Master Horizontal Vertical Analysis: A Complete Guide

Financial statements, such as those scrutinized by the SEC (Securities and Exchange Commission), provide the raw data for performing horizontal vertical analysis. Corporate finance professionals routinely leverage horizontal vertical analysis to assess a company’s performance over time. This analysis, often facilitated by tools like Microsoft Excel, offers critical insights into trends and variances. Mastering horizontal vertical analysis empowers analysts to make informed decisions and advise stakeholders effectively on the financial health of the business.

Financial statement analysis is the bedrock of sound investment and credit decisions. Two cornerstones of this analysis are horizontal and vertical analysis. These techniques offer distinct yet complementary perspectives on a company’s financial health. They dissect financial data to reveal underlying trends and proportional relationships that are often obscured in raw numbers.

Defining Horizontal Analysis: Tracking Changes Over Time

Horizontal analysis, also known as trend analysis, focuses on the changes in financial statement items across different reporting periods.

Essentially, it compares financial data from one period to another. It highlights increases or decreases in specific line items. This could be year-over-year, quarter-over-quarter, or across any chosen timeframe.

The primary goal is to identify significant trends and patterns that indicate a company’s growth, decline, or stability. By calculating the percentage change in key financial metrics, analysts can quickly pinpoint areas of improvement or concern. For example, a consistent increase in revenue may signal strong market demand. A sharp rise in operating expenses could warrant further investigation.

Defining Vertical Analysis: Understanding Proportional Relationships

In contrast to horizontal analysis, vertical analysis, also known as common-size analysis, examines the proportional relationship of items within a single financial statement.

It expresses each item as a percentage of a base figure. For the income statement, the base figure is typically revenue. For the balance sheet, it’s usually total assets.

This normalization allows for easy comparison of companies of different sizes. It helps identify how different components contribute to the overall financial picture. For example, vertical analysis of the income statement reveals the percentage of revenue consumed by the cost of goods sold or operating expenses. Analyzing the balance sheet highlights the proportion of assets financed by debt versus equity.

The Importance of Horizontal and Vertical Analysis

Both horizontal and vertical analysis are essential tools for a comprehensive financial statement review. When used in tandem, they provide a powerful framework for understanding a company’s financial performance and position.

Gaining a Comprehensive View

Horizontal analysis reveals trends over time. Vertical analysis provides a snapshot of the current financial structure. Combining these techniques offers a richer understanding of a company’s financial narrative.

For instance, a company might show revenue growth (horizontal analysis). Vertical analysis might reveal that its cost of goods sold is increasing as a percentage of revenue. This could indicate declining profitability or increased production costs.

Assisting Investors and Creditors

Investors use these analyses to assess a company’s growth potential, profitability, and risk profile. This informs their investment decisions. Creditors rely on these analyses to evaluate a company’s ability to repay its debts. This helps them determine the creditworthiness of potential borrowers.

By understanding the trends and proportions within a company’s financial statements, both investors and creditors can make more informed and prudent decisions. They can more accurately assess risk and potential return.

Financial statement analysis provides a powerful lens through which to evaluate a company’s financial performance and position. Horizontal and vertical analyses are two essential tools for unlocking the insights hidden within these statements. Before diving into the mechanics of these analyses, it’s crucial to understand the underlying financial statements themselves.

Understanding the Foundation: Financial Statements

Financial statements are the bedrock of business analysis. They provide a structured representation of a company’s financial performance (income statement), financial position (balance sheet), and cash flows (cash flow statement). These statements, prepared in accordance with accounting standards, offer a standardized view of a company’s financial activities.

The Role of Financial Statements in Business Analysis

Financial statements are the primary source of data for horizontal and vertical analysis. They allow analysts to:

• Assess a company’s profitability, solvency, and liquidity.

• Compare a company’s performance over time or against its competitors.

• Identify trends and potential risks or opportunities.

• Make informed investment and credit decisions.

• Evaluate management’s stewardship of the company’s resources.

Deep Dive into the Income Statement

The income statement, sometimes called the profit and loss (P&L) statement, summarizes a company’s financial performance over a specific period, typically a quarter or a year.

Significance of Income Statement Line Items

Key line items in the income statement include:

• Revenue: Represents the income generated from the company’s primary business activities. It’s the top line and a crucial indicator of sales and market demand.

