Question

On January 1, 2009, a U.S. firm made an investment in Germany that will generate $5 million annually in depreciation, converted at 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 wirite-off is taken at the end of the year

Answer 1

Answer

$1,958,815

Explanation

• We'll expect the exchange rate to remain constant.

Under the above condition:

• The Real Dollar value of the German Mark is expected to decline at the same rate as the Real Mark value (5 % Inflation)
• Hence, the Real dollar value of the Tax writes off will decline at the rate of 5% p.a
• Given German tax rate as 50%, then a depreciation charge of $5 million is worth $2.5 million (Half) in 2005 dollars.
• If the real dollar value of this write-off is declining at the rate of 5% annually, then its real value in 2009 (Since tax write-off is taken at the end of the year).

The Equation to find the Expected real value is given as below

$PV = FV \frac{1}{(1+r)^{n}}$

Where FV = Future value = $2.5 million

r = discount rate = 5%

n = Number of years = 5

$PV = 2,500,000 \frac{1}{(1+0.05)^{5}}$

$PV = 2,500,000 \frac{1}{(1.05)^{5}}$

or

Expected value = 2.5 Million x (PV Factor @ 5%)

$2,500,000 x 0.783526 = $1,958,815

You get factor value from PV Table or using a caluclator.

Hope this helps :)

Regards,

Mike