Vertical analysis, also known as common-size analysis, involves expressing each item in a financial statement as a percentage of a base amount within the same period. Comparing net profit to sales is a classic example of vertical analysis, as it evaluates the profitability margin relative to total revenue.

The Times Interest Earned ratio, also known as the interest coverage ratio, measures how many times a company can pay its interest expenses from its operating income. It is a critical indicator of solvency and financial risk, showing the margin of safety a company has to meet its debt obligations.

Residual income is the net operating income that an investment earns above the minimum required return on its operating assets. The formula is: Residual Income = Operating Income - (Total Investment * Required Rate of Return). First, calculate the required return: $2,650,000 * 0.13 = $344,500. Then, subtract this from the operating income: $375,000 - $344,500 = $30,500. This metric helps in evaluating performance beyond simple accounting profit.

A higher inventory turnover ratio is generally interpreted as a positive indicator of operational efficiency. It suggests that a company is successfully managing its stock levels by selling goods rapidly, which minimizes holding costs and demonstrates strong demand for the company's products.

While gross profit rate is important, the quick ratio is a liquidity measure, not a profitability measure. Investors focusing on future profitability are typically more concerned with sales growth and operating margins. Note: This answer is provided as per the source, though gross profit rate is generally considered highly relevant to profitability analysis.

Cost of Goods Sold (COGS) is 75% of $100,000 = $75,000. Average inventory is ($10,000 + $15,000) / 2 = $12,500. Inventory turnover = COGS / Average Inventory = $75,000 / $12,500 = 6 times.

The DuPont analysis model demonstrates that Return on Investment (ROI) can be broken down into two distinct components: profitability, measured by the return on sales (net profit margin), and efficiency, measured by investment turnover (asset turnover). Multiplying these two ratios together yields the overall Return on Investment, allowing managers to identify whether performance issues stem from profit margins or asset utilization.

The inventory turnover ratio measures how many times a company's inventory is sold and replaced over a period. It is calculated by dividing the Cost of Goods Sold (CGS) by the average inventory or closing inventory. This ratio helps assess the efficiency of inventory management.

Return on investment (ROI) is a performance measure used to evaluate the efficiency of an investment. It is frequently referred to interchangeably as the accrual accounting rate of return or simply the accounting rate of return. Both terms describe the ratio of net income to the cost of the investment, providing a standardized way to compare profitability across different capital projects or business units.

A low ROI indicates that a company is not generating sufficient profit relative to the capital invested. This often stems from either inefficient management of operational resources or holding excessive assets that do not contribute effectively to revenue generation.