Modigliani and Miller developed two different theories regarding the capital structure of the companies. To be more precise, they developed the first theory which was later updated to incorporate the existence of tax. Modigliani and Miller theories are considered as a cornerstone of the corporate finance research.
Their first theory suggested that the decision of funding a company by issuing debt or by issuing capital is irrelevant. In other words, weighted average of cost of capital will not change by altering the ratio of debt and capital. The basic assumptions include the absence of tax and the absence of transaction costs.. They suggested that when companies issue cheaper debt, the cost of equity should increase (due to the fact that debt might be cheaper but it is riskier) keeping the cost of debt at the same levels.
They later updated their theory to include tax. They suggested that due to the tax shield or in other words due to the fact that interest payments are tax deductible, issuing debt is a cheaper options no matter how risky it is. Therefore, the optimal capital structure is to have a fully leveraged company.