Hamilton & Jacobs

Hamilton & Jacobs (H&J) is a global investment company, providing start-up capital to promising new ventures around the world. Due to the nature of its business, H&J holds funds in a variety of countries and converts between currencies as needs arise in different parts of the world. Several months ago, the company moved $16 million into Japanese yen (JPY) when one U.S. dollar (USD) was worth 75 yen. Since that time, the value of the dollar has fallen sharply, where it now requires almost 110 yen to purchase 1 dollar.

Besides its holdings of yen, H&J also currently owns 6 million European EUROs and 30 million Swiss Francs (CHF). H&Js chief economic forecaster is predicting that all of the currencies it is presently holding will continue to gain strength against the dollar for the rest of the year. As a result, the company would like to convert all its surplus currency holdings back to U.S. dollars until the economic picture improves.

The bank H&J uses for currency conversions charges different transaction fees for converting between various currencies. The following table summarizes the transaction fess (expressed as a percentage of the amount converted) for US dollars (USD), Australian dollars (AUD), British pounds (GBP), European Euros (EURO), Indian Rupees (INR), Japanese yen (JPY), Singapore dollars (SGD), and Swiss Francs (CHF).

	Transaction Fee Table
FROM\TO	USD	AUD	GBP	EUR	INR	JPY	SGD	CHF
USD		0.10%	0.50%	0.40%	0.40%	0.40%	0.25%	0.50%
AUD	0.10%		0.70%	0.50%	0.30%	0.30%	0.75%	0.75%
GBP	0.50%	0.70%		0.70%	0.70%	0.40%	0.45%	0.50%
EUR	0.40%	0.50%	0.70%		0.05%	0.10%	0.10%	0.10%
INR	0.40%	0.30%	0.70%	0.05%		0.20%	0.10%	0.10%
JPY	0.40%	0.30%	0.40%	0.10%	0.20%		0.05%	0.50%
SGD	0.25%	0.75%	0.45%	0.10%	0.10%	0.05%		0.50%
CHF	0.50%	0.75%	0.50%	0.10%	0.10%	0.50%	0.50%

Because it costs differing amounts to convert between various currencies, H&J determined that converting existing holdings directly into US dollars may not be the best strategy. Instead, it might be less expensive to convert existing holdings to an intermediate currency before converting the result back to US dollars. The following table summarizes the current exchange rates for converting from one currency to another.

	Exchange Rate Table
From\To	USD	AUD	GBP	EUR	INR	JPY	SGD	CHF
USD	1	1.29249	0.55337	0.80425	43.5000	109.920	1.64790	1.24870
AUD	0.77370	1	0.42815	0.62225	33.6560	85.0451	1.27498	0.96612
GBP	1.80710	2.33566	1	1.45335	78.6088	198.636	2.97792	2.25652
EUR	1.24340	1.60708	0.68806	1	54.0879	136.675	2.04900	1.55263
INR	0.02299	0.02971	0.01272	0.01849	1	2.5269	0.03788	0.02871
JPY	0.00910	0.01176	0.00503	0.00732	0.39574	1	0.01499	0.01136
SGD	0.60683	0.78433	0.33581	0.48804	26.3972	66.7031	1	0.75775
CHF	0.80083	1.03507	0.44316	0.64407	34.8362	88.0275	1.31969	1

The exchange rate table indicates, for instance, that one Japanese yen can be converted into 0.00910 US dollars. So 100,000 yen would produce $910 US. However, the banks 0.40% fee for this transaction would reduce the net amount received to . So H&J wants your assistance in determining the best way to convert all of its non-US currency holdings back into US dollars.

1. Draw a network flow diagram for this problem.

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

3. What is the optimal solution?

4. If H&J converted each non-US currency it owns directly into US dollars, how many US dollars would it have?

5. Suppose H&J wants to perform the same conversion but also leave $5 million in Australian dollars. What is the optimal solution in this case?