mastering financial mathematics in microsoft excel contents

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MASTERINGFINANCIAL

MATHEMATICS

A practical guide forbusiness calculations

in Microsoftreg Excel

ALASTAIR L DAY

second edition

bull An invaluable explanation of basic calculations and

their underlying financial concepts

bull Includes a companion CD with practical examples

exercises and templates



Mastering Financial Mathematicsin Microsoftreg Excel



In an increasingly competitive world we believe itrsquos quality of

thinking that gives you the edge ndash 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 smarterand faster you can go

Thatrsquos why we work with the best minds in business and financeto 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 andelectronic 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 tellus about the books yoursquod like to find you can visit us at

wwwpearsonedcouk



Mastering FinancialMathematics in

Microsoftreg Excel

A practical guide for business calculations

Second Edition

ALASTAIR L DAY



PEARSON EDUCATION LIMITED

Edinburgh GateHarlow CM20 2JETel +44 (0)1279 623623Fax +44 (0)1279 431059

Website wwwpearsonedcouk

First published in Great Britain in 2005Second edition 2010

copy Pearson Education Limited 2005 2010

The right of Alastair Day to be identified as author of this work has been assertedby him in accordance with the Copyright Designs and Patents Act 1988

ISBN 978-0-273-73033-0

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication DataDay Alastair L Mastering financial mathematics in Microsoft Excel a practical guide forbusiness 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 HF5691D39 2010

6500285554--dc22 2010005343

All rights reserved No part of this publication may be reproduced storedin a retrieval system or transmitted in any form or by any means electronicmechanical photocopying recording or otherwise without either the priorwritten permission of the publisher or a licence permitting restricted copyingin the United Kingdom issued by the Copyright Licensing Agency LtdSaffron House 6ndash10 Kirby Street London EC1N 8TS This book may not belent resold hired out or otherwise disposed of by way of trade in any form ofbinding or cover other than that in which it is published without the priorconsent of the Publishers

Microsoft product screen shots reprinted with permission from MicrosoftCorporation

10 9 8 7 6 5 4 3 2 114 13 12 11 10

Typeset in Garamond 115135pt by 30Printed and bound in Great Britain by Ashford Colour Press Ltd Gosport Hants

The Publisherrsquos policy is to use paper manufactured from sustainable forests



v

Contents

Acknowledgements x

About the author xi

Conventions xii

Overview xiii

Warranty and disclaimer xv

1 Introduction 1

Overview 3 Common Excel errors 4 Systematic design method 6 Auditing 10 Summary 12

2 Basic financial arithmetic 13

Simple interest 15 Compound interest 19 Nominal and effective rates 24 Continuous discounting 26 Conversions and comparisons 27 Exercise 28 Summary 28

3 Cash flows 29

Net present value 31 Internal rate of return 34 XNPV and XIRR 37 XNPV periodic example 38 Modified internal rate of return 39 Exercise 41 Summary 41



vi

4 Bonds calculations 43

Description 45 Cash flows 48 Zero coupons 50

Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59

5 Bonds risks61

Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77

6 Floating rate securities 79

Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91

7 Amortization and depreciation 93

Amortization 95

Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108

Contents



vii

8 Swaps 109

Definitions 111 How swaps save money 114 Advantages of swaps 115

Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124

9 Forward interest rates 125

Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138

10 Futures 139

Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147

Hedging example two 149 Exercise 152 Summary 152

11 Foreign exchange 153

Risk 155 Spot rates 157 Longer dates 161 Equivalence 162

Comparisons and arbitrage 164 Exercise 165 Summary 165

Contents



12 Options 167

Description 169 Terminology 170 Underlying asset 172

Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188

Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198

13 Real options 199

Real options 201 Black Scholes model 202 Binomial model 203

Exercise 205 Summary 205

14 Valuation 207

Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215

Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230

15 Leasing 231

Economics of leasing 233 Interest rates 235 Classification 236

Amortization 241 Accounting 242 Settlements 243

viii

Contents



Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253

16 Basic statistics 255

Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302


Appendices 307

1 Exercise answers functions list software installation and licence 309

2 An introduction to Microsoftreg Office 2007 (Office 12) 345

Index 359

ix

Contents



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 OrsquoSullivan and Laura Blake of Pearson Education have

