BetaCorp is a corporation that has two primary business lines personal hygiene and consumer off-the-shelf pharmaceuticals. We are estimating its levered beta for the purpose of determining its cost of equity. The personal hygiene subsidiary is worth USD$\mathrm{ 2}0$ million while the consumer pharma subsidiary is worth USD $30$ million. The firm has a debt$-$to$-$equity ratio of $1.$ Assume that the tax rate for all firms is $30\%.$ The risk$-$free rate is $7\%$ and the market risk premium is $6\%.$ The following information is for firms with comparable systematic risk: Comparable Firms Average Beta Average D$/$E Ratio Personal Hygiene $0\mathrm{.}920\%$ Medical $1\mathrm{.}260\%$ 

a$.$ Estimate the bottom$-$up levered beta for Beta Corp.

b$.$ Estimate cost of equity