a. Create a spreadsheet model for this problem and solve it.

b. What is the optimal trading plan?

c. What is the optimal transaction cost (in equivalent USD)?

d. Suppose that another executive thinks that holding $250,000 USD in each currency is excessive and wants to lower the amount to $50,000 USD in each currency. Does this help to lower the transaction cost? Why or why not?

e. Suppose the exchange rate for converting USD to GBP increased from 0.6409 to 0.6414. What would happen to the optimal solution in this case?

Baldwin Enterprises is a large manufacturing company with operations and sales divisions located in the United States and several other countries. The CFO of the organization, Wes Hamrick, is concerned about the amount of money Baldwin has been paying in transaction costs in the foreign exchange markets and has asked you to help optimize Baldwin’s foreign exchange treasury functions.

With operations in several countries, Baldwin maintains cash assets in several different currencies: U.S. dollars (USD), the European Union’s euro (EUR), Great Britain’s pound (GBP), Hong Kong dollars (HKD), and Japanese yen (JPY). To meet the different cash flow requirements associated with its operations around the world, Baldwin often must move funds from one location (and currency) to another. For instance, to pay an unexpected maintenance expense at its facility in Japan, Baldwin might need to convert some of its holdings in U.S. dollars to Japanese yen.

The foreign exchange (FX) market is a network of financial institutions and brokers in which individuals, businesses, banks, and governments buy and sell the currencies of different countries. They do so to finance international trade, invest or do business abroad, or speculate on currency price changes. The FX market operates 24 hours a day and represents the largest and most liquid marketplace in the global economy. On average, the equivalent of about $1.5 trillion in different currencies is traded daily in the FX market around the world. The liquidity of the market provides businesses with access to international markets for goods and services by providing foreign currency necessary for transactions worldwide.

The FX market operates in much the same way as a stock or commodity market; there is a bid price and ask price for each commodity (or, in this case, currency). A bid price is the price at which the market is willing to buy a particular currency and the ask price is the price at which the market is willing to sell a currency. The ask prices are typically slightly higher than the bid prices for the same currency— representing the transaction cost or the profit earned by the organizations that keep the market liquid. The following table summarizes the current FX rates for the currencies Baldwin currently holds. The entries in this table represent the conversion rates from the row currencies to the column currencies.

For example, the table indicates that one British pound (GBP) can be exchanged (or sold) for 1.5593 U.S. dollars (USD). Thus, $1.5593 is the bid price, in U.S. dollars, for one British pound. Alternatively, the table indicates one U.S. dollar (USD) can be exchanged (sold) for 0.6409 British pounds (GBP). So, it takes about 1.5603 U.S. dollars (or 1/0.6409) to buy one British pound (or the ask price, in U.S. dollars, for one British pound is roughly $1.5603).
Notice that if you took one British pound, converted it to 1.5593 U.S. dollars, and then converted those 1.5593 dollars back to British pounds, you would end up with only 0.999355 British pounds (i.e., 1 × 1.5593 × 0.6409 = 0.999355). The money that you lose in this exchange is the transaction cost.
Baldwin’s current portfolio of cash holdings includes 2 million USD, 5 million EUR, 1 million GBP, 3 million HKD, and 30 million JPY. This portfolio is equivalent to $9,058,710 USD under the current exchange rates (given above). Wes has asked you to design a currency trading plan that would increase Baldwin’s euro and yen holdings to 8 million EUR and 54 JPY, respectively, while maintaining the equivalent of at least $250,000 USD in each currency. Baldwin measures transaction costs as the change in the USD equivalent value of the portfolio.

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Convert/To USD JPY 1.01864 0.6409 7.7985 118.55 0.6295 7.6552 116.41 184.97 EUR GBP HKD USD EUR GBP HKD JPY 0.9724 1.5593 1.5881 0.12812 0.1304 0.0821 0.00843 0.00856 0.0054 12.154 0.0658 15.1005