Scenario: USASuperCars sells luxury sports cars. It has just signed a contract to sell in New Year’s Day (01-01-2016) time, a batch of these super cars to various customers around the globe. The following table shows the orders from eight 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 of the expected value and standard deviation of these have been provided by the Bank of America for all but one (EUR) of the currencies. 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 Expected value
(Mean) Standard Deviation
UK 10 £ 57,500 $ 1.4MM/£ $ 0.041/£
France 2 65,000 € NOT AVAILABLE NOT AVAILABLE
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 2 CAD 97,000 $0.824YY/CAD $0.0342/CAD
Canada 2 2 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) For the exchange rate of EUR/USD, where estimates are not available, create an estimate by using the daily closing values of the exchange rate from the last 24 months. Argue which period might be most relevant, if you decide to use less than the full 24-month period to create your estimate. Assume that the exchange rate is normally distributed, calculate the mean and the standard deviation, and use these to fill in the values for France in the table of orders.
2) Specify the distribution and report the mean and the standard deviation of total revenue in $.
3) a) What is the probability that this revenue will exceed $ 2,280,000?
b) What is the probability that this revenue will be less than $ 2,160,000?
4) HSBC offers to pay a certain sum of $2,150,000, in return for the uncertain revenue in local currencies. Give an opinion as to whether this is 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 is the bank taking, apart from the uncertainty in the exchange rates?
7) If the offer is to pay the certain sum next week rather than on New Year’s Day, 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. 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 5th 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 New Year’s Day?
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 statistical jargon. The report should be printed, and formatted with the highest possible quality of presentation. It must contain 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 words.