FIN 3010 Module 5 Break-Even and Gearing Problems Example

How Fixed Costs and Debt Magnify Results: Break-Even, DOL, DFL and Earnings per Share at a Plastics Molder

Student Name

Bachelor of Science in Business Administration, Thomas Edison State University

FIN-3010: Principles of Finance

Mentor Name

Month Day, Year

How Fixed Costs and Debt Magnify Results: Break-Even, DOL, DFL and Earnings per Share at a Plastics Molder

Corporate finance's first topic is how a firm's cost and financing structure affects its risk and return. The problems below apply that topic to Delair Precision Molding, a composite maker of injection-molded plastic parts in Camden County, New Jersey. It sells parts at an average of $12 per unit, with variable costs of $7 per unit and fixed operating costs of $1.5 million a year, including $400,000 of depreciation. It has $3.5 million of debt carrying $250,000 of annual interest, 500,000 shares outstanding and a 25% tax rate. The textbook's measures of this magnifying effect appear below by their standard abbreviations, DOL for operating, DFL for financial and DTL for the combined effect, and the effect itself is called gearing (Mayo & Lavelle, 2024).

Problem 1: Break-Even Volume

Problem 2: Cash Break-Even

Depreciation is a fixed cost that does not use cash. How many units must the company sell to cover its cash fixed costs?

Between 220,000 and 300,000 units the firm reports accounting losses but still covers its cash costs, which matters for survival in a weak year.

Problem 3: Operating Results and DOL at 450,000 Units

DFL rises as interest grows relative to EBIT. If Delair borrowed another $2 million at the same 7.1% rate to buy equipment, interest would rise to about $392,000, EBT at 450,000 units would fall to about $358,000 and DFL would rise to about 2.1, making each swing in operating profit hit shareholders harder.

A DOL of 3.0 means that, at this volume, each 1% change in sales changes EBIT by about 3%. The closer the company operates to its break-even point, the higher DOL becomes and the more volatile its operating profit.

Problem 4: DFL, DTL and Earnings per Share

Problem 5: The Effect of a 10% Sales Increase

The 10% rise in sales becomes a 30% rise in EBIT, as DOL predicts, and a 45% rise in earnings per share, as DTL predicts. The same arithmetic works in reverse: a 10% drop in sales would cut EPS by 45%, to about $0.41.

Why Gearing Matters to Investors

These multipliers are not only classroom ratios; they affect how risky a company's shares are. Lev (1974) examined firms in several industries and found that those with a higher proportion of fixed operating costs had more volatile and riskier stock returns. Mandelker and Rhee (1984) found that the degrees of operating and financial gearing together explained a large part of the differences in firms' systematic risk, or beta. For Delair, the combination of a capital-intensive molding operation and meaningful debt means shareholders face amplified swings in earnings. Managers can respond by keeping debt moderate while the company operates near break-even, by negotiating variable rather than fixed costs where possible, such as paying for some maintenance by machine hour, or by building a cash cushion for weak years. Each choice reduces DTL at the cost of some upside when sales are strong.

References

Lev, B. (1974). On the association between operating leverage and risk. Journal of Financial and Quantitative Analysis, 9(4), 627-641. https://doi.org/10.2307/2329764

Mandelker, G. N., & Rhee, S. G. (1984). The impact of the degrees of operating and financial leverage on systematic risk of common stock. Journal of Financial and Quantitative Analysis, 19(1), 45-57. https://doi.org/10.2307/2331000

Mayo, H. B., & Lavelle, M. (2024). Basic finance: An introduction to financial institutions, investments, and management (13th ed.). Cengage Learning.