You have been asked to estimate the beta for a large South Korean company, with large holdings in steel and financial services. A regression of stock returns against the local market index yields a beta of 1.10, but the firm is 15% of the index. You have collected the average betas for global companies in each of the sectors, as well as the average debt equity ratios in each sector:
Setor Average Regression Beta Average D/E ratio
Steel 1.18 30%
Financial
Services 1.14 70%
The average tax rate for these industries is 40%.
In the most recent period, the company you are analyzing earned 70% of its operating income from steel and 30% from financial services. The firm also had a debt/equity ratio of 150%, and a tax rate of 30%. Estimate the levered beta for the company.

Levered beta for the company = (Weight of steel business*levered beta of steel business) + (Weight of financial services business*levered beta of financial services business)

Levered beta of steel business = Unlevered beta of steel sector*[1+(1 - firm's tax rate)*(firm's debt/equity ratio)

levered beta of financial services business = Unlevered beta of financial services sector*[1+(1 - firm's tax rate)*(firm's debt/equity ratio)

Unlevered beta of steel sector = Current beta of steel sector/[1+(1 - avg. tax rate of firms in the sector)*(Avg. debt/equity ratio of the sector)

Unlevered beta of steel sector = 1.18/[1+((1-0.4)*0.3)]

Unlevered beta of steel sector = 1.18/[1+(0.6*0.3)]

Unlevered beta of steel sector = 1.18/(1+0.18)

Unlevered beta of steel sector = 1.18/1.18

Unlevered beta of steel sector = 1

Levered beta of steel business = 1*[1+((1-0.3)*1.5)]

Levered beta of steel business = 1*[1+(0.7*1.5)]

Levered beta of steel business = 1*(1+1.05)

Levered beta of steel business = 1*2.05

Levered beta of steel business = 2.05

Unlevered beta of financial services sector = Current beta of financial services sector/[1+(1 - avg. tax rate of firms in the sector)*(Avg. debt/equity ratio of the sector)

Unlevered beta of financial services sector = 1.14/[1+((1-0.4)*0.7)]

Unlevered beta of financial services sector =1.14/[1+(0.6*0.7)]

Unlevered beta of financial services sector = 1.14/(1+0.42)

Unlevered beta of financial services sector = 1.14/1.42

Unlevered beta of financial services sector = 0.80

Levered beta of financial services business = 0.8*[1+((1-0.3)*1.5)] = 0.8*[1+(0.7*1.5)] = 0.8*(1+1.05) = 0.8*2.05 = 1.64

Levered beta for the company = (0.7*2.05) + (0.3*1.64)

Levered beta for the company = 1.44 + 0.49

Levered beta for the company = 1.93

Hence, the levered beta for the company is 1.93.