Question

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?

Answer 1

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)