Translation Exposure

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Erick Peters
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1 Translation Exposure An Example 1 Preliminary Statements Table 1 provides the balance sheets as of December 31, 2001, and December 31, 2002, for Pacotilles du Rhône, Inc., (PRI, a French subsidiary of a U.S. corporation. PRI has been acquired on December 31, 2001, time at which the exchange rate was $ /E. The exchange rate on December 31, 2002, was $ /E, and the average exchange rate for 2002 was $ /E (these values come from Pacotilles du Rhône, Inc and 2002 Balance Sheets (in millions of E Assets Liabilities and Owners Equity Cash Payables Receivables Current Debt Inventory Long-term debt Current assets Total liabilities Fixed assets 880 1,280 Common stock Accum. depr. (150 (360 Ret. earnings Net fixed asset Total equity Total 1,299 1,780 Total 1,299 1,780 Table 1: Pre-translation balance sheets for Pacotilles du Rhône. 1

2 Pacotilles du Rhône, Inc Income Statement (in millions of E Revenues 1,290 Cost of goods sold (540 Other expenses (414 Depreciation expense (210 Net income 126 Table 2: Pre-translation 2002 income statement for Pacotilles du Rhône. 2 Translation Using the Current-Rate Method Under the current-rate method, all income statement items are translated using the average exchange rate for the income statement period, i.e. $ /E, as shown in Table 3. From this income statement, translated retained earnings for 2002 are $120, which is the change in retained earnings that will appear on the translated balance sheet. Pacotilles du Rhône, Inc Income Statement, Current-Rate Translation Item E Rate $ Revenues 1,290 $ /E 1,219 Cost of goods sold (540 $ /E (510 Other expenses (414 $ /E (391 Depreciation expense (210 $ /E (198 Net income Table 3: 2002 income statement translated using the current-rate method. For the balance sheet, the current-rate method translates all assets and all liabilities at the exchange rate in effect on the balance sheet date. That is, all assets and liabilities on the 2001 balance sheet have been translated at the rate $ /E, and all assets and liabilities on the 2002 balance sheet have been translated at the rate $ /E. All equity items are 2

3 translated at their historical rate. Since no common stock is issued in 2002, the rate used to translate common stock in each year is the rate in effect on December 31, 2001, which is $ /E. This gives E230 $ /E = $205. For retained earnings, the amount on the 2001 balance sheet is translated at the December 31, 2001, exchange rate, which gives E504 $ /E = $449. The change in retained earnings has to be consistent with the income statement, so accumulated retained earnings for 2002 are = $569. Imbalances due to translation are recorded in a different account, the cumulative translation adjustment (CTA account. Since all the 2001 balance sheet items are translated at the same rate, there is no need for adjusment and thus the CTA account shows a zero balance in On the other hand, since the 2002 balance sheet items are not all translated at the same rate, the CTA account shows a positive balance in 2002 due to the euro appreciation. The translated balance sheets are depicted in Table 4. Pacotilles du Rhône, Inc and 2002 Balance Sheets, Current-Rate Translation Assets Liabilities and Owners Equity Cash Payables Receivables Current Debt Inventory Long-term debt Current assets Total liabilities Fixed assets 784 1,342 Common stock Accum. depr. (134 (377 Ret. earnings Net fixed asset Total equity CTA Total 1,157 1,867 Total 1,157 1,867 Table 4: Balance sheets translated using the current-rate method. 3

4 2.1 Calculating the Translation Gain (Loss Let S i and S i denote the exchange rate (in home currency per foreign currency on year i s balance sheet and the average exchange rate during year i, respectively, and let NA i = A i L i and NA i,i+1 denote net assets in year i s balance sheet and the change in net assets from year i to year i + 1, respectively. Under the current-rate method, the translation gain for year i, denoted T G i, is given by T G i = ( S i S i 1 NAi 1 + ( S i S i NAi 1,i. Note that this gives the change in CTA, not the CTA balance, except for the first year of operations. The translation gain in the present example is T G 2002 = ( S 2002 S 2001 NA ( S 2002 S 2002 NA2001,2002 = ( (1, ( (1, }{{} 734 = = Translation Using the Temporal Method Under the temporal method, all monetary assets (cash and accounts receivable in the present example and all monetary liabilities (accounts payable, current debt and long-term debt in the present example are translated using the exchange rate in effect on the balance sheet date, which is $ /E for 2001 and $ /E for On the income statement, revenues and other expenses are translated at the 2002 average exchange rate, which is $ /E. All other items have to be treated separately. (i Fixed Assets Fixed assets are translated at their historical rate. For fixed assets in the Dec. 31, 2001, balance sheet, this gives E880 $ /E = $784. 4

