Mastering financial mathematics in Microsoft Excel: a practical guide for business calculations, 2nd Edition

in Microsoft® Excel

A practical guide for business calculations Alastair Day has worked in the finance industry for more than 25 years in treasury and marketing functions and was formerly a director of a vendor leasing company specializing in the IT and technology industries. After sale to a public company he established Systematic Finance as a consultancy specializing in: • Financial modelling – review, design, build and audit • Training in financial modelling, corporate finance, leasing and credit analysis on an in-house and public basis throughout Europe, Middle East, Africa, Asia and America • Finance and operating lease structuring as a consultant and lessor Alastair is author of two other modelling books published by FT Prentice Hall: Mastering Financial Modelling and Mastering Risk Modelling both of which are in their second editions, as well as other books and publications on financial analysis and leasing.

MASTERING FINANCIAL mathematics

in Microsoft Excel ®

second edition

A practical guide for business calculations Mastering Financial Mathematics in Microsoft® Excel provides a comprehensive set of tools, methods and formulas which apply Excel to solving mathematical problems. This practical guide: • Explains basic calculations for mathematical finance • Shows how to use formulas using straightforward Excel templates • Provides a CD of basic templates This fully revised and updated guide is an essential companion for anyone involved in finance, from company accountants, through to analysts, treasury managers and business students. Explaining basic calculations and using examples and exercises, the book covers: • Cash flows • Bonds calculations and bonds risks • Amortization and depreciation • Forward interest rates and futures • Foreign exchange • Valuation • Leasing

Alastair has a degree in Economics and German from London University and an MBA from the Open University Business School.

MASTERING FINANCIAL MATHEMATICS

MASTERING FINANCIAL mathematics

A practical guide for business calculations

mastering financial mathematics in Microsoft® Excel

• A  n invaluable explanation of basic calculations and their underlying financial concepts • Includes a companion CD with practical examples, exercises and templates

MASTERING FINANCIAL mathematics

in Microsoft® Excel

A practical guide for business calculations

Mastering Financial Mathematics in Microsoft® Excel is a practical guide to using Excel for financial mathematics. This new edition includes: • Excel 2007 • Addition of a glossary of key terms • Functions list in English and European languages • Continuity check on all formats, layouts and charts • More worked examples • Addition of exercises at the end of each chapter to help build models

second edition

DAY

FINANCE

second edition

Visit our website at

www.pearson-books.com Visit our website at

www.pearson-books.com

CVR_DAY0330_02_SE_CVR.indd 1

Alastair L. Day 31/3/10 10:50:49

Mastering Financial Mathematics in Microsoft® Excel

In an increasingly competitive world, we believe it’s quality of thinking that gives you the edge – an idea that opens new doors, a technique that solves a problem, or an insight that simply makes sense of it all. The more you know, the smarter and faster you can go. That’s why we work with the best minds in business and finance to bring cutting-edge thinking and best learning practice to a global market. Under a range of leading imprints, including Financial Times Prentice Hall, we create world-class print publications and electronic products bringing our readers knowledge, skills and understanding, which can be applied whether studying or at work. To find out more about Pearson Education publications, or tell us about the books you’d like to find, you can visit us at www.pearsoned.co.uk

Mastering Financial Mathematics in Microsoft® Excel A practical guide for business calculations Second Edition

ALASTAIR L. DAY

PEARSON EDUCATION LIMITED Edinburgh Gate Harlow CM20 2JE Tel: +44 (0)1279 623623 Fax: +44 (0)1279 431059 Website: www.pearsoned.co.uk First published in Great Britain in 2005 Second edition 2010 © Pearson Education Limited 2005, 2010 The right of Alastair Day to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. ISBN 978-0-273-73033-0 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Day, Alastair L. Mastering financial mathematics in Microsoft Excel : a practical guide for business calculations / Alastair Day. -- 2nd ed. p. cm. -- (Market editions) Includes index. ISBN 978-0-273-73033-0 (pbk.) 1. Business mathematics. 2. Microsoft Excel (Computer file) I. Title. HF5691.D39 2010 650.0285'554--dc22 2010005343 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. This book may not be lent, resold, hired out or otherwise disposed of by way of trade in any form of binding or cover other than that in which it is published, without the prior consent of the Publishers. Microsoft product screen shots reprinted with permission from Microsoft Corporation. 10 9 8 7 6 5 4 3 2 1 14 13 12 11 10 Typeset in Garamond 11.5/13.5pt by 30 Printed and bound in Great Britain by Ashford Colour Press Ltd, Gosport, Hants The Publisher’s policy is to use paper manufactured from sustainable forests.

