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Equity beta and rate of return

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North Pole Fishing Equipment Corporation and South Pole Fishing Equipment Corporation would have identical equity betas of 1.2 if both of them were all-equity financed. The capital structures of the two firms are as follows:

North Pole South Pole
Debt $1,000,000 $1,500,000
Equity $1,500,000 $1,000,000

The expected return on the market portfolio is 12.75 percent, and the risk-free rate is 4.25 percent. Both firms are subject to a corporate tax rate of 35 percent. Assume the debt beta of each of the two firms equals 0.

1. What is the equity beta of each of the two firms?
2. What is the required rate of return on each of the two firm's equity?

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The solution explains how to calculate the equity beta and the required rate of return.

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a. The equity beta of a firm financed entirely by equity is equal to its unlevered beta.

Find each of the firm's equity betas, given an unlevered beta of 1.2.

North Pole

βEquity = [1 + (1-TC)(B/S)]βUnlevered

where βEquity = the equity beta
βUnlevered = the unlevered beta
TC = the corporate tax rate
B = the value of the firm's debt
S = the value of the firm's equity

In this problem:

Unlevered = ...

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