Assume that the export price of a Nissan XTerra from Osaka, Japan is ¥3,750,000. The exchange rate is ¥121.84/$. The forecast rate of inflation in the United States is 2.8% per year and is 0.6% in Japan.
a. What is the export price of the XTerra at the beginning of the year expressed in US dollars?
b. Assuming purchasing power parity holds, what should the exchange rate be at the end of the year?
c. Assuming 100% pass-thru of exchange rate changes, what should be the dollar price of an XTerra at the end of the year?
d. Assuming 75% pass-thru of exchange rate changes, what should be the dollar price of an XTerra at the end of the year?
a. The export price of the XTerra at the beginning of the year expressed in US dollars can be calculated by dividing the export price in yen by the exchange rate:
(¥3,750,000) / (¥121.84/$) = $30,759.85
So, the export price of the XTerra at the beginning of the year is approximately $30,759.85.
b. If purchasing power parity holds, the exchange rate at the end of the year can be calculated by considering the difference in inflation rates between the two countries:
Assuming the forecast rate of inflation in the United States is 2.8% and in Japan is 0.6%, we can calculate the expected change in the exchange rate as follows:
Expected change in exchange rate = (1 + US inflation rate) / (1 + Japanese inflation rate)
Expected change in exchange rate = (1 + 2.8%) / (1 + 0.6%)
Expected change in exchange rate = 1.028 / 1.006
Expected change in exchange rate ≈ 1.021
So, the expected exchange rate at the end of the year would be approximately ¥121.84/$ × 1.021 = ¥124.30/$.
c. Assuming 100% pass-thru of exchange rate changes, the dollar price of an XTerra at the end of the year would be the export price at the beginning of the year multiplied by the exchange rate at the end of the year:
Dollar price of an XTerra at the end of the year = $30,759.85 × ¥124.30/$
(Note: We assume that the exchange rate hasn't changed over the year for simplicity)
d. Assuming 75% pass-thru of exchange rate changes, the dollar price of an XTerra at the end of the year would be 75% of the price calculated in part (c):
Dollar price of an XTerra at the end of the year = 75% × (Dollar price calculated in part (c))
a. To find the export price of the XTerra at the beginning of the year in US dollars, we need to convert the yen price into dollars using the exchange rate.
Export price in yen: ¥3,750,000
Exchange rate: ¥121.84/$
Export price in dollars = (Export price in yen) / (Exchange rate)
Export price in dollars = ¥3,750,000 / ¥121.84/$
Using a currency converter, we find that ¥3,750,000 is approximately $30,754.02. Therefore, the export price of the XTerra at the beginning of the year is approximately $30,754.02.
b. According to purchasing power parity (PPP), the exchange rate should adjust to account for the difference in inflation rates between the two countries.
PPP exchange rate = Initial exchange rate * [(1 + Inflation rate in the United States) / (1 + Inflation rate in Japan)]
Initial exchange rate = ¥121.84/$
Inflation rate in the United States = 2.8%
Inflation rate in Japan = 0.6%
PPP exchange rate = ¥121.84/$ * [(1 + 0.028) / (1 + 0.006)]
PPP exchange rate = ¥121.84/$ * 1.028 / 1.006
Using a calculator, we find that the PPP exchange rate should be approximately ¥124.12/$ at the end of the year.
c. Assuming 100% pass-thru of exchange rate changes, the dollar price of an XTerra at the end of the year will be determined by the PPP exchange rate.
Dollar price at the end of the year = Export price in yen * PPP exchange rate
Dollar price at the end of the year = ¥3,750,000 * ¥124.12/$
Using a calculator, we find that the dollar price of an XTerra at the end of the year, assuming 100% pass-thru of exchange rate changes, should be approximately $30,786.75.
d. Assuming 75% pass-thru of exchange rate changes means that only 75% of the exchange rate changes will be passed on to the dollar price of the XTerra at the end of the year.
