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This course text is part of the learning content for this Edinburgh Business School course. In addition to this printed course text, you should also have access to the course website in this subject, which will provide you with more learning content, the Profiler software and past examination questions and answers. The content of this course text is updated from time to time, and all changes are reflected in the version of the text that appears on the accompanying website at http://coursewebsites.ebsglobal.net/. Most updates are minor, and examination questions will avoid any new or significantly altered material for two years following publication of the relevant material on the website. You can check the version of the course text via the version release number to be found on the front page of the text, and compare this to the version number of the latest PDF version of the text on the website. If you are studying this course as part of a tutored programme, you should contact your Centre for further information on any changes. Full terms and conditions that apply to students on any of the Edinburgh Business School courses are available on the website www.ebsglobal.net, and should have been notified to you either by Edinburgh Business School or by the centre or regional partner through whom you purchased your course. If this is not the case, please contact Edinburgh Business School at the address below: Edinburgh Business School Heriot-Watt University Edinburgh EH14 4AS United Kingdom Tel + 44 (0) 131 451 3090 Fax + 44 (0) 131 451 3002 Email enquiries@ebs.hw.ac.uk Website www.ebsglobal.net The courses are updated on a regular basis to take account of errors, omissions and recent developments. If you'd like to suggest a change to this course, please contact us: comments@ebs.hw.ac.uk.
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Finance Kenneth J Boudreaux is Professor of Economics and Finance at the AB Freeman School of Business, Tulane University, New Orleans, US. Professor Boudreaux is an eminent scholar in finance, known widely for his ability to combine cutting- edge knowledge of the field with understandable explanations to professionals. In addition to being a successful researcher and university professor, he has for the past two decades lectured extensively to executives on topics in finance, in all parts of the world. Professor Boudreaux is the co-author of The Basic Theory of Corporate Finance, a widely used graduate-level text, and has published significant scholarly research on issues in corporate finance, securities markets and corporate restructuring. His research is frequently cited in journals of finance and economics world wide. Professor Boudreaux is an active consultant to the business world, and regularly performs analyses involving financial issues for firms across industries that include shipping, petroleum exploration and production, airlines, consumer products and computers. Included on this list are: Atlantic Container Lines, British Petroleum, Central Gulf Lines, Exxon, Hewlett-Packard, Petroleum Helicopters and Reckitt & Colman. Notwithstanding Professor Boudreaux’s wide experience, all organisations referred to in the worked examples are for illustrative purposes only and are entirely fictitious.
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First Published in Great Britain in 1996. © Kenneth J Boudreaux 2002, 2003 The rights of Kenneth J Boudreaux to be identified as Author of this Work has been asserted in accord- ance with the Copyright, Designs and Patents Act 1988. 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 the prior written permission of the Publishers. 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.
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Contents Module 1 The Basic Ideas, Scope and Tools of Finance 1/1 1.1 Introduction 1/1 1.2 Financial Markets and Participants 1/3 1.3 A Simple Financial Market 1/6 1.4 More Realistic Financial Markets 1/18 1.5 Interest Rates, Interest Rate Futures and Yields 1/30 Learning Summary 1/42 Review Questions 1/43 Case Study 1.1: Bond and Interest Rate Arithmetic 1/48 Case Study 1.2: A Multiple-Period Resource Reallocation 1/49 Module 2 Fundamentals of Company Investment Decisions 2/1 2.1 Introduction 2/1 2.2 Investment Decisions and Shareholder Wealth 2/2 2.3 Investment Decisions in All-Equity Corporations 2/6 2.4 Investment Decisions in Borrowing Corporations 2/10 2.5 Share Values and Price/Earnings Ratios 2/13 Learning Summary 2/17 Review Questions 2/17 Module 3 Earnings, Profit and Cash Flow 3/1 3.1 Introduction 3/1 3.2 Corporate Cash Flows 3/2 3.3 Cash Flows and Profits 3/8 Learning Summary 3/12 Review Questions 3/13 Module 4 Company Investment Decisions Using the Weighted Average Cost of Capital 4/1 4.1 Introduction 4/1 4.2 Free Cash Flow and Profits for Borrowing Corporations 4/2 4.3 Investment Value for Borrowing Corporations 4/6 4.4 Investment NPV and the Weighted Average Cost of Capital 4/8 4.5 The Adjusted Present Value Technique 4/14 4.6 The Choice of NPV Techniques 4/16 Finance Edinburgh Business School v
