MATHEMATICAL APPROACH TO CURRENCY DEVALUATION AND EXCHANGE RATE

MATHEMATICAL APPROACH TO CURRENCY DEVALUATION AND EXCHANGE RATE

Exchange rate is the rate at which countries exchange their currency or the rate at which a country decides to buy or sell her currency in relation to other currencies of the world.

Example 1                           

Assuming that Nigeria is willing to buy or sell cocoa at N400.00 per ton and the U.S.A. is willing to buy or sell at $50.00, then the value of the two currencies can be fixed as:

N400.00      =        $50.00

N8.00          =        $1.00

The exchange rate is therefore $ 1.00 to N8.00.

Example 2

  • Let us assume that the initial exchange rate of the Nigerian naira and the US dollar is N1.00 = $5.00
  • A Nigeria importer is to purchase 60 computer systems at a cost of $40.00 each from the USA.

Total amount required to purchase the computer system = (60 x $40.00 ) = $2,40.00

  • Since the exchange rate is N1.00 = $5.00, total amount of naira required:

$2,40.00        =          $2.40.00

     5

               =            N480.00

This means that a Nigerian Importer would spendN480.00 to import the 60 computer systems to Nigeria.

  • If Nigeria devalues her currency by 100%, the new exchange rate would be N2.00 = $5.00 or N1.00 = S2.50.
  •  The amount of money the Nigerian importer will have to spend will now be

        $2,400.00            =           #2.400.00

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=                         N960.00
N960.00 would be required to import the same 60 computer systems.

Example 3

In year A, 80 naira exchanged for a dollar and later in year B, 130 naira exchanged for a dollar through the forces of demand and supply.

  • State the effect of the above on the value of the dollar.
  •  How much, in naira, would be needed to purchase N50,000 dollar worth of a generator for the US A in year A?
  • How much, in naira, would be needed for the same purpose in year B?
  • (i)    Calculate the percentage change in the value of the naira between year A and B.
  • From your calculation, state the effect on the value of the naira.

Solution

  • The value of the dollar appreciated.
  • In year A,

N80 x $50,000 =          N4,000,000.00
# 4,000,000.00 would be needed.

  • In year B,

N130  x  $50,000 =

N6,500,000.00

N6,500,000.00 would be needed.

(d)(i)  percentage change in the value of the Naira

          =          N130 – N80

                         N80              x          100

=          50        x          100

            80                    1

ii.         The value of naira has depreciated.

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