3. With the possibility of the US Congress relaxing restrictions on cutting old

Question

3. With the possibility of the US Congress relaxing restrictions on cutting old growth, a local lumber company is considering an expansion of its facilities. The company believes it can sell lumber for $0.18/board foot. A board foot is a measure of lumber. The tax rate for the company is 30%. The company has the following two opportunities:



• Build factory A with an annual fixed cost of $20 million and variable costs of $0.10/board foot. This factory has an annual capacity of 500 million board feet.



• Build factory B with annual fixed costs of $10 million and variable costs of $0.12/board foot. This factory has annual capacity of 300 million board feet.



Required:



a. What is the break-even point in board feet for factory A?

b. If the company wants to generate an after tax profit of $2 million with factory B, How many board feet would the company have to process and sell?

c. If demand for lumber is uncertain, which factory is riskier?

d. At what level of board feet would the after-tax profit of the two factories be the same?

Explanation / Answer

a.      Break-even point of Factory A = $10,000,000/($0.15 - $0.10) = 200,000,000 board-feet

b.      To achieve an after-tax profit of $3,000,000:

            [$10,000,000 + ($3,000,000/(1 - .3))]/($0.15 - $0.09) = 321, 423,571 board-feet

c.      Factory B has higher fixed costs, but lower variable costs per unit. If the demand for lumber is lower than expected, Factory B will have a more difficult time recovering its fixed costs. The break-even point for factory A is lower than the break-even point for factory B. Therefore, Factory B is the riskier investment.

d.      The after-tax profits of the two factories will be the same when:

              (1 - .3)[($0.15 - $0.10)(Quantity) - $10,000,000]

              = (1 - .3)[($0.15 - $0.09)(Quantity) - $15,000,000]

            Quantity = 500 million board feet

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