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.
a. $S = $C,
180x = 126x + 540,000,
180x - 126x = 540,000,
54x = 540,000,
X = 10,000 Units = Break-even point.
b. S = 180 * 10,000 = $1,800,000 to break-even.
c. Same procedure as a.
To calculate the answers to these questions, we need to understand the concept of break-even analysis and use the following formulas:
Break-even point (units) = Fixed costs / Contribution margin per unit
Dollar sales volume = Break-even point (units) * Average selling price per unit
Profit or loss = (Number of units sold * Contribution margin per unit) - Fixed costs
Degree of operating leverage = Contribution margin / Net income
Now let's calculate the answers to each question step-by-step:
a. To find the break-even point in units, we need to calculate the contribution margin per unit. The contribution margin per unit is the selling price per unit minus the variable cost per unit. So, in this case, the contribution margin per unit would be:
Contribution margin per unit = Average selling price per unit - Variable cost per unit
= $180 - $126
= $54
Now we can determine the break-even point in units:
Break-even point (units) = Fixed costs / Contribution margin per unit
= $540,000 / $54
= 10,000 units
Therefore, the break-even point for the company is 10,000 units.
b. To find the dollar sales volume needed to reach the break-even point, we can use the formula:
Dollar sales volume = Break-even point (units) * Average selling price per unit
= 10,000 units * $180
= $1,800,000
Thus, the firm must achieve a dollar sales volume of $1,800,000 to reach the break-even point.
c. To determine the profit or loss at different levels of production sold, we can use the formula:
Profit or loss = (Number of units sold * Contribution margin per unit) - Fixed costs
For 12,000 units:
Profit or loss = (12,000 * $54) - $540,000
= $648,000 - $540,000
= $108,000 profit
For 15,000 units:
Profit or loss = (15,000 * $54) - $540,000
= $810,000 - $540,000
= $270,000 profit
For 20,000 units:
Profit or loss = (20,000 * $54) - $540,000
= $1,080,000 - $540,000
= $540,000 profit
Therefore, at 12,000 units, the firm would have a $108,000 profit, at 15,000 units the firm would have a $270,000 profit, and at 20,000 units the firm would have a $540,000 profit.
d. The degree of operating leverage can be calculated using the formula:
Degree of operating leverage = Contribution margin / Net income
At 12,000 units:
Degree of operating leverage = ($54 * 12,000) / $108,000
= 648,000 / 108,000
= 6
At 15,000 units:
Degree of operating leverage = ($54 * 15,000) / $270,000
= 810,000 / 270,000
= 3
At 20,000 units:
Degree of operating leverage = ($54 * 20,000) / $540,000
= 1,080,000 / 540,000
= 2
Thus, the degree of operating leverage is 6 at 12,000 units, 3 at 15,000 units, and 2 at 20,000 units.