Financial leverage for multi-period levered investments

Return on Equity (ROE) is one of the most popular performance metric related to equity involved in one-period investment. According to the Modigliani and Miller leverage formula, that applies to one-period levered investments, if the rate of Return on Investment (ROI) is not less than the Rate of Debt (ROD) then external financing increases ROE. The aim of this paper is to extend the Modigliani and Miller leverage formula to multi-period appraisals. First, we define the multi-period ROE as the Equity cash-flow Internal Rate of Return. Then, we achieve sufficient and necessary conditions to guaranteeing that external financing has beneficial effects on ROE. If projects are financed by up-front funds, as it is typical in long-term project financing, the Modigliani and Miller leverage formula can be extended.