• Cost of Goods Sold (COGS): The direct costs associated with producing goods or services sold.

• Gross Profit: Revenue less COGS, representing the profit earned before operating expenses.

• Operating Expenses: Expenses incurred in running the business, such as salaries, rent, and marketing expenses.

• Operating Income: Gross profit less operating expenses, reflecting the profitability of the company’s core operations.

• Net Income: The bottom line, representing the company’s profit after all expenses, including interest and taxes.

Horizontal Analysis of the Income Statement

Horizontal analysis of the income statement involves comparing these line items across different periods. For example, comparing revenue, COGS, and operating expenses year-over-year can reveal:

• Growth trends: Is revenue increasing or decreasing?

• Efficiency: Is the company managing its costs effectively?

• Profitability: Is the company’s profit margin improving or declining?

A significant increase in revenue combined with a decrease in operating expenses could signal improved efficiency and profitability. Conversely, a decline in revenue coupled with rising costs might indicate challenges in the market or operational inefficiencies.

Vertical Analysis of the Income Statement

Vertical analysis of the income statement expresses each line item as a percentage of revenue. This is also referred to as a common-size income statement. For instance:

• COGS as a percentage of revenue indicates the cost of producing goods relative to sales.

• Operating expenses as a percentage of revenue reveals how efficiently the company is managing its overhead.

• Net income as a percentage of revenue (the net profit margin) shows the company’s overall profitability.

Vertical analysis allows for easy comparison of companies of different sizes, as it normalizes the data based on revenue. It helps identify which expenses are consuming a significant portion of revenue and warrant closer scrutiny.

Exploring the Balance Sheet

The balance sheet provides a snapshot of a company’s assets, liabilities, and equity at a specific point in time. It follows the fundamental accounting equation: Assets = Liabilities + Equity.

Impact of Balance Sheet Components on Financial Health

• Assets: Resources owned by the company.
  Examples include cash, accounts receivable, inventory, and property, plant, and equipment (PP&E). The composition of assets reveals how the company invests its resources.

• Liabilities: Obligations owed to others. Examples include accounts payable, salaries payable, and debt.
  High levels of debt can increase financial risk.

• Equity: The owners’ stake in the company. It represents the residual interest in the assets after deducting liabilities.
  Equity reflects the company’s net worth.

Horizontal Analysis of the Balance Sheet

Horizontal analysis of the balance sheet involves comparing asset, liability, and equity balances across different periods. This reveals trends in:

• Asset growth: Is the company expanding its asset base?

• Debt levels: Is the company increasing its reliance on debt financing?

• Equity accumulation: Is the company retaining earnings and building equity?

For instance, a significant increase in accounts receivable might indicate a slowdown in collections or potential credit risk. A sharp rise in debt could signal increased financial leverage.

Vertical Analysis of the Balance Sheet

Vertical analysis of the balance sheet expresses each item as a percentage of total assets. This provides insights into:

• The composition of assets: What proportion of assets are current vs. long-term?

• The capital structure: What proportion of assets are financed by debt vs. equity?

A high percentage of current assets might indicate strong liquidity. A high percentage of debt financing could suggest increased financial risk.

Analyzing the Cash Flow Statement

The cash flow statement summarizes the movement of cash both into and out of a company during a specific period. It categorizes cash flows into three activities: operating, investing, and financing.

Relevance of Operating, Investing, and Financing Activities

• Operating Activities: Cash flows generated from the company’s normal business operations. This is a key indicator of a company’s ability to generate cash from its core business.

• Investing Activities: Cash flows related to the purchase and sale of long-term assets, such as property, plant, and equipment (PP&E).

• Financing Activities: Cash flows related to debt, equity, and dividends.

Horizontal Analysis of the Cash Flow Statement

Horizontal analysis of the cash flow statement involves tracking trends in cash flows from operating, investing, and financing activities over time. For example:

• Consistent positive cash flow from operations suggests a healthy and sustainable business model.

• Significant cash outflows for investing activities might indicate expansion or acquisition plans.

• Cash inflows from financing activities could signal the need for external funding.

Key Insights from Individual Line Items

Analyzing individual line items within each category can provide further insights. For example:

• An increase in cash receipts from customers indicates strong sales.

