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Finance: Earnings per Share and the Break-Even Point

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1. Ensco Lighting Company has fixed costs of \$100,000, sells its units for \$28, and has variable costs of \$15.50 per unit.

a. Compute the break-even point.
b. Ms. Watts comes up with a new plan to cut fixed costs to \$75,000. However, more labor will now be required, which will increase variable costs per unit to \$17. The sales price will remain at \$28. What is the new break-even point?
c. Under the new plan, what is likely to happen to profitability at very high volume levels (compared to the old plan)?

2. Air Filter, Inc., sells its products for \$6 per unit. It has the following costs:

Rent: \$100,000
Factory labor: \$1.20 per unit
Executive salaries: \$89,000
Raw material: \$.60 per unit

Separate the expenses between fixed and variable cost per unit. Using this information and the sales price per unit of \$6, compute the break-even point.

3. Gibson & Sons, an appliance manufacturer, computes its break-even point strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are \$1,200,000, but 25 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is \$2.40. How many units does the firm need to sell to reach the cash break-even point?

4. University Catering sells 50-pound bags of popcorn to university dormitories for \$10 a bag. The fixed costs of this operation are \$80,000, while the variable costs of the popcorn are \$.10 per pound.

a. What is the break-even point in bags?
b. Calculate the profit or loss on 12,000 bags and on 25,000 bags.
c. What is the degree of operating leverage at 20,000 bags and at 25,000 bags? Why does the degree of operating leverage change as the quantity sold increases?

5. Mr. Katz is in the widget business. He currently sells 2 million widgets a year at \$4 each. His variable cost to produce the widgets is \$3 per unit, and he has \$1,500,000 in fixed costs. His sales-to-assets ratio is four times, and 40 percent of his assets are financed with 9 percent debt, with the balance financed by common stock at \$10 per share. The tax rate is 30 percent.

His brother-in-law, Mr. Doberman, says Mr. Katz is doing it all wrong. By reducing his price to \$3.75 a widget, he could increase his volume of units sold by 40 percent. Fixed costs would remain constant, and variable costs would remain \$3 per unit. His sales-to-assets ratio would be 5 times. Furthermore, he could increase his debt-to-assets ratio to 50 percent, with the balance in common stock. It is assumed that the interest rate would go up by 1 percent and the price of stock would remain constant.

a. Compute earnings per share under the Katz plan.
b. Compute earnings per share under the Doberman plan.
c. Mr. Katz's wife does not think that fixed costs would remain constant under the Doberman plan but that they would go up by 20 percent. If this is the case, should Mr. Katz shift to the Doberman plan, based on earnings per share?