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Contents Learning Summary 4/18 Review Questions 4/21 Module 5 Estimating Cash Flows for Investment Projects 5/1 5.1 Introduction 5/1 5.2 A Cash-Flow Estimation Example 5/4 5.3 Calculating the NPV, APV and IRR of the Example 5/12 Learning Summary 5/14 Review Questions 5/18 Module 6 Applications of Company Investment Analysis 6/1 6.1 Introduction 6/2 6.2 The Payback Period 6/2 6.3 The Average (Accounting) Return on Investment 6/4 6.4 Internal Rate of Return vs. Net Present Value 6/5 6.5 The Cost–Benefit Ratio and the Profitability Index 6/15 6.6 Summary of Alternatives to the NPV 6/17 6.7 Capital Rationing 6/18 6.8 Investment Interrelatedness 6/22 6.9 Renewable Investments 6/25 6.10 Inflation and Company Investment Decisions 6/28 6.11 Leasing 6/34 6.12 Managing the Investment Process 6/38 Learning Summary 6/41 Review Questions 6/42 Module 7 Risk and Company Investment Decisions 7/1 7.1 Introduction 7/1 7.2 Risk and Individuals 7/3 7.3 The Market Model and Individual Asset Risk 7/10 7.4 Using the Capital Asset Pricing Model in Evaluating Company Investment Decisions 7/17 7.5 Other Considerations in Risk and Company Investments 7/26 Learning Summary 7/29 Review Questions 7/33 Case Study 7.1: NOSE plc 7/36 vi Edinburgh Business School Finance
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Contents Module 8 Company Dividend Policy 8/1 8.1 Introduction 8/1 8.2 Dividend Irrelevancy I 8/2 8.3 Dividends and Market Frictions 8/6 8.4 Dividend Clienteles: Irrelevancy II 8/11 8.5 Other Considerations in Dividend Policy 8/13 Learning Summary 8/16 Review Questions 8/18 Module 9 Company Capital Structure 9/1 9.1 Introduction 9/1 9.2 Capital Structure, Risk and Capital Costs 9/2 9.3 Capital Structure Irrelevance I: M&M 9/11 9.4 Capital Structure Decisions and Taxes 9/18 9.5 Capital Structure and Agency Problems 9/26 9.6 Making the Company Borrowing Decision 9/34 Learning Summary 9/40 Review Questions 9/41 Case Study 9.1: R-D Star Productions plc 9/43 Module 10 Working Capital Management 10/1 10.1 Introduction 10/1 10.2 Risk, Return and Term 10/2 10.3 Management of Short-Term Assets and Financings 10/8 10.4 Cash Budgeting and Short-Term Financial Management 10/21 Learning Summary 10/23 10.5 Appendix to Module 10: Financial and Ratio Analysis 10/24 Review Questions 10/46 Module 11 International Financial Management 11/1 11.1 Introduction 11/1 11.2 The Foreign Exchange Markets 11/3 11.3 International Financial Management 11/10 Learning Summary 11/16 Review Questions 11/18 Finance Edinburgh Business School vii
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Contents Module 12 Options, Agency, Derivatives and Financial Engineering 12/1 12.1 Introduction 12/2 12.2 Options 12/2 12.3 Agency 12/32 12.4 Derivatives 12/36 12.5 Financial Engineering 12/41 Learning Summary 12/43 12.6 Appendix 1 to Module 12: an Alternative Derivation of Binomial Call Option Value 12/44 12.7 Appendix 2 to Module 12: A Numerical Application of Agency Theory 12/47 Review Questions 12/53 Appendix 1 Statistical Tables A1/1 Appendix 2 Examination Formula Sheet A2/1 Appendix 3 Practice Final Examinations A3/1 Practice Final Examination 1 3/2 Practice Final Examination 2 3/14 Examination Answers 3/25 Appendix 4 Answers to Review Questions A4/1 Module 1 4/1 Module 2 4/17 Module 3 4/19 Module 4 4/20 Module 5 4/22 Module 6 4/26 Module 7 4/29 Module 8 4/33 Module 9 4/35 Module 10 4/44 Module 11 4/47 Module 12 4/49 Index I/1 viii Edinburgh Business School Finance
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Module 1 The Basic Ideas, Scope and Tools of Finance Contents 1.1 Introduction.............................................................................................1/1 1.2 Financial Markets and Participants.......................................................1/3 1.3 A Simple Financial Market.....................................................................1/6 1.4 More Realistic Financial Markets ....................................................... 1/18 1.5 Interest Rates, Interest Rate Futures and Yields ............................. 1/30 Learning Summary......................................................................................... 1/42 Review Questions ........................................................................................... 1/43 Case Study 1.1: Bond and Interest Rate Arithmetic .................................. 1/48 Case Study 1.2: A Multiple-Period Resource Reallocation ........................ 1/49 Learning Objectives This module introduces the student to Finance as a subject area. It describes the participants in financial markets, the decisions they must make, and the basic process- es that are common to all such financial decisions. The module discusses the roles of borrowers, lenders, equity, security issuers and purchasers, and the sources of value for each. Because finance is inherently a quantitative and economic subject, this introductory module devotes much effort to instructing the student in the essential quantitative techniques of financial valuation, including discounting, present valuation, determination of rates of return, and some important financial economics relating to interest rates and security valuation. The module introduces some specialised financial concepts such as ‘yield to maturity’ and the ‘term structure’ of interest rates. It includes the first of several perspectives on the important company decision tools ‘net present value’ and ‘internal rate of return’. The module finishes with an illustration of the usefulness of even these basic financial techniques in understanding a market that remains mysterious to many financial practitioners: forward and futures markets for interest rates. In this module the student will learn the essence of the financial environment, along with the basic quantitative tools of financial valuation that are used throughout the course. 1.1 Introduction In this first module of the finance course you will study the basic concepts and techniques of analysis in finance. We shall investigate ideas of market value, of investment decision-making, of interest rates, and of various kinds of financial Finance Edinburgh Business School 1/1
