Business and the International Economy » Exchange Rate Calculations

What you'll learn this session

Study time: 30 minutes

How to calculate exchange rates between different currencies
Understanding the difference between buying and selling rates
How exchange rate changes affect businesses and consumers
Real-world examples of currency conversion in international trade
The impact of exchange rate fluctuations on business costs and profits

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Introduction to Exchange Rate Calculations

Exchange rates are like the price tags for different countries' money. Just as you might pay £2 for a chocolate bar, you might pay £1.20 to buy $1.50 worth of American sweets online. Understanding how to calculate these rates is crucial for any business trading internationally - and it's simpler than you might think!

When businesses buy goods from other countries or sell their products abroad, they need to convert their money from one currency to another. Getting these calculations right can mean the difference between profit and loss.

Key Definitions:

Exchange Rate: The price of one currency expressed in terms of another currency.
Base Currency: The first currency in an exchange rate pair (e.g., in GBP/USD, GBP is the base).
Quote Currency: The second currency in a pair, showing how much is needed to buy one unit of the base currency.
Appreciation: When a currency increases in value against another currency.
Depreciation: When a currency decreases in value against another currency.

💰 Basic Exchange Rate Formula

Amount in New Currency = Amount in Original Currency × Exchange Rate

Example: £100 × 1.25 (GBP/USD rate) = $125

This means £100 is worth $125 when the exchange rate is 1.25.

Understanding Exchange Rate Quotes

Exchange rates are typically shown in pairs, like GBP/USD = 1.25. This means 1 British pound equals 1.25 US dollars. But here's where it gets interesting - banks and currency exchanges often quote two rates: a buying rate and a selling rate.

Buying vs Selling Rates

Think of a currency exchange like any other shop. They buy currency from you at one price and sell it to you at a slightly higher price - that's how they make their profit!

📈 Bank Buying Rate

The rate at which the bank buys foreign currency from you. This is usually lower and less favourable to you.

Example: Bank buys USD at 1.20

📉 Bank Selling Rate

The rate at which the bank sells foreign currency to you. This is usually higher.

Example: Bank sells USD at 1.25

📊 The Spread

The difference between buying and selling rates. This is the bank's profit margin.

Example: 1.25 - 1.20 = 0.05 spread

Real Example: Holiday Money

Sarah wants to buy €500 for her trip to Spain. The bank's selling rate is GBP/EUR = 1.15. She needs: €500 ÷ 1.15 = £434.78. When she returns with €100 left over, the bank's buying rate is 1.10, so she gets: €100 × 1.10 = £110. Notice how the rates work against her both ways!

Practical Exchange Rate Calculations

Let's work through some real business scenarios to see how exchange rate calculations work in practice.

Converting FROM Pounds to Foreign Currency

When you want to convert pounds to another currency, you multiply by the exchange rate.

Formula: Foreign Currency = Pounds × Exchange Rate

🇬🇧 Example 1: UK Company Buying from USA

TechStart Ltd wants to buy software licences costing $10,000 from an American company.

Exchange rate: GBP/USD = 1.30

Calculation: £10,000 ÷ 1.30 = £7,692.31

The company needs £7,692.31 to buy $10,000 worth of software.

Converting TO Pounds from Foreign Currency

When converting foreign currency back to pounds, you divide by the exchange rate.

Formula: Pounds = Foreign Currency ÷ Exchange Rate

🇪🇺 Example 2: UK Company Selling to Europe

Fashion Forward Ltd sells clothes to Germany for €25,000.

Exchange rate: GBP/EUR = 1.18

Calculation: €25,000 ÷ 1.18 = £21,186.44

The company will receive £21,186.44 when the euros are converted.

Impact of Exchange Rate Changes

Exchange rates change constantly and these changes can significantly affect business profits and costs. Understanding this impact is crucial for international business success.

📈 When the Pound Strengthens

Good for: UK importers (buying foreign goods becomes cheaper)

Bad for: UK exporters (UK goods become more expensive for foreign buyers)

Example: If GBP/USD rises from 1.25 to 1.35, a £100 UK product now costs $135 instead of $125 for American buyers.

📉 When the Pound Weakens

Good for: UK exporters (UK goods become cheaper for foreign buyers)

Bad for: UK importers (foreign goods become more expensive)

Example: If GBP/USD falls from 1.25 to 1.15, that same £100 UK product now costs only $115 for American buyers.

Case Study: Brexit and the Pound

After the Brexit referendum in June 2016, the pound fell sharply against major currencies. GBP/USD dropped from about 1.50 to 1.20 within months. This made UK exports more competitive globally, but increased costs for UK businesses importing raw materials. Many UK manufacturers saw their import costs rise by 20-25%, forcing them to either raise prices or accept lower profit margins.

Advanced Exchange Rate Scenarios

Real business situations often involve more complex calculations, especially when dealing with multiple currencies or changing rates over time.

Cross-Currency Calculations

Sometimes you need to convert between two foreign currencies using the pound as an intermediary.

🇯🇵 Example: Converting Yen to Euros

A UK business receives ¥1,000,000 from Japan and wants to convert it to euros for a European supplier.

GBP/JPY = 150 and GBP/EUR = 1.20

Step 1: ¥1,000,000 ÷ 150 = £6,666.67

Step 2: £6,666.67 × 1.20 = €8,000

Calculating Percentage Changes

Understanding how much exchange rates have changed helps businesses plan and assess risk.

Formula: Percentage Change = (New Rate - Old Rate) ÷ Old Rate × 100

📊 Example: Rate Change Impact

GBP/USD changed from 1.25 to 1.30 over three months.

Calculation: (1.30 - 1.25) ÷ 1.25 × 100 = 4% increase

This means the pound strengthened by 4% against the dollar, making US imports 4% cheaper for UK businesses.

Practical Tips for Exchange Rate Calculations

Here are some essential tips to help you master exchange rate calculations and avoid common mistakes.

✅ Always Check the Direction

Make sure you know which way you're converting. Are you buying foreign currency or selling it? The calculation method differs!

💡 Consider the Spread

Remember that banks and exchanges charge different rates for buying and selling. Always use the rate that applies to your transaction.

🕑 Timing Matters

Exchange rates change constantly. A rate quoted in the morning might be different by afternoon, especially during volatile periods.

Common Mistake Alert!

Many students confuse when to multiply and when to divide. Remember: if the exchange rate is GBP/USD = 1.25, this means £1 = $1.25. So to convert £100 to dollars, you multiply (£100 × 1.25 = $125). To convert $125 to pounds, you divide ($125 ÷ 1.25 = £100).

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