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Homework Set 3

Your company is assessing the wisdom of investing in a new process to manufacture a product that it currently produces, hexamethylchickenwire (6MCW). Unfortunately, the methylation reaction to produce 6MCW is not highly selective and will proceed to higher methylations, producing heptamethylchickenwire (7MCW) and octamethylchickenwire (8MCW), both of which are hazardous wastes and must be disposed of at a cost of 50 USD/T and 60 USD/T, respectively.

The manufacturing unit will consist of a methylation reactor and recovery section. The recovery section for the product contains two towers. The desired product is recovered as a heart-cut, with the overhead of the first tower, primarily methanol and lower methylation products, being recycled to the front-end of the reactor. The bottoms of the second tower contain the 7MCW and 8MCW.

According to pilot plant results obtained from the Technology division, overall plant selectivities (which include reactor selectivities and distillation recoveries) have the following probabilities of occurring after scale-up to full production:

Capacity for the unit is 130 kT/yr.

Variable margin for this newest increment of 6MCW, excluding by-product disposal (i.e. variable margin is based on raw materials and product only), has an expected value of 100 USD/T, with a standard deviation of 10 USD/T. Sales volume in the first year of operation is expected to be 100 kT, with a standard deviation of 10 kT. Sales volume is expected to grow approximately with U.S. gross domestic product at 3 %/yr, with a standard deviation of 0.5 %/yr.

Fixed costs for the operating the unit have an expected value of 2 million USD/year, with a standard deviation of 400 thousand USD/yr.

The total erected cost (TEC) of the unit is composed of capital of 20 million USD (estimated mean), with a 10 % probability that the capital cost is less than 17 million USD and a 90 % probability that the capital cost is less than 23 million USD. The expected value of expense associated with construction is 2 million USD, with a standard deviation of 200 thousand USD. Forty percent of TEC (capital and expense) are expended the year before start-up, and sixty percent of TEC are expended the year of start-up (assume start-up on December 31).

The project will have a ten-year economic life. Depreciation will be according to MACRS, using the five-year schedule for chemical equipment. The average income tax rate for the company is 40 %. The company's cost of capital is 14 %.

Using @RISK, prepare a capital budget statement for the project. Show the distribution of net present value for the project.

Here are a few notes to help you interpret the problem:

• Assume all probability distributions are normal.
• The expected value of a normal distribution is its mean.
• Remember, capacity is limited. You cannot sell what you do not make (use a MIN function to set a ceiling on production).
• Expense associated with construction is not depreciable but is deducted from profits in the years it occurs.
• USD is an abbreviation for U.S. dollars.
• Tons are metric tons (2,204.62 lbs/T).

Updated: Saturday, March 19, 2011