Exchange Rates and Currency Exchange

A Canadian manufacturer requires parts from the United States. It purchases from its supplier in lots of 100,000 units at a price of $US$7.25$ per unit. Since the last time the manufacturer made a purchase, the Canadian dollar has appreciated $0.0178$ from the previous mid-rate of $US$1.0218$ per $C$$. If the sell rate is 1.5% above the mid-rate, how have the manufacturer's costs changed?

Solution

Calculate the cost of the product both before and after the currency appreciation. The difference between the two numbers is the change in the manufacturer's costs.

What You Already Know

Step 1:

The following purchase and exchange rates are known:

Current Currency = Total Purchase = $100,000 × $7.25 = US$725,000$

Mid-Rate = $1.0218$

Sell Rate = 1.5% higher

Canadian appreciation = $0.0178$

How You Will Get There

Step 2:

Calculate the old and new sell rates, factoring in the currency appreciation. Notice that the Current Currency is in US dollars but the sell rates are per Canadian dollar. You will need to invert the rates so that the exchange rate is expressed per US dollar to match the Current Currency.

Step 3:

Apply Formula 7.4 for each transaction.

Step 4:

Calculate the difference between the two numbers to determine the change in cost.

Perform

Step 2:

Previous Sell Rate = $1.0218 × (1 + 0.015) = 1.0371\ per\ C$$

Previous Sell Rate = $\frac{1}{1.0371}=0.9642\ per\ US$$

If the Canadian dollar has appreciated, it buys more US dollars per $C$$ . Therefore,

New Sell Rate = $(1.0218 + 0.0178) × (1 + 0.015) = 1.0552\ per\ C$$

New Sell Rate = $\frac{1}{1.0552}=0.9477\ per\ US$$

Step 3:

Previous $C$$ = $0.9642 × $725,000 = $699,045$

New $C$$ = $0.9477 × $725,000 = $687,082.50$

Step 4:

Change in Cost = New $C$$ − Previous $C$$ = $$687,082.50 − $699,045 = −$11,962.50$

The manufacturer has its input costs decrease by $$11,962.50$ since $C$ 1$ now purchases more $US$$.