On January 1, 2009, a U. S. firm made an investment in Germany that will generate $5 million annually in depreciation, converted at the current spot rate. Projected annual rates of inflation in Germany and in the United States are 5 percent and 2 percent, respectively. The real exchange rate is expected to remain constant, and the German tax rate is 50 percent. Required: Calculate the expected real value (in terms of January 1, 2009, dollars) of the depreciation charge in year 2013. Assume that the tax write-off is taken at the end of the year.

The expected real value (in terms of January 1, 2009, dollars) of the depreciation charge in year 2013 will be $1,958,815.416.

Explanation:

It is expected that the value of the dollar in the German market will fall at the same rate as that of the real market value of the dollar when we envisage the exchange rate will remain the same. Thus the depreciation of the tax write-off in terms of its real value in dollars will fall at 5% every year from 2009 to 2013.

Therefore, at a tax rate of 50% in Germany, a $2.5 million charge on depreciation on the investment of $5 million will result in 2013.

To calculate the real value of the dollar at an inflation of 5% yearly in 2013

When the tax rate in German is 50%, then charges of depreciation of $5 million will equal4$2.5 million in 2013 dollars. When the dollar's real value of this write-off is declining due to the inflation at 5% annually, the real value in 2013 will be calculated as:

Given: $2,500,000 (P/F, 5%, 5years); 0.78356 (factor for calculating the amount to be recieved after 5years)

= $2,500,000 * 0.78356

= $1,958,815.416