provided valuable support and backing for this project

x



xi

About the author

Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-

tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in

983119 financial modelling ndash review design build and audit

983119 training in financial modelling corporate finance leasing and credit

analysis on an in-house and public basis throughout Europe Middle East

Africa and America

983119 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 LondonUniversity and an MBA from the Open University Business School



xii

Conventions

983119 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

983119 Items on the menu bars also shown in Courier For example

Select Tools Goal Seek

983119 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(INTNPERPVFVTYPE)

983119 Cell formulas are also shown in Courier For example

=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))

983119 Equations are formed with the equation editor and shown in normal

notation For example net present value

(CashFlow) N

NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N

983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this

is used for simplicity to avoid repetition



xiii

Overview

WHO NEEDS THIS BOOK

More than 20 years ago I used a Hewlett Packard 38C to calculate interest

rates and analyse cash flows and then progressed to an HP 41C with a printer

magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program

lease versus purchase or lessor lease evaluation cash flows and structure more

complex lease structures This is before IBM launched the personal compu-

ter in the early 1980s Since that time I have progressed through calculators

such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide

dedicated user screens and allow you to undertake financial mathematics

While calculators are much easier than tables or earlier methods they can

be difficult to use without errors When I run training courses on the basic

financial calculations the main drawback is only too obvious you cannot see

your inputs or check the interim calculations and therefore delegates always

want to see a map of the variables to understand the answer

While I have continued to use financial calculators which have now been

augmented with other programs on mobile phones using Windows Mobile

or a selection of applications on Apple iPhones and have in the past created

programs in Basic the most comprehensive medium for financial mathe-

matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and

Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg

Office 2007 which remains little changed in the core financial functions

through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and

increasingly on their laptops phones or pocket computers the objective

of this book is to explain the basic calculations for mathematical finance

backed up by simple templates for further use and development together

with examples and exercises If you work through each of the chapters in the

book and try the exercises you will improve your Excel skills and obtain a

better grasp of the underlying financial concepts

My other modelling books published by FT Prentice Hall Mastering

Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design

using ideas of best practice coupled with methods of auditing and testing



xiv

This book adheres to systematic spreadsheet best practice and adopts the

same colour scheme method and layout

The key objectives for this book are to

983119 provide explanation of key financial formulas and subject areas

983119 show the use of the formulas using straightforward Excel templates

983119 introduce examples and exercises for extension work

983119 provide a library of basic templates for further development

This book aims to assist two key groups

983119 practitioners who want a manual of financial mathematics from which

they can gain immediate use and payback

983119 business students who need a textbook which is more geared to Excel

solutions than some college manualsThe areas of responsibility where the book should be of interest are