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Module 1 / The Basic Ideas, Scope and Tools of Finance markets. It is always good to have some general appreciation of a subject before its details are studied, and this is particularly true of finance, which is a very large and complex field of study. This module will supply you with that essential understanding, providing you with information on a number of fundamental concepts that can be applied again and again to the solution of real financial problems. Finance is the economics of allocating resources across time. This definition, of course, is not particularly informative, but an example of a financial transaction that is governed by it may help you to understand the definition. Thus, suppose a new audio device, the digital audio tape player, has just come onto the market. Being an audiophile, you must have one. Economic logic says that if you had the resources to purchase it you would, because your satisfaction would increase by exchanging cash for the digital device. But suppose that you had neither the cash nor other assets that could be readily sold for enough cash to purchase the player. Would you be able to buy it? The answer is that you may or may not be able to, depending upon whether you can convince someone to lend you the money. Whether you can is a function both of the tangible assets you have and the expectation of developing more assets in the future from which your creditor can expect to be paid. Because you do not have the tangible financial resources now to buy what you want, by borrowing you can shift some of your future resources back to the present so as to enable you to buy what you desire. You are buying the player with resources that you do not yet have in hand but are expected to get sometime in the future. And from the perspec- tive of the lender, an exactly opposite transaction will take place: the lender gives up some present resources in exchange for those that you are expected to provide in the future as you pay off the loan. This shifting around, or reallocation of re- sources in time, is the essence of finance. This example is useful because it can also help us to understand why finance is an important subject. Think how many transactions have this essence of shifting resources around in time. We must include not only the borrowing and lending of money by individuals, but by governments, corporations and other institutions. And the borrowing and lending of money are not the only ways in which resources are reallocated in time. When a company issues equity capital (in other words, raises money from its owners) it is undertaking a financial transaction similar to your borrowing to get the tape player; that is, it is accepting money now and giving in exchange a promise to return money in the future (in the form of corporate dividends). The owners of the company are engaging in a financial transaction with the company that is very similar to the one that occurs between you and the lender in the financing of your tape player. Think how many purchases and sales of tangible assets are made possible by the ability to shift resources across time. All personal credit purchases, much of corporate asset acquisition, and a great deal of a government’s providing of assets and services would not be possible without underlying financial transactions. Understanding the finance characteristic of these activities is an important part of being educated in business. 1/2 Edinburgh Business School Finance
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Module 1 / The Basic Ideas, Scope and Tools of Finance The above array of transactions that have important financial dimensions is im- pressive in its breadth, but it can be intimidating in the complexity it implies for the study of finance. We shall nowhere deny that finance is a large and complex field, but its study need not be terribly intricate, at least at the outset. In this course our approach will be first to create a very simple model of a financial market wherein participants (the individuals, companies and governments in the market) can engage in rudimentary financial transactions. That model is useful in acquainting ourselves with the basic ideas common to all financial transactions. Once these have been developed, we shall gradually include more and more realism in the model, until we can deal with the characteristics of financial markets and transactions that we see in actual practice. 