Erin McQueen purchased 50 shares of BMW, a German stock traded on the Frankfurt Exchange, for 64.5 euros (€) per share exactly 1 year ago when the exchange rate was 0.67 €/US$. Today the stock is trading at 71.8 (€) per share, and the exchange rate is 0.75 €/US$.
a. Did the depreciate or appreciate relative to the US$ during the past year? Explain.
b. How much in US$ did Erin pay for her 50 shares of BMW when she purchased them a year ago?
c. For how much in US$ can Erin sell her BMW shares today?
d. Ignoring brokerage fees and taxes, how much profit (or loss) in US$ will Erin realize on her BMW stock if she sells it today?
Answer:
a. The euro appreciated against the US dollar.
At the beginning of the past year, the €/$ exchange rate was 0.67. This means $0.67 was required to buy one Euro.
At the end of the year, the €/$ exchange rate was $0.75, meaning $0.75 are needed to buy one Euro.
Since it costs more U.S. dollars to buy one Euro at the end of the year, the USD has depreciated against the euro and the euro has appreciated against the USD .
b. Erin paid $4813.43
for the purchase of 50 BMW shares a year ago.
Share price of BMW a year ago = €64.50
Price for 50 BMW shares = €3225 (€64.50 × 50)
€/$ = 0.67
Price in $ = $4813.432836
(3225/0.67)
c. Erin can sell her BMW shares for $4786.67
Share price of BMW a year ago = €71.8
Price for 50 BMW shares = €3590 (€71.8 × 50)
€/$ = 0.75
Price in $ = $4786.666667
(3590/0.75)
d. Erin will lose $26.76 if she sells today.
Gain or Loss = Today's price ($) - Price a year ago ($)
Gain or Loss = -26.76616915
($4786.666667
- 4813.432836)
