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A firm’s cash flow exposure to a specific risk is a quantitative measure of how the cash flow is related to that risk. If one knows the firm’s exposure to an interest rate, one can tell by how much the firm’s cash flow changes if that interest rate changes, for instance, by 10 basis points. This tells us how we can reduce the volatility of the firm’s cash flow by hedging it against unanticipated changes in that interest rate.
If the firm has more cash flow than it can use profitably when cash flow is high, a risk management policy that reduces the variance of cash flow at low cost increases firm value. Consider a simple risk management policy whereby XYZ enters a financial contract such that it receives cash when its cash flow is low and pays cash when its cash flow is high. As long as this financial contract is fairly priced, this risk management policy increases the value of firm XYZ because it insures that it does not miss out on profitable investment opportunities. 2How can XYZ implement this risk management policy? To start with, it has to know the distribution of its cash flow. However, by itself, the distribution of cash flow is not very useful. Suppose that XYZ management finds out that there is one chance out of 20 that its cash flow will be low enough that its investment strategy cannot be implemented. This information tells XYZ management that there are benefits to risk management. However, to achieve these benefits, XYZ management must find out how the cash flow is affected by risks that XYZ’s management can hedge through financial transactions. In the language of risk management practice, the firm must find out its exposure to risks that can be hedged. Knowing these exposures allows XYZ to hedge. Any mistake in quantifying a firm’s exposures may lead the firm to adopt inappropriate hedges. With the wrong hedge, risk management can increase rather than decrease the volatility of cash.
In addition to risks that affect it only, XYZ faces risks that affect other firms as well. For instance, a depreciation of the dollar means that for a constant dollar price of its cars in the U.S. XYZ will receive fewer pounds. An increase in the price of crude oil means that the demand for cars will fall and XYZ’s sales will drop. Broad-based risks corresponding to random changes in prices of macroeconomic variables such as exchange rate changes are called market risks. They are not under the control of individual firms and correspond to market prices that affect the economy as a whole. These risks can be managed with financial instruments that can be used for hedging purposes by a large number of firms. An example of such a financial instrument would be a forward contract on the dollar. The payoff of such a financial instrument does not depend at all on XYZ. However, XYZ can sell dollars forward to reduce the dependence of its pound income on the dollar exchange rate. To do that, XYZ has to figure out the size of the forward position that hedges its exchange rate risks. This position will depend on how changes in the exchange rate affect XYZ’s cash flows. The extent to which changes in the exchange rate affect XYZ’s cash flows is called XYZ’s exposure to the exchange rate. Consider XYZ’s cash flow for 1998. Let’s consider a base case of constant exchange rates and no inflation. Let’s assume that XYZ will export 22,000 cars to the US in 1998 and sell each
car for $20,000. It will also sell 22,000 cars in the U.K. Suppose that there is no other source of uncertainty in XYZ’s cash flow. In this case, XYZ will receive $440m in 1998. The pound value of this amount will be $440m times the pound price of the dollar. If the only effect of a change in the exchange rate for XYZ is to change the pound value of the dollar sales, then $440m is the dollar exposure of the cash flow. Multiplying the exchange rate change by the exposure yields the cash flow impact of the change in the exchange rate.Exposure measures are like dollar duration measures. Dollar duration
provides an estimate of the dollar change in the value of a bond for a small yield change.
It therefore measures the exposure of the bond to yield changes. Exposure to a specific
market risk measures the dollar change in the value of a cash flow ( cash flow) or a
financial asset for a unit change in that market variable ( M):
Exposure to M = Cash flow/ M
With the example, exposure to the exchange rate is equal to $440m x M/ M = $440m, where M
is the change in the exchange rate. Suppose that the dollar appreciates 10%, so that its
price in pounds goes from 0.5 to 0.55. In this case, the cash flow impact of the
appreciation is an increase in cash flow equal to 440m x 0.05, which is £22m. This number
is obtained by multiplying the exposure by the pound change in the price of the dollar.
