+1 862 207 3288 Decisions in USASuperCars
Scenario: USASuperCars sells luxury sports cars. It has just signed a contract to sell, in a years’ time,
a batch of these cars to various customers around the globe. The following table shows the orders of
seven customers. The selling prices are fixed and in local currencies at the exchange rate prevailing
at the time of the delivery. Of course there is uncertainty in the exchange rates, and in order to cope
with this uncertainty estimates as well as standard deviation of these have been provided by the
Bank of America. The report that came with these estimates stated that these rates are normally
distributed and independent.
Worldwide Orders Exchange Rate (to $)
Customer Quantity Selling Price Mean Standard
Deviation
UK 12 £ 57,500 $ 1.4MM/£ $ 0.041/£
Japan 1 5 Y 8,400,000 $0.009DD/Y $0.00045/Y
Japan 2 3 Y 9,000,000 $0.009DD/Y $0.00045/Y
Canada 1 1 CAD 97,000 $0.824YY/CAD $0.0342/CAD
Canada 2 3 CAD 100,000 $0.824YY/CAD $0.0342/CAD
South Africa 2 R 4,100,000 $.0.0211/R $.0.00083/R
USA 1 $100,000
DD/MM/YY Is your Date of Birth
Questions:
1) Find the distribution and report the mean and the standard deviation of the
total revenue in $
2) a) What is the probability that this revenue will exceed $ 2,200,000?
b) What is the probability that this revenue will exceed $ 2,225,000?
3) a) What is the probability that this revenue will be less than $ 2,160,000?
b) What is the probability that this revenue will be less than $ 2,130,000?
4) HSBC offers to pay a sure sum of $2,150,000 in return for the revenue in local currencies.
What do you think, is this a good offer for USASuperCars or not?
5) In USASuperCars, the Sales manager is willing to accept HSBC’s offer, but the CEO is not.
Who is more risk-averse?
6) What other risks the bank is taking apart from the uncertainty in the exchange rates?
7) If the offer is to pay the sure sum in three months’ time rather than in twelve months’ time,
would that make any difference? When would the bank and when the company would
prefer the payment to be made, and why?
8) USASuperCars has accepted HSBC’s offer. Now consider the bank’s risk, assuming the bank
will convert all currencies into US dollars at the prevailing exchange rates. What is the
probability that the bank will incur a loss?
9) The bank defines its Value-at-Risk as the loss that occurs at the 5
th
percentile of the
uncertain revenue (5% left tail of the distribution). What is the bank’s Value-at-Risk and
what is the bank’s expected profit?
10) What other options does the bank has if they decide not to convert all/some of the
currencies in twelve months’ time?
Marking scheme: 50% of the mark comes from the aforementioned ten questions (5% for each), and
50% from the overall presentation of the ‘business’ report.
A ‘business’ report must have a nice cover, a good executive summary, an introduction and a main
body that reads through smoothly and uses ‘lay terms’, not using statistical jargon and be printed,
bound and formatted with the highest possible quality. It must contain a lot of graphs and as much
‘colour’ as possible. No assumptions should be made on the academic background and experience of
the potential readership. References should be used carefully and the majority coming from
practitioner/business sources (www, the press, etc) and any technical details /analysis should be in
an appendix. Overall the main body should not be more than 2500.
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