Consider the following firm with a capital structure of 15% debt, 80% equity and

Question

Consider the following firm with a capital structure of 15% debt, 80% equity and 5% preferred stock. The oustanding debt has a yield-to-maturity of 4%, whearas both regular equity and preferred equity are currently priced at $100. The regular annual dividends are expected to be $5 next year growing at 2% annually. Preferred dividends are $4.75 per year. The firm pays 20% in taxes. Based on this information, what is the overall firm beta of this firm, given a risk free rate of return of 2% and an expected return on the market portfolio equal to 8%?

Explanation / Answer

Solution :- Using the dividend discount model, Required return on the equity is computed as follows :-

Required return on equity = (Expected dividend on equity / Current equity price) + Growth in dividends.

= (5 / 100) + 0.02

= 0.05 + 0.02

= 0.07 i.e., 7 %

Overall beta of firm is calculated using the Capital asset pricing model (CAPM) in finance. Accordingly, The calculation of beta is as follows :-

Required return on equity = Risk free return + Beta * (Return on market portfolio - Risk free return).

7 % = 2 % + Beta * (8 % - 2 %)

7 % = 2 % + Beta * 6 %

7 % - 2 % = Beta * 6 %

Beta = 5 % / 6 %

Beta = 0.8334 (approx).

Conclusion :- Overall beta of firm in the given question = 0.8334 (approx).

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