## Relative Purchasing Power Parity

As a practical matter, a relative version of purchasing power parity has evolved. Relative purchasing power parity does not tell us what determines the absolute level of the exchange rate. Instead, it tells what determines the change in the exchange rate over time.

The Basic Idea Suppose the British pound-U.S. dollar exchange rate is currently S0 = £.50. Further suppose that the inflation rate in Britain is predicted to be 10 percent over the coming year, and (for the moment) the inflation rate in the United States is predicted to be zero. What do you think the exchange rate will be in a year?

If you think about it, you see that a dollar currently costs .50 pounds in Britain. With 10 percent inflation, we expect prices in Britain to generally rise by 10 percent. So we expect that the price of a dollar will go up by 10 percent, and the exchange rate should rise to £.50 x 1.1 = £.55.

If the inflation rate in the United States is not zero, then we need to worry about the relative inflation rates in the two countries. For example, suppose the U.S. inflation rate is predicted to be 4 percent. Relative to prices in the United States, prices in Britain are rising at a rate of 10% - 4% = 6% per year. So we expect the price of the dollar to rise by 6 percent, and the predicted exchange rate is £.50 x 1.06 = £.53.

The Result In general, relative PPP says that the change in the exchange rate is determined by the difference in the inflation rates of the two countries. To be more specific, we will use the following notation:

S0 = Current (Time 0) spot exchange rate (foreign currency per dollar) E(St) = Expected exchange rate in t periods hUS = Inflation rate in the United States hFC = Foreign country inflation rate

Based on our discussion just preceding, relative PPP says that the expected percentage change in the exchange rate over the next year, [E(S1) - S0]/S0, is:

In words, relative PPP simply says that the expected percentage change in the exchange rate is equal to the difference in inflation rates. If we rearrange this slightly, we get:

This result makes a certain amount of sense, but care must be used in quoting the exchange rate.

In our example involving Britain and the United States, relative PPP tells us that the exchange rate will rise by hFC - hUS = 10% - 4% = 6% per year. Assuming the difference in inflation rates doesn't change, the expected exchange rate in two years, E(S2), will therefore be:

Notice that we could have written this as:

In general, relative PPP says that the expected exchange rate at some time in the future,

As we will see, this is a very useful relationship.

Because we don't really expect absolute PPP to hold for most goods, we will focus on relative PPP in our following discussion. Henceforth, when we refer to PPP without further qualification, we mean relative PPP.

It's All Relative

Suppose the Japanese exchange rate is currently 105 yen per dollar. The inflation rate in Japan over the next three years will run, say, 2 percent per year, whereas the U.S. inflation rate will be 6 percent. Based on relative PPP, what will the exchange rate be in three years?

Because the U.S. inflation rate is higher, we expect that a dollar will become less valuable. The exchange rate change will be 2% - 6% = -4% per year. Over three years, the exchange rate will fall to:

E(53) = So X [1 + (hFo - hs)]3 = 105 X [1 + (-.04)]3 = 92.90

Currency Appreciation and Depreciation We frequently hear things like "the dollar strengthened (or weakened) in financial markets today" or "the dollar is expected to appreciate (or depreciate) relative to the pound." When we say that the dollar strengthens or appreciates, we mean that the value of a dollar rises, so it takes more foreign currency to buy a dollar.

What happens to the exchange rates as currencies fluctuate in value depends on how exchange rates are quoted. Because we are quoting them as units of foreign currency per dollar, the exchange rate moves in the same direction as the value of the dollar: it rises as the dollar strengthens, and it falls as the dollar weakens.

Relative PPP tells us that the exchange rate will rise if the U.S. inflation rate is lower than the foreign country's. This happens because the foreign currency depreciates in value and therefore weakens relative to the dollar.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VIII. Topics in Corporate Finance

22. International Corporate Finance

© The McGraw-Hill Companies, 2002

PART EIGHT Topics in Corporate Finance

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