arXiv subjects

Mikhail V. Sokolov

Publications and source records attributed to Mikhail V. Sokolov.

3 recordsLinked to original sources

arXiv2026

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.

econ.GN↗

arXiv2026

Defining the payback period for nonconventional cash flows: an axiomatic approach

The payback period is unambiguously defined for conventional investment projects, projects in which a series of cash outflows is followed by a series of cash inflows. Its definition for nonconventional projects is more challenging, since their balances (cumulative cash flow streams) may have multiple break-even points. Academics and practitioners offer a few contradictory recipes to manage this issue, suggesting to use the first break-even point of the balance, the last break-even point of the balance, or the moment in time at which the cumulative sum of net cash inflows first exceeds the total sum of net cash outflows. In this paper, we show that the last break-even point of the project balance is the only definition of the payback period consistent with a set of economically meaningful axioms. An analogous result is established for the discounted payback period.

econ.GN↗

arXiv2024

NPV, IRR, PI, PP, and DPP: a unified view

This paper introduces a class of investment project's profitability metrics that includes the net present value (NPV) criterion (which labels a project as weakly profitable if its NPV is nonnegative), internal rate of return (IRR), profitability index (PI), payback period (PP), and discounted payback period (DPP) as special cases. We develop an axiomatic characterization of this class, as well as of the mentioned conventional metrics within the class. The proposed approach offers several key contributions. First, it provides a unified interpretation of profitability metrics as indicators of a project's financial stability across various economic scenarios. Second, it reveals that, except for the NPV criterion, a profitability metric is inherently undefined for some projects. In particular, this implies that any extension of IRR to the space of all projects does not meet a set of reasonable conditions. A similar conclusion is valid for the other mentioned conventional metrics. For each of these metrics, we offer a characterization of the pairs of comparable projects and identify the largest set of projects to which the metric can be unequivocally extended. Third, our study identifies conditions under which the application of one metric is superior to others, helping to guide decision-makers in selecting the most appropriate metric for specific investment contexts.

econ.GN↗