Immediate help needed for the following two questions: 15-12A. (Break-even point) You are a hard-working analyst in the office of financial operations for a manufacturing firm that produces a single product. You have developed the following cost structure information for this company. All of it pertains to an output level of 10 million units. Using this information, find the break-even point in units of output for the firm.

Return on operating assets = 25%
Operating asset turnover = 5 times
Operating assets = $20 million
Degree of operating leverage = 4 times

15-13A. (Break-even point and operating leverage) Allison Radios manufactures a complete line of radio and communication equipment for law enforcement agencies. The average selling price of its finished product is $180 per unit. The variable cost for these same units is $126. Allison
Radios incurs fixed costs of $540,000 per year.

a. What is the break-even point in units for the company?
b. What is the dollar sales volume the firm must achieve in order to reach the break-even
point?

c. What would be the firm’s profit or loss at the following units of production sold:
12,000 units? 15,000 units? 20,000 units?

d. Find the degree of operating leverage for the production and sales levels given in part (c).

ABC and XYZ Companies have the following sales, variable cost, and fixed cost. If sales increase by $10,000 at each company, then:

15-12A: To find the break-even point in units of output for the firm, you can use the following formula:

Break-even point (in units) = Fixed Costs / (Selling Price per unit - Variable Cost per unit)

Given the information provided, we will use the formula:

Break-even point (in units) = $20,000,000 / [(1 - 0.25) x 5]

First, calculate the operating margin:

Operating margin = 1 - Return on operating assets
= 1 - 0.25
= 0.75

Then, calculate the break-even point:

Break-even point (in units) = $20,000,000 / (0.75 x 5)
= $20,000,000 / 3.75
= 5,333,333 units (rounded to the nearest whole number)

Therefore, the break-even point in units of output for the firm is approximately 5,333,333 units.

15-13A:
a. To find the break-even point in units for the company, you can use the following formula:

Break-even point (in units) = Fixed Costs / (Selling Price per unit - Variable Cost per unit)

Given the information provided, the selling price per unit is $180 and the variable cost per unit is $126. The fixed costs per year are $540,000. Now we can calculate the break-even point:

Break-even point (in units) = $540,000 / ($180 - $126)
= $540,000 / $54
= 10,000 units

Therefore, the break-even point in units for the company is 10,000 units.

b. To find the dollar sales volume the firm must achieve to reach the break-even point, you can multiply the break-even point in units by the selling price per unit:

Dollar sales volume (at break-even) = Break-even point (in units) x Selling Price per unit
= 10,000 units x $180
= $1,800,000

Therefore, the dollar sales volume the firm must achieve to reach the break-even point is $1,800,000.

c. To find the firm's profit or loss at different units of production sold, we can use the formula:

Profit or Loss = (Units of Production Sold x Selling Price per unit) - (Fixed Costs + (Units of Production Sold x Variable Cost per unit))

Given the fixed costs of $540,000, the selling price per unit of $180, and the variable cost per unit of $126, we can calculate the profit or loss at the different units of production sold:

For 12,000 units:
Profit or Loss = (12,000 x $180) - ($540,000 + (12,000 x $126))
= $2,160,000 - ($540,000 + $1,512,000)
= $2,160,000 - $2,052,000
= $108,000 profit

For 15,000 units:
Profit or Loss = (15,000 x $180) - ($540,000 + (15,000 x $126))
= $2,700,000 - ($540,000 + $1,890,000)
= $2,700,000 - $2,430,000
= $270,000 profit

For 20,000 units:
Profit or Loss = (20,000 x $180) - ($540,000 + (20,000 x $126))
= $3,600,000 - ($540,000 + $2,520,000)
= $3,600,000 - $3,060,000
= $540,000 profit

Therefore, the firm's profit or loss at 12,000 units sold is $108,000 profit, at 15,000 units sold is $270,000 profit, and at 20,000 units sold is $540,000 profit.

d. To find the degree of operating leverage, which measures the change in operating income for a given change in sales, you can use the formula:

Degree of Operating Leverage = (Change in Operating Income) / (Change in Sales)

Given the profit or loss at different units of production sold, we can calculate the degree of operating leverage for each scenario:

For 12,000 units:
Degree of Operating Leverage = ($108,000 - $0) / ($2,160,000 - $1,800,000)
= $108,000 / $360,000
= 0.3

For 15,000 units:
Degree of Operating Leverage = ($270,000 - $108,000) / ($2,700,000 - $2,160,000)
= $162,000 / $540,000
= 0.3

For 20,000 units:
Degree of Operating Leverage = ($540,000 - $270,000) / ($3,600,000 - $2,700,000)
= $270,000 / $900,000
= 0.3

Therefore, the degree of operating leverage for the production and sales levels given in part (c) is 0.3.