1.2 Financial Markets and Participants In a developed economy most people participate frequently in financial markets. Individuals borrow from and lend to financial institutions such as banks. Corporations similarly transact with banks, but they also use financial markets through other intermediaries such as investment bankers (companies that help raise money directly from other companies and individuals), and insurance companies (which lend your insurance premiums to other companies). Governments also borrow and lend to individuals, companies and financial institutions. It is useful to have a general picture in our minds of why companies, individuals and governments use financial markets. We already have one example: you can use the financial market to facilitate your purchase of the tape player. That transaction shifts some of your future resources to the present (by borrowing), and increases your satisfaction. Other types of participants often engage in the same type of transaction. Governments regularly shift future resources to the present so as to allow greater present consumption by citizens. They do that by borrowing in the financial markets with the promise to repay the loans with future cash inflows of the type expected by governments (taxes, more borrowing, etc.). One of the most common motivations for participating in financial markets is to shift future re- sources to the present so as to increase present consumption, and thus satisfaction. On the other hand, individuals, governments and companies also sometimes find themselves with more current resources than they wish to consume at present. They can shift present resources to the future by making them available to the financial markets. They can shift these resources by lending them, by buying ordinary (ownership) shares in a company, or by a number of other transactions. In exchange for giving up current resources, they get an expectation of increased future re- sources in the form, for example, of interest and principal payments from the amounts lent, and dividends and capital gains on the ordinary shares purchased. Individuals and institutions engaging in such transactions are happier with less present and more future resources, and that is their motivation for participating in financial markets. The money that they provide to the financial markets, of course, is the same money borrowed by others wishing to increase their present consump- tion by shifting resources from the future to the present. Depending upon a participant’s resources and preferences for consuming them across time, that Finance Edinburgh Business School 1/3
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Module 1 / The Basic Ideas, Scope and Tools of Finance participant may at various times be a lender, a borrower, or both. Such financial transactions are motivated by a desire to increase satisfaction by changing the time allocation of resources. Financial market participants borrow or otherwise raise money not only to alter their patterns of consumption but also to make investments in real assets. In finance, we distinguish between financial investments (such as borrowing, lending or buying ordinary shares), and real asset investments (such as building a new factory or buying a piece of equipment to be used in production). Whereas financial investments serve the purpose of reallocating resources across time, real asset investment can actually create new future resources that did not before exist. Real asset investment is obviously an important activity. Many economists feel that it may be the single most important activity in determining how wealthy people are. Without financial markets, however, participants with ideas for good investments would find it difficult or impossible to get the money necessary to undertake those investments. Financial markets are the bridge between those willing to give up present consumption of resources in order to increase future consumption, and those in need of present resources in order to undertake real asset investment. This is another important function of financial markets. The provision of funds for real asset investment is important, but just as im- portant is the allocative information that financial markets provide to those interested in making real asset investments. Financial markets can help the investor tell whether a proposed real asset investment is worthwhile by comparing the returns from the investment with those available on competing uses of the re- sources. If the financial market did not do that, some other authority, such as the government, would. There often are significant differences between the decisions that would be made by a government and by competitive financial markets. There is one other important service provided by financial markets to partici- pants. We can describe this generally as risk adjustment. We are not yet ready to give a rigorous definition of risk in financial transactions, but your own intuitions about risk will serve as an acceptable definition for now. Financial market partici- pants are risk-averse. That phrase means that their dislike for risk would, for example, cause them to choose the less risky of two otherwise identical investments. This implies not that participants reject risky transactions, but that the riskiness of an opportunity affects the price that they are willing to pay for it. Because financial markets have such wide variety of riskinesses available, participants can combine borrowings, lendings, the buying and selling of shares, and other transactions to shape the riskiness of their position to be whatever makes them most satisfied. Such decisions made by participants also influence the information that financial markets give to potential real asset investors, as above. In sum, financial markets allow participants to reallocate resources across time, to decide correctly about – and make – real asset investments, and shape the riskiness of their holdings. All of these services are inherent in the transactions that partici- pants make in those markets. 1/4 Edinburgh Business School Finance
