Target Profit — Compute target profit sales volume (units and dollars)

Historical Context & Motivation

Managers have always needed to answer a deceptively simple question: how much must we sell to earn a specific profit? Long before formal cost accounting frameworks existed, merchants and manufacturers relied on intuition and experience to set sales targets. The development of cost-volume-profit (CVP) analysis in the early twentieth century transformed that intuition into a rigorous, repeatable analytical process. Target profit analysis sits at the heart of CVP, extending the break-even concept by asking not merely when losses end, but when a desired level of profitability begins.

The core question that target profit analysis addresses is both practical and strategic: given a company's cost structure, what sales volume—expressed in units or in revenue dollars—is needed to generate a specific, predetermined profit? Unlike break-even analysis, which identifies the zero-profit threshold, target profit analysis sets a positive earnings goal and works backward to the required activity level. This makes it an indispensable tool for budgeting, goal setting, and evaluating the feasibility of strategic plans.

Core Principles & Definitions

Target profit analysis rests on several foundational concepts that you likely encountered when studying break-even analysis. Here we sharpen those definitions and introduce the specific logic that extends the break-even framework to a profit-earning objective. Understanding these building blocks is essential before moving to the formulas.

Visual Explanation — The CVP Graph with a Target Profit Line

A CVP graph is the most intuitive way to see where target profit is achieved. The diagram below plots total revenue and total costs against the number of units sold. The break-even point occurs where the two lines intersect. Target profit is reached at a higher volume, where the vertical distance between the total revenue line and the total cost line equals the desired profit.

Notice that the target profit volume always lies to the right of the break-even point on the horizontal axis. This makes intuitive sense: you must first cover all fixed costs (break-even), and then continue selling additional units whose contribution margins accumulate into the desired profit. The steeper the total revenue line relative to the total cost line, the fewer additional units are needed beyond break-even to reach the target, because each unit's contribution margin is larger.

Mathematical Framework

The target profit formulas are derived directly from the fundamental CVP equation. At the target profit volume, total revenue minus total costs equals the desired profit. By rearranging terms and substituting the contribution margin, we arrive at two compact expressions—one for units and one for dollars.

Derivation from the CVP Equation

Setting Profit equal to the target profit (TP) and factoring Q from the revenue and variable cost terms yields: TP = Q × (SP − VC) − FC. The quantity (SP − VC) is the contribution margin per unit (CM/u). Solving for Q:

When management wants the answer in revenue dollars rather than units—common for multi-product firms—we use the contribution margin ratio (CM ratio = CM per unit ÷ SP). The formula becomes:

Detailed Breakdown — Units vs. Dollars & the Contribution Margin Ratio

Although the unit-based and dollar-based formulas are algebraically equivalent, each serves a distinct managerial purpose. The unit formula is most useful when a firm sells a single product and wants a concrete production or sales target. The dollar formula is preferred when dealing with multiple products, a sales mix, or situations where unit data is unavailable. The diagram below illustrates how the two formulas relate.

Worked Example

Pinnacle Sports Equipment manufactures a single product—a premium yoga mat. Management wants to know how many mats it must sell, and the total revenue it must generate, to earn a target profit of $60,000 for the quarter. The following data are available:

Strengths, Limitations, and Practical Considerations

Target profit analysis is a powerful planning tool, but like all models it rests on simplifying assumptions. Understanding where it excels and where it falls short will help you apply it wisely in real business settings.

Connection to Advanced Theory — After-Tax Target Profit & Multi-Product Analysis

In practice, many firms set profit targets on an after-tax basis because shareholders and analysts evaluate net income rather than operating income. Additionally, multi-product companies must account for the sales mix when computing a weighted-average contribution margin. The table below contrasts the basic target profit model you learned in this lesson with these two common extensions.

The after-tax adjustment is straightforward and frequently tested in intermediate cost accounting courses. If a firm wants an after-tax profit of $90,000 and the tax rate is 25%, the before-tax target profit becomes $90,000 ÷ (1 − 0.25) = $120,000. You would then plug $120,000 into the standard formula as TP. Multi-product analysis introduces the concept of a composite (weighted-average) contribution margin, which weights each product's CM by its proportion in the sales mix. These extensions build directly on the foundation you have mastered in this lesson.

Practice Problems

Summary