Question

You are tasked with estimating the cost of capital for a firm. The risk-free rate is 3.2%, the expected rate of return on the market is 17.9%. Now, another similar company (similar unlevered cost of capital) has a debt-to-equity ratio of 1 to 5. It has a debt beta near zero and an equity market-beta of 1.1. Your own firm has more debt, for a debt-to-equity ratio of 1 to 1, with a debt beta of 0.5. What is a good estimate for your equity cost of capital?

Answer 1

The relationship between asset (unlevered) beta, debt beta & equity beta is given by the following formula:

Let us first calculate the Asset beta of the other firm as follows:

This unleveraged beta of the other firm should be equal to or firm's unlevered beta

So we can now calculate our firm's equity beta using this as:

Now we can use CAPM to find the equity cost of capital as:

Equity cost of capital
= Rf + Be * (Market return - Rf)
here Rf is the risk free rate = 3.2% and market return = 17.9%
Putting these values in the formula:
Equity Cost of capital		=3.2% + 1.33 * (17.9% -3.2%)
			22.75%

Thus the cost of capital is 22.75%