Modigliani & Miller proved that (with tax) the only difference between the total market value of a company with and without gearing will be due to the fact that more gearing means more interest payable, and that the tax relief on the interest will make the total market value higher. (Just as more gearing makes the WACC lower).
Have another look at the chapter in the Course Notes on M&M, because APV comes directly from what M&M proved.