Alpha Values

Your question has nothing to do with alpha values!

Everyone has always agreed that more gearing in a company makes things more risky for shareholders and therefore shareholders will require a higher return (and thus a higher cost of equity).

Modigliani and Miller studied this, and on the assumption of perfect knowledge etc. etc. they produced a formula that gave the shareholders required rate of return (and therefore cost of equity) for any level of gearing. Higher gearing results in a higher cost of equity.

In a perfect world, the cost of debt will remain constant (because in theory debt is risk free) except at very high levels of gearing. Also, the cost of debt will be lower than cost of equity because it has less risk that equity and therefore investors require a lower return.

Without tax, M&M discovered that as more gearing was introduced into the company, the net effect on the WACC of a higher cost of equity, but a larger proportion of cheap debt. results in the WACC staying constant.

However, when tax is introduced it make the cost of debt lower (because of tax relied on the interest) and therefore with higher levels of gearing the WACC will fall.