In the short-run, most cash flow exposure is transaction exposure and transaction exposure is measured quite precisely by the accounting system. Transaction exposure is the extent to which the value of transactions already entered into is affected by market risks. Next, suppose we consider the exposure of XYZ for the quarterly cash flow four quarters from now. The firm’s exposure will consist of two components. One component will still be transaction exposure resulting from booked transactions. For instance, XYZ might receive or make payments in dollars that are already contracted for and booked today. It might have dollar debt requiring coupon payments at that time. The other component will be contractual exposures that are not associated with booked transactions. XYZ will have contractual agreements, implicit or explicit, that affect its exposure at that horizon. For instance, it might have made commitments to dealers about prices. Even though these commitments do not result in booked transactions, they cannot be changed easily if at all. Such commitments create contractual exposures. These exposures do not show up on the firm’s balance sheet, yet any change in the exchange rate affects the value of the firm through its effect on the domestic currency value of these commitments.
With contractual exposures, the foreign currency amount of the exposure is generally fixed and is not affected by exchange rate changes. For instance, if XYZ has promised to deliver a fixed number of cars to dealers in the U.S. at a fixed dollar price, this creates a contractual exposure. The pound value of the payments from the dealers is simply the dollar value of these payments translated at the exchange rate that prevails when the payments are made. For such an exposure, the relevant exchange rate is the nominal exchange rate at the time of these payments.
Let’s now look at the exposure of cash flows three years from now. Very little of that exposure is contractual exposure. In fact, as the exchange rate changes, XYZ can change its production, marketing, sourcing strategies. If the exchange rate changes so that keeping sales in the U.S. constant is not profitable, then XYZ can change its sales in the U.S. It can develop new markets or new products. The exposure at long horizons is a competitive exposure. Changes in market prices such as exchange rates affect the firm’s competitive position. The nature of the exposure therefore depends on the markets in which the firm does business. Others have called this exposure an operating exposure or an economic exposure. Contractual losses due to exchange rate changes are economic losses, which makes the concept of economic exposure not adequate to describe the exposure we have in mind. Operating exposure ignores the strategic implications of exchange rate changes - exchange rate changes do not affect only the profitability of current operations but what the firm does and where it does it. Although in our discussion of competitive exposures we focus mostly on exchange rate competitive exposures, the firm’s competitive position is generally affected by changes in other market prices.
2.1.1. Determining Exposure Horizons
Exposure depends on the period over which it is measured. For instance, in the
short-run, a firm cannot change the location of its plants. In the long-run, it can do so.
Consequently, there may be little exposure to the real exchange rate in the long run. This
raises the question: Which exposure should a firm focus on? Should it be short-run
exposure or long-run exposure? The answer depends on why the firm is estimating its
exposure. Let’s consider various reasons for why a firm practices risk management and
their implications for the choice of the horizon over which to compute exposures:
A. To avoid default and bankruptcy. In this case, the
firm faces deadlines where it has to make specific payments and covenants that it has to
meet. The firm will therefore have to make sure that it has enough resources at these
specific times. These deadlines will define the periods over which it computes exposures.
B. To minimize the present value of tax payments. Typically, the firm will be concerned
about risks taking place over the tax year.
C. To enable the implementation of a strategic plan. With a strategic plan that is
implemented over several years, the firm wants to insure the availability of the resources
necessary to implement the plan. The firm will therefore want to understand the risks that
affect these resources over the planning period.
2.2 Competitive Exposure
Shocks to exchange rates affect the firm’s balance sheet through translation
exposure. A firm’s assets and liabilities in foreign currencies have to be translated
into the domestic currency at the end of the firm’s fiscal year. As exchange rates
change unexpectedly, the value of the firm’s assets and liabilities can change
dramatically. The exposure of a firm’s balance sheet is easy to figure out since
every foreign currency asset and liability needs to be translated at the end of the fiscal
year and accounting conventions prescribe for each asset and liability whether this
translation takes place at the current exchange rate or at some historical exchange rate.
