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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