## **Section II. INVESTORS AND MARKETS

## ****PART ONE. INVESTMENT DECISION RULES

## Chapter 15. THE FINANCIAL MARKETS

*Now let’s talk finance*

This section will analyse the behaviour of the investor who buys financial instruments that the financial manager is trying to sell. Investors are free to buy a security or not and, if they decide to buy it, they are then free to hold it or resell it in the secondary market.

The financial investor seeks two types of returns: the risk-free interest rate (which we call the time value of money) and a reward for risk-taking. This section looks at these two types of returns in detail but, first, here are some general observations about financial markets.

## Section 15.1 THE ROLE OF CAPITAL MARKETS

The primary role of a financial system is to bring together economic agents with surplus financial resources, such as households, and those with net financial needs, such as companies and governments. This relationship is illustrated below:

To use the terminology of John Gurley and Edward Shaw (1960), the parties can be brought together **directly** or **indirectly**.

In the first case, known as **direct finance**, the parties with excess financial resources directly finance those with financial needs. The financial system serves as a **broker**, matching the supply of funds with the corresponding demand. This is what happens when an individual shareholder subscribes to a listed company’s share issue or when a bank places a corporate bond issue with individual investors.

In the second case, or **indirect finance**, financial intermediaries, such as banks, buy “securities” – i.e. loans – “issued” by companies. The banks in turn collect funds, in the form of demand or savings deposits, or issue their own securities that they place with investors. In this model, the financial system serves as a gatekeeper between suppliers and users of capital and performs the function of **intermediation**.

When you deposit money in a bank, the bank uses your money to make loans to companies. Similarly, when you buy bonds issued by a financial institution, you enable the institution to finance the needs of other industrial and commercial enterprises through loans. Lastly, when you buy an insurance policy, you and other investors pay premiums that the insurance company uses to invest in the bond market, the property market, etc.

This activity is called **intermediation**, and is very different from the role of a mere broker in the direct finance model.

With direct finance, the amounts that pass through the broker’s hands do not appear on its balance sheet, because all the broker does is to put the investor and issuer in direct contact with each other. Only brokerage fees and commissions appear on a brokerage firm’s profit and loss, or **income**, statement.

In intermediation, the situation is very different. The intermediary shows all resources on the liabilities side of its balance sheet, regardless of their nature: from deposits to bonds to shareholders’ equity. Capital serves as the creditors’ ultimate guarantee. On the assets side, the intermediary shows all uses of funds, regardless of their nature: loans, investments, etc. The intermediary earns a return on the funds it employs and pays interest on the resources. These cash flows appear in its income statement in the form of revenues and expenses. The difference, or spread, between the two constitutes the intermediary’s earnings.

The intermediary’s balance sheet and income statement thus function as holding tanks for both parties – those who have surplus capital and those who need it:

Today’s economy is experiencing increasing **disintermediation**, characterised by the following phenomena:

- more companies are obtaining financing directly from capital markets; and
- more companies and individuals are investing directly in capital markets.

When capital markets are underdeveloped, an economy functions primarily on debt financing. Conversely, when capital markets are sufficiently well developed, companies are no longer restricted to debt, and they can then choose to increase their equity financing. Taking a page from the economist John Hicks, it is possible to speak of **bank-based economies** and **market-based economies**.

In a **bank-based economy**, the capital market is underdeveloped and only a small portion of corporate financing needs are met through the issuance of securities. Therefore, bank financing predominates. Companies borrow heavily from banks, whose refinancing needs are mainly covered by the central bank.

The lender’s risk is that the corporate borrower will not generate enough cash flow to service the debt and repay the **principal**, or amount of the loan.

In a **market-based economy**, companies cover most of their financing needs by issuing financial securities (shares, bonds, commercial paper, etc.) directly to investors. A capital market economy is characterised by direct solicitation of investors’ funds. Economic agents with surplus resources invest a large portion of their funds directly in the capital markets by buying companies’ shares, bonds, commercial paper or other short-term negotiable debt. They do this either directly or through mutual funds. Intermediation gives way to the brokerage function, and the business model of financial institutions evolves towards the placement of companies’ securities directly with investors.

In this economic model, bank loans are extended primarily to households in the form of consumer credit, mortgage loans, etc., as well as to small enterprises that do not have access to the capital markets.

The following graphs provide the best illustration of the rising importance of capital markets.

## Section 15.2 PRIMARY, SECONDARY AND DERIVATIVE MARKETS

### 1/ FROM THE PRIMARY MARKET TO THE SECONDARY MARKET

**The new issues market (i.e. creation of securities) is called the primary market.** Subsequent transactions involving these securities take place on the **secondary market**. Both markets, like any market, are defined by two basic elements: the product (the security) and the price (its value).

Thus, shares issued or created when a company is founded can later be floated on a stock exchange, just as long-term bonds may be used by speculators for short-term strategies. The life of a financial security is intimately connected with the fact that it can be bought or sold at any moment.

From the point of view of the company, the distinction between the primary and secondary markets is fundamental. **The primary market is the market for “new” financial products**, from equity issues to bond issues and everything in between. It is the market for newly minted financial securities where the company can raise fresh money.

**Conversely, the secondary market is the market for “used” financial products.** Securities bought and sold on this market have already been created and are now simply changing hands, without any new securities being created and consequently without any new money for the company.

The primary market enables companies, financial institutions, governments and local authorities to obtain financial resources by issuing securities. These securities are then listed and traded on secondary markets. The job of the secondary market is to ensure that securities are properly priced and traded. This is the essence of **liquidity**: facilitating the purchase or sale of a security.

The distinction between primary and secondary markets is conceptual only. The two markets are not separated from each other. A given financial investor can buy either existing shares or new shares issued during a capital increase, for example.

If there is often more emphasis placed on the primary market, it is because the function of the financial markets is, first and foremost, to ensure equilibrium between financing needs and the sources of finance. Secondary markets, where securities can change hands, constitute a kind of financial “innovation”.

### 2/ THE FUNCTION OF THE SECONDARY MARKET

Financial investors do not intend to remain invested in a particular asset indefinitely. Even before they buy a security, they begin thinking about how they will **exit**. As a result, they are constantly evaluating whether they should buy or sell such and such an asset.

Monetising is relatively easy when the security is a short-term one. All the investor has to do is wait until maturity. The need for an exit strategy grows with the maturity of the investment and is greatest for equity investments, whose maturity is unlimited. The only way a shareholder can exit their investment is to sell their shares to someone else.

As an example, the successful business person who floats their company on the stock exchange, thereby selling part of their shares to new shareholders, diversifies their own portfolio, which before flotation was essentially concentrated in one investment.

**Liquidity** refers to the ability to convert an instrument into cash quickly and without loss of value. It affords the opportunity to trade a financial instrument at a “listed” price and in large quantities without disrupting the market. An investment is liquid when an investor can buy or sell it in large quantities without causing a change in its market price.

The secondary market is therefore a **zero-sum game** between investors, because what one investor buys, another investor sells. In principle, the secondary market operates completely independently from the issuer of the securities.

A company that issues a bond today knows that a certain amount of funds will remain available in each future year. This knowledge is based on the bond’s amortisation schedule. During that time, however, the investors holding the bonds will have changed.

Secondary market transactions do not show up in macroeconomic statistics on capital formation, earning them the scorn of some observers who claim that the secondary market does nothing to further economic development, but only bails out the initial investors.

We believe this thinking is misguided and reflects great ignorance about the function of secondary markets in the economy. Remember that a financial investor is constantly comparing the primary and secondary markets. They care little whether a “new” or a “used” security is being bought, so long as they have the same characteristics.

In fact, the quality of a primary market for a security depends greatly on the quality of its secondary market. Think about it: who would want to buy a financial security on the primary market, knowing that it will be difficult to sell it on the secondary market?

The secondary market determines the price at which the company can issue its securities on the primary market, because investors are constantly deciding between existing investments and proposed new investments.

We have seen that it would be a mistake to think that a financial manager takes no interest in the secondary market for the securities issued by the company. On the contrary, it is on the secondary market that the company’s financial “raw material” is priced every day. When the raw material is equities, there is another reason the company cannot afford to turn its back on the secondary market: this is where investors trade the voting rights in the company’s affairs and, by extension, control of the company.

### 3/ DERIVATIVE MARKETS: FUTURES AND OPTIONS

Derivative markets are where securities that derive their value from another asset (share, bond, commodity or even climate index) are traded. There are two main types of derivative products: options (which we will develop in Chapter 23 as they have become a key matter in financial theory and practice) and futures (Chapter 51).

Derivative instruments are tailored especially to the management of financial risk. By using derivatives, the financial manager chooses a price – expressed as an interest rate, an exchange rate or the price of a raw material – that is independent of the company’s financing or investment term. Derivatives are also highly liquid. The financial manager can change their mind at any time at a minimal cost.

Options and futures allow one to take important risks with a reduced initial outlay due to their leverage effect (this is called speculation), or on the contrary to transfer risks to a third party (hedging), and this is what companies normally use them for.

## Section 15.3 THE FUNCTIONS OF A FINANCIAL SYSTEM

The job of a financial system is to efficiently create financial liquidity for those investment projects that promise the highest profitability and that maximise collective utility.

However, unlike other types of markets, a financial system does more than just achieve equilibrium between supply and demand. A financial system allows investors to convert current revenues into future consumption. It also provides current resources for borrowers, at the cost of reduced future spending.

Robert Merton and Zvi Bodie have isolated **six essential functions** of a financial system:

**A financial system provides means of payment to facilitate transactions.**Cheques, debit and credit cards, electronic transfers, bitcoins, etc. are all means of payment that individuals can use to facilitate the acquisition of goods and services. Imagine if everything could only be paid for with bills and coins!**A financial system provides a means of pooling funds for financing large, indivisible projects. A financial system is also a mechanism for subdividing the capital of a company so that investors can diversify their investments.**If factory owners had to rely on just their own savings, they would very soon run out of investible funds. Indeed, without a financial system’s support, Nestlé and British Telecom would not exist. The system enables the entrepreneur to gain access to the savings of millions of individuals, thereby diversifying and expanding their sources of financing. In return, the entrepreneur is expected to achieve a certain level of performance. Returning to our example of a factory, if you were to invest in your neighbour’s steel plant, you might have trouble getting your money back if you should suddenly need it. A financial system enables investors to hold their assets in a much more liquid form: shares, bank accounts, etc.**A financial system distributes financial resources across time and space, as well as between different sectors of the economy.**The financial system allows capital to be allocated in a myriad of ways. For example, young people can borrow to buy a house or people approaching retirement can save to offset future decreases in income. Even a developing nation can obtain resources to finance further development. And when an industrialised country generates more savings than it can absorb, it invests those surpluses through financial systems. In this way, “old economies” use their excess resources to finance “new economies”.**A financial system provides tools for managing risk.**It is particularly risky (and inefficient as we will see later) for an individual to invest all of their funds in a single company because, if the company goes bankrupt, they lose everything. By creating collective savings vehicles, such as mutual funds, brokers and other intermediaries enable individuals to reduce their risk by diversifying their exposure. Similarly, an insurance company pools the risk of millions of people and insures them against risks they would otherwise be unable to assume individually.**A financial system provides price information at very low cost. This facilitates decentralised decision-making.**Asset prices and interest rates constitute information used by individuals in their decisions about how to consume, save or divide their funds among different assets. But research and analysis of the available information on the financial condition of the borrower is time-consuming, costly and typically beyond the scope of the layperson. Yet when a financial institution does this work on behalf of thousands of investors, the cost is greatly reduced.**A financial system provides the means for reducing conflict between the parties to a contract.**Contracting parties often have difficulty monitoring each other’s behaviour. Sometimes conflicts arise because each party has different amounts of information and divergent contractual ties. For example, an investor gives money to a fund manager in the hope that they will manage the funds in the investor’s best interests (and not their own!). If the fund manager does not uphold their end of the bargain, the market will lose confidence in them. Typically, the consequence of such behaviour is that they will be replaced by a more conscientious manager.

## Section 15.4 THE RELATIONSHIP BETWEEN BANKS AND COMPANIES

Not so long ago, banks could be classified as:

**Commercial banks**that schematically collected funds from individuals and lent to corporates.**Investment banks**that provided advisory services (mergers and acquisitions, wealth management) and played the role of a broker (placement of shares, of bonds) but without “using their balance sheet”.

Since the beginning of this century, large financial conglomerates have emerged both in the US and Europe. This resulted from mega-mergers between commercial banks and investment banks: BNP/Paribas, Citicorp/Travelers Group, Chase Manhattan/JP Morgan, Bank of America/Merrill Lynch, or the transition by investment banks towards commercial banking (Goldman Sachs, Mediobanca) or the reverse (Credit Suisse, Credit Agricole).

This trend, eased by changes in regulation (in particular in the US with the reform of the Glass–Steagall Act in 1999), shows a willingness of large banking groups to adopt the business model of a universal bank (also called “one-stop shopping”) in a context of increasing internationalisation and complexity. This is particularly true for certain business lines like corporate finance or fund management, in which size constitutes a real competitive advantage.

Following the 2008 financial crisis, there emerged a certain political willingness to split up large banking groups again, specifically in order to separate deposits from market-related activities. This idea (not only guided by the protection of households’ deposits) has only partially materialised in laws (in the US, France, the UK) aimed mainly at confining speculative operations and avoiding market activities that put clients’ deposits at risk (Volker regulation in particular).

Large banking groups now generally include the following business lines:

**Retail banking**: for individuals and small and medium-sized corporates. Retail banks serve as intermediaries between those who have surplus funds and those who require financing. The banks collect resources from the former and lend money to the latter. They have millions of clients and therefore adopt an industrial organisation. The larger the bank’s portfolio, the lower the risk – thanks once again to the law of large numbers. Retail banking is an extremely competitive activity. After taking into account the cost of risk, profit margins are very thin. Bank loans are somewhat standard products, so it is relatively easy for customers to play one bank off against another to obtain more favourable terms. Retail banks have developed ancillary services to add value to the products that they offer to their corporate customers. Accordingly, they offer a variety of means of payment to help companies move funds efficiently from one place to another. They also help clients to manage their cash flows or their short-term investments (see Chapter 50). A retail banking division also generally includes some specific financial services for individuals (e.g. consumer credit) or for corporates (factoring, leasing, etc.), as such services are used mostly by small and medium-sized firms.**Corporate and investment banking (CIB)**: provides large corporates with sophisticated services. Such banks have, at most, a few thousand clients and offer primarily the following services:**Access to equity markets (equity capital markets, ECM)**: investment banks help companies prepare and carry out initial public offerings on the stock market. Later on, investment banks can continue to help these companies by raising additional funds through capital increases. They also advise companies on the issuance of instruments that may one day become shares of stock, such as warrants and convertible bonds (see Chapter 24) or the disposal of blocks of a listed subsidiary.**Access to bond markets (debt capital markets, DCM)**: similarly, investment banks help large and medium-sized companies raise funds directly from investors through the issuance of bonds. The techniques of placing securities, and in particular the role of the investment bank in this type of transaction, will be discussed in Chapter 25. The investment bank’s trading room is where its role as “matchmaker” between the investor and the issuer takes on its full meaning.**Merger and acquisition (M&A) advisory services**: these investment banking services are not directly linked to corporate financing or the capital markets, although a public issue of bonds or shares often accompanies an acquisition (see Chapter 45). The first three activities are called**investment banking**.**Bank financing**: syndicated loans, bilateral lines, structured financing (see Chapter 21).**Access to foreign exchange, interest rate and commodities markets**: for the hedging of risk. The bank also uses these desks for speculating on its own account (see Chapter 51).

**Asset management**: has its own clients – institutional investors and high-net-worth individuals – but also serves some of the retail banking clients through mutual funds. The asset management arm may sometimes use some of the products tailored by the investment banking division (hedging, order execution). This business is increasingly operated by players that are independent (totally or partially) from large banks.

Besides these global banking groups operating across all banking activities, some players have focused on certain targeted services like mergers and acquisitions and asset management (Lazard and Rothschild, for example), retail (it is the case for internet based new banks like N26, Revolut or Orange Bank) or specific geographical areas (Mediobanca and Lloyds Bank, for example).

The 2020 crisis (after 2008) demonstrated again the central role played by banks in the economy. They are suppliers of liquidity; they are also an indicator of investor risk aversion. The basic duty of a bank is to assess risk and repackage it while eliminating the diversifiable risk.

## Section 15.5 THEORETICAL FRAMEWORK: EFFICIENT MARKETS

In an efficient market, prices instantly reflect the consequences of past events and all expectations about future events. As all known factors are already integrated into current prices, it is therefore impossible to predict future variations in the price of a financial instrument. Only new information will change the value of the security. Future information is, by definition, unpredictable, so changes in the price of a security are random. This is the origin of the **random walk** character of daily returns in the securities markets.

Competition between financial investors is so fierce that prices adjust to new information almost instantaneously. At every moment, a financial instrument trades at a price determined by its return and its risk as perceived by its investors.

Eugene Fama (1970) has developed the following three tests to determine whether a market is efficient: ability to predict future prices, market response to specific events, impact of insider information on the market.

In a **weak-form** efficient market, it is impossible to predict future returns. Existing prices already reflect all the information that can be gleaned from studying **past prices** and **trading volumes**. **The efficient market hypothesis says that technical analysis has no practical value**, nor do martingales (martingales in the ordinary, not the mathematical, sense). For example, the notion that “if a stock rises three consecutive times, buy it; if it declines two consecutive times, sell it” is irrelevant. Similarly, the efficient market hypothesis says that models relating future returns to interest rates, dividend yields, the spread between short- and long-term interest rates or other parameters are equally worthless.

A **semi-strong** efficient market reflects all publicly available information, as found in annual reports, newspaper and magazine articles, prospectuses, announcements of new contracts, of a merger, of an increase in the dividend, etc. This hypothesis can be empirically tested by studying the reaction of market prices to company events (**event studies**). In fact, the price of a stock reacts immediately to any announcement of relevant new information regarding a company. In an efficient market, no impact should be observable prior to the announcement, nor during the days following the announcement. In other words, prices should adjust rapidly only at the time any new information is announced.

In order to prevent investors with prior access to information from using it to their advantage (and therefore to the detriment of other investors), stock market regulators suggest that firms communicate before market opening or after market closure, or suspend trading prior to a mid-session announcement of information that is highly likely to have a significant impact on the share price. Trading resumes a few hours later or the following day so as to ensure that all interested parties receive the information. Then, when trading resumes, no investor has been short-changed.

In a **strongly** efficient financial market, investors with privileged or insider information or with a monopoly on certain information are unable to influence securities prices. This holds true only when financial market regulators have the power to prohibit and punish the use of insider information.

In theory, professional investment managers have expert knowledge that is supposed to enable them to post better performances than the market average. However, without using any inside information, the efficient market hypothesis says that market experts have no edge over the layperson. In fact, in an efficient market, the experts’ performance is slightly below the market average, in a proportion directly related to the management fees they charge!

Actual markets approach the theory of an efficient market when participants have low-cost access to all information, transaction costs are low, the market is liquid and investors are rational.

Take the example of a stock whose price is expected to rise 10% tomorrow. In an efficient market, its price will rise today to a level consistent with the expected gain. “Tomorrow’s” price will be discounted to today. Today’s price becomes an estimate of the value of tomorrow’s price.

## Section 15.6 ANOTHER THEORETICAL FRAMEWORK UNDER CONSTRUCTION: BEHAVIOURAL FINANCE

Since the end of the 1960s, a large number of research papers have focused on testing the efficiency of markets. It is probably the most tested assumption of finance! Since the early 1980s, researchers (notably Thaler and Kahneman) have highlighted a number of “anomalies” that tend to go against the efficiency of markets:

**Excess volatility.**The first issue with efficient market theory seems very intuitive: how can markets be so volatile? Information on Sanofi is not published every second. Nevertheless, the share price does move at each instant. There seems to be some kind of noise around fundamental value. As described by Benoit Mandelbrot, who first used fractals in economics, prices evolve in a discrete way rather than in a continuous manner.**Dual listing and closed-end funds.**Dual listings are shares of twin companies listed on two different markets. Their stream of dividends is, by definition, identical but we can observe that their price can differ over a long period of time. Similarly, the price of a closed-end fund (made up of shares of listed companies) can differ from the sum of the value of its components. Conglomerate discount (see Chapter 42) cannot explain the magnitude of the discount for certain funds and certainly not the premium for some others. It is interesting to see that these discounts can prevail over a long period of time, therefore making any arbitrage (although easy to conceptualise) hard to put in place.**Calendar anomalies.**Stocks seem to perform less well on Mondays than on other days of the week and provide higher returns in the month of January compared to other months of the year (in particular for small and medium-sized enterprises). Nevertheless, these calendar anomalies are not material enough to allow for systematic and profitable arbitrage given transaction costs. For each of these observations, some justifications consistent with the rationality of investor behaviour can be put forward.**Meteorological anomalies.**There is consistent observation that stock prices perform better when the sun shines than when it rains. There again, although statistically significant, these anomalies are not material enough to generate arbitrage opportunities.

There are some grounds to think a certain number of situations challenge the validity of the efficient market theory. Nevertheless, Eugene Fama, one of the founders of this theory, defends it strongly. He calls into question the methodologies used to find anomalies. **Behavioural finance rejects the founding assumption of market efficiency: what if investors were not rational?** It tries to build on other fields of social science to derive new conclusions. For example, economists will work with neuroscientists and psychologists to understand individual economic choices. This allows us to suppose that some decisions are influenced by circumstances and the environment.

One of the first tests for understanding people’s reasoning in making a choice is based on lotteries (gains with certain probabilities). The following attitudes can be observed:

- Gains and losses are not treated equally by investors: they will take risks when the probability of losing is high (they prefer a 50% chance of losing 100 to losing 50 for sure) whereas they will prefer a small gain if the probability is high (getting 50 for sure rather than a 50% chance of 100).
- If the difference (delta) in probability is narrow, the investor will choose the lottery with the highest return possible, but if the delta in probability is high, the investor will think in terms of weighted average return. This may generate some paradoxes: preferring Natixis to UBS, UBS to Mediobanca but Mediobanca to Natixis! This could drive an asset manager mad!

The lack of rationality of some investors would not be a problem if arbitrage made it possible to correct anomalies and if efficiency could be brought back rapidly. Unfortunately, anomalies can be observed over the long term.

The theory of mimicry is an illustration of behavioural finance. The economist André Orléan has distinguished three types of mimicry:

**Normative mimicry**– which could also be called “conformism”. Its impact on finance is limited and is beyond the scope of this text.**Informational mimicry**– which consists of imitating others because they supposedly know more. It constitutes a rational response to a problem of dissemination of information, provided the proportion of imitators in the group is not too high. Otherwise, even if it is not in line with objective economic data, imitation reinforces the most popular choice, which can then interfere with efficient dissemination of information.**Self-mimicry**– which attempts to predict the behaviour of the majority in order to imitate it. The “right” decision then depends on the collective behaviour of all other market participants and can become a self-fulfilling prophecy, i.e. an equilibrium that exists because everyone thinks it will exist. This behaviour departs from traditional economic analysis, which holds that financial value results from real economic value.

The surge in the price of the video game company Gamestop, which went from $18 to $325 in 20 days in January 2021, or that of AMC (movie theatres), which went from $13 to $60 in the first half of 2021, are illustrations of a frenetic mimicry, totally disconnected from the economic situation, real or even possible, of these companies. These surges are rooted in the compulsive buying of tens of thousands of people who have never read a single page of the Vernimmen, or any other finance textbook, but who encourage and intoxicate each other on social networks.