These assets and liabilities are known in the foreign currency so that the exposure itself
is known. Sometimes, translation exposure can be quite important. This will be the case
when the firm has to maintain some accounting ratios to avoid default and these accounting
ratios involve translated accounts. In general, however, translation exposure is not
particularly important for firms because they are not close to technical default based on
accounting covenants.
2.3.1. What if the firm focuses on the wrong
exposure?
An oft-cited example is the case of a European airline concerned about the volatility
of its cash flow. It therefore decides to hedge transactions exposure. Its most important
transaction is an order of planes from Boeing. The payment will have to be made in
dollars. The company interprets this to mean that the firm is short dollars and hedges by
buying dollars forward. During the period of time that the hedge is maintained, the dollar
depreciates and the airline loses money on the forward contract that it makes up in its
cash position. Yet, the firm’s cash flow is low enough to create concern despite the
transaction hedging. What went wrong? The prices that the airline charges are fixed in
dollars because of the structure of the airline market. Hence, if the dollar falls, the
airline loses income in its home currency. This does not correspond to booked transactions
when the firm decides on its risk management policy, so that focusing on transaction
exposure, the airline forgot about the exposure inherent in its operations. Because of the
airline’s blindness to its competitive exposure, its risk management policy was
inadequate. Had the firm taken into account its competitive exposure, it could have hedged
its cash flow effectively.
3. Using the pro forma statement to
evaluate exposures.
We will focus on XYZ and its exchange rate exposure throughout the chapter. Boxes show
how the concepts we develop in this and the next section can be applied to the case of
firm ABC which has a commodity exposure. Let’s go back to the cash flow statement of
XYZ. We can forecast the cash flow statement for a particular year based on assumptions
about the variables that affect cash flow. Let’s say that the only random variable
that affects XYZ’s cash flow is the dollar/pound exchange rate. The cash flow
exposure of XYZ to the exchange rate is the sum of the exposures of the components of the
cash flow statement. To see this, consider our simple cash flow statement for XYZ:
Cash flow = Sales - Costs of goods sold - Taxes – Investment
The exposure of cash flow to the exchange rate is the impact of a unit change in the exchange rate. Consequently, the impact on cash flow of a £0.01 change in the pound price of the dollar is:
Cash flow exposure x 0.01 However, using the right-hand side of the cash flow equation, it follows that the impact of a £0.01 change in the exchange rate on cash flow must be equal to its impact on sales minus its impact on costs of goods sold, minus its impact on taxes, and minus its impact on investment.
We can look at the cash flow of XYZ for 1998 keeping the assumptions of the previous section and assuming 10% growth in sales, costs and investment:
Cash flow = Sales - Costs of goods sold - Taxes - Investment
27.5m = 440m - 330m - 0.25x110m - 55m
A change in the exchange rate can affect each component of cash flow. Suppose first that it changes only the pound value of U.S. sales. In this case, the exposure of cash flow is simply the amount of sales in the U.S. times 1 minus the tax rate. The tax rate is generally ignored in discussions o f exposure, but it is important. If the dollar depreciates, this reduces the firm’s cash flow, but it also reduces its taxable income. Each pound lost because of the decrease in the pound value of dollar sales means that taxes paid are reduced by a quarter of a pound. We can obtain this exposure by noticing that the pound value of U.S. sales is:
Dollar price per car x Number of cars sold x Pound price of the dollar
If the dollar price per car and the number of cars sold are constant, t he dollar revenue is constant. The dollar exposure of XYZ is then simply that dollar amount times one minus the tax rate. In this case:
Cash flow exposure of XYZ to the dollar = Dollar revenue of XYZ x (1 - 0.25)
Using the pro forma cash flow statement, this corresponds to $440m x (1 - 0.25) = $330m. The cash flow exposure can then be used to compute cash flow under different assumptions about exchange rate changes. First, suppose that one believes that the worst possible exchange rate move is a ten percent depreciation. In this case, one can use the exposure measure to compute the cash flow shortfall if that ten percent depreciation takes place. Note that a ten percent depreciation means that cash flow has a short-fall relative to no depreciation of Cash flow exposure of XYZ to the dollar x Pound value of 10% depreciation of the dollar Remember that we assume the pound to be worth two dollars in the base case. Hence, this means that a 10% depreciation of the dollar brings the dollar from £0.50 to £0.45.Consequently, with our assumptions, this short-fall is worth £16.5m, namely 330m x 0.05. Alternatively, one can use the exposure to compute the volatility of cash flow. Remember that with our assumptions, the dollar exchange rate is the only risk affecting cash flow. Consequently:
Volatility of cash flow = Exposure x Volatility of exchange rate
