Bridging the Gap Between ROE and IRR

Internal rate of return (IRR) measures the level annual return over the life of an investment, whereas return on equity (ROE) measures the return over each accounting period. This paper develops the relationships between IRR and ROE by presenting and proving four algebraic theorems involving IRR and ROE. These theorems are developed using generic investment terminology that does not rely on any specific accounting basis. The relationships are then expressed using U.S. statutory and GAAP terminology. The paper demonstrates that IRR is not just a statutory concept and ROE is not just a GAAP concept. Financial projections for a hypothetical insurance product illustrate these relationships.