Abstract
Investments are often justified and accepted based on the IRR as the main criterion of profitability. However, that criterion is hardly ever used to evaluate some financial instruments (e.g. short sales, options, futures and swaps). This is partially due to the fact that some instruments possess a cash flow describing a borrowing rather than an investment. Others have a non-conventional cash flow and, consequently, the IRR may be meaningless or impossible to determine. We describe a non-conventional cash flow of a financial instrument as a non-conventional project consisting of a sequence of single-period (simple) projects. Each simple project has only two cash flows with opposite signs therefore the IRR for the simple project is always determined. If there is a decomposition in which each simple project has the same IRR value, then that value is the IRR of the non-conventional project. If a decomposition of the non-conventional project into simple projects with the same IRR is impossible, the non-conventional project’s IRR does not exist. If a simple project is an investment then the IRR is a rate of return for an investor. If a simple project is a loan then the IRR is an interest rate for the borrower, but not for the investor. Therefore the NPV method estimates a non-conventional project for two different participants simultaneously that leads to problems with definition of IRR. In order the loan’s IRR would be a rate of return for the investor, but not an interest rate for the borrower, the sign of IRR should be replaced to opposite one. The paper discusses how to use the Generalized Net Present Value (GNPV) method to calculate a yield of the financial instrument with non-conventional cash flow. The function GNPV(r, p) depends on two rates: finance and reinvestment ones that determine a cost of funding and a rate of return, respectively. The equation GNPV (r, -r) = 0 is investigated in the paper. The solution of that equation is the Generalized Average Rate of Return (GARR). We suggest using the GARR as a new measure of a yield for evaluating financial instruments possessing a non-conventional cash flow and estimating a portfolio’s performance over period with contributions and withdrawals.
Highlights
The concept of “return” is a basic theme in finance theory and finance textbooks [Alexander et al, 2001; Brealey et al, 2011; Markowits, 1952]
The NPV function depends on a single argument; it is, critical, even in the case of conventional projects, to determine whether the internal rate of return (IRR) is a rate of return on investment or an interest rate of borrowing? The Generalized Net Present Value (GNPV) method unequivocally uses two different rates for financing and reinvestment
The IRR is a rate of return of an investment project only with conventional cash flows
Summary
The concept of “return” is a basic theme in finance theory and finance textbooks [Alexander et al, 2001; Brealey et al, 2011; Markowits, 1952]. The NPV function depends on a single argument; it is, critical, even in the case of conventional projects, to determine whether the IRR is a rate of return on investment or an interest rate of borrowing? The difference between Bos and Walker’s approach and the NPV method is that they estimate a loan project for an investor but not a borrower They considered a portfolio with withdrawals and contributions over a single period. The equation GNPV(r, -r) = 0 has at most one real root according to the Theorem In this case, the root r is the GARR, i.e. it is a constant rate of return for all one-period investments and borrowings estimated for an investor. The GARR could be the rate of return of the whole non-conventional project estimated for an investor
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
