Suppose a firm’s business operations mirror movements in the economy as a whole

Question

Suppose a firm’s business operations mirror movements in the economy as a whole very closely—that is, the firm’s asset beta is 1. Find the equity beta for this firm for debt–equity ratios of 0, 2.2, 6.8, and 22. (Do not round intermediate calculations and round your final answer to 1 decimal place (e.g., 32.1).)

Suppose a firm’s business operations mirror movements in the economy as a whole very closely—that is, the firm’s asset beta is 1. Find the equity beta for this firm for debt–equity ratios of 0, 2.2, 6.8, and 22. (Do not round intermediate calculations and round your final answer to 1 decimal place (e.g., 32.1).)

Explanation / Answer

We have following formula for Equity Beta:

Equity Beta = Asset beta x (1+ (1-t) x D/E)

Since tax rate is not given, we will assume it to be zer0, so t would be 0, and the equity beta formula will be reduced to:

Equity beta = asset beta x (1+ D/E)

Debt equity ratio =0

Equity beta = 1 x (1+0)

                       = 1

Debt equity ratio =2.2

Equity beta = 1 x (1+2.2)

                       = 3.20

Debt equity ratio =6.8

Equity beta = 1 x (1+6.80)

                       = 7.80

Debt equity ratio =22

Equity beta = 1 x (1+22)

                       = 23

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