Measuring and Managing Operating Exposure to the Exchange Rate

Transcription

1 Chapter 18 Measuring and Managing Operating Exposure to the Exchange Rate Quiz Questions True-False Questions 1. A firm that has no operations abroad does not face any operating exposure. 2. Only firms with exports, or firms that compete against foreign exporters, face operating exposure. 3. A firm that denominates all of its contracts in home currency, or hedges all of its foreign currency contracts, faces no operating exposure. 4. Almost every firm faces some operating exposure, although some firms are exposed only indirectly (through the country's general economic activity). 5. As large economies have a big impact on world economic activity, companies in such a country tend to be very exposed to exchange rates. 6. Small economies tend to fix their exchange rate relative to the currency of larger economies, or tend to create currency zones (like the EMS). Therefore, companies in small economies tend to be less exposed to exchange rates. 7. The smaller a country, the more open the economy. Therefore, exposure is relevant for firms. 8. Everything else being the same, the larger the monopolistic power of a firm, the smaller its exposure because such a firm has more degrees of freedom in adjusting its marketing policy. 9. Consider an exporting firm that has substantial monopolistic power in its product market. Everything else being the same, the more elastic foreign demand is, the more an exporting firm will profit from a devaluation of its own currency. Similarly, the less elastic foreign demand is, the less an exporting firm will be hurt by an appreciation of its own currency. 10. Most information needed to measure operating exposure can be inferred from the firm s past export and import contracts. A. 1. false; 2. false; 3. false; 4. true; 5. false; 6. false: the risk may be lower, but not the exposure; 7. true; 8. true; 9. false: not enough information 1 ; 10. false. Multiple Choice Questions Choose the correct answer(s). Q1. In a small, completely open economy, 1 Let profits equal π = S p * (x) - c(x) where x = exports. Profit maximization means S x p* (x) - c(x) x x = 0. Therefore, π S = x p* (x) + [ S x p* (x) - c(x) x x ] x S = x p* (x). Without knowing what is held constant, it is

2 18-2 Exercises + Solutions International Financial Markets and the Firm (a) (b) (c) (d) (e) (f) (g) PPP holds relative to the surrounding countries. A 10 percent devaluation of the host currency will be offset by a 10 percent rise in the host country prices. The value of a foreign subsidiary, in units of the foreign parent s home currency, is unaffected by exchange rate changes. The real value of a foreign subsidiary to an investor from the host country is unaffected by exchange rate changes. In the absence of contracts with a value fixed in host currency, the real value of a foreign subsidiary to an investor from the parent s home country is unaffected by exchange rate changes. In the absence of contracts with a value that is fixed in foreign currency, the real value of a foreign subsidiary to an investor from the host country is unaffected by exchange rate changes. There is little or no advantage to using one's own currency: exchange rate policy has virtually no effects. A1. (a) and (g) are correct. (b) is wrong: the price rise will be percent; (c) and (d) overlook contracts fixed in nominal terms; (e) and (f) should read "in the absence of contracts fixed in any currency". Q2. In a completely closed economy, (a) PPP holds relative to the surrounding countries. (b) A 10 percent devaluation of the host currency will be offset by a 10 percent rise in the host country prices. (c) The value of a foreign subsidiary, in units of the foreign parent s home currency, is unaffected by exchange rate changes. (d) The real value of a foreign subsidiary to an investor from the host country is unaffected by exchange rate changes. (e) In the absence of contracts with a value fixed in host currency, the real value of a foreign subsidiary to an investor from the parent s home country is unaffected by exchange rate changes. (f) In the absence of contracts with a value that is fixed in foreign currency, the real value of a foreign subsidiary to an investor from the host country is unaffected by exchange rate changes. (g) There is little or no advantage to having an own currency: exchange rate policy has virtually no effects. A2. (f), (g). Q3. In an economy that is neither perfectly open nor completely closed: (a) Consider a company that produces and sells in this economy. Apart from contractual exposure effects, its value in terms of its own (local) currency is positively exposed to the value of other currencies. (b) The value of an importing firm located in this economy could either go up or go down when the local currency devalues: the effect depends on such factors as the elasticity of local demand and foreign supply. (c) Consider a company that produces and sells in this economy. Apart from contractual exposure effects, its value in terms of a foreign currency is positively exposed to the value of its currency expressed in terms of other currencies. A3. (a), (b): when costs increase, the value of the firm cannot; (c): the home currency value could go up, but this effect may be smaller than the effect of a host country devaluation. Q4. Suppose that the value of the firm, expressed in terms of the owner s currency, is a linear function of the exchange rate up to random noise: (a) The firm s exposure is the constant a t,t in V T (i) = a t,t + b t,t S T (i) + e t,t (i) (b) The exposure is hedged by buying forward b t,t units of foreign currency.

