Question

Suppose the spot rate for U.S. expressed in C$ is C$1.20 and the expected annual inflation rate in Canada is 2.5% and that in the United States 2%.  Using PPP forecasting model, calculate one-year forecast for the U.S. dollar.  Will the dollar appreciate or depreciate? By what percentage?

Answer 1

Solution:

As per the Purchasing power Parity (PPP) forecasting model

Exchange rate differential = Inflation rate differential

( Forward Rate / Spot Rate ) = [ ( 1 + Inflation Rate in Currency A ) / ( 1 + Inflation Rate in Currency B ) ] ⁿ

Where n = No. of years

As per the Information given in the question we have

Canadian inflation rate = 2.5% annualized ( Currency A )

United States inflation rate = 2 % annualized ( Currency B )

n = 1 year

Spot rate of the United States dollar is C$ 1.20

Thus CD $ / $ = ( A /B ) = C$ 1.20

Applying the above values in the formula / Equation we have

Forward Rate / 1.20 = [ ( 1 + 0.025 ) / ( 1 + 0.02 ) ] ¹

Forward Rate = (1.025 / 1.02 ) * 1.20

Forward Rate = 1.004902 * 1.20

Forward Rate = 1.205882

Forward Rate = 1.2059 ( when rounded off to four decimal places )

Thus the United States dollar's spot exchange rate in a year = Forward Rate = $ 1.2059

Calculation of percentage of appreciation or depreciation :

As per the information given in the question the quote given is direct quote.

The formula for calculating the percentage of appreciation or depreciation for a given Direct quote is

= [ ( Forward rate – Spot rate ) / Spot rate ] * 100

As per the information given in the question we have

Forward rate of United States Dollar = $ 1.205882     ;   Spot rate of United States Dollar = $ 1.20   ;

Applying the above values in the formula we have

= [ ( 1.205882 – 1.20 ) / 1.20 ] * 100

= [ 0.005882 / 1.20 ] * 100

= 0.004902 * 100

= 0.4902 %

Since the solution is positive, it is inferred that the dollar appreciates by 0.4902 %