• A decrease in cash payments to suppliers might suggest improved inventory management.

• Increased borrowing could reflect expansion plans or financial distress.

Performing Horizontal Analysis: A Step-by-Step Guide

After understanding the financial statements, we can now delve into the practical application of horizontal analysis. This technique provides a clear view of how a company’s financial performance evolves over time, enabling insightful comparisons and identification of key trends. Let’s explore a step-by-step guide to effectively perform horizontal analysis.

Selecting the Base Year and Current Year for Comparison

The foundation of horizontal analysis lies in choosing appropriate periods for comparison. The base year serves as the starting point against which subsequent years are measured.

The current year is the period you’re comparing against the base year. The selection of these years is crucial for meaningful analysis.

Criteria for Selection

• Relevance: The periods should be relevant to the analysis you’re conducting. Comparing periods affected by significantly different economic conditions might skew the results.
• Consistency: Ensure the accounting methods used are consistent across the periods being compared. Changes in accounting policies can distort the analysis.
• Representativeness: The base year should be a typical or representative period for the company’s performance, avoiding periods of significant abnormality if possible.

Calculating Percentage Changes

Once the base and current years are selected, the next step involves calculating the percentage change for each line item in the financial statements.

This calculation quantifies the extent of the change from the base year to the current year.

The Formula

The formula for calculating percentage change is:

Percentage Change = ((Current Year Value - Base Year Value) / Base Year Value)

**100

Practical Example

Let’s say a company’s revenue was \$1,000,000 in the base year and \$1,200,000 in the current year.

The percentage change in revenue would be:

((\$1,200,000 - \$1,000,000) / \$1,000,000)** 100 = 20%

This indicates a 20% increase in revenue from the base year to the current year.

Interpreting the Results

Calculating percentage changes is only half the battle. The real value of horizontal analysis lies in interpreting these changes to identify significant trends and anomalies.

Identifying Significant Trends

Large percentage increases or decreases warrant further investigation. A significant increase in revenue might indicate successful expansion efforts.

Conversely, a sharp decline in net income could signal operational inefficiencies or increased competition.

Spotting Anomalies

Anomalies are unusual or unexpected changes that deviate from established patterns. These could be one-time events or potential indicators of underlying problems.

Investigating anomalies can reveal hidden issues or opportunities that might otherwise go unnoticed.

Example Using Comparative Financial Statements

Comparative financial statements present financial data for multiple periods side-by-side, facilitating horizontal analysis.

Illustration

Imagine a comparative income statement showing the following data for two years:

Line Item	Year 1 (Base)	Year 2 (Current)	Percentage Change
Revenue	\$2,000,000	\$2,500,000	25%
Cost of Goods Sold	\$1,200,000	\$1,600,000	33.33%
Operating Expenses	\$500,000	\$600,000	20%
Net Income	\$300,000	\$300,000	0%

Analysis

While revenue increased by 25%, the cost of goods sold increased by a higher percentage (33.33%), resulting in stagnant net income.

This suggests that the company’s profitability is being negatively impacted by rising costs, requiring further scrutiny.

Limitations of Horizontal Analysis

While horizontal analysis is a valuable tool, it’s important to be aware of its limitations.

Potential Misinterpretations

• Base Year Distortions: If the base year is not representative, the percentage changes may be misleading.
• Ignoring External Factors: Horizontal analysis focuses on internal trends and may not account for external factors (economic conditions, industry changes) that influence performance.
• Scale of Operations: Percentage changes can be misleading when dealing with small numbers. A small absolute change can result in a large percentage change, which may not be material.

By understanding these limitations, you can use horizontal analysis more effectively and avoid potential misinterpretations.

Performing Vertical Analysis: A Detailed Walkthrough

Having explored how horizontal analysis unveils trends across different periods, we now turn our attention to vertical analysis. This technique offers a different perspective, focusing on the internal structure of a financial statement at a specific point in time. By understanding the proportional relationship between individual items, we can gain insights into a company’s efficiency, profitability, and financial stability. Let’s delve into the practical steps involved in performing vertical analysis.

