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Linear Programming Application: Foreign Exchange Management | FIN 203, Exams of Finance

Material Type: Exam; Professor: Akinc; Class: Applied Quantitative Analysis for Finance; Subject: Finance; University: Wake Forest University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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LINEAR PROGRAMMING APLICATION:
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
10.503796 1.023410 0.6336675 1.075746
1.953200 12.033450 1.2160491 2.097731
0.959232 0.491107 10.6161569 0.608742
1.546790 0.791930 1.612530 11.680435
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 = $1.969065
Questions
1. What is the dollar value of the basket of currencies the company holds currently
before any exchanges are undertaken?
2. Write out a linear programming model to determine the set of exchanges to be
made so that all cash requirements are satisfied and the sum of the dollar value of
all currencies held after the exchanges is maximized.
Hint: Use the decision variables:
Xij= amount of currency i sold to obtain currency j. Notice that this has the
effect of reducing currency i by Xij and increasing currency by aij Xij. For
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LINEAR PROGRAMMING APLICATION:

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

  1. What is the dollar value of the basket of currencies the company holds currently before any exchanges are undertaken?
  2. Write out a linear programming model to determine the set of exchanges to be made so that all cash requirements are satisfied and the sum of the dollar value of all currencies held after the exchanges is maximized. Hint: Use the decision variables: Xij = amount of currency i sold to obtain currency j. Notice that this has the effect of reducing currency i by Xij and increasing currency by aij Xij. For

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.

  1. Use Solver to determine the best set of currency exchanges.
  2. If the requirement for GBP and CAD did not exist would the best strategy be to stay pat? Or, is there an opportunity to improve the dollar value of the existing basket of currencies with some carefully considered exchanges?
  3. Assume the requirements for GBP is 5 million instead of 4? What effect will this have on the problem and its solution?
  4. Suppose, for a moment, the bid- ask prices were such that if one started with one dollar, exchanged it for some GBPs, exchanged the GBPs for AUDs and finally exchanged the AUDs back into dollars one ended up with more than one dollar. Can such a situation persist for a long time? Explain your reasoning briefly. If you tried to solve the linear programming above in 2 with such exchange rates, what can you say about the solution of the problem?