Introduction
If you’re studying managerial accounting, you’ve likely come across the 15-4 Application Problem—a popular exercise focused on evaluating performance using responsibility accounting. This problem not only tests your understanding of departmental accountability but also introduces you to key performance metrics like ROI (Return on Investment) and residual income.
These tools are vital for businesses that want to assess how well different segments or departments are contributing to the overall profitability of the company. In this blog post, we’ll walk you through the concepts behind the 15-4 problem, show how to solve it, and offer practical tips for applying these ideas in real business situations.
What the 15-4 Application Problem Is All About
This problem usually involves a company with two or more investment centers. You’re given key financial figures such as:
- Sales
- Operating Income
- Average Operating Assets
- Minimum Required Rate of Return
Using this data, the goal is to evaluate performance using two core measures:
- Return on Investment (ROI)
- Residual Income (RI)
These are crucial tools in responsibility accounting, where each department or unit is accountable for its own revenue and costs. According to Investopedia, ROI helps managers compare the profitability of different investment opportunities, while residual income shows the dollar value of profit above a required return.
Step-by-Step: How to Solve 15-4 Using ROI and Residual Income
Let’s say you’re analyzing the performance of Division A and Division B.
You are given:
- Division A:
- Sales: $1,000,000
- Net Operating Income: $200,000
- Average Operating Assets: $800,000
- Division B:
- Sales: $1,500,000
- Net Operating Income: $210,000
- Average Operating Assets: $1,200,000
The company’s required return is 10%.
Step 1: Calculate ROI
The formula is:
ROI = Net Operating Income ÷ Average Operating Assets
For Division A:
$200,000 ÷ $800,000 = 25%
For Division B:
$210,000 ÷ $1,200,000 = 17.5%
Although Division B has higher income in dollars, Division A is more efficient at using its assets.
As explained by the Corporate Finance Institute, ROI reveals how effectively a division is using its assets to generate profit.
Step 2: Calculate Residual Income
The formula is:
RI = Net Operating Income – (Average Operating Assets × Minimum Required Rate of Return)
For Division A:
$200,000 – ($800,000 × 10%) = $200,000 – $80,000 = $120,000
For Division B:
$210,000 – ($1,200,000 × 10%) = $210,000 – $120,000 = $90,000
Here, Division A still outperforms. It earns $120,000 above the company’s required return, whereas Division B earns only $90,000 over the minimum.
This metric, as described in AccountingTools, is helpful because it encourages investment in profitable projects even if they lower the division’s ROI.
Which Division Is Performing Better?
Using both ROI and residual income offers a clearer picture than using just one metric. In our example, Division A shows stronger performance under both measures, making it the more efficient and profitable unit.
This aligns with responsibility accounting, where departments are evaluated based on the results they control. Managers should not be penalized for factors outside their influence, and that’s why residual income is often preferred over ROI in performance reviews.
Common Pitfalls to Avoid in 15-4
- Focusing solely on ROI: High ROI doesn’t always mean better decision-making if new investments are rejected simply because they lower the percentage.
- Ignoring asset base: A division with fewer assets may look better on ROI, but RI shows the true dollar contribution.
- Overlooking qualitative factors: Performance metrics should be used with managerial insights—numbers alone don’t tell the full story.
Why This Problem Matters in Real Life
Many large organizations use ROI and RI to assess divisional managers. These metrics are not just academic—they help companies determine where to allocate resources, which teams are driving profit, and how effectively managers are using their capital.
According to Harvard Business Review, using financial performance metrics like residual income helps align manager goals with company-wide objectives and improves long-term decision-making.
The 15-4 Application Problem offers a rich, real-world scenario to apply concepts like ROI and residual income, making it a vital part of your accounting education. By mastering this problem, you’re learning how to critically evaluate performance in a decentralized organization—and how to make smarter, data-backed decisions.