Question

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.

Answer 1

When we expect the exchange rate to remain unchanged, then real dollar value of the German mark is likely to decline at the similar rate as the real mark value, i.e. 5% inflation rate annually in Germany. Thus we can conclude that the real dollar value of the depreciation tax write-off will fall at 5% annually.

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:

= $2,500,000 (P/F , 5%, 5years)

= $2,500,000 * 0.78356

= $1,958,815.416