An effective interest rate cap: a clarification

The national legislation of many countries imposes restrictions on lending rates known as interest rate caps (or ceilings). In most cases, the effective (rather than nominal) interest rate is restricted, which includes all commissions and fees associated with a loan. Typically, the generic wording of this restriction is ambiguous in two respects. First, the literature provides several nonequivalent concepts of internal rate of return (IRR). Since the effective interest rate is the IRR of the cash flow stream of a loan, the wording should specify which concept of IRR is used. Second, most definitions of IRR are partial in the sense that there are cash flow streams that have no IRR. Thus, the wording is vague for loans whose cash flow streams have no IRR. This paper aims to clarify these two ambiguities. First, we clarify the concept of IRR. We axiomatize the conventional definition of IRR (as a unique root of the IRR polynomial) and show that any extension to a larger set of cash flows necessarily violates reasonable conditions. Second, given this result, we show how to derive an effective interest rate cap. We prove that there is a unique solution consistent with a set of natural axioms.