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Module 1 / The Basic Ideas, Scope and Tools of Finance 1.2.1 Market Interest Rates and Prices When some participants wish to bring future resources to the present by borrowing, and others wish to shift present resources to the future by lending, the possibility of beneficial transactions is obvious (the potential lenders can provide current re- sources to the potential borrowers in exchange for the borrowers’ promises to provide future resources to the lenders, making both groups happier). But they must decide on the amount of future resources to be exchanged for present ones. In other words, the lenders and borrowers must agree how many pounds of future resources it will be necessary to expect in exchange for each pound of current resources provided. The financial market makes that decision for participants by setting the market interest rate. The market interest rate is the rate of exchange between present and future resources. It tells participants how many pounds are expected to be provided in the future for each pound of resources provided now. For example, if the market interest rate is 8 per cent per year, a lender can expect to receive 108 at the end of the year for each 100 lent at the beginning. The 108 comprises the 100 originally lent plus 8 as interest or compensation for lending. The relative demand and supply of resources to be borrowed and lent determines the market interest rate. (The market interest rate is always positive, because lenders have the alternative of simply keeping their money, and will therefore not agree to getting less in the future than they give up now.) There is actually no such thing as the market interest rate. There are many market interest rates, all of which exist at the same time. The reason why there can simulta- neously be many market interest rates is that interest rates can cover different lengths of time in the future, and different riskinesses of transactions. For example, it is entirely possible that the interest rate for borrowing across a two-year period is different from that for borrowing across a one-year period, because of the relative demand and supply of lendable resources over those times. And the interest rate that applies to borrowings by a risky company will be higher than that paid by the government (which controls the presses that can print currency to pay off its loans), because lenders are risk-averse and require greater expected compensation in future resources from risky borrowers. From that perspective, there are even more ‘interest rates’ than we tend to regard as such. Suppose, for example, that you were to purchase ordinary shares from a company with the expectation of getting future dividends in return. We do not describe that transaction as lending money to the company, nor is there a quoted interest rate, but in general economic terms the transaction is very similar to lending. You are giving up present pounds for the expectation of future pounds. Financial markets do not quote an interest rate for your purchase of ordinary shares, but they do quote a price for the shares. And when you receive dividends or cash from selling the shares, you will earn a rate of return that is similar to an interest rate. In other words the market price is telling you how much you must ‘lend’ to the company in order to get the expected future dividends and increases in value. This information is almost the same as quoting a market interest rate for the transaction, as we shall now see. Finance Edinburgh Business School 1/5
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Module 1 / The Basic Ideas, Scope and Tools of Finance 1.3 A Simple Financial Market 1.3.1 Shifting Resources in Time Financial markets are complicated when there are many different kinds of partici- pants, when the transactions that they make are risky, and when those transactions cover several periods of time. Before we finish studying finance we shall deal with all of those things. First, however, we must develop the basic concepts inherent in all financial transactions. We shall do this with the simplest financial model that can accomplish that goal. The first financial market we shall examine therefore has the following characteristics: 1. We assume away all ‘frictions’ such as taxes, costs of transacting (brokerage fees) and costs of finding information. 2. We assume away all risk. Whenever a transaction is agreed upon, all of its terms will be kept by everyone. 3. Time is very simple in this market. There is only ‘now’ and ‘later’, with one period of time between. All financial transactions take place ‘now’ and have their resolution (for example, pay their interest and principal) ‘later’. In this kind of financial market we need not distinguish between types of partici- pants, because individuals, governments and companies would all have the same risk (none), pay the same taxes (none), and last the same time (one period). That is not to say that all participants are exactly the same, however. As a matter of fact they will be different enough to present a surprisingly realistic picture of a quite diverse market. Suppose in this market there is a participant who will receive both £1000 ‘now’ and £1540 ‘later’. (You can regard this as a set of earnings for work that the participant expects to do, a set of inheritance payments from a deceased relative, or anything else that produces the two amounts. Because there are no taxes and receipt of the payments is certain, their source is irrelevant.) The participant could consume (spend) the £1000 immediately, wait until ‘later’, and then also consume the £1540. Actually, if there was no financial market, the participant would have no choice but to consume in that pattern, because he or she could not shift resources (the ex- pected cash flows) around in time. Figure 1.1 shows how that set of cash flows, point E, appears on a graph with CF1, the cash flow expected ‘later’ (we call ‘later’ t1 for ‘time period one’) on the vertical axis and CF0, the ‘now’ (t0) cash flow on the horizontal. 1/6 Edinburgh Business School Finance
