Company X currently has an all$-$equity capital structure. The company has expected annual cash flows of $$7,200$ and a cost of capital of $12\%.$ Assume that all cash flows are perpetual.

Now suppose Company X plans to issue $$20,000$ in debt at a cost of $4\%$ and use the proceeds to buy back and reduce outstanding equity by $$20,000.$ This action leaves the total invested capital unchanged.

What is the new cost of capital $($WACC$)?$ Show your work.