The use and meaning of all solutions (interest rates) to the time value of money equation.

Osborne, Michael James (2010) The use and meaning of all solutions (interest rates) to the time value of money equation. PhD thesis, Middlesex University. [Thesis]

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Abstract

The time value of money (TVM) equation is a key equation in economics and finance. It takes the form of an nth order polynomial having n roots. It is usual to calculate and use only one root (interest rate). The remaining (n-1) roots are
mostly complex or negative, and are usually discarded. In this thesis it is shown that the unorthodox roots (interest rates) should not be ignored because they have utility
and meaning.
New expressions are developed for existing concepts in economics and finance. The concepts include duration in bond mathematics, net present value (NPV) in capital budgeting, the value of a stock of capital in capital theory, and the total charge for credit in loan analysis. The new expressions for these concepts employ all possible interest rates as components.
The new expressions provide solutions to puzzles. In bond mathematics, the new equation for duration delivers what previous formulas for duration fail to provide: an accurate measure of the impact of a change in interest rate on the price of a bond.
In capital budgeting, the new equation for NPV offers a resolution to the debate about the relative merits of NPV and internal rate of return (IRR) as investment criteria. In
economics, a solution is proposed to the reswitching debate in the Cambridge capital controversies. In credit analysis, a new relationship is developed between the total charge for credit and the orthodox measure of the cost of a loan, the annual percentage rate (APR). The result implies that the complicated APR need no longer be the focus of consumer credit legislation; the total charge for credit and its variants suffice.
The new analysis not only employs all interest rates, it also endows them with meaning. The suggested interpretation of a complete cluster of interest rates sheds new light on the meaning of orthodox rates such as IRR and APR.

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