Question

A chemical manufacturer is setting up capacity in Europe and North America for the next three years. The annual demand for each market is 1 million Kilograms (kg) and is likely to stay at that level. The two choices under consideration are building 2 million units of capacity in North America (Option 1) or building 1 million units of capacity in each of the two locations (Option2). Building two plants will insure an additional one time cost of 1.5 million. The variable cost of production in North America (for either a large or a small plant) is currently $5/kg, where the cost in Europe is 4 euro/kg. The current exchange rate is 1 euro for the U.S. $1.20. Over each of the next three years, the dollar is expected to strengthen by 6%, with a probability of 0.6, or weaken by 4%, with a probability of 0.4. Assume a discount factor of 8%. What should the chemical manufacturer do? Provide two options’ NPVs.

Answer 1

Incremental Initial cost for building capcity in Europe = $1,500,000

Variable cost in US = $ 5 per kg | Variable cost in Europe = 4 Euro per kg

Current Exchange rate = 1.20 USD/Euro | Discount rate = 8%

Probability of 6% strength in USD against Euro = 60% | Probability of 4% weakness in USD against Euro = 40%

We can find expected Exchange rate for each year using the given information and find the Variable cost saving for each year.

Strengthening of USD against Euro means lesser dollars for each Euro.

Expected Exchange rate at year 1 = 1.20 * (1 - (60% * 6% - 40% * 4%)) = 1.1760 USD/Euro

Expected Exchange rate at Year 2 = 1.176 * (1 - (60% * 6% - 40% * 4%)) = 1.1525 USD/Euro

Expected Exchange rate at Year 3 = 1.1525 * (1 - (60% * 6% - 40% * 4%)) = 1.1294 USD/Euro

Using the above exchange rates, we can find the Variable cost savings which can be achieved by building a plant in Europe of 1,000,000 capcity.

Total VC Savings in Year 1 = (5 - 4 * 1.176)*1,000,000 = $ 296,000

Total VC Savings in Year 2 = (5 - 4 * 1.1525)*1,000,000 = $ 390,080

Total VC Savings in Year 3 = (5 - 4 * 1.294)*1,000,000 = $ 482,278.40

Now using the discount rate, we can find the Present Value of the Variable cost savings.

PV of Year 1 Savings = 296,000 / (1+8%) = 274,074.07

PV of Year 2 Savings = 390,080 / (1+8%)² = 334,430.73

PV of Year 3 Savings = 482,278.40 / (1+8%)³ = 382,848.14

Total Present Value of the VC Savings = 274,074.07 + 334,430.73 + 382,848.14 = 991,352.94

NPV = PV of VC savings - Initial Cost

NPV = 991,352.94 - 1,500,000 = $ -508,647.06

Hence, the cost savings which can be achieved by opening another plant in Europe doesn't justify the additional cost of 1,500,000 as NPV is negative. Therefore, the company should build 2 million capacity in North America.