983119 CFOs and finance directors

983119 financial controllers

983119 financial analysts and executives

983119 accountants

983119 corporate finance specialists

983119

treasury managers 983119 risk managers

983119 academics business and MBA students

Therefore people interested in this book range from a company accountant

who wants a reference book to academics and business students who need a

financial mathematics manual in Excel The book has an international bias

and will provide examples which are relevant to the UK and overseas

HOW TO USE THIS BOOK

983119 Install the Excel application templates using the simple SETUP com-

mand The files will install automatically together with a program group

and icons There is a key to the file names on page 343

983119 Work through each of the chapters and the examples

983119 Use the manual spreadsheets and templates as a reference guide for fur-

ther work

983119 Practise develop and improve your efficiency and competence with Excel

Alastair L Day

Email adaysystemcouk or Internet wwwfinancial-modelscom

Overview



xv

Warranty and disclaimer

The financial models used in the book have not been formally audited and

no representation warranty or undertaking (express or implied) is made and

no responsibility is taken or accepted by Systematic Finance and its direc-

tors as to the adequacy accuracy completeness or reasonableness of the

financial models and the company excludes liability thereof

In particular no responsibility is taken or accepted by the company and

all liability is excluded by the company for the accuracy of the computations

comprised therein and the assumptions upon which such computations are

based In addition the reader receives and uses the financial models entirely

at his own risk and no responsibility is taken or accepted by the Company

and accordingly all liability is excluded by the company for any losses which

may result from the use of the financial models whether as a direct or indi-

rect consequence of a computer virus or otherwise

Microsoft Microsoft Excel Windows and Windows XP are either re-

gistered trademarks or trademarks of Microsoft Corporation in the United

States andor other countries Screen shots reprinted by permission from

Microsoft Corporation



1



Mastering Financial Mathematicsin Microsoftreg Excel







global market





wwwpearsonedcouk




Microsoftreg Excel


Second Edition

ALASTAIR L DAY









ISBN 978-0-273-73033-0



6500285554--dc22 2010005343



10 9 8 7 6 5 4 3 2 114 13 12 11 10





v

Contents

Acknowledgements x

About the author xi

Conventions xii

Overview xiii


1 Introduction 1




3 Cash flows 29




vi




5 Bonds risks61





Amortization 95


Contents



vii

8 Swaps 109





10 Futures 139






Contents



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1







global market





wwwpearsonedcouk




Microsoftreg Excel


Second Edition

ALASTAIR L DAY









ISBN 978-0-273-73033-0



6500285554--dc22 2010005343



10 9 8 7 6 5 4 3 2 114 13 12 11 10





v

Contents

Acknowledgements x

About the author xi

Conventions xii

Overview xiii


1 Introduction 1




3 Cash flows 29




vi




5 Bonds risks61





Amortization 95


Contents



vii

8 Swaps 109





10 Futures 139






Contents



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1




Microsoftreg Excel


Second Edition

ALASTAIR L DAY









ISBN 978-0-273-73033-0



6500285554--dc22 2010005343



10 9 8 7 6 5 4 3 2 114 13 12 11 10





v

Contents

Acknowledgements x

About the author xi

Conventions xii

Overview xiii


1 Introduction 1




3 Cash flows 29




vi




5 Bonds risks61





Amortization 95


Contents



vii

8 Swaps 109





10 Futures 139






Contents



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1









ISBN 978-0-273-73033-0



6500285554--dc22 2010005343



10 9 8 7 6 5 4 3 2 114 13 12 11 10





v

Contents

Acknowledgements x

About the author xi

Conventions xii

Overview xiii


1 Introduction 1




3 Cash flows 29




vi




5 Bonds risks61





Amortization 95


Contents



vii

8 Swaps 109





10 Futures 139






Contents



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



v

Contents

Acknowledgements x

About the author xi

Conventions xii

Overview xiii


1 Introduction 1




3 Cash flows 29




vi




5 Bonds risks61





Amortization 95


Contents



vii

8 Swaps 109





10 Futures 139






Contents



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



vi




5 Bonds risks61





Amortization 95


Contents



vii

8 Swaps 109





10 Futures 139






Contents



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



vii

8 Swaps 109





10 Futures 139






Contents



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



12 Options 167




13 Real options 199



14 Valuation 207



15 Leasing 231



viii

Contents







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1







Appendices 307



Index 359

ix

Contents



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



Acknowledgements





x



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



xi

About the author






Africa and America








xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



xii

Conventions


Courier For example









=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-

C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))



(CashFlow) N






xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



xiii

Overview

WHO NEEDS THIS BOOK

































xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



xiv
















983119 accountants


983119













ther work


Alastair L Day


Overview



xv





















1



xv





















1



1

mastering financial mathematics in microsoft excel contents

Documents

financial analysis

financial modelling

practical examples

updated guide

underlying financial

modelling books

mathematical finance

business students