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Module 1 / The Basic Ideas, Scope and Tools of Finance CF 1 F £2640 B £1870 E £1540 £1320 A P 0 CF 0 £700£1000£1200 £2400 Figure 1.1 The financial exchange line Suppose that the participant does not particularly like this pattern of consump- tion and prefers to consume somewhat more than £1000 at t0. He can accomplish that by borrowing some money at t0 with the promise to repay it with interest at t1. Suppose further that the balance of potential borrowers and lenders has resulted in a market interest rate of 10 per cent. With such a market interest rate, the participant could, for example, increase his t0 consumption to £1200 by borrowing £200 now and promising to repay that amount plus 10 per cent interest at t1. He would owe £200 × (1 + 10%), or £220 at t1, so at t1 he could consume £1540 minus £220, or £1320. The move from his original pattern (point E) to this new pattern (point A) is shown in Figure 1.1. The financial market also allows participants to shift resources into the future by deferring current consumption. If the participant originally decides that £1000 of present consumption is too much, he could, for example, lend £300 of his t0 money and get in return an increase of £300 × (1.10) = £330 at t1. That transaction is shown as a move from E to B in Figure 1.1. You may have noticed already that if we were to join all of the points we have discussed in Figure 1.1, they would form a straight line (we shall henceforth call this a financial exchange line, and for convenience we shall also use the letter i to stand for the interest rate). Actually, any transaction that a participant with this initial endowment might take by borrowing or lending at the market rate of interest will produce a result that lies on that straight line between the two axes. For Finance Edinburgh Business School 1/7
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Module 1 / The Basic Ideas, Scope and Tools of Finance example, if all cash flows were transferred to t1, there would be £[1540 + (1000 × 1.10)], or £2640 for t1, and nothing for t0 (point F).1 On the other hand, if all cash flows were shifted to t0, the participant would have £1000 plus whatever he could borrow at t0 with a promise to repay £1540 at t1. How much is this? For each £1 we borrow at t0, we must repay £1 × (1 + i) at t1, so we can borrow (using CFt to mean ‘cash flow at time t’) where ܨܥଵ ൌ ܨܥሺ1 ݅ ሻ ܨܥଵ ܨܥ ൌ ሺ1 ݅ ሻ Thus in our example: £1540 ܨܥ ൌ 1.10 ൌ £1400 The participant could borrow £1400 at t0 with the promise to pay £1540 at t1, the £1540 comprising £1400 of principal and £140 of interest. The maximum amount the participant could consume at t0 is thus £2400, consisting of the original £1000 cash flow, plus the £1400 which can be borrowed at t0 with the promise to repay £1540 at t1. This is point P in Figure 1.1, £2400 at t0 and £0 at t1. Believe it or not we have just done a calculation and arrived at a result that is of the greatest importance and underlies many of the ideas of finance. Discovering that £1540 at t1 is worth £1400 at t0 is called finding the present value of the £1540. Present value is defined as the amount of money you must invest or lend at the present time so as to end up with a particular amount of money in the future. Here, you would necessarily invest £1400 at t0 at 10 per cent interest to end up with £1540 at t1, so £1400 is the present (t0) value of £1540 at t1. The person or institution that was willing to lend the participant £1400 must have done just that type of calculation. Finding the present value of a future cash flow is often called discounting the cash flow. In the above example, £1400 is the ‘discounted value of the £1540’, or the ‘present value of the t1 £1540, discounted at 10 per cent per period’. From the calculations above you can see the type of information that the present value gives us about the future cash flow it represents. For example, should the participant’s expectation of receiving t1 cash flow increase to greater than £1540, he could borrow more than £1400 at t0 (and vice versa for a smaller t1 expectation). Or if the t1 cash flow expectation becomes risky, the lender will require a return higher than 10 per cent to compensate for the risk being borne. (The risk here is that when t1 arrives, the full amount of the £1540 expectation does not appear.) If the interest rate 1 The market interest rate is thus really an ‘exchange rate’ between present and future resources. It tells us the price of t1 pounds in terms of t0 pounds. The exchange line in Figure 1.1 and the market interest rate are thus giving us the same basic information. It should not surprise you to hear that the steepness or slope of the exchange line (the ratio of exchanging t0 for t1 pounds) is determined by the market interest rate. The higher is the market interest rate, the more steep is the slope of the exchange line. In plain words, this says imply that the higher is the interest rate, the more pounds you must promise at t1 in order to borrow a pound at t0 – which you doubtless knew already! 1/8 Edinburgh Business School Finance
