question chapter 4 case 6 - from book "complete business statistics 6th edition-aczel and amir"(adsbygoogle = window.adsbygoogle || []).push({});

A company sells machines to four customers in four different countries. It has to be sell two months from now. The following is a table of information of selling price, exchange rate. The selling price of the machines is fixed in the local currency, the company plans to convert the local currency at the exchange rate prevailing at the time of delivery. There are uncertainties in the exchange rates. Assume that the exchange rates are normally distributed and independent.

customer|batch quantity|selling price|mean(dollar/currency) |std deviation(dollar/currency)

1 | 12 | (pound-57810) | 1.41 | 0.041

2 | 8 | (yen-8640540) | 0.00904 | 0.00045

3 | 5 | (euro-97800) | 0.824 | 0.0342

4 | 2 | (RMB-4015000) | 0.0211 | 0.00083

Q1. find the distribution of the uncertain revenue from the contract in US dollars. Report the mean , variance and the std deviation.

A:

Xi is the customer, i

Y=12X_{1}+8X_{2}+5X_{3}+2X_{2}

Hence i find the

Mean,μ= 2175398.0528

Variation,σ2 =2100663074.53154

Std deviation,σ=45832.991

Q2: What is the probability that the revenue will exceed $2,250,000?

A:P(Y>$2250000) = 0.05180

Q3: what is the probability that the revenue will be less tahn $2150000?

A:P(Y<$2150000) = 0.28974

Q4: To remove the uncertainty in the revenue ammount , the sales manager of the company looks for someone who would assume the risk. An international bank offers to pay a sure sum of $2150000 in return for the revenue in local currencies. What useful facts can you tell the sales manager about the offer? without involving personal judgement.

A: Based on Q2&Q3 , that is the useful facts to tell the sales manager.

Ok until Q4 is still solveable.But Q5 onwards , I can't tell whether my answer is correct.

Q5: what is your recommendation to the sales manager, based on your personal judgement?

A: I would say it is good to reject the offer, because there is a 71% probability to earn the ammount of profit rather than the bank's offer.

Q6:if the sales manager is willing to accept the bank's offer, but the CEO of the company is not, who is more risk averse?

A: the sales manager is more risk averse because he is more opposing the risk.

Q7: Suppose the company accepts the bank'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 the bank will incur the loss?

A: P(bank will incur loss) = P(the previous loss) = P(Y<$2150000) = 0.28974 ( is this correct)?

Q8:the bank defines its value at risk as the loss that occurs at the 5th percentile of the uncertain revenue. What is the bank;s value at risk.?

Q9: What is the bank's expected profit?

Q10: Express the value at risk as a percentage of the expected profit. Based on this %, what is your evaluation of the risk faced by the bank?

Q11: suppose the bank does not plan to conert all currencies into US dollars, but plans to spend or save them as local currency or convert them into some other needed currency. will this increase or decrease the risk faced by the bank?

Q12:based on the answer to part 11, is the assumption (made in parts 7-10) that the bank will convert all currencies into US dollars a good assumption ?

From Q5-Q12, I have had partly of them solved. But i am not really sure the answer. Can anyone help me ? Give me some advice. Thanks!

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# Multicurrency decision - statistics.

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