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Material Type: Exam; Professor: Akinc; Class: Applied Quantitative Analysis for Finance; Subject: Finance; University: Wake Forest University; Term: Unknown 1989;
Typology: Exams
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Foreign Exchange Management Deac International has manufacturing and sales operations in five major trading countries: United States, United Kingdom, Canada, Germany and Australia. Because of the different cash needs in the different regions at various times, it is often necessary to move available funds from one region to another. In general, there will be numerous ways to exchange available currencies satisfy the requirements. On this particular Tuesday the divisions in The United Kingdom and Canada are short of cash: 4 million GBP and 6 million CAD is required. The divisions in the United States, Germany and Australia have excess cash of 2 million dollars, 3 million Euros and 8 million AUDs. The prevailing exchange rates are as follows: USD GBP CAD EUR AUD 1 0.503796 1.023410 0.6336675 1. 1.953200 1 2.033450 1.2160491 2. 0.959232 0.491107 1 0.6161569 0. 1.546790 0.791930 1.612530 1 1. 0.915700 0.468820 0.954620 0.5919960 1 We will refer to the rate in row i and column j as aij which is the bid price of currency i in units of currency j. For instance a person with a British pound will receive $1.9532 in exchange. $1.9532 is then the bid price for a unit of GBP in US dollars. On the other hand, if a person wants to buy a GBP he will receive 0.503796 GBP for every US dollar. This means that it takes 1/0.503796 = $1.984930 to purchase one GBP. This is the ask price of GBP to a person with US dollars. The slight difference between the bid and ask prices represents the transaction cost of trading in the market. Normally the bid and ask prices are such that there is no arbitrage opportunity-- if one kept exchanging money from one denomination to another and back again one would lose money Because there are many ways of redistributing the cash to satisfy the shortages, the challenge for the manager is to find the most efficient exchanges of currencies. Due to comparatively short-term high US interest rates, Deac International wants to maximize the “dollar value” of all the currencies held. For any currency the dollar value is defined to be the average of the bid and the ask prices. For instance, the dollar value of one GBP is ($1.9532 + $1.98493) /2 = $1. Questions
example, if one were to sell X 12 dollars to buy pounds, one’s dollars would be reduced by X 12 but the GBP balance would increase by a 12 X 12 or by 0. X 12 GBP. Yi = Final balance of currency i held. Notice that the final amount of any currency, i held will be equal to the known beginning holding of that currency, (2 million for dollars, for instance) less the amounts of currency i used to buy other currencies, plus any other currency exchanged into currency i. Use this reasoning to write equations relating Y , final holding variables to X, exchange variables.