted average of their betas. If we view all the assets of a firm as a portfolio of debt and equation, (the two sides of the balance sheet of the firm), the market value of the firm (V) equals the asset value as well as the sum total of the market values of debt (D) and equity (E). Therefore, the weighted average of debt and equity betas should he equal to the assets beta.

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It is evident from the above equation that in an all-equity or unlevered firm. the value of equity beta is equal to the assets beta.. This is referred to as the unlevered beta. Determination of assets beta from observed securities  termed  of beta involves determination of equity beta. with given assets beta, for the proposed financing structure. using equation 3.31 (similar to. the determination of K, under net operating income (NO)) approach).

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These concepts are relevant in the context of the determination of (i) the required rate of return for a new project/firm, and (ii) the required rate of return on equity shares (cost of equity) with change in the financing structure. When the new project does not entail any change in business and financial risks of firm, the beta of the existing assets of the firm may be used as a proxy for the project beta, Similarly, the required rate of return on the initial public offer (IPO) of a company may be determined based on the observed betas of a comparable firm.

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