Evaluation of Financial Instruments Possessing Non-Conventional Cash Flow
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 certain 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. Other instruments have a non-conventional cash flow and, consequently, the IRR may be meaningless or impossible to determine. We may 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 determinable. If a functional decomposition is applied in which each simple project is shown to have the same IRR value, then that value is the IRR of the non-conventional project. However, where 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 is seen to estimate a non-conventional project for two different participants simultaneously, which leads to problems with the definition of the IRR. In order that the loan's IRR would be a rate of return for the investor, but not an interest rate for the borrower, the sign of the IRR should be replaced with the opposite one.
This paper discusses how to use the Generalized Net Present Value (GNPV) method to calculate a yield of a financial instrument with a non-conventional cash flow. The function GNPV(r, p) depends on two rates: a finance rate and a reinvestment rate, which 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 time with contributions and withdrawals.