Contents Acknowledgements About the author Conventions Overview Warranty and disclaimer

x xi xii xiii xv

1 Introduction Overview Common Excel errors Systematic design method Auditing Summary

1 3 4 6 10 12

2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary

13 15 19 24 26 27 28 28

3 Cash flows Net present value Internal rate of return XNPV and XIRR XNPV periodic example Modified internal rate of return Exercise Summary

29 31 34 37 38 39 41 41

v

Contents

4 Bonds calculations Description Cash flows Zero coupons Yield Yield to call Price and yield relationship Yield curve pricing Other yield measures Yield measures Exercise Summary

43 45 48 50 51 51 53 53 55 57 59 59

5 Bonds risks Risks Duration Convexity Comparison Exercise Summary

61 63 66 70 75 77 77

6 Floating rate securities Floating rates Characteristics of interest rate securities Yield evaluation Coupon stripping Exercise Summary

79 81 82 84 89 90 91

7 Amortization and depreciation Amortization Full amortization Delayed payments Sum of digits Straight line and declining balance depreciation UK declining balance method Double declining balance depreciation French depreciation Exercise Summary

vi

93 95 97 97 100 101 103 104 105 107 108

Contents

8 Swaps Definitions How swaps save money Advantages of swaps Terminating interest rate swaps Implicit credit risk Worked single currency swap Valuation Cross currency swap Worked example Swaptions Exercise Summary

109 111 114 115 116 117 117 119 120 121 122 124 124

9 Forward interest rates Definitions Example forward rates Hedging principles Forward rate agreement Yield curves Exercise Summary

125 127 127 130 131 134 138 138

10 Futures Futures market Terminology Benefits Clearinghouse operation Bond futures Hedging mechanisms Hedging example one Hedging example two Exercise Summary

139 141 142 143 144 145 145 147 149 152 152

11 Foreign exchange Risk Spot rates Longer dates Equivalence Comparisons and arbitrage Exercise Summary

153 155 157 161 162 164 165 165 vii

Contents

viii

12 Options Description Terminology Underlying asset Call options Put options Example Covered call Insurance using a stock and a long put Pricing models Black Scholes model Call put parity Greeks Binomial models Comparison to Black Scholes Exercise Summary

167 169 170 172 172 176 178 180 182 182 184 187 188 191 194 198 198

13 Real options Real options Black Scholes model Binomial model Exercise Summary

199 201 202 203 205 205

14 Valuation Valuation methods Assets Market methods Multi-period dividend discount models Free cash flow valuation Adjusted present value Economic profit Exercise Summary

207 209 210 211 213 215 224 227 229 230

15 Leasing Economics of leasing Interest rates Classification Amortization Accounting Settlements

231 233 235 236 241 242 243

Contents

Lessor evaluation Lessee evaluation Exercise Summary 16 Basic statistics Methods Descriptive statistics Probability distributions Sampling/Central Limit Theorem Hypothesis testing Correlation and regression LINEST function Exercise Summary

246 250 252 253 255 257 257 270 277 282 293 302 304 304

Appendices 1 Exercise answers, functions list, software installation and licence 2 An introduction to Microsoft® Office 2007 (Office 12)

307 309 345

Index

359

ix

Acknowledgements I would like to thank Angela, Matthew and Frances, for their support and assistance with the completion of this book. In addition, Christopher Cudmore, Martina O’Sullivan and Laura Blake of Pearson Education have provided valuable support and backing for this project.

x

About the author Alastair Day has worked in the finance industry for more than 25 years in treasury and marketing functions and was formerly a director of a vendor leasing company specializing in the IT and technology industries. After rapid growth, the directors sold the enterprise to a public company and he established Systematic Finance as a consultancy specializing in: OO OO

OO

financial modelling – review, design, build and audit; training in financial modelling, corporate finance, leasing and credit analysis on an in-house and public basis throughout Europe, Middle East, Africa and America; finance and operating lease structuring as a consultant and lessor.

Alastair is author of three modelling books published by FT Prentice Hall: Mastering Financial Modelling; Mastering Risk Modelling, and Mastering Financial Mathematics in Excel, apart from other books and publications on financial analysis and leasing. Alastair has a degree in Economics and German from London University and an MBA from the Open University Business School.

xi

Conventions

OO

The main part of the text is set in AGaramond, whereas entries are set in Courier. For example:

Enter the Scenario Name as Base Case OO

Items on the menu bars also shown in Courier. For example:

Select Tools, Goal Seek OO

The names of functions are in Courier capitals. This is the payment function, which requires inputs for the interest rate, number of periods, present value and future value. =PMT(INT,NPER,PV,FV,TYPE)

OO

Cell formulas are also shown in Courier. For example: =IF($C$75=1,IF($B25>C$22,$B25-C$22-C$23,C$23),IF($B25