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 4 million units of capacity in North America?

Answer 1

1.

	Option 1 - Facilities at NA and Europe
Year	Initial Investment	Variable Cost - NA	Expected % strength of $	Expected Exchange Rate	Variable Cost - EU	Total Cost	Discount Factors	Present Value
0	$2					$2	1.00	$2.00
1		$20	-2.50%	$1.30	$23.34	$43	0.91	$39.40
2		$20	-2.50%	$1.26	$22.76	$43	0.83	$35.34
3		$20	-2.50%	$1.23	$22.19	$42	0.75	$31.70
						Present Value (M$)=	$108.44

2.

	Option 2 - Facility only at NA
Year	Initial Investment	Variable Cost	Total Cost	Discount Factors	Present Value
0	$0		$0	1.00	$0.00
1		$40	$40	0.91	$36.36
2		$40	$40	0.83	$33.06
3		$40	$40	0.75	$30.05
			Present Value (M$)=	$99.47

Note that the difference of the two present values is $108.44 - $99.47 = $8.97 million

Out of the given options, for

1) NPV = $152,375,753
2) NPV = $143,681,525

The difference becomes equal to $8.7 million which is close to our calculated value of $8.97 million. So, we can choose these two answers. Note that there is no way to find these NPVs from the given data because a) the cash inflows i.e. the revenues are not given, b) the absolute values of initial investments are not given, only the excess $2 million for the two-plant option is indicated.

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