Assume that your company is made up of two divisions. Division $1$ comprises $40$ percent of the company while Division $2$ makes up $60$ percent of the company. The levered beta for the company as a whole is equal to $1\mathrm{.}20$ and the company's debt$/$value ratio is $50$ percent $($you may $$sume that appropriate values for Division $1$ and $2$ are also $50$ percent$).$ If the risk$-$free rate is $3\mathrm{.}0$ percent, the market risk premium is $6\mathrm{.}00$ percent, the marginal tax rate is $40$ percent, and the before$-$tax cost of debt is $8\mathrm{.}00$ percent then, as you can calculate, the WACC for the company is $7\mathrm{.}50$ percent.

As you can also calculate, using the Hamada equations, the unlevered beta for the company as a whole is $0\mathrm{.}75.$

Now assume that other "pure" companies equivalent to Division $2$ have an average unlevered beta of $0\mathrm{.}64.$ Using this proxy for Division $2\text{'}$s unlevered beta, you should be able to determine $($back out$)$ the unlevered beta for Division $1,$ re$-$lever both betas, calculate the corresponding cost of equity, and then determine the appropriate WACC for each division. $($For the purposes of levering and un$-$levering betas, you may use the Hamada equations and assume that the beta for debt is equal to zero.$)$ Given this information, determine the appropriate WACC for Division $1.$