Canada National Bank has 10 million British pounds (£) in one-year assets and £8 million in one-year liabilities. In addition, it has one-year liabilities of 4 million euros (€). Assets are earning 8 percent and both liabilities are being paid at a rate of 8 percent. All interest and principal will be paid at the end of the year. If the year-end spot exchange rate for the British pound is $1.50/£ and the liabilities pay 8 percent, what is the maximum that the € can appreciate and the bank still maintain a zero profit?

Question

Quizplus · Accepted Answer

First, we need to find the net investment position in pounds:

Net investment = assets - liabilities in pounds
Net investment = £10m - £8m
Net investment = £2m

Next, we need to convert the euro liabilities to pounds using the spot exchange rate:

€4m x 1.50/€ = £6m

Now the net investment position is:

Net investment = £2m - £6m
Net investment = -£4m

This means the bank is short £4m, so it needs to borrow £4m at the one-year rate of 8 percent to cover its liabilities. The cost of borrowing £4m is:

Cost of borrowing = £4m x 8% = £0.32m

Therefore, the bank needs to earn at least £0.32m in interest to break even. At an 8 percent interest rate, it can earn £0.8m on its £10m asset position. So, its total profit would be:

Total profit = £0.8m - £0.32m
Total profit = £0.48m

We now need to convert this profit to euros using the spot exchange rate:

£0.48m / 1.50 = €0.32m

This means that if the euro appreciates more than €0.32m, the bank will make a loss. We can find the maximum euro appreciation by dividing this amount by the euro liabilities:

Maximum euro appreciation = €0.32m / €4m = 0.08

So, the euro can appreciate up to 8 percent (or €1.08/€) before the bank makes a loss. This is equivalent to a euro-to-dollar exchange rate of:

€1.08/€ x $1.50/£ = $1.62/€

Finally, we need to find the maximum euro-to-dollar exchange rate that will allow the euro to appreciate up to $1.62/€. Dividing $1 by $1.62/€ gives:

$1 / $1.62/€ = €0.62/$

So, the maximum euro-to-dollar exchange rate is €0.62/$, or the euro can appreciate up to €1.33/$ (which is answer choice B) before the bank makes a loss.

Canada National Bank Has 10 Million British Pounds (£) in One-Year