An effective interest rate cap: a clarification

Many countries impose regulatory restrictions on lending rates known as interest rate caps. In most cases, these restrictions apply to the effective (rather than nominal) interest rate, a measure which incorporates all commissions and fees associated with a loan. Because the effective interest rate is the internal rate of return (IRR) of the loan's cash flow stream, this regulatory rule becomes ambiguous for loans that do not have a conventional IRR. This paper resolves this ambiguity. We begin by clarifying the concept of IRR. We axiomatize the conventional definition of IRR (as a unique root of the IRR polynomial) and demonstrate that any extension to a larger domain necessarily violates a natural axiom. Building on this result, we show that there is a unique extension of the interest rate cap to all loans consistent with a set of economically meaningful axioms. The rule we characterize takes the form of a net present value test. This result is general, and applies to any setting where one wishes to extend an IRR-based threshold rule to arbitrary cash flows. Applications include lending and deposit rates regulation, investment screening, and capital budgeting, where the standard decision rule accepts a project if its IRR exceeds the hurdle rate.