3 International Financial Markets and the Firm Exercises + Solutions 18-3 A4. (a), (b), and (c) are all false. Q5. Suppose that the value of the firm, expressed in terms of the owner s currency, is a non-linear function of the exchange rate up to random noise. Suppose you fit a linear regression through this relationship, and you hedge with a forward sale with size equal to the regression coefficient. (a) All risk will be eliminated. (b) There is remaining risk, but it is entirely independent of the realized value of the exchange rate. (c) There is remaining risk, but it is uncorrelated the realized value of the exchange rate. (d) There is no way to further reduce the variance of the firm s hedged value. (e) There is no way to further reduce the variance of the firm s hedged value if only exchange rate hedges can be used. (f) There is no way to further reduce the variance of the firm s hedged value if only linear exchange rate hedges can be used. A5. (c), (f). Exercises SynClear, of Seattle, Washington, produces equipment to clean up polluted waters. It has a subsidiary in Canada that imports and markets its parent s products. The value of this subsidiary, in terms of CAD, has recently decreased to CAD 5m due to a depreciation in the CAD relative to the USD (from the traditional level of USD/CAD 0.85 to about 0.75). SynClear s analysts argue that the value in CAD may very well return to its former level if, as seems reasonable, the uncertainty created by Canada s rising government deficit and Quebec s possible secession is resolved. If the CAD recovers, SynClear s products would be less expensive in terms of CAD, and the CAD value of the subsidiary would rise to about 6.5m. E1. From the parent s (USD) perspective, is the exposure of SynClear Canada to the USD/CAD exchange rate positive or negative? What is the sign of the exposure? A1. S low = 0.75; the value in USD is 5m 0.75 = USD S high = 0.85; the value in USD is 6.5m 0.85 = USD Thus, the exposure is strongly positive. This is because SynClear Canada is an importing firm. The stronger the CAD, the more competitive US products are in Canada and, therefore, the more profits SynClear Canada will make. E2. Determine the exposure, and verify that the corresponding forward hedge eliminates this exposure. Use a forward rate of USD/CAD 0.80, and USD/CAD 0.75 and 0.85 as the possible future spot rates. A m 3.75m B = = CAD 17.75m. If S = 0.75, the value in USD is ( ) = USD If S = 0.75, the value in USD is ( ) = USD E3. SynClear s chairman argues that, as the exposure is positive and the only possible exchange rate change is an appreciation of the CAD, the only possible change is an increase in the value of the subsidiary. Therefore, he continues, the firm should not hedge: why give away the chance of gain? How do you evaluate this argument?

4 18-4 Exercises + Solutions International Financial Markets and the Firm A3. The chairman overlooks two facts. First, only part of the gain from an appreciation is eliminated by the hedge. Second, if the appreciation does not materialize, SynClear will have a gain from the forward contract that alleviates the competitiveness problems associated with a low value of the CAD. In short, the hedge swaps part of the gain from an appreciation for a partial gain in case there is no appreciation. In the remainder of this series of exercises, SynClear Canada s cash flows and market values are assumed, more realistically, to depend on other factors than just the exchange rate. The Canadian economy can be in a recession, or booming, or somewhere in between, and the state of the economy is a second determinant of the demand for SynClear s products. The table below summarizes the value of the firm in each state and the probability of each state: State of the economy Boom Medium Recession Conditional Expectation S T = 0.85: probability n.a. value (USD) S T = 0.75: probability n.a. value (USD) E4. What are the expected cash flows conditional on each value of the exchange rate? A4. USD 4.70m when S T = 0.85, and USD 4.00m when S T = E5. Compute the exposure, the optimal forward hedge, and the value of the hedged firm in each state. The forward rate is still USD/CAD A5. The exposure is: = CAD 7m. (V hedged S T = 0.85) = (V unhedged S=0.85) + 7m ( ) = (V hedged S T = 0.75) = (V unhedged S=0.75) + 7m ( ) = State of the economy Boom Medium Recession Conditional Expectation S T = 0.85: probability n.a. value (USD) S T = 0.75: probability n.a. value (USD) The conditional expectations have become independent of the exchange rate, but there still is as much sensitivity to the state of the economy as before, in the sense that the deviation of each possible outcome from its conditional expected value is the same as in the absence of hedging. Mind-Expanding Exercises

