How do you find cost of capital when there is constant leverage ratio?

(Conceptual understanding)

If there is a firm that has two divisions, both are levered with a constant debt/value (thus, constant leverage) ratio. And you are trying to find the cost of capital of division A, given that another private outside company (whose company is pure-play with what division A does) has d/e = q, cost of equity = w, market risk premium = e, risk free rate = r, and corporate tax = y.

a) To find cost of capital, do you have to find the leveraged beta, and use that according to CAPM?

OR

Is the cost of capital = r_wacc ?

b) When finding the value of the firm (value of both divisions), do you use the cash flows of each division discounted by r_wacc? Or would the rwacc be different for each division since it would depend on their individual cost of capital for their respective divisions?