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 $0.89068/E. The exchange rate on December 31, 2002, was $1.04862/E, and the average exchange rate for 2002 was $0.94486/E (these values come from http://pacific.commerce.ubc.ca/xr/data.html. Pacotilles du Rhône, Inc. 2001 and 2002 Balance Sheets (in millions of E Assets Liabilities and Owners Equity 2001 2002 2001 2002 Cash 54 190 Payables 275 310 Receivables 320 430 Current Debt 130 150 Inventory 195 240 Long-term debt 160 460 Current assets 569 860 Total liabilities 565 920 Fixed assets 880 1,280 Common stock 230 230 Accum. depr. (150 (360 Ret. earnings 504 630 Net fixed asset 730 920 Total equity 734 860 Total 1,299 1,780 Total 1,299 1,780 Table 1: Pre-translation balance sheets for Pacotilles du Rhône. 1
Pacotilles du Rhône, Inc. 2002 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. $0.944645/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. 2002 Income Statement, Current-Rate Translation Item E Rate $ Revenues 1,290 $0.94486/E 1,219 Cost of goods sold (540 $0.94486/E (510 Other expenses (414 $0.94486/E (391 Depreciation expense (210 $0.94486/E (198 Net income 126 120 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 $0.89068/E, and all assets and liabilities on the 2002 balance sheet have been translated at the rate $1.04862/E. All equity items are 2
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 $0.89068/E. This gives E230 $0.89068/E = $205. For retained earnings, the amount on the 2001 balance sheet is translated at the December 31, 2001, exchange rate, which gives E504 $0.89068/E = $449. The change in retained earnings has to be consistent with the income statement, so accumulated retained earnings for 2002 are 449 + 120 = $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 2001. 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. 2001 and 2002 Balance Sheets, Current-Rate Translation Assets Liabilities and Owners Equity 2001 2002 2001 2002 Cash 48 199 Payables 245 325 Receivables 285 451 Current Debt 116 157 Inventory 174 252 Long-term debt 142 482 Current assets 507 902 Total liabilities 503 964 Fixed assets 784 1,342 Common stock 205 205 Accum. depr. (134 (377 Ret. earnings 449 569 Net fixed asset 650 965 Total equity 654 774 CTA 0 129 Total 1,157 1,867 Total 1,157 1,867 Table 4: Balance sheets translated using the current-rate method. 3
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 NA2001 + ( S 2002 S 2002 NA2001,2002 = (1.04862 0.89068(1, 299 565 + (1.04862 0.94486(1, 780 920 734 }{{} 734 = 0.15794 734 + 0.10376 126 = 129. 3 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 $0.89068/E for 2001 and $1.04862/E for 2002. On the income statement, revenues and other expenses are translated at the 2002 average exchange rate, which is $0.94486/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 $0.89068/E = $784. 4
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 $0.89068/E + (E1, 280 E880 $0.94486/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 2002. 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 = 880 400 $0.89068/E + $0.94486/E = $0.90761/E. 1, 280 1, 280 The translated 2002 depreciation expense is then E210 $0.90761/E = $191. Translated 2001 accumulated depreciation is E150 $0.89068/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 $0.89068/E, and 540 195 = E345 has been purchased in 2002, which is translated at the average exchange rate for the period, i.e. $0.94486/E. Translated 2002 COGS is then E195 $0.89068/E + 345 $0.94486/E = $500. (iv Inventory 2001 inventory is translated at its historical rate, which is $0.89068/E in this case, and thus translated 2001 inventory = E195 $0.89068/E = $174. 5
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. + 540 }{{} 2002 COGS 195 }{{} 2001 inv. = E585. 2002 purchases are translated at the 2002 average exchange rate, $0.94486/E, and translated 2002 inventory is obtained as follows: 2002 inv. = 174 }{{} tr. 2001 inv. + 585 0.94486 }{{} tr. 2001 pur. 500 }{{} tr. 2002 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 545 449 = $96, the translated 2002 net income has to be adjusted downward by $41. The 2002 income statement and the 2001-2002 balance sheets translated using the temporal method are depicted in tables 5 and 6. 3.1 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
In the present example, we have NMA 2001 = 54 + 320 565 = 191, NMA 2002 = 190 + 430 920 = 300, NMA 2001,2002 = 300 ( 191 = 110, and thus the translation gain for 2002 is T G 2002 = ( S 2002 S 2001 NMA2001 + ( S 2002 S 2002 NMA2001,2002 = (1.04862 0.89068( 191 + (1.04862 0.94486( 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. 2002 Income Statement, Temporal Translation Item E Rate $ Revenues 1,290 $0.94486/E 1,219 Cost of goods sold (540 (500 Other expenses (414 $0.94486/E (391 Depreciation expense (210 $0.90761/E (191 Net income before adjustment 126 137 Translation loss (0 (41 Net income 126 96 Table 5: 2002 income statement translated using the temporal method. 7
Pacotilles du Rhône, Inc. 2001 and 2002 Balance Sheets, Temporal Translation Assets Liabilities and Owners Equity 2001 2002 2001 2002 Cash 48 199 Payables 245 325 Receivables 285 451 Current Debt 116 157 Inventory 174 227 Long-term debt 142 482 Current assets 507 877 Total liabilities 503 964 Fixed assets 784 1,162 Common stock 205 205 Accum. depr. (134 (325 Ret. earnings 449 545 Net fixed asset 650 837 Total equity 654 750 Total 1,157 1,714 Total 1,157 1,714 Table 6: Balance sheets translated using the temporal method. 8