An effective interest rate cap: a clarification

TL;DR

This paper clarifies how to consistently extend interest rate caps based on IRR to all loans, resolving ambiguities for non-conventional cash flows using a unique, axiomatic approach.

Contribution

It axiomatizes the IRR concept and characterizes a unique, economically meaningful extension of interest rate caps applicable to any cash flow scenario.

Findings

Established the axiomatic basis for IRR extension.

Proved the uniqueness of the IRR-based extension under natural axioms.

Presented a net present value test as the extension rule.

Abstract

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.