Question

In: Finance

Company X is setting up capacity in Europe and North America for the next three years....

Company X is setting up capacity in Europe and North America for the next three years. Annual demand in each market is 2 million kilograms (kg) and is likely to stay at that level. The two choices under consideration are building 4 million units of capacity in North America or building 2 million units of capacity in each of the two locations. Building two plants will incur an additional one-time cost of $2 million. The variable cost of production in North America (for either a large or a small plant) is currently $10/kg, whereas the cost in Europe is 9 euro/kg. The current exchange rate is 1 euro for U.S. $1.33. Over each of the next three years, the dollar is expected to strengthen (NOT rise) by 10 percent, with a probability of 0.5, or weaken(NOT drop) by 5 percent, with a probability of 0.5. Assume a discount factor of 10 percent.

What is the Year 0 net present value of building 2 million units of capacity in each of Europe AND North America?

Solutions

Expert Solution

Change in Eur /USD rate Probability % Increase /(Decrease ) Probability Weighted % Increase /(Decrease )
0.5 10% 5.00%
0.5 -5% -2.50%
Total 2.50%
So the expected increase in exchnage rate increase is 2.5% per annum
Year 1 Year 2 Year 3
Eur /USD rate with 2.5% strengthening of USD ( USD value reduces by 2.5% each year against USD)                     1.297                  1.264                       1.233
Variable cost Comparison Year 1 Year 2 Year 3
Option 1
Making 4M units in NA @$10/kg $       40,000,000 $    40,000,000 $          40,000,000
Option 2 cost
Making 2 M units in Europe @Euo 9/kg converted to USD at the respective years rate $       23,341,500 $    22,757,963 $          22,189,013
Making 2 M units @$10/kg in NA $       20,000,000 $    20,000,000 $          20,000,000
Total Variable cost in Option 2 $       43,341,500 $    42,757,963 $          42,189,013
Incremental Variable cost in Option 2 $         3,341,500 $       2,757,963 $            2,189,013
NPV of of buildining 2M units in NA and 2M units in Europe.
Initial Investment Year 0 Year 1 Year 2 Year 3
Incremental One time cost $       (2,000,000)
Incremental Variable cost $     (3,341,500) $          (2,757,963) $     (2,189,013)
Total Incremental cost $       (2,000,000) $     (3,341,500) $          (2,757,963) $     (2,189,013)
Discount factor @10% $                        1 $                      1 $                           1 $                      1
PV of Incremental cost $       (2,000,000) $     (3,037,758) $          (2,279,180) $     (1,644,606)
NPV =sum of PV of discounted incremental cost $       (8,961,544)
So the NPV of building 2 million units of capacity in each of NA and Eurpoe is = $          (8,961,544)

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