Estimating the Unlevered Beta The CFO of Sterling Chemical is interested in evaluating the cost of equity capital for his firm. However, Sterling uses very little debt in its capital structure (the firms debt-to-equity capitalization ratio is only 20%), while larger chemical firms use substantially higher amounts of debt. The following table shows the levered equity betas, debt-to-equity ratios, and debt betas for three of the largest chemical firms:

Use the information given above to estimate the unlevered equity betas for each of the companies.

If Sterlings debt-to-equity capitalization ratio is .20 and its debt beta is .30, what is your estimate of the firms levered equity beta?

In addition, could you please explain what formula you used and why? I have found multiple formulas in the book and then an additional one on other chegg solutions and I just don't understand what one to use and why.

Company Name Levered Equity Betas Debt/Equity Capitalization Assumed Debt Betas Eastman Chemical Co. (EMN) 1.79 30.77% 0.30 Celanese Corp. (CE) 1.98 23.55% 0.30 Dow Chemical Company (DOW) 1.71 21.60% 0.30