Firm Has Sales Of 10 Million And Variable Costs

Firm Has Sales Of 10 Million Variable Costs Of

A firm has sales of $10 million, variable costs of $4 million, fixed expenses of $1.5 million, interest costs of $2 million, and a 30 percent average tax rate. Compute its Degree of Operating Leverage (DOL), Degree of Financial Leverage (DFL), and Degree of Combined Leverage (DCL). Additionally, analyze the company's expected earnings before interest and taxes (EBIT) and net income if sales increase or decrease by specified percentages.

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Firm Has Sales Of 10 Million Variable Costs Of

Firm Has Sales Of 10 Million Variable Costs Of

The financial analysis of a firm with specified sales and costs provides essential insights into how operating and financial leverage amplify the impact of sales fluctuations on earnings and profitability. The calculation of the Degree of Operating Leverage (DOL), Degree of Financial Leverage (DFL), and Degree of Combined Leverage (DCL) allows managers and investors to understand the sensitivity of EBIT and net income to changes in sales levels, facilitating informed decision-making.

Introduction

Fundamentally, leverage measures the extent to which a company's fixed costs, whether operating or financial, influence its profitability relative to sales changes. Operating leverage stems from fixed operational costs and impacts EBIT, while financial leverage originates from fixed financial costs such as interest expenses and affects net income. Combining these concepts yields comprehensive insights into the firm's risk profile and degree of earnings variability.

Calculating Leverage Ratios and Their Significance

1. Degree of Operating Leverage (DOL)

The DOL quantifies how a percentage change in sales affects EBIT. It is calculated at a given level of sales, typically demonstrated as:

DOL = (Sales - Variable Costs) / (Sales - Variable Costs - Fixed Operating Expenses)

For the company in question:

- Sales (S) = $10 million

- Variable Costs (VC) = $4 million

- Fixed Operating Expenses (FC) = $1.5 million

Substituting the numbers:

DOL = ($10M - $4M) / ($10M - $4M - $1.5M) = $6M / $4.5M ≈ 1.33

2. Degree of Financial Leverage (DFL)

The DFL measures the sensitivity of net income to EBIT, influenced by fixed financial costs, primarily interest. It is computed as:

DFL = EBIT / (EBIT - Interest)

First, calculate EBIT:

EBIT = Sales - Variable Costs - Fixed Operating Expenses = $10M - $4M - $1.5M = $4.5 million.

Interest costs = $2 million.

Therefore:

DFL = $4.5M / ($4.5M - $2M) = $4.5M / $2.5M = 1.8

3. Degree of Combined Leverage (DCL)

The DCL combines operating and financial leverage, indicating total leverage effect. It can be derived from:

DCL = DOL × DFL ≈ 1.33 × 1.8 ≈ 2.394

This ratio signifies that a 1% change in sales results in approximately a 2.39% change in net income, under the base sales level.

Impact of Sales Changes on EBIT and Net Income

1. Sales Increase by 10%

Projected sales:

$10M × 1.10 = $11M

New EBIT:

= (New Sales - Variable Costs - Fixed Operating Expenses)

Variable costs typically change proportionally:

Variable costs at increased sales:

($4M / $10M) × $11M = $4.4M

EBIT = $11M - $4.4M - $1.5M = $5.1M

Net income:

Interest remains unchanged at $2M.

Earnings before taxes (EBT):

$5.1M - $2M = $3.1M

Tax (30%):

$3.1M × 0.30 = $0.93M

Net income:

$3.1M - $0.93M = $2.17M

2. Sales Decrease by 20%

Projected sales:

$10M × 0.80 = $8M

Variable costs decrease proportionally:

($4M / $10M) × $8M = $3.2M

EBIT:

$8M - $3.2M - $1.5M = $3.3M

Net income:

EBIT - Interest = $3.3M - $2M = $1.3M

Taxes:

$1.3M × 0.30 = $0.39M

Net income:

$1.3M - $0.39M = $0.91M

Conclusion

The leverage ratios depict a moderate risk profile; the DOL of roughly 1.33 indicates that EBIT is sensitive but not excessively volatile relative to sales changes. The financial leverage amplifies earnings fluctuations, with a DFL of 1.8, implying that interest expenses significantly influence net income sensitivity. The combined leverage suggests that a 1% change in sales causes an approximate 2.39% shift in net income, highlighting the importance of sales stability for profit predictability.

The analysis of sales increases and decreases illustrates expected EBIT and net income fluctuations—highlighting the company's vulnerability to sales volatility. An increase in sales enhances profitability substantially, whereas a decline exerts significant downward pressure on net income. These insights assist in strategic planning and risk management, emphasizing the importance of operating efficiency and debt management.

References

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