Miller & Modigliani

If a company raised more debt finance, the the fact that the cost of debt is lower than the cost of equity is going to reduce the WACC. However because there is then higher gearing and therefore more risk to shareholders, the cost of equity is going to increase, which will increase the WACC.
So….the WACC is likely to change.
M&M proved that if there is no tax, then the lower cost of debt and the higher cost of equity balance off, and the WACC stays constant – in which case it does not matter how a company raises finance because the overall cost stays the same.
However, if there is tax, then the cost of debt gets cheaper still (because interest is tax allowable) and this means that the WACC will fall when more debt is raised. So…..a company should raise as much debt as possible because the WACC will fall.
There are many assumptions in their proof. The important ones are:
They assume debt is irredeemable
They assume a perfect market (no transaction costs etc)
They assume perfect knowledge (that shareholders have perfect knowledge about what the company is planning)
They ignore the possibility of the company going bankrupt (which would make things more risky for everyone)

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