Suppose that the volatility of the exchange rate is 10% p.a. In this case, the pound volatility of 1998 cash flow viewed from the beginning of 1997 depends on the volatility of the exchange rate over a two-year period. This volatility is the square root of two times 10%, or 14.14%. This gives us a cash flow volatility of 14.14% of 330, or £46.66m. Using the volatility of cash flow, we can compute a Value at Risk measure. For instance, there is a one chance in twenty that cash flow will be at least £76.99m below projections assuming no change in the exchange rate. Remember that if the cash flow is distributed normally, the fifth percentile of the distribution of cash flow is 1.65 times the volatility of cash flow. Consequently, £46.66 x 1.65 gives us £76.99m.
The analysis becomes more complicated if the dollar price of cars and/or the quantity of cars sold in the U.S. also change with the dollar exchange rate. It is still possible to compute the worst outcome if one believes that the dollar will at most depreciate by 10%. In this case, however, one has to make assumptions about the demand curve and the marginal cost curve. We consider the case corresponding to figure 2, but for simplicity we assume that XYZ only sells in the U.S. and does not sell in the U.K. Let’s further assume that the marginal revenue of selling in the U.S. for XYZ is fixed and does not depend on the actions of XYZ because XYZ sells in a highly competitive market. This dollar marginal revenue is equal to the price of a car, that is $20,000. The marginal cost in pounds for XYZ depends on the cost function of XYZ. We assume that the total cost for XYZ is given by the following function:
Cost = 10m + 0.25 x (Quantity produced)
Consider the numbers from Table 1 but ignore taxes for simplicity. We assumed that XYZ sold cars in the U.S. at $20,000 a piece and sold 20,000 cars there. Using our cost function, the marginal cost of a car produced is:
Marginal cost of a car produced = 0.5 x (Quantity produced)
If XYZ produces 20,000 cars, the marginal cost of a car is 0.5 x 20,000, which amounts to £10,000 or, when the dollar costs £0.5, $20,000. Consequently, when XYZ sells 20,000 cars in the U.S. ,marginal cost equals marginal revenue. In this case, XYZ’s profit is £100m. Suppose now that the dollar depreciates by 10%. In this case, the quantity sold in the U.S. becomes 18,000. The profit falls to £81m. Figure 3 shows the pound profit as a function of the exchange rate. This is a nonlinear function. This means that to compute the loss resulting from a depreciation of the dollar we have to compute the profits for the exchange rate after the depreciation and compare them to the profits before the depreciation. Instead of having one exposure measure that applies irrespective of the magnitude of the exchange rate change, we now have an exposure measure for each exchange rate change! This suggests that the only way we can figure out the exposure of XYZ in this case is by computing profits for various scenarios. There is an alternative, however , which is to use an approximation for the exposure similar to duration. Remember that duration measures the sensitivity of a bond price to a small change in the yield. Using a similar measure here, we can compute the sensitivity of profits to a small change in the exchange rate evaluated at the current exchange rate. This sensitivity is given by the slope of the profit function when the exchange rate is 0.5:
Exposure = Change in profits for a small change in the exchange rate from its current value Expressed in terms of a unit change in the exchange rate, the exposure approximated this way is equal to $400m, which correspond to the dollar sales at that exchange rate. Using this approximation, we find that a £0.05 decrease in the value of the dollar decreases pound profits by £20m. Computing the loss by comparing profits when the exchange rate is £0.45 to profits when the exchange rate is £0.50, we get instead that the depreciation reduces profits by £19m. The two numbers are sufficiently close that measuring the exposure using a duration-like approximation works well. This obviously need not always be the case. One issue that arises from investigating the approximation we used is whether the result that the exposure to a small change in the exchange rate is equal to sales in that currency at the current exchange rate is a general result. In a recent working paper, Marston (1996) argues that this result holds in a large number of cases. For instance, it holds both in the monopolistic case and the duopoly case where the firms take into account the impact of their actions on their competitor. Note however that we ignored taxes. Had we taken into account taxes, we would have needed to use dollar sales times one minus the tax rate. In the example we just discussed, XYZ had to have a fair amount of information to compute its exposure to a large exchange rate change and ended up with an exposure that itself depended on the level of the exchange rate. Despite being complicated, the example we looked at was heavily simplified. For instance, there was only a single source of risk.This raises the question of whether there are alternative approaches that can be used when the analytical approach we described cannot be used in practical situations or can be used to complement this analytical approach. We discuss suchalternative approaches in the next two sections. First, in section 4, we show how to use a firm’s past history to get a measure of exposure. Then, in section 5, we discuss simulation approaches.
