Firm A Has $10,000 In Assets Entirely Financed With Equity

Firm A Has 10000 In Assets Entirely Financed With Equity Firm B Als

Firm A has $10,000 in assets entirely financed with equity. Firm B also has $10,000 in assets, but these assets are financed by $5,000 in debt (with a 10 percent rate of interest) and $5,000 in equity. Both firms sell 10,000 units of output at $2.50 per unit. The variable costs of production are $1, and fixed production costs are $12,000. (To ease the calculation, assume no income tax.)

a. What is the operating income (EBIT) for both firms?

b. What are the earnings after interest?

c. If sales increase by 10 percent to 11,000 units, by what percentage will each firm’s earnings after interest increase? To answer the question, determine the earnings after taxes and compute the percentage increase in these earnings from the answers you derived in part b.

d. Why are the percentage changes different?

Paper For Above instruction

The analysis of how financial structure influences firm profitability and earnings sensitivity to sales changes is fundamental in corporate finance. This paper examines two firms, A and B, distinguished by their capital structures—equity financing only versus a combination of debt and equity—and evaluates their operating and net incomes under varying sales levels. Through this comparative analysis, we explore the implications of leverage and capital structure on earnings stability and growth potential, ultimately illustrating core principles of financial leverage, the cost of debt, and their effects on shareholder returns.

Introduction

Capital structure decisions are central to corporate finance, affecting a firm's profitability, risk, and valuation. The Modigliani-Miller theorem initially suggested that, under perfect market conditions, a firm's value is unaffected by its capital structure. However, real-world frictions such as taxes, bankruptcy costs, and agency problems make leverage a meaningful factor influencing earnings and risk. This analysis examines two hypothetical firms with identical asset bases but differing financing structures to understand how leverage affects operating income, earnings after interest, and sensitivity of earnings to sales changes.

Capital Structure and Operating Income

Firm A is financed entirely with equity, with assets totaling $10,000. Firm B's assets are also $10,000 but financed with $5,000 debt (costing 10% interest) and $5,000 equity. Both firms sell 10,000 units at $2.50, with variable costs of $1 per unit and fixed costs of $12,000. The first step involves calculating the operating income or EBIT for both firms.

Calculation of Operating Income (EBIT)

Sales revenue for both firms is 10,000 units × $2.50 = $25,000. Variable costs at $1 per unit are 10,000 × $1 = $10,000. Fixed costs are $12,000, which together with variable costs sum to $22,000.

Operational income or EBIT is calculated as:

EBIT = Sales - Variable Costs - Fixed Costs

Therefore, EBIT = $25,000 - $10,000 - $12,000 = $3,000 for both firms, as fixed and variable costs are the same and sales volume is identical.

Hence, operating income for both firms initially is $3,000, unaffected by capital structure at this stage.

Earnings After Interest

Next, considering the financial costs, only Firm B incurs interest expenses due to debt. The interest expense is 10% of $5,000, i.e., $500. Consequently, earnings before taxes (EBT) for Firm B is EBIT minus interest, i.e.,

EBT_B = $3,000 - $500 = $2,500

For Firm A, which is entirely equity-financed, no interest costs are incurred, so earnings after interest (which equals net income, assuming no taxes) are simply EBIT, i.e.,

Net income_A = $3,000

Impact of Sales Increase by 10%

If sales increase by 10%, units sold rise from 10,000 to 11,000. Revenue becomes 11,000 × $2.50 = $27,500. Variable costs increase proportionally, now 11,000 × $1 = $11,000. Fixed costs remain fixed at $12,000.

New EBIT is:

EBIT_new = $27,500 - $11,000 - $12,000 = $4,500

For Firm A, which has no debt, net income after interest remains $4,500 (since no interest costs), implying a percentage increase of:

[(4,500 - 3,000) / 3,000] × 100% = 50%

For Firm B, interest costs are unchanged at $500. Earnings before interest after increased sales are $4,500, so earnings after interest are:

EBT_new = $4,500 - $500 = $4,000

The initial earnings after interest (from part b) for Firm B were $2,500 at 10,000 units. Now, with increased sales:

Percentage increase in earnings after interest = [(4,000 - 2,500) / 2,500] × 100% = 60%

Analysis of Different Percentage Changes

The differing percentage increases—50% for Firm A and 60% for Firm B—highlight the effects of leverage. While EBIT increased by 50% due to sales growth, the debt-leveraged firm's net earnings after interest increased by an additional margin because the fixed interest expense of $500 remains constant regardless of sales volume. This leverage effect magnifies the percentage change in net income attributable to operating leverage, demonstrating how debt amplifies earnings sensitivity to sales fluctuations.

Conclusion

The analysis confirms that leverage influences not only the level of earnings but also their responsiveness to sales changes. Firm A's entirely equity financing results in proportional earnings growth, while Firm B's debt structure amplifies earnings volatility, increasing percentage gains in the firm's net income upon sales growth. However, this potential for higher gains comes with increased risk, emphasizing the importance of strategic capital structuring based on a company's risk tolerance and market conditions.

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