Mimetic phenomena can be accentuated by **program trading**, which involves the computer programs used by some traders that rely on pre-programmed buy or sell decisions. These programs can schedule liquidating a position (i.e. selling an investment) if the loss exceeds a certain level. A practical issue with such programs was illustrated on 21 February 2021 by the flash crash of the bitcoin, which lost 34% before recovering its initial price in just one hour.

If some want to destroy efficient market theory, they will have to propose a viable alternative. As of today, the models proposed by “behaviourists” cannot be used, they merely model the behaviour of investors towards investment decisions and products.

## Section 15.7 INVESTORS’ BEHAVIOUR

At any given point in time, each investor is either:

- a hedger;
- a speculator; or
- an arbitrageur.

### 1/ HEDGING

When an investor attempts to protect himself from risks they do not wish to assume, they are said to be **hedging**. The term “to hedge” describes a general concept that underlies certain investment decisions, for example, the decision to match a long-term investment with long-term financing, to finance a risky industrial investment with equity rather than debt, etc.

This is simple, natural and healthy behaviour for non-financial managers. Hedging protects a manufacturing company’s margin, i.e. the difference between revenue and expenses, from uncertainties in areas relating to technical expertise, human resources, sales and marketing, etc. Hedging allows the economic value of a project or line of business to be managed independently of fluctuations in the capital markets.

Accordingly, a European company that exports products to the US may sell dollars forward against euros, guaranteeing itself a fixed exchange rate for its future dollar-denominated revenues. The company is then said to have hedged its exposure to fluctuations in currency exchange rates.

### 2/ SPECULATION

In contrast to hedging, which eliminates risk by transferring it to a party willing to assume it, speculation is the assumption of risk. A speculator takes a position when they make a bet on the future value of an asset. If they think its price will rise, they buy it. If it rises, they win the bet; if not, they lose. If they are to receive dollars in a month’s time, they may take no action now because they think the dollar will rise in value between now and then. If they have long-term investments to make, they may finance them with short-term funds because they think that interest rates will decline in the meantime and they will be able to refinance at lower cost later. This behaviour is diametrically opposed to that of the hedger.

**Traders are professional speculators.**They spend their time buying currencies, bonds, shares or options that they think will appreciate in value and they sell them when they think they are about to decline. Not surprisingly, their motto is “*Buy low, sell high, play golf!*”**But the investor is also a speculator most of the time.**When an investor predicts cash flows, they are speculating about the future. This is a very important point, and you must be careful not to interpret “speculation” negatively. Every investor speculates when they invest, but their speculation is not necessarily reckless. It is founded on a conviction, a set of skills and an analysis of the risks involved. The only difference is that some investors speculate more heavily than others by assuming more risk.

People often criticise the financial markets for allowing speculation. Yet speculators play a fundamental role in the market, an economically healthy role, by assuming the risks that other participants do not want to accept. In this way, speculators minimise the risk borne by others.

Accordingly, a European manufacturing company with outstanding dollar-denominated debt that wants to protect itself against exchange rate risk (i.e. a rise in the value of the dollar vs. the euro) can transfer this risk by buying dollars forward from a speculator willing to take that risk. By buying dollars forward today, the company knows the exact dollar/euro exchange rate at which it will repay its loan. It has thus eliminated its exchange rate risk. Conversely, the speculator runs the risk of a fluctuation in the value of the dollar between the time they sell the dollars forward to the company and the time they deliver them, i.e. when the company’s loan comes due.

Likewise, if a market’s long-term financing needs are not satisfied, but there is a surplus of short-term savings, then sooner or later a speculator will (fortunately) come along and assume the risk of borrowing short term in order to lend long term. In so doing, the speculator assumes intermediation risk.

What, then, do people mean by a “speculative market”? A speculative market is a market in which all the participants are speculators. Market forces, divorced from economic reality, become self-sustaining because everyone is under the influence of the same phenomenon. Once a sufficient number of speculators think that a stock will rise, their purchases alone are enough to make the stock price rise. Their example prompts other speculators to follow suit, the price rises further, and so on. But at the first hint of a downward revision in expectations, the mechanism goes into reverse and the share price falls dramatically. When this happens, many speculators will try to liquidate positions in order to pay off loans contracted to buy shares in the first place, thereby further accentuating the downfall.

### 3/ ARBITRAGE

In contrast to the speculator, the arbitrageur is not in the business of assuming risk or having a view on future price of an asset. Instead, they try to earn a profit by exploiting tiny discrepancies which may appear on different markets that are not in equilibrium.

An arbitrageur will notice that Solvay shares are trading slightly lower in London than in Brussels. They will buy Solvay shares in London and sell them simultaneously (or nearly so) at a higher price in Brussels. By buying in London, the arbitrageur bids the price up in London; by selling in Brussels, they drive the price down there. They, or other arbitrageurs, then repeat the process until the prices in the two markets are perfectly in line, or in equilibrium.

In principle, the arbitrageur assumes no risk, even though each separate transaction involves a certain degree of risk.

Arbitrage is of paramount importance in a market. By **destroying opportunities as it uncovers them**, arbitrage participates in the development of new markets by creating liquidity. It also eliminates the temporary imperfections that can appear from time to time. As soon as disequilibrium appears, arbitrageurs buy and sell assets and increase market liquidity. It is through their very actions that the disequilibrium is reduced to zero. Once equilibrium is reached, arbitrageurs stop trading and wait for the next opportunity.

Arbitrage transactions are all the faster to intervene (by computer programs nowadays) when the securities markets are liquid. Otherwise, imbalances may persist for some time on very illiquid securities. Market liquidity and progress in technology make arbitrage opportunities more and more complex and rare. Therefore, some arbitrators are forced in practice to take a certain amount of risk and therefore a speculative component normally foreign to arbitration in the pure sense of the term. In particular, the example given of Solvay is interesting to understand the concept of arbitrage but has not been relevant for quite some time.

Throughout this book, you will see that financial miracles are impossible because arbitrage levels the playing field between assets exhibiting the same level of risk.

You should also be aware that the three types of behaviour described here do not correspond to three mutually exclusive categories of investors. A market participant who is primarily a speculator might carry out arbitrage activities or partially hedge their position. A hedger might decide to hedge only part of their position and speculate on the remaining portion, etc.

The reader will not be fooled by the colloquial use of some words. “Hedge funds” do not operate hedging transactions but are most often involved in speculating. Otherwise, what explanation is there for the fact that they can earn or lose millions of dollars in a few days?

Moreover, these three types of behaviour exist simultaneously in every market. A market cannot function only with hedgers, because there will be no one to assume the risks they don’t want to take.^{1} As we saw above, a market composed wholly of speculators is not viable either. Finally, a market consisting only of arbitrageurs would be even more difficult to imagine.

## SUMMARY

## QUESTIONS

## ANSWERS

## BIBLIOGRAPHY

## NOTES

## Chapter 16. THE TIME VALUE OF MONEY AND NET PRESENT VALUE

*A bird in the hand is worth two in the bush*

For economic progress to be possible, in normal economic conditions, there must be a time value of money, even in a risk-free environment. This fundamental concept gives rise to the techniques of capitalisation, discounting and net present value, described below.

## Section 16.1 CAPITALISATION

Consider an example of a businessman who invests €100,000 in his business at the end of 2011 and then sells it 10 years later for €1,800,000. In the meantime, he receives no income from his business, nor does he invest any additional funds into it. Here is a simple problem: given an initial outlay of €100,000 that becomes €1,800,000 in 10 years, and without any outside funds being invested in the business, what is the return on the businessman’s investment?

His profit after 10 years was €1,700,000 (€1,800,000 – €100,000) on an initial outlay of €100,000. Hence, his return was (1,700,000 / 100,000) or 1,700% over a period of 10 years.

Is this a good result or not?

Actually, the return is not quite as impressive as it first looks. To find the annual return, our first thought might be to divide the total return (1,700%) by the number of years (10) and say that the average return is 170% per year.

While this may look like a reasonable approach, it is in fact far from accurate. The value 170% has nothing to do with an annual return, which compares the funds invested and the funds recovered after one year. In the case above, there is no income for 10 years. Usually, calculating interest assumes a flow of revenue each year, which can then be reinvested, and which in turn begins producing additional interest.

There is only one sensible way to calculate the return on the above investment. First, it is necessary to seek the rate of return on a hypothetical investment that would generate income at the end of each year. After 10 years, the rate of return on the initial investment will have to have transformed €100,000 into €1,800,000. Further, the income generated must not be paid out, but rather it has to be reinvested (in which case the income is said to be **capitalised**).

Therefore, we are now trying to calculate the annual return on an investment that grows from €100,000 into €1,800,000 after 10 years, with all annual income to be reinvested each year.

An initial attempt to solve this problem can be made using a rate of return equal to 10%. If, at the end of 2011, €100,000 is invested at that rate, it will produce 10% × €100,000, or €10,000 in interest in 2012.

This €10,000 will then be added to the initial capital outlay and begin, in turn, to produce interest. (Hence the term “to capitalise”, which means to add to capital.) The capital thus becomes €110,000 and produces 10% × €110,000 in interest in 2013, i.e. €10,000 on the initial outlay plus €1,000 on the interest from the €10,000 interest earned in 2012 (10% × €10,000). As the interest is reinvested, the capital becomes €110,000 + €11,000, or €121,000, which will produce €12,100 in interest in 2014, and so on.

If we keep doing this until 2020, we obtain a final sum of €259,374, as shown in the table.

Year | Capital at the beginning of the period (€) (1) | Income (€) (2) = 10% × (1) | Capital at the end of the period (€) = (1) + (2) |
---|---|---|---|

2012 | 100,000 | 10,000 | 110,000 |

2013 | 110,000 | 11,000 | 121,000 |

2014 | 121,000 | 12,100 | 133,100 |

2015 | 133,100 | 13,310 | 146,410 |

2016 | 146,410 | 14,641 | 161,051 |

2017 | 161,051 | 16,105 | 177,156 |

2018 | 177,156 | 17,716 | 194,872 |

2019 | 194,872 | 19,487 | 214,359 |

2020 | 214,359 | 21,436 | 235,795 |

2021 | 235,795 | 23,579 | 259,374 |

Each year, interest is capitalised and itself produces interest. This is called **compound interest**. This is easy to express in a formula:

which can be generalised into the following:

where *V* is a sum and *r* the rate of return.

Hence, *V*_{2012} = *V*_{2011} × (1 + 10%), but the same principle can also yield:

All these equations can be consolidated into the following:

Or, more generally:

where *V*_{0} is the initial value of the investment, *r* is the rate of return and *n* is the duration of the investment in years.

This is a simple equation that gets us from the initial capital to the terminal capital. Terminal capital is a function of the rate *r* and the duration *n*.

Now it is possible to determine the annual return. In the example, the annual rate of return is not 170%, but 33.5% (which is not bad, all the same!). Therefore, 33.5% is the rate on an investment that transforms €100,000 into €1,800,000 in 10 years, with annual income assumed to be reinvested every year at the same rate.

To calculate the return on an investment that does not distribute income, it is possible to reason by analogy. This is done using an investment that, over the same duration, transforms the same initial capital into the same terminal capital and produces annual income reinvested at the same rate of return. At 33.5%, annual income of €33,500 for 10 years (plus the initial investment of €100,000 paid back after the tenth year) is exactly the same as not receiving any income for 10 years and then receiving €1,800,000 in the tenth year.

Over a long period of time, the impact of a change in the capitalisation rate on the terminal value looks as follows:

This increase in terminal value is especially important in equity valuations. The example we gave earlier of the businessman selling his company after 10 years is typical. The lower the income he has received on his investment, the more he would expect to receive when selling it. Only a high valuation would give him a return that makes economic sense.

The lack of intermediate income must be offset by a high terminal valuation. The same line of reasoning applies to an industrial investment that does not produce any income during the first few years. The longer it takes it to produce its first income, the greater that income must be in order to produce a satisfactory return.

Tripling one’s capital in 16 years, doubling it in 10 years or simply asking for a 7.177% annual return all amount to the same thing, since the rate of return is the same.

No distinction has been made in this chapter between income, reimbursement and actual cash flow. Regardless of whether income is paid out or reinvested, it has been shown that the slightest change in the timing of income modifies the rate of return.

To simplify, consider an investment of 100, which must be paid off at the end of year 1, with an interest accrued of 10. Suppose, however, that the borrower is negligent and the lender absent-minded, and the borrower repays the principal and the interest one year later than they should. The return on a well-managed investment that is equivalent to the so-called 10% on our absent-minded investor’s loan can be expressed as:

This return is less than half of the initially expected return!

It is not accounting and legal appearances that matter, but rather actual cash flows.

## Section 16.2 DISCOUNTING

### 1/ WHAT DOES IT MEAN TO DISCOUNT A SUM?

Discounting into today’s euros helps us compare a sum that will not be produced until later. Technically speaking, what is discounting?

**To discount is to “depreciate” the future. It is to be more rigorous with future cash flows than present cash flows, because future cash flows cannot be spent or invested immediately**. First, take tomorrow’s cash flow and then apply to it a multiplier coefficient below 1, which is called a discounting factor. The discounting factor is used to express a future value as a present value, thus reflecting the depreciation brought on by time.

Consider an offer whereby someone will give you €1,000 in five years. As you will not receive this sum for another five years, you can apply a discounting factor to it, for example, 0.6. The present, or today’s, value of this future sum is then 600. Having discounted the future value to a present value, we can then compare it to other values. For example, it is preferable to receive 650 today rather than 1,000 in five years, as the present value of 1,000 five years out is 600, and that is below 650.

Remember that investors discount because**they demand a certain rate of return**. If a security pays you 110 in one year and you wish to see a return of 10% on your investment, the most you would pay today for the security (i.e. its present value) is 100. At this price (100) and for the amount you know you will receive in one year (110), you will get a return of 10% on your investment of 100. However, if a return of 11% is required on the investment, then the price you are willing to pay changes. In this case, you would be willing to pay no more than 99.1 for the security because the gain would have been 10.9 (or 11% of 99.1), which will still give you a final payment of 110.

Discounting converts a future value into a present value. This is the opposite result of capitalisation.

Discounting converts future values into present values, while capitalisation converts present values into future ones. Hence, to return to the example above, €1,800,000 in 10 years discounted at 33.5% is today worth €100,000. €100,000 today will be worth €1,800,000 when capitalised at 33.5% over 10 years.

### 2/ DISCOUNTING AND CAPITALISATION FACTORS

To discount a sum, the same mathematical formulas are used as those for capitalising a sum. Discounting calculates the sum in the opposite direction to capitalising.

To get from €100,000 today to €1,800,000 in 10 years, we multiply 100,000 by (1 + 0.335)^{10}, or 18. The number 18 is the **capitalisation factor**.

To get from €1,800,000 in 10 years to its present value today, we would have to multiply €1,800,000 by 1 / (1 + 0.335)^{10}, or 0.056. 0.056 is the **discounting factor**, which is the inverse of the coefficient of capitalisation. The present value of €1,800,000 in 10 years at a 33.5% rate is €100,000.

More generally:

which is the exact opposite of the capitalisation formula.

1 / (1 + *r*)^{n} is the **discounting factor**, which depreciates *V*_{n} and converts it into a present value *V*_{0}. It is most often below 1, as discounting rates are generally positive.

## Section 16.3 PRESENT VALUE AND NET PRESENT VALUE OF A FINANCIAL SECURITY

Owning a financial security such as a stock or a bond means owning the right to receive cash flows (dividend, interest, reimbursement, etc.) according to the specific terms of the security.

### 1/ FROM THE PRESENT VALUE OF A SECURITY …

**The present value (PV) of a security is the sum of its discounted cash flows,** i.e.:

where *F*_{n} are the cash flows generated by the security, *r* is the applied discounting rate and *n* is the number of years for which the security is discounted.

All securities also have a **market value**, particularly on the secondary market. Market value is the price at which a security can be bought or sold.

**Net present value (NPV) is the difference between present value and market value ( V**

_{0}

**):**

If the net present value of a security is greater than its market value, then it will be worth more in the future than the market has presently valued it at. Therefore, you will probably want to invest in it, i.e. to invest in the upside potential of its value.

If, however, the security’s present value is below its market value, then you should sell it at once (as its net present value is negative), for **its market value is sure to diminish**.

### 2/ … TO ITS FAIR VALUE

If an imbalance occurs between a security’s market value and its present value, then efficient markets will seek to re-establish balance and reduce net present value to zero. Investors acting on efficient markets seek out investments offering positive net present value, in order to realise that value. When they do so, they push net present value towards zero, ultimately arriving at the fair value of the security.

### 3/ APPLYING THE CONCEPT OF NET PRESENT VALUE TO OTHER INVESTMENTS

Up to this point, the discussion has been limited to financial securities. However, the concepts of present value and net present value can easily be applied to any investment, such as the construction of a new factory, the launch of a new product, the takeover of a competing company or any other asset that will generate positive and/or negative cash flows.

The concept of net present value can be interpreted in three different ways:

**The value created by an investment**– for example, if the investment requires an outlay of €100 and the present value of its future cash flow is €110, then the investor has become €10 wealthier.**The maximum additional amount that the investor is willing to pay to make the investment**– if the investor pays up to €10 more, they have not necessarily made a bad deal, as they are paying up to €110 for an asset that is worth €110.**The difference between the present value of the investment (€110) and its market value (€100).**

## Section 16.4 WHAT DOES NET PRESENT VALUE DEPEND ON?

While net present value is obviously based on the amount and timing of cash flows, it is worth examining how it varies with the discounting rate.

The higher the discounting rate, the more future cash flow is depreciated and, therefore, the lower is the present value. **Net present value declines in inverse proportion to the discounting rate**, thus reflecting investor demand for a greater return (i.e. greater value attributed to time).

Take the following example of an asset (e.g. a financial security or a capital investment) with a market value of 2 and with cash flows as follows:

Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Cash flow | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |

A 20% discounting rate would produce the following discounting factors:

Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Discounting factor | 0.833 | 0.694 | 0.579 | 0.482 | 0.402 |

Present value of cash flow | 0.67 | 0.56 | 0.46 | 0.39 | 0.32 |

As a result, the present value of this investment is 2.40.^{1} As its market value is 2, its net present value is 0.40.

If the discounting rate changes, the following values are obtained:

Discounting rate | 0% | 10% | 20% | 25% | 30% | 35% |
---|---|---|---|---|---|---|

Present value of the investment | 4 | 3.03 | 2.39 | 2.15 | 1.95 | 1.78 |

Market value | 2 | 2 | 2 | 2 | 2 | 2 |

Net present value | 2 | 1.03 | 0.39 | 0.15 | −0.05 | −0.22 |

Which would then look like this graphically:

## Section 16.5 SOME EXAMPLES OF SIMPLIFICATION OF PRESENT VALUE CALCULATIONS

For those occasions when you are without your favourite spreadsheet program, you may find the following formulas handy in calculating present value.

### 1/ THE VALUE OF AN ANNUITY *F* OVER *N* YEARS, BEGINNING IN YEAR 1

or:

For the two formulas above, the sum of the geometric series can be expressed more simply as:

So, if *F* = 0.8, *r* = 20% and *n* = 5, then the present value is indeed 2.4.

Further, is equal to the sum of the first *n* discounting factors.

### 2/ THE VALUE OF A PERPETUITY

A **perpetuity** is a constant stream of cash flows without end. By adding this feature to the previous case, the formula then looks like this:

As *n* approaches infinity in the formula of the previous paragraph, this can be shortened to the following:

The present value of a €100 perpetuity discounted back at 10% per year is thus:

A €100 perpetuity discounted at 10% is worth €1,000 in today’s euros. If the investor demands a 20% return, then the same perpetuity is worth €500.

### 3/ THE VALUE OF AN ANNUITY THAT GROWS AT RATE *G* FOR *N* YEARS

In this case, the *F*_{0} cash flow rises annually by *g* for *n* years.

Thus:

or:

*Note*: the first cash flow actually paid out is *F*_{0} × (1 + *g*).

Thus, a security that has just paid out 0.8, and with this 0.8 growing by 10% each year for the four following years, has – at a discounting rate of 20% – a present value of:

### 4/ THE VALUE OF A PERPETUITY THAT GROWS AT RATE *G* (GROWING PERPETUITY)

As *n* approaches infinity, the previous formula can be expressed as follows:

As long as *r* > *g*. The present value is thus equal to the next year’s cash flow divided by the difference between the discounting rate and the annual growth rate.

For example, a security with an annual return of 0.8, growing by 10% annually to infinity, has, at a rate of 20%, *PV* = 0.8 / (0.2 – 0.1) = 8.0.

## SUMMARY

## QUESTIONS

## EXERCISES

## ANSWERS

## BIBLIOGRAPHY

## NOTE

## Chapter 17. THE INTERNAL RATE OF RETURN

*A well-deserved return*

If net present value (NPV) is inversely proportional to the discounting rate, then there must exist a discounting rate that makes NPV equal to zero.

To apply this concept to capital expenditure, simply replace “yield to maturity” by “IRR”, as the two terms mean the same thing. It is just that one is applied to financial securities (yield to maturity) and the other to capital expenditure (IRR).

## Section 17.1 CALCULATING YIELD TO MATURITY

To calculate yield to maturity, make *r* the unknown and simply use the NPV formula again. The rate *r* is determined as follows:

To use the same example from Section 16.4:

In other words, an investment’s yield to maturity is the rate at which its market value is equal to the present value of the investment’s future cash flows.

In our illustration, the IRR is about 28.6% (see figure in Section 16.4).

## Section 17.2 YIELD TO MATURITY AS AN INVESTMENT CRITERION

The yield to maturity is frequently used in financial markets because it represents for the investor the return to be expected for a given level of risk, which they can then compare to their required return rate, thereby simplifying the investment decision.

The decision-making rule is very simple: if an investment’s yield to maturity is higher than the investor’s required return, they will make the investment or buy the security. Otherwise, they will abandon the investment or sell the security.

In our example, since the yield to maturity (28.6%) is higher than the return demanded by the investor (20%), they should make the investment. If the market value of the same investment were 3 (and not 2), the yield to maturity would be 10.4%, and they should not invest.

Hence, at fair value, the yield to maturity is identical to the market’s required return. In other words, net present value is nil (this will be developed further in Chapter 26).

## Section 17.3 THE LIMITS OF YIELD TO MATURITY OR IRR

With this new investment-decision-making criterion, it is now necessary to consider how IRR can be used vis-à-vis net present value. It is also important to investigate whether or not these two criteria could somehow produce contradictory conclusions.

If it is a simple matter of whether or not to buy into a given investment, or whether or not to invest in a project, then the two criteria produce exactly the same result, as shown in the example.

If the cash flow schedule is the same, then calculating the NPV by choosing the discounting rate and calculating the internal rate of return (and comparing it with the discounting rate) are two sides of the same mathematical coin.

The issue is, however, a bit more complex when it comes to choosing between several securities or projects, which is usually the case. Comparing several streams of cash flows (securities) should make it possible to choose between them.

### 1/ THE REINVESTMENT RATE AND THE MODIFIED IRR (MIRR)

Consider two investments *A* and *B*, with the following cash flows:

Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Investment A | 6 | 0.5 | |||||

Investment B | 2 | 3 | 0 | 0 | 2.1 | 0 | 5.1 |

At a 5% discount rate, the present value of investment *A* is 6.17 and that of investment *B* is 9.90. If investment *A*‘s market value is 5, its net present value is 1.17. If investment *B*‘s market value is 7.5, its net present value is 2.40.

Now calculate the IRR. It is 27.8% for investment *A* and 12.7% for investment *B*. Or, to sum up:

NPV at 5% | IRR% | |
---|---|---|

Investment A | 1.17 | 27.8 |

Investment B | 2.40 | 12.7 |

Investment *A* delivers a rate of return that is much higher than the required return (27.8% vs. 5%) during a short period of time. Investment *B*‘s rate of return is much lower (12.7% vs. 27.8%), but is still higher than the 5% required return demanded and is delivered over a far longer period (seven years vs. two). Our NPV and internal rate of return models are telling us two different things. So, should we buy investment *A* or investment *B*?

At first glance, investment *B* would appear to be the more attractive of the two. Its NPV is higher and it creates the most value: 2.40 vs. 1.17.

However, some might say that investment *A* is more attractive, as cash flows are received earlier than with investment *B* and therefore can be reinvested sooner in high-return projects. While that is theoretically possible, it is the strong (and optimistic) form of the theory because competition among investors and the mechanisms of arbitrage tend to move net present values towards zero. Net present values moving towards zero means that exceptional rates of return converge towards the required rate of return, thereby eliminating the possibility of long-lasting high-return projects.

Given the convergence of the exceptional rates towards required rates of return, it is more reasonable to suppose that cash flows from investment *A* will be reinvested at the required rate of return of 5%. The exceptional rate of 27.8% is unlikely to be recurrent.

And this is exactly what happens if we adopt the NPV decision rule. The NPV in fact assumes that the reinvestment of interim cash flows is made at the required rate of return. The IRR assumes that the reinvestment rate of interim cash flows is simply the IRR itself. However, in equilibrium, it is unreasonable to think that the company can continue to invest at the same rate of the (sometimes) exceptional IRR of a specific project. Instead, it is much more reasonable to assume that, at best, the company can invest at the required rate of return.

However, a solution to the reinvestment rate problem of IRR is the **modified IRR (MIRR)**.

So, by capitalising cash flow from investments *A* and *B* at the required rate of return (5%) up to period 7, we obtain from investment *A* in period 7: 6 × 1.005^{6} + 0.5 × 1.05^{5}, or 8.68. From investment *B* we obtain 2 × 1.05^{6} + 3 × 1.05^{5} + 2.1 × 1.05^{2} + 5.1, or 13.9. The internal rate of return that allows for investment A in capitalising over seven years to reach 8.68 is 8.20%; it is often called modified IRR. For investment B, the modified IRR is 9.24%.

We have thus reconciled the NPV and internal rate of return models.

Some might say that it is not consistent to expect investment *A* to create more value than investment *B*, as only 5 has been invested in *A* vs. 7.5 for *B*. Even if we could buy an additional “half-share” of *A*, in order to equalise the purchase price, the NPV of our new investment in *A* would only be 1.17 × 1.5 = 1.76, which would still be less than investment *B*‘s NPV of 2.40. For the reasons discussed above, we are unlikely to find another investment with a return identical to that of investment *A*.

Instead, we should assume that the 2.5 in additional investment would produce the required rate of return (5%) for seven years. In this case, NPV would remain, by definition, at 1.17, whereas the internal rate of return of this investment would fall to 11%. NPV and the internal rate of return would once again lead us to conclude that investment *B* is the more attractive investment.

In fact, the NPV criterion is a better choice criterion than the IRR because it assumes that the intermediate flows of the investment are reinvested at the required rate of return (the discount rate), whereas in the calculation of the IRR they are assumed to be reinvested at that rate. The latter assumption is very strong because, if the IRR is higher than the required rate of return, it assumes that the company will always find projects that yield more than the required rate of return.

### 2/ MULTIPLE OR NO IRR

Finally, there are some rare cases where the use of the IRR leads to a deadlock. Consider the following investments:

Year | 0 | 1 | 2 |
---|---|---|---|

Project A | 4 | −7 | 4 |

Project B | −1 | 7.2 | −7.2 |

Project A has no IRR. Thus, we have no benchmark for deciding if it is a good investment or not. Although the NPV remains positive for all the discount rates, it remains only *slightly* positive and the company may decide not to do it.

Project B has two IRRs, and we do not know which is the right one. There is no good reason to use one over the other. Investments with “unconventional” cash flow sequences are rare, but they can happen. Consider a firm that is cutting timber in a forest. The timber is cut, sold and the firm gets an immediate profit. But, when harvesting is complete, the firm may be forced to replant the forest at considerable expense.

The IRR criterion does not allow for the ranking of different investment opportunities. It only allows us to determine whether one project yields at least the return required by investors. When the IRR does not allow us to judge whether an investment project should be undertaken or not (e.g. no IRR or several IRRs), the NPV should be analysed.

## Section 17.4 EFFECTIVE ANNUAL RATE, NOMINAL RATES AND PROPORTIONAL RATES

We have just discovered the IRR, but many readers will be more aware of the interest rate, especially those planning to take out a loan. How can we reconcile the two?

Consider someone who wants to lend you €1,000 today at 10% for four years. This 10% means **10% per year** and constitutes the **nominal rate of return** of your loan. This rate will be the basis for calculating interest, proportional to the time elapsed and the amount borrowed. Assume that you will pay interest annually, at the end of each annual period rather than at the beginning.

### 1/ THE CONCEPT OF EFFECTIVE ANNUAL RATE

Now what happens when interest is paid not once but several times per year?

Suppose that somebody lends you money at 10% but says (somewhere in the fine print at the bottom of the page) that interest will have to be paid on a half-yearly basis. For example, suppose you borrowed €100 on 1 January and then had to pay €5 in interest on 1 July and €5 on 1 January of the following year, as well as the €100 in principal at the same date.

This is not the same as borrowing €100 and repaying €110 one year later. The amount of interest may be the same (5 + 5 = 10), but the payment schedule is not. In the first case, you will have to pay €5 on 1 July (just before leaving on summer holiday), which you could have kept until the following 1 January in the second case. In the first case you pay €5, instead of investing it for six months as you could have done in the second case.

As a result, the loan in the first case costs more than a loan at 10% with interest due annually. Its effective rate is not 10%, since interest is not being paid on the benchmark annual terms.

To avoid comparing apples and oranges, a financial officer must take into account the effective date of disbursement. We know that one euro today is not the same as one euro tomorrow. Obviously, the financial officer wants to postpone expenditure and accelerate receipts, thereby having the money work for them. So, naturally, the repayment schedule matters when calculating the rate.

Which is the best approach to take? If the interest rate is 10%, with interest payable every six months, then the interest rate is 5% **for six months**. We then have to calculate **an effective annual rate** (and not for six months), which is our point of reference and our constant concern.

Two rates referring to two different maturities are said to be equivalent if the future value of the same amount at the same date is the same with the two rates.

In our example, the lender receives €5 on 1 July which, compounded over six months, becomes 5 + (10% × 5) / 2 = €5.25 on the following 1 January, the date on which they receive the second €5 interest payment. So, over one year, they will have received €10.25 in interest on a €100 investment.

Therefore, the effective annual rate is 10.25%. This is the real cost of the loan, since the return for the lender is equal to the cost for the borrower.

If the apparent rate (or nominal rate) (*r*_{a}) is to be paid *n* times per year, then the effective annual rate (*t*) is obtained by compounding this nominal rate *n* times after first dividing it by *n*:

where *n* is the number of interest payments in the year and *r*_{a} / *n* the proportional rate during one period, or *t* = (1 + *r*_{a} / *n*)^{n} − 1.

In our example:

The effective interest rate is thus 10.25%, while the nominal rate is 10%.

It should be common sense that an investment at 10% paying interest every six months produces a higher return at year end than an investment paying interest annually. In the first case, interest is compounded after six months and thus produces interest on interest for the next six months. Obviously, a loan on which interest is due every six months will cost more than one on which interest is charged annually.

The table below gives the returns produced by an investment (a loan) at 10% with varying instalment frequencies:

The effective annual rate can be calculated on any timescale. For example, a financial officer might wish to use continuous rates. This might mean, for example, a 10% rate producing €100, paid out evenly throughout the year on a principal of €1,000. As long as the financial officer is familiar with a rate corresponding to interest paid once a year, they will keep this rate as a reference rate.

By definition, IRR and yields to maturity are effective annual rates.

### 2/ THE CONCEPT OF PROPORTIONAL RATE

In our example of a loan at 10%, we would say that the 5% rate over six months is **proportional** to the 10% rate over one year. More generally, two rates are proportional if they are in the same proportion to each other as the periods to which they apply.

For example, 10% per year is proportional to 5% per half-year or 2.5% per quarter, but 5% half-yearly is not equivalent to 10% annually. **Effective annual rate and proportional rates are therefore two completely different concepts that should not be confused.**

Proportional rates serve only to simplify calculations, but they hide the true cost of a loan. Only the effective annual rate (10.25%/year) gives the true cost, unlike the proportional rate (10%/year).

When the time span between two interest payment dates is less than one year, the proportional rate is lower than the effective annual rate (10% is less than 10.25%). When maturity is more than a year, the proportional rate overestimates the effective annual rate. This is rare, whereas the first case is quite frequent on money markets, where money is lent or borrowed for short periods of time.

As we will see, the bond market practice can be misleading for the investor focusing on par value: bonds are sold above or below par value, the number of days used in calculating interest can vary, bonds may be repaid above par value, and so on. And, most importantly, on the secondary market, a bond’s present value depends on fluctuations in market interest rates.

## Section 17.5 SOME MORE FINANCIAL MATHEMATICS: LOAN REPAYMENT TERMS

The first problem is how and when will you pay off the loan?

**Repayment terms constitute the method of amortisation of the loan.** Take the following examples.

### 1/ BULLET REPAYMENT

The entire loan is paid back at maturity.

The cash flow table would look like this:

Period | Principal still due | Interest | Amortisation of principal | Annuity |
---|---|---|---|---|

1 | 1,000 | 100 | 0 | 100 |

2 | 1,000 | 100 | 0 | 100 |

3 | 1,000 | 100 | 0 | 100 |

4 | 1,000 | 100 | 1,000 | 1,100 |

**Total debt service** is the annual sum of interest and principal to be paid back. This is also called debt servicing at each due date.

### 2/ CONSTANT (OR LINEAR) AMORTISATION

Each year, the borrower pays off a constant proportion of the principal, corresponding to 1/*n*, where *n* is the initial maturity of the loan.

The cash flow table would look like this:

Period | Principal still due | Interest | Amortisation of principal | Annuity |
---|---|---|---|---|

1 | 1,000 | 100 | 250 | 350 |

2 | 750 | 75 | 250 | 325 |

3 | 500 | 50 | 250 | 300 |

4 | 250 | 25 | 250 | 275 |

### 3/ EQUAL INSTALMENTS

The borrower may want to allocate a fixed sum to the service of debt (capital repayment and interests).

Based on the discounting method described previously, consider a constant annuity *A*, such that the sum of the four discounted annuities is equal to the present value of the principal, or €1,000:

This means that the NPV of the 10% loan is nil; in other words, the 10% nominal rate of interest is also the internal rate of return of the loan.

Using the formula from Section 16.5, paragraph 1, the previous formula can be expressed as follows:

*A* = €315.47. Hence, the following repayment schedule:

Period | Principal still due | Interest | Amortisation of principal | Annuity |
---|---|---|---|---|

1 | 1,000 | 100 | 215.47 | 315.47 |

2 | 784.53 | 78.45 | 237.02 | 315.47 |

3 | 547.51 | 54.75 | 260.72 | 315.47 |

4 | 286.79 | 28.68 | 286.79 | 315.47 |

In this case, the interest for each period is indeed equivalent to 10% of the remaining principal (i.e. the nominal rate of return) and the loan is fully paid off in the fourth year. Internal rate of return and nominal rate of interest are identical, as calculation is on an annual basis and the repayment of principal coincides with the payment of interest.

Regardless of which side of the loan you are on, both work the same way. We start with invested (or borrowed) capital, which produces income (or incurs interest costs) at the end of each period. Eventually, the loan is then either paid back (leading to a decline in future revenues or in interest to be paid) or held on to, thus producing a constant flow of income (or a constant cost of interest).

### 4/ INTEREST AND PRINCIPAL BOTH PAID WHEN THE LOAN MATURES

In this case, the borrower pays nothing until the loan matures. The sum that the borrower will have to pay at maturity is none other than the future value of the sum borrowed, capitalised at the interest rate of the loan:

This is how the repayment schedule would look:

Period | Principal and interest still due | Amortisation of principal | Interest payments | Annuity |
---|---|---|---|---|

1 | 1,000 | 0 | 0 | 0 |

2 | 1,100 | 0 | 0 | 0 |

3 | 1,219 | 0 | 0 | 0 |

4 | 1,331 | 1,331 | 1,331 | 1,464.1 |

This is a zero-coupon loan.

## SUMMARY

## QUESTIONS

## EXERCISES

## ANSWERS

## BIBLIOGRAPHY

## NOTE

## ****PART TWO. THE RISK OF SECURITIES AND THE REQUIRED RATE OF RETURN

# After having covered the basics of finance (discounting, capitalisation, value and interest rates), it is time to delve deeper into another fundamental concept: risk. Risk is the uncertainty over future asset values and future returns. For better or for worse, without risk, finance would be quite boring!

Risk means uncertainty today over the cash flows and value of an asset tomorrow. Of course, it is possible to review all the factors that could have a negative or positive impact on an asset, quantify each one and measure the total impact on the asset’s value. In reality, it is infinitely more practical to boil all the risks down to a single figure.

## Chapter 18. RISK AND RETURN

*The spice of finance*

Investors who buy financial securities face risks because they do not know with certainty the future selling price of their securities, nor the cash flows they will receive in the meantime. This chapter will try to explain and measure this risk, and also examine its repercussions.

## Section 18.1 SOURCES OF RISK

There are various risks involved in financial securities, including:

**Industrial, commercial and labour risks, etc.**There are so many types of risk in this category that we cannot list them all here. They include lack of competitiveness, emergence of new competitors, technological breakthroughs, an inadequate sales network, strikes and so on. These risks tend to lower cash flow expectations and thus have an immediate impact on the value of the stock.

**Liquidity risk**This is the risk of not being able to sell an asset at its fair value as a result of either a liquidity discount or the complete absence of a market or buyers.

**Credit risk**This is the risk that a creditor will lose their entire investment if a debtor cannot repay them in full, even if the debtor’s assets are liquidated. Traders call this

**counterparty risk**.**Foreign exchange**(**FX) risk**Fluctuations in exchange rates can lead to a loss of value of assets denominated in foreign currencies. Similarly, higher exchange rates can increase the value of debt denominated in foreign currencies when translated into the company’s reporting currency base.

**Interest rate risk**The holder of financial securities is exposed to the risk of interest rate fluctuations. Even if the issuer fulfils their commitments entirely, there is still the risk of a capital loss or, at the very least, an opportunity loss.

**Systemic risk**This is the risk of collapse of the overall financial system through the bankruptcy chain and the domino effect linked to the interdependency of market players.

**Political risk**This includes risks created by a particular political situation or decisions by political authorities, such as nationalisation without sufficient compensation, revolution, exclusion from certain markets, discriminatory tax policies, inability to repatriate capital, etc.

**Regulatory risk**A change in the law or in regulations can directly affect the return expected in a particular sector. Pharmaceuticals, banks and insurance companies, among others, tend to be on the front lines here.

**Inflation risk**This is the risk that the investor will recover their investment with a depreciated currency, i.e. that they will receive a return below the inflation rate. A flagrant historical example is the hyperinflation in Germany in the 1920s.

**The risk of a fraud**This is the risk that some parties (internal or external) will lie or cheat. The most common examples are insider trading, CEO fraud or ransomware.

**Natural disaster risks**These include storms, earthquakes, volcanic eruptions, cyclones, tidal waves, etc., which destroy assets, or of a pandemic that stops the activity or restrains it a lot. The recent past has demonstrated that those risks cannot be neglected.

**Economic risk**This type of risk is characterised by bull or bear markets, anticipation of an acceleration or a slowdown in business activity or changes in labour productivity.

The list is nearly endless; however, at this point it is important to highlight two points:

- most financial analysis mentioned and developed in this book tends to generalise the concept of risk and highlight its impact on valuations, rather than analysing it in depth. So, given the extent to which markets are efficient and evaluate risk correctly, it is not necessary to redo what others have already done; and
- risk is always present. The so-called risk-free rate, to be discussed later, is simply a manner of speaking.
**Risk is always present, and to say that risk can be eliminated is either to be excessively confident or to be unable to think about the future – both very serious faults for an investor.**

Obviously, any serious investment study should begin with a precise analysis of the risks involved.

The knowledge gleaned from analysts with extensive experience in the business, mixed with common sense, allows us to classify risks into two categories:

- economic risks (political, natural, inflation, fraud and other risks), which threaten cash flows from investments and which come from the “real economy”; and
- financial risks (liquidity, currency, interest rate and other risks), which do not directly affect cash flow, but nonetheless do come into the financial sphere. These risks are due to external financial events, and not to the nature of the issuer.

## Section 18.2 RISK AND FLUCTUATION IN THE VALUE OF A SECURITY

All of the aforementioned risks can penalise the financial performance of companies and their future cash flows. Obviously, if a risk materialises that seriously hurts company cash flows, then investors will seek to sell their securities. Consequently, the value of the security falls.

Moreover, if a company is exposed to significant risk, then some investors will be reluctant to buy its securities. Even before risk materialises, investors’ perceptions that a company’s future cash flows are uncertain or volatile will serve to reduce the value of its securities.

Most modern finance is based on the premise that investors seek to reduce the uncertainty of their future cash flows. By its very nature, risk increases the uncertainty of an asset’s future cash flow, and it therefore follows that such uncertainty will be priced into the market value of a security.

Investors consider risk only to the extent that it affects the value of the security. Risks can affect value by changing anticipations of cash flows or the rate at which these cash flows are discounted.

To begin with, it is important to realise that in corporate finance no fundamental distinction is made between the risk of asset revaluation and the risk of asset devaluation.

That is to say, whether investors expect the value of an asset to rise (upside) or decrease (downside) is immaterial.^{1} It is the fact that risk exists in the first place that is of significance and affects how investors behave.

Consider, for example, a security with the following cash flows expected for years 1 to 4:

Year | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Cash flow (in €) | 100 | 120 | 150 | 190 |

Imagine the value of this security is estimated to be €2,000 in five years. Assuming a 9% discounting rate, its value today would be:

If a sudden sharp rise in interest rates raises the discounting rate to 13%, the value of the security becomes:

The security’s value has fallen by 15% whereas cash flows have not changed.

However, if the company comes out with a new product that raises projected cash flow by 20%, with no further change in the discounting rate, the security’s value then becomes:

The security’s value increases for reasons specific to the company, not because of a fall of interest rates in the market.

Now, suppose that there is an improvement in the overall economic outlook that lowers the discounting rate to 10%. If there is no change in expected cash flows, the stock’s value would be:

Again, there has been no change in the stock’s intrinsic characteristics and yet its value has risen by 12%.

If there is stiff price competition, then previous cash flow projections will have to be adjusted downward by 10%. If all cash flows fall by the same percentage and the discounting rate remains constant, the value of the company becomes:

Once again, the security’s value decreases for reasons specific to the company, not because of a fall in the market.

In the previous example, a European investor would have lost 10% of their investment (from €2,009 to €1,808). If, in the interim, the euro had risen from $1.10 to $1.31, a US investor would have gained 7% (from $2,210 to $2,365).

A closer analysis shows that some securities are more volatile than others, i.e. their price fluctuates more widely. We say that these stocks are “riskier”. **The riskier a stock is, the more volatile its price, and vice versa.** Conversely, the less risky a security is, the less volatile its price, and vice versa.

Volatility can be measured mathematically by **variance** and **standard deviation**.

Typically, it is safe to assume that risk dissipates over the long term. The erratic fluctuations in the short term give way to the clear outperformance of equities over bonds, and bonds over money-market investments. The chart below tends to back up this point of view. It presents data on the **path of wealth** (POW) for the three asset classes. The POW measures the growth of €1 invested in any given asset, assuming that all proceeds are reinvested in the same asset.

As is easily seen from the chart, risk does dissipate, but only over the long term. In other words, an investor must be able to invest their funds and then do without them during this long-term timeframe. It sometimes requires strong nerves not to give in to the temptation to sell when prices collapse, as happened with stock markets in 1929, 1974, 2001, 2008, or 2011.

Since 1900, UK stocks have delivered an average annual return after inflation of 5.4%. Yet, during 39 of those years the returns were negative, in particular in 1974, when investors lost 57% on a representative portfolio of UK stocks.

And in worst-case scenarios, it must not be overlooked that some financial markets vanished entirely, including the Russian equity market after the 1917 revolution, the German bond market with the hyperinflation of 1921–1923, the Japanese and German equity markets in 1945, and the Chinese equity market in 1949. Over the stretch of one century, these may be exceptional events, but they have enormous repercussions when they do occur.

## Section 18.3 TOOLS FOR MEASURING RETURN AND RISK

### 1/ EXPECTED RETURN

To begin, it must be realised that a security’s rate of return and the value of a financial security are actually two sides of the same coin. The rate of return will be considered first.

**The holding-period return** is calculated from the sum total of cash flows for a given investment, i.e. income, in the form of interest or dividends earned on the funds invested and the resulting capital gain or loss when the security is sold.

If just one period is examined, then the return on a financial security can be expressed as follows:

Here, *F*_{1} is the income received by the investor during the period, *V*_{0} is the value of the security at the beginning of the period and *V*_{1} is the value of the security at the end of the period.

In an uncertain world, investors cannot calculate their returns in advance, as the value of the security is unknown at the end of the period. In some cases, the same is true for the income to be received during the period.

Therefore, investors use the concept of **expected return**, which is the average of possible returns weighted by their likelihood of occurring. Familiarity with the science of statistics should aid in understanding the notion of expected outcome.

Given security A with 12 chances out of 100 of showing a return of −22%, 74 chances out of 100 of showing a return of 6% and 14 chances out of 100 of showing a return of 16%, its expected return would then be:

More generally, expected return or expected outcome is equal to:

where *r*_{t} is a possible return and *p*_{t} the probability of it occurring.

### 2/ STANDARD DEVIATION, A RISK-ANALYSIS TOOL

Intuitively, the greater the risk on an investment, the wider the variations in its return, and the more uncertain that return is. While the holder of a government bond is sure to receive their coupons (unless the government goes bankrupt!), this is far from true for the shareholder of a biotech company. They could lose everything, show a decent return or hit the jackpot.

Therefore, the risk carried by a security can be looked at in terms of the dispersion of its possible returns around an average return. Consequently, risk can be measured mathematically by the variance of its return, i.e. by the sum of the squares of the deviation of each return from expected outcome, weighted by the likelihood of each of the possible returns occurring, or:

Standard deviation in returns is the most often used measure to evaluate the risk of an investment. Standard deviation is expressed as the square root of the variance:

The variance of investment A above is therefore:

where *V*(*r*) = 1%, which corresponds to a standard deviation of 10%.

## Section 18.4 MARKET AND SPECIFIC RISK

Risk in finance is materialised by fluctuation of value, which is equivalent to fluctuation of returns. Hence, one figure summarises all of the different risks, the knowledge of which does not really matter. Only the impact on value is important.

Fluctuations in the value of a security can be due to:

- fluctuations in the entire market. The market could rise as a whole after an unexpected cut in interest rates, stronger-than-expected economic growth figures, etc. All stocks will then rise, although some will move more than others. The same thing can occur when the entire market moves downward; or
- factors specific to the company that do not affect the market as a whole, such as a major order, the bankruptcy of a competitor, a new regulation affecting the company’s products, a scandal over fraud on product tests, discovering contaminated products, etc.

These two sources of fluctuation produce two types of risk: market risk and specific risk.

**Market, systematic or undiversifiable risk**is due to trends in the entire economy, tax policy, interest rates, inflation, etc. Remember, this is**the risk of the security correlated to market risk**. To varying degrees, market risk affects all securities. For example, if a nation switches to a 35-hour working week with no adjustment in wages, all companies will be affected. However, in such a case, it stands to reason that textile makers will be affected more than cement companies.**Specific, intrinsic or idiosyncratic risk**is independent of market-wide phenomena and is due to factors affecting just the one company, such as mismanagement, a factory fire, an invention that renders a company’s main product line obsolete, etc. (In the next chapter, it will be shown how this risk can be eliminated by diversification, a reason why this risk is also sometimes call diversifiable risk.)

Market volatility can be economic or financial in origin, but it can also result from anticipation of flows (dividends, capital gains, etc.) or a variation in the cost of equity. For example, an overheating of the economy could raise the cost of equity (i.e. after an increase in the central bank rate) and reduce anticipated cash flows due to weaker demand. Together, these two factors could exert a double downward pressure on financial securities.

Since market risk and specific risk are independent, they can be measured independently and we can apply Pythagoras’s theorem (in more mathematical terms, the two risk vectors are orthogonal) to the overall risk of a single security:

The systematic risk presented by a financial security is frequently expressed in terms of its sensitivity to market fluctuations. This is done via a linear regression between periodic market returns (*r*_{Mt}) and the periodic returns of each security *J*: *r*_{Jt}. This yields the regression line expressed in the following equation:

*β*_{J} is a parameter specific to each investment *J* and it expresses the relationship between fluctuations in the value of *J* and the market. It is thus a coefficient of volatility or of sensitivity. We call it the **beta** or the **beta coefficient**.

A security’s total risk is reflected in the standard deviation of its return, *s*(*r*_{J}).

A security’s **market risk** is therefore equal to *β*_{J} × σ(*r*_{M}), where σ(*r*_{M}) is the standard deviation of the market return. Therefore it is also proportional to the beta, i.e. the security’s market-linked volatility. The higher the beta, the greater the market risk borne by the security. If *β* >1, then the security’s returns move at a ratio of greater than 1:1 with respect to the market. Conversely, securities whose beta is below 1 are less affected by market fluctuations.

The **specific risk** of security *J* is equal to the standard deviation of the different residuals ε_{J} of the regression line, expressed as σ(ε_{J}), i.e. the variations in the stock that are not tied to market variations.

This can be expressed mathematically as follows:

## Section 18.5 THE BETA COEFFICIENT

### 1/ CALCULATING BETA

*β* measures a security’s sensitivity to market risk. For security *J*, it is mathematically obtained by performing a regression analysis of security returns versus market returns.

Hence:

Here, Cov(*r*_{J}, *r*_{M}) is the covariance of the return of security *J* with that of the market, and *V*(*r*_{M}) is the variance of the market return. This can be represented as:

More intuitively, *β* corresponds to the slope of the regression of the security’s return versus that of the market. The line we obtain is defined as the **characteristic line** of a security.

As an example, we have calculated the *β* for Orange and it stands at 0.61.

The *β* of Orange used to be higher in the late 1990s (1.83). The stock was more volatile than the market, its market risk was high. With the mobile telecom and Internet market maturing, the industry became less risky and the *β* of Orange is now 1, as shown in the following graph:

### 2/ PARAMETERS BEHIND BETA

By definition, the market *β* is equal to 1. *β* of fixed-income securities ranges from about 0 to 0.5. The *β* of equities is usually higher than 0.5, and normally between 0.5 and 1.5. We are not aware of any simple investment products with a negative *β*, and shares with a *β* greater than 2 are quite exceptional.

To illustrate, the table below presents betas, as of 2019, of the members of the Euro Stoxx 50 index:

Beta of the Eurostoxx 50 | |||||||||
---|---|---|---|---|---|---|---|---|---|

Linde | 0.47 | L’Oréal | 0.76 | SAP | 0.92 | Siemens | 1.07 | AXA | 1.21 |

Royal Ahold Delhaize | 0.59 | Inditex | 0.76 | AB InBev | 0.92 | Bayer | 1.10 | ASML | 1.27 |

Amadeus | 0.61 | Unilever | 0.77 | Vivendi | 0.92 | Telefonica | 1.12 | Volkswagen | 1.35 |

Danone | 0.68 | Eni | 0.79 | Deutsche Post | 0.97 | Philips | 1.12 | ING | 1.38 |

Deutsche Telekom | 0.68 | Adidas | 0.81 | Total | 0.97 | Daimler | 1.15 | BNP Paribas | 1.39 |

EssilorLuxottica | 0.69 | Unibail-Rodamco-Westfield | 0.82 | Fresenius | 1.01 | Airbus | 1.16 | Nokia | 1.40 |

Orange | 0.72 | Munich Re | 0.82 | Safran | 1.03 | LVMH | 1.17 | BBVA | 1.42 |

Sanofi | 0.72 | Vinci | 0.87 | Allianz | 1.03 | Kering | 1.18 | Société Générale | 1.46 |

Iberdrola | 0.75 | Engie | 0.88 | BMW | 1.06 | Schneider | 1.21 | Intesa Sanpaolo | 1.46 |

Enel | 0.75 | Air Liquide | 0.91 | BASF | 1.07 | CRH | 1.21 | Santander | 1.56 |

*Source*: Factset, 2019

For a given security, the following parameters explain the value of beta:

#### (a) Sensitivity of the stock’s sector to the state of the economy

The greater the effect of the state of the economy on a business sector, the higher its *β* is – temporary work is one such highly exposed sector. Another example is automakers, which tend to have a *β* close to 1. There is an old saying in North America, “As General Motors goes, so goes the economy”. This serves to highlight how GM’s financial health is to some extent a reflection of the health of the entire economy. Thus, beta analysis can show how GM will be directly affected by macroeconomic shifts.

#### (b) Cost structure

The greater the proportion of fixed costs to total costs, the higher the breakeven point, and the more volatile the cash flows. Companies that have a high ratio of fixed costs (such as cement makers) have a high *β*, while those with a low ratio of fixed costs (such as mass-market service retailers) have a low *β*.

#### (c) Financial structure

The greater a company’s debt, the greater its financing costs. Financing costs are fixed costs which increase a company’s breakeven point and, hence, its earnings volatility. The heavier a company’s debt or the more heavily leveraged the company is, the higher the *β* of its shares is.

#### (d) Visibility on company performance

The quality of management and the clarity and quantity of information the market has about a company will all have a direct influence on its beta. All other factors being equal, if a company gives out little or low-quality information, the *β* of its stock will be higher as the market will factor the lack of visibility into the share price.

#### (e) Earnings growth

The higher the forecast rate of earnings growth, the higher the *β*. Most of a company’s value in cash flows is far down the road and thus highly sensitive to any change in assumptions.

## Section 18.6 PORTFOLIO RISK

### 1/ THE FORMULA APPROACH

Consider the following two stocks, Heineken and Criteo, which have the following characteristics:

Heineken % | Criteo % | |
---|---|---|

Expected return: E(r) | 6 | 13 |

Risk: σ(r) | 10 | 17 |

As is clear from this table, Criteo offers a higher expected return while presenting a greater risk than Heineken. Inversely, Heineken offers a lower expected return but also presents less risk.

**These two investments are not directly comparable.** Investing in Criteo means accepting more risk in exchange for a higher return, whereas investing in Heineken means playing it relatively safe.

Therefore, there is no clear-cut basis by which to choose between Criteo and Heineken. However, the problem can be looked at in another way: **would buying a combination of Criteo and Heineken shares be preferable to buying just one or the other?**

It is likely that the investor will seek to diversify and create a **portfolio** made up of Criteo shares (in a proportion of *X*_{C}) and Heineken shares (in a proportion of *X*_{H}). This way, they will expect a return equal to the weighted average return of each of these two stocks, or:

where *X*_{C} + *X*_{H} = 1.

Depending on the proportion of Criteo shares in the portfolio (*X*_{C}), the portfolio would look like this:

X_{C} (%) | 0 | 25 | 33.3 | 50 | 66.7 | 75 | 100 |

E(r_{H,C}) (%) | 6 | 7.8 | 8.3 | 9.5 | 10.7 | 11.3 | 13 |

The portfolio’s variance is determined as follows:

where Cov(*r*_{H}, *r*_{C}) is the covariance. It measures the degree to which Heineken and Criteo fluctuate together. It is equal to:

Here, *p*_{i,j} is the probability of joint occurrence and ρ_{H,C} is the correlation coefficient of returns offered by Heineken and Criteo. The correlation coefficient is a number between −1 (where the correlation between returns on the two stocks will be perfectly negative) and 1 (where the correlation between returns on the two stocks will be perfectly positive). Correlation coefficients are usually positive, as most stocks rise together in a bullish market and fall together in a bearish market.

By plugging the variables back into our variance equation above, we obtain:

Given that:

it is therefore possible to say:

or:

Therefore, the overall risk of a portfolio consisting of Criteo and Heineken shares is less than the weighted average of the risks of the two stocks.

Assuming that ρ_{H,C} is equal to 0.5 (from the figures in the above example), we obtain the following:

X (%) | 0 | 25 | 33.3 | 50 | 66.7 | 75 | 100 |

σ(r_{H,C}) (%) | 10.0 | 10.3 | 10.7 | 11.8 | 13.3 | 14.2 | 17.0 |

Hence, a portfolio consisting of 50% Criteo and 50% Heineken has a standard deviation of 11.8% or less than the average of Criteo and Heineken, which is (50% × 17%) + (50% × 10%) = 13.5%.

On a chart, it looks like this:

Only a correlation coefficient of 1 creates a portfolio risk that is equal to the average of its component risks.

CORRELATION BETWEEN DIFFERENT STOCK MARKETS (2014–2019)

Brazil | China | France | Germany | Morocco | Switzerland | UK | United States | |
---|---|---|---|---|---|---|---|---|

Brazil | 1.00 | 0.30 | 0.68 | 0.67 | 0.82 | 0.38 | 0.72 | 0.90 |

China | 0.30 | 1.00 | 0.66 | 0.70 | 0.44 | 0.52 | 0.36 | 0.47 |

France | 0.68 | 0.66 | 1.00 | 0.97 | 0.78 | 0.69 | 0.82 | 0.84 |

Germany | 0.67 | 0.70 | 0.97 | 1.00 | 0.84 | 0.63 | 0.84 | 0.83 |

Morocco | 0.82 | 0.44 | 0.78 | 0.84 | 1.00 | 0.40 | 0.83 | 0.85 |

Switzerland | 0.38 | 0.52 | 0.69 | 0.63 | 0.40 | 1.00 | 0.54 | 0.46 |

UK | 0.72 | 0.36 | 0.82 | 0.84 | 0.83 | 0.54 | 1.00 | 0.77 |

United States | 0.90 | 0.47 | 0.84 | 0.83 | 0.85 | 0.46 | 0.77 | 1.00 |

*Source*: Data from Factset

Emerging markets still bring diversification and are more correlated among themselves than with developed countries.

However, sector diversification is still highly efficient thanks to the low correlation coefficients among different industries:

**CORRELATION BETWEEN ECONOMIC SECTORS WORLDWIDE (2014–2019)**

Sector | Banks | Automotive | Pharmaceuticals & Biotech | Oil & Gas | Construction | Softwares | Energy | Agriculture & Food chain | Retailing | Metals & Mining | Aerospace & Defence |
---|---|---|---|---|---|---|---|---|---|---|---|

Banks | 1.00 | 0.75 | 0.52 | 0.35 | 0.66 | 0.74 | 0.26 | 0.56 | 0.66 | 0.71 | 0.79 |

Automotive | 0.75 | 1.00 | 0.49 | 0.24 | 0.43 | 0.28 | 0.21 | 0.31 | 0.24 | 0.38 | 0.35 |

Pharmaceuticals & Biotech | 0.52 | 0.49 | 1.00 | −0.20 | 0.54 | 0.57 | −0.30 | 0.73 | 0.64 | 0.00 | 0.56 |

Oil & Gas | 0.35 | 0.24 | −0.20 | 1.00 | −0.25 | 0.04 | 0.99 | −0.25 | −0.03 | 0.79 | 0.11 |

Construction | 0.66 | 0.43 | 0.54 | −0.25 | 1.00 | 0.77 | −0.34 | 0,89 | 0,74 | 0,24 | 0.76 |

Softwares | 0.74 | 0.28 | 0.57 | 0.04 | 0.77 | 1.00 | −0.10 | 0.78 | 0.97 | 0.48 | 0.99 |

Energy | 0.26 | 0.21 | −0.30 | 0.99 | −0.34 | −0.10 | 1.00 | −0.36 | −0.16 | 0.72 | −0.02 |

Agriculture & Food chain | 0.56 | 0.31 | 0.73 | −0.25 | 0.89 | 0.78 | −0.36 | 1.00 | 0.78 | 0.15 | 0.76 |

Retailing | 0.66 | 0.24 | 0.64 | −0.03 | 0.74 | 0.97 | −0.16 | 0.78 | 1.00 | 0.36 | 0.95 |

Metals & Mining | 0.71 | 0.38 | 0.00 | 0.79 | 0.24 | 0.48 | 0.72 | 0.15 | 0.36 | 1.00 | 0.55 |

Aerospace & Defence | 0.79 | 0.35 | 0.56 | 0.11 | 0.76 | 0.99 | −0.02 | 0.76 | 0.95 | 0.55 | 1.00 |

*Source*: Data from Factset

## Section 18.7 CHOOSING AMONG SEVERAL RISKY ASSETS AND THE EFFICIENT FRONTIER

This section will address the following questions: why is it correct to say that the beta of an asset should be measured in relation to the market portfolio? Above all, what is the market portfolio?

To begin, it is useful to study the impact of the correlation coefficient on diversification. Again, the same two securities will be analysed: Criteo (C) and Heineken (H). By varying *ρ*_{H,C} between −1 and +1, we obtain:

Proportion of C shares in portfolio (X_{C}) (%) | 0 | 25 | 33.3 | 50 | 66.7 | 75 | 100 | |
---|---|---|---|---|---|---|---|---|

Return on the portfolio: E(r_{H,C}) (%) | 6.0 | 7.8 | 8.3 | 9.5 | 10.7 | 11.3 | 13.0 | |

Portfolio risk σ(r_{H,C}) (%) | ρ_{H,C} = −1 | 10.0 | 3.3 | 1.0 | 3.5 | 8.0 | 10.3 | 17.0 |

ρ_{H,C} = −0.5 | 10.0 | 6.5 | 6.2 | 7.4 | 10.1 | 11.7 | 17.0 | |

ρ_{H,C} = 0 | 10.0 | 8.6 | 8.7 | 9.9 | 11.8 | 13.0 | 17.0 | |

ρ_{H,C} = 0.3 | 10.0 | 9.7 | 10.0 | 11.1 | 12.7 | 13.7 | 17.0 | |

ρ_{H,C} = 0.5 | 10.0 | 10.3 | 10.7 | 11.8 | 13.3 | 14.2 | 17.0 | |

ρ_{H,C} = 1 | 10.0 | 11.8 | 12.3 | 13.5 | 14.7 | 15.3 | 17.0 |

Note the following caveats:

- If Criteo and Heineken were perfectly correlated (i.e. the correlation coefficient was 1), then diversification would have no effect. All possible portfolios would lie on a line linking the risk/return point of Criteo with that of Heineken. Risk would increase in direct proportion to Criteo’s stock added.
- If the two stocks were perfectly inversely correlated (correlation coefficient −1), then diversification would be total. However, there is little chance of this occurring, as both companies are exposed to the same economic conditions.
- Generally speaking, Criteo and Heineken are positively, but imperfectly, correlated and diversification is based on the desired amount of risk.

With a fixed correlation coefficient of 0.3, there are portfolios that offer different returns at the same level of risk. Thus, a portfolio consisting of two-thirds Heineken and one-third Criteo shows the same risk (10%) as a portfolio consisting of just Heineken, but returns 8.3% versus only 6% for Heineken.

There is no reason for an investor to choose a given combination if another offers a better (efficient) return at the same level of risk.

Efficient portfolios (such as a combination of Criteo and Heineken shares) offer investors the best risk–return ratio (i.e. minimum risk for a given return).

For any portfolio that does not lie on the **efficient frontier**, another can be found that, given the level of risk, offers a greater return or that, at the same return, entails less risk.

With a larger number of stocks, i.e. more than just two, the investor can improve their efficient frontier, as shown in the following chart.

## Section 18.8 CHOOSING BETWEEN SEVERAL RISKY ASSETS AND A RISK-FREE ASSET: THE CAPITAL MARKET LINE

### 1/ RISK-FREE ASSETS

By definition, **risk-free assets are those whose returns**, the risk-free rate (*r*_{F}), **are certain**. The standard deviation of their return is thus zero. Traditionally, this is illustrated with government bonds, although we can no longer assume that the government cannot go bankrupt, given the high levels of debt in many countries. This has now led us to view the 1-month Treasury bill as risk-free (e.g. the German bill for the Eurozone, the US Treasury bill for the US).

If a portfolio has a risk-free asset F in proportion (1 − *X*_{H}) and the portfolio consists exclusively of Heineken shares, then the portfolio’s expected return *E*(*r*_{H,F}) will be equal to:

The portfolio’s expected return is equal to the return of the risk-free asset, plus a risk premium, multiplied by the proportion of Heineken shares in the portfolio. The risk premium is the difference between the expected return on Heineken and the return on the risk-free asset.

How much risk does the portfolio carry? Its risk will simply be the risk of the Heineken stock, commensurate with its proportion in the portfolio, expressed as follows:

If investors want to increase their expected return, they will increase *X*_{H}. They could even borrow money at the risk-free rate and use the funds to buy Heineken stock, but the risk carried by their portfolio would rise commensurately.

By combining the previous two equations, we can eliminate *X*_{H}, thus deriving the following equation:

Continuing with the Heineken example, and assuming that *r*_{F} is 3%, with 50% of the portfolio consisting of a risk-free asset, the following is obtained:

Hence:

For a portfolio that includes a risk-free asset, there is a linear relationship between expected return and risk. To lower a portfolio’s risk, simply liquidate some of the portfolio’s stock and put the proceeds into a risk-free asset. To increase risk, it is only necessary to borrow at the risk-free rate and invest in a stock with risk.

### 2/ RISK-FREE ASSETS AND THE EFFICIENT FRONTIER

The risk–return profile can be chosen by combining risk-free assets and a stock portfolio (the alpha portfolio on the chart below). This new portfolio will be on a line that connects the risk-free rate to the portfolio alpha that has been chosen. But as we can observe on the chart, this portfolio is not the best portfolio. Portfolio P provides a better return for the same risk. Portfolio P is situated on the line tangential to the efficient frontier. There is no other portfolio than P that offers a better return for the same amount of risk-taking. What is portfolio P made up of? It’s made up of a combination of the portfolio of risky assets M (located on the efficient frontier at the tangential point with the line originating from the risk-free rate) and the risk-free asset.

Investors’ taste for risk can vary, yet the above graph demonstrates that the shrewd investor should be investing in portfolio M. It is then a matter of adjusting the risk exposure by adding or subtracting risk-free assets.

If all investors acquire the same portfolio, then this portfolio must contain all existing shares. To understand why, suppose that stock *i* was not in portfolio M. In that case, nobody would want to buy it, since all investors hold portfolio M. Consequently, there would be no market for it and it would cease to exist.

The weighting of stock *i* in a market portfolio will necessarily be the value of the single security divided by the sum of all the assets. As we are assuming fair value, this will be the fair value of *i*.

### 3/ CAPITAL MARKET LINE

The expected return of a portfolio consisting of the market portfolio and the risk-free asset can be expressed by the following equation:

where *E*(*r*_{P}) is the portfolio’s expected return, *r*_{F} the risk-free rate, *E*(*r*_{M}) the return on the market portfolio, σ_{P} the portfolio’s risk and σ_{M} the risk of the market portfolio.

This is the equation of the **capital market line**.

The most efficient portfolios in terms of return and risk will always be on the capital market line. The tangent point at M constitutes the optimal combination for *all* investors. If we introduce the assumption that all investors have **homogeneous expectations**, i.e. that they have the same opinions on expected returns and risk of financial assets, then the efficient frontier of risky assets will be the same for all of them. The capital market line is the same for all investors and thus each of them would hold a combination of the portfolio M and the risk-free asset.

It is reasonable to say that the portfolio M includes all the assets weighted for their market capitalisation. This is defined as the **market portfolio**. The market portfolio is the portfolio that all investors hold a fraction of, proportional to the market’s capitalisation.

## Section 18.9 HOW PORTFOLIO MANAGEMENT WORKS

The financial theory described so far seems to give a clear suggestion: in efficient markets, invest only in highly diversified mutual funds and in government bonds.

The asset management industry is one of the most important industries in the modern economy, managing €55,000bn worldwide (40% of this amount being invested in shares and 22% in bonds, the rest in short-term debts and multi-assets). Managers are employees of banks, insurance companies or independent.

However, as our readers know, not all investors subscribe to this theory. Some take other approaches, described below. Sometimes investors combine different approaches.

The strategy that is closest to financial theory is index tracking, also known as passive management. It consists of trying to follow the performance of a market index. **Index trackers** are ideal tools for the investor who believes strongly in market efficiency. They also benefit from scale effect and therefore have reduced operating costs. Index trackers can be listed on a market and are then called exchange-traded funds (ETFs). Most stock markets now have a specific market segment for the listing of trackers. Across global markets, over 7,845 trackers are listed for a total amount of over $8,331bn.

In terms of portfolio management, we shall consider the difference between a **top-down** and a **bottom-up** approach. In a top-down approach, investors focus on the asset class (shares, bonds, money-market funds) and the international markets in which they wish to invest (i.e. the individual securities chosen are of little importance). In a bottom-up approach (commonly known as stock-picking), investors choose stocks on the basis of their specific characteristics, not the sector in which they belong. The goal of the bottom-up approach is to find that rare pearl, i.e. the stock that is undervalued by the market, which is identified through fundamental analysis, a method of seeking the intrinsic value of a stock. Investors following this approach believe that sooner or later, market value will approach intrinsic value.

These stocks can be growth stocks, i.e. companies who are operating in a fast-growing industry; or value stocks, i.e. firms operating in more mature sectors but which offer long-term performance. At the opposite end you will find yield stocks whose return comes almost exclusively from the dividend paid, and their market price is then pretty stable.

Investors who focus on technical analysis, the so-called chartists, do not seek to determine the value of a stock. Instead, these investors conduct detailed studies of trends in a stock’s market value and transaction volumes in the hope of spotting short-term trends.

Another type of fund management has arisen since the mid-1990s, so-called **alternative management**, which gives itself total freedom of investment tools, whether listed or not: equities, bonds, currencies, commodities, etc., and of investment styles: buying, short selling, derivatives (see Chapter 23), heavy reliance on debt, and shareholder activism. Its objective is not to duplicate the performance of any index, but to obtain positive returns regardless of the state of the market and thus to offer additional diversification. An example of alternative management is the **hedge fund**, which is a speculative fund seeking high returns and relying heavily on derivatives, and options in particular. Hedge funds use leverage and commit capital in excess of their equity.

At the beginning of 2021, over 7,000 hedge funds were active in the world and had about $3,800bn under management.

In recent years, hedge funds’ risk-adjusted performance has been above that of traditional management, this even in bearish markets, with a relatively low correlation with other investment opportunities.

Hedge funds may present some restrictions on investing (minimum size). **Funds of funds** allow a larger number of investors to invest in hedge funds. The funds of funds pick up the best hedge fund managers and package their products to be offered to a wide number of investors.

Last but not least are private equity funds, which invest mainly in non-listed firms at different stages of maturity, via LBOs or otherwise (see Chapter 47). Their growing scope of investments is slowly turning them into an alternative to stock markets.

Regardless of the investment strategies and tools used, asset management is currently witnessing a rise in responsible investment, which applies environmental, social and governance (ESG, see Chapter 1) criteria to investment choices. Worldwide, approximately a third of assets under management are managed according to ESG criteria. This figure reaches 49% in Europe. Under the influence of the ultimate beneficiaries of these funds, and the conviction of a certain number of managers, responsible investment is becoming the norm, especially since in some countries regulations require managers to explicitly detail their policies with regards to ESG criteria.

Within this category, SRI (socially responsible investment, see Chapter 1) strategies focus on selecting the most advanced companies in terms of sustainable development.

## SUMMARY

## QUESTIONS

## EXERCISES

## ANSWERS

## BIBLIOGRAPHY

## NOTE

## Chapter 19. THE REQUIRED RATE OF RETURN

*A ship in a harbour is safe but that is not what ships are built for*

The previous chapter described the important concepts of risk, return and the market portfolio. It also highlighted the notion of risk premium (i.e. the difference between the return on the portfolio and the risk-free rate); this chapter continues to explore the risk premium in greater depth.

Investors must look at the big picture, first by investing in the market portfolio, then by borrowing or by investing in risk-free instruments commensurate with the level of risk they wish to assume. This approach allows them to assess an investment by merely determining the additional return and risk it adds to the market portfolio.

We now want to know how to get from *r* (the discounting rate used in calculating company value) to *k* (the return required by investors on a specific security).

Remember that this approach applies only if the investor owns a perfectly diversified portfolio.

Here is why: the greater the risk assumed by the financial investor, the higher their required rate of return. However, if they make just one investment and that turns out to be a failure, their required rate of return will matter little, as they will have lost everything.

With this in mind, it is easier to understand that the risk premium is relevant only if the financial investor manages not just a single investment, but a diversified portfolio of investments. In this case, the failure of one investment should be offset by the return achieved by other investments, which should thereby produce a suitable return for the portfolio as a whole.

This is the main difference between an industrial investment and a financial investment.

An entrepreneur who sets up their own company does not act like a financial investor, as they own just one investment. As their assets are not diversified, it is a matter of “life or death” for the firm that the investment succeeds. The law of averages in risk diversification does not apply to them.^{1}

The financial investor, on the other hand, needs portfolio management tools to estimate the risk–return on each of their investments. Portfolio theory is not the main objective here, but it is useful to introduce some basic notions with which financial managers must be familiar.

## Section 19.1 RETURN REQUIRED BY INVESTORS: THE CAPM

The CAPM (capital asset pricing model) was developed in the late 1950s and 1960s. Based on the work of Harry Markowitz, William Sharpe, John Lintner and Jack Treynor, it is now universally applied.

The CAPM is based on the assumption that investors act rationally and have at their disposal all relevant information on financial securities (see “efficient markets” in Chapter 15). Like the investor in Chapter 18, they seek to maximise their return, at a given level of risk.

The capital market line that we described in the previous chapter set the relationship for the return of a portfolio. CAPM aims at defining the same relationship but for a specific security (and not for a portfolio) in order to determine the return required for this security depending on its risk.

Remember that in order to minimise total risk, investors seek to reduce that component which can be reduced, i.e. the specific risk. They do so by diversifying their portfolios.

It can be observed that diversification reduces specific risk fairly quickly.

As a result, when stocks are fairly valued, investors will receive a return only on the portion of risk that they cannot eliminate – the market risk, or the non-diversifiable risk. Indeed, in a market in which arbitrage is theoretically possible, they will not be amply remunerated for a risk that they could otherwise eliminate themselves by simply diversifying their portfolios.

This means that the required rate of return (*k*) is equal to the risk-free rate *r*_{F},^{2} plus the risk premium for the non-diversifiable risk, i.e. the market risk.

This can be expressed as follows:

where *k*_{M} is the required rate of return for the market and *β* the sensitivity coefficient described previously.

Note that the coefficient *β* measures the non-diversifiable risk of an asset and not its total risk. So it is possible to have a stock that is, on the whole, highly risky but with a low *β* if it is only loosely correlated with the market.

The difference between the return expected on the market as a whole and the risk-free rate is called the **equity risk premium**.

Over the very long term (120 years!), the historical risk premium has been as follows:

Belgium | 3.0% | South Africa | 6.0% |

China (1993–2020) | 4.6% | Spain | 3.3% |

France | 5.5% | Switzerland | 3.9% |

Germany (exc. 1922/23) | 6.2% | US | 5.8% |

Italy | 5.6% | UK | 4.3% |

India | 6.1% | Europe | 3.5% |

Japan | 6.1% | World | 4.4% |

Russia (1995–2020) | 7.4% |

*Source*: Crédit Suisse Global Investment Returns Yearbook, 2021. Equity risk premium compared to short-term interest rates.

The equity risk premium can be historical or expected (or anticipated). The historical risk premium is equal to the annual performance of equity markets (including dividends) minus the risk-free rate. The expected risk premium is not directly observable. However, it can be calculated by estimating the future cash flows of all the companies, and then finding the discount rate that equates those cash flows with current share prices, from which we deduct the risk-free interest rate. This expected risk premium is the one used in the CAPM.

To determine the risk premium for each stock, simply multiply the market risk premium by the stock’s beta coefficient.

Hence, if the risk-free rate is –0.5% and the expected risk premium is 8.0%, a shareholder in the French car subcontractor Valeo will expect a return of –0.5% + 1.56 × 8.00% = 12.0%, if Valeo’s *β* is 1.56, while a shareholder in L’Oreal will expect –0.5% + 0.70 × 8.0% = 5.1%, as L’Oreal’s *β* is 0.70.

## Section 19.2 THE SECURITY MARKET LINE

The research house Associés en Finance publishes the securities market line^{3} for the entire eurozone. It is calculated on the basis of the **expected return** on the *y*-axis and the **beta coefficient of each stock** on the *x*-axis.

The securities market line is quite instructive. It helps determine the required rate of return on a security on the basis of the only risk that is remunerated, i.e. the market risk.

Shifts in the securities market line itself characterise the nature of changes in the markets and make it easier to understand them:

- a parallel shift, with no variation in slope (which represents the equity risk premium), reflects a change in interest rates. For example, a cut in interest rates normally leads to a downward shift and thus a general appreciation of all stocks;
- a non-parallel shift (or pivoting) reflects a change in the risk premium and thus in the remuneration of risk. In this case, the riskiest stocks will move the most, whereas the least risky stocks may not be significantly affected.

In addition, the position of points vis-à-vis the market line serves as a decision-making tool. The above chart tells us that Orange offers too high an expected return for its risk. Investors will realise this and buy it, thus raising its price and lowering expected return. A stock that is “above” the securities market line is thus undervalued, while a stock that is “below” the securities market line (like Adidas) is overvalued.

But do not rush to place an order. Since this chart was printed, prices have had plenty of time to adjust.

## Section 19.3 LIMITS OF THE CAPM

The CAPM assumes that markets are efficient and it is without a doubt the most widely used model in modern finance. But if we wanted to be facetious, we would say that each element of the CAPM poses a practical problem!

### 1/ THE LIMITS OF DIVERSIFICATION

The CAPM is a development of portfolio theory and is based on the assumption that diversification helps to reduce risk reducing it to the non-diversifiable risk. A study by Campbell *et al*. (2001) shows that diversification is increasingly complex and that nowadays a portfolio of at least 50 stocks is required to reduce risk significantly.

This is due, among other things, to the greater volatility of individual stocks, although markets as a whole are no more volatile. Other reasons for this phenomenon are the arrival on the market of riskier companies, such as biotech, Internet and younger companies, and the near extinction of conglomerates, which, by nature, provided some diversification in and of themselves.

Meanwhile, the correlation between market return and return on individual stocks is falling. This may undermine the relevancy of the CAPM. Statistically, beta is becoming less and less relevant.

### 2/ DIFFICULTIES IN PRACTICAL APPLICATION OF THE CAPM

The first difficulty one encounters when using the CAPM is determining the risk-free rate which, all things considered, is just a theoretical concept.

Practitioners usually use as a risk-free rate the yield of long-term government bonds. They put forward the similar weighted average duration of the cash flows of the assets to be valued and of long-term bonds. The issue is that long-term government bonds are not without risk: their value can fluctuate in time depending on changes in interest rates (which is inevitable given the long period of time since their issue). Even investors that plan to keep government bonds until their maturity suffer from these interest rate fluctuations for the reinvestment of coupons. In addition, unanticipated changes in inflation can impact what could have appeared as a risk-free investment. Finally, there remains the solvency risk of the issuer. The increasing levels of debt of most Western countries mean that this risk is not just theoretical, as demonstrated in recent years in Greece.

Therefore, it appears more rational to use as a risk-free rate the short-term interest rate. Short-term bills are virtually not impacted by changes in interest, coupon reinvestment risk does not exist and bankruptcy risk is minor. For the Eurozone, the risk-free rate could be assessed on the basis of the return on short-term German Treasury bills.

The three key global providers of equity market risk premium data (Ibbotson, Dimson-Marsh-Staunton and Associés en Finance) propose a computation of the market risk premium based on long-term interest rates or short-term interest rates. The most important factor is not to add a short-term interest rate to a market premium computed on the basis of long-term rates, or the reverse.

Roll (1997) has pointed out that determining a market portfolio is not as easy as one would like to think. In theory, the market portfolio is not solely made up of stocks or even just financial assets, but of all the assets that can be acquired. It is therefore impossible, in practice, to come up with a true market portfolio, especially when looking at it from an international point of view.

However, we still have to determine the return expected from the market portfolio. As the CAPM is used for making forecasts, it can also be used to calculate the return expected from a security based upon the return expected from the market portfolio, as well as the security’s anticipated risk (its *β*). However, “anticipated” data cannot be observed directly in the market, and so forecasts must be made on the basis of historical data and macroeconomic data. For some countries, such as emerging nations, this is not easy!

### 3/ THE INSTABILITY OF *β*

The main criticism of beta is its instability over time. It boils down a large amount of information into a single figure, and this strength becomes its weakness.

The CAPM is used to make forecasts. It can be used to calculate expected return on the basis of anticipated risk. Therefore, it would be better to use a forecast *β* rather than a historical value, especially when the coefficient is not stable over time.

For this reason, calculations must often be adjusted to reflect the regularity of earnings and dividends, and visibility on the sector. Blume *et al*. (1975) have sought to demonstrate a convergence of *β* towards 1. This seems counterintuitive to us as some sectors will always have a beta greater than 1. In addition, the recent crisis has demonstrated that, in difficult times, the gap between high *β* and low *β* increases.

### 4/ THE THEORETICAL LIMITS OF CAPM AND MARKETS AT FAIR VALUE

The CAPM assumes markets are fairly valued. But markets are not necessarily always at fair value. The fact that technical analysis has become so prominent on trading floors shows that market operators themselves have doubts about market efficiency (see Chapter 18).

Moreover, the theory of efficient markets in general, and the CAPM in particular, is based on the premise that market operators have rational expectations. To be applicable, the model must be accepted by everyone as being universally correct. The development of parallel theories shows that this is not necessarily the case.

The bias mentioned above has led the CAPM to be considered as just one theoretical explanation for the functioning of the financial markets. Other theories and methods have been developed, but they have not (yet?) achieved the attractiveness of the CAPM, due to the simplicity of its concepts. We should not lose hope: a study by Ferguson and Shockley (2003) posits that all weaknesses of the CAPM could be attributable to a mis-estimation of the market portfolio and that they would disappear if not only stocks, but also bonds (and other investment opportunities), were included, as the theory suggests.

## Section 19.4 MULTIFACTOR MODELS

### 1/ THE ARBITRAGE PRICING THEORY

In some ways the APT (arbitrage pricing theory) model is an extended version of the CAPM. The CAPM assumes that the return on a security is a function of its market risk and therefore depends on a single factor: market prices. The APT model, as proposed by Stephen Ross, assumes that the risk premium is a function of several variables, not just one, i.e. macroeconomic variables (*V*_{1}, *V*_{2},…, *V*_{n}) as well as company “noise”.

So, for security *J*:

The model does not define which *V* factors are to be used. Ross’s original article uses the following factors, which are based on quantitative analyses: inflation, manufacturing output, risk premium and yield curve.

Comparing the APT model to the market portfolio, we can see that APT has replaced the notion (hard to measure in practice) of return expected by the market with a series of variables which, unfortunately, must still be determined. This is why APT is a portfolio management tool and not a tool for valuing stocks.

### 2/ THE FAMA–FRENCH MODEL

There are offshoots from the APT that have sought to explain historical returns by company-specific factors rather than the general macroeconomic factors in the APT.

For example, Eugene Fama and Kenneth French (1992) have isolated three factors: market return (as in the CAPM), price/book value (see Chapter 31) and the gap in returns between large caps and small caps (which lends credence to the notion of a liquidity effect).

Other factors can be added to this list, including P/E, market capitalisation, yield and even past performance (which is a direct contradiction of efficient market theory). However, these are based on purely empirical approaches, not theoretical ones. While they criticise the CAPM, they offer no better alternative model.

### 3/ LIQUIDITY PREMIUM, SIZE PREMIUM AND INVESTOR PROTECTION

Among the factors used in determining risk, the criteria by which liquidity can be measured (size, free float, transaction volumes, bid–ask spread) are often statistically significant. In other words, the required return on a security often appears to be a function of liquidity.

Hamon and Jacquillat (1999) have demonstrated the existence of a liquidity premium in Europe, which is nil for large caps and significant for small caps. The liquidity premium should be added to the return derived from the CAPM to arrive at the total return expected by the shareholder. Hamon and Jacquillat use the term “market plane” (instead of securities market line). Under their model, expected return on a security is a linear equation with two parameters: the market premium and the liquidity premium. Let us report the definition from the original article:

In May 2020, Associés en Finance estimated the market plane parameters for eurozone stocks at:

The liquidity premium, which is expected in addition to the required rate of return, finds its opposite number in the notion of “liquidity discount”.

## Section 19.5 FRACTALS AND OTHER LEADS

The theory of a market in equilibrium is based on the assumption that prices have reached an equilibrium. It therefore assumes that there is an equilibrium between offer and demand and that it is reached at every moment on financial markets (thanks to the arbitrage principle). From this equilibrium, no one can predict how prices will move: they follow a random path.

Some research proposes that market prices do not follow random paths as the market in equilibrium theory predicts. In particular, extreme events (strong price growth or large drops) occur much more frequently than would be predicted by classical theory.

Several theories have been developed to model the evolution of prices and allow for possible massive price movements (in particular, crashes).

Some have tried to use chaotic functions to model prices. Chaotic here does not mean illogical or random. The term is used for perfectly predictable series of data that appear to be illogical. These models are used in a number of sciences, including economics.

Mandelbrot has put forward that fractals (or to be more precise, multi-fractals) could provide accurate representations of market price movements. This assumption does not fit with the efficient market theory, not only because the statistical rule for modelling prices is different, but more importantly because Mandelbrot’s assumptions imply that prices have memory, i.e. that they are not independent from past prices.

## Section 19.6 TERM STRUCTURE OF INTEREST RATES

Because it is a single-period model, the CAPM draws no distinction between short-term and long-term interest rates. As has been discussed, a money-market fund does not offer the same annual rate of return as a 10-year bond. An entire body of financial research is devoted to understanding movements in interest rates and, in particular, how different maturities are linked. This is the study of how the yield curve, which at a point in time relates the yield to maturity to the maturity (or duration) of bonds, is formed.

### 1/ THE VARIOUS YIELD CURVES

By charting the interest rate for the same categories of risk at all maturities, the investor obtains the yield curve that reflects the anticipation of all financial market operators.

The concept of premium helps explain why the interest rate of any financial asset is generally proportional to its maturity.

Generally speaking, the yield curve reflects the market’s anticipation regarding:

- long-term inflation;
- the central bank’s monetary policy; and
- the issuing country’s debt management policy.

Hence, during a period of economic recovery, the yield curve tends to be “normal” (i.e. long yields are higher than short yields). The steepness of the slope depends on:

- how strong an expected recovery is;
- what expectations the market has about the risk of inflation; and
- the extent to which the market expects a rapid increase in central banks’ intervention rates (to calm inflationary risks).

For the euro, the curve’s upward slope in 2021 is due to the extremely low (currently negative) levels reached by short-term rates, following European Central Bank (ECB) interventions to avoid a major economic downturn and to support the economy.

In contrast, when a recession follows a period of growth, the yield curve tends to reverse itself (with long-term rates falling below short-term rates). The steepness of the negative slope depends on:

- how strong expectations of recovery are;
- how credible the central bank’s policy is (i.e. how firm the central banks are in fighting inflation); and
- the extent to which inflationary trends appear to be diminishing (despite the recession, if inflationary trends are very strong then long-term rates will tend to remain stable, and the curve could actually be flat for some time).

This is what could be observed at the beginning of 2021 in relation to the dollar.

Lastly, when rates are low, the curve cannot remain flat for any length of time because investors will buy fixed-rate bonds. As long as investors expect that their capital gain, which is tied to falling long-term rates, is more than the cost of short-term financing, they will continue to purchase fixed-rate bonds. However, when long-term rates seem to have reached a lower limit, these expectations will disappear because investors will demand a differential between long-term and short-term rates’ yield on their investment. This results in:

- either a rebound in long-term rates; or
- stable long-term rates if short-term rates fall because of central bank policies; and
- a steepening in the curve, the degree of which will depend on the currency.

We then revert to the upward slope since the end of 2008 for the Swiss franc.

### 2/ RELATIONSHIP BETWEEN INTEREST RATES AND MATURITIES

By no means are short-term and long-term rates completely disconnected. In fact, there is a fundamental and direct link between them.

About 20 years ago, this relationship was less apparent and common consensus favoured the **theory of segmentation**, which said that supply and demand balanced out across markets, with no connection among them, i.e. the long-term bond market and the short-term bond market.

As seen above, this theory is generally no longer valid, even though each investor will tend to focus on their own timeframe. It is worthwhile reviewing the basic mechanisms. For example, an investor who wishes to invest on a two-year time basis has two options:

- invest for two years at today’s fixed rate, which is the interest rate for any two-year investment; or
- invest the funds for one year, is paid the one-year interest rate at the end of the year, and then repeat the process.

In a **risk-free environment**, these two investments would produce the same return, as the investor would already know the return that they would be offered on the market in one year for a one-year bond. As they also know the current one-year rate, they can determine the return on a two-year zero-coupon bond.

where _{0}*r*_{2} is the current two-year rate, _{1}*r*_{1} the one-year rate in one year and _{0}*r*_{1} the current one-year rate.

Hence:

If today the one-year interest rate is 3% and the two-year interest rate is 4%, this means that the market expects the one-year interest rate to reach 5% in one year, as

An increase in short-term rates is then anticipated by the market.

In such a world, the shape of the yield curve provides some valuable information. For example, if long-term rates are higher than short-term rates, this necessarily implies that investors are anticipating an increase in interest rates.

This theory assumes that investors are not sensitive to risk and therefore that there is no preference for a short-term or a long-term investment. This does not deal with the attention that investors pay to liquidity, as demonstrated by recent events on financial markets.

### 3/ TAKING LIQUIDITY INTO CONSIDERATION

The first theories to highlight the existence of a premium to reflect the relative lack of liquidity of long-term investments were the **preferred habitat theory** and the **liquidity preference theory**.

In the mid-1960s, Modigliani and Sutch advanced the theory of preferred habitat, which says that investors prefer certain investment timeframes. Companies that wish to issue securities whose timeframe is considered undesirable will thus have to pay a premium to attract investors.

The theory of liquidity preference is based on the same assumption, but goes further in assuming that the preferred habitat of all investors is the short term. Investors preferring liquidity will require a liquidity premium if they are to invest for the long term.

Even if investors anticipate fixed short-term rates, the yield curve will slope upward due to the liquidity premiums.

### 4/ YIELD CURVES AND VALUATION OF SECURITIES

After having studied the yield curve, it is easier to understand that the discounting of all the cash flows from a fixed-income security at a single rate, regardless of the period when they are paid, is an oversimplification, although this is the method that will be used throughout this text for stocks and capital expenditure. It would be wrong to use it for bonds.

In order to be more rigorous, it is necessary to discount each flow with the interest rate of the yield curve corresponding to its maturity: the one-year rate for next year’s income stream, the three-year rate for flows paid in three years, etc. Ultimately, yield to maturity is similar to an average of these different rates.

## SUMMARY

## QUESTIONS

## EXERCISES

## ANSWERS

## BIBLIOGRAPHY

## NOTES

- 1
*However, the very fact that the entrepreneur does not diversify their portfolio means that they must achieve strong performances in managing their company, as they have everything to lose. So they are likely to take steps to reduce risk*. - 2
*For the risk-free rate, k*_{F}*is equal to r*_{F}*. The required rate of return is equal to the return that is actually received, as the asset has no risk*. - 3
*It differs from the capital market line, which has the total risks of the security on the x-axis, not the β coefficient*.

## ****PART THREE. FINANCIAL SECURITIES

# There is a great variety of financial instruments, each of which has the following characteristics:

- it is a contract …
- … executed over time, and …
- its value derives solely from the series of cash flows it represents.

Indeed, from a mathematical and more theoretical viewpoint, a financial instrument is defined as a **schedule of future cash flows**.

Holding a financial security is the same as holding the right to receive the cash flows, as defined in the terms and conditions. Conversely, for the issuer, creating a financial instrument is the same as committing to paying out a series of cash flows. In return for this right to receive cash flows or for taking on this commitment, the company will issue a security at a certain price, enabling it to raise the funds needed to run its business.

You’ve undoubtedly heard people say that the financial manager’s stock-in-trade is “paper”. Digitalisation has now turned financial instruments from paper documents into intangible book entries, reducing them to the information they contain, i.e. the contract. The essence of finance is, and will always be, **negotiation** between an issuer seeking new funds and the investors interested in buying the instruments that represent the underlying obligations. And negotiation means markets, be they credit markets, bond markets, stock markets, etc.

Time, or the term of the financial security, introduces the notion of time remuneration and **risk**. A debt instrument that promises cash flows over time, for example, entails risk, even if the borrower is very creditworthy. This seems strange to many people who consider that “a deal is a deal” or “a person’s word is their bond”. Yet, experience has shown that a wide variety of risks can affect the payment of those cash flows, including political risk, strikes, natural disasters, pandemics and other events.

The financial logic that we have seen in the previous chapters is used to analyse and choose among a firm’s investment options. The financial manager transforms flows of goods and services, deriving from the company’s industrial and other business assets, into cash flows. You will soon understand that the world of finance is one of **managing rights on the one hand and commitments on the other, both expressed in terms of cash flows**.

In a market for financial instruments, it is not the actual flows that are sold, but the rights associated with them. The investor, i.e. the buyer of the security, acquires the rights granted by the instrument. The issuing company assumes contractual obligations deriving from the instrument, regardless of who the owner of the instrument is.

For example, commodity futures markets make it possible to perform purely financial transactions. You can buy sugar “forward”, via financial instruments called futures contracts, knowing full well that you will never take delivery of the sugar into your warehouse. Instead, you will close out the position prior to maturity. The financial manager thus trades on a market for real goods (sugar), using contracts that can be unwound prior to or at maturity.

A property investor acts similarly. After acquiring real property, the value of which fluctuates, they can lease it or resell it. Viewed this way, real property is as fungible as any other property and is akin to a financial asset.

Clearly, these assets exhibit different degrees of “financiality”. To take the argument one step further, you turn a painting into a financial instrument when you put it in your safe in the hope of realising a gain when you sell it.

The distinction between a real asset and a financial asset is therefore subtle but fundamental. It lies either in the nature of the contract or in the investor’s motivation, as in the example of the painting.

Lastly, the purchase of a financial security differs from the purchase of a durable good in that the financial security is undifferentiated. A large number of investors can buy the same financial security. In contrast, acquiring a specific office building or building an industrial plant is a very specific, unique investment.

## Chapter 20. BONDS

*Fixing the interest*

Unlike equity, for which shares are the legal form of the security, bank and financial debt can take the form of bank loans or debt securities. The predominant form of debt securities is a bond.

A debt security is a financial instrument representing the borrower’s obligation to the lender from whom they have received funds. If the initial maturity of the security is over one year, it will be called a bond.

This obligation provides for a schedule of cash flows defining the terms of repayment of the funds and the lender’s remuneration in the interval. The remuneration may be fixed during the life of the debt or floating if it is linked to a benchmark or index.

Unlike conventional bank loans, debt securities can be traded on secondary markets (stock exchanges, money markets, mortgage markets, interbank markets, over the counter (OTC) markets). Other than this, their logic remains the same and all the reasoning presented in this chapter also applies for bank loans. Debt securities are bonds, commercial paper, Treasury bills and notes, certificates of deposit and mortgage-backed bonds or mortgage bonds. Furthermore, the current trend is to securitise loans to make them negotiable.

Disintermediation was not the only factor fuelling the growth of bond markets. The increasing difficulty of obtaining bank loans was another, as banks realised that the interest margin on such loans did not offer sufficient return on equity. This pushed companies to turn to bond markets to raise the funds that banks had become reluctant to advance. The increasingly burdensome solvency and liquidity constraints imposed on banks (Basel III and IV) has increased the share of financing insured by the debt capital markets even further (see Chapter 39).

Investors have welcomed the emergence of corporate bonds offering higher yields than government bonds. Of course, these higher returns come at the cost of higher risks.

Many of the explanations and examples offered in this chapter deal with bonds, but they can easily be applied to all kinds of debt instruments. We shall take the example of the Ahold Delhaize 2030 bond issue with the following features:

## Section 20.1 BASIC CONCEPTS

### 1/ THE PRINCIPAL

#### (a) Nominal or face value

Loans that can be publicly traded are divided into a certain number of units giving the same rights for the same fraction of the debt. *The nominal, face or par value is €100,000 in the Ahold Delhaize case*.

The nominal value is used to calculate the interest payments. In the simplest cases (which is not the case for Ahold Delhaize), it equals the amount of money the issuer received for each bond and that the issuer will repay upon redemption.

#### (b) Issue price

The issue price is the price at which the bonds are issued; that is, the price investors pay for each bond. *The Ahold Delhaize bond was issued on 18 March 2021 at a price of €99,630, i.e. 99.63% of its face value*.

Depending on the characteristics of the issue, the issue price may be higher than the face value (issued at a premium), lower than the face value (issued at a discount) or equal to the face value (at par).

#### (c) Redemption

When a loan is amortised, it is said to be redeemed. In Chapter 17 we looked at the various ways a loan can be repaid:

- redemption at maturity, or on a bullet repayment basis.
*This is the case in the Ahold Delhaize issue*; - redemption in equal slices (or series), or constant amortisation;
- redemption in fixed instalments.

Other methods exist, such as determining which bonds are redeemed by lottery… there is no end to financial creativity!

A **deferred redemption period** is a grace period, generally at the beginning of the bond’s life, during which the issuer does not have to repay the principal.

The terms of the issue may also include provisions for **early redemption** (call options) or retraction (put options). A call option (see Chapter 23) gives the issuer the right to buy back all or part of the issue prior to the maturity date, while a put option allows the bondholder to demand early repayment.

A **redemption premium or discount** arises where the redemption value is higher or lower than the nominal value.

#### (d) Maturity of the bond

The life of a bond extends from its issue date to its final redemption date. Where the bond is redeemed in several instalments, the **average maturity** of the bond corresponds to the average of each of the repayment periods.

*The Ahold Delhaize bonds have a maturity* of nine years.

#### (e) Guarantees

Repayment of the principal (and interest) on a bond borrowing can be guaranteed by the issuer, the parent company and less often for corporates by collateral (i.e. mortgages), pledges or warranties. Bonds are rarely secured, while commercial paper and certificates of deposit can, in theory, be secured but in fact never are.

*The bonds issued by Ahold Delhaize do not benefit from a guarantee*.

### 2/ INCOME

#### (a) Issue date

The issue date is the date on which interest begins to accrue. It may or may not coincide with the **settlement date**, when investors actually pay for the bonds purchased.

*In the case of the Ahold Delhaize bond, these two dates coincide. Interest begins to accrue on the settlement date*.

#### (b) Interest rate

The coupon or nominal rate is used to calculate the interest (or coupon, in the case of a bond) payable to the lenders. Interest is calculated by multiplying the nominal rate by the nominal or par value of the bond.

*On the Ahold Delhaize issue, the coupon rate is 0.375% and the coupon payment is €375*. However, if Ahold Delhaize did not reduce its carbon emissions by 29% between 2018 and 2025 (scope 1 and 2) and its food waste (discarded food) by 32% between 2016 and 2025, then the annual coupon would increase to €625. This provision makes this bond a sustainable one.

In addition to coupon payments, investors may also gain additional remuneration if the issue price is lower than the par value (*which is the case for Ahold Delhaize*). This is the issuance premium. If the issue price is higher than the par value, the lender’s return will be lower than the coupon rate.

#### (c) Periodicity of coupon payments

Coupon payments can be made every year, half-year, quarter, month or even more frequently. On certain borrowings, the interval is longer, since the total compounded interest earned is paid only upon redemption. Such bonds are called **zero-coupon bonds**.

In some cases, the interest is **prepaid**; that is, the company pays the interest at the beginning of the period to which it relates. In general, however, the **accrued** interest is paid at the end of the period to which it relates.

*The Ahold Delhaize issue pays accrued interest on an annual basis*.

## Section 20.2 THE YIELD TO MATURITY

The actual return on an investment (or the cost of a loan for the borrower) depends on a number of factors: the difference between the settlement date and the issue date, the issue premium/discount, the redemption premium/discount, the deferred redemption period and the coupon payment interval. As a result, the nominal rate is not very meaningful.

We have seen that the **yield to maturity** (Chapter 17) cancels out the bond’s present net value; that is, the difference between the issue price and the present value of future flows on the bond. **Note that for bonds, the yield to maturity ( y) and the internal rate of return are identical.** This yield, calculated on the settlement date when investors pay for their bonds, takes into account any timing differences between the right to receive income and the actual cash payment.

*In the case of the Ahold Delhaize bond issue*:

i.e. *y* = 0.417%. The yield to maturity, before taxation and intermediaries’ fees, represents:

**for investors**, the rate of return they would receive by holding the bonds until maturity, assuming that the interest payments are reinvested at the same yield to maturity, which is a very strong assumption;**for the issuer**, the pre-tax actuarial cost of the loan.

From the point of view of the investor, the bond schedule must take into account intermediation costs and the tax status of the income earned. For the issuer, the gross cost to maturity is higher because of the commissions paid to intermediaries. This increases the actuarial cost of the borrowing. In addition, the issuer pays the intermediaries (**paying agents**) in charge of paying the interest and reimbursing the principal (generally between 0.2 and 0.4% on the Euro Investment Grade market). Lastly, the issuer can deduct the coupon payments in whole or in part to compute its corporate income tax, thus reducing the actual cost of the loan.

### 1/ SPREADS

The spread is the difference between the rate of return on a bond and that on a benchmark used by the market. In the eurozone, the benchmark for long-term debt is most often the interest rate swap (IRS) rate^{1}; sometimes the spread to government bond yields is also mentioned. For floating-rate bonds and bank loans (which are most often with floating rates), the spread is measured to a short-term rate, the three- or six-month Euribor in the eurozone.

*The Ahold Delhaize bond was issued with a spread of 41 basis points (0.41%) to mid swap rate, meaning that Ahold Delhaize had to pay 0.41% more per year than the risk-free rate to raise funds*.

The spread is a key parameter for valuing bonds, particularly at the time of issue. It depends on the perceived credit quality of the issuer and the maturity of the issue, which are reflected in the credit rating and the guarantees given. Spreads are, of course, a relative concept, depending on the bonds being compared. The stronger the creditworthiness of the issuer and the market’s appetite for risk, the lower the margin will be.

### 2/ THE SECONDARY MARKET

Once the subscription period is over, the price at which the bonds were sold (their issue price) becomes a thing of the past. The value of the instrument begins to fluctuate on the secondary market. Consequently, the yield to maturity published in the prospectus applies only at the time of issue; after that, it fluctuates in step with the value of the bond. Note that, as with equity issues, there is usually a small increase in the price of bonds just after they are issued (the price is said to be tightening). New issues usually offer a small yield premium (new issue premium)

Theoretically, changes in the bond’s yield to maturity on the secondary market do not directly concern the borrower, since the cost of the debt was fixed when it was contracted.

For the borrower, the yield on the secondary market is merely an **opportunity cost**; that is, the **cost of refunding** for issuing new bonds. It represents the “real” cost of debt, but is not shown in the company accounts where the debt is recorded at its historical cost, regardless of any fluctuations in its value on the secondary market. The market value of debt can only be found in the notes to IFRS accounts.

### 3/ LISTING TECHNIQUES

The price of bonds listed on stock markets is expressed as a percentage of the nominal value. In fact, they are treated as though the nominal value of each bond were €100. Thus, a bond with a nominal value of €50,000 will not be listed at €49,500 but at 99% (49,500 / 50,000 × 100). Similarly, a bond with a nominal value of €10,000 will be listed at 99%, rather than €9,900. This makes it easier to compare bond prices.

For the comparison to be relevant, the prices must not include the fraction of annual interest already accrued. Otherwise, the price of a bond with a 5% coupon would be 105 just before its coupon payment date and 100 just after. This is why bonds are quoted **net of accrued interest**. Bond tables thus show both the price expressed as a percentage of the nominal value and the fraction of accrued interest, which is also given as a percentage of the nominal value.

*On 5 May 2021, the Ahold Delhaize bond traded at 99.2% with 0.042% accrued interest. Buying the Ahold Delhaize bond then would have cost (excl. any trading fee or tax) €99,242: €100,000* × *(99.2% + 0.042%)*.

Certain debt securities, mainly fixed-rate Treasury notes with annual interest payments, are quoted at their yield to maturity.

By now you have probably realised that the price of a bond does not reflect its actual cost. A bond trading at 105% may be more or less expensive than a bond trading at 96%. **The yield to maturity is the most important criterion, allowing investors to evaluate various investment opportunities according to the degree of risk they are willing to accept and the length of their investment.** However, it merely offers a temporary estimate of the **promised** return; this may be different from the **expected** return, which incorporates the probability of default of the bond.

### 4/ FURTHER ISSUES AND ASSIMILATION

Having made one bond issue, the same company can later issue other bonds (informally, this is called a **tap issue**) with the same features (time to maturity, coupon rate, coupon payment schedule, redemption price and guarantees, etc.), so that they are interchangeable. This enables the various issues to be grouped as one for a larger total amount. Assimilation makes it possible to reduce administrative expenses and enhance liquidity on the secondary market.

Nevertheless, the drawback for the issuer is that it concentrates maturity on one date, which is not in line with sound financial policy.

Bonds assimilated are issued with the same features as the bonds with which they are interchangeable. The only difference is in the issue price,^{2} which is shaped by market conditions that are very likely to have changed since the original issue.

## Section 20.3 FLOATING-RATE BONDS

So far we have looked only at fixed-income debt securities. The cash flow schedule for these securities is laid down clearly when they are issued. These are very popular in periods of low interest rates, and currently represent 84% of euro-denominated bond issues. Let us now cover the various securities that give rise to cash flows that are not totally fixed from the very outset, but follow preset rules (10% of all bond issuances in 2020).

### 1/ THE MECHANICS OF THE COUPON

The coupon of a floating-rate bond (floating rate note, FRN or “floats”) is not fixed, but is indexed to an observable market rate, generally a short-term rate, such as a six-month Euribor. In other words, the coupon rate is periodically reset based on some reference rate plus a spread. When each coupon is presented for payment, its value is calculated as a function of the market rate, based on the formula:

This cancels out the interest rate risk, since the issuer of the security is certain of paying interest at exactly the market rate at all times. Likewise, the investor is assured at all times of receiving a return in line with the market rate. Consequently, there is no reason for the price of a variable-rate bond to move very far from its par value unless the issuer’s solvency changes.

### 2/ INDEX-LINKED SECURITIES

Floating rates, as described in the first paragraph of this section, are indexed to a market interest rate. Broadly speaking, however, a bond’s coupons may be indexed to any index or price provided that it is clearly defined from a contractual standpoint. Such securities are known as **index-linked securities**.

For instance, most European countries have issued bonds indexed to inflation. The coupon paid each year, as well as the redemption price, is reset to take into account the rise in the price index since the bond was launched. As a result, the investor benefits from complete protection against inflation. Likewise, Mexican companies have brought to market bonds linked to oil prices, while other companies have issued bonds indexed to their own share price.

The following table shows the main reference rates in Europe.

**REFERENCE RATES IN EUROPE**

Reference rate | Definition | As at April 2021 |
---|---|---|

EONIA (Euro Overnight Index Average) | Traditional European money-market rate. Since end 2019 it is computed as €STR +8.5 basis points. It should disappear end 2021 and be replaced by €STR. | −0.42% |

€STR (European Short-Term Rate) | The new European money-market rate that replaces EONIA. It is an interest rate computed based on real loans and not only declared loans as was EONIA. | –0.56% |

EURIBOR (European Interbank Offered Rate) | European money-market rate corresponding to the arithmetic mean of offered rates on the European banking market for a given maturity (between 1 week and 12 months). Sponsored by the European Banking Federation and published by Reuters, it is based on daily quotes provided by 43 European banks. | −0.53% (3 months) |

LIBOR (London Interbank Offered Rate) | Money-market rate observed in London corresponding to the arithmetic mean of offered rates on the London banking market for a given maturity (between 1 and 12 months) and a given currency (euro, sterling, dollar, etc.). It will be replaced in 2021/2022 by ECB RFR (€), SONIA (£) and SOFR ($). | −0.54% (euro 3 months) |

IRS | The IRS rate indicates the fixed interest rate that will equate the present value of the fixed-rate payments with the present value of the floating-rate payments in an interest rate swap contract. The convention in the market is for the swap market makers to set the floating leg – normally at Euribor – and then quote the fixed rate that is payable for that maturity. |

## Section 20.4 GREEN AND SOCIALLY RESPONSIBLE BONDS

Responsible bonds include three categories of bonds that are, in terms of their financial flows, conventional bonds, but which incorporate ESG aspects.

The issuer of green bonds commits to use the funds for environmentally positive investments or expenditures (as defined by the company, usually assisted by an independent firm).

Tracking expenditure and allocating a funding source to a particular job requires a specific organisation that is unusual for finance management. This organisation has a cost. However, as investors have been willing to buy green bonds at a slightly higher price than a conventional bond since autumn 2020, the so-called greenium, the extra cost is more or less offset for companies. Green bonds are, even if companies sometimes deny it, a communication tool but also a means of internal mobilisation. Paradoxically, many green bond issuers operate in industries whose ecological character is not immediately obvious: energy (EDF, Engie), automotive (Toyota). Some have therefore launched the concept of transition bonds, which are bonds that specifically finance the energy transition.

The volume of green bond issues is growing very quickly, but remains modest (€265bn in 2020) compared to the bond market (around 5%).

Social bonds finance projects with a social connotation. For example, Icade issued a €600m social bond in 2020 to facilitate access to healthcare for all. This is a €130bn market where the share of companies is structurally low (a few billion euros of issues per year).

Since the autumn of 2020, sustainable bonds (or sustainability-linked bonds, SLBs) have experienced very strong growth driven by companies that, because of their sector of activity, do not necessarily have investments to make in the energy transition or quantifiable social objectives requiring heavy investments. In contrast to green or social bonds, which are qualified as such because of the use of funds, sustainable bonds can be used for any purpose. Their sustainability comes from the interest rate they pay to lenders, which can be increased if they do not meet quantified ESG targets, normally ambitious ones, that they have set themselves: reducing greenhouse gas emissions, increasing recycling, switching to 100% renewable electricity, increasing the proportion of women in management teams, training disadvantaged people in energy management, etc. Ahold Delhaize’s obligation is a sustainable obligation.

As with green bonds, the green premium (the greenium) increases, making this form of financing cheaper than a conventional bond, at least as long as the company is able to meet its ESG objectives. The relatively small sustainable bond market (around €70bn in 2020) will clearly continue to grow strongly in the future and could become the norm for companies.

As evidence of the growth of this market, the principles of these issues are now standardised in the Green Bonds Principles (GBP), the Social Bond Principles (SBP) and the Sustainability-Linked Bond Principles (SLBP).

## Section 20.5 THE VOLATILITY OF DEBT SECURITIES

The holder of a debt security may have regarded themself as protected having chosen this type of security, but they actually face three types of risk:

**interest rate risk**and**coupon reinvestment risk**, which affect almost solely fixed-rate securities;**credit risk**, which affects fixed-rate and variable-rate securities alike. We will consider this at greater length in the following section.

### 1/ CHANGES IN THE PRICE OF A FIXED-RATE BOND CAUSED BY INTEREST RATE FLUCTUATIONS

#### (a) Definition

What would happen if, at the end of the subscription period for the Ahold Delhaize 0.375% bond, the market interest rate rose to 0.875% (scenario 1) or fell to 0% (scenario 2)? In the first scenario, the bondholder would obviously attempt to sell the Ahold Delhaize bond to buy securities yielding 0.875%. The price of the bond would fall such that the bond offered its buyer a yield to maturity of 0.875%. Conversely, if the market rate fell to 0%, holders of the Ahold Delhaize bond would hold onto their bonds, which yield 0.375%, while the market interest rate for the same risk level is now 0%. Other investors would attempt to buy them, and the price of the bond would rise to a level at which the bond offered its buyer a yield to maturity of 0%.

An upward (or downward) change in interest rates therefore leads to a fall (or rise) in the present value of a fixed-rate bond, irrespective of the issuer’s financial condition.

As we have seen, if the yield on our Ahold Delhaize bond is 0.375%, its price is 100%.

But if its yield to maturity rises to 0.875% (a 0.5 point increase or 50 basis points), its price will change to:

i.e. a decrease of 4.3%. This shows that holders of bonds face a risk to their capital, and this risk is by no means merely theoretical, given the fluctuations in interest rates over the medium term.

#### (b) Measures: modified duration and convexity

The modified duration of a bond measures the percentage change in its price for a given change in interest rates. The price of a bond with a modified duration of 4 will increase by 4% when interest rates fall from 7% to 6%, while the price of another bond with a modified duration of 3 will increase by just 3%.

From a mathematical standpoint, modified duration can be defined as the absolute value of the first derivative of a bond’s price with respect to interest rates, divided by the price:

where *r* is the market rate and *F*_{t} the cash flows generated by the bond.

Turning back to the example of the Ahold Delhaize bond at its issuance date, we arrive at a modified duration of 8.83.

Modified duration is therefore a way of calculating the percentage change in the price of a bond for a given change in interest rates. It simply involves multiplying the change in interest rates by the bond’s modified duration. A rise in interest rates from 0.375% to 0.875% therefore leads to a price decrease of 0.5% × 8.83 = 4.41%, i.e. from 100% to 100 × (1 − 4.41%) = 95.59%.

We note a discrepancy of 0.101% with the price calculated previously (95.691%). Modified duration is valid solely at the point where it is calculated (i.e. 0.417% here). The further we move away from this point, the more skewed it becomes. For instance, at a yield of 0.875% it is 8.79 rather than 8.83. This will skew calculation of the new price of the bond, but the distortion will be small if the fluctuation in interest rates is also limited in size. From a geometrical standpoint, the modified duration is the first derivative of price with respect to interest rates and it reflects the slope of the tangent to the price/yield curve. Since this forms part of a hyperbolic curve, the slope of the tangent is not constant and moves in line with interest rates.

#### (c) Parameters influencing modified duration

Let’s consider the following three bonds:

Bond | A | B | C |
---|---|---|---|

Coupon | 5% | 5% | 0% |

Price | 100 | 100 | 100 |

Yield to maturity | 5% | 5% | 5% |

Redemption price | 100 | 100 | 432.2 |

Residual life | 5 years | 15 years | 30 years |

How much are these bonds worth in the event of interest rate fluctuations?

Market interest rates (%) | A | B | C |
---|---|---|---|

1 | 119.4 | 155.5 | 320.7 |

5 | 100 | 100 | 100 |

10 | 81.0 | 62.0 | 24.8 |

15 | 66.5 | 41.5 | 6.5 |

Note that the **longer the maturity of a bond, the greater its sensitivity to a change in interest rates**.

Modified duration is primarily a function of the maturity date. **The closer a bond gets to its maturity date, the closer its price moves towards its redemption value and the more its sensitivity to interest rates decreases.** Conversely, the longer it is until the bond matures, the greater its sensitivity to interest rate fluctuations.

Modified duration also depends on two other parameters, which are nonetheless of secondary importance to the time-to-maturity factor:

**the bond’s coupon rate**: the lower the coupon rate, the higher its modified duration;**market rates**: the lower the level of market rates, the higher a bond’s modified duration.

Modified duration represents an investment tool used systematically by fixed-income portfolio managers. If they anticipate a decline in interest rates, they opt for bonds with a higher modified duration, i.e. a longer time to maturity and a very low coupon rate, or even zero-coupon bonds, to maximise their capital gains.

Conversely, if portfolio managers expect a rise in interest rates, they focus on bonds with a low modified duration (i.e. due to mature shortly and carrying a high coupon) in order to minimise their capital losses.

**Convexity** is the second derivative of price with respect to interest rates. **It measures the relative change in a bond’s modified duration for a small fluctuation in interest rates.** Convexity expresses the speed of appreciation or the sluggishness of depreciation in the price of the bond if interest rates decline or rise.

### 2/ COUPON REINVESTMENT RISK

As we have seen, the holder of a bond does not know at what rate its coupons will be reinvested throughout the bond’s lifetime. Only zero-coupon bonds afford protection against this risk, simply because they do not carry any coupons!

First of all, note that this risk factor is the mirror image of the previous one. If interest rates rise, then the investor suffers a capital loss but is able to reinvest coupon payments at a higher rate than the initial yield to maturity. Conversely, a fall in interest rates leads to a loss on the reinvestment of coupons and to a capital gain.

Intuitively, it seems clear that for any fixed-income debt portfolio or security, there is a period over which:

- the loss on the reinvestment of coupons will be offset by the capital gain on the sale of the bond if interest rates decline;
- the gain on the reinvestment of coupons will be offset by the capital loss on the sale of the bond if interest rates rise.

All in all, once this period ends, the overall value of the portfolio (i.e. bonds plus reinvested coupons) is the same, and the investors will have achieved a return on investment identical to the yield to maturity indicated when the bond was issued.

In such circumstances, the portfolio is said to be **immunised**, i.e. it is protected against the risk of fluctuations in interest rates (capital risk and coupon reinvestment risk). This time period is known as the **duration** of a bond. It may be calculated at any time, either at issue or throughout the whole life of the bond.

For instance, an investor who wants to be assured of achieving a certain return on investment over a period of three years will choose a portfolio of debt securities with a duration of three years.

Note that the duration of a zero-coupon bond is equal to its remaining life.

In mathematical terms, duration is calculated as follows:

Duration can be regarded as being akin to the discounted average life of all the cash flows of a bond (i.e. interest and capital). The numerator comprises the discounted cash flows weighted by the number of years to maturity, while the denominator reflects the present value of the debt.

*The Ahold Delhaize bond has a duration of 8.86 years at issue*.

*We can see that 8.83 × (1 + 0.417%) = 8.86 years*.

Turning our attention back to modified duration, we can say that it is explained by the duration of a bond, which brings together in a single concept the various determinants of modified duration, i.e. time to maturity, coupon rate and market rates.

## Section 20.6 DEFAULT RISK AND THE ROLE OF RATING

Default risk can be measured on the basis of a traditional financial analysis of the borrower’s situation or by using credit scoring, as we saw in Chapter 8. Specialised agencies, which analyse the risk of default, issue ratings that reflect the quality of the borrower’s signature. There are three agencies that dominate the market – Standard & Poor’s, Moody’s and Fitch – but with the rise of a debt capital market for mid-sized companies, new rating agencies have emerged (e.g. Spread Research, Scope Credit Rating, or Egan-Jones).

Rating agencies provide ratings for companies, banks, sovereign states and municipalities. They can decide to rate a specific issue or to give an absolute rating for the issuer (rating given to first-ranking debt). Rating agencies also distinguish between short- and long-term prospects.

Some examples of short-term debt ratings:

Moody’s | Standard & Poor’s and Fitch | Definition | Examples (May 2021) |
---|---|---|---|

Prime 1 | A–1 | Superior ability to meet obligations | Sanofi, Nestlé, France |

Prime 2 | A–2 | Strong ability to repay obligations | Iberdrola, Deutsche Bank |

Prime 3 | A–3 | Acceptable ability to repay obligations | Morocco, ArcelorMittal |

Not Prime | B | Speculative | Senegal, Lufthansa |

C | Vulnerable | Argentina | |

D | Insolvent | Venezuela, Lebanon |

Some examples of long-term debt ratings:

Moody’s | Standard & Poor’s and Fitch | Definition | Examples (May 2021) |
---|---|---|---|

Aaa | AAA | Best quality, lowest risk | Germany, Australia Johnson & Johnson, Microsoft |

Aa | AA | High quality. Very strong ability to meet payment obligations | Nestlé, Sanofi, Apple, France |

A | A | Upper-medium grade. Issuer has strong capacity to meet its obligations | BASF, BNP Paribas, LVMH, Unilever |

Baa | BBB | Medium grade. Issuer has satisfactory capacity to meet its obligations | Morocco, Italy, Telefónica, Pernod Ricard |

Ba | BB | Speculative. Uncertainty of issuer’s capacity to meet its obligations | Renault, Attijariwafa Bank, Vietnam |

B | B | Issuer has poor capacity to meet its obligations | Casino, Pakistan |

Caa | CCC | Poor standing. Danger with respect to payment of interest and return of principal | CGG, Democratic Republic of Congo |

Ca | CC | Highly speculative. Often in default | Belize |

C | C | Close to insolvency | |

D or SD | Insolvent! | Vallourec, Lebanon |

Rating services also add an **outlook** to the rating they give – stable, positive or negative – which indicates the likely trend of the rating over the two to three years ahead.

Short- and medium-term ratings may be modified by a + or − or a numerical modifier, which indicates the position of the company within its generic rating category. This is referred to as a *notch*, such as between AA– and A+. The **watchlist** alerts investors that an event such as an acquisition, disposal or merger, once it has been weighed into the analysis, is likely to lead to a change in the rating. A company on the watchlist is likely to be upgraded when the expected outcome is positive, downgraded when the expected outcome is negative and, when the agency is unable to determine the outcome, it indicates an unknown change.

The term *split rating* is used when several rating agencies evaluate the same company and do not give equivalent ratings (Ba+ and BBB– for example).

Ratings between AAA and BBB− are referred to as **investment grade**, and those between BB+ and D as **speculative grade** (or **non-investment grade**). The distinction between these two types of risk is important to investors, especially institutional investors, who often are not permitted to buy the risky speculative grade bonds!

Bonds at the edge of the investment grade frontier, rated BB+/BB are called crossover bonds. This is an intermediate category that links the investment grade and non-investment grade categories. Depending on the state of the market, the definition of cross-over can vary and even include companies rated BB– in well-oriented markets.

In Europe, rating agencies generally rate companies at their request, which enables them to access privileged information (medium-term plans, contacts with management). Rating agencies very rarely rate companies without management cooperation. When they do, the accuracy of the rating depends on the quality of the information about the company available on the market. If the company does not require a public rating immediately (or if it does not like the rating allocated!), it may request that it be kept **confidential**, and it is then referred to as a *shadow rating*. The cost for a firm to get a first rating is quite high (over €500,000 on average, to which should be added an annual cost of over €100,000).

The rating process, which can take up to three months, differs from the scoring process as it is not only a quantitative analysis. The agency will also take into account:

- the size of the company
- the positioning of the company in its sector;
- the analysis of the financial data;
- the current capital structure but also the financing strategy.

Most rating agencies have developed teams capable of assessing the ESG aspects of an issuer or bond, or even acquired specialised agencies such as Vigeo Eiris acquired by Moody’s.

## SUMMARY

## QUESTIONS

## EXERCISES

## ANSWERS

## BIBLIOGRAPHY

## NOTES

## Chapter 21. OTHER DEBT PRODUCTS

*Back to flows and financial analysis*

The “mathematics” we studied in Chapters 16 and 17, dealing with present value and internal rate of return, can also be applied to investment decisions and financial securities. These theories will not be covered again in detail, since the only real novelty is of a semantic nature. In the sections on financial securities, we calculated the yield to maturity. The same approach holds for analysing industrial investments, whereby we calculate a rate that takes the present value to zero. This is called the internal rate of return (IRR). **Internal rate of return and yield to maturity are thus the same.**

This chapter will discuss:

- the cash flows to be factored into investment decisions, which are called
**incremental cash flows**; and **other investment criteria**, which are less relevant than NPV and IRR and have proven disappointing in the past. As financial managers, you should nevertheless be aware of them, even if they are more pertinent to accounting work than financial management: payback period, accounting rate of return, profitability indicator.

## Section 28.1 THE PREDOMINANCE OF NPV AND THE IMPORTANCE OF IRR

Each investment has a **net present value (NPV), which is equal to the amount of value created**. Remember that the net present value of an investment is the value of the positive and negative cash flows arising from an investment, discounted at the rate of return required by the market. The rate of return is based upon the investment’s risk.

From a financial standpoint, and if forecasts are correct, an investment with positive NPV is worth making since it will create value. Conversely, an investment with negative NPV should be avoided as it will destroy value.

Sometimes investments with negative NPV are made for strategic reasons, such as to protect a position in the industry sector or to open up new markets with strong, yet hard-to-quantify, growth potential. It must be kept in mind that if the NPV is really negative, it will certainly lead to the destruction of value. Sooner or later, projects with negative NPV have to be offset by other investments with positive NPV that create value. Without doing so, the company will be headed for ruin.

The internal rate of return (IRR) is simply the rate of return on an investment. Given an investment’s degree of risk, it is financially worthwhile if the IRR is higher than the required return. On the other hand, if the IRR is lower than the risk-based required rate of return, the investment will serve no financial purpose.

Net present value (NPV) measures the value created by the investment and is the best criterion for selecting or rejecting an investment, whether it is industrial or financial. When it is simply a matter of deciding whether or not to make an investment, NPV and IRR produce the same outcome. However, if the choice is between two mutually exclusive investments, net present value is more reliable than the internal rate of return.

From a conceptual and methodological point of view, NPV is a better criterion as it takes into account risk (payback ratio does not), the whole stream of cash flows (idem) and assumes that intermediate cash flows are reinvested at the cost of capital, which is more realistic than IRR (which implicitly assumes reinvestment at the IRR, which may be above the cost of capital).

Actual computation of NPV is not always well applied. Indeed, some managers discount cash flows using the cost of capital of the group and not at a rate that reflects the market risk of the specific project. **It should be kept in mind that a very risky project will increase the overall risk of the firm and thus should be discounted at a higher rate** (and vice versa). We will highlight this point in the next chapter.

Graham and Harvey (May 2001) conducted a broad survey of corporate and financial managers to determine which tools and criteria they use when making financial decisions. They asked them to indicate how frequently they used several capital budgeting methods. The findings showed that net present value and internal rate of return carry the greatest weight, and justifiably so. Some 75% of financial managers systematically value investments according to these two criteria. This proportion increases over time demonstrating that pedagogy in finance is not useless.

Interestingly, large firms apply these criteria more often than small and medium-sized companies, and MBA graduates use them systematically while older managers tend to rely on the payback ratio.

Conclusions are slightly different for small and medium companies for which (according to a study by Danielson and Scott) intuition comes first (26%), then payback ratio (19%), ROCE (14%) and NPV (12%).

## Section 28.2 THE MAIN LINES OF REASONING

All investment decisions must comply with the following six principles:

- consider cash flows rather than accounting data;
- reason in terms of incremental cash flows, considering only those associated with the project;
- reason in terms of opportunity;
- disregard the type of financing;
- consider taxation; and
- above all, be
**consistent**.

### 1/ REASON IN TERMS OF CASH FLOWS

We have already seen that the return on an investment is assessed in terms of the resulting cash flows. Indeed, only cash flows can be invested and earn interest or be used to repay a debt and stop the payment of its interests. One must therefore analyse the negative and positive cash flows, and not the accounting income and expenses. These accounting measures are irrelevant because they do not take into account working capital generated by the investment and include depreciation, which is a non-cash item.

We stress the fact that in finance, an amount costs only when it is disbursed and earns only when it is received, regardless of the accounting treatment applied to it.

### 2/ REASON IN TERMS OF INCREMENTAL FLOWS

**When considering an investment, one must take into account the flows it generates, all the flows derived from the investment, and nothing else but these flows.** It is crucial to assess all the consequences of an investment upon a company’s cash position. Some of these are self-evident and easy to measure, and others are less so.

A movie theatre group plans to launch a new complex, and substantial costs have already been incurred in its design. Should these be included in the investment’s cash flows? The answer is no, since the costs have already been incurred regardless of whether or not the complex is actually built. These are **sunk costs**. Therefore, they should not be considered part of the investment expenditure.

It would be absurd to carry out an investment simply because the preparations were costly and one hopes to recoup funds that, in any case, have already been spent. The only valid reason for pursuing an investment is that it is likely to create value.

Now, if the personnel department has to administer an additional 20 employees hired for the new complex (e.g. 5% of its total workforce), should 5% of the department’s costs be allocated to the new project? Again, the answer is no. With or without the new complex, the personnel department is part of overhead costs. As a general rule, structural costs cannot be attributed, even in part, to an investment because they are independent of it. Structural expenses would only be affected if the planned investment generates additional costs – which in our example is recruitment expenses.

However, design and overheads will be priced (to the extent possible given the competitive environment) into the ticket charged for entry to the new complex. Finance here differs quite markedly from management control.

A perfume company is about to launch a new product line that may cut sales of its existing perfumes by half. Should this decline be factored into the calculation of the investment’s return? Yes, because the new product line will prompt a shift in consumer behaviour: the decline in cash flow from the older perfume stems directly from the introduction of this new product.

Nevertheless, we can mention that in certain very specific sectors with very low marginal costs, this reasoning may lead to overinvestment, creating overcapacity and therefore price wars.

### 3/ REASON IN TERMS OF OPPORTUNITY

For financial managers, an asset’s value is its market value, which is the price at which it can be bought (investment decision) or sold (divestment decision). From this standpoint, its book or historic value is of no interest whatsoever, except for tax purposes (taxes payable on book capital gains, tax credit on capital losses, etc.).

For example, if a project is carried out on company land that was previously unused, the land’s after-tax resale value must be considered when valuing the investment. After all, in principle, the company can choose between selling the land and booking the after-tax sales price, or using the land for the new project. Note that the book value of the land does not enter into this line of reasoning.

The opportunity principle boils down to some very simple rules:

- if a company decides to hold on to a business, this implies that it should be prepared to buy that business (if it did not already own it) in identical operating circumstances; and
- if a company decides to hold on to a financial security that is trading at a given price, this security is identical to one that it should be prepared to buy (if it did not already own it) at the same price.

**Financial managers are, in effect, “asset dealers”.** They must introduce this approach within their company, even if it means standing up to other managers who view their respective business operations as essential and viable. Only by systematically confronting these two viewpoints can a company balance its decision-making and management processes.

Theoretically, a financial manager does not view any activity as essential, regardless of whether it is one of the company’s core businesses or a potential new venture. The CFO must constantly be prepared to question each activity and reason in terms of:

- buying and selling assets; and
- entering or withdrawing from an economic sector of activity.

The concept of necessity should be interpreted as regards the strategy of the firm, the investment is then a tool for achieving this strategy; a necessary tool, hence highly profitable.

### 4/ DISREGARD THE TYPE OF FINANCING

When comparing an investment’s return with its cost of financing, the two items must be considered separately.

In practice, since the discount rate corresponds to the required rate of return necessary to cover the total cost of financing the investment, interest expense, repayments or dividends should not be included in the flows. **Only operating and investment flows are taken into account, but never financing flows. This is the same distinction that was made in Chapter 2.** Failure to do so would skew the project’s net present value. This would also overstate its IRR, since the impact of financing would be included twice:

- first, within the weighted average cost of capital for this investment, which is its cost of financing; and
- second, at the cash flow level.

To demonstrate this, consider, for example, an investment with the following flows:

Year | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Investment flows | −100 | 15 | 15 | 115 |

The NPV of this investment is 7.2 (if cash flows are discounted at 12%) and its IRR is 15%. Now, assume that 20% of the investment was financed by debt at an annual after-tax cost of 6%. Then it is possible to deduct the debt flows from the investment flows and calculate its NPV and IRR:

Year | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Investment flows | −100 | 15.0 | 15.0 | 115.0 |

Debt financing flows | 20 | −1.2 | −1.2 | −21.2 |

Net flows to equity | −80 | 13.8 | 13.8 | 93.8 |

With a rate of 12%, the NPV is 10.1 and the IRR is 17.2%. Now, if 50% of the investment were financed by debt, the NPV would rise to 14.4 and the IRR to 24%. At 80% debt financing, NPV works out to 18.7 and the IRR to 51%.

This demonstrates that by taking on various degrees of debt, it is possible to manipulate the NPV and IRR. This is the same as using the financial leverage that was discussed in Chapter 12. However, this is a slippery slope. It can lead unwary companies to invest in projects whose low industrial profitability is offset by high debt, which in fact increases the risk considerably.

When debt increases, so does the required return on equity as the risk increases for shareholders, as we have seen in Chapter 12. It would be incorrect to continue valuing the previous NPV at a constant discount rate of 12%. The discount rate has to be raised in conjunction with the level of debt. This corrects our reasoning and NPV remains constant. The IRR is now higher, but the minimum required return has risen as well to reflect the greater degree of risk of an investment financed by borrowings.

It would be absurd to believe that one can undertake an investment because it generates an IRR of 10% whereas the corresponding debt can be financed at a rate of 7%. In fact, the debt is only available because the company has equity that acts as collateral for creditors. Equity has to be remunerated, and this is not reflected in the 7% interest on the debt. No company can be fully financed by debt, and it is therefore impossible to establish a direct comparison between the cost of debt and the project’s return.

### 5/ CONSIDER TAXATION

Clearly, taxation is an issue because corporate executives endeavour to maximise their **after-tax** flows; it goes without saying that this is done while respecting fiscal regulations. Consider that:

- additional depreciation generates tax savings that must be factored into the equation;
- the cash flows generated by the investment give rise to taxes, which must be included as well; and
- certain tax shields offer tax credits, carbon credits, rebates, subsidies, allowances and other advantages for carrying out investment projects.

In practice, it is better to value a project using after-tax cash flows and an after-tax discount rate in order to factor in the various tax benefits from an investment. Therefore, the return required by investors and creditors is calculated after tax.

In cases where cash flows are discounted before tax, it is important to ascertain that all flows and components of weighted average cost of capital are considered before taxes as well.

### 6/ BE CONSISTENT!

The best advice we can give to our readers is to always be consistent. If the basis of valuation is constant euro values – that is, excluding inflation – be sure that the discount rate excludes inflation as well. We recommend using current euro values, because the discount rate already includes the market’s inflation expectations.

If it is a pre-tax valuation, make sure the discount rate reflects the pre-tax required rate of return. We recommend using after-tax valuations because a world without taxes only exists in textbooks!

And if flows are denominated in a given currency, the discount rate must correspond to the interest rate in that currency as well.

### 7/ AND WHAT ABOUT ENERGY TRANSITION?

Should the urgency of energy transition not lead to the adoption of new investment selection criteria in order to facilitate it? We do not think so. Current criteria can quite easily account for incentives favouring energy transition, be it in terms of flows (subsidies, carbon credits, etc.) or the discount rate, as we will see in Chapter 29.

This being said, a company is not forced to select, from among mutually exclusive investments, the one with the best NPV if it goes with a high carbon footprint. It should be noted that such a situation would reflect an unsatisfactory incentive/regulatory balance put in place by governments. The company may even decide to hold on to an investment with a negative NPV in order to help the planet. But in a competitive market, a firm cannot be virtuous on its own. It will find it difficult to behave in this way unless, on the other hand, it makes investments with a positive NPV to offset its virtuous behaviour.

## Section 28.3 WHICH CASH FLOWS ARE RELEVANT?

In practice, three types of cash flow must be considered when assessing an investment: **operating flows, investment flows and extraordinary flows**. Financial managers try to plan both the amount of a cash flow and its timing. In other words, they draw up projections of the cash flows on the investment.

Where the investment has a limited life, it is possible to anticipate its cash flows over the entire period. But, in general, the duration of an investment is not predetermined, and one assumes that at some point in the future it will be either wound up or sold. This means that the financial manager has to forecast all cash flows over a given period with an explicit forecast period, and reason in terms of *residual (or salvage) value* beyond that horizon. The residual value reflects the flows extending beyond the explicit investment horizon, and on into infinity. Although the discounted residual value is frequently very low since it is very far off in time, it should not be neglected. Its book value is sometimes zero, but its economic value may be quite significant since accounting depreciation may differ from economic depreciation. If some of the assets may be sold off, one must also factor in any taxes on capital gains.

### 1/ OPERATING FLOWS

The investment’s contribution to total earnings before interest, taxes, depreciation and amortisation (EBITDA) must be calculated. It represents the difference between the additional income and expenses arising from the investment, excluding depreciation and amortisation.

Then, from EBITDA, the **theoretical** tax on the additional operating profit must be deducted. This tax is then calculated by multiplying the tax rate borne by the project with the differential on the operating profit, taking into account any tax-loss carryforwards which could be used.

It is essential to deduct changes in working capital from EBITDA. Unfortunately, many people tend to forget this. In most cases, working capital is just a matter of a time lag. It builds up gradually, grows with the business and is retrieved when the business is discontinued. A euro capitalised today in working capital can be retrieved in 10 years’ time, but it will not be worth the same. Money invested in working capital is not lost. It is simply capitalised until the investment is discontinued. However, this capitalisation carries a cost, which is reflected in the discounted amount.

### 2/ INVESTMENT FLOWS

Investment in fixed assets comprises investment in maintenance, production capacity and growth, whether in the form of tangible assets (machinery, land, buildings, etc.) or intangible assets (research and development, patents and licences, business capital, etc.) or financial assets (shares in subsidiaries) for external growth.

The investment must be assessed for each period, as the investment is not necessarily restricted to just one year, nor spread evenly over the period. Once again, remember that our approach is based on cash and not accounting data. The investment flows must be recognised when they are paid, not when the decisions to make them were incurred. And finally, do not forget to reason in terms of net investment; that is, after any disposals, investment subsidies and other tax credits.

### 3/ EXTRAORDINARY FLOWS

It may seem surprising to mention extraordinary items when projecting estimated cash flows. However, financial managers frequently know in advance that certain expenses that have not been booked under EBITDA (litigation, tax audits, etc.) will be disbursed in the near future. These expenses must all be included on an after-tax basis in the calculation of estimated free cash flow.

Extraordinary flows can usually be anticipated at the beginning of the period since they reflect known items. Beyond a two-year horizon, it is generally assumed that they will be zero.

This gives us the following cash flow table:

Periods | 0 | 1 | … | n |
---|---|---|---|---|

Incremental EBITDA | + | + | + + | |

− Incremental tax on operating profit | − | − | − | |

− Change in incremental working capital | − − | − − | − | + + |

− Investments | − − − | − | − | |

+ Divestments after tax | + | + | + + | |

− Extraordinary marginal expenses | − | |||

= Cash flow to be discounted = Free cash flows | − − | + | + | + + |

## Section 28.4 OTHER INVESTMENT CRITERIA

### 1/ THE PAYBACK PERIOD

The payback period is the time necessary to recover the initial outlay on an investment. Where annual free cash flows are identical, the payback period is equal to:

For the following investment:

Period | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Cash flows | −2.1 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |

the payback period is 2.1 / 0.8 = 2.6 years.

Where the annual flows are not identical, the cumulative cash flows are compared with the amount invested, as below:

Period | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Cash flows | −1 | 0.3 | 0.4 | 0.4 | 0.5 | 0.2 |

Cumulative cash flows | 0.3 | 0.7 | 1.1 | 1.6 | 1.8 |

The cumulative flow is 0.7 for period 2 and 1.1 for period 3. The payback period is thus two to three years. A linear interpolation gives us a payback period of 2.75 years.

Once the payback period has been calculated, it is compared with a cut-off date determined by the financial manager. If the payback period is longer than the cut-off period, then the investment should be rejected. Clearly, when the perceived risk on the investment is high, the company will look for a very short payback period in order to get its money back before it is too late!

The payback ratio is used as an indicator of an investment’s risk and profitability. However, it can lead to the wrong decision, as shown in the example below of investments A and B.

Flows in period 0 | Flows in period 1 | Flows in period 2 | Flows in period 3 | Recovery within | 20% NPV | |
---|---|---|---|---|---|---|

Investment A | −1,000 | 500 | 400 | 600 | 2 years and 2 months | 42 |

Investment B | −1,000 | 500 | 500 | 100 | 2 years | −178 |

The payback rule would prompt us to choose investment B, even though investment A has positive NPV but B does not. The payback rule can be misleading because it does not take all flows into account.

Moreover, because it considers that a euro today is worth the same as a euro tomorrow, the payback rule does not factor in the time value of money. To remedy this, one sometimes calculates a discounted payback period representing the time needed for the project to have positive NPV. Returning to the example, with a 20% discount rate, it then becomes:

Year | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Cumulative present values | −2.1 | −1.43 | −0.88 | −0.41 | −0.03 | 0.29 |

The discounted payback period is now 4 years compared with 2.6 years before discounting. Discounted or not, the payback period is a risk indicator, since the shorter it is, the lower the risk of the investment. **That said, it ignores the most fundamental aspect of risk: the uncertainty of estimating liquidity flows.** Therefore, it is just an approximate indicator since it only measures liquidity.

However, the payback ratio is fully suited to productive investments that affect neither the company’s level of activity nor its strategy. Its very simplicity encourages employees to suggest productivity improvements that can be seen to be profitable without having to perform lengthy calculations. It only requires common sense. However, calculating flows in innovative sectors can be something of a shot in the dark.

It should be noted that some companies calculate the NPV of their potential investments over a limited period (5 years for example); cash flows beyond this period are considered too uncertain and are neglected. In such cases, the practice is equivalent to the discounted payback period.

### 2/ RETURN ON CAPITAL EMPLOYED

The return on capital employed (ROCE) represents the increase in after-tax operating profit generated by the investment over the year divided by the capital employed (sum of fixed assets and the working capital generated by the investment):

The average accounting return can also be calculated, which is the average of annual ROCEs over the life of the investment. The computation of ROCE takes into account the after-tax operating profit and capital employed (working capital plus the residual investment after depreciation).

By not taking into account when cash flows occur accounting rates of return generally overstate the rates of return (as high returns are more distant in time). Another drawback with accounting rates of return is that they maximise rates without considering the corresponding risk.

On the surface, it may seem that there is no connection between return on capital employed and the internal rate of return. The first discounts flows, while the second calculates book wealth. And yet, taken over a year, their outcomes are identical. An amount of 100 that increases to 110 a year later has an IRR of 100 = 110 / (1 + *r*), so *r* = 10%, and ROCE of 10 / 100, or 10%.

ROCE and IRR are equal over a given period of time. ROCE is therefore calculated by period, while IRR and NPV are computed for the entire life of the investment.

**Although accounting rates of return should not be used as investment or financing criteria, they can be useful financial control tools.**

Sooner or later, an IRR has to be translated into an accounting rate of return. If not, the investment has not generated the anticipated ex-post return and has not achieved its purpose. We strongly advise you to question any differences between IRR and ROCE, i.e. do profits arise unevenly over the period (starting out slowly or not at all and then gathering momentum), what is the amount of terminal value, are there calculation errors, is the hypothesis on the return of cash flows ploughed back in the business correct, etc.?

### 3/ CAPITAL RATIONING AND THE PRESENT VALUE INDEX

Sometimes there is a strict capital constraint imposed on the firm, and it is faced with more NPV-positive projects than it can afford. In order to determine which project(s) to pursue, some use the **present value index (PVI)**. This is the present value of cash inflows divided by the present value of cash outflow:

By using the PVI, financial managers can rank the different projects and then select the investment with the highest PVI – that is, the project with the highest NPV relative to the present value of outflows. After making this selection, if the total amount of capital available has not been fully exhausted, the managers should then invest in the project with the second-highest PVI, and so on until no more capital remains to invest as long as PVI remains above 1.

Our reader will have noticed that just like the IRR, the profitability index does not take into account the size of the project, and two projects with the same IP can generate very different NPVs!

## SUMMARY

## QUESTIONS

## EXERCISES

## ANSWERS

## BIBLIOGRAPHY

## Chapter 22. SHARES

*Back to flows and financial analysis*

The “mathematics” we studied in Chapters 16 and 17, dealing with present value and internal rate of return, can also be applied to investment decisions and financial securities. These theories will not be covered again in detail, since the only real novelty is of a semantic nature. In the sections on financial securities, we calculated the yield to maturity. The same approach holds for analysing industrial investments, whereby we calculate a rate that takes the present value to zero. This is called the internal rate of return (IRR). **Internal rate of return and yield to maturity are thus the same.**

This chapter will discuss:

- the cash flows to be factored into investment decisions, which are called
**incremental cash flows**; and **other investment criteria**, which are less relevant than NPV and IRR and have proven disappointing in the past. As financial managers, you should nevertheless be aware of them, even if they are more pertinent to accounting work than financial management: payback period, accounting rate of return, profitability indicator.

## Section 28.1 THE PREDOMINANCE OF NPV AND THE IMPORTANCE OF IRR

Each investment has a **net present value (NPV), which is equal to the amount of value created**. Remember that the net present value of an investment is the value of the positive and negative cash flows arising from an investment, discounted at the rate of return required by the market. The rate of return is based upon the investment’s risk.

From a financial standpoint, and if forecasts are correct, an investment with positive NPV is worth making since it will create value. Conversely, an investment with negative NPV should be avoided as it will destroy value.

Sometimes investments with negative NPV are made for strategic reasons, such as to protect a position in the industry sector or to open up new markets with strong, yet hard-to-quantify, growth potential. It must be kept in mind that if the NPV is really negative, it will certainly lead to the destruction of value. Sooner or later, projects with negative NPV have to be offset by other investments with positive NPV that create value. Without doing so, the company will be headed for ruin.

The internal rate of return (IRR) is simply the rate of return on an investment. Given an investment’s degree of risk, it is financially worthwhile if the IRR is higher than the required return. On the other hand, if the IRR is lower than the risk-based required rate of return, the investment will serve no financial purpose.

Net present value (NPV) measures the value created by the investment and is the best criterion for selecting or rejecting an investment, whether it is industrial or financial. When it is simply a matter of deciding whether or not to make an investment, NPV and IRR produce the same outcome. However, if the choice is between two mutually exclusive investments, net present value is more reliable than the internal rate of return.

From a conceptual and methodological point of view, NPV is a better criterion as it takes into account risk (payback ratio does not), the whole stream of cash flows (idem) and assumes that intermediate cash flows are reinvested at the cost of capital, which is more realistic than IRR (which implicitly assumes reinvestment at the IRR, which may be above the cost of capital).

Actual computation of NPV is not always well applied. Indeed, some managers discount cash flows using the cost of capital of the group and not at a rate that reflects the market risk of the specific project. **It should be kept in mind that a very risky project will increase the overall risk of the firm and thus should be discounted at a higher rate** (and vice versa). We will highlight this point in the next chapter.

Graham and Harvey (May 2001) conducted a broad survey of corporate and financial managers to determine which tools and criteria they use when making financial decisions. They asked them to indicate how frequently they used several capital budgeting methods. The findings showed that net present value and internal rate of return carry the greatest weight, and justifiably so. Some 75% of financial managers systematically value investments according to these two criteria. This proportion increases over time demonstrating that pedagogy in finance is not useless.

Interestingly, large firms apply these criteria more often than small and medium-sized companies, and MBA graduates use them systematically while older managers tend to rely on the payback ratio.

Conclusions are slightly different for small and medium companies for which (according to a study by Danielson and Scott) intuition comes first (26%), then payback ratio (19%), ROCE (14%) and NPV (12%).

## Section 28.2 THE MAIN LINES OF REASONING

All investment decisions must comply with the following six principles:

- consider cash flows rather than accounting data;
- reason in terms of incremental cash flows, considering only those associated with the project;
- reason in terms of opportunity;
- disregard the type of financing;
- consider taxation; and
- above all, be
**consistent**.

### 1/ REASON IN TERMS OF CASH FLOWS

We have already seen that the return on an investment is assessed in terms of the resulting cash flows. Indeed, only cash flows can be invested and earn interest or be used to repay a debt and stop the payment of its interests. One must therefore analyse the negative and positive cash flows, and not the accounting income and expenses. These accounting measures are irrelevant because they do not take into account working capital generated by the investment and include depreciation, which is a non-cash item.

We stress the fact that in finance, an amount costs only when it is disbursed and earns only when it is received, regardless of the accounting treatment applied to it.

### 2/ REASON IN TERMS OF INCREMENTAL FLOWS

**When considering an investment, one must take into account the flows it generates, all the flows derived from the investment, and nothing else but these flows.** It is crucial to assess all the consequences of an investment upon a company’s cash position. Some of these are self-evident and easy to measure, and others are less so.

A movie theatre group plans to launch a new complex, and substantial costs have already been incurred in its design. Should these be included in the investment’s cash flows? The answer is no, since the costs have already been incurred regardless of whether or not the complex is actually built. These are **sunk costs**. Therefore, they should not be considered part of the investment expenditure.

It would be absurd to carry out an investment simply because the preparations were costly and one hopes to recoup funds that, in any case, have already been spent. The only valid reason for pursuing an investment is that it is likely to create value.

Now, if the personnel department has to administer an additional 20 employees hired for the new complex (e.g. 5% of its total workforce), should 5% of the department’s costs be allocated to the new project? Again, the answer is no. With or without the new complex, the personnel department is part of overhead costs. As a general rule, structural costs cannot be attributed, even in part, to an investment because they are independent of it. Structural expenses would only be affected if the planned investment generates additional costs – which in our example is recruitment expenses.

However, design and overheads will be priced (to the extent possible given the competitive environment) into the ticket charged for entry to the new complex. Finance here differs quite markedly from management control.

A perfume company is about to launch a new product line that may cut sales of its existing perfumes by half. Should this decline be factored into the calculation of the investment’s return? Yes, because the new product line will prompt a shift in consumer behaviour: the decline in cash flow from the older perfume stems directly from the introduction of this new product.

Nevertheless, we can mention that in certain very specific sectors with very low marginal costs, this reasoning may lead to overinvestment, creating overcapacity and therefore price wars.

### 3/ REASON IN TERMS OF OPPORTUNITY

For financial managers, an asset’s value is its market value, which is the price at which it can be bought (investment decision) or sold (divestment decision). From this standpoint, its book or historic value is of no interest whatsoever, except for tax purposes (taxes payable on book capital gains, tax credit on capital losses, etc.).

For example, if a project is carried out on company land that was previously unused, the land’s after-tax resale value must be considered when valuing the investment. After all, in principle, the company can choose between selling the land and booking the after-tax sales price, or using the land for the new project. Note that the book value of the land does not enter into this line of reasoning.

The opportunity principle boils down to some very simple rules:

- if a company decides to hold on to a business, this implies that it should be prepared to buy that business (if it did not already own it) in identical operating circumstances; and
- if a company decides to hold on to a financial security that is trading at a given price, this security is identical to one that it should be prepared to buy (if it did not already own it) at the same price.

**Financial managers are, in effect, “asset dealers”.** They must introduce this approach within their company, even if it means standing up to other managers who view their respective business operations as essential and viable. Only by systematically confronting these two viewpoints can a company balance its decision-making and management processes.

Theoretically, a financial manager does not view any activity as essential, regardless of whether it is one of the company’s core businesses or a potential new venture. The CFO must constantly be prepared to question each activity and reason in terms of:

- buying and selling assets; and
- entering or withdrawing from an economic sector of activity.

The concept of necessity should be interpreted as regards the strategy of the firm, the investment is then a tool for achieving this strategy; a necessary tool, hence highly profitable.

### 4/ DISREGARD THE TYPE OF FINANCING

When comparing an investment’s return with its cost of financing, the two items must be considered separately.

In practice, since the discount rate corresponds to the required rate of return necessary to cover the total cost of financing the investment, interest expense, repayments or dividends should not be included in the flows. **Only operating and investment flows are taken into account, but never financing flows. This is the same distinction that was made in Chapter 2.** Failure to do so would skew the project’s net present value. This would also overstate its IRR, since the impact of financing would be included twice:

- first, within the weighted average cost of capital for this investment, which is its cost of financing; and
- second, at the cash flow level.

To demonstrate this, consider, for example, an investment with the following flows:

Year | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Investment flows | −100 | 15 | 15 | 115 |

The NPV of this investment is 7.2 (if cash flows are discounted at 12%) and its IRR is 15%. Now, assume that 20% of the investment was financed by debt at an annual after-tax cost of 6%. Then it is possible to deduct the debt flows from the investment flows and calculate its NPV and IRR:

Year | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Investment flows | −100 | 15.0 | 15.0 | 115.0 |

Debt financing flows | 20 | −1.2 | −1.2 | −21.2 |

Net flows to equity | −80 | 13.8 | 13.8 | 93.8 |

With a rate of 12%, the NPV is 10.1 and the IRR is 17.2%. Now, if 50% of the investment were financed by debt, the NPV would rise to 14.4 and the IRR to 24%. At 80% debt financing, NPV works out to 18.7 and the IRR to 51%.

This demonstrates that by taking on various degrees of debt, it is possible to manipulate the NPV and IRR. This is the same as using the financial leverage that was discussed in Chapter 12. However, this is a slippery slope. It can lead unwary companies to invest in projects whose low industrial profitability is offset by high debt, which in fact increases the risk considerably.

When debt increases, so does the required return on equity as the risk increases for shareholders, as we have seen in Chapter 12. It would be incorrect to continue valuing the previous NPV at a constant discount rate of 12%. The discount rate has to be raised in conjunction with the level of debt. This corrects our reasoning and NPV remains constant. The IRR is now higher, but the minimum required return has risen as well to reflect the greater degree of risk of an investment financed by borrowings.

It would be absurd to believe that one can undertake an investment because it generates an IRR of 10% whereas the corresponding debt can be financed at a rate of 7%. In fact, the debt is only available because the company has equity that acts as collateral for creditors. Equity has to be remunerated, and this is not reflected in the 7% interest on the debt. No company can be fully financed by debt, and it is therefore impossible to establish a direct comparison between the cost of debt and the project’s return.

### 5/ CONSIDER TAXATION

Clearly, taxation is an issue because corporate executives endeavour to maximise their **after-tax** flows; it goes without saying that this is done while respecting fiscal regulations. Consider that:

- additional depreciation generates tax savings that must be factored into the equation;
- the cash flows generated by the investment give rise to taxes, which must be included as well; and
- certain tax shields offer tax credits, carbon credits, rebates, subsidies, allowances and other advantages for carrying out investment projects.

In practice, it is better to value a project using after-tax cash flows and an after-tax discount rate in order to factor in the various tax benefits from an investment. Therefore, the return required by investors and creditors is calculated after tax.

In cases where cash flows are discounted before tax, it is important to ascertain that all flows and components of weighted average cost of capital are considered before taxes as well.

### 6/ BE CONSISTENT!

The best advice we can give to our readers is to always be consistent. If the basis of valuation is constant euro values – that is, excluding inflation – be sure that the discount rate excludes inflation as well. We recommend using current euro values, because the discount rate already includes the market’s inflation expectations.

If it is a pre-tax valuation, make sure the discount rate reflects the pre-tax required rate of return. We recommend using after-tax valuations because a world without taxes only exists in textbooks!

And if flows are denominated in a given currency, the discount rate must correspond to the interest rate in that currency as well.

### 7/ AND WHAT ABOUT ENERGY TRANSITION?

Should the urgency of energy transition not lead to the adoption of new investment selection criteria in order to facilitate it? We do not think so. Current criteria can quite easily account for incentives favouring energy transition, be it in terms of flows (subsidies, carbon credits, etc.) or the discount rate, as we will see in Chapter 29.

This being said, a company is not forced to select, from among mutually exclusive investments, the one with the best NPV if it goes with a high carbon footprint. It should be noted that such a situation would reflect an unsatisfactory incentive/regulatory balance put in place by governments. The company may even decide to hold on to an investment with a negative NPV in order to help the planet. But in a competitive market, a firm cannot be virtuous on its own. It will find it difficult to behave in this way unless, on the other hand, it makes investments with a positive NPV to offset its virtuous behaviour.

## Section 28.3 WHICH CASH FLOWS ARE RELEVANT?

In practice, three types of cash flow must be considered when assessing an investment: **operating flows, investment flows and extraordinary flows**. Financial managers try to plan both the amount of a cash flow and its timing. In other words, they draw up projections of the cash flows on the investment.

Where the investment has a limited life, it is possible to anticipate its cash flows over the entire period. But, in general, the duration of an investment is not predetermined, and one assumes that at some point in the future it will be either wound up or sold. This means that the financial manager has to forecast all cash flows over a given period with an explicit forecast period, and reason in terms of *residual (or salvage) value* beyond that horizon. The residual value reflects the flows extending beyond the explicit investment horizon, and on into infinity. Although the discounted residual value is frequently very low since it is very far off in time, it should not be neglected. Its book value is sometimes zero, but its economic value may be quite significant since accounting depreciation may differ from economic depreciation. If some of the assets may be sold off, one must also factor in any taxes on capital gains.

### 1/ OPERATING FLOWS

The investment’s contribution to total earnings before interest, taxes, depreciation and amortisation (EBITDA) must be calculated. It represents the difference between the additional income and expenses arising from the investment, excluding depreciation and amortisation.

Then, from EBITDA, the **theoretical** tax on the additional operating profit must be deducted. This tax is then calculated by multiplying the tax rate borne by the project with the differential on the operating profit, taking into account any tax-loss carryforwards which could be used.

It is essential to deduct changes in working capital from EBITDA. Unfortunately, many people tend to forget this. In most cases, working capital is just a matter of a time lag. It builds up gradually, grows with the business and is retrieved when the business is discontinued. A euro capitalised today in working capital can be retrieved in 10 years’ time, but it will not be worth the same. Money invested in working capital is not lost. It is simply capitalised until the investment is discontinued. However, this capitalisation carries a cost, which is reflected in the discounted amount.

### 2/ INVESTMENT FLOWS

Investment in fixed assets comprises investment in maintenance, production capacity and growth, whether in the form of tangible assets (machinery, land, buildings, etc.) or intangible assets (research and development, patents and licences, business capital, etc.) or financial assets (shares in subsidiaries) for external growth.

The investment must be assessed for each period, as the investment is not necessarily restricted to just one year, nor spread evenly over the period. Once again, remember that our approach is based on cash and not accounting data. The investment flows must be recognised when they are paid, not when the decisions to make them were incurred. And finally, do not forget to reason in terms of net investment; that is, after any disposals, investment subsidies and other tax credits.

### 3/ EXTRAORDINARY FLOWS

It may seem surprising to mention extraordinary items when projecting estimated cash flows. However, financial managers frequently know in advance that certain expenses that have not been booked under EBITDA (litigation, tax audits, etc.) will be disbursed in the near future. These expenses must all be included on an after-tax basis in the calculation of estimated free cash flow.

Extraordinary flows can usually be anticipated at the beginning of the period since they reflect known items. Beyond a two-year horizon, it is generally assumed that they will be zero.

This gives us the following cash flow table:

Periods | 0 | 1 | … | n |
---|---|---|---|---|

Incremental EBITDA | + | + | + + | |

− Incremental tax on operating profit | − | − | − | |

− Change in incremental working capital | − − | − − | − | + + |

− Investments | − − − | − | − | |

+ Divestments after tax | + | + | + + | |

− Extraordinary marginal expenses | − | |||

= Cash flow to be discounted = Free cash flows | − − | + | + | + + |

## Section 28.4 OTHER INVESTMENT CRITERIA

### 1/ THE PAYBACK PERIOD

The payback period is the time necessary to recover the initial outlay on an investment. Where annual free cash flows are identical, the payback period is equal to:

For the following investment:

Period | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Cash flows | −2.1 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |

the payback period is 2.1 / 0.8 = 2.6 years.

Where the annual flows are not identical, the cumulative cash flows are compared with the amount invested, as below:

Period | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Cash flows | −1 | 0.3 | 0.4 | 0.4 | 0.5 | 0.2 |

Cumulative cash flows | 0.3 | 0.7 | 1.1 | 1.6 | 1.8 |

The cumulative flow is 0.7 for period 2 and 1.1 for period 3. The payback period is thus two to three years. A linear interpolation gives us a payback period of 2.75 years.

Once the payback period has been calculated, it is compared with a cut-off date determined by the financial manager. If the payback period is longer than the cut-off period, then the investment should be rejected. Clearly, when the perceived risk on the investment is high, the company will look for a very short payback period in order to get its money back before it is too late!

The payback ratio is used as an indicator of an investment’s risk and profitability. However, it can lead to the wrong decision, as shown in the example below of investments A and B.

Flows in period 0 | Flows in period 1 | Flows in period 2 | Flows in period 3 | Recovery within | 20% NPV | |
---|---|---|---|---|---|---|

Investment A | −1,000 | 500 | 400 | 600 | 2 years and 2 months | 42 |

Investment B | −1,000 | 500 | 500 | 100 | 2 years | −178 |

The payback rule would prompt us to choose investment B, even though investment A has positive NPV but B does not. The payback rule can be misleading because it does not take all flows into account.

Moreover, because it considers that a euro today is worth the same as a euro tomorrow, the payback rule does not factor in the time value of money. To remedy this, one sometimes calculates a discounted payback period representing the time needed for the project to have positive NPV. Returning to the example, with a 20% discount rate, it then becomes:

Year | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Cumulative present values | −2.1 | −1.43 | −0.88 | −0.41 | −0.03 | 0.29 |

The discounted payback period is now 4 years compared with 2.6 years before discounting. Discounted or not, the payback period is a risk indicator, since the shorter it is, the lower the risk of the investment. **That said, it ignores the most fundamental aspect of risk: the uncertainty of estimating liquidity flows.** Therefore, it is just an approximate indicator since it only measures liquidity.

However, the payback ratio is fully suited to productive investments that affect neither the company’s level of activity nor its strategy. Its very simplicity encourages employees to suggest productivity improvements that can be seen to be profitable without having to perform lengthy calculations. It only requires common sense. However, calculating flows in innovative sectors can be something of a shot in the dark.

It should be noted that some companies calculate the NPV of their potential investments over a limited period (5 years for example); cash flows beyond this period are considered too uncertain and are neglected. In such cases, the practice is equivalent to the discounted payback period.

### 2/ RETURN ON CAPITAL EMPLOYED

The return on capital employed (ROCE) represents the increase in after-tax operating profit generated by the investment over the year divided by the capital employed (sum of fixed assets and the working capital generated by the investment):

The average accounting return can also be calculated, which is the average of annual ROCEs over the life of the investment. The computation of ROCE takes into account the after-tax operating profit and capital employed (working capital plus the residual investment after depreciation).

By not taking into account when cash flows occur accounting rates of return generally overstate the rates of return (as high returns are more distant in time). Another drawback with accounting rates of return is that they maximise rates without considering the corresponding risk.

On the surface, it may seem that there is no connection between return on capital employed and the internal rate of return. The first discounts flows, while the second calculates book wealth. And yet, taken over a year, their outcomes are identical. An amount of 100 that increases to 110 a year later has an IRR of 100 = 110 / (1 + *r*), so *r* = 10%, and ROCE of 10 / 100, or 10%.

ROCE and IRR are equal over a given period of time. ROCE is therefore calculated by period, while IRR and NPV are computed for the entire life of the investment.

**Although accounting rates of return should not be used as investment or financing criteria, they can be useful financial control tools.**

Sooner or later, an IRR has to be translated into an accounting rate of return. If not, the investment has not generated the anticipated ex-post return and has not achieved its purpose. We strongly advise you to question any differences between IRR and ROCE, i.e. do profits arise unevenly over the period (starting out slowly or not at all and then gathering momentum), what is the amount of terminal value, are there calculation errors, is the hypothesis on the return of cash flows ploughed back in the business correct, etc.?

### 3/ CAPITAL RATIONING AND THE PRESENT VALUE INDEX

Sometimes there is a strict capital constraint imposed on the firm, and it is faced with more NPV-positive projects than it can afford. In order to determine which project(s) to pursue, some use the **present value index (PVI)**. This is the present value of cash inflows divided by the present value of cash outflow:

By using the PVI, financial managers can rank the different projects and then select the investment with the highest PVI – that is, the project with the highest NPV relative to the present value of outflows. After making this selection, if the total amount of capital available has not been fully exhausted, the managers should then invest in the project with the second-highest PVI, and so on until no more capital remains to invest as long as PVI remains above 1.

Our reader will have noticed that just like the IRR, the profitability index does not take into account the size of the project, and two projects with the same IP can generate very different NPVs!