Calculate the Degree of Operational Leverage for the following firm.*2 points4.005.004.785.78

1. Break Down the Problem

To calculate the Degree of Operating Leverage (DOL), we will need to find the percentage change in operating income (EBIT) and the percentage change in sales. The formula for DOL at a certain level of sales is:

$DOL = \frac{\% \text{ Change in EBIT}}{\% \text{ Change in Sales}}$

2. Relevant Concepts

Let's denote:

• Sales for current year (S1) = 4.00
• Sales for next year (S2) = 5.00
• EBIT (Operating Income) for current year (E1) = 4.78
• EBIT for next year (E2) = 5.78

We will calculate % Change in Sales and % Change in EBIT first.

3. Analysis and Detail

Step 1: Calculate % Change in Sales

$\% \text{ Change in Sales} = \frac{S2 - S1}{S1} \times 100$

Substituting the values:

$\% \text{ Change in Sales} = \frac{5.00 - 4.00}{4.00} \times 100 = \frac{1.00}{4.00} \times 100 = 25\%$

Step 2: Calculate % Change in EBIT

$\% \text{ Change in EBIT} = \frac{E2 - E1}{E1} \times 100$

Substituting the values:

$\% \text{ Change in EBIT} = \frac{5.78 - 4.78}{4.78} \times 100 = \frac{1.00}{4.78} \times 100 \approx 20.92\%$

4. Verify and Summarize

Now, we will calculate the DOL using the values we have found for % Change in Sales and % Change in EBIT.

$DOL = \frac{\% \text{ Change in EBIT}}{\% \text{ Change in Sales}} = \frac{20.92}{25} \approx 0.837$

Final Answer

The Degree of Operating Leverage (DOL) for the firm is approximately 0.837.