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Module 1 / The Basic Ideas, Scope and Tools of Finance increases, you can see that the present value, and thus the amount that the participant can borrow against it, declines. So the present value of a future cash flow is the amount that a willing and informed lender would agree to lend, getting in return a claim upon the future cash amount. The amount of the present value will depend upon the expected size and risk of the cash flow, and when it is expected to occur. How much you can borrow by promising to pay an expected future amount is an important interpretation of present value, but by no means is it the only, or even the most important, interpretation. Present value is also an accurate representation of what the financial market does when it sets a price on a financial asset. For example, suppose that our participant does not wish to borrow money, but instead wishes to sell outright the expectation of receiving cash at t1. The participant can do this by issuing a security that endows its owner with the legal right to claim the t1 cash flow. This security could be a simple piece of paper with the agreement written upon it, or could be a very formal contract of the type issued by companies when they borrow money or issue shares. For how much do you think the participant might sell such a security? Everyone thinking of buying will of course examine alternatives to buying this security. (Economists call such alternatives opportunity costs because they represent the ‘costs’ of doing this instead of something else, in the sense of an opportunity forgone.) They will discover that for each t0 £1 used to buy the security, £1.10 at t1 will be returned by other same-risk investments in the financial market (for example, lending at 10 per cent). That being the case, the participant will be able to sell the security for no more than £1400 (the present value of £1540 at t1 discounted at 10 per cent), because potential buyers need only lend £1400 to the financial market at t0 in order to get £1540 at t1, exactly what the security promises. And because of the competitive nature of financial markets, the security will not sell for less than £1400, because if it did it would provide a cash return the same as other alternatives, but at a lower present price. As potential buyers of the security begin bidding against each other, the security’s price must increase or decline to the point where its expected future cash flow costs the same as that future cash flow acquired by any other means. Present value is thus the market value of a security when market interest rates or opportunity rates of return are used as discount rates. This is perhaps the most important application of the notion of present value. This brings us to another important application of the present-value idea. We have seen that the present value of all of our participant’s present and future resources (cash flows) is £2400. This amount also has a special name in finance: it is known as present wealth. Present wealth is a useful concept in that it tells us the total value of a participant’s entire time-specified resources with a single number. It is even more important because it can be used as a benchmark or standard to judge whether someone is going to be better or worse off because of a proposed financial decision. But we shall need to introduce a few more ideas before we can develop that point as completely as it deserves. One thing we can now see readily from Figure 1.1 is that one cannot change present wealth merely by transacting (borrowing and lending at the market rate) in Finance Edinburgh Business School 1/9
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Module 1 / The Basic Ideas, Scope and Tools of Finance the financial market. Though borrowing and lending will move us up and down the financial exchange line, and thereby allow us to choose the time allocation of our present wealth that makes us most happy, such transactions cannot move the line and therefore cannot change our wealth. The reason is easy enough to deduce. In financial markets, by buying and selling securities (or borrowing and lending), the total amount of wealth that is associated with those securities is unchanged. So if one wishes to increase one’s wealth by buying and selling in those markets, one would be forced to find another participant who, doubtless inadvertently, would allow his wealth to be reduced. As we shall see soon, the odds of doing so are low. 1.3.2 Investing If we cannot expect to change our wealth by transacting in financial markets, how can we get richer? The answer is by investing in real assets. This type of financial activity can change our present wealth because it is not necessary to find someone else to give us part of their wealth in order for ours to increase. Investing in real assets such as productive machinery, new production facilities, research, or a new product line to be marketed, because it creates new future cash flows that did not previously exist, can generate new wealth that was not there before. Of