Dollar price at the end of the year = [Export price in yen * PPP exchange rate] * 0.75
Dollar price at the end of the year = [¥3,750,000 * ¥124.12/$] * 0.75
Using a calculator, we find that the dollar price of an XTerra at the end of the year, assuming 75% pass-thru of exchange rate changes, should be approximately $23,090.06.
a. To calculate the export price of the XTerra at the beginning of the year expressed in US dollars, we need to convert the price from yen to dollars using the exchange rate.
Export price of XTerra in yen: ¥3,750,000
Exchange rate: ¥121.84/$
Export price of XTerra in dollars: ¥3,750,000 / ¥121.84/$ = $30,784.35
Therefore, the export price of the XTerra at the beginning of the year expressed in US dollars is approximately $30,784.35.
b. Purchasing power parity (PPP) is the theory that states the exchange rate between two currencies should equal the ratio of their price levels. Assuming PPP holds, we can calculate the expected exchange rate at the end of the year based on the inflation rates.
Rate of inflation in the United States: 2.8%
Rate of inflation in Japan: 0.6%
Expected exchange rate at the end of the year:
(1 + inflation in the United States) / (1 + inflation in Japan) = (1 + 0.028) / (1 + 0.006) = 1.028 / 1.006 = 1.0219
Therefore, assuming PPP holds, the exchange rate at the end of the year should be approximately ¥121.84/$ * 1.0219 = ¥124.56/$.
c. Assuming 100% pass-thru of exchange rate changes means all changes in the exchange rate will be fully reflected in the dollar price of an XTerra. We can calculate the expected dollar price of an XTerra at the end of the year using the exchange rate calculated in part b.
Expected dollar price of an XTerra at the end of the year: ¥3,750,000 / ¥124.56/$ = $30,086.16
Therefore, assuming 100% pass-thru of exchange rate changes, the dollar price of an XTerra at the end of the year should be approximately $30,086.16.
d. Assuming 75% pass-thru of exchange rate changes means only 75% of the changes in the exchange rate will be reflected in the dollar price of an XTerra. To calculate the expected dollar price of an XTerra at the end of the year, we need to consider the 75% pass-thru rate.
Expected dollar price of an XTerra at the end of the year: ¥3,750,000 / ¥124.56/$ * 0.75 = $22,564.62
Therefore, assuming 75% pass-thru of exchange rate changes, the dollar price of an XTerra at the end of the year should be approximately $22,564.62.
Initial spot exchange rate (¥/$) 110.60
Initial price of a Nissan Xterra (¥) 2,800,000
Expected US dollar inflation rate for the coming year 2.000%
Expected Japanese yen inflation rate for the coming year 0.000%
Desired rate of pass through by Nissan 70.000%
a. What was the export price for the XTerra at the beginning of the year?
Year-beginning price of an XTerra (¥) 2,800,000
Spot exchange rate (¥/$) 110.60
Year-beginning price of a XTerra ($) $25,316.46
b. What is the expected spot rate at the end of the year assuming PPP?
Initial spot rate (¥/$) 110.60
Expected US$ inflation 2.00%
Expected Japanese yen inflation 0.00%
Expected spot rate at end of year assuming PPP (¥/$) 108.43
c. Assuming complete pass through, what will the price be in US$ in one year?
Price of XTerra at beginning of year (¥) 2,800,000
Japanese yen inflation over the year 0.000%
Price of XTerra at end of year (¥) 2,800,000
Expected spot rate one year from now assuming PPP (¥/$) 108.43
Price of XTerra at end of year in ($) $25,822.78
d. Assuming partial pass through, what will the price be in US$ in one year?
Price of XTerra at end of year (¥) 2,800,000
Amount of expected exchange rate change, in percent (from PPP) 2.000%
Proportion of exchange rate change passed through by Nissan 70.000%
Proportional percentage change 1.400%
Effective exchange rate used by Nissan to price in US$ for end of year 109.073
Price of XTerra at end of year ($) $25,671