3.1. Example: Pro Forma Exposure Measurement -
ABC Manufacturing
ABC Manufacturing produces small household appliances and kitchen utensils. The
firm’ s small appliances division uses small electric motors that require copper
wiring to produce. Additionally, the kitchen utensils division makes pots, pans and other
small kitchen utensils from aluminum. The firm uses a just-in-time production process and
thus purchases its copper and aluminum on the open market at regular intervals. The new
treasurer feels that she will need to hedge the price of copper and aluminum but is unsure
about the exposure of cash flow to commodity prices.
She decides to conduct a pro-forma analysis to evaluate the exposure of cash flow to the prices of both aluminum and copper. She knows that these prices will affect the overall cash flow but since the uses of the products vary between the subsidiaries, she wants to know the components of the cash flow statement that are affected. After careful analysis she concludes that in the small appliance subsidiary copper and aluminum each accounts for about 10% of the total cost of sales. Conversely, in the kitchen utensils division, the cost of aluminum accounts for 60% of the cost of sales while copper is an insignificant component of the cost of sales. Each subsidiary accounts for half of the total sales of the firm. From a simple pro forma analysis the treasurer concludes that a 10% increase in the price of aluminum and copper, assuming no hedging by the firm, will increase the cost of sales in the small appliances division by 2% (1% each for copper and aluminum) and in the kitchen utensils division by 6% due to the aluminum price increase.
The treasurer is not sure how much of the increase in cost can be passed on to the customer. The marketing manager informs her that the sales in both subsidiaries are very price sensitive due to the competitiveness of the industry. Therefore, past increases in the price of copper and aluminum were not fully passed on to the customer. In fact, the marketing manager informs the treasurer that as a first estimate, she can assume that none of the cost will be passed on to the customer.
ABC Manufacturing Corporation
1996 Pro Forma Cash Flow Statement
($Millions)
Small Appliances Utensils Total
| Revenue | 150 | 150 | 300 |
| Cost Of Sales | (120) | (100) | (220) |
| Taxes(34%) | (10.2) | (17) | (27.2) |
| Net Cash Flow | 19.8 | 33 | 52.8 |
ABC Manufacturing Corporation
Pro Forma Cash Flow After a 10% increase in the cost of Copper and Aluminum
Small Appliances Utensils Total
| Reveneue | 150 | 150 | 300 |
| Cost Of Sales | (122.4) | (106) | (228.4) |
| Taxes(34%) | (9.4) | (15) | (24.4) |
| Net Cash Flow | 18.2 | 29 | 47.2 |
From the pro forma analysis it can be seen that the 10% increase in the costs of aluminum and copper results in a 3.82% increase in the cost of sales for the firm while the resultant effect on the firm’s cash flow is a decrease of 10.6%. The $8.4 million dollar increase in the firm’s costs will result in a $5.6 million decrease in cash flow. The difference in the dollar change between cost of sales and cash flow is due to the tax rate.