Exchange Rates and Money That Changes Value
When Nepali rupees are changed into a foreign currency, a bank or a money changer uses an exchange rate such as \( \text{£}1 = \text{Rs. } 150 \). The rate tells you how many rupees one unit of the foreign currency costs. Every calculation in this topic starts from two simple moves made with that rate.
Exchange rate: the rate at which the currency of one country is exchanged for the currency of another. In Nepal it is fixed each day by Nepal Rastra Bank, the central bank of the country.
Rupees into foreign currency: divide by the rate. Foreign currency into rupees: multiply by the rate.
An exchange rate does not stay still. It can rise or fall from one day to the next. A person who changes rupees into foreign money, keeps it for a few days and then changes it back will usually not get the same number of rupees. The foreign notes in the pocket are the same notes, but each one is now worth a different amount in rupees. The difference between the rupees paid out and the rupees received back is a profit or a loss.
Devaluation and Revaluation of the Rupee
Devaluation: the Nepali rupee is devalued when it loses value against a foreign currency. More rupees are then needed to buy one unit of that currency, so the exchange rate goes up.
Revaluation: the Nepali rupee is revalued when it gains value against a foreign currency. Fewer rupees are then needed to buy one unit of that currency, so the exchange rate goes down.
Think of a pound sterling that costs Rs. 150 today. If the rupee is devalued, the same pound might cost Rs. 157.50 next week, because each rupee now buys less. If the rupee is revalued, the pound might cost only Rs. 142.50, because each rupee now buys more. Notice that the rate always moves in the opposite direction to the value of the rupee.
| What changes | Rupee devalued | Rupee revalued |
| Value of the rupee | Falls | Rises |
| Rupees needed for 1 unit of foreign currency | More | Fewer |
| Exchange rate | Goes up | Goes down |
| Person holding foreign currency | Gains | Loses |
Some problems say that Nepali currency is inflated or deflated instead. Inflated means the rupee has lost value, so treat it like a devaluation: the rate goes up. Deflated means the rupee has gained value, so treat it like a revaluation: the rate goes down. Decide which way the rate moves before you calculate anything.
Finding the New Exchange Rate
A change of R% is always worked out on the old rate. Call the old rate \( r \) rupees for one unit of foreign currency, and the new rate \( r_1 \). When the rupee is devalued, R% of the old rate is added:
\[ r_1 = r + \frac{R}{100} \times r \]
When the rupee is revalued, R% of the old rate is taken away:
\[ r_1 = r - \frac{R}{100} \times r \]
Take \( r = 150 \) and a change of 5%. Since \( \frac{5}{100} \times 150 = 7.50 \), a devaluation makes the new rate \( 150 + 7.50 = 157.50 \) rupees, and a revaluation makes it \( 150 - 7.50 = 142.50 \) rupees.
Worked Example: A Loss When the Rupee Gains Value
A businessman changes Rs. 8,40,000 into pounds sterling when \( \text{£}1 = \text{Rs. } 150 \). Five days later the Nepali rupee is revalued by 5%, and he changes all his pounds back into rupees. Find his profit or loss.
Step 1: Changing the rupees into pounds, so dividing by the rate:
\[ 8{,}40{,}000 \div 150 = \text{£}\,5{,}600 \]
Step 2: Finding how much the rate falls, which is 5% of Rs. 150:
\[ \frac{5}{100} \times 150 = \text{Rs. } 7.50 \]
Step 3: Subtracting this fall from the old rate, because the rupee gained value, gives the new rate:
\[ \text{£}1 = \text{Rs. } (150 - 7.50) = \text{Rs. } 142.50 \]
Step 4: Changing the £5,600 back into rupees at the new rate, so multiplying:
\[ 5{,}600 \times 142.50 = \text{Rs. } 7{,}98{,}000 \]
Step 5: Comparing the rupees received with the rupees paid. He received less, so this is a loss:
\[ 8{,}40{,}000 - 7{,}98{,}000 = \text{Rs. } 42{,}000 \]
The businessman makes a loss of Rs. 42,000. He still had exactly £5,600 in his hand. The only thing that changed is that each pound now fetches Rs. 142.50 instead of Rs. 150.
Worked Example: A Profit When the Rupee Is Devalued
A trader in Kathmandu changes Rs. 7,00,000 into euros at \( \text{€}1 = \text{Rs. } 140 \) to pay for machines from Germany. The order is delayed, and a week later the rupee has been devalued by 5%. He changes all his euros back into rupees. Find his profit or loss.
Step 1: Changing the rupees into euros, so dividing by the rate:
\[ 7{,}00{,}000 \div 140 = \text{€}\,5{,}000 \]
Step 2: Finding how much the rate rises, which is 5% of Rs. 140:
\[ \frac{5}{100} \times 140 = \text{Rs. } 7 \]
Step 3: Adding this rise to the old rate, because the rupee lost value, gives the new rate:
\[ \text{€}1 = \text{Rs. } (140 + 7) = \text{Rs. } 147 \]
Step 4: Changing the €5,000 back into rupees at the new rate, so multiplying:
\[ 5{,}000 \times 147 = \text{Rs. } 7{,}35{,}000 \]
Step 5: Comparing the rupees received with the rupees paid. He received more, so this is a profit:
\[ 7{,}35{,}000 - 7{,}00{,}000 = \text{Rs. } 35{,}000 \]
The trader makes a profit of Rs. 35,000. The same five thousand euros are now worth more rupees, because each rupee has become weaker. Compare this with the previous example: for someone holding foreign currency, a devaluation brings a gain and a revaluation brings a loss.
