A chemical manufacturer 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 loca-tions. 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 cur-rent exchange rate is 1 euro for U. S. $1.33. Over each of the next three years, the dollar is expected to strengthen by 10 percent, with a probability of 0.5, or weaken by 5 per-cent, with a probability of 0.5. Assume a discount factor of 10 percent. What should the chemical manufacturer do? At what initial cost differential from building the two plants will the chemical manufacturer be indifferent between the two options?

Explanation:

The two choices under consideration are building 4 million units of capacity in North America

YEAR                        1                    2                           3  

Production and Sales 4,000,000.00   4,000,000.00   4,000,000.00  

Variable cost @ 10  40,000,000.00   40,000,000.00   40,000,000.00  

Divide by:

Conversion Factor  1.33                         1.33                     1.33  

Multiply by:

Growth(.1*.5)+(-.05*.5) 1.025                        1.025^2                  1.025^3  

NET CASHFLOWS  30,827,068.00   31,597,744.00   32,387,688.00  

DCF @ 10%     0.909090909           0.83                  0.75  

Present Values  28,024,607.27   26,113,838.02   24,333,349.36  

NET TOTAL COST 78,471,794.65  

or building 2 million units of capacity in each of the two loca-tions. Building two plants will incur an additional one-time cost of $2 million.

YEAR                  0            1                      2                              3  

Production and Sales       4,000,000.00      4,000,000.00   4,000,000.00  

Variable cost @ [(10+9)/2] 38,000,000.00  38,000,000.00   38,000,000.00  

Additional cost  2,000,000.00      

Conversion Factor     1.33     1.33                   1.33                       1.33  

Growth(.1*.5)+(-.05*.5)    1.025              1.025^2              1.025^3  

CASHFLOWS  1,503,759.40  29,285,714.29  30,017,857.00  30,768,304.00  

DCF @ 10%       1          0.909090909    0.8264462810.751314801  

Present Value 1,503,759.40  26,623,376.62   24,808,146.28   23,116,682.19  

NET TOTAL COST = 76,051,964.50  

DECISION: The manufacturer should build 2 plants in 2 different locations because it gives a lower net present cost

At what initial cost differential from building the two plants will the chemical manufacturer be indifferent between the two options?

The difference in both options came from the fact that variable cost is lower in Europe and building the plant is more expensive. If there is no increase in cost and variable cost is same everywhere, then both options will be same.

month 1 start amount =$3287.90 interest=(3287.90x0.0145/12)3.97 total to pay=$3291.81 paid =$1200 balance =$2,091.87

month 2 starting amount= $2,091.87 interest =$25.28 total to pay =$2117.15 paid =$1200 balance $917.15

month 3 starting amount =$917.15 interest =$11.08 total to pay =$928.23 paid =$928.23 balance =$0 total to pay 1200+1200+928.23 = $3328.23 it will take 3 months to pay a total of $3328.23