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					                                 Translation Exposure

                                               An Example



1      Preliminary Statements
Table 1 provides the balance sheets as of December 31, 2001, and December 31, 2002,
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for Pacotilles du Rhˆne, 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).

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                                      Pacotilles du Rhˆne, 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


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                Table 1: Pre-translation balance sheets for Pacotilles du Rhˆne.




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                                   Pacotilles du Rhˆne, 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


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          Table 2: Pre-translation 2002 income statement for Pacotilles du Rhˆne.

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.

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                                   Pacotilles du Rhˆne, 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

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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.

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                                      Pacotilles du Rhˆne, 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.




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2.1      Calculating the Translation Gain (Loss)
           ¯
Let Si and Si 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 N Ai = Ai −Li
and ∆N Ai,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 Gi , is given by

                      T Gi =    Si − Si−1 N Ai−1 +           ¯
                                                        Si − Si ∆N Ai−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 G2002 =       S2002 − S2001 N A2001 +             ¯
                                            S2002 − S2002 ∆N A2001,2002

           = (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.

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    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 ac-
    quired 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:

                                 × $0.89068/E +        × $0.94486/E = $0.90761/E.
                           880                   400
        blended rate =
                          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.

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      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     +     540   −   195     =           E585.
                                 2002 inv.   2002 COGS   2001 inv.
      2002 purchases are translated at the 2002 average exchange rate, $0.94486/E, and
      translated 2002 inventory is obtained as follows:

          2002 inv. =         174      + 585 × 0.94486 −       500     = $227.
                         tr. 2001 inv.   tr. 2001 pur.   tr. 2002 COGS

 (v) Retained Earnings     Under the temporal method, accumulated retained earnings in-
      clude 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 tem-
poral method are depicted in tables 5 and 6.


3.1    Calculating the Translation Gain (Loss)
                      ¯
As before, let Si and Si 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
N M Ai = M Ai − M Li and ∆N M Ai,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 Gi , is given by

                  T Gi =    Si − Si−1 N M Ai−1 +          ¯
                                                     Si − Si ∆N M Ai−1,i .

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In the present example, we have

                      N M A2001 = 54 + 320 − 565 = − 191,
                      N M A2002 = 190 + 430 − 920 = − 300,
                      ∆N M A2001,2002 = − 300 − (−191) = − 110,

and thus the translation gain for 2002 is

          T G2002 =      S2002 − S2001 N M A2001 +            ¯
                                                      S2002 − S2002 ∆N M A2001,2002

                   = (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.

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                                    Pacotilles du Rhˆne, 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.




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                                   Pacotilles du Rhˆne, 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.




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