Table Of ContentMultiple Interest Rate Analysis
DOI: 10.1057/9781137372772
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DOI: 10.1057/9781137372772
Multiple Interest Rate
Analysis: Theory and
Applications
Michael J. Osborne
Lecturer in Finance, University of Sussex, UK
DOI: 10.1057/9781137372772
© Michael J. Osborne 2014
Softcover re print of t he hard cover 1st edition 2014 978-1-137-37276-5
All rights reserved. No reproduction, copy or transmission of this
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in accordance with the Copyright, Designs and Patents Act 1988.
First published 2014 by
PALGRAVE MACMILLAN
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ISBN: 978–1–137–37277–2 PDF
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Contents
List of Illustrations vii
Preface ix
Acknowledgments xi
1 Multiple-Interest-Rate Analysis: What It Is
and Why It Is Important 1
2 Motivation 9
3 Four Key Results of Multiple-Interest-Rate
Analysis 12
4 I s APR a Robust Measure of the
Cost of Consumer Credit? 43
5 Multiple-Interest-Rate Analysis Demonstrates
Why the IRR Pitfalls Are Irrelevant and
Provides a Better Reason to Prefer
NPV as an Investment Criterion 61
6 An Accurate Formula Is Derived for
the Impact of a Shift in Yield on
the Price of a Bond 82
7 Multiple-Interest-Rate Analysis Sheds
Light on the Reswitching Phenomenon 92
8 A Summing Up 105
DOI: 10.1057/9781137372772 v
vi Contents
Appendix 1: A Compendium of Observations on
Multiple-Interest-Rate Analysis 109
Appendix 2: Why Now? 119
Appendix 3: On the Calculation of Polynomial Roots 124
References 127
Index 133
DOI: 10.1057/9781137372772
List of Illustrations
Tables
2.1 The dangers of discarding data 11
3.1 Interest rates when {c} = {3, 1, 4, 2} and
i
p = 7.9250 19
3.2 The amortization schedule for the
cash flows in equation (3.5a) 21
3.3 The amortization schedule for the
cash flows {3, 1, 4, 2} when r = 0.1 24
1
3.4 Interest rates when the cash flows are
{c"}and p = 7.9250 29
i
3.5 The amortization schedule for the
cash flows {c*} when m = 0.047619 30
i 1
4.1 Conventional financial statistics for loan A 52
4.2 All APRs and their mark-ups over the cost of
funds for loan A 53
4.3 Conventional financial statistics for loan B 54
4.4 All APRs and their mark-ups over the cost of
funds for loan B 55
5.1 Cash flow illustrating the multiple IRR pitfall 70
5.2 The IRR equation for the oil-pump project 70
5.3 The NPV equation for the oil-pump project 70
5.4 Cash flows having no real-valued IRR 72
5.5 Complex-valued IRRs for the cash flows
in Table 5.4 72
5.6 Cash flows, NPV, and IRR for two mutually
exclusive projects 73
5.7 All five IRRs and costs of capital for the
projects in Table 5.6 73
DOI: 10.1057/9781137372772 vii
viii List of Illustrations
5.8 An investment project with costs of capital from
a non-flat yield curve 75
5.9 Multiple interest rates from the cash flows in
Table 5.8 valued using a non-flat yield curve 76
5.10 Cash flows for a typical public-private partnership 78
7.1 Income streams valued at various interest rates and
‘products-of-interest-rates’ 99
7.2 Wage rates in different technologies valued at
various interest rates and ‘products-of-interest-rates’ 102
A3.1 Time to calculate the roots of random
polynomials of various degrees 126
A3.2 Equipment employed to calculate the times in Table A3.1 126
Figures
1.1 The roots (1+r) and interest rates (r) of the
j
equation (1+r)3 = 1.6 6
3.1 The four roots and interest rates (r) for equation (3.9a) 20
j
3.2 Macaulay duration of a bond represented in the
complex plane 41
7.1 Fisher’s odd phenomenon: the present values of
two income streams (P and P ) at various orthodox
A B
interest rates demonstrating switching and reswitching 95
7.2 Fisher’s odd phenomenon reinterpreted:
the present values of two income streams
(P and P ) at various ‘products-of-all-interest rates’
A B
demonstrating no switching 98
7.3 The Sraffa-Pasinetti model: wage rates w and w at
a b
various orthodox interest rates demonstrating
switching and reswitching 101
7.4 The Sraffa-Pasinetti model: wage rates w and w at
a b
various ‘products-of-all-interest-rates’ demonstrating
switching but no reswitching 103
A1.1 The roots and interest rates of a par bond in
the complex plane 113
A1.2 The roots and interest rates of a zero coupon bond in the
complex plane 116
DOI: 10.1057/9781137372772
Preface
The time value of money (TVM) is an essential concept in
banking, economics, and finance. It impacts people’s lives
when they negotiate a loan to buy a car or a mortgage to
buy a house, borrow money to set up a business, enter a
pension scheme, or purchase an annuity at retirement.
The concept finds application in the products of whole-
sale finance, some of which made headlines during the
financial crisis of 2007-8. The TVM equation embody-
ing the concept is employed millions of times every day
around the world by financial institutions, corporations,
governments, and finance professionals such as account-
ants and investment analysts. Despite this ubiquity, this
monograph argues that the time value of money equation
has not been fully explored.
Multiple-interest-rate analysis gives new insight into the
TVM equation, solving some of its long-standing puzzles
and improving its existing applications. The first three
chapters introduce multiple-interest-rate analysis. Chapter
1 is a simple summary of the analysis, both what it is and
what it is not. Chapter 2 describes the motivation behind
its development. Chapter 3 is most important because it
introduces multiple-interest-rate analysis by means of
four key results. This chapter is unavoidably mathemati-
cal because it questions the current understanding of the
TVM equation.
Chapters 4 to 7 describe applications of the key results
of multiple-interest-rate analysis to various puzzles and
problems in economics and finance. Chapter 4 concerns
retail finance and it demonstrates that consumer credit
DOI: 10.1057/9781137372772 ix
