# Unlever/Lever beta

From Qbank:

Degen Company is considering a project in the commercial printing business. Its debt currently has a yield of 12%. Degen has a leverage ratio of 2.3 and a marginal tax rate of 30%. Hodgkins Inc., a publicly traded firm that operates only in the commercial printing business, has a marginal tax rate of 25%, a debt-to-equity ratio of 2.0, and an equity beta of 1.3. The risk-free rate is 3% and the expected return on the market portfolio is 9%. The appropriate WACC to use in evaluating Degen’s project is closest to:

A) 8.6%. B) 8.9%. C) 9.2%.

Hodgkins’ asset beta: We are given Degen’s leverage ratio (assets-to-equity) as equal to 2.3. If we assign the value of 1 to equity (A/E = 2.3/1), then debt (and the debt-to-equity ratio) must be 2.3 − 1 = 1.3.

Equity beta for the project:

βPROJECT = 0.52[1 + (1 − 0.3)(1.3)] = 0.9932

Project cost of equity = 3% + 0.9932(9% − 3%) = 8.96%

Degen’s capital structure weight for debt is 1.3/2.3 = 56.5%, and its weight for equity is 1/2.3 = 43.5%.

The appropriate WACC for the project is therefore: 0.565(12%)(1 − 0.3) + 0.435(8.96%) = 8.64%.

So I got the right answer, but only from having done the question before. I don’t really grasp the whole unlever/lever process. Is it something to do with adjusting Hodgkins equity beta to their overall beta (since are a purely commercial printing business with no other interests), then adjusting this to Degens asset beta, which we can then use to find Degens cost of equity? I guess the question is really whats the difference between asset beta and project beta (equity beta?)…

Unlevering and [re]levering beta accounts for the different capital structures between the 2 firms. So if you worked for a company in industry X and were considering expanding operations into industry Y, you would need to adjust your WACC (since it’s a completely new type of project, and the risk level would be different). In CAPM, RFR and the Mkt premium would be the same but the Beta (risk) for the project would be different. So to account for this you pick a comparable company and use their beta. But you have to account for their different capital structure (debt levels) since it may not be the same as yours, more debt or equity would affect the beta number. I’m pretty sure the comprable company’s beta is equity beta, and then after you unlever that, it becomes project beta. It looks like they didn’t unlever it in that explanation though.