A Shorter Way to the Profit or Loss
In both examples the amount of foreign currency held never changed. Only the rate changed. So the profit or loss is simply the foreign currency held multiplied by the change in the rate. If \( F \) is the amount of foreign currency held, the profit or loss in rupees is:
\[ F \times (r_1 - r) \]
A positive answer is a profit and a negative answer is a loss. Checking the pound example: \( 5{,}600 \times (142.50 - 150) \) works out to \( -42{,}000 \), a loss of Rs. 42,000. Checking the euro example: \( 5{,}000 \times (147 - 140) = 35{,}000 \), a profit of Rs. 35,000. Both agree with the long method.
The rule also works backwards. If the rate for each euro rose by Rs. 7 and someone's profit was Rs. 35,000, they must have held \( 35{,}000 \div 7 = \text{€}\,5{,}000 \).
Pricing Goods for Export
Nepal sells pashmina, carpets, tea and handicrafts to buyers abroad. A buyer in Europe pays in euros, so the Nepali seller must turn a cost in rupees into a price in euros. The price is built up in a fixed order, because each percentage is worked out on the amount reached before it.
Export tax: a tax paid to the government on goods sent out of the country for sale. It is a percentage of the cost of the goods, and it becomes part of the trader's total cost price.
- Find the cost of the goods in rupees: the number of items multiplied by the price of one.
- Add the export tax, worked out as a percentage of that cost. The result is the total cost price.
- Add the profit, worked out as a percentage of the total cost price including the tax. The result is the selling price.
- Change the selling price into the foreign currency by dividing by the exchange rate.
The third and fourth jobs can be swapped. You may change the cost into euros first and then add the profit in euros. Both ways give the same answer, apart from a small difference caused by rounding.
Worked Example: Pashmina Shawls Sold in Euros
A businessman of Nepali origin living in Norway buys 900 pashmina shawls in Kathmandu at Rs. 4,000 each. He pays 5% export tax to export them and wants a profit of 20%. For how many euros should he sell all the shawls? (\( \text{€}1 = \text{Rs. } 130 \))
Method 1: change the cost into euros first, then add the profit.
Step 1: Finding the cost of 900 shawls:
\[ 900 \times 4{,}000 = \text{Rs. } 36{,}00{,}000 \]
Step 2: Finding the export tax, which is 5% of the cost:
\[ \frac{5}{100} \times 36{,}00{,}000 = \text{Rs. } 1{,}80{,}000 \]
Step 3: Adding the tax to the cost to get the total cost price:
\[ 36{,}00{,}000 + 1{,}80{,}000 = \text{Rs. } 37{,}80{,}000 \]
Step 4: Changing the total cost price into euros by dividing by 130:
\[ 37{,}80{,}000 \div 130 = \text{€}\,29{,}076.92 \]
Step 5: Finding the 20% profit in euros:
\[ \frac{20}{100} \times 29{,}076.92 = \text{€}\,5{,}815.38 \]
Step 6: Adding the profit to the cost price to get the selling price of all the shawls:
\[ 29{,}076.92 + 5{,}815.38 = \text{€}\,34{,}892.30 \]
Method 2: add the profit in rupees first, then change the whole selling price into euros in one go.
Step 1: The total cost price with tax is Rs. 37,80,000, as found above. Finding the 20% profit on it:
\[ \frac{20}{100} \times 37{,}80{,}000 = \text{Rs. } 7{,}56{,}000 \]
Step 2: Adding the profit to get the selling price in rupees:
\[ 37{,}80{,}000 + 7{,}56{,}000 = \text{Rs. } 45{,}36{,}000 \]
Step 3: Changing the selling price into euros by dividing by 130:
\[ 45{,}36{,}000 \div 130 = \text{€}\,34{,}892.31 \]
So all 900 shawls should be sold for about €34,892.30, which is roughly €38.77 for each shawl.
The two methods end one cent apart. That is not a fault in either method. Method 1 rounded €29,076.923... to €29,076.92 in the middle, and that tiny cut carried through to the answer. When you can, round only at the last step, as Method 2 does. Also, the 20% profit is worked out on the cost including tax, Rs. 37,80,000, and not on the price of the shawls alone.
When More Than One Tax Is Added
Goods brought into Nepal from abroad often carry customs duty and then 13% VAT. Each tax is a percentage of the amount reached so far, so the VAT is charged on the price that already includes the customs duty. Suppose a watch is bought in Europe for €200 when \( \text{€}1 = \text{Rs. } 130 \), and it carries 10% customs duty and 13% VAT.
Step 1: Changing the price of the watch into rupees, so multiplying:
\[ 200 \times 130 = \text{Rs. } 26{,}000 \]
Step 2: Adding the customs duty. Since 10% of Rs. 26,000 is Rs. 2,600, the price becomes:
\[ 26{,}000 + 2{,}600 = \text{Rs. } 28{,}600 \]
Step 3: Adding the VAT. Since 13% of Rs. 28,600 is Rs. 3,718, the price becomes:
\[ 28{,}600 + 3{,}718 = \text{Rs. } 32{,}318 \]
Break-even price: the selling price at which there is neither profit nor loss. It is equal to the full cost price, including every tax paid.
So if the watch is sold on to someone for Rs. 32,318, the seller neither gains nor loses. Selling above that price gives a profit, and selling below it gives a loss.
Do not add 10% and 13% to make 23% of Rs. 26,000. That gives Rs. 31,980, which is too little, because it forgets that the VAT is charged on the customs duty as well.
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