Treck Co. expects to pay €200,000 in one month for its imports from Spain. It also expects to receive €250,000 for its exports to Italy in one month. Treck Co. estimates the standard deviation of monthly percentage changes of the euro to be 3 percent over the last 40 months. Assume that these percentage changes are normally distributed. Using the value-at-risk (VaR) method based on a 95 percent confidence level, what is the maximum one-month loss in dollars if the expected percentage change of the euro during next month is -2 percent? Assume that the current spot rate of the euro (before considering the maximum one-month loss) is $1.23.
A) -$38,468
B) -$21,371
C) -$17,097
D) -$4,274

Question

Quizplus · Accepted Answer

First, we need to convert the payables and receivables to dollars:
- Payables: €200,000 x $1.23/€ = $246,000
- Receivables: €250,000 x $1.23/€ = $307,500

Next, we need to calculate the potential loss due to exchange rate fluctuations. The expected percentage change of the euro is given as 2%, which means that the exchange rate could either increase or decrease by this amount. To calculate the maximum loss at a 95% confidence level, we use the following formula:

VaR = Z x SD x V

Where: 
Z = the number of standard deviations corresponding to a 95% confidence level, which is 1.645
SD = the standard deviation of monthly percentage changes, which is 3%
V = the value of the payables or receivables, which is $246,000 or $307,500

For the payables, the potential loss is calculated as:
VaR = 1.645 x 3% x $246,000 = $12,737

For the receivables, the potential loss is calculated as:
VaR = 1.645 x 3% x $307,500 = $15,930

So the total potential loss is $12,737 + $15,930 = $28,667.

However, since the question asks for the maximum one-month loss in dollars, we need to multiply this amount by the expected percentage change of the euro:
Loss = $28,667 x 2% = $573.34

Therefore, the maximum one-month loss in dollars is $573.34, which is closest to answer choice D: $4,274.

Treck Co Expects to Pay €200,000 in One Month for Its