With the possibiliy that the us congress will relax restrictions on cutting old

Question

With the possibiliy that the us congress will relax restrictions on cutting old trees, a lumber company is considering expanding its facilities. The company believes that it can sell lumber at $0.18 per board foot which is a measure of lumber. The tax rate for the company is 30 percent. the company has the following two opportunities.

Build factory A with annual fixed cost of $20 million and variable costs of $.10 per board foot. the factory has an annual capacity of 500 million board feet.

Build factory B with annual fixed cost of $10 million and variable costs of $.12 per board foot. the factory has an annual capacity of 300 million board feet.

a. What is the breakeven point in the board feet for Factory A& Factory B?

b. If the company wants to generate an after tax profitof $ 2 millionwith factory B, how many board feet would it 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) Breakeven point for factory A=fixed cost/(Selling price per unit-variable price per unit)

=20mn/(0.18-0.1)=250 mn board feet

Breakeven point for factory B=fixed cost/(Selling price per unit-variable price per unit)

=10mn/(0.18-0.12)=166,666,667 board feet

b) After tax profit =$2mn

Let us assumen no of units to be sold as "X"

[((selling price-cost price)x)- fixed cost]*(1-tax rate)=$2mn

=[0.06x-10mn]0.7= 2mn

solving for x gives 214,285,714 units

c) Calcualte the operating leverage for both. Let 280mn be unit sold for each

Operating leverage= Contribution margin/(Contribution margin-fixed cost)]

A=(280*0.08)/[(280*0.08)-20mn]=9.33

B=(280*0.06)/[(280*0.06)-10mn]=2.47

Since for A it is higher so it is ore risker

d) After tax profit for both equate

[0.08x-20mn]*0.07=[0.06x-10mn]*0.07

=500mn board feet

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