5 International Financial Markets and the Firm Exercises + Solutions 18-5 We modify the SynClear Canada example: there are five possible exchange rates, and SynClear Canada s value, in USD is a nonlinear function of the exchange rate. For simplicity, we ignore risk caused by other factors than the exchange rate: from the text, or from Exercises 4 and 5, we already know how to handle other risks. The value V as a function of the exchange rate S is as follows: S T Probability V T (S T ) (in USD) ME1. Suppose SynClear USA wants to use a linear hedge. What is the linear regression of V T (S T ) on S T? (Note that you have to take into account the fact that the outcomes are not equally probable. A correct but computationally simple way to do this is to compute a linear regression on your pocket calculator, as if you had ten equally probably outcomes where the case "S T = 0.775" occurs two times, the case "S T = 0.80" four times, and the case "S T = 0.825" two times.) A1. The linear regression is V T (S T ) = (7 S T ) + residual. ME2. (a) (b) (c) If the forward rate is USD/CAD 0.80, what is the value of the firm after this linear hedge? What is the expected value? Is the deviation from the mean predictable on the basis of the exchange rate? A2. (a) Add a forward sale with of CAD 7m. S T V T (S T ) (in USD) m (S T 0.8) V T,hedged (b) The expected value, hedged, is USD 4.42m. (c) Because we know what the deviation from the mean will be for each value of S T, the residuals are uncorrelated with S T, but not independent of S T. ME3. (a) (b) (c) What portfolio of options would eliminate all uncertainty? What is the future value of the hedged subsidiary? The hedge that you engineered in part (b) locks in a rather low value for the subsidiary. Does this mean that hedging using a portfolio of options lowers the value of the participation? A3. (a) The single linear hedge considered in ME1 and ME2 fails to eliminate all risk because the exposure is not the same everywhere. For example, between the exchange rates 0.75 and 0.775, the exposure is: = CAD 10m. Make similar computations for all other pairs of "adjacent" outcomes: S T V T (S T ) (in USD) Local exposure (CAD) 10m 8m 6m 4m The local exposure of the hedge portfolio must be the negative of the local exposure of V T (S) T. Obtaining an exchange rate exposure equal to of CAD 10m by selling a call on CAD 10m with strike price X 1 = 0.75 is too large, in absolute

6 18-6 Exercises + Solutions International Financial Markets and the Firm value, for exchange rates that exceed For S T > we can lower the exposure to CAD 8m by adding a (long) call on CAD 2m with strike price X 2 = 0.775, and so on. The table below summarizes the solution: Local exposure of each call S T Size Strike price m X 1 = m -10m -10m -10m 2m X 2 = m 2m 2m 2m X 3 = m 2m 2m X 2 = m Total exposure of hedge -10m -8m -6m -4m (b) The future value of the hedged subsidiary now always equals USD (c) No. The parent also obtains up-front revenue for writing the (relatively expensive) call on CAD 10m at X = The cost of buying the additional calls does not offset this up-front revenue because (1) the higher the strike price, the lower the value of a call option, and (2) the three additional calls are for smaller amounts of CAD than CAD 10m. Thus, the total portfolio of calls surely generates up-front income, which compensates for the lower future value of the hedged firm. ME4. To value the subsidiary, you could construct a replicating portfolio. How would you construct this portfolio? A4. First reverse all the signs of the option positions: buy a call on CAD 10m at X 1 = 0.75, sell a call on CAD 2m at X 2 = 0.775, and so on. The payoff from this option portfolio will have the same curvature as the value of the subsidiary, but the option portfolio has a zero value for S T = 0.75, whereas the subsidiary has a value of USD 4m for S T = That is, the payoff from the options portfolio is too low by USD 4m everywhere. To increase the payoff from the options portfolio by USD 4m everywhere, buy a USD bond with future value equal to 4m. The portfolio of the bond and the four options will perfectly replicate the value of the subsidiary.

