Question

# You are estimating a fundamental beta for a company with two divisions. Division A has LTM...

You are estimating a fundamental beta for a company with two divisions. Division A has LTM sales of \$2,611.5 million and division B has LTM sales of \$1,015.5 million. The average cash-adjusted unlevered beta for firms in a sector comparable to division A is 1.24 and the average cash-adjusted unlevered beta for firms in a sector comparable to division B is 0.97. The average enterprise value to sales multiple for firms in a sector comparable to division A is 2.84x and the average enterprise value to sales multiple for firms in a sector comparable to division B is 2.43x. The firm you are evaluating has a 20.6% debt financing (i.e., debt-to-enterprise value = 20.6%) and cash to enterprise value of 1.8%. Assume a 21% tax rate for both this firm and the sector averages. If you weight the division betas based on estimated enterprise value of each division, what is the firm’s fundamental equity beta?

Weighted average beta= 1.24+0.97/2=1.105

Weighted average D/E=20.6% or (.20)

tax bracket = 21% or (.21)

Bu​​=βL​​/1+(1−T)×D​/E

Where D/E is the average debt-to-equity ratio of the comparable companies, T is the tax rate, Bu the unlevered beta, and BL the levered beta.

Bu=1.105​/1+(1−.21)×.20

Bu=1.105​/1+(.79)×.20

Bu=1.105​/1+(.158)

Bu=1.105​/1.158

=.9542

Hence, we get the unlevered beta= .9542

In the final step, we need to re-lever the equity using the target debt-to-equity ratio of the private company, which equals .206.

βL​​=βU​×[1+(1+T)×D​/E]

=0.9542*(1+(1-.21)*0.206

=0.9542*(1+(.79)*0.206

=0.9542*(1+(0.16274)

=0.9542*(1.16274)

=1.1094

Therefore, firm’s fundamental equity beta =1.1094

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