Individual Financing Strategy Problems Prepare A Response

Individualfinancing Strategy Problemspreparea Response To Problem 1 In

Prepare a response to Problem 1 in Chapter 20 of Basic Finance. The problem involves two firms, A and B, which both have $10,000 in assets. Firm A is financed solely with equity, while Firm B has $5,000 in debt with a 10% interest rate and $5,000 in equity. Both firms sell 10,000 units at $2.50 per unit, with variable costs of $1 per unit and fixed costs of $12,000. Assume no income tax.

Questions include calculating the operating income (EBIT) for both firms, earnings after interest, the percentage increase in earnings after interest if sales increase by 10% to 11,000 units, and explaining why the percentage changes differ.

Paper For Above instruction

Introduction

Financial leverage plays a crucial role in determining a firm's profitability and risk profile. Comparing two companies with identical assets but different financing structures offers insights into how debt influences operating income, earnings, and growth potential. This paper analyzes the financial outcomes for Firm A and Firm B, considering their structure, sales increase, and resultant percentage changes in earnings. The analysis uses fundamental principles of financial management, including EBIT, interest expenses, and leverage effects, illustrating the implications of different capital structures.

Scenario Description

Both Firm A and Firm B possess assets valued at $10,000. Firm A is financed entirely through equity, meaning it has no interest expenses, while Firm B’s $10,000 assets are financed equally by equity and debt. The debt bears a 10% interest rate, amounting to $500 annually. Both firms produce and sell 10,000 units at a selling price of $2.50 per unit, with variable costs of $1 per unit and fixed costs of $12,000. Since no income tax is assumed, calculations focus on operating income (EBIT), earnings after interest, and the impact of sales growth.

A. Operating Income (EBIT) Calculation

Operating income, or EBIT, is derived by subtracting total variable and fixed costs from total sales revenue. The calculation is identical for both firms initially, as the sales volume and costs are the same.

Variable costs total: 10,000 units × $1 = $10,000.

Total revenue: 10,000 units × $2.50 = $25,000.

Fixed costs: $12,000.

EBIT for both firms: Revenue - Variable Costs - Fixed Costs = $25,000 - $10,000 - $12,000 = $3,000.

Thus, the operating income for both Firm A and Firm B is $3,000.

B. Earnings After Interest Calculation

Interest expense affects only Firm B, owing to its debt structure. For Firm A, earnings after interest are the same as EBIT, since it has no interest expenses. For Firm B, earnings after interest = EBIT - interest expense = $3,000 - $500 = $2,500.

Therefore, the earnings after interest are:

  • Firm A: $3,000
  • Firm B: $2,500

C. Impact of a 10% Increase in Sales

The sales increase by 10%, raising units sold from 10,000 to 11,000. This change affects total revenue and costs, influencing subsequent earnings.

New units sold: 11,000.

New revenue: 11,000 × $2.50 = $27,500.

Variable costs: 11,000 × $1 = $11,000.

Fixed costs remain unchanged at $12,000.

New EBIT: $27,500 - $11,000 - $12,000 = $4,500.

Interest expense for Firm B remains $500, so earnings after interest become: $4,500 - $500 = $4,000.

Calculating the percentage increase in earnings after interest:

  • Firm A: (($3,000 - $2,500) / $2,500) × 100 = 20%
  • Firm B: (($4,000 - $2,500) / $2,500) × 100 = 60%

Hence, Firm A’s earnings after interest increase by 20%, and Firm B’s by 60%, showcasing the amplifying effect of leverage.

D. Explanation of Different Percentage Changes

The differing percentage increases in earnings after interest are primarily due to financial leverage. Firm B’s debt introduces fixed interest expenses. When sales increase, the additional contribution to EBIT, beyond fixed costs, significantly impacts net income. In contrast, Firm A, with no debt, exhibits a linear increase, with earnings rising proportionally with EBIT. The leverage in Firm B magnifies the percentage change because fixed-interest expenses lead to a higher proportionate increase in earnings after interest, emphasizing the risk and reward trade-off inherent in debt financing.

Conclusion

This analysis underscores the importance of financial structure in shaping a company's profitability response to sales changes. While debt can enhance returns through leverage, it also introduces risk, highlighting the necessity for strategic balance based on market and operational conditions.

References

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