Question

Assume that you are the international trade manager of XYZ Inc. Because your firm exports goods, to Mexico, your job as international trade manger requires you to forecast the value of year, your firm exported one-billion-peso worth of products to Mexico. The exchange rate between US dollar and Mexican peso was $.02/peso. Now, you are expecting that the following changes will take place in the markets. Assume that everything else remains the same.

1. Last year, the inflation rate in the US was 3% and 8% in Mexico. Now, you are expecting that the following change will take place in the markets. Next, year, the inflation in the US is expected to be 2% while it will increase to 9% in Mexico. With each percentage change in the differential inflation, there will be a 5% change in the demand for exports by the Mexican customers. In addition, for each percentage change in the differential inflation, there will be a 1.5% change in the value of the Mexican peso. Explain how the above changes will affect the value of exports of your company to Mexico.

2. Last year, GDP growth rate in the US was 2.5% while it was 3% in Mexico. Next year, you expect that the national income of US will increase by 3% while Mexican national income, will increase by 4.5%. for each percentage change in the differential national income, there will be a 3% change in the differential national income, there will be a 2% change in the value of the peso. Explain how the above changes will affect the value of exports of your company to Mexico.

Please list detailed steps as to how you came up with your answers.

Answer 1

(1) Value of exports

According to Relative Purchasing Power of Parity relationship, the rate of change in exchange rates is approximately equal to the differential inflation between two countries. The currency of the country with higher inflation will depreciate against current of the country with lower inflation in order maintain the equilibrium price conditions of law of one price.

In the given case, the inflation is projected to be 9% at 7% higher than the inflation of 2% projected for US. Hence, the Mexican Peso is expected to depreciate against US dollars. The problem states that for each percentage change in inflation differential, the Mexicon Peso will depreciate by 1.5%. The inflation differential was 5% previous year and it is expected to be 7% next year. The inflation differential has increased by 2%. Hence, Peso will depreciate by 2 * 1.5% = 3% (Note however that as per relative PPP, the exchange rate change is given by expected inflation differential itself which will be 7% for next year. Since the actual percentage change level is given with respect to inflation differential change, we shall follow that).

Also, the problem states that the demand will change by 5% for each percentage change in inflation differential. When the Peso depreciates, it become more costlier for Mexicans to import from US. For example, if a mexican peso could purchase 0.05 US dollar worth of goods previous year, it will purchase much less when peso depreciates to say 0.04 USD/Peso due to US dollar appreciation (or peso depreciation). Hence, exports to Mexico will decline by 5%.

Overall Revenue change = R2 * E2 - R1*E1

where R is revenue in Peso and E is exchange rate expressed as US dollar per Peso

Due to inflation changes, R2 = 0.95 * R1 ==> due to 5% decline in exports

and E2 = E1 * 0.9709 ==> due to 3% depreciation in Peso, the dollar will appreciate by ( 1 / 1.03)

Overall revenue change = 0.95*R1 * E1*0.9709 - R1*E1 = R1 * E1 * (0.95*0.9709-1) = - 0.07765 * R1 * E1

Hence, the exports value to Mexico in terms of Dollars will decline by 7.77%

(Note: In terms of exports value in Pesos, the R2 will be 95% of R1 and E2 will be 1.03% of E1 and hence, the value change in Pesos will be equal to (0.95*1.03 - 1) = - 2.15% - a decline in Peso value by 2.15%)

2) The percentage change in differential national income = (4.5% - 3%) - (3% - 2.5%)= 1% (increase in mexican GDP)

For each percentage change in national income, there will be 2% change in value of peso. Hence, there will be 1 * 2% change = 2% change in Pesos.

The GDP growth rates are proportional to interest rates of a country. As GDP grows, the interest rates are also expected to increase. Hence, to determine the impact on exchange rate, we can consider that equivalent change in interest rates will occur in both the countries. This means a 1% differential GDP growth increase in Mexico is equivalent to 1% increase in interest rates in Mexico.

We can now use "Uncovered Interest Parity theory" to forecast the impact of interest rates on exchange rates. As per this theory, the interest differential is proportional to th expected change in interest rates in two countries. The country with higher interest rate will find its currency depreciating against the currency whose country's interest rates are lower.

Hence, as per Uncovered IRP, the higher interest rates in Mexico due to higher GDP growth rate will lead to depreciation of Mexican Peso.

As per the problem, 1% change in differential inflation leads to 2% change. Since the data gives 1% change in differential inflation, there will be 2% depreciation in Mexican Peso.

Revenue change = R2 * E2 - R1 * E1

where R is revenue expressed in Peso and E is dollar per Peso.

Assuming quantity exported is same, the depreciation of 2% in Peso is equivalent to appreciation of 1/1.02 in terms of dollar

Change in dollar revenue = R1 * (0.9804*E1) - R1 * E1 = 1.96% (R1*E1)

Hence, dollar revenue will decline by 1.96%

In terms of Peso value assuming revenue in terms of dollar is constant

Change in Peso value = R1 * (1.02*E1) - R1*E1 = 1.02 * (R1*E1)

Hence, 2% depreciation in peso will lead to 2% increase in value of exports in terms of Pesos.