course not all real-asset investments are wealth-increasing. Investments are not free; we must give up some resources in order to undertake an investment. If the present value of the amounts we give up is greater than the present value of what we gain from the investment, the investment will decrease our present wealth. Because that will allow us to consume less across time, it is a bad investment. Of course a good investment would produce more wealth than it uses, and would therefore be desirable. Figure 1.2 shows how real-asset investments work in our simple financial market. Suppose that our participant discovers an opportunity to invest £550 at t0 in a real asset that is expected to return £770 at t1. In Figure 1.2 this appears as a move from point E to point I. That investment would result in t1 resources of £2310 and t0 resources of £450. Should this opportunity be accepted or not? The answer is that it depends upon the effect on the participant’s present wealth. 1/10 Edinburgh Business School Finance
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Module 1 / The Basic Ideas, Scope and Tools of Finance CF 1 F' £2640 F £2310 I N £1540 E P P' 0 £450 £1000 £2400 £2550 CF 0 Figure 1.2 Investment and the financial exchange line To see this, consider Figure 1.2 (point I) again. Looking at the cash-flow time pattern that results from the investment, you might be tempted to answer that the participant would be willing to accept the investment if he or she prefers this new pattern to the one without the investment (point E). But that would be the wrong answer, because it ignores the participant’s additional opportunities to borrow and lend at the market interest rate, reallocating the new resources across time. We can see this by creating a new financial exchange line going through point I, the point at which the participant will end up if only the investment is undertaken. All of the points along the line through I are accessible to the participant if he or she both invests in the real asset and either borrows or lends. The important thing to notice about this situation is that the participant must be better off than he or she was without the investment. As long as the participant prefers more capacity to consume, you can see easily that – regardless of location on the original exchange line – the participant can now find a location on the new exchange line that will allow more consumption at both t0 and t1. This is simply because the exchange line has been shifted outwards from the origin by the invest- ment and is parallel to the original line. (It is parallel because the market interest rate, which determines the line’s slope, has not changed.) Finance Edinburgh Business School 1/11
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Module 1 / The Basic Ideas, Scope and Tools of Finance We can calculate the amount of this parallel shift by seeing how far the line’s intercept has moved along the horizontal axis. As before, this means taking the present value of any position on the new line. Since we know point I already, we can use it: ܨܥଵ ܸܲ ൌ ሺ1 ݅ ሻ £2310 ൌ £450 ሺ1.10ሻ ൌ £2550 The outward shift in the exchange line is to £2550 at t0. But this is also the hori- zontal intercept of the new exchange line, which (from what we know about the discounted value of future resources) is our participant’s new present wealth. So we have also discovered that his or her present wealth will increase from its original level of £2400 to £2550 with the investment. Remember that we are trying to connect the investment’s desirability to the par- ticipant’s change in present wealth. The last step in that process is easy: since any outward shift in the exchange line signals a good investment, and since any outward shift is an increase in present wealth, any investment that increases present wealth is a good one. That is simply another way of saying what we said earlier: investments are desirable when they produce more present value than they cost. 1.3.3 Net Present Value Although you may have found it interesting to see how an investment is judged for desirability by calculating its effect on our participant’s present wealth, the technique is somewhat cumbersome. Fortunately, there is a much more direct method of testing the desirability of an investment, which gives the same answers as the present wealth calculation. This approach deals directly with the investment’s cash flows, and does not require that any particular participant’s resources be used in the calculation. In finance this technique is called net present value; it is simply the present value of the difference between an investment’s cash inflows and outflows. Recall that our participant’s investment requires an outlay of £550 at t0, and returns £770 at t1. If we calculate the present value of the t1 cash inflow and subtract the (already present value of the) t0 outflow we get: ܨܥଵ PV inflow െ PV outflow ൌ ܨܥ െ ሺ1 ݅ሻ £770 ൌ െ £550 ሺ1.1ሻ ൌ £700 െ £550 ൌ £150 The difference between the present values of the cash inflows and outflows of the investment is +£150. That number is the net present value of the investment. Net present value, or NPV as it is commonly known, is a very important concept for a number of reasons. First, notice that the NPV of the investment, £150, is exactly equal to the change in the present wealth (£2550 − £2400) of our participant, were he 1/12 Edinburgh Business School Finance
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