# Company X is setting up capaci

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

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

Answer:

 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 exchnagerate increase is 2.5% per annum Year 1 Year 2 Year 3 Eur /USD rate with 2.5% strengtheningof USD ( USD value reduces by 2.5% each year againstUSD) 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/kgconverted to USD at the respective years rate \$      23,341,500 \$   22,757,963 \$         22,189,013 Making 2 M units @\$10/kg inNA \$      20,000,000 \$   20,000,000 \$         20,000,000 Total Variable cost in Option2 \$      43,341,500 \$   42,757,963 \$         42,189,013 Incremental Variable cost in Option2 \$        3,341,500 \$      2,757,963 \$           2,189,013
 NPV of of buildining 2M unitsin 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 discountedincremental cost \$      (8,961,544) So the NPV of building 2 million unitsof capacity in each of NA and Eurpoe is = \$         (8,961,544)

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