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 five 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 £ 57,000 $ 1.41/£ $ 0.041/£
Japan 1 5 Y 8,500,000 $0.00904/Y $0.00045/Y
Japan 2 3 Y 9,000,000 $0.00904/Y $0.00045/Y
Canada 1 1 € 97,000 $0.824/CAD $0.0342/CAD
Canada 2 3 € 100,000 $0.824/CAD $0.0342/CAD
South Africa 2 R 4,100,000 $.0.0211/R $.0.00083/R
USA 1 $100,000
Questions:
1) Find the distribution and report the mean and the standard deviation of the uncertain 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 $ 2,150,000? b) What is the probability that this revenue will be less than $ 2,120,000? 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 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 twelve months’ time?
