Utilizing comparable companies, A$,$ B$,$ and C$,$ find the equity company for Company D$,$ which has a ratio of market value debt to market value equity of $0\mathrm{.}6.$

Company A has an equity beta of $1\mathrm{.}0,$ no preferred stock, and a debt$-$to$-$equity ratio of $0\mathrm{.}3.$

Company B has an equity beta of $2\mathrm{.}0,$ no preferred stock, and a debt$-$to$-$equity ratio of $0\mathrm{.}4.$

Company C has an equity beta of $3\mathrm{.}0,$ no preferred stock, and a debt$-$to$-$equity ratio of $0\mathrm{.}5.$

First unlever the equity betas of Companies A$,$ B$,$ and C$,$ then compute the average, and then relever the average but using Company D$$s financial characteristics.

Part $1)$ Use Hamada$$s Equation when unlevering and relevering. The relevant tax rate is $30\%.$

Part $2)$ Assume all companies have a debt beta of $0\mathrm{.}1,$ and use the formulas included below to unlever and relever.

Part $3)$ What is the key assumption used to derive Hamada$$s Equation? $($A$)$ the debt is constant and risk$-$free, $($B$)$ the value of the tax shield has the same beta as equity, or $($C$)$ the debt$-$to$-$equity ratio is constant over time.

Formulas for Part $2)$: