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20 Corporate Risk Management In this Chapter: Why Companies Manage Corporate Risks Managing Operational, Business and Financial Risks Forwards and Futures Swaps Financial Options Option Valuation Real Options Agency Costs
LEARNING OBJECTIVES Explain the factors that make it desirable for firms to manage their risks. Describe the risks faced by firms and how they are managed. Define forward and futures contracts and be able to determine their prices. Define interest rate and cross-currency swaps and know how they are valued. Define a call option and a put option and describe the payoff function for each of these options. 6. List and describe the factors that affect the value of an option. 7. Name some of the real options that occur in business and explain why traditional NPV analysis does not accurately incorporate their values. 8. Describe how the agency costs of debt and equity are related to options. 1. 2. 3. 4. 5.
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old conjures up visions of treasure hoards and beautiful works of art. More prosaically, it is used today in dentistry and electronics because of its resistance to corrosion and its excellent characteristics for conducting electricity. While gold has largely lost its functions as a currency and store of wealth, it is nevertheless in demand and a considerable number of mining companies are involved in its extraction – two of the largest are Barrick Gold and AngloGold Ashanti. For gold producers such as Barrick, it is the reason for their huge investment in deep mines with their expensive extraction equipment. They invest in order to sell the gold they mine. Unfortunately, the value of gold fluctuates a lot. The collapse of the Bretton Woods agreement, when gold was worth $35/oz, considerably raised its price such that it peaked at over $850/oz in 1980. In the following years, the gold price drifted downwards with occasional recoveries, until it touched a low of $252.80/oz in 2000. During this period, gold miners faced a dilemma. Mining gold was expensive and much of the cost had to be paid upfront in drilling the deep shafts to the ore deposits; the cost of extraction was also high. A declining price for their output was bad news.
Source: www.RealTerm.de, used by permission.
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Because of the falling gold price following the peak in the 1980s, Barrick Gold and AngloGold Ashanti, and other mining companies, faced the prospect of having to meet their large production costs out of a declining revenue stream as the gold price trended downwards. Their solution was to sell forward part or all of their production at a fixed price. This ensured a minimum price for their production, gave them a stable cash flow and allowed them to raise finance, since investors were reassured they would be paid back with a high degree of certainty. By 1999, these forward sales transactions represented more than a year of total output by the entire industry.1
CHAPTER PREVIEW The gold mining industry illustrates a key challenge for companies. What set of risks should companies take and what risks can the company lay off elsewhere? A key factor in determining corporate risk management policies is the nature and extent of these risks. Generally, companies will accept risks in their core business areas where they have a degree of competitive advantage. On the other hand, they will seek to eliminate or minimise other risks that have the capacity to derail the company from its objective of creating value for shareholders. Generally, firms will seek to manage macroeconomic risks, such as interest rate, commodity price, currency and credit risks. Corporate risk management can take a number of forms, which boil down to either the way the company organises its means of production or the use of financial instruments, principally derivatives, to modify the underlying risks in acceptable ways – or more typically a combination of both processes. We begin with a discussion of the rationale for corporate risk management before briefly looking at corporate risk management processes. We then examine the way derivatives are valued. Derivatives fall into two broad categories: those where the buyer or seller is locked into the contract and those that allow the buyer to walk away, if they should choose to do so. There are a number of different derivative instruments, variously known as forwards, futures, swaps and options. We will show that the first three are all similar. Options are different in nature. A forward contract, such as those used by gold mining companies, allows the buyer or seller to set the price at which they will purchase or sell a commodity or financial asset at a given date in the future. Futures contracts do the same thing, but are traded on an exchange, just like a company’s shares. Swaps are slightly more complicated in that there are multiple cash flows, but serve essentially the same purpose of setting prices now for a predetermined number of exchanges in future periods. The buyer or seller of a forward, futures or swap has specific obligations that last until the contract is completed and, in particular, both parties must complete the transaction whatever the circumstances in the future. On the other hand, the buyer or owner of an option has the right, but not the obligation, to purchase or sell a commodity or financial asset, such as a share, at a pre-specified price on or before a given date. This means that option buyers only have to complete the transaction if they choose to do so. We then turn to options on real assets, known as real options. Real options often arise in corporate investment decisions. Managers often have options to delay investing in a project, expand a project, abandon a project, change the technology employed in a project, and so on. You will see that the value of these options is not adequately reflected in an NPV analysis. We next revisit the agency costs of debt that we discussed in Chapter 16. In particular, we show how option-like payoffs contribute to the dividend payout, asset substitution and underinvestment conflicts. We follow this discussion with a related discussion of how option-like payoffs contribute to conflicts between shareholders and the managers who work for them.
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WHY COMPANIES MANAGE CORPORATE RISKS Learning Objective 1 Explain the factors that make it desirable for firms to manage their risks. In Chapter 6, we explained the nature of discounted cash flows and valuation. Value depends on the size, timing and riskiness of future cash flows and the rate of return required by investors. This suggests that corporate risk management may add value if it can positively affect expected cash flows and the required rate of return that is appropriate to those cash flows. A simple example will illustrate the point. Let us assume that a gold producer will have an annual cash flow of D 500 million over the next 30 years, after which mining operations cease.2 The appropriate risk-adjusted discount rate for the cash flows is 12%. Recall that the discount rate reflects the riskiness of the underlying cash flows. The present value of the business today is therefore simply D 500 million times a 30-year annuity at 12% (8.0552), or D 4028 million (D 500 8.0552). Now the company decides to engage in risk management activity that costs it D 50 million per year over the life of the mine. At the same time, the required rate of return, given that the cash flows have less risk, is reduced to 10% (the annuity factor will now be 9.4269). The new value becomes (D 500 D 50) 9.4269 ¼ D 4242 million. Using risk management in this situation has raised the value of the firm by D 214 million (D 4242 D 4028 ¼ D 214 million). Consequently, the owners of the business are better off if the gold producer undertakes risk management. A number of different factors will influence the extent to which firms manage their risks. These include financial reporting, corporate taxation, the costs of bankruptcy and contracting with providers of capital, as well as issues such as agency costs and employee compensation and retention. Furthermore, shareholders benefit when a company manages its risks in ways they cannot reproduce
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themselves. For instance, tax losses at the company level are not directly transferable to shareholders, so asymmetries in payoffs may lead firms to manage these risks. If the company does not hedge, there will be variability in the cash flows it generates from its operations as economic conditions change and the prices of its inputs and outputs change. Shortfalls, as a result of adverse movements in output prices or input costs, will either mean the company has to raise money externally or reduce its future investments – and consequently may have to pass up on attractive positive net present value projects. As we have seen in Chapter 15, raising external capital is costly and time-consuming. In addition, the issues discussed in Chapter 16 about the effect of capital structure and the problems of financial distress apply. These affect the ability of firms to raise external finance when distressed. A case in point is the British company BAe, or British Aerospace as it was then. In the 1980s, it had diversified away from aerospace into property and automobiles (by acquiring the Rover Group). In 1991, it suddenly indicated that all was not well in its businesses and announced a £432 million rights issue to repair its balance sheet. Shareholders were angry at the unexpected losses and having to subscribe more capital. For a while, there was a real risk of the company not getting the money it needed. The chairman and other senior managers were forced to resign and a new management team was recruited before shareholders were willing to subscribe for the new shares on offer.3 Taxes may also help explain why firms engage in risk management. If the tax system operates in such a way that the tax paid by the company rises with the amount of profit or earnings, it becomes attractive for firms to reduce the uncertainty of future earnings. In this situation, a more volatile earnings stream leads to higher expected taxes than a less volatile earnings stream. The reason is that firms have a number of potential tax offsets, such as tax depreciation and allowances, which act to reduce their taxable income. These are generally fixed in size so that if pre-tax earnings increase, they are likely to pay a higher tax rate overall. As
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Risk Management Can Help Firms Avoid Having to Raise Capital When it is Difficult to Do So A key question external providers of finance wish to resolve when firms come asking for new funds is the company’s motivation. The added disclosure required when external finance is being sought rapidly determines whether the company is in trouble – or not. If the finance is required to rescue the company, is this the management’s fault or just bad luck? It is difficult for outsiders to know whether the financially troubled condition of the company is a result of bad management or simply bad luck. If the managers are at fault, lenders do not wish, as the saying goes, ‘to throw good money after bad’ by providing more finance to a failing management. Better to wind up or sell the firm. Consequently, from the perspective of a company’s managers, seeking external finance when things have gone wrong is to be avoided as much as possible. Undertaking risk management that reduces the likelihood of financial distress and the need for external finance makes sense when providers of finance find it difficult to understand what is happening in the business.
we also saw in Chapter 3, many countries have a low starter rate of company tax. For instance, take the example of a company that has pre-tax earnings of either D 50 or D 200 with equal probability and will pay an effective rate of tax of 25% if its earnings are low or 35% if it has high earnings. The expected profit before tax will be D 125 (D 50 0.50 þ D 200 0.50). The expected tax will be D 40 ([D 50 0.25] 0.50 þ [D 200 0.35] 0.50). The expected after-tax profit will then be D 125 D 40 ¼ D 85. Now consider the situation where the company can use risk management to eliminate the variability in future pre-tax earnings such that it will have earnings before tax of D 125 with complete certainty. The corporate tax rate for this level of income is 27%. The company will pay D 34 in tax (D 125 0.27). The after-tax earnings are now D 125 D 34 ¼ D 91. The company has saved D 6 in taxes and increased after-tax profits from an expected D 85 to D 91. In this situation, risk management creates value for shareholders. As the opening vignette indicates, lenders are concerned about repayment. For a given level of debt, risk management can reduce the probability that a company will find itself in the situation where it is finding it hard or is unable to repay the debt. As Chapter 16 indicates, in situations
where financial distress is costly, risk management may increase the firm’s debt capacity. Higher debt levels may also be desirable in reducing agency problems and where this creates increased risk of financial distress, risk management is likely to be beneficial. A key rationale for firms to engage in risk management is that they are better able to address problems of managerial motivation, capture the benefits of tax management and reduce the costs of financial distress in ways that shareholders cannot. The ability of firms to manage their risks may also allow them to exploit investment opportunities that they would otherwise have to pass by because it is costly or impossible to raise external finance. There is less rationale for firms to manage those risks that shareholders and lenders can easily manage for themselves. For instance, it is not clear that unrelated diversification at the company level is beneficial since shareholders are able to create well-diversified portfolios by holding shares in a range of different companies at less cost and with more flexibility.
The Risk Management Process Companies need a risk management process. At its simplest, it requires them to examine their
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Risk Management Can Help Firms Address Capital Market Imperfections Corporate risk management is desirable when capital market imperfections and asymmetries reduce the value of firms and make access to outside finance costly for firms that do not control risks. Unless this rationale is present, risk management should be left to capital providers. operations in the broadest sense in order to recognise the risks that can affect the firm’s future cash flows. This involves identifying the risks, their assessment or evaluation, the selection of the risk management techniques, their implementation and keeping the programme under review. For instance, the pizza restaurant group would want to look at where it sources its inputs and in what way, what could go wrong when preparing, serving and delivering pizzas. At the same time, it would also consider how wider factors outside the company, such as the economy and social trends, might affect the business’s future profitability. The process can be broken down into a number of logical steps. These would typically include:
Identification. This would involve the financial manager in surveying the various business units and determining the profile of the business risks involved. Exposures can be simply classified according to the way they could affect the firm’s operations. For instance, the pizza restaurant group may use an integrated accounting system – failure here would have a major effect in that the company may be unable to operate. Hence, the risk that such a critical system could fail would be classified as having a very significant impact. Evaluation. Wherever possible, the impact of the risk is quantified in monetary terms. This helps in ranking the risks according to the severity of their effect. When combined with estimates of their frequency, this provides a way of scoring the result. For instance, at individual pizza restaurants, it may be that there are often inconsistencies in the till receipts against goods sold. However, their monetary effect is likely to be very small.
Hence, while problems in this area are frequent, their severity is minimal. A decision would need to be reached as to whether this risk needs managing. On the other hand, the IT system failure may be very infrequent – but its impact on the business could be seen as very severe. Management. The final element is a clear framework for managing the risks once they have been identified and evaluated. Here a key criterion is whether they have the capacity to derail the firm’s strategy. The management of the risks is therefore integrated into the company’s strategic goals. At the operational level, the company will establish procedures and assign responsibility to oversee the management of these unacceptable risks. Hence, it is often the function of the financial manager to use financial techniques or source instruments to mitigate the risks. For instance, by buying insurance cover against specific risks. Review. The final step is to repeat the process and keep the risks under review, since conditions change and firms evolve over time.
Before You Go On 1. What two factors affect the value of a business that can be modified when a firm manages its risks? 2. What firm-specific reasons may prompt a business to engage in risk management? 3. What are the adverse consequences to companies from changes in input and output prices?
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MANAGING OPERATIONAL, BUSINESS AND FINANCIAL RISKS Learning Objective 2 Describe the risks faced by firms and how they are managed. Every transaction a firm undertakes includes multiple risks. For instance, Volkswagen sells its cars in the Chinese market. In doing so, Volkswagen is betting that its cars are competitive in that market. However, it is also betting on the exchange rate between the renminbi and the euro. In the past, the renminbi has been linked to the US dollar and hence has fluctuated against the euro as the US dollar has risen and fallen over time.4 In order to develop its market presence in China, Volkswagen has to invest in this market by advertising the attractions of its cars and developing a dealer and repair network. These investments would be lost if changes in the market made it unattractive to the company. Volkswagen may be upbeat about the opportunity to sell its cars in China, but be less optimistic on the future of the exchange rate. A fall in the renminbi would leave it selling cars at a loss and hence the currency risk reduces the attractiveness of the fast-growing Chinese market. The solution is to split these risks, and for the company to accept the risks in which it sees itself as having a competitive advantage and removing those which can derail its business strategy. The company would therefore seek to manage the currency risk in such a way as to eliminate the problem. The risks that a company such as Volkswagen faces are either operational risks or market risks. Operational risks are either internal to the firm or arise from the nature and extent of its activities. The internal risks are largely under the control of management in that decisions on how the firm sets up and operates its production systems can be organised so as to minimise the risks involved. On the other hand, many of the external risks are the result of changes in macroeconomic
conditions and relate to changes in interest rates, commodity prices and exchange rates. These are market risks, and companies seek to reduce the effect of these on the firm’s operations and profitability. In addition, transactions with third parties create credit risk, which was discussed in Chapter 14.
Operational risks any risk arising from the execution of a company’s business functions
Market risks exposure to a change in the value of some market factor, such as interest rates, foreign exchange rates, equity or commodity prices
Operational and Business Risks Companies such as Volkswagen are involved in complex activities and face a number of internal and external risks. There are risks in its production processes from potential factory fires, breakdown in critical equipment and the development of new technologies that render existing ones redundant or uncompetitive. Some of these production risks are insurable. Firms also have input and output risks. The gold mining companies described at the start of this chapter have significant output risk from unexpected changes in the market price of gold over time. These price risks affect both the costs of a firm’s inputs and its outputs and hence its future profitability. Typically, these risks include commodities, raw materials, finished products, interest rates, energy, currencies and the prices of other market-determined inputs and outputs.
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Production risk
Hedging
all the elements of the production process that can go wrong: for instance, fires and equipment failures
any technique designed to reduce or eliminate risk; for example, taking two positions that will offset each other if prices change
Price risks changes in the prices of a firm’s inputs and outputs over time due to changes in demand and supply
To the extent that a company has changes in input prices (from unanticipated supply effects) and outputs (from unanticipated demand effects), it will experience variability in its cash flows. At a basic level, it will want to ensure that revenues cover all its costs. Since it incurs costs before revenues, this is to some extent a timing problem. However, firms may have trouble in raising prices. In the case of Volkswagen, if the demand for its cars was independent of their price, a fall in the value of the renminbi against the euro would be compensated for by increasing the sales price in China to maintain the value in euros. For most firms, a number of factors may prevent this happening: (1) local competitors will be largely unaffected by the movement in the currency; (2) demand may be significantly conditional on price; and (3) other foreign suppliers may be willing to cut their local currency prices to maintain or increase their market share.
Risk Management Methods Companies have a range of techniques that they can use to reduce the risks they face. Some of these relate to the way the firm operates. The solution for the company is to anticipate that prices will change and to position itself accordingly. Continuing our Volkswagen example, the company could organise itself so as to site in China that part of its production facilities that supplies the market. Then, costs and revenues would both be in the same currency. When cash flows are matched in this way, it is known as hedging.
As indicated above, Volkswagen can set up manufacturing facilities in the markets in which it sells its cars. This works to an extent, but can lead to a dispersion of production and higher costs than concentrating facilities in units that can benefit from economies of scale and scope. Typically, firms will organise themselves to be efficient producers and seek to address the remaining risks by using the capital markets to hedge – a process known as financial risk management. This involves the company in dealing in financial instruments that are designed to transfer or modify risks. This can involve the firm using insurance or derivatives. A great advantage of these instruments is that they are low cost and can be added and removed as required as circumstances change. Contrast this to the time and expense involved if the company decides to change the location of its production or switches the markets in which it sells.5
Financial risk management the practice of protecting and creating economic value in a firm by using financial instruments to manage exposure to risks
Insurance a contract that protects against the financial losses (in whole or in part) of specified unexpected events
Derivatives financial instruments or securities whose value varies with the value of an underlying asset
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Financial Risk Management Allows Firms to Exploit their Comparative Advantages A key reason firms use financial hedging is that they want to optimise the way they go about their business but also only accept those risks in which they have a competitive advantage. By using the financial markets to lay off those risks that the firm is unwilling or unable to accept, it both ensures that these risks do not derail its strategy and allows it to concentrate resources in areas where it has the best prospects of earning good returns.
There are three generic ways in which a firm can manage its various risks that involve hedging, insurance and diversification. The choice of method will depend on a number of factors. When a firm hedges, it reduces its exposure to the possibility of a loss but this also leads to the firm giving up the possibility of a gain. Insurance means paying a premium, the cost of the insurance, to avoid losses. In this case, the company retains the possibility of gain, but eliminates the exposure to potential loss. Note the difference between hedging and insurance: with hedging, the risk of loss is eliminated by giving up the potential for gain; with insurance, you pay a premium to eliminate the risk of loss and retain the potential for gain. Companies also use diversification to reduce their risks. We know from the way portfolios work that the aggregated portfolio risk will be less than the sum of the individual risks as long as the
components of the portfolio are less than perfectly correlated.6 As discussed earlier, while Volkswagen will not aim to exactly match its production facilities to its markets, nevertheless it does operate a number of different production facilities spread around the globe. This diversification makes sense in that it does reduce Volkswagen’s overall risks. But diversification of this kind is only advisable to the extent that it does not adversely affect the firm’s operational efficiency. As mentioned earlier, firms will seek to be efficient producers and use financial instruments to manage the remaining risks. As we will see later, when we look at how derivatives are valued, the cost of risk management will depend on the future uncertainty. The higher this uncertainty, the greater the costs involved. While risk management is costly, there are real benefits to companies from being able to manage their risks by hedging, through insurance or via
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Corporate Risk Management Decisions are Based on Cost--Benefit Trade-offs There are a number of different methods that, taken together, companies use to manage their risks. Companies will weigh the costs of using the method against the benefit of risk reduction. Companies can use diversification, insurance and hedging. These have different costs and benefits. Hence, there is no single solution that is appropriate in all circumstances. The benefits and costs of each approach have to be worked out for each method for all the different risks.
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diversification, and to reduce or eliminate the risks that would otherwise lead firms to underinvest in productive projects. Over time, to cater to the needs of firms, various organisations and contractual arrangements have emerged to expand the scope of diversification and by providing greater specialisation in risk management. For instance, insurance companies cover a wide range of production and other risks while derivatives markets in forward contracts, futures, swaps and options have a prominent place in financial markets.
Before You Go On 1. In what areas does a company face risks from its business? 2. What are the different ways in which a company can manage its risks? 3. What determines the balance between operational hedging and financial hedging?
FORWARDS AND FUTURES Learning Objective 3 Define forward and futures contracts and be able to determine their prices. A forward contract involves a delayed sale and purchase by the two parties to the contract. Consider the situation where Airbus is selling one of its commercial jets to a customer. These are usually manufactured to order and delivery may take place several years later. What are the risks for both sides if the terms and conditions are not set at the outset? Exhibit 20.1 shows a payoff diagram that graphically illustrates the way the buyer and seller are exposed to the future uncertain changes in the price of the airliner. First and foremost, both parties have price risk in that –
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when the delivery date finally arrives – the price for Airbus jets has changed. Airbus will do well if demand is high and aircraft prices have risen. The buyer will lose out by having to pay more. Equally, if demand is low and jetliner prices have fallen, the buyer wins as they pay less – and Airbus receives less. Given the uncertainties about the future price, both parties stand to lose if future prices are not the same as the current price for the airliner. They both have an incentive to ensure the contract for the aircraft specifies a price for the aircraft today but payable upon delivery. Commercial arrangements where prices and quantities are agreed today for future delivery are forward contracts. These contrast to spot contracts, where the buyer and seller make an immediate exchange.
Forward contract agreement between two parties to buy or sell an asset at a specified point of time in the future at a price agreed today
Because forward contracts address the price risk facing buyers and sellers, they are very common in business. In addition to commercial contracts, such as that between Airbus and its client, there are numerous financial forward contracts that can be negotiated in the financial markets and these cover a very wide range of business risks. There are contracts on currencies, commodities, interest rates, stock market indices and individual shares, credit risks, energy and even the weather – to list the most common types.
Valuing a Forward Contract As the Airbus example illustrates, these contracts work by ‘locking-in’ the prices at which firms buy and sell in the future. What should determine the price for the forward contract? In Chapter 5, we looked at investment and future values and so we
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Panel A: Airbus Industries Payoff Profile Profit
Airbus gains if market price for A310 is above €50 million after 2 years
€10
Panel B: Customer’s Payoff Profile Profit Client gains if market price for A310 is below €50 million after 2 years
€10
A310 price at maturity €40
(€10) Loss
€50
Airbus loses if market price for A310 is below €50 million after 2 years
€60 A310 price at maturity (€10)
€40
Loss
€50
€60
Client loses if market price for A310 is above €50 million after 2 years
Exhibit 20.1: Payoff Diagrams for the Price Risks Facing the A310 Buyer and Airbus Industries A payoff diagram shows the profit and loss from the deferred purchase of the A310 jet. If, when the contract is agreed, the contracted price is D 50 million and it does not change, neither buyer nor seller gains. If the price rises, the buyer loses and the seller gains, the profit and loss being the difference between the original price and the new price. So if the price rises to D 60 million, the seller has a profit of D 10 million and the buyer loses D 10 million. The gains and losses for both sides are the same and hence the payoffs to both parties are symmetrical. Panel A shows the payoff profile for Airbus Industries. The company will profit if the market price of the A310 airliner is above D 50 million in 2 years’ time. It will lose if the market price is below D 50 million. How much it will lose will depend on the future price uncertainty for the A310. Panel B shows the customer’s payoff profile. You will notice it has exactly the reverse set of gains and losses. The customer’s risk is exactly the opposite of that of Airbus Industries in that it loses if the price rises and gains if the price falls. Both Airbus and the customer have an incentive to manage the risk that the price will change. They will do so by entering into a forward contract that establishes the price now that will be paid upon delivery in 2 years’ time.
already know how to value future cash flows. A forward contract works in exactly the same way, except we want to start with the current price of what will be delivered in the future and work out its future value. At its simplest, a forward contract therefore will be determined by Equation (5.1): FVn ¼ PV ð1 þ iÞn where: FVn ¼ future value of investment at the end of period n PV ¼ original principal or present value i ¼ rate of interest per period, which is often a year
n ¼ number of periods (typically a year, but it can be a quarter, a month, a day or some other period of time) (1 þ i)n ¼ future value factor Let us assume that Airbus is selling the A310 model to the customer as described earlier. These are listed for immediate delivery at a price of D 50 million each. However, the agreed delivery date is 2 years away and the annual rate of interest for euros is 4%. The forward price will therefore be D 50 (1 þ 0.04)2 ¼ D 54.08 million. If there are no other factors that affect the forward price, this is a fair deal to both sides. The client could immediately buy at D 50 million. On the
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other hand, if they do not want the aircraft immediately, they have use of the money for the two intervening years and – if they invest it at the 4% interest rate – they will earn D 4.08 million, so will be no better or worse off from buying immediately or waiting. What of Airbus? If they sell the A310 for forward delivery, they receive D 54.08 million. The present value of this is D 50 million. By agreeing to sell at the higher forward price, they are compensated for the delay in receiving the money. Airbus has to wait two years to get the price of the aircraft and – notionally at least – may have to borrow the money while it waits to deliver the A310 to the customer. It can borrow the present value of the forward price – which is, of course, D 50 million. The forward price is such that it is fair to both sides and compensates them for the delayed delivery. The pricing of forward contracts is known as the cost of carry and equates the gains and losses of both sides such that neither wins or loses. As such, it is a zero net present value transaction in that – as shown above – neither the buyer nor the seller loses out from the delay. The cost of carry may take account of more than just interest rates as it includes all those elements that change the value between the present and the future and is the net cost to the seller in the transaction. For instance, Airbus may have to store the aircraft for the two years and will incur costs from doing so. This would raise the future price of the aircraft. On the other hand, it is possible that Airbus could lease out the aircraft and earn income over the two years, something the client could also do. Airbus gains from this, but the buyer loses the opportunity to gain the rental income until the time for delivery.7 This will reduce the forward price.
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The difference between the cash market price and the forward price (PV – FV) will be the cost of carry and will include the costs and benefits from the delay. The elements that go into the cost of carry and their effects on the forward price are as follows:
The interest rate (i) will work to increase the cost of carry and hence the forward price. Storage costs and wastage (u) will increase the cost of carry and the forward price. Some assets are subject to wastage when stored, such as agricultural commodities which tend to deteriorate over time, and this will mean the amount that can be delivered eventually will be less than the amount stored initially. Any income received prior to delivery will decrease the cost of carry and the forward price because it is a benefit to the seller. This is often expressed as a yield (q). Expressed this way, income on the asset can be viewed as a negative interest rate. A quantification of the benefits of immediate ownership or availability. This is known as the convenience yield (y) and can be thought of as negative storage costs! For instance, companies that use commodities which are vital to their business operations – and where there is restricted supply – may stockpile needed supplies and forego income in order to have a guaranteed availability. The convenience yield only applies to consumption assets and will be zero for forwards on financial assets. The effects of the factors that influence the cost of carry are illustrated in Exhibit 20.2.
Convenience yield Cost of carry the net cost of ‘carrying’ or holding an asset for future delivery
a non-monetary return derived from the physical ownership of an asset or commodity
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Factors that raise the forward price: • interest rates (i) • storage and wastage cost (u)
Current value of asset (PV)
Future value of asset at time m FVm
y Cost of carr
Factors that lower the forward price: • income from the asset (q) • convenience yield (y)
T=0
T=m Maturity of forward contract
Exhibit 20.2: Factors that Affect the Cost of Carry in a Forward Contract The price difference between the current market, the present value (PV) and the forward price (FV) will be determined by the interplay of those factors that contribute to the cost of carry: (1) interest rates and (2) storage and wastage costs, which act to increase the forward price; (3) income from the asset and (4) the convenience yield, which reduce the forward price. Note that, because of this interaction, it is quite possible that the forward price is lower than the current market price.
Let us continue the A310 example and see how the factors influence the cost of carry. We have already worked out the case where the only factor is interest rates. In this case, the forward price is D 54.08 million. If Airbus has to store the airliner for the two years, it will incur costs. Assume that storage costs are 1% of the aircraft’s value per year. This is like adding on 1% to the interest rate, so the future value will be D 55.13 million [D 50 (1 þ 0.04 þ 0.01)2]. On the other hand, if Airbus can lease out the aircraft for two years and earn 3% of the value of the aircraft in lease payments, this will have the effect of reducing the future value. Without leasing, the future value is D 54.08 million. The lease payments act like a negative interest rate and reduce the future value, so we need to discount the FV by the leasing rate (1 þ 0.03)2, such that D 54.08/(1.03)2 ¼ D 50.98 million. If there were a convenience yield attached to having physical ownership of the A310, this would also serve to reduce the forward price.
The full cost-of-carry formula is therefore: PV
ð1 þ i þ uÞm ¼ FVm ð 1 þ q þ yÞ m
ð20:1Þ
where: PV ¼ current price or present value i ¼ rate of interest per period (which is often a year) u ¼ storage cost per period, expressed as an interest rate q ¼ income from the asset per period, expressed as an interest rate y ¼ convenience yield per period FVm ¼ future value at the maturity of the forward contract m ¼ number of periods to maturity of the forward contract; a period is typically a year, but can be some other period, such as a quarter, month or some other unit of time
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Learning by Doing Application 20.1 Problem: You are the purchasing manager at the pizza restaurant chain and are becoming increasingly alarmed by the way the price of wheat is increasing and the effect it is having on the ability to set prices, plan expenditure and its effects on profit margins. Therefore, in order to facilitate planning within the company and to fix the cost of a major ingredient, you decide you would like to hedge and ‘lock in’ the price of flour for the coming year. You estimate you will need 50 tonnes and decide that a 1-year forward contract is the appropriate hedging instrument. The current price for flour is D 175 per tonne, the interest rate is 4% and your contacts in the industry tell you that storage costs are 2% per year. At what price will you be able to execute a forward contract?
We should point out that the cost-of-carry model is quite adaptable. For instance, we may not be able to work out the storage cost as an interest rate. Nevertheless, if we know what the storage costs will be in money, we can still use the model. Going back to our Airbus example, let us assume that Airbus contracts with a maintenance company to store the aircraft and the company says it will need to be paid D 0.60 million at the end of year 1 and D 0.75 million at the end of year 2 to store, maintain and service the aircraft. We can simply apply our understanding of the way the cost-ofcarry model works and that these are costs that need to be added to the agreed forward sale price. When only interest rates affect the cost of carry, we have a future value of D 54.08 million. We cansimply add to this the future value of the storage costs. The timeline for the transaction will be as follows:
Approach: We need to apply Equation (20.1) to determine the future price at which the forward contract will be agreed. To get the correct value, we need to include both the current interest rate and the storage costs in the costof-carry formula. Solution: Applying Equation (20.1) gives: PV
ð1 þ i þ uÞm ¼ FVm ð1 þ q þ y Þm
D 175
ð1 þ 0:04 þ 0:02Þ ð 1 þ 0 þ 0Þ
¼ D 185:50 per tonne
0
4%
€50
1
€0.60
2 Year
€0.75 FV = ?
We need to work out the value at year 2, which involves the following calculations: PVAircraft ð1 þ iÞ2 ¼ FVAircraft; Year 2 þ FVStorage; Year 1 ð1 þ iÞ ¼ FVYear 1 storage; Year 2 þ FVStorage; Year 2 ¼ Forward price D 50 ð1:04Þ2 ¼ D 54:08 þ D 0:60 ð1:04Þ ¼ D 0:624 þ D 0:75 ¼ D 55:454 million The forward price that Airbus requires so that it is no better or worse off from selling the A310 today is D 55.454 million.8 This price includes the foregone use of the sales proceeds and storage costs.
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Learning by Doing Application 20.2 Problem: You are the majority owner of the pizza restaurant group. The company is doing very well at the moment and the shares are currently worth D 80. However, you need to have a considerable sum of money in two years’ time to provide for your daughter’s university education. You are aware that the value of your shares can fall over this period and if so, as a result, you may have to sell more shares than you would like. As your company intends to pay a dividend of D 5.20 at the end of the current year and you anticipate a dividend of D 5.60 at the end of year two, you want to receive these dividends and not sell the shares until you actually need the money. The current two-year riskfree interest rate is 4% per year. What will be the fair price for the forward sale of your shares? Approach: We apply the cost-of-carry model and adapt Equation (20.1) to take account of the specific dividends that will be paid on the shares over the life forward contract. Application: We present-value the future dividend payments and find the price of the shares
The Value of a Forward Contract Prior to Maturity As Exhibit 20.1 indicates, the payoff for both parties to a forward contract is symmetrical. The buyer and seller’s gains and losses are the same, but arise due to changes in the market price of the A310 airliner. Once the terms of the forward contract are agreed (we will take D 54.08 million as the contract price), the value of the contract to either party will change as the market price of the asset to be delivered changes. For instance, let us assume that one year has elapsed. Airbus has raised the price of its A310 model to D 52 million. At the same
excluding the two dividend payments and then future-value this ex-dividend share price for two years: Present value of dividends ¼
D 5:20 D 5:60 þ 2 1:04 ð1:04Þ
¼ D 5:00 þ D 5:18 ¼ D 10:18 Ex-dividend share price ¼ D 80:00 D 10:18 ¼ D 69:82 Forward price ¼ D 69:82 ð1:04Þ
2
¼ D 75:517 The forward price for the shares is D 75.517 each. You can now determine, based on the money you need for your daughter’s education, how many shares you need to sell in the forward contract. Note that, as discussed in the text, due to the value leakage from the dividends, the twoyear forward price of D 75.52 is below the current market price of D 80.
time, interest rates have also changed and are now 5% per year. What is the contract worth? The payoff at maturity for Airbus, the seller, will be the difference between the market price and the agreed price, namely D 54.08 D 52 ¼ D 2.08 million. They will not receive this for another year, so the present value will be D 1.98 million (D 2.08/1.05). If Airbus is making a profit from the transaction, then the customer must be losing an equal amount. Note the effect that greater price changes have on the gains and losses from the contract before maturity. If the A310 price had risen to
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D 60 million, the payoff from the contract would be D 5.92 million (D 60 D 54.08). The present value is D 5.638 million (D 5.92/1.05). What we find is that the greater the changes in price over the life of the forward contract, the greater the value of the forward contract prior to maturity. This shows that the greater the price uncertainty for a firm’s inputs and outputs, the greater is the incentive to hedge out these risks and the more valuable the forward contract becomes.
Futures Contracts You may have realised there is a problem with forward contracts. Think of the situation facing Airbus, if in two years’ time the market price of the A310 is now D 40 million. The customer has every incentive not to honour the agreement, and buy the same aircraft elsewhere and save D 14.08 million by doing so (D 54.08 – D 40). To ensure it is not left nursing a loss, Airbus will only enter into the forward transaction at the outset if it thinks the customer will honour the forward contract regardless of what happens to the future price at maturity – and, of course, the customer has the same worries. A major problem therefore is that forward contracts are subject to what is called counterparty credit risk and this materialises when the other party fails to fulfil its obligations. This will always happen to the party that stands to gain from adhering to the contract. If the price after two years was D 60 million, the customer will not renege on the contract even if they do not want the airliner. This is because they can immediately resell it at a profit! Problems with the creditworthiness of counterparties in forward contracts limit the possible parties a company can deal with using forward contracts to those that it knows will pay even if it means they are losing out as a result.
CORPORATE RISK MANAGEMENT
Futures contracts were developed specifically to deal with the counterparty problem. They do this in a number of ways:
All contracts are made with a clearing house and not directly between buyers and sellers. This means if one of the parties defaults, the contract is still good for the other party since they have a contract with the clearing house. To protect the clearing house from losses due to defaults, both buyers and sellers have to post a goodwill deposit when buying or selling a futures contract, known as margin, to cover possible losses. The amount that is posted is enough to cover anticipated daily price changes in the contract plus an additional safety margin. The values of futures contracts to the buyer and seller are updated daily and the amounts debited and credited to the goodwill deposit. If the amount in the goodwill deposit account (margin account) falls below some predetermined level, further margin is required by the party incurring the losses. If this fails to materialise, the contract is terminated and the margin account used to cover any losses by the clearing house. Contracts are standardised to facilitate the market and trading is carried out through an organised exchange.
Futures contract a standardised, transferable, exchangetraded contract that requires the delivery of a specified asset at a predetermined price on a specified future date
Counterparty credit risk
Margin
the risk that the other party to a transaction will be unable or unwilling to honour their commitments
collateral that the holder of a futures contract has to deposit to cover the credit risk
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These institutional and functional changes made to the way forward contracts work create exchange-traded futures contracts. Because these contracts are standardised and a central counterparty acts as the buyer and seller for market users, there is a liquid market in futures. Buyers can enter the market very rapidly and find sellers through the exchange. Unlike a forward contract that has to be unwound with the other party, when the buyer comes to sell through the exchange they can easily find another market user who wants to take on their position. Furthermore, transaction costs are very low and this adds to the attraction of the instruments for short-term risk management purposes. As a result, there are large volumes of futures contracts being traded on numerous exchanges. The most important ones in Europe are the NYSE/Euronext/Liffe group and EUREX. The largest exchange in the world is the Chicago-based CME Group.
bonds, for which there are futures contracts. This means that hedging will be less than perfect. For companies, using futures or forwards involves a trade-off between the advantages of having a ready market and low transaction costs and using a standardised contract, in futures; and being able to agree to buy and sell a specific asset and the problems of credit risk and illiquidity, in forward contracts. Apart from the institutional arrangements and the fact that using futures requires both buyer and seller to post margin, as far as companies are concerned, forwards and futures serve very much the same purpose: both types of contract allow firms to set the prices at which they enter into a specific purchase or sale transaction in the future and to manage the price risk for inputs or outputs.
Before You Go On WEB The major exchanges have information about their contracts and how they can be used. The two major ones in Europe are the NYSE Euronext group http://www .euronext.com and Eurex http://www .eurexchange.com. The largest exchange in the world is the CME Group in Chicago http://www.cmegroup.com.
Typically, a futures contract will be based on a representative asset for the particular asset class or a recognised benchmark asset. For instance, the copper futures contract traded on the London Metal Exchange, a commodities futures exchange, specifies that it must be Grade A copper bars conforming to a defined standard of purity. A number of asset types have no representative asset. An example is corporate bonds, and there is no corporate bond futures contract since there is no such thing as a ‘representative company’. In this case, market participants have to use government
1. What are the elements that go to determine the price at which a forward contract is agreed? Which elements will increase the forward price and which elements will reduce the forward price? 2. How does a forward contract create counterparty credit risk? 3. What are the main differences between a forward contract and a futures contract?
SWAPS Learning Objective 4 Define interest rate and cross-currency swaps and know how they are valued. Companies often enter into long-term agreements that have predetermined cash flows. For instance, a company may borrow via issuing a fixed-rate bond. Other companies, in particular small ones that do
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would rather make fixed payments on its loan – i.e., just like a bond’s payments. What it would like to do is exchange the variable-rate liability for a fixed set of payments. This is precisely what interest rate swaps do. They are agreements where one party agrees to make a set of fixed interest payments to another party conditional upon the other party making variable payments in exchange. To determine the payment amounts, the contract specifies a notional amount of principal to calculate what each party is due. The variable rate is determined using an index of interest rates, such as the euro interbank offered rate (Euribor). Take the example of SEBA AG, a German machinery manufacturer that has borrowed D 20 million at a floating rate from Commerzbank. The company wants to lock in the interest it will pay on this loan and enters into a five-year interest swap that exactly matches the amount and maturity of the loan. The fixed rate is preset at 5% and hence the fixed side (also called the coupon) on the swap will be D 1 million (D 20 million 0.05) and that for the floating side will be D 20 million Euribort. This is ‘reset’ at each period, which for simplicity we will assume is 1 year, although in most cases it is more frequent – typically, every six months, to match the interest due on the loan. The swap would therefore have the following cash flows:
not have access to the bond market, have to borrow at a variable rate from a bank or other financial institution. These fixed or variable-rate loans may create undesirable risks. Managers like to be able to plan ahead and know the costs of the various factors of production. For a company to borrow at a variable rate creates the risk that interest rates increase over the life of the loan. This is likely to happen just when there is also pressure on the firm’s profit margins and sales. It is therefore desirable to manage the interest rate risk. It is possible to use forward and futures contracts to do this. However, these have some disadvantages: there may not be suitable contracts for the longer maturities or they are expensive and the prices will change with the maturity of the contracts. Think back to the Airbus example: if the contract had been for three years, the forward price would have been more than the two-year price, given the way the cost-of-carry formula works. Furthermore, forwards and futures only cover a single purchase or sale transaction.
Interest rate swap exchange agreement where one party exchanges a stream of interest payments for another party’s stream of cash flows
0 [A] Fixed rate payment (millions) [B] Indexed (floating rate) payment
CORPORATE RISK MANAGEMENT
1
2
3
4
–€1
–€1
–€1
–€1
þ Euribor1 D 20 million
þ Euribor2 D 20 million
þ Euribor3 D 20 million
þ Euribor4 D 20 million
þ Euribor5 D 20 million
D 1 þ Euribor1 D 20 million
D 1 þ Euribor2 D 20 million
D 1 þ Euribor3 D 20 million
D 1 þ Euribor4 D 20 million
D 1 þ Euribor5 D 20 million
5 Years
–€1
Combining A þ B Net cash flow
Swaps get around the problems with forwards and futures by using the same price for all the exchanges in cash flows. Take the situation where a company borrows money at a variable rate, but
In this transaction SEBA has borrowed via a loan, where the interest rate is set by reference to Euribor. By using the interest rate swap, the company has transformed the payment flows such that
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Euribor interest payment on loan
SEBA
SEBA AG enters into an interest rate swap transaction with Ribo Bank Euribor Ribo Bank
SEBA
(swap counterparty)
5%
Effect of the interest rate swap on SEBA AG’s payment flows on its loan Euribor interest payment on loan
Euribor Ribo Bank
SEBA
(swap counterparty)
5%
Exhibit 20.3: How the Interest Rate Swap Transforms SEBA AG’s Floating-Rate Liability into a Fixed-Rate Liability The interest rate swap transforms SEBA’s floating-rate loan payments into fixed-rate payments when SEBA contracts to pay the fixed rate, or coupon, on the swap and receive the floating-rate payments. As a result, the floating rate it receives matches the payments it makes on the loan and its obligation is now to make the fixed payment of 5% on the notional amount of the swap. As the loan and the swap are both for D 20 million, the company has a fixed-rate payment each year of D 1 million from entering into the swap.
its loan now has a fixed interest payment of 5% per year with a known future interest payment at the end of each year of D 1 million. Exhibit 20.3 illustrates the way the loan’s variable interest rate is transformed into a fixed rate by adding the interest rate swap. An interest rate swap allows a company such as SEBA to make either fixed-rate payments or
floating-rate payments. Hence, the swap would work equally well if SEBA had borrowed at a fixed rate and wanted to make a floating-rate payment. Because companies and financial institutions often have offsetting needs, a market in swaps brokered via major banks has evolved and a major bank will usually be the counterparty to any corporate swap transaction.
Learning by Doing Application 20.3 Problem: As the financial manager at the pizza restaurant group, you note there is an inverse relationship between the revenues of the restaurants and interest rates. This means that if interest rates rise, the group’s cash flow suffers
disproportionately since revenues go down just when interest costs go up. The pizza restaurant business has borrowings of D 5 million that mature in four years’ time. These consist of a loan that has an interest rate indexed to Euribor
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will receive Euribor from the swaps counterparty. This will result in the following:
plus 2%. The four-year interest rate swaps rate is 3.25%. What can you do to reduce the effect of higher interest rates on the group’s cash flow? What will be the fixed rate if you use an interest rate swap?
Loan Payments in Payments out
Approach: You need to enter into an interest rate swap to ‘lock in’ the current swaps rate plus the margin over Euribor – the interest rate index – that the pizza restaurant pays on its loan for the next four years.
(Euribor þ 2.0%)
Interest Rate Swap
Net
3.25% þ Euribor
3.25% 2.0% 5.25%
By entering into the swap, the pizza restaurant group can obtain a fixed rate of 5.25% on its borrowings. Even if interest rates rise over the four years, the group’s total interest expense is now fixed at D 262 500 per year (D 5 million 0.0525).
Application: The pizza restaurant group agrees to pay on the fixed (coupon) side of the four-year swap, which is 3.25% per year. In exchange, it
Valuing Interest Rate Swaps
lending, we can use our understanding of how to value the fixed side and the floating side to determine the swap’s value. The swap’s value will simply be:
The value of an interest rate swap will be the difference between the payments that the company makes and those it receives. We can apply our understanding of how cash flows are valued by noting that a swap is created if we borrow at a floating rate and agree to pay the indexed rate and use the proceeds to invest in a fixed-rate par bond. The cash flows from these transactions will look as follows:
0
CORPORATE RISK MANAGEMENT
Value of interest rate swap ¼ Value of bond with swap coupon rate value of loan with swap floating rate
ð20:2Þ
In Chapter 8, we learned that the way to price bonds is to discount their cash flows using
1
2
3
4
n Years
[A] Borrow amount P at a floating rate (i %)
þP
P i1%
P i1%
P i1%
P i1%
P i1% P
[B] Invest proceeds P in a fixed-rate par bond paying k%
P
þ P k%
þP k%
þP k%
þP k%
þP k% þP
—
P i1% þP k%
P i1% þP k%
P i1% þP k%
P i1% þP k%
P i1% þP k%
Combining A þ B Net cash flow
The net payments will be simply the interest differential between the fixed side payment and the then prevailing floating-rate payment. Since the swap is simply the product of a package made up of a floating-rate borrowing and a fixed-rate
Equation (8.1): PB ¼
C1 C2 Cn þ F n þ þ þ 2 1 þ i ð1 þ iÞ ð1 þ iÞn
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where:
þ
[A] Fixed-rate payment (millions) [B] Indexed (floating-rate) payments (millions) Combining A þ B Net cash flow
1
D 4:383 ð1:04383Þ4
þ
D 4:383 ð1:04383Þ5
þ
D 100 ð1:04383Þ5
PB ¼ D 100 million D 4:0 D 4:2 D 4:4 þ þ 1:04383 ð1:04383Þ2 ð1:04383Þ3
PL ¼
þ
This will work well for the fixed side. But what of the floating side? We know what the interest rate is for the first period since we will know the value of the index, but we do not know what the interest rates will be at t ¼ 2 and thereafter. This makes it seemingly impossible to value the floating-rate loan. However, this is to ignore the fact that at the start of period 2, the loan’s interest rate will be set by the index at the then current prevailing interest rate. This means that the loan value will be its par value or principal amount. This means that the value of the loan will be its principal amount at the reset date. Let us check this out by assuming that we have perfect foresight and know the interest rates that will prevail on the fixed and floating sides of the following D 100 million five-year interest rate swap that has a fixed-rate payment of 4.383%:
0
D 4:383 D 4:383 D 4:383 þ þ 1:04383 ð1:04383Þ2 ð1:04383Þ3
PB ¼
PB ¼ price of the bond or present value of the stream of cash payments Ct ¼ coupon payment in period t, where t ¼ 1, 2, 3, . . . , n Fn ¼ par value or face value (principal amount) to be paid at maturity i ¼ market interest rate (discount rate or market yield) n ¼ number of periods to maturity
D 4:6 ð1:04383Þ4
þ
D 4:8 ð1:04383Þ5
þ
D 100 ð1:04383Þ5
PL ¼ D 100 million The value of this swap is zero since both sides have equal value (PB ¼ PL). We would call this an ‘at-market’ swap since it has a zero net present value. Just as with forwards and futures, the price at which we can enter swaps that are being offered in the market is their fair value. In the above swap, neither side stands to win or lose. Of course, in practice, the payer and receiver of the floating payment do not know in advance what these payments will be. However, since we know that the floating side remains at or very close to the notional principal on the swap, all the value change will occur as the present value of the fixed payments rise and fall with changes in interest rates.9 An ‘off-market’ interest rate swap is valued in the same way as an at-market interest rate swap by
2
3
4
5 Years
D 4.383 þD 4.0
D 4.383 þD 4.2
D 4.383 þD 4.4
D 4.383 þD 4.6
D 4.383 þD 4.8
D 0.383
D 0.183
þD 0.017
þD 0.217
þD 0.417
The five-year interest rate is 4.383% per year. We first present-value the cash flows, treating the fixed-rate side as a bond and the floating-rate side as a loan (where, exceptionally, we know what these floating-rate payments will be):
noting that the floating-rate side is unaffected by changes in interest rates. What will be the value of a five-year swap when the fixed side or coupon payment is not 4.383%, but 3.90% and 4.70%, respectively?
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To answer this question, we simply need to recalculate the fixed side of the swap with the new coupon rates: PB;3:9% ¼
D 3:9 D 3:9 D 3:9 þ þ 1:04383 ð1:04383Þ2 ð1:04383Þ3 þ
D 3:9 ð1:04383Þ4
þ
D 3:9 ð1:04383Þ5
þ
þ
ð1:04383Þ5
D 4:7 D 4:7 D 4:7 þ þ 1:04383 ð1:04383Þ2 ð1:04383Þ3 D 4:7 ð1:04383Þ
4
þ
D 4:7 5
ð1:04383Þ
þ
are in forwards and futures, and hence the gains and losses here will depend on whether one is paying or receiving the fixed rate. The situation will therefore be:
D 100
PB ¼ D 97:874 million PB;4:7% ¼
CORPORATE RISK MANAGEMENT
D 100 ð1:04383Þ5
PB ¼ D 101:397 million So in the case where the coupon rate is less than the market interest rate or at-market swaps coupon rate (3.9% < 4.383%), the value of the swap will be þD 2.126 million ( D 97.874 þ D 100). In the case where the coupon rate on the swap is greater than the market interest rate (4.7% > 4.383%), the value of the swap will be D 1.397 million. Of course, there are two sides to a swap, just as there
Receive the fixed rate (Pay the floating rate) Pay the fixed rate (Receive the floating rate)
Coupon Rate > At-market Swaps Rate
Coupon Rate < At-market Swaps Rate
Swap will have a negative value
Swap will have a positive value
Swap will have a positive value
Swap will have a negative value
Swaps are direct obligations between the two parties, like forwards, and have the same problem with counterparty credit risk. Credit risk will arise if the present value of the future receipts is greater than the present value of future payments.
Learning by Doing Application 20.4 Problem: The current four-year ‘at-market’ interest rate swaps rate is 4.00%. You have a swap with exactly four years to maturity with a notional principal amount of D 50 million and you are receiving a fixed rate of 3.75% on the swap. What is the swap’s value? Approach: We apply the swap valuation approach where we treat the value of the swap as the difference between a fixed-rate bond (PB) and a floating-rate loan (PL) in order to work out the net present value of the swap, taking the floating-side value to be the notional principal amount.
Application: The amount of interest (or the coupon payment) on the fixed side of the swap will be D 1 875 000 (D 50 000 000 0.0375). The present value of the bond element (PB) will therefore be: PB ¼
D 1 875000 D 1 875000 D 1 875000 þ þ 2 3 1:04 ð1:04Þ ð1:04Þ þ
D 1 875000 4
þ
D 50 000 000 4
ð1:04Þ ð1:04Þ ¼ D 1 802 885 þ D 1 733 543 þ D 1 666 868 þ D 44 342 967 ¼ D 49 546 263
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The value of the swap will be PB – PL, that is þD 49 546 263 D 50 000 000, or D 453 737. From your perspective, the swap
is a liability since the present value of the payments out exceeds the present value of the payments to be received. That is, 3.75% < 4.00%.
Cross-Currency Swaps
What we need to understand at this point is that by using a cross-currency swap, Airbus has effectively made a fixed-rate loan in euros against a fixed-rate borrowing in US dollars.
A cross-currency swap is like an interest rate swap except that instead of being in one currency, it involves the exchange of cash flows between two different currencies. So, for instance, one side of a cross-currency swap may be denominated in US dollars and the other side in euros. In this case, for the swap to work, both parties must exchange both the interestpayments.Forexample,ifAirbusentersintoa cross-currency swap for D 100 million at an agreed exchange rate of US D 1.3000 ¼ D 1, with fixed interest payments of 3.5% in euros and 4.1% in US dollars for five years – where it pays in US dollars and receives in euros – the cash flows will be as follows:10
Cash flows in euros (millions) Cash flows in US dollars (millions)
Cross-currency swap the exchange of principal and interest in one currency for the principal and interest in another currency
There are a good many reasons why Airbus, or any other company, might want to enter into a
0
1
2
3
4
–€100
+€3.5
+€3.5
+€3.5
+€3.5
+$130
–$5.33
–$5.33
–$5.33
–$5.33
To receive the US dollars, Airbus provides D 100 million at the start of the transaction. The euro-side interest payments are D 3.5 million (D 100 0.035). On the dollar side, Airbus initially receives D 130 million (that is, D 100m 1.3000) based on the agreed exchange rate. The interest is $5.33 million ($130 0.041). At the maturity of the swap, both parties re-exchange the principal. A key feature of the cross-currency swap is that the exchange rate is fixed throughout. In the next chapter we discuss how exchange rates work and why managing exchange rate risk is important.
5 Years
+€3.5 +€100 –$5.33 –$130
cross-currency swap. In Airbus’s case, its costs and borrowings will be largely in euros, but its airliner sales will be largely in US dollars. Therefore, the motivation may be to reduce the effect of currency movements on its costs, which are largely in euros. Other motivations include using the company’s borrowing cost advantage in euros to fund US dollar-denominated investments, such as a North American subsidiary. The motivations for corporate risk management discussed at the start of the chapter stimulate the corporate use of crosscurrency swaps.
Learning by Doing Application 20.5 Problem: The pizza restaurant group is considering expanding its operations into Sweden. You have been tasked with providing the necessary
finance to support this move, which is estimated to need D 2 million. You have been in contact with a Swedish bank and they say the company
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can borrow Swedish krona (SKr) 20 million at a fixed rate of 6.20% per year for five years. In your research, you discover you can do a crosscurrency swap between the euro and the Swedish krona for five years at 6.10% per year against a fixed rate in euros of 5.10% per year. The company currently has the ability to raise fixed rate using an interest rate swap as per Learning by Doing 20.3 at 5.25% per year. Which represents the better financing deal? Approach: We need to compare the two alternatives, which are (1) borrowing directly from the Swedish bank or (2) borrowing in euros and using the cross-currency swap to obtain the Swedish krona for the new venture.
Valuing Cross-Currency Swaps The valuation of cross-currency swaps is the same as that for interest rate swaps. We simply presentvalue the cash flows of the two sides and convert one of the present values into the other currency using the prevailing exchange rate. Let us value the Airbus swap given above and, to do so, we will assume that one year has passed and interest rates and the exchange rate have both changed. The exchange rate has now moved to $1.3500 ¼ D 1, that is, the US dollar has fallen against the euro. The interest rate in US dollars has risen slightly to 4.5%, as has that in euros, which is now 3.75%. The original market conditions at the initiation of the cross-currency swap and the new market conditions and changes are given below: Original Market Conditions Euro interest rate US dollar interest rate Foreign exchange rate Maturity
3.50% 4.10% $1.300/D 5 years
Using the current market conditions, we now revalue the swap using the same approach that we used for the interest rate swap. We therefore present-value the remaining cash flows as follows:
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Solution: The two alternatives provide the following cost of borrowing: (1) Direct borrowing from the Swedish bank is 6.20%. (2) The swaps rate is euros 5.10% and 6.10% in Swedish krona. The company pays 0.15% on its euro borrowing (5.25% – 5.10%) but pays 0.20% less on its Swedish krona via the swap (6.30% – 6.10%). Netting the two differences means that it is saving a modest 0.05% per year (0.15% – 0.20%) by borrowing in euros and swapping into Swedish krona. Borrowing in euros and swapping to fixed rate in euros gives an all-in cost of 6.15% in Swedish krona.
D 3:5 D 3:5 D 3:5 þ þ 2 1:0375 ð1:0375Þ ð1:0375Þ3 D 103:5 þ ð1:0375Þ4 ¼ D 99:087 million $5:33 $5:33 $5:33 þ þ PB;US dollars ¼ 2 1:045 ð1:045Þ ð1:045Þ3 $135:33 þ ¼ $128:134 million ð1:045Þ2 The last step is to convert one of the currencies into the other at the current exchange rate for the US dollar and the euro ($1.3500/D ). The value of the swap in euros is therefore D 4.173 million (D 99.087 – $128.134/$1.3500). Of course, this value will depend on whether one is receiving PB;euro ¼
Market Conditions After One Year 3.75% 4.50% $1.3500/D 4 years
Change From Original Market Conditions þ0.25% þ0.40% þ$0.0500 1 year
the euro cash flows or the US dollar ones. For one side, it is a gain and for the other side, a loss. To better understand where the gains and losses are coming from, we can break the swap
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into its constituent value change components: (1) change in value of euro component, (2) change in value of US dollar component and (3) changes in the exchange rate. We therefore have:
originally borrowed. To put it another way, to replace the dollar-denominated cash flows, Airbus can provide $128.134 million rather than the original $130 million, thus saving $1.866 million.
Original Value
New Value
(1) Euro-side value change (2) US dollar-side value change
D 100 $130
D 99.087 $128.134
(3) Change from movement in the currency
$130
$135
(millions)
(1 þ 2 þ 3) Net effect of changes in value The table shows that the components of value change have led to the cross-currency swap either being an asset (if the party is paying US dollars and receiving euros) or a liability (if receiving US dollars and paying euros). We will look at the cross-currency swap from Airbus’s perspective, but this is simply a mirror image to that of the counterparty on the other side of the swap. From the table we can see that there is a change in value of D 0.913 million (D 99.087 D 100) from the increase in the rate of interest on the euro side of the swap. The original interest rate was 3.50% and it has increased to 3.75%. This leads to a reduction in the present value of the cash flows denominated in euros that Airbus will receive. The same has happened for the US dollar side, where interest rates have risen from 4.10% to 4.50% and the value has fallen from $130 million to $128.134 million ( $1.866). Whether this is good or bad news depends on whether one is paying or receiving US dollars on the cross-currency swap. As the dollar side is a liability to Airbus since it is paying, a reduction in value is good news. This is because Airbus can now terminate the swap at the current market conditions and pay back less than
Value if Paying the Euros and Receiving the US Dollars
Value if Paying the US Dollars and Receiving the Euros
þD 0.913 $1.866 or D 1.382 ( $1.866/$1.3500) $5 or D 3.704 ( $5/$1.3500) D 4.173
D 0.913 þ$1.866 or þD 1.382 ($1.866/$1.3500) þ$5 or þD 3.704 ($5/$1.3500) þD 4.173
If Airbus had been receiving the US dollar cash flows, it would have lost money from the change in interest rates – as it has done from the increase in the rate of interest in the euro. The same logic applies for the change in the value of exchange rate between the euro and the US dollar. The original swap required $130 million to equate to D 100 million; with the fall in value of the US dollar, $135 million is needed. This means an additional $5 million is needed, depending on whether one is due to repay or receive dollars. Since Airbus is due to repay $130 million, it now needs fewer euros to repay the originally contracted amount of $130 million. At the start, D 100 million bought $130 million, now D 100 million buys $135 million, so Airbus would only need to provide $130/$135 D 100 million (D 96.296), saving D 3.704 million. Adding all these effects together, and converting the dollars to euros, gives a net change in value of D 4.173 million. This is the sum that the euro payer (US dollar receiver) needs to pay to the euro receiver (US dollar payer) to terminate the swap. Since Airbus has contracted to pay US dollars and receive euros, it will receive D 4.173 million if the swap is terminated by mutual agreement.11
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Learning by Doing Application 20.6 Problem: The pizza restaurant decided to use the cross-currency swap discussed in Learning by Doing 20.5 and entered into a 5-year agreement to pay Swedish krona (SKr) and receive euros. The fixed rate on the swap is 6.30% in krona per year and 5.10% in euros. The amount of the swap is D 2 million and SKr 19.6 million, respectively. It is now the pizza restaurant’s year end and the auditors want to know what is the swap’s current value as, under the IFRS rules, derivative transactions need to be marked-to-market and reported on the company’s balance sheet. That is, they need to be revalued to their fair value for financial reporting purposes. Since the swap was initiated, one year has passed and the exchange rate of the euro to the Swedish krona is now at SKr 9.9/D , the Swedish krona interest rate for four-year swaps is 6.25% and that for euros is 5.05%. What is the swap’s fair value for reporting purposes?
PB;euro ¼
Approach: We need to apply the valuation approach for cross-currency swaps where we present-value the two sets of remaining cash flows for the four years at the now-prevailing interest rates and convert the two sides to a common currency before determining the net value. The pizza restaurant group is paying Swedish krona (which is the liability side) and receiving euros (the asset side). Since the reporting currency is the euro, it is necessary to convert the value of the cross-currency swap to this currency. Solution: We first need to calculate the remaining cash flows on the two sides of the swap. The euro side is worth D 2 million and the interest rate is 5.10%, so the fixed payments are D 102 000 per year (D 2 million 0.051%). On the krona side, the fixed payment is SKr 1 196 000 (SKr 19.6 6.10).
D 102 000 D 102 000 D 102 000 D 2 102 000 þ þ þ 1:0505 ð1:0505Þ2 ð1:0505Þ3 ð1:0505Þ4
¼ D 2 003 542 PB;SKr ¼
SKr 1 196 000 SKr 1 196 000 þ 1:0625 ð1:0625Þ2 þ
SKr 1 196 000 ð1:0625Þ3
þ
SKr 21 196 000 ð1:0625Þ4
¼ SKr 19 498 706
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The final stage is to convert the krona value into euros (we do this since the pizza restaurant reports its results in euros) at the current exchange rate, which gives a value in euros of D 1 969 566 (SKr 19 498 706/SKr 9.9/D ). The company receives the euros, so this is a
cash inflow and pays the krona, so the net value of the swap is D 33 976 (D 2 003 542 D 1 969 566). This is a positive value, so this is the amount that will be reported as a longterm financial asset on the balance sheet at the year-end.
Before You Go On
Underlying asset
1. How can we characterise the cash flows from an interest rate swap and a crosscurrency swap? 2. Why does a swap only have credit risk when it has a positive value? 3. In what ways do swaps transform the risk of firmsâ&#x20AC;&#x2122; assets and liabilities?
the asset from which the value of an option is derived
Exercise (expiration) date the last date on which an option can be exercised
FINANCIAL OPTIONS Learning Objective 5
Strike (exercise) price
Define a call option and a put option and describe the payoff function for each of these options.
the price at which the owner of an option has the right to buy or sell the underlying asset
A financial option is a derivative in that, like forwards, futures and swaps, its value is derived from the value of another asset. The owner of a financial option has the right, but not the obligation, to buy or sell an asset on or before a specified date for a specified price. The asset that the owner has a right to buy or sell is known as the underlying asset. The last date on which an option can be exercised is called the exercise date, or expiration date, and the price at which the option holder can buy or sell the asset is called the strike price, or exercise price.
Financial option the right to buy or sell a financial security, such as a share of stock, on or before a specified date for a specified price
Call Options Let us consider how the value of an option is derived from the value of an underlying asset. Suppose you own an option to buy one share of Siemens AG, the German engineering company, for D 50 and today is the exercise date â&#x20AC;&#x201C; if you do not exercise the option today, it will expire and become worthless. If the price of Siemens shares is less than D 50, it does not make sense to exercise your option, because if you did, you would be paying D 50 for something you could buy for less than D 50 in the open market. Similarly, if the share price is D 50, there is no benefit to be had from exercising your option. If, however, the price is above D 50, then you will benefit from exercising the option. Even if you do not want to own the Siemens share, you can buy it for D 50 and
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immediately turn around and sell it for a profit. The value of the option to you is the difference between the market price of Siemens shares and the strike price of the option. For example, if the Siemens shares are trading for D 60 in the market, then the option is worth D 10 (D 60 share price D 50 strike price) to you. If the shares are trading at D 70, then the value of the option is D 20 (D 70 D 50), and so on. The relation between the value of an option and the price (value) of the underlying asset – such as the Siemens shares – is known as the option payoff function. Part A in Exhibit 20.4 illustrates the payoff function at expiration (actually, the instant before the option expires) for the owner of an option that is like the option on the Siemens shares we just discussed. This option is known as a
CORPORATE RISK MANAGEMENT
call option because it gives the owner the right to buy, or ‘call’, the underlying asset.
Option payoff function the function that shows how the value of an option varies with the value of the underlying asset
Call option an option to buy the underlying asset
Value of Call Option at Expiration
A. Owner (buyer) of a call option
The value of a call option increases one for one with an increase in the value of the underlying asset when the value of that asset is above the strike price. 0
Strike price Value (price) of Underlying Asset
B. Seller of call option Value of Seller’s Position at Expiration of Call Option
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0 The value of the seller’s position decreases one for one with an increase in the value of the underlying asset when the value of that asset is above the strike price.
Strike price Value (price) of Underlying Asset
Exhibit 20.4: Payoff Functions for a Call Option at Expiration At the instant before it expires, the value of a call option to the owner equals either: (1) zero, if the value of the underlying asset is less than or equal to the strike price, or (2) the value of the underlying asset less the value of the strike price, if the value of the underlying asset is greater than the strike price. The value of the seller’s position equals either: (1) zero, if the value of the underlying asset is less than or equal to the strike price, or (2) the strike price less the value of the underlying asset if the value of the underlying asset is greater than the strike price.
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With an exercise price of D 50, the value of the Siemens call option equals D 0 if the price of the underlying shares is D 50 or less. As we noted earlier, it would not make sense to exercise the option if the price of the shares is not greater than D 50. Since an option is the right to buy or sell an underlying asset, rather than an obligation to buy or sell, the owner of the option can simply let it expire if it does not make sense to exercise it. This limits the downside for the owner of the option to D 0. In this way, options are very different to the forwards, futures and swaps discussed earlier. If the underlying asset price is above the strike price, the value of the call option at exercise increases unit for unit with the price of the underlying asset. You can see this relation in part A of the exhibit. For every euro that the asset price exceeds the strike price, the value of the call option increases by one euro. In other words, the slope of the payoff function equals one when the underlying asset price is above the exercise price. Part B of Exhibit 20.4 illustrates the payoff function for a person who sells a call option (also known as writing the option). Notice that the payoff function for the seller (or writer) is the mirror image of that for the owner (buyer) of the call option. This makes sense, since any gain for the owner is a loss for the seller. To see why this is true, let us return to the Siemens option example. Recall that if the shares are trading at D 60 when the option expires, the call option is worth D 10 to the owner, who can purchase the shares for D 50 and then immediately sell them on the market for D 60. The seller of the call option, though, must sell shares that are worth D 60 for D 50 â&#x20AC;&#x201C; resulting in a D 10 loss. Part B of Exhibit 20.4 shows that the payoff to the seller of the call option is never positive. It is negative when the price of the underlying asset is greater than the strike price, and it equals zero when the price of the underlying asset is equal to or less than the strike price. You may be wondering why anyone would ever sell a call option if the return were never positive. The reason is simply
that the buyer pays the seller a fee to purchase the option. This fee, known as the call premium, makes the total return to the seller positive when the price of the underlying asset is near or below the strike price.
Call premium the price that the buyer of a call option pays the seller for that option
A call premium is just like the premium you pay when you purchase insurance for your car. In return for the insurance premium, the insurance company agrees to pay you if certain events occur, such as if you collide with another car or if a hailstorm damages the car. The seller of a call option is simply selling insurance to the buyer which pays the buyer when the value of the underlying asset is above the strike price.
Put Options While the owner of a call option has the right to buy the underlying asset at a pre-specified price on or before the expiration date, the owner of a put option has the right to sell the underlying asset at a pre-specified price. The payoff function for the owner of a put option is similar to that for a call option but it is the reverse in the sense that the owner of a put option profits if the price of the underlying asset is below the strike price. This is illustrated in Exhibit 20.5.
Put option an option to sell the underlying asset
Part A of the exhibit shows that the owner of a put option will not want to exercise that option if the price of the underlying asset is above the strike price. Obviously, it does not make sense to sell an asset for less than you can get on the open market.
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Value of Put Option at Expiration
A. Owner (buyer) of a put option
0
The value of a put option increases one for one with a decrease in the value of the underlying asset when the value of that asset is below the strike price. Strike price Value (price) of Underlying Asset
B. Seller of put option Value of Sellerâ&#x20AC;&#x2122;s Position at Expiration of Put Option
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0 The value of the sellerâ&#x20AC;&#x2122;s position decreases one for one with an decrease in the value of the underlying asset when the value of that asset is below the strike price.
Strike price Value (price) of Underlying Asset
Exhibit 20.5: Payoff Functions for Put Option at Expiration At the instant before it expires, the value of a put option to the owner equals either: (1) zero, if the value of the underlying asset is greater than or equal to the strike price, or (2) the strike price less the value of the underlying asset, if the value of the underlying asset is less than the strike price. The value to the seller of a put option equals either: (1) zero, if the value of the underlying asset is greater than or equal to the strike price, or (2) the value of the underlying asset less the strike price, if the value of the underlying asset is less than the strike price.
When the value of the underlying asset is below the strike price, however, the owner of the put option will find it profitable to exercise the option. For example, suppose that you own a put option that is expiring today and that entitles you to sell shares in Siemens for D 50. If the current price of Siemens shares in the market is D 45, the put option is worth D 5, because exercising the option will enable you to buy the shares for D 45 and then turn around and sell them for D 50. Similarly, if the current price of Siemens shares is D 30, the put option is worth D 20, because you can buy the shares for D 30 and sell them for D 50. Part B of Exhibit 20.5 shows that the payoff for the seller of the put option is negative when the price of the underlying asset is below the strike price. This is because the seller of the put option is obliged to
purchase the asset at a price that is higher than its market price. For instance, in the Siemens put option example, if the exercise price is D 50 and the current market price is D 30, the seller of the put option must buy the shares for D 50 but can only sell them for D 30. This results in a D 20 loss. As with a call option, the payoff for the seller of a put option, which is illustrated in part B of Exhibit 20.5, is never positive. The seller of a put option hopes to profit from the fee, or put premium, that he or she receives from the buyer of the put option.
Put premium the price that the buyer of a put option pays the seller of that option
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BUILDING INTUITI
N
Payoff Functions for Options are Not Linear Payoff functions for options are not straight lines. This is because the owners of options have the right, rather than the obligation, to buy or sell the underlying assets. If it is not in the owner’s best interest to exercise an option, he or she can simply let it expire without exercising it. This limits the owner’s potential loss to the value of the premium he or she paid for the option. This makes options from forwards, futures and swaps where the gains and losses are symmetrical.
American, European and Bermudan Options At the beginning of this section, we said that the owner of a financial option has the right to buy or sell a specific asset on or before a specified date for a specified price. In the real world, there are actually several different arrangements concerning when an option can be exercised. Some options can only be exercised on the expiration date. These are known as European options. Other options, known as American options, can be exercised at any point in time on or before the expiration date. There are also exotic options, such as so-called Bermudan options, which can be exercised only on specific dates during the life of the option. Most exchange-traded options are American options.
More on the Shapes of Option Payoff Functions It is important to note that the payoff functions in Exhibits 20.4 and 20.5 illustrate the values of options to owners and sellers at the instant before
they expire. These payoff functions have similar, but somewhat different, shapes at earlier points in time. We discuss why this is the case in the next section. It is also important to recognise that the payoff functions in Exhibits 20.4 and 20.5 are not straight lines for all possible values of the underlying asset. Each payoff function has a ‘kink’ at the strike price. This kink exists because the owner of the option has a right, not an obligation, to buy or sell the underlying asset. If it is not in the owner’s interest to exercise the option, he or she can simply let it lapse. Later, we will discuss how this feature of options causes agency problems and how it can be useful in managing the risks faced by a firm.
WEB You can learn more about call options and put options on the Options.Net website at: http://www.theoptions.net/option-tradingstrategies/pay-off-diagrams-for-option/.
Decision-Making Example 20.1 When it Makes Sense to Exercise an Option Situation: You own a call option and a put option on Fiat shares. The strike price for both of these options is D 8 and both options expire today. If the current price of Fiat shares is D 7, would you exercise either of these options? If so, which one?
Decision: You should exercise the put option. It allows you to sell Fiat shares for D 8 that would cost you only D 7 to buy. It does not make sense to exercise the call option because the strike price is greater than the market price of Fiat shares.
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Before You Go On 1. What is a call option and what do the payoff functions for the owner and seller of a call option look like? 2. What is a put option, and what do the payoff functions for the owner and seller of a put option look like? 3. Why does the payoff function for an option have a kink in it?
OPTION VALUATION Learning Objective 6 List and describe the factors that affect the value of an option. We saw in the last section that determining the value of a call or a put option at the instant before it expires is relatively simple. For a call option, if the value of the underlying asset is less than or equal to the strike price, the value of the option to the owner is zero. If the value of the underlying asset is greater than the strike price, the value to the owner is simply the value of the underlying asset minus the strike price. For a put option, if the value of the underlying asset is greater than or equal to the strike price, the value of the option is zero to the owner. If the value of the underlying asset is less than the strike price, the value to the owner is the strike price minus the value of the underlying asset. It is more complicated to determine the value of an option at a point in time before its expiration date. We do not know exactly how the value of the underlying asset will change over time and therefore we do not know what value we will ultimately receive from the option. In this section, we discuss the key variables that affect the value of an option prior to expiration and describe one method that is commonly used to value options. Our objective is not to make you an expert in option valuation but
CORPORATE RISK MANAGEMENT
rather to help you develop some intuition about what makes an option more or less valuable. This intuition will help you better understand how options affect corporate finance decisions.
Limits on Option Values We will begin by using some common sense to put limits on what the value of a call option can possibly be prior to its expiration date. We focus on call options here because, as you will see, there is a simple relation that enables us to calculate the value of a put option once we know the value of a call option with the same strike price and expiration date. We already know that the value of a call option can never be less than zero, since the owner of the option can always decide not to exercise it, if doing so is not beneficial. A second limit on the value of a call option is that it can never be greater than the value of the underlying asset. It would not make sense to pay more for the right to buy an asset than you would pay for the asset itself. These two limits suggest that the value of a call option prior to expiration must be in the shaded area in part A of Exhibit 20.6. The shaded area is bounded below by the horizontal axis, because the value of the option must be greater than zero, and it is bounded above by the line that slopes upward at a 45-degree angle, because an option value greater than this would exceed the value of the underlying asset. There are two other limits on the value of a call option prior to expiration, and these limits are somewhat more subtle. First, the value of a call option prior to the expiration date will never be less than the value of that option if it were exercised immediately. This is true because there is always a possibility that the value of the underlying asset will be greater than it is today at some time before the option expires. Of course, it is possible that the value will be lower but, since the value of the option cannot be less than zero and there is no limit on how high it can go, the expected effect of an increase in the value of the underlying asset on the value of the option is greater than the expected
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A. Possible values with first two limits Value of Call Option
The first two limits tell us that the value of a call option prior to expiration must fall within this shaded area.
0 Current Value of Underlying Asset
B. Possible values with all four limits
0
The four limits tell us that the value of a call option prior to expiration will actually fall within this shaded area. C. Typical payoff function for call option prior to expiration Value of Call Option
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Present Value of Strike Price Current Value of Underlying Asset
Value of call option prior to expiration
0 Strike Price Current Value of Underlying Asset
Exhibit 20.6: Possible Values of a Call Option Prior to Expiration The value of a call option: (1) must be greater or equal to zero (horizontal axis) and (2) cannot be greater than the value of the underlying asset (45-degree line). In addition to the two limits illustrated in part A, the value of a call option prior to expiration: (3) will never be less than the value of the option if it were exercised immediately where (4) the value of the option is calculated using the present value of the strike price, discounted from the expiration date at the risk-free interest rate. These conditions are both illustrated by the lower 45-degree angle. Part C shows the typical relation between the value of a call option prior to expiration and its value at expiration. The value of the option prior to expiration is farthest from the value of the option at expiration when the price of the underlying asset is near the strike price.
effect of a decrease. The bottom line is that, prior to expiration, the value of a call option will be greater than the value represented by the solid line in part A of Exhibit 20.4.12 The final limit arises because of the time value of money. When we consider the value of a call option at some time prior to expiration, we must compare the current value of the underlying asset with the present value of the strike price, discounted at the risk-free interest rate. We would be comparing apples and oranges if we did not do this. The present value of the strike price is the amount that an investor would have to invest in risk-free securities at any point prior to the expiration date to ensure that he or she would have enough money to exercise the option when it expired. Thus, when we compare the value of a call option prior to expiration with the value at
expiration, represented by the solid line in part A of Exhibit 20.4, we must use the present value of the strike price to draw the line. The shaded area in part B of Exhibit 20.6 illustrates the possible values for a call option prior to expiration under all four of the limits we have discussed. In practice, we find that, prior to expiration, call options have a shape that is very similar to the one illustrated by the dotted line in part C of Exhibit 20.6. Notice that this dotted line approaches zero as the value of the underlying asset gets very small relative to the strike price. This makes sense because, with a very low asset value, it becomes highly unlikely that the owner of the option will ever choose to exercise it. On the right side of the dotted line, you can see that the value of a call option prior to expiration approaches the value of the call option at expiration.
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This is because, when the current value of the underlying asset is far to the right of the kink in the payoff function, the probability that this value will fall below the strike price is very small. In other words, the expected effect of an increase in the value of the underlying asset on the value of the option is no longer much greater than the expected effect of a decrease. In this situation, the call option is very much like a forward contract on the underlying asset. Finally, notice that the dotted line is furthest above the value of the call option at expiration when the price of the underlying asset is near the strike price. At the strike price, the expected effect of an increase in the value of the underlying asset on the value of the option exceeds the expected effect of a decrease by the greatest amount.
Variables that Affect Option Values Five variables affect the value of a call option prior to expiration. Four of them are related to the following questions: 1. How likely is it that the value of the underlying asset will be higher than the strike price the instant before the option expires? 2. How far above the strike price might it be? The first two variables are relatively easy to understand. They are the current value of the underlying asset and the strike price. The higher the current value of the underlying asset, the more likely it is that the value of the asset will be above the strike price when the call option nears expiration. Furthermore, the higher the current value of the asset, the greater the likely difference between the value of the asset and the strike price. This means that, holding the strike price constant, investors will pay more for a call option if the underlying asset value is higher, because the expected value of the option as it nears expiration is higher.13 For example, suppose that you are considering purchasing a three-month American call option on Siemens shares with a strike price of D 50. You should be willing to pay more for
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this option if the current price of Siemens shares is D 55 than if it is D 50. The opposite relation applies to the strike price. That is, the lower the strike price, the more likely that the value of the underlying asset will be higher than the strike price when the option nears expiration. In addition, the lower the strike price, the greater the likely difference between these two amounts. Thus, the lower the strike price, the more valuable the option is likely to be at expiration. Of course, if the option is expected to be more valuable at expiration, it will also be more valuable at any point prior to expiration. Returning to our Siemens example, we see that a call option with a strike price of D 45 is worth more than a call option with a strike price of D 50. We turn next to two variables that affect the value of call options in somewhat more subtle ways. These variables are the volatility of the value of the underlying asset and the time until the expiration of the option. To understand how these factors affect the value of a call option, recall from part C of Exhibit 20.6 that the payoffs function for a call option prior to expiration is not symmetric. If the value of the underlying asset is well above the strike price, then the value of the option varies in much the same way as the value of the underlying asset. However, if the value of the underlying asset is well below the strike price, then the value of the option approaches zero but changes at a much lower rate than the value of the underlying asset changes. It does not matter if the underlying asset value is just a little bit below the strike price or is worthless â&#x20AC;&#x201C; a call option cannot be worth less than zero. To show how the volatility of the underlying asset value affects the value of an option, we will consider a call option on an underlying asset that has a value exactly equal to the strike price of the option. The value of this option will increase more when the value of the underlying asset goes up than it will decrease when the value of the underlying asset goes down. Let us suppose that the value of the underlying asset is equally likely to go up or down. In this case, the further the value of the asset is likely to move (the greater its volatility), the
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higher will be the value of a call option on this asset. In other words, the greater the volatility of the underlying asset value, the higher the value of a call option on the asset prior to expiration. In our Siemens example, suppose the strike price for a call option on Siemens shares is D 50, the current price of the shares is D 50 and the option expires in one year. Further, suppose that the standard deviation, s, of the return on the Siemens shares is 30% per year. Recall from the discussion in Chapter 7 that with a standard deviation of 30%, there is a 5% chance that the Siemens share price will change by more than 58.8% (1.96 standard deviations 30%) by the time the option expires. In other words, there is a 5% chance that the Siemens share price will be less than D 20.60 (D 50 [1 – 0.588]) or greater than D 79.40 (D 50 [1þ0.588]) in a year. If, instead of 30%, the standard deviation of Siemens shares were 40% per year, there would be a 5% chance that the price would be below D 10.80 or above D 89.20. (You should check these numbers to make sure you know how they are calculated.) As you can see, with the higher standard deviation the share price is more volatile. Investors will pay more for an option on a share that has a more volatile price, because the potential change in the price is greater. The time until the expiration affects the value of a call option through its effect on the volatility of the value of the underlying asset. The greater the time to maturity, the more the value of the underlying asset is likely to change by the time the option expires. For example, we will return once again to the Siemens example. Suppose that the option expires in two years rather than in one year. People who study statistics have found that the standard deviation of the return on an asset increases over time by the square root of n, where n is the number of periods. Thus, if the standard deviation of the return on Siemens shares is 30% per year, the standard deviation over two years will be:
Clearly, then, a two-year option will be worth more than a one-year option if all the other characteristics of the two options are the same. We have now discussed four of the five variables that affect the value of an option. The fifth variable is the risk-free rate of interest. The value of a call option increases with the risk-free interest rate. Exercising a call option involves paying cash in the future for the underlying asset. The higher the interest rate, the lower the present value of the amount that the owner of a call option will have to pay to exercise it.
WEB You can read about what affects the values of financial options and how they are traded at the websites for the Chicago Board Options Exchange (CBOE) at: http://www.cboe.com/ and the International Securities Exchange (ISE) at: http://www.iseoptions.com/.
The Binomial Option Pricing Model In this section, we use a simple model to show how we can calculate the value of a call option at some point in time before the expiration date. This model assumes that the underlying asset will have one of only two possible values when the option expires. The value of the underlying asset will either increase to some value above the strike price or decrease to some value below the strike price.
Arbitrage buying and selling assets in a way that takes advantage of price discrepancies and yields a profit greater than that which would be expected based solely on the risk of the individual investments
s2 years ¼ s ðnÞ1=2 ¼ 30 ð2Þ1=2 ¼ 30 1:414 ¼ 42:42%
To solve for the value of the call option using this model, we must assume that investors have no
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arbitrage opportunities with regard to this option. Arbitrage is the act of buying and selling assets in a way that yields a return above that suggested by the Security Market Line (SML), which we discussed in Chapter 7. In other words, the absence of arbitrage opportunities means that investors cannot earn a return that is greater than that justified by the systematic risk associated with an investment. As an example of an arbitrage opportunity, suppose that the shares of a particular company are being sold for a lower price in one country than in another country. An investor could simultaneously buy the shares in the country where they are less expensive and sell them in the country where they are more expensive. Assuming that the profit exceeds any transaction costs, the investor would earn an instantaneous risk-free profit. Since it is instantaneous, this profit would be, by definition, above the SML because the SML would predict that the expected return on a risk-free investment is zero if the holding period is zero. To value the call option in our simple model, we will first create a portfolio that consists of the asset underlying the call option and a risk-free loan. The relative investments in these two assets will be selected so that the combination of the asset and the loan has the same cash flows as the call option, regardless of whether the value of the underlying asset goes up or down. This is called a replicating portfolio, since it replicates the cash flows of the option. The replicating portfolio must have the same
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value as the option today, since it has the same cash flows as the call option in all possible future outcomes. If the replicating portfolio did not have the same value as the option, an investor could construct an arbitrage portfolio by buying the cheaper of the two and selling the more expensive of the two. Such trading would eventually drive the values of the option and the replicating portfolio together. To see how a replicating portfolio is constructed, consider an example. Suppose that DRYAD SA shares currently trade for D 50 and that its price will be either D 70 or D 40 in one year. We want to determine the value of a call option to buy DRYAD shares for D 55 in one year. First, notice that the value of this option is D 15 if the share price goes up to D 70 (D 70 D 55 Âź D 15) and that it is zero if the share price goes down to D 40, since the option will not be exercised. Suppose also that the risk-free rate is 5%. We can construct a portfolio consisting of x DRYAD SA shares and a risk-free loan with a value of y euros that produces a payoff of either D 70 or D 40. As you will see, this risk-free loan may involve either borrowing or lending. For each risk-free euro lend, we know that we will receive D 1.05 regardless of what happens to the price of the DRYAD shares. In the same way, if we borrow D 1, we will owe D 1.05 at the end of the year. The value of the shares, the risk-free loan, and the option today and at expiration can be illustrated as follows:
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The value of each asset when the share price goes up to D 70 is shown on the right arrow and the value when the shares go down to D 40 is shown on the left arrow. Notice that we do not know the value of the option today – that is what we are trying to calculate. We can write two equations that define the replicating portfolio that we want to construct: D 15 ¼ ðD 70 xÞ þ ð1:05 yÞ D 0 ¼ ðD 40 xÞ þ ð1:05 yÞ The first equation represents the case in which the share price increases to D 70 and the second equation represents the case in which the share price goes down to D 40. The first equation says that we want the portfolio to be worth D 15 when the share price increases to D 70 and that the D 15 value will consist of x shares worth D 70 and a risk-free loan with a face value of y and a value in one year of D 1.05 per euro of face value. Similarly, the second equation says that if the share price falls to D 40, we want the portfolio to be worth zero (D 0). In this case, the portfolio will consist of x shares worth D 40 and a risk-free loan with a face value of y and a value in one year of D 1.05 per euro of face value. Since we have two equations and there are two unknowns, x and y, we can solve for the values of the unknowns. Recall from your algebra class that we can solve for x and y by first writing one equation in terms of either x or y and then substituting the result into the second equation. For example, the first equation can be written in terms of x as follows: x¼
D 15 ð1:05 yÞ D 70
Now, substituting into the second equation gives us: D 15 ð1:05 yÞ D 0 ¼ D 40 þ ð1:05 yÞ D 70 We can now solve this equation for y. For example, we can write this relation as follows:
D 15 ð1:05 yÞ þ ð1:05 yÞ D 0 ¼ D 40 D 70 D 0 ¼ D 8:5714 ð0:6 yÞ þ ð1:05 yÞ D 0 ¼ D 8:5714 þ 0:45y 0:45y ¼ D 8:5714 Therefore: y¼
D 8:5714 ¼ D 19:05 0:45
Finally, substituting this value back into the first equation gives us the value of x: D 15 ð1:05 D 19:05Þ D 70 D 15 þ D 20:00 x¼ D 70 x ¼ 0:5 x¼
This tells us that the replicating portfolio consists of half a DRYAD SA share (x ¼ 0.50) and a D 19.05 risk-free loan (y ¼ 19.05).14 The negative value for y tells us that we would borrow, rather than lend, D 19.05 at the risk-free interest rate. If we buy half a share and borrow D 19.05, then in one year our replicating portfolio will have exactly the same payoff as the call option with a strike price of D 55. If the value of the shares declined to D 40, we would own half a share worth D 20 and we would owe D 19.05 1.05 ¼ D 20 on the loan. Since the value of the half-share would exactly equal the amount owed on the loan, the portfolio would have a total value of exactly zero. In contrast, if the value of the shares increased to D 70, the half a share would be worth D 35. Since we would still owe only D 20 in this case, the portfolio would have a total value of D 15. Since these payoffs are the same as those for the option, this portfolio must have the same value as the option. At this point, we know what the replicating portfolio is and we know that the replicating portfolio must have the same value as the call option. Now all we have to do to estimate the value of the call option is figure out what is the present value of the replicating portfolio. To do this, we simply
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determine how much of our own money we would actually have to invest to construct the replicating portfolio. In our example, we could use the D 19.05 loan to help purchase the shares, so we would not have to come up with all the money for the shares on our own. In fact, since DRYAD SA shares are currently worth D 50, a half share would cost only D 25. Therefore, we would have to come up with only D 5.95 (D 25.00 – D 19.05) over and above the amount received from the loan to buy the shares. Since D 5.95 is the amount of money that we would actually have to invest to obtain the replicating portfolio, it is the value of this portfolio and therefore the value of the option. The equation for calculating the value of the replicating portfolio, and therefore the value of the call option, can be expressed as follows: Value of the call option today ¼ C ¼ ðD 50 yÞ þ ð1 yÞ ¼ ðD 50 0:5Þ þ ð1 D 19:05Þ ¼ D 5:95 Notice, too, that the strike price, the current price of the underlying shares, the possible future prices of the underlying shares and the risk-free
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interest rate are all that entered into our calculations. We did not even mention the probabilities that the share price would go up or down at any point. That is because the volatility of the underlying shares value is accounted for by how far apart the two possible future values are. Similarly, the time to expiration is not directly considered. However, the time to expiration affects how high and how low the share price can be when the option expires.15 This model may seem surprisingly simple. However, that is largely because we chose to illustrate a simple example. The model can be extended in several ways. For example, we can incorporate possible prices for the underlying asset between now and the expiration date of the option. The underlying asset price might take one of two values one month (or day or hour) from now, and then for each of those values there might be two possible values in the following month (day or hour), and so on. Solving a model such as this requires us to work backwards from the expiration date to find the value of the option at each intermediate date and price until we finally arrive at the value of the option today. Most modern option pricing models are extensions of this type of model.
Learning by Doing Application 20.7
Valuing a Call Option Problem: You are considering purchasing a call option on Le Terrain Agricole SA shares. Le Terrain Agricole shares currently trade for D 35 and you predict that its price will be either D 25 or D 50 in one year. The call option would enable you to buy Le Terrain Agricole shares in one year for D 30. What is this option worth if the risk-free interest rate is 4%? Approach: The value of the option can be determined by computing the cost of constructing
a portfolio that replicates the payoffs from that option. Solution: The option will be worth D 20 if the share price rises to D 50 (D 50 D 30 strike price) and will be worth D 0 if the share price declines to D 25. Therefore, the replicating portfolio for this option can be determined from the following two equations: D 20 ¼ ðD 50 x Þ þ ð1:04 y Þ D 0 ¼ ðD 25 x Þ þ ð1:04 y Þ
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Solving for x and y, we find that x ¼ 0.80 and y ¼ D 19.23. Therefore, the replicating portfolio consists of 0.8 Le Terrain Agricole shares and a D 19.23 loan. Since 0.8 of a share would cost D 28 (0.8 D 35) and D 19.23 of this amount
Put--Call Parity Put--call parity the relation between the value of a call option on an asset and the value of a put option on the same asset that has the same exercise price
To this point, our discussion has focused on call options. As mentioned earlier, this is possible because there is a simple relation that enables us to calculate the value of a put option once we know the value of a call option with the same strike price and expiration date. This relation is called put–call parity. The formula for put–call parity is: P ¼ C þ Xe rt V
ð20:3Þ
where P is the value of the put option, C is the value of the call option, X is the strike price, r is the risk-free interest rate, t is the amount of time before the option expires, and V is the current value of the underlying asset. The term e rt is the exponential function that you can calculate using
would be covered by the loan, this replicating portfolio would cost D 8.77 (D 28.00 D 19.23) to construct. Therefore, the call option is worth D 8.77.
the ‘ex’ key on your calculator; it is simply a discount factor that assumes continuous compounding. It is important to make sure that the r and t are both stated in the same units of time (for example, months or years). To see how this formula works, we will consider the option on the DRYAD SA shares that we just valued. We know that C ¼ D 5.95, X ¼ D 55, r ¼ 0.05, t ¼ 1 and V ¼ D 50. Substituting these values into the put–call parity formula and solving for P, we get: P ¼ D 5:95 þ D 55e ð0:05Þð1Þ D 50 ¼ D 5:95 þ D 52:32 D 50 ¼ D 8:27 Notice that the variables used in this calculation are the same variables that determine the value of a call option. This means that the same factors that affect the value of a call option also affect the value of a put option. Notice, too, that the value of the put option (D 8.27) is greater than the value of the call option (D 5.95) in this example. This will not always be true. However, it is true in our example because the current share price of D 50 is below the D 55 strike price.
Learning by Doing Application 20.8
Valuing a Put Option Problem: In Learning by Doing Application 20.7, we found that a call option on Le Terrain Agricole SA shares is worth D 8.77 when the share price is D 35, the strike price is D 30, the risk-free interest rate is 4% and the time to
maturity is 1 year. What is the value of a put option on the shares if the strike price and all other variables have the same values? Approach: Use the put–call parity relation, Equation (20.3), to calculate the value of a put option.
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Solution: The value of the put option is as follows: P ¼ C þ Xe rt V P ¼ D 8:77 þ D 30e ð0:04Þð1Þ D 35 ¼ D 8:77 þ D 28:82 D 35 ¼ D 2:59
Options and Risk Management We have seen how options have kinked payoffs. This makes them very useful for corporate risk management. To see how risks can be managed using options, consider an oil company that is producing and selling oil to refiners. Suppose that the price of crude oil has recently risen above $130 per barrel and the company wants to make sure that, even if prices drop below $125 per barrel, it will receive at least $125 per barrel for each barrel of oil that it sells during the next three months. If the company plans to sell 100 000 barrels of oil in the next three months, the financial manager can hedge the price risk by purchasing put options on 100 000 barrels of oil with a strike price of $125 per barrel plus the cost of the options. The maturity dates on the options must be selected to match the timing of the company’s oil output over the next three months. In addition, the actual strike prices on the options must be slightly greater than $125 to account for the premiums that the company pays to purchase the options. This will ensure that the company actually receives $125 per barrel after paying for the options. One interesting benefit of using options in this way is that they provide downside protection but do not limit the upside to the company if oil prices continue to increase. Put options give the company the right to sell its oil at the strike price if crude oil prices fall but, because there is no obligation to sell, the company can still benefit if oil prices increase. As discussed earlier, this is just like buying insurance. In fact, insurance contracts can be seen as specialised put options. In addition to using options and other derivative instruments to manage commodity price risks, as in the oil company example, companies can use
CORPORATE RISK MANAGEMENT
Note that the value of the put option is less than the value of the call option in this example. This is because the current price of the shares is above the strike price.
these instruments to manage risks associated with changing interest rates and exchange rates. Large swings in interest rates can cause a great deal of volatility in the net income of a highly financially leveraged company whose managers rely on floating-rate debt. As interest rates go up and down, the company’s interest expense also goes up and down, which can lead to cash flow problems. Options can also be used to manage risks associated with foreign exchange rates. For example, as we discussed earlier, the revenues that a company reports can be strongly affected by changes in exchange rates if the company manufactures products in Europe and has significant sales in foreign currencies. If the euro strengthens against foreign currencies, the company will have to increase the overseas prices of its products in order to maintain the same euro price per unit. This, in turn, can prompt consumers in overseas markets to purchase fewer of the company’s products. By using options and other derivative instruments to protect against exchange rate movements, managers can limit declines in revenues that occur because of such movements. Finally, options can be used to manage risks associated with equity prices. This is especially important to companies that have traditional definedbenefit pension plans, which provide retirees with guaranteed retirement payments. Companies are required to put money aside to cover the costs of these payments and this money is partially invested in equities. When the stock market declines significantly, these companies must replace any lost value with new contributions, which must come from earnings. As you might expect, companies are very interested in managing the risk that they will have to make such contributions.
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Before You Go On 1. What are the limits on the value of a call option prior to its expiration date? 2. What variables affect the value of a call option? 3. Why are the variables that affect the value of a put option the same as those that affect the value of a call option?
REAL OPTIONS Learning Objective 7 Name some of the real options that occur in business and explain why traditional NPV analysis does not accurately incorporate their values. Many investments in business involve real options â&#x20AC;&#x201C; options on real assets. NPV analysis does not adequately reflect the value of these options. While it is not always possible to directly estimate the value of the real options associated with a project, it is important to recognise that they exist when we perform a project analysis. If we do not even consider them, we are ignoring potentially important sources of value. In this section, we provide an overview of the types of real options commonly associated with real investments.
WEB You can find a list of websites with information about real options at: http://www.realoptions.com/resources_links.htm.
Real option an option for which the underlying asset is a real asset
Options to Defer Investment Companies often have considerable flexibility as to the timing of their investments. For instance, consider the case of an oil company that owns property expected to contain oil deposits. The oil company can choose to wait to see what happens to oil prices before deciding whether to invest in developing the deposits. This ability to wait and see involves what is known as an option to defer investment. The underlying asset in this option is the stream of cash flows that the developed oil field would produce, while the strike price is the amount of money that the company would have to spend to develop it (drill the well and build any necessary infrastructure). Just as the value of shares might go up or down, the value of the cash flows produced by the oil field might increase or decrease with the price of oil. Property developers often purchase options on land. For example, a developer might pay a landowner D 100 000 for a one-year option to purchase a property at a particular price. By accepting the payment, the landowner agrees not to sell the property to anyone else for a year. Such an option provides the developer with time to make a final decision regarding whether or not to actually purchase the land and proceed with a project. Since the developer will still have to buy the land if he or she decides to proceed with the project, the cost of the option reflects a cost of being able to collect more information before making a final decision. The value of an option to defer investment is not reflected in an NPV analysis. Recall that the NPV rule tells us to accept a project with a positive NPV and to reject one with a negative NPV. NPV analysis does not allow for the possibility of deferring an investment decision. It assumes that we invest either now or never. However, if we have the option of deferring an investment decision, it may make sense to do so. After all, a project that has a negative NPV today might have a positive NPV at some point in the future. The price of the product may increase, production costs may decline or the cost of capital may go down, making the project
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attractive. We need not assume that an investment that is unattractive today will never be attractive.
Options to Make Follow-On Investments Another very important type of real option is an optiontomakefollow-oninvestments.Someprojects open the door to future business opportunities that wouldnot otherwisebeavailable.Forexample,atthe end of 2008, Electricit e de France (EDF) acquired a controlling interest in the UK’s sole nuclear energy utility, British Energy plc, for £12.5 billion. At first glance,thisdidnotlooklikeaverygoodmovesincean NPV analysis of the purchase carried out by outside analysts indicated that the acquisition would be, at best, only marginally positive. However, the move created options for a wide range of follow-on investments. The NPV analysis did not take account of the fact that the UK electricity market, which traditionally relied largely on fossil fuels, was changing and renewable and nuclear power generation were both seen as the way forward. By acquiring British Energy and agreeing to build two new power stations in the UK, based on its tried and tested designs, EDF would be able to rapidly add to its generating capacity if market demand and the economics of nuclear power made further investments attractive. In fact, the acquisition provided EDF with several different options to make follow-on investments, not just to make additional investments in nuclear capacity. Without these, EDF would probably not have been willing to acquire British Energy – or pay the amount it did. In other words, acquiring British Energy provided EDF with options to enter other areas of the UK’s energy market. Another example of an option to make followon investments concerns an investment in a new technology that can be extended to other products. For instance, in the early 1990s, Airbus invested in a computer-aided aircraft design system as part of the development of the A380 series aircraft. This system allowed the company to complete much more of the design work for a new aircraft on a computer before building a prototype, thereby lowering the cost of designing and building a
CORPORATE RISK MANAGEMENT
new aircraft. While the cost of the new system and the associated facilities was high, the investment provided benefits that extended well beyond the project. For example, the technologies could be used in the design of other new aircraft, both civilian and military. By reducing the cost of developing new aircraft, the design system had the potential to make projects economically attractive that would not have been attractive otherwise. Options to make follow-on investments are inherently difficult to value because, at the time we are evaluating the original project, it may not be obvious what the follow-on projects will be. Even if we know what the projects will be, we are unlikely to have enough information to estimate what they are worth. Of course, this makes it impossible to estimate directly the value of any option associated with them. Nevertheless, it is important for managers to consider options to make follow-on investments when evaluating projects. Doing so is a central part of the process of evaluating projects in the context of the overall strategy of the firm. Projects that lead to investment opportunities that are consistent with a company’s overall strategy are more valuable than otherwise similar projects that do not.
WEB Real options are considered by NASA when space systems and other investments are evaluated. See the following page on the NASA website for references to additional readings in this area: http://ceh.nasa.gov/ webhelpfiles/Real_Option_Valuation.htm.
Options to Change Operations In addition to options to defer investment and options to make follow-on investments, which are real options related to the investment decisions themselves, there are also real options that are related to the flexibility managers have once an investment decision has been made. These options, which include the options to change operations
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and to abandon a project, affect the NPV of a project and must be taken into account at the time the investment decision is made. In an NPV analysis, we discount the expected cash flows from a project. We often consider several alternative scenarios and use our estimates of the probabilities associated with those scenarios to compute the expected cash flows. While this sort of analysis does consider alternative scenarios, it does not fully account for the fact that once a project has begun, the managers at a company have options to change operations as business conditions change. This means that there is a value associated with being able to change operations that is not fully reflected in a scenario analysis. The changes that managers might make can involve something as simple as reducing output if prices decline or increasing output if prices increase. Businesses do this all the time in response to changing demand for their goods and services. At the extreme, managers might temporarily suspend operations entirely if business conditions are weak. This is quite common in the auto industry, where we often hear of plants being temporarily shut down during periods of slow auto sales. Other changes in operations can involve fundamentally altering the way in which a product is produced, as when a new production technology becomes available, making the old technology uncompetitive. Having the flexibility to react to changing business conditions can be very valuable. Since we do not know how conditions are likely to change, however, it can be difficult to estimate just how valuable this flexibility will be. Nevertheless, we can see that managers do recognise the importance of flexibility by observing how they structure projects. For example, most modern office buildings do not have permanent internal walls. Not having permanent walls provides flexibility in configuring the offices and workspaces in the building. If more people must be put into a building than originally anticipated, the workspaces can be compressed to fit them. If the company finds that it does not need all of the space, having a flexible interior makes it easier to change things so that the excess space can be leased. Similarly, when
a company plans to build a new manufacturing facility, it often acquires more land than is immediately needed and designs the facility to accommodate the addition of unexpected increases in production capacity. Building flexibility into a project costs money, but this can be money well spent if things change unexpectedly. The flexibility to expand, scale back or temporarily shut down a project, or to change the methods or technology employed in a project, are all options that managers should consider when evaluating projects. Projects with more flexibility in these dimensions are inherently more valuable.
Options to Abandon Projects A project can also be terminated if things do not go as well as anticipated.16 In other words, management often has an option to abandon a project. The ability to choose to terminate a project is a bit like a put option. By shutting down the project, management is saving money that would otherwise be lost if the project kept going. The amount saved represents the gain from exercising this option. As with flexibility, we can see that managers recognise the importance of having an option to abandon a project by observing the way they design projects. Consider, for example, that most industrial buildings are built like big boxes that can easily be reconfigured as manufacturing spaces, warehouses or even retail outlets, depending on which use is most valuable. Suppose a company is building a facility to use as a warehouse. If the building is only able to accommodate a warehouse, it might end up sitting empty for long periods of time â&#x20AC;&#x201C; for example, if the area has excess warehouse space at some point in the future. Designing the building so that it can be reconfigured relatively inexpensively for some other use increases the likelihood that the building will remain fully utilised in the future.
Concluding Comments on NPV Analysis and Real Options We have stated that NPV analysis does not deal well with real options. This is true because the riskiness of a project that has real options
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associated with it varies with time and the appropriate discount rate varies with the risk. For example, deciding to expand operations may be very risky, but until the decision is actually made, the option to expand is relatively risk free. In order to use NPV analysis to value such an option, we would not only have to estimate all the cash flows associated with the expansion, but would also have to estimate the probability that we would actually undertake the expansion and determine the appro-
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priate rate at which to discount the incremental cash flows from the expansion back to the present. The discount rate might even change with the value of the underlying asset. In some cases, we can incorporate the value of a real option into an investment analysis by valuing the option separately and then adding this value to the NPV estimate. In these cases, we value the real option using valuation methods similar to those used to value financial options.
Decision-Making Example 20.2 The Value of Real Options Situation: You work for a company that manufactures cardboard packaging for consumer product companies under long-term contracts. For example, your company manufactures the boxes for several popular cereal and pharmaceutical products. You have just won a large fiveyear contract to produce packaging materials for a company that sells furniture on the Internet. Since this contract will require you to produce much larger boxes than you currently can produce, you must purchase some new equipment. You have narrowed your choices to two alternatives. The first is a capital-intensive process that will cost more up-front but will be less expensive to operate. This process requires very specialised equipment that can be used only for the type of packaging that your furniture
Before You Go On 1. What is a real option? 2. What are four different types of real options commonly found in business? 3. Is it always possible to estimate the value of a real option? Why or why not?
client needs. The second alternative is a labourintensive process that will require a smaller upfront investment but will have higher unit costs. This process involves equipment that can be used to produce a wide range of other packages. If the expected life of both alternatives is 10 years and you estimate the NPV to be the same for both, which should you choose? Decision: You should choose the labour-intensive alternative. Your contract is only for five years and there is a chance that it will not be renewed before the equipmentâ&#x20AC;&#x2122;s useful life is over. If the contract is not renewed, it will be easier to convert the labour-intensive equipment to another use. In other words, the labour-intensive alternative gives you the added value of having the option to abandon producing packaging for furniture.
AGENCY COSTS Learning Objective 8 Describe how the agency costs of debt and equity are related to options. Agency conflicts arise between shareholders and debtholders and between shareholders and
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managers because the interests of shareholders, lenders (creditors) and managers are not perfectly aligned. In fact, their interests can greatly diverge. One reason is that the claims they have against the cash flows produced by the firm have payoff functions that look like different types of options. We now discuss how these payoff functions lead to agency conflicts and their related costs.
Agency Costs of Debt In Chapter 16, we discussed agency costs that arise in a company that uses debt financing. We noted that these costs occur because the incentives of people who lend to a company differ from those of the shareholders. If you were to carefully reread those discussions now, you might notice that the problems we discussed arise because the payoff functions for shareholders and lenders (creditors) differ like those for the different options we have been discussing. To understand why this is the case, consider a company that has a single loan outstanding. This loan will mature next year and all of the interest and principal will be due at that time. Now, consider what happens when the debt matures. On the one hand, if the value of the company is less than the amount owed on the debt, the shareholders will simply default and the lenders will take control of theassetsofthecompany.Theshareholderclaimswill be worth zero in this case. If, on the other hand, the valueofthecompanyisgreaterthantheamountowed on the loan, the shareholders will pay off the loan and retain control of the assets. In this case, the shareholderclaimswillbeworththedifferencebetweenthe value of the firm and the amount owed to the lenders. In other words, the payoff function for the shareholders looks exactly like that for the owner of a call option, where the strike price is the amount owed on the loan and the underlying asset is the firm itself. If the value of the firm exceeds the strike price, the shareholders will choose to exercise their option; and if it does not exceed the strike price, they will let their option expire unexercised. Part A of Exhibit 20.7 illustrates the payoff function for the shareholders in this simple example. The payoff function for the lenders in our example is illustrated in part B of Exhibit 20.7.
If the value of the firm is less than the amount owed, the lenders receive only the assets of the firm; and if the value of the firm is greater than the amount owed, the lenders receive only the amount owed. One way to think about the payoff function for the lenders is that when they lend money to the firm, they are essentially selling a put option to the shareholders.17 This option gives the shareholders the right to ‘put’ the assets to the lenders with a strike price that equals the amount they owe. When the value of the firm is less than the strike price, the shareholders will exercise their option by defaulting. Of course, the shareholders are able to default and walk away only because our bankruptcy laws limit their liability to the amount that they have invested in the company.
The Dividend Payout Problem Knowing that debt and equity claims are like options in which the underlying asset is the firm, we can use the intuition gained from the discussion of the determinants of option value to better understand the agency costs of debt. The incentives that shareholders of a leveraged firm have to pay themselves dividends arise because of their option to default. If a company faces some realistic risk of going bankrupt, the shareholders might decide that they are better off taking money out of the firm by paying themselves dividends. This situation can arise because the shareholders know that the bankruptcy laws limit their possible losses. If the firm goes bankrupt and the lenders end up receiving, for example, 50% rather than 80% of what they are owed, it will make no difference to the shareholders, who will get nothing from the liquidation of the company’s assets in either case.
The Asset Substitution Problem In Chapter 16, we saw that when bankruptcy is possible, shareholders have an incentive to invest in very risky projects, some of which might even have negative NPVs. Shareholders have this incentive because they receive all of the benefits if things turn out well but do not bear all of the costs if things turn out poorly. Since equity claims are like call options on the assets of the firm, this asset
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Value of Equity
When the firm value is below the face value of the debt, the shareholders default and the equity is worth zero. When the value of the firm is above the face value of the debt and the equity is worth the difference between the firm value and the face value of the debt.
0 Face Value of Loan
Firm Value
When the firm value is below the face value of the debt, the shareholders default and the lenders receive the value of the firm.
Value of Loan
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When the value of the firm is above the face value of the debt, the shareholders repay the debt and the lenders receive the face value of the debt.
0 Face Value of Loan
Firm Value
Exhibit 20.7: Payoff Functions for Shareholders and Lenders The equity in a leveraged company is like a call option on the underlying assets of the firm. The shareholders exercise their option by paying off the debt if the firm is worth more than the face value of the debt when the debt matures. If the value of the firm is lower than the face value of the debt, the shareholders can default (let their option expire) without incurring losses beyond their investment in the firm. The lenders’ payoff function is like that for the seller of a put option. They have effectively agreed to purchase the firm for an amount that equals the face value of the firm’s debt, at the discretion of the shareholders.
substitution problem should not be surprising. We pointed out earlier in this chapter that the more volatile the value of the underlying asset, the more valuable a call option on that asset will be. Shareholders of leveraged firms know this and therefore have an incentive to invest in risky projects that increase the overall volatility of the value of their companies’ assets. Lenders, in contrast, do not want the firm to invest in high-risk projects. As you can see from their payoff function in Exhibit 20.7, the lenders bear costs as the value of the firm drops below the amount they are owed but do not benefit at all as the value of the firm’s assets increases above the amount that they are owed. Lenders to companies that are worth more than they are owed can only expect to lose when a project increases the overall riskiness of a company’s assets.
The Underinvestment Problem Chapter 16 also explained that shareholders have incentives to turn down positive NPV projects when all of the benefits are likely to go to the lenders. You can see how this underinvestment problem arises from the differences in the payoff functions in Exhibit 20.7. Suppose that the company will owe D 10 million when the loan matures, that the company is currently worth D 5 million and that the loan matures next week. This company is financially distressed because its assets are not even worth as much as its outstanding debt – so it is unlikely to have enough money to finance new investments. Now suppose that management identifies a positive NPV project that would require a D 3 million investment and that has a positive NPV of D 1 million which will be realised before the debt payment must be made. Management would have
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a hard time convincing the shareholders to invest an additional D 3 million in the firm, because even if the investment turns out to be worth D 4 million, all of the money will go to the lenders. The shareholders have a strong incentive to turn down this positive NPV project.
Agency Costs of Equity So far, we have assumed that managers act in the best interests of the shareholders. Since managers are hired to manage the firm on behalf of the shareholders, this might appear to be a reasonable assumption. However, as you already know, managers do not always act in the shareholders’ best interests. This is because the payoff function for a manager can be quite different from that for shareholders. In fact, a manager’s payoff function can look a lot like a lender’s payoff function. To see how this is possible, consider the connection between managers’ personal wealth and the performance of the companies for which they work. The present value of managers’ future earnings is a large part of their overall wealth. If a company gets into financial difficulty and a manager is viewed as responsible, that manager could lose his or her job and find it difficult to obtain a similar job at another company. Of course, the most obvious way for a company to get into financial difficulty is to default on its debt. Therefore, as long as a company is able to avoid defaulting on its debt, a manager has a reasonable chance of retaining his or her job. Once the firm defaults, the chances of job loss increase dramatically. In addition, researchers have found that senior managers of financially distressed large public companies who lose their jobs find it difficult to obtain similar jobs afterwards.18 We might also expect that the worse the company’s financial distress, the worse the manager’s future employment prospects and the lower the present value of the compensation that he or she can expect to receive in the future. If this is so, when the value of a firm is less than the amount it owes, the payoff function for a manager will look something like that for the lender in part B of Exhibit 20.7 – it will slope downwards as the value of the firm decreases.
On the positive side, we would expect the present value of a manager’s future earnings to increase with the value of the firm when this value is above the amount that the company owes to its lenders. Managers will receive larger bonuses and larger pay raises and any shares or options that they receive will be more valuable. However, these increases will not be nearly as large as those for shareholders. The shareholders are not likely to give the managers a large proportion of any increase in firm value. The net result is that the payoff function for managers can look something like the one in Exhibit 20.8. The fact that the payoff function for a manager resembles that for a lender means that managers, like lenders, have incentives to invest in less risky assets and to distribute less value through dividends and share repurchases than the shareholders would like them to. These tendencies are reinforced by the fact that managers are individuals who do not hold diversified portfolios, since most of their wealth is tied to the performance of their firms. Managers tend to make conservative investment, financing and dividend decisions because the personal cost to them of failure can be very great. Boards of directors understand how the incentives of managers differ from those of shareholders. Consequently, boards put a great deal of effort into designing compensation plans that make the payoff functions for managers look as much as possible like those of shareholders. Ultimately, this is a key to minimising agency conflicts between shareholders and the managers that represent them.
Before You Go On 1. What do the payoff functions for shareholders and lenders look like? 2. What does the payoff function for a typical manager look like?
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Value of Manager’s Future Compensation
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0 Face Value of Loan
Firm Value
Exhibit 20.8: Representative Payoff Function for a Manager The payoff function for a manager with a typical compensation arrangement is more similar in shape to the payoff function for a lender than for a shareholder. While a shareholder’s payoff function is flat to the left of the face value of the loan, the value of the manager’s compensation is downward sloping, much like the payoff of a lender. When the value of the firm is greater than the face value of the loan, the value of the manager’s compensation does not increase as much as the value of the firm’s shares (the line of the payoff function is not as steep). Because managers’ payoff functions differ from those for shareholders, managers have incentives to take actions that are not in the best interests of shareholders.
SUMMARY OF LEARNING OBJECTIVES 1. Explain the factors that make it desirable for firms to manage their risks. Companies have a number of risks from inputs, production and outputs that increase the variability of their cash flows. Factors that will influence the decision to manage these risks include: financial reporting, corporate taxation, bankruptcy costs, the cost of capital, agency costs and employee compensation and retention. Firms start by first identifying the risks they face, evaluating them and managing these in appropriate ways and keeping their risks under review. A key motivation for firms to manage certain risks is that they can add value by so doing and are able to manage some risks that shareholders cannot, such as tax losses. 2. Describe the risks faced by firms and how they are managed. Risks from a firm’s operations and unanticipated changes to market prices or rates lead to undesirable cash flow volatility. Companies can use insurance against production risks. Firms can hedge their risks by taking positions that offset each other if prices change. For market risks, they can adjust their exposures to risks associated with commodity prices, interest rates, foreign exchange rates and equity prices by using financial risk management. Derivatives, such as forward contracts, futures, swaps and options, are frequently used since they are flexible and are low cost. The cost of risk management depends on future uncertainty and this has to be weighed against the benefits of risk reduction. 3. Define forward and futures contracts and be able to determine their prices. A forward contract is an agreement to buy and sell an asset at a predetermined price at a future date. The key elements for the delayed sale determined in advance are (1) the forward date, (2) the
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5.
6.
7.
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asset and (3) the agreed price. A futures contract is a standardised forward contract that is traded on an organised exchange and is very similar to a forward contract. The pricing of forwards and futures is known as the cost of carry and is based on time value of money principles such that the forward price, when the transaction is agreed, is determined so that neither side is worse off as a result. The risk-free interest rate to the forward date and any costs associated with storing the asset will raise the future price. Income earned by the asset and the demand for physical ownership â&#x20AC;&#x201C; known as the convenience yield â&#x20AC;&#x201C; will reduce the forward price. The balance between these factors will determine whether the forward price is higher or lower than the current price. Over time, the relationship between the contracted forward price and the current price will change and one party will own an asset and the other will have a liability. This means that forward contracts have credit risk. Futures contracts were developed to address this problem, as well as providing liquidity since futures contracts are made with a centralised clearing house that facilitates buying and selling on the exchange. Futures users are required to post margin that protects the clearing house against default. Define interest rate and cross-currency swaps and know how they are valued. An interest rate swap is an agreement to exchange a set of fixed future cash flows against a set of cash flows based on an index of interest rates using a notional principal amount that determines the amounts to be paid. A cross-currency swap involves exchanging cash flows in one currency against corresponding payments in another currency. As such, a cross-currency swap can be considered a package of borrowing and lending where a term loan in one currency is financed by lending in another currency. When initially transacted, swap terms are designed so that the present value of the cash flows from both sides is equal. Changes in market conditions mean that, over time, the present values of each side of the swap will diverge and the swap will become either a liability or an asset. A swap will have credit risk if the present value of the cash flows to be received is greater than the present value of the cash flows to be paid out. Companies use swaps for assetliability risk management purposes and, in the case of cross-currency swaps, to fund or borrow in different currencies without incurring exchange rate risk. Define a call option and a put option, and describe the payoff function for each of these options. An option is the right, but not the obligation, to buy or sell an asset for a given price on or before a specific date. The price is called the strike or exercise price and the date is called the exercise date or expiration date of the option. The right to buy the asset is known as a call option. The payoff from a call option equals zero if the value of the underlying asset is less than the strike price at expiration. If the value of the underlying asset is higher than the strike price at expiration, then the payoff from a call option is equal to the value of the asset value minus the strike price. The right to sell the asset is called a put option. The payoff from a put option is zero if the value of the underlying asset is greater than the strike price at expiration. If the value is lower than the strike price, then the payoff from a put option equals the strike price minus the value of the underlying asset. List and describe the factors that affect the value of an option. The value of an option is affected by five factors: (1) the current price of the underlying asset, (2) the strike price of the option, (3) the volatility of the value of the underlying asset, (4) the time left until the expiration of the option and (5) the risk-free rate. Name some of the real options that occur in business and explain why traditional NPV analysis does not accurately incorporate their values. Real options that are associated with investments include options to defer investment, make follow-on investments, change operations and abandon projects. Traditional NPV analysis is designed to make a decision to accept or reject a project at a particular point in time. It is not
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designed to include the potential value associated with deferring the investment decision. Incorporating the value of the other options into an NPV framework is technically possible but would be very difficult to do because the rate used to discount the cash flows would change over time with their riskiness. In addition, the information necessary to value real options using the NPV approach is not always available. 8. Describe how the agency costs of debt and equity are related to options. The chapter discusses two principal classes of agency conflicts. The first is between shareholders and lenders. When there is a risk of bankruptcy, shareholders may have incentives to increase the volatility of the firm’s assets, turn down positive NPV projects or pay out assets in the form of dividends. Shareholders have these incentives because their payoff functions look like those for the owner of a call option. The other principal class of agency conflicts is between managers and owners. Managers tend to prefer less risk than shareholders do and prefer to distribute fewer assets in the form of dividends because their payoff functions are more like those of lenders than those of shareholders are. These preferences are magnified by the fact that managers are risk-averse individuals whose portfolios are not well diversified.
SUMMARY OF KEY EQUATIONS Equation
Description
Formula
(20.1)
Cost of carry
PV
(20.2)
Interest rate swap value
Value of interest rate swap ¼ Value of bond with swap coupon rate – value of loan with floating rate
(20.3)
Put–call parity
P ¼ C þ Xe rT V
ð1 þ i þ uÞm ¼ FVm ð 1 þ q þ yÞ m
SELF-STUDY PROBLEMS 20.1. What will determine whether a firm should – or should not – manage particular risks in its business? 20.2. You own property which has a value of D 5 million and will pay rental income of D 450 000 at the end of the first year and D 500 000 at the end of the second year. You
have been approached by a property company and they would like you to sell the property to them at the end of the second year but at a price agreed today. The interest rate is 4.3% per year. What would be a fair price for the property, if agreed now?
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20.3. Your company is considering opening a new factory in the Middle East to serve the growing demand for your product there. Your home currency is the euro but you need US dollars for the investment that will cost US$25 million and will last for five years. You decide that a cross-currency swap is the best way of financing the investment. The exchange rate between the US dollar and the euro is $1.3475 ¼ D 1 and the fiveyear swap rates for the euro and the US dollar are 3.5% and 4.2% per year, respectively, paid annually. Lay out the cash flows for the swap. 20.4. Deutsche Euroshop AG shares are currently selling for D 12. Over the next year, the company is undertaking a new supermarket project. If the project is successful, the com-
pany’s shares are expected to rise to D 24. If the project fails, the shares are expected to fall to D 8. The risk-free interest rate is 6%. Calculate the value today of a one-year call option on one Deutsche Euroshop share with a strike price of D 20. 20.5. Fiera Milano S.p.A. is an Italian company that organises trade fairs and is listed on the Milan Stock Exchange. The company’s shares are currently trading at D 50. Depending on the outlook for the economy and the demand for trade conferences, the company’s share price is expected to be either D 65 or D 30 in six months. The risk-free interest rate is 8% per year. What is the value of a put option on one Fiera Milano share that has a D 40 strike price?
SOLUTIONS TO SELF-STUDY PROBLEMS 20.1. The decision will be based on assessing the costs versus the benefits. Firms will manage those risks for which the benefits can only be captured by the firm but not its owners. These include, but are not limited to, corporate taxation, bankruptcy costs, the cost of capital from outside providers, employee compensation and retention and financial reporting. 20.2. We want to apply the cost of carry model to determine the forward price, knowing that we have discrete value distributions at the end of years 1 and 2. We start by presentvaluing these at the risk-free interest rate and subtracting them from the value of the property before then future-valuing the property at the risk-free interest rate for two years:
D 450 000 ¼ D 431 448 1:043 D 500 000 ¼ ¼ D 459 623 ð1:043Þ2
PVYear 1 income ¼ PVYear 1 income
Forward price ¼ ðD 5 000 000 D 431 448 D 459 623Þ ð1:043Þ2 ¼ D 4 469 895 The two-year forward price will be D 4 469 895. 20.3. The first step is to determine the amount of euros that are required in exchange for receiving US25 million at the start of the swap. With an exchange rate of $1.3475/D this requires $25 000 000/$1.3475 ¼ D 18 552 876 to be paid at the start. The interest on the euro side will therefore be
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D 18 552 876 0.035 ¼ D 649 351 per year. For the US dollar side, it is $25 000 000 0.042 ¼ $1 050 000 per year. From the perspective of the company, the cross-currency swap cash flows will look as follows: Cash Flows for the Cross-Currency Swap Time (years) Euros US dollars 0 1 2 3 4 5a 5b
18 552 876 649 351 649 351 649 351 649 351 649 351 18 552 876
25 000 000 1 050 000 1 050 000 1 050 000 1 050 000 1 050 000 25 000 000
20.4. First determine the payoffs for the shares, a risk-free loan and the call option under the two possible outcomes. In one year, the share price is expected to be either D 8 or D 24. The loan will be worth D 1.06 regardless of whether the project is successful. If the project fails, the share price will be less than the strike price of the call option. The option will not be exercised and will be worth D 0. If the project is successful, the share price will be higher than the strike price of the call option. The option will be exercised and its value will be the difference between the share price and the strike price, D 4.
CORPORATE RISK MANAGEMENT
The shares and loan can be used to create a replicating portfolio which has the same payoff as the call option: ðD 8 xÞ ð1:06 yÞ ¼ D 0 ð$24 xÞ ð1:06 yÞ ¼ D 4 Solving the two equations yields: x ¼ 0.25, y ¼ D 1.887 The value of the call option is the same as the current value of this portfolio: ðD 12 0:25Þ ðD 1 D 1:887Þ ¼ 1:11 20.5. Here we solve directly for the value of the put option. First we determine the payoffs for the shares, a risk-free bond and the put option under the two possible outcomes. To determine the payoff of the bond in six months’ time, we must calculate the six-month risk-free interest rate given the one-year risk-free rate listed in the problem statement: Six-month risk-free rate ¼ ð1 þ 0:08Þ1=2 1 ¼ 1:039; or 3:9%
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The payoffs are therefore:
Now we can use the shares and the bond to create a replicating portfolio, which will give the same payoff as the put option: ðD 30 xÞ ð1:039 yÞ ¼ D 10 ðD 65 xÞ ð1:039 yÞ ¼ D 0 Solving the two equations, we determine x ¼ 0.286, y ¼ D 17.87 The value if the put option is the same as the current value of this portfolio: ðD 50 0:286Þ ðD 1 D 17:87Þ ¼ D 3:58
Alternatively, you could solve this problem by calculating the value of a call option with the same strike price of D 40 and then using the put–call parity relation. The value of the call option is D 15.09 (you may like to check this by calculating it yourself) and the value of the associated put option calculated using the put–call parity relation is D 3.52. The difference (D 3.58 vs. D 3.52) is due to rounding and the compounding assumption for the discount rate.
CRITICAL THINKING QUESTIONS 20.1. A manufacturer of consumer products which is based in France is considering entering a new market in a Latin American country by exporting its products for sale there. Detail the various risks it has from expanding into this new market. 20.2. There are active markets in forward contracts on financial securities, such as exchange rates, equities and interest rates and on commodities, the principal ones being base and precious metals, agricultural and energy commodities. Why will there be a consumption yield for
commodity forward contracts and not for financial securities? What are the implications for the forward price from this difference? 20.3. For a company wanting to hedge its exposures, what are the attractions and disadvantages of using futures markets rather than forward markets for this purpose? 20.4. A swap contract is simply an exchange of two sets of cash flows over an agreed period. The interest rate swap exchanges a set of predetermined and fixed payments based on a notional principal for a floating set of
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20.5.
20.6.
20.7.
20.8.
payments based on an interest rate index. What other possible types of swaps can be created given the way such swaps work? Which is likely to have more credit risk, an interest rate swap or a cross-currency swap â&#x20AC;&#x201C; and why? A writer of a call option may or may not actually own the underlying asset. If he or she owns the asset, and therefore will have the asset available to deliver should the option be exercised, he or she is said to be writing a covered call. Otherwise, he or she is writing a naked call and will have to buy the underlying asset on the open market should the option be exercised. Draw the payoff diagram of a covered call (including the value of the owned underlying asset) and compare it with the payoff of other options. What kinds of real options should be considered in the following situations? a. Fiat S.p.A. is considering two sites for a new car factory. One is just large enough for the planned facility, while the other is three times larger. b. Hellenistic Cruises is purchasing three new cruise ships to be built sequentially. The first ship will commence construction today and will take one year to build. The second will then be started. Hellenistic Cruises can cancel the order for a given cruise ship at any time before construction begins for a small fee. Zukunft Betrieb AG is considering a factory that will include an option to expand
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operations in three years. If things go well, the anticipated expansion will have a value of D 10 million and will cost D 2 million to undertake. Otherwise, the anticipated expansion will have a value of only D 1 million and will not take place. What information would we need in order to analyse this capital budgeting problem using the traditional NPV approach that we would not need using option valuation techniques? 20.9. Companies frequently include employee share options as part of the compensation for their managers and sometimes for all their employees. These options allow the holder to buy the shares of the company for a preset price like any other option, but they usually have very long maturities, of up to 10 years not being uncommon. The goal of share option plans is to align the incentives of employees and shareholders. What are the implications of these plans for current shareholders? 20.10. You are a bondholder of DRYAD SA. Using option-pricing theory, explain what agency concerns you would have if DRYAD SA were in danger of bankruptcy. 20.11. A bond covenant is part of a bond contract that restricts the behaviour of the firm, barring it from taking certain actions. Using the terminology of options, explain why a bond contract might include a covenant preventing the firm from making large dividend payments to its shareholders.
QUESTIONS AND PROBLEMS Basic 20.1. Managing corporate risks: Why do companies usually seek to hedge out the risks from financial markets? 20.2. Managing corporate risks: Renault, the French carmaker, sells its vehicles within
Europe and elsewhere. What effect has the introduction of the euro in France, Germany, Spain, Italy and other member countries had on Renaultâ&#x20AC;&#x2122;s sales in these countries?
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20.3. Forward contracts: What are the three elements that have to be defined in a forward contract? 20.4. Forward contracts: What are the payoff profiles for (a) a long forward and (b) a short forward at maturity? 20.5. Forward contract valuation: What factors raise the price of a forward contract and what factors reduce the value of a forward contract? 20.6. Swaps: There are four possible types of cross-currency swaps based on the nature of the cash flows to the two parties. What are the four possible types? 20.7. Option characteristics: Explain how the payoff functions differ for the owner (buyer) and the seller of a call option. Of a put option. 20.8. Option valuation: What is the value of an option if the share price is zero? What if the share price is extremely high (relative to the strike price)? 20.9. Option valuation: Like owners of shares, owners of options can lose no more than the amount they invested. They are far more likely to lose that full amount but they cannot lose more. Do sellers of options have the same limitation on their losses? 20.10. Option valuation: What is the value at expiration of a call option with a strike price of D 65 if the share price is D 1? D 50? D 65? D 100? D 1000? 20.11. Option valuation: Suppose you have an option to buy NASDAL shares for D 100. The option expires tomorrow and the current price of NASDAL shares is D 95. How much is your option worth? 20.12. Option valuation: You hold an American option to sell one share of Cimbalom. The option expires tomorrow. The strike price of the option is D 50 and the current share price is D 49. What is the value of exercising the option today? If you wanted to sell the option instead, about how much would you expect to receive?
20.13. Real options: What is the difference between a financial option and a real option? 20.14. Real options: List and describe four different types of real options that are associated with investment projects. 20.15. Agency costs: How are options related to the agency costs of debt and equity?
Intermediate 20.16. Managing corporate risks: Why do companies prefer to use financial hedging, if available, rather than operational hedging? When might operational hedging be a better choice? 20.17. Risk management methods: When might a company prefer to use insurance rather than hedging to protect itself against a particular risk? 20.18. Forward contract valuation: If the current asset price is D 350 and the risk-free interest rate is 3% per year, the asset provides a continuous dividend yield of 5.2% per year, what will be the forward price for the asset in a forward contract if the agreed delivery date is 18 months? 20.19. Forward contracts: Whatwillbe thevalue of the forward contract in 20.18 if the contract nowhassixmonthstomaturity,thespotasset price is now D 355, the risk-free interest rate is 3.6% per year and the dividend yield is now 4.7% per year? If you had taken a long position in the contract in 20.18, is the forward contract now an asset or a liability? 20.20. Interest rate swap valuation: Valencia Fabricaci on SA has an interest rate swap where it pays a fixed rate of 4.6% per year. The notional amount of the swap is D 30 million and the swap has currently exactly 3 years to maturity. The current 3-year swap rate is 3.9%. What is the value of the swap and, from Valencia Fabricaci onâ&#x20AC;&#x2122;s perspective, is the swap an asset or a liability? 20.21. Option valuation: Shares of Motores Socrates SA are currently trading for D 40 and will either rise to D 50 or fall to D 35 in one
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20.22.
20.23.
20.24.
20.25.
month. The risk-free interest rate for one month is 1.5%. What is the value of a one-month call option with a strike price of D 40? Option valuation: Again assume that the price of Motores Socrates SA shares will either rise to D 50 or fall to D 35 in one month and that the risk-free interest rate for one month is 1.5%. How much is an option with a strike price of D 40 worth if the current share price is D 45 instead of D 40? Option valuation: You are considering a three-month put on Budowlanych Krakow. The company’s shares currently trade at Zloty 10.0 and in three months will either rise to Zl. 15.0 or fall to Zl. 7.0. The risk-free interest rate for three months is 2%. What is the appropriate price for a put with a strike price of Zl. 9.0? Option valuation: You hold a European put option on Cannello S.p.A. with a strike price of D 100. Things have not been going too well for Cannello. The current share price is D 2 and you think that it will either rise to D 3 or fall to D 1.50 at the expiration of your option. The appropriate risk-free interest rate is 5%. What is the value of the option? If this were an American option, would it be worth more? Other options: A golden parachute is part of a manager’s compensation package that makes a large lump-sum payment in the event that the manager is fired (or loses his or her job in a merger, for example). This seems ill-advised to most people when first hearing about it. Explain how a golden parachute can help reduce agency costs between shareholders and managers.
Advanced 20.26. Consider the following two strategies for investing in a company’s shares: a. buy the shares immediately and hold them for 6 months for D 100 before selling these at the end of the six months;
CORPORATE RISK MANAGEMENT
b. take a long position in a 6-month forward contract for D 102 and immediately sell the shares at the maturity of the contract. The six-month rate of interest is 2%. What will your payoff be in six months’ time from both strategies if the share price is D 110 and D 95? What is the effect on the payoffs if after you have decided, the company subsequently announces and pays a dividend of D 5 at the end of month five? 20.27. You want to enter into four sequential forward contracts with maturities of 6, 12, 18 and 24 months, respectively. The risk-free rate of interest for the four periods is 3.0, 3.5, 3.7 and 4.0% per year, respectively. If the spot price is D 350 today, what will be the forward prices at which you can transact, if the asset has a dividend yield of 3.6% per year? What do the prices you calculate tell us about the way forward markets work? 20.28. Two years ago, FabricaSc ~ao Azulejos de Lisboa SA (FALSA) entered into an interest rate swap for D 25 million with a maturity of 7 years where the company makes a fixed payment of 4.5% per year against Euribor. Now the company wants to terminate the swap. The five-year swap rate is 4.0%. Will FALSA pay or receive to terminate the swap and how much is involved? 20.29. Dynamo Plastics plc entered into a five-year cross-currency swap for £10 million against the euro when the exchange rate was D 1.25/ £ and the sterling fixed interest rate was 4.5% per year and that for the euro was 3.7% per year. Dynamo Plastics agreed to pay pounds sterling and receive the euro. Exactly two years have passed and the company wants to terminate the swap. The euro is now trading at D 1.10, the sterling 3-year fixed swap rate is 3.2% and the euro 3-year swap rate is 2.8% per year. What is the value change on the swap, will Dynamo Plastics gain or lose from termination, and what are the component value changes from the changes in market conditions?
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20.30. Consider the following payoff diagram.
Find a combination of calls, puts, riskfree bonds and shares that has this payoff. (You need not use all of these instruments, and there are many possible solutions.) 20.31. Consider the payoff structures of the following two portfolios: a. Buying a call option on one share in one month at a strike price of D 50 and saving the present value of D 50 (so that at expiration it will have grown to D 50 with interest). b. Buying a put option on one share in one month at a strike price of D 50 and buying one share. What conclusion can you draw about the relation between call prices and put prices? 20.32. One way to extend the binomial pricing model is by including multiple time periods. Suppose Splittime, Inc. shares are currently trading at $100. In one month, the price will either increase by $10 (to $110) or decrease by $10 (to $90). The following month will be the same. The price will either increase by $10 or decrease by $10. Notice that in two months, the price could be $120, $100 or $80. The risk-free rate is 1% per month. Find the value today of an option to buy one share of Splittime in two months for a strike price of $105.
(Hint: To do this, first find the value of the option at each of the two possible onemonth prices. Then use those values as the payoffs at one month and find the value today.) 20.33. Spin The Wheel Company has assets currently worth £10 million in the form of one-year risk-free bonds that will return 10%. The company has debt with a face value of £5.5 million due in one year. (No interest payments will be made.) The shareholders decided to sell £8 million of the risk-free bonds and to invest the money in a very risky venture. This venture consists of Mr William Kid’s taking the money now and, in one year, flipping a coin. If it comes up heads, Mr Kid will pay Spin The Wheel £17.6 million. If it is tails, Spin The Wheel gets nothing. (Notice that this is a zero NPV investment.) a. What is the value of the debt and equity before the shareholders make this ‘investment’? b. Using the binomial pricing model, with the payoff to the equity holders representing the option and the assets of the company representing the underlying asset, estimate the value of the equity after the shareholders make the investment. c. What is the new value of the debt after the investment? 20.34. The payoff function for the holder of straight debt looks like that for the seller of a put option. Convertible debt is straight debt plus a call option on a firm’s shares. How does the addition of a call option to straight debt affect the concern that lenders have about the asset substitution problem, and why?
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SAMPLE TEST PROBLEMS 20.1. Draw the payoff diagram representing the payoff for a combination of buying a call with a strike price of D 40 and selling a call with a strike price of D 50. What would the buyer of such an option hope would happen to the share price? 20.2. Of the five variables identified as affecting the value of an option, which will have the opposite effects on the value of a put and the value of a call? That is, for which variables will a given change increase the value of a call and decrease the value of a put (or vice versa)? 20.3. What kinds of real options are being described? a. Fred’s Cheap Cars buys the empty field adjacent to its car lot.
b. Midway through construction, Maxival AG stops construction of an office building that it had planned to use as a corporate headquarters. c. Lidl, the German discount retailer, opens its first new store in Morocco. 20.4. If you fail to account for the real options available in a given project, what error might you make in your capital budgeting decision? 20.5. Suppose you are a wheat farmer. Assuming that there is an active market in wheat futures contracts, what trades might you want to use to protect yourself against falling wheat prices? What would be the cost of using them?
ENDNOTES 1. Since 2000, the price has risen spectacularly such that by the spring of 2010, the price was over $1100/oz. Needless to say, gold producers have quickly moved to remove many of the forward contracts that locked them in at lower prices. Notably, Barrick Gold announced in the autumn of 2009 that it would spend $2.9 billion to repurchase forward and other derivative contracts. 2. For simplicity, we will assume there is no salvage or environmental costs at the end of the mining operations. 3. In 1992, BAe made provisions and write-downs of £1 billion, at that time the largest corporate writedown in UK history, to cover staff redundancies and losses in its regional aircraft division. 4. We discuss the foreign exchange market and currency management in the next chapter when looking at international financial management. 5. Economists refer to investment in production facilities as irreversible. The costs involved are largely upfront and will be hard to recover later if the company should change its mind. We will look at this problem from a capital budgeting perspective later in the chapter when we discuss real options. 6. Portfolio theory is discussed in Chapter 7. 7. In this case, there is depreciation in the value to be considered since, if Airbus leases the aircraft, it will no longer be ‘new’. The buyer will be receiving a less valuable airplane and would not be willing to pay the full price for a new aircraft. This will reduce the forward price. In financial contracts where depreciation is not an issue, the income received by the seller prior to delivery acts as a negative interest rate and reduces the forward price.
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8. We could also have present-valued these costs and then future-valued the total. It will give the same result [D 50 þ D 0.60/(1.04) þ D 0.75/(1.04)2] (1.04)2 ¼ D 55.454 million. 9. Revisit Chapter 8 to review the discussion on how interest rates affect the prices of bonds. 10. The way foreign exchange is quoted and how the currency market works is examined in detail in the next chapter. 11. It can be shown that using this money, Airbus can replace the cross-currency swap with a swap using the current market conditions and be no better or worse off as a result. The sum paid to terminate the swap is used to subsidise the future payments on the new ‘at-market’ swap such that Airbus has undisturbed cash flows that are exactly the same as those of the original swap. 12. Even if the value of the option ever fell below the line to the right of the exercise price in part A of Exhibit 20.1, it would not stay there. This is because investors would be able to make an instant profit by buying the option, exercising it to get the underlying asset and then selling the underlying asset. Such trading by investors would drive the price of the option back above the line. 13. We are focusing in this discussion on what the value of the underlying asset is likely to be immediately before the option expires because it does not generally make sense to exercise an option before then as long as there is a chance that the value of the underlying asset could increase further. An exception is when the value of the underlying asset is not expected to be higher as the expiration of the option nears because value is being distributed to the owners of the underlying asset (for example, through dividend payments). In a situation like this, it can be appropriate to exercise a call option immediately before such a payment. There are also situations where it is advantageous to exercise a put option early. Such situations can arise if it is very likely that the option will be exercised at expiration. When this happens, the value received from exercising the option today can exceed the present value of the amount that is expected to be received if the option is exercised immediately before expiration. 14. We can also compute the value of x and y by noting that the combined positions in the upper fork and the lower fork are equal if we hold the replicating portfolio and sell the call option (otherwise, the portfolio is not riskless). This means that ðD 70 xÞ þ ð1:05 yÞ D 15 ¼ ðD 40 xÞþ ð1:05 yÞ 0. Simplifying, we have ðD 70 xÞ ðD 40 xÞ ¼ D 15. Therefore, as before, x ¼ 0.5. Knowing x, we can now solve for y, since ðD 40 0:5Þ ¼ ð1:05 yÞ and therefore, y ¼ D 19.05 as before. 15. There are other ways to solve the binomial pricing problem than by actually finding an equivalent portfolio. They differ only in the calculations, however. The underlying concepts are identical. See any advanced investments textbook for details. 16. An exception exists where a contractual agreement prevents the project from being terminated without payment of a penalty that is equivalent to the remaining value of the project. 17. This payoff function is actually like that from the combination of selling a put option and buying a risk-free loan. Lenders receive the face value of the loan from the risk-free bond, but they might have to pay some or all of that value in losses on the put option. Since the risk-free loan payout is unaffected by changes in the value of the firm, it does not affect the discussion above. 18. S. C. Gilson, Management turnover and financial distress, Journal of Financial Economics 25 (1989) 241–262.