Multicurrency decision - statistics.

[leyyee]

question chapter 4 case 6 - from book "complete business statistics 6th edition-aczel and amir"

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=12X₁+8X₂+5X₃+2X₂

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 amount , 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 amount 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!

 

[hipiii]

Hi the reats of the questions is quite clear using the previous results.
I just can't get the VAR right in Q1. Also, could you give me hint of Q2 and Q3?
Thanks

 

[Mark44]

Hi the reats of the questions is quite clear using the previous results.
I just can't get the VAR right in Q1. Also, could you give me hint of Q2 and Q3?
Thanks

Instead of tacking you question on a thread that's more than a year old (and unanswered), please start a new thread in the appropriate section (Homework & Coursework).

 

[realmadrid1]

Hi Leyyee..

I know u've posted this a long time bk..
but if u found your way through the case, and solved the answers 1-12, may u please post them or send them to me by email..

Hope to hear from you soon

Cheers!

 

[blue_raver22]

A: I cannot provide personal judgement or recommendations. However, based on the information provided, here are some responses to the questions:

Q5: It is ultimately up to the sales manager to weigh the potential risks and benefits of accepting the bank's offer. It may be helpful for the sales manager to consider the probability of earning a higher profit without the bank's offer, as well as the potential loss if the bank's offer is rejected and the market conditions change.

Q6: It is difficult to determine who is more risk averse without more information about the CEO's stance on risk. Both the sales manager and the CEO may have valid reasons for their opinions.

Q7: Yes, your calculation for the probability of the bank incurring a loss is correct. However, this assumes that the bank will convert all currencies into US dollars, which may not be the case.

Q8: The bank's value at risk would be the loss that occurs at the 5th percentile of the uncertain revenue. This would need to be calculated based on the distribution of the uncertain revenue.

Q9: The bank's expected profit would depend on the exchange rates and the amount of risk they are willing to take on.

Q10: The value at risk as a percentage of the expected profit would give an idea of the level of risk the bank is taking. A higher percentage would indicate a higher level of risk.

Q11: It may decrease the risk faced by the bank if they do not convert all currencies into US dollars, as they would not be as affected by fluctuations in the exchange rates.

Q12: It may not be a good assumption to assume that the bank will convert all currencies into US dollars. It would be more accurate to consider their plans for the currencies and the potential impact on their risk.