What analysis determines how changes in costs and volume impact a company's profits?

The correct choice, which is cost-volume-profit analysis, is crucial because it specifically examines the relationship between a company's costs, sales volume, and profits. This analysis helps businesses understand how changes in their cost structures, selling prices, and production volumes can influence overall profitability. By evaluating the interplay of these elements, managers can make informed decisions regarding pricing strategies, budgeting, and financial forecasting.

Cost-volume-profit analysis incorporates various factors, such as fixed and variable costs, sales price per unit, and the quantity of units sold. It is particularly useful for understanding the break-even point—the level of sales at which total revenues equal total costs—allowing managers to determine the minimum required sales to avoid losses. Moreover, it enables assessment of how different levels of output affect the company's bottom line, helping business leaders strategize for optimal performance.

In contrast, other options like break-even analysis focus on identifying the specific point where revenues equal costs, but they do not delve into the broader relationship among costs, volume, and profits comprehensively. Variance analysis, on the other hand, is concerned primarily with comparing actual performance to budgeted performance, while ratio analysis focuses on financial ratios and metrics that do not directly correlate with changes in cost-volume-profit dynamics.