7 Chapter 19 Accounting Exposure Quiz True-False Questions 1. As taxes on the subsidiary s income are invariably computed by the host country on the basis of the subsidiary s income statement, there is no need whatsoever to translate this income into the parent s home currency for tax purposes. 2. Taxes are always based on the parent s consolidated world-wide income (which, of course, requires translation). 3. The choice of the translation method is similar to the choice between LIFO, FIFO, or average cost no accounting method can possibly affect the true value of the firm. 4. Accounting exposure is irrelevant if taxes are not affected. It follows that the firm need not worry about exchange rate changes at all. 5. The International Accounting Standards Committee has imposed the current rate method world-wide. 6. According to the monetary/non-monetary method, the true value of a real asset is the same in the two countries, and it is given by its foreigncurrency value translated at the current rate. Ans. 1. false; 2. false; 3. false: there is a tax effect for inventory reporting methods, but in the US, there is no such impact from the choice of a translation method; 4. false: the second part is wrong, economic exposure matters; 5. false: the IASC only makes recommendations; 6. false: it uses the foreign currency value translated at the historic rate. Matching Questions Which exposure concept translation exposure or economic exposure matches best with the following statement? This exposure: 1. Has to do with the firm s cash flows and market value. 2. Is forward-looking. 3. Ignores off-balance-sheet items and future operations. 4. Only exists for firms with foreign subsidiaries. 5. Is relevant for all firms in a nonsheltered sector, including firms that potentially could become exporters or could potentially have to compete against foreign imports. 6. Depends on the accounting method used if and only if the accounting method affects taxes. 7. Depends on economic reality. Ans. 1. economic; 2. economic; 3. translation; 4. translation; 5. economic; 6. economic; 7. economic. Which translation method(s), if any, match(es) best with the following statement? The translation methods are Current Rate, Currenct/Non-Current, Monetary/Non-Monetary. 1. Maximum consistency between the translated Asset and Liability statements and the originals (in host currency). 2. Imperfect consistency between the changes in the translated Asset and Liability statements and the translated Profit and Loss statement. 3. Short-term liabilities are exposed, but long-term liabilities are not.

8 19-2 Exercises + Solutions International Financial Markets and the Firm 4. Short-term real assets are exposed, but long-term real assets are not. 5. Short-term financial assets are exposed. 6. Exposure corresponds with net working capital. 7. Exchange rates are viewed as mean-reverting. 8. PPP holds. 9. Exposure corresponds to Net Worth. 10. Most firms have translation gains when the host currency appreciates. 11. For most firms, exposure to the exchange rate (units of the parent s home currency per unit of foreign currency) is negative. That is, there is a translation gain if the host currency depreciates. 12. PPP holds, so real assets are not exposed. Ans. 1. current rate; 2. all methods; 3. current/non-current; 4. current/non-current; 5. all methods; 6. current/non-current; 7. current-non-current; 8. monetary/non-monetary; 9. current rate; 10. current rate, and current/non-current; 11. monetary/non-monetary; 12. monetary/non-monetary. Exercises E1. Why does the need arise to translate the financial statements of subsidiaries into a reference currency? A1. A firm's translates the financial statements of its subsidiaries into a reference currency because: Income earned by the foreign subsidiary is taxable in the parent's home currency, and therefore, a tax basis must be established. Most countries require consolidation of the parent's and the subsidiary's financial statements for reporting purposes. The financial statements are needed to make investment and financing decisions and to evaluate the performance of the firm. Translation makes it possible to create comparable performance measures. A benchmark is needed when valuing the firm. E2. You are given the following balance sheet information for the first two years of a Norwegian subsidiary s life, 19X3 and 19X4 (in millions of NOK, the subsidiary s currency). P. Sercu and R. Uppal Version January 1994 Printout September 23, 1999

