By Amy Gonzalez,2014-11-22 18:18
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    Changing prices are often associated with inflation (deflation), but this is not necessary because prices can change individually dues to changes in demand. It is only when all prices rise together that one has inflation. This rise in all prices is often associated with changes in the money supply: Too many dollars chasing too few goods. As an aside the word dollars comes from the German “thal” meaning hill. Silver for “thalers” was mined at Joachims Thal.)

    Our concern is with inflation not changes in individual prices. We are concerned with what happens when the dollar loses its value. Inflation is typically measured by a basket of goods: Paasche looks at how the price of an "old" basket of goods has changed; Laspeyres looks at how the price of a "new" basket of goods has changed.

    Prices of non-monetary goods tend to rise with the increase in dollars i.e., they maintain their real value, but increase in nominal value. Monetary assets and liabilities are distinguished by being denominated in fixed dollars. In times of inflation, therefore, monetary assets lose their real value, but maintain their nominal value.

Purchasing power parity

    Inflation also affects the price foreigners are prepared to pay for dollars -- equivalently how much of their goods they are willing to give us for our dollars. Absent government intervention the exchange rate between countries tends to move opposite to the rate of inflation so as to keep the real cost of goods in line. Consider the following example:

    Assume the dollar was worth 120 yen so that American beef that costs us $10 per pound would cost the Japanese 1,200 yen. Assume that we have inflation that raises the price we pay for our beef 20 percent to $12. Note that we are assuming unchanged demand and supply of beef -- all that has changed is a 20 percent increase in the number of dollars in circulation. The Japanese have the same amount of yen and would want to pay the same amount in yen for their beef. The exchange rate drops obligingly, therefore, to 100 yen for one dollar. The $12 beef, thus, continues to cost the Japanese 120 yen.

    Now reverse the situation. Assume first that the exchange rate was 100 yen to the dollar. Assume further that the yen, now, experiences 20 percent inflation. Initially it cost 1,000 yen to purchase beef at $10 per pound. After a round of inflation in Japan, it will cost them 1,200 yen to buy the same $10 beef. To reveal this increase in yen cost, the dollar-yen exchange rate will rise to 120 yen to the dollar.

    We can formalize these relationships with the following equation:

     * Michael F. van Breda, 2005


    er = er x (1+ us_inf)/(1 + for_inf) 10

    where er = the exchange rate before (0) and after (1)

     us_inf = inflation rate in the United States

     for_inf = inflation rate in the foreign country

    This equation captures what is often called the purchasing power parity theory, which simply states that goods should cost the same around the world.

Fisher equation

    In a variation of the PPP equation, assume that one is able to buy a currency forward. In other words, one enters into an executory contract with the bank to swap dollars for a foreign currency at some future point in time at a set rate determined “today.” This is

    the so-called forward rate. One has two options when planning a purchase of foreign currency.

    i. One can buy that foreign currency at today’s spot rate and invest it in the foreign

    country until it is needed.

    ii. One can invest one’s money at home until the foreign currency is needed and

    then swap it at the spot rate obtaining then.

Arbitrage forces these two strategies to be the same i.e.,

     Dollars invested x (1 + us_int) x er = Dollars x er x (1 + for_int) fs

Where int = interest rate both US (us) and foreign (for)

Reformatting this we have:

     er = er x (1 + us_int)/(1+ for_int) fs

where subscript f = forward rate and s = spot rate

    But nominal rates of interest are the product of the real rate and the rate of inflation. If one assumes that the real rate is the same in both countries then the equation resolves to the PPP equation above. If the risk is perceived to be different in the two countries then one must add a risk factor to the equation.

Holding gains and losses

    Assume now that a Japanese firm acquires 100 pounds of beer ready for transport to Japan. The beef cost them $1,000 or 120,000 yen. Before the beef is shipped, inflation of


    20 percent is experiences in the United States. The current cost of the beef is, therefore, $1,200. In dollar terms, the Japanese have enjoyed a holding gain of $200.

    However, because of purchasing power parity, the dollar-yen rate will fall to 100 yen to the dollar. As a result, the beef ; even at its current cost ; will still cost the Japanese

    120,000 yen. In other words, from the perspective of the host currency, there has been neither gain nor loss. This makes sense because the inflation was experienced in the US, not in Japan.

    Consider the situation with inflation occurring in Japan. As before, we begin with a rate of 100 yen to the dollar and beef costing $1,000 or 100,000 yen. Due to inflation in Japan, the exchange rate falls to 120 yen to the dollar. Beef continues to cost $1,000 in the US, but it now costs 120,000 yen in Japan. Therefore, the Japanese will show a holding gain of 20,000 yen in nominal yen. Appropriately, dollar accounting will show neither gain nor loss. And equally appropriately, if we adjust for inflation by using constant dollars the nominal holding gain disappears too.

Monetary gains and losses

    Now let us assume that the Japanese had lent us money that we had agreed to repay in yen. Say they lent us 1,200 yen, say, which translated into $10 at an exchange rate of 120 yen to the dollar. After inflation in the United States of 20 percent, the exchange rate would fall to 100 yen to the dollar and we would have to find $12 to be able to purchase 1,200 yen to repay them. We would have suffered a monetary loss. Note that the Japanese would still be receiving their 1,200 yen. Since we assumed that there was no inflation in Japan, the value of the receivable in Japan would remain unchanged both in nominal and in real terms

    But let us say that we had agreed to repay them in dollars. We would give them the $10 that they had lent us. Only now it would only buy 1,000 yen. They would have suffered the monetary loss, as a result.

We can set this discussion out as follows:

    Inflation in USA Inflation in Japan

Historical cost $1,000 120,000 $1,000 120,000

    Current cost $1,200 120,000 $1,000 144,000

    Holding gain $ 200 0 $ 0 24,000


    What the above says is that when we transact with companies abroad and we make our contracts out in dollars, then we have nothing to worry about when the exchange rate

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    fluctuates. On the other hand when our transactions are denominated in their currency, then we have to take inflation on our side and on theirs into account e.g.,

    We make a sale of $120 dollars at a time when the yen is 120 to the dollar. We

    are paid when the yen is 144 to the dollar. The deal is denominated in yen. We

    denote accounts that are really in yen terms by [Y].

    dr Accounts Receivable $120 [Y]

     cr Revenue $120

    To record a sale of $120 x 120 = 14,400 yen. Strictly speaking the receivable is 14,400 yen. The sale will be paid for in yen. These have to be taken to the bank and swapped for dollars at the spot rate that day. Since the rate has gone up to 144, we will receive $100 only.

    dr Cash $100 [Y]

     Realized Loss 20

     cr Accounts Receivable $120

To record the receipt of Y14,400 at 144 to the dollar.

    Note this is a realized loss. The question now arises, as it does with accounting for inflation, what should one do with an Accounts Receivable balance denominated in dollars at the end of the year. Should one leave it at $120, which effectively says, translate it at the original exchange rate or should one translate it at the current rate. If one translates it at the current rate one has an unrealized loss of $20. Note these are monetary losses.

    Very little in our analysis changes when we assume that the price changes are occurring abroad. A rise in the exchange rate can reflect deflation on our side -- more yen are needed to buy dollars that are in short supply. A rise in the exchange rate can also reflect inflation on their side -- more yen are needed to buy dollars because there is an excess of yen. The effect is identical -- all that changes is the explanatory story.

    The above analysis uses the so-called two-step approach. A one-step approach assumes that the revenue account is not closed until the deal is complete. The only effect is to make the realized loss into an offset against revenue i.e., the net revenue earned is $100. The US favors the two-step; most others favor the one-step. The bottom line is the same.


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