Consider a simple firm that has the following market$-$value balance sheet:

Next year, there are two possible values for its assets, each equally likely: $$1,180$ and $$970.$ Its debt will be due with

$5\mathrm{.}2\%$ interest. Because all of the cash flows from the assets must go to either the debt or the equity, if you hold a

portfolio of the debt and equity in the same proportions as the firm's capital structure, your portfolio should earn

exactly the expected return on the firm's assets. Show that a portfolio invested $44\%$ in the firm's debt and $56\%$ in its

equity will have the same expected return as the assets of the firm. That is$,$ show that the firm's pre$-$tax WACC is the

same as the expected return on its assets.