Financial Leverage in Multi-Period Appraisal : Do ROE and APV Move in the Same Direction?

This paper addresses a classical problem in corporate finance concerning the impact of leverage on financial performance measures. A popular leverage formula suggests to increase the leverage to raise the Return on Equity (ROE), if the condition that the rate of Return of Investment (ROI) is higher than the Rate of Debt (ROD) is met. Since financial projects are typically spread over time, we question whether this leverage rule holds also in multi-period appraisals. First, we define the multi-period ROE as the Internal Rate of Return (IRR) of the equity cash flow (ECF) generated by the project investment. Then we state sufficient and necessary conditions for leverage to raise ROE. For levered investments where debt is paid back by the project cash inflow, leverage rule holds in multi-period appraisals. Second, we wonder whether leverage has a favorable impact on the economic value creation, where this latter is measured by the Adjusted Present Value (APV) of the project. The conjecture is false even for single-period projects. We show that the economic value creation crucially depends upon the Opportunity Cost of Equity (OCE). We issue that APV is positive and increasing in leverage if and only if: (1) ROI is higher than OCE; and (2) OCE is higher than ROD. Clearly, if both conditions hold, ROI is higher than ROD as requested for single period appraisals. However, if the double condition flaws down, then leverage destroys APV and debt should be kept at a minimum