Question

Fire company is a service firm with current service revenue of $900,000 and a 40% contribution margin. Its fixed costs are $200,000. Ice company has current sales of $420,000 and a 30% contribution margin. Its fixed costs are $90,000.

(a) What is the margin of safety for Fire and Ice?
(b) Compare the margin of safety in dollars between the two companies. Which is stronger?
(c) Compare the margin of safety in percentage between the two companies. Now which one is stronger?
(d) Compute the degree of operating leverage for both companies. Which company will benefit most from a 10% increase in sales? Explain why. Illustrate your findings in an income statement that is increased by 10%.

Answer 1

The margin of safety in both dollars and percentage is greater for Fire Company, making it financially stronger. However, Ice Company has a higher degree of operating leverage, meaning it will benefit more from an increase in sales.

Step-by-step explanation:

The margin of safety measures how much sales can decrease before a business reaches its breakeven point. It's calculated by subtracting breakeven sales from actual sales. The degree of operating leverage indicates how a percentage change in sales volume will affect operating income due to fixed costs.

Let's solve for Fire and Ice companies:

1. Fire Company's Margin of Safety:

Breakeven Sales = Fixed Costs / Contribution Margin Ratio = $200,000 / 0.40 = $500,000

Margin of Safety in Dollars = Actual Sales - Breakeven Sales = $900,000 - $500,000 = $400,000

Margin of Safety Percentage = Margin of Safety in Dollars / Actual Sales = $400,000 / $900,000 = 44.44%

1. Ice Company's Margin of Safety:

Breakeven Sales = Fixed Costs / Contribution Margin Ratio = $90,000 / 0.30 = $300,000

Margin of Safety in Dollars = Actual Sales - Breakeven Sales = $420,000 - $300,000 = $120,000

Margin of Safety Percentage = Margin of Safety in Dollars / Actual Sales = $120,000 / $420,000 = 28.57%

1. Comparing Margins of Safety in Dollars:

Fire Company has the higher margin of safety in dollars ($400,000) compared to Ice Company ($120,000), indicating Fire Company is stronger financially in terms of sales cushion.

1. Comparing Margins of Safety in Percentage:

In terms of percentages, Fire Company is also stronger, with a higher margin of safety of 44.44%, compared to Ice Company's 28.57%.

1. Degree of Operating Leverage (DOL):

For Fire:
DOL = Total Contribution / Net Operating Income
Net Operating Income = (Sales - Variable Costs) - Fixed Costs
Net Operating Income = ($900,000 - ($900,000 * 0.60)) - $200,000
Net Operating Income = $360,000 - $200,000 = $160,000
DOL = $360,000 / $160,000 = 2.25

For Ice:
Net Operating Income = ($420,000 - ($420,000 * 0.70)) - $90,000
Net Operating Income = $126,000 - $90,000 = $36,000
DOL = $126,000 / $36,000 = 3.5

Ice Company has a higher DOL, meaning it will benefit more from a 10% increase in sales because its profits will rise more for each percentage increase in sales than Fire Company.