5 For fixed assets in the Dec. 31, 2002, balance sheet, net new investments in 2002 are translated at the average exchange rate for that period, which gives E880 $ /E + (E1, 280 E880 $ /E = $784 + $378 = $1, 162. }{{} net investment (ii Depreciation Depreciation expense in 2002 consists of the depreciation of assets acquired on Dec 31, 2001, and depreciation of assets acquired during The exchange rate used for 2002 depreciation expense is then a weighted average of the exchange rates used for fixed assets, sometimes called blended rate. This rate is obtained as follows: blended rate = $ /E + $ /E = $ /E. 1, 280 1, 280 The translated 2002 depreciation expense is then E210 $ /E = $191. Translated 2001 accumulated depreciation is E150 $ /E = $134, and translated 2002 accumulated depreciation is $134 + $191 = $325. (iii COGS In 2002, COGS is E540. From this amount, E195 was taken from the firm s inventory on Dec. 31, 2001, which is translated at the rate $ /E, and = E345 has been purchased in 2002, which is translated at the average exchange rate for the period, i.e. $ /E. Translated 2002 COGS is then E195 $ /E $ /E = $500. (iv Inventory 2001 inventory is translated at its historical rate, which is $ /E in this case, and thus translated 2001 inventory = E195 $ /E = $174. 5

6 Given the inventory on Dec. 31, 2001, the inventory on Dec. 31, 2002, and the 2002 COGS, we can find 2002 purchases as follows: 2002 purchases = 240 }{{} 2002 inv }{{} 2002 COGS 195 }{{} 2001 inv. = E purchases are translated at the 2002 average exchange rate, $ /E, and translated 2002 inventory is obtained as follows: 2002 inv. = 174 }{{} tr inv }{{} tr pur. 500 }{{} tr COGS = $227. (v Retained Earnings Under the temporal method, accumulated retained earnings include any imbalance from the balance sheet, and thus the income statement has to be adjusted such that the difference between the 2002 accumulated retained earnings and the 2001 accumulated retained earnings is consistent with the net income on the translated income statement. The difference between translated accumulated retained earnings being = $96, the translated 2002 net income has to be adjusted downward by $41. The 2002 income statement and the balance sheets translated using the temporal method are depicted in tables 5 and Calculating the Translation Gain (Loss As before, let S i and S i denote the exchange rate (in home currency per foreign currency on year i s balance sheet and the average exchange rate during year i, respectively, and let NMA i = MA i ML i and NMA i,i+1 denote net monetary assets in year i s balance sheet and the change in net monetary assets from year i to year i + 1, respectively. Under the temporal method, the translation gain for year i, denoted T G i, is given by T G i = ( S i S i 1 NMAi 1 + ( S i S i NMAi 1,i. 6

7 In the present example, we have NMA 2001 = = 191, NMA 2002 = = 300, NMA 2001,2002 = 300 ( 191 = 110, and thus the translation gain for 2002 is T G 2002 = ( S 2002 S 2001 NMA ( S 2002 S 2002 NMA2001,2002 = ( ( ( ( 110 = $41. Note that we have a translation loss under the temporal method, whereas the current-rate method gave us a translation gain. This arises because there are more assets than liabilities but less monetary assets than monetary liabilities. Pacotilles du Rhône, Inc Income Statement, Temporal Translation Item E Rate $ Revenues 1,290 $ /E 1,219 Cost of goods sold (540 (500 Other expenses (414 $ /E (391 Depreciation expense (210 $ /E (191 Net income before adjustment Translation loss (0 (41 Net income Table 5: 2002 income statement translated using the temporal method. 7

8 Pacotilles du Rhône, Inc and 2002 Balance Sheets, Temporal Translation Assets Liabilities and Owners Equity Cash Payables Receivables Current Debt Inventory Long-term debt Current assets Total liabilities Fixed assets 784 1,162 Common stock Accum. depr. (134 (325 Ret. earnings Net fixed asset Total equity Total 1,157 1,714 Total 1,157 1,714 Table 6: Balance sheets translated using the temporal method. 8

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