Scenario: Corvette sells luxury sports cars. It has just signed a contract to sell, Twelve months from now, 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
Customer
Quantity
Selling Price
Mean
Standard
Deviation
UK
12
£ 57,810
$ 1.41/£
$ 0.041/£
Japan
8
Y 8,640,540
$0.00904/Y
$0.00045/Y
France 1
2
€ 97,500
$0.824/€
$0.0342/€
France 2
3
€ 98,000
$0.824/€
$0.0342/€
South Africa
2
R 4,015,000
$.0.0211/R
$.0.00083/R
Questions:
1) Find the distribution and report the mean and the standard deviation of the uncertain revenue in $
How to get the mean µ:
(UK Quantity X selling price X exchange rate ) ( Standard deviation )+ (Japan Quantity X selling price X exchange rate ) ( Standard deviation )+ (France 1&2 Quantity X selling price X exchange rate ) ( Standard deviation )+ (South Africa Quantity X selling price X exchange rate ) ( Standard deviation ) = Mean 2,175,398
How to get the Standard deviation σ:
(UK Quantity)² (selling price )² ( Standard deviation )² +(Japan Quantity)² (selling price )² ( Standard deviation )² + (France 1& 2 Quantity)² (selling price )² ( Standard deviation )² + (South Africa Quantity)² (selling price )² ( Standard deviation )² = Variance so take the square root of the variance and you will get the standard deviation so = σ 44,345
2) What is the probability that this revenue will exceed $ 2,250,000?
P = = = 1.682 = 0.0462
x
P(X>x)
2250000
0.0462
3) What is the probability that this revenue will exceed $ 2,500,000?
P = = = 7.3199 = 0
x
P(X>x)
2500000
0.0000
4) What is the probability that this revenue will be less than $ 2,150,000?
P = = = -0.572 = 0.2834
P(X<x) x 0.2834
2150000
5) What is the probability that this revenue will be less than $ 2,000,000?
P = = = -3.955 = 0
P(X<x) x 0.0000
2000000
6) 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 Corvette or not?
The offer is not good, because it is less than exchange revenue.
7) In Corvette, the Sales manager is willing to accept HSBC’s offer, but the CEO is not. Who is more risk-averse? The CEO is more risk-averse than sales manager.
8) What other risks the bank is taking apart from the uncertainty in the exchange rates?
Insurance on sports car is higher than ordinary car, because the sport car is more risky.
Maintenance is higher than ordinary car.
9) 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?
Yes it is difference, because:
a) The company gets the money early by 9 months.
b) It
