LINEAR PROGRAMMING APLICATION Foreign Exchange Management Deac International Has

linear programming aplication: foreign exchange management deac international has manufacturing and sales operations in five major trad

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
1.075746

1.953200
1
2.033450
1.2160491
2.097731

0.959232
0.491107
1
0.6161569
0.608742

1.546790
0.791930
1.612530
1
1.680435

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 example, if one were to sell X12 dollars to buy
pounds, one’s dollars would be reduced by X12 but the GBP balance
would increase by a12 X12 or by 0.503796 X12 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.
3.
Use Solver to determine the best set of currency exchanges.
3.
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?
3.
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?