9 International Financial Markets and the Firm Exercises + Solutions page 19-3 ASSETS Liquidities 3 Inventory 4 Fixed assets Investments 19X3 4 Investments 19X LIABILITIES Equity Equity 19X3 4 New equity mid-19x4 1 5 Retained earnings 19X4 2 Long-term debt Issued 19X3 2 Issued 19X4 1 3 Short-term debt 2 12 Notes: end 19X3 and 19X4, the exchange rate was USD/NOK 0.30 and 0.15, respectively. The rate in mid-19x4, when the equity was increased, was Fixed assets were bought in 19X3 and 19X4; the figures shown are net of all 19X3-5 depreciation. Assume that the firm uses the current rate method to translate its subsidiary s asset and liability statement. (a) Compute the exposure of these 19X4 balance sheet items to the 19X5 exchange rate. (b) Translate this balance sheet into USD once assuming a rate of USD/NOK 0.20 at the end of 19X5, and once assuming a rate of USD/NOK That is, compute the translated values of all items except equity adjustments, compute the total value of the assets, and finally compute the equity adjustments as the item that (c) balances the totals for assets and liabilities. Verify that the exposure, as computed in (a), multiplied by the difference in the two 19X5 rates (USD/NOK 0.05), produces the difference in the equity adjustments computed in part (b); that is, verify that Net Worth = Exposure S. A2. (a) Exposure = net worth = 12m (3m + 2m) = NOK 7m. (b) P. Sercu and R. Uppal Version January 1994 Printout September 23, 1999

10 19-4 Exercises + Solutions International Financial Markets and the Firm USD/NOK NOK At 0.20 At 0.25 ASSETS Liquidities Inventory Fixed assets LIABILITIES Equity Equity 19X New equity mid-19x Retained earnings 19X Equity adjustments n.a. <0.26> 0.09 Long-term debt Short-term debt (c) The equity adjustments differ by USD (0.09 ( 0.26)) = USD 0.35 = exposure S = NOK 7m E3. In the previous exercise, change the translation method to the current/non-current method. A3. (a) Exposure = short-term assets short-term liabilities = (3m + 4m) 2m = NOK 5m. (b) USD/NOK NOK at 0.20 at 0.25 ASSETS liquidities inventory fixed assets investments 19X investments 19X LIABILITIES equity equity 19X new equity mid-19x retained earnings 19X equity adjustments n/a <0.06> 0.19 long-t debt issued 19X issued 19X short-t debt (c) The equity adjustments differ by USD (0.19 ( 0.06)) = USD 0.25 = exposure S = NOK 5m E4. In the previous exercise, change the translation method to the monetary/non-monetary method. P. Sercu and R. Uppal Version January 1994 Printout September 23, 1999

11 International Financial Markets and the Firm Exercises + Solutions page 19-5 A4. (a) Exposure = monetary assets liabilities = 3m (3m + 2m) = NOK 2m. (b) USD/NOK NOK at 0.20 at 0.25 ASSETS liquidities inventory fixed assets investments 19X investments 19X LIABILITIES equity equity 19X new equity mid-19x retained earnings 19X equity adjustments n/a <0.11> <0.21> long-t debt short-t debt (c) The equity adjustments differ by USD (( 0.21) ( 0.11)) = USD 0.10 = exposure S = = NOK -2m Mind-Expanding Exercise ME1. In the above exercises, we asked you to compute the exposure of the 19X4 balance sheet items to the 19X5 exchange rate not exposure of the 19X5 balance sheet items to the 19X5 exchange rate. Verify that the traditional definitions of exposure net worth, net working capital, or the net monetary position work perfectly only if we restrict attention to assets and liabilities that were in place one year before the translation. A1. For assets and liabilities added in the reporting period 19X5, in the exercises there is no distinction between the historic rate and the current exchange rate. Thus, for the 19X5 additions, the current rate still affects the translation even if the balance sheet item is deemed to be unexposed. For instance, investments made in 19X5 will be translated at the 19X5 exchange rate under all methods, which means that the 19X5 exchange rate partly affects the converted value of assets even under the monetary/non-monetary or current/non-current methods. Similarly, earnings retained in 19X5 will be translated at the 19X5 rate, so that the translated net worth is affected by the 19X5 exchange rate, and so on. P. Sercu and R. Uppal Version January 1994 Printout September 23, 1999

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