Choosing the Base Figure

The cornerstone of vertical analysis is the selection of an appropriate base figure. This figure serves as the benchmark against which all other items in the financial statement are compared. The choice of the base figure depends on the specific financial statement being analyzed.

For the income statement, net revenue (or sales) is almost universally used as the base. This allows you to express each line item, such as the cost of goods sold or operating expenses, as a percentage of total revenue.

On the balance sheet, total assets are typically used as the base figure. This enables analysis of the proportion of current assets, fixed assets, and other assets that constitute the company’s asset base. Similarly, each liability and equity item can be expressed as a percentage of total assets, providing insights into the company’s capital structure.

The cash flow statement is less commonly subjected to vertical analysis, but when it is, total revenue or total cash inflows might be used as the base. However, its application on the cash flow statement is less straightforward and less common than on the income statement and balance sheet.

The key is to select a base figure that provides a meaningful context for understanding the relative importance of other items in the statement.

Calculating Percentage of Base

Once the base figure is selected, the next step involves calculating the percentage of base for each line item. This calculation quantifies the proportion of each item in relation to the base.

The formula for calculating the percentage of base is straightforward:

Percentage of Base = (Line Item Value / Base Figure) 100

**

For example, if a company has net revenue of $1,000,000 and the cost of goods sold is $600,000, the percentage of base for the cost of goods sold would be:

($600,000 / $1,000,000) 100 = 60%**

This indicates that the cost of goods sold represents 60% of the company’s revenue.

Let’s consider another example using the balance sheet. If total assets are $5,000,000 and accounts receivable are $500,000, the percentage of base for accounts receivable would be:

($500,000 / $5,000,000) 100 = 10%*

This indicates that accounts receivable represent 10% of the company’s total assets.

Performing these calculations for all relevant line items provides a comprehensive view of the financial statement’s internal structure.

Interpreting the Results

The real power of vertical analysis lies in interpreting the calculated percentages. These percentages reveal the proportional relationship of each item to the base figure, allowing for meaningful comparisons and the identification of key trends.

For the income statement, analyzing the percentage of base for expenses can highlight areas where costs are disproportionately high. For example, a significant increase in the percentage of operating expenses relative to revenue could indicate inefficiencies in the company’s operations.
A higher percentage may point towards cost-cutting measures that could improve profitability.
Furthermore, monitoring changes in the gross profit margin (revenue less cost of goods sold, expressed as a percentage of revenue) can provide insights into the company’s pricing strategy and cost management effectiveness.

On the balance sheet, analyzing the percentage of base for different asset categories can reveal how a company allocates its resources. A high percentage of current assets may indicate strong liquidity, while a high percentage of fixed assets may suggest a capital-intensive business model.
It could also mean that the company is unable to effectively convert its current assets to cash.

Analyzing the percentage of base for liabilities and equity can provide insights into the company’s capital structure and financial leverage. A high percentage of debt may indicate higher financial risk, while a high percentage of equity may suggest a more conservative financial approach.

Identifying significant deviations from industry benchmarks or historical trends is crucial. These deviations may signal potential problems or opportunities that warrant further investigation.

Using the Current and Previous Year

While vertical analysis focuses on a single period, it becomes even more powerful when used to compare the current year’s percentages to those of the previous year. This allows you to identify shifts in the company’s financial structure and performance over time.

For example, if the percentage of cost of goods sold relative to revenue has increased significantly from the previous year, it could indicate rising input costs or inefficiencies in production. Conversely, a decrease in the percentage of operating expenses relative to revenue could suggest improved operational efficiency or successful cost-cutting measures.

By comparing vertical analyses across multiple periods, you can gain a deeper understanding of how a company’s financial structure and performance are evolving. This can help you identify potential risks and opportunities that may not be apparent from analyzing a single period in isolation.

Limitations of Vertical Analysis

Despite its usefulness, vertical analysis has certain limitations that must be considered when interpreting the results.

Firstly, vertical analysis only provides insights into the internal structure of a financial statement. It does not provide any information about the overall size or growth of the company. For example, a company may have a consistent percentage of operating expenses relative to revenue, but if the company’s revenue is declining, the absolute amount of operating expenses may still be a cause for concern.

Secondly, vertical analysis can be affected by changes in accounting policies or practices. If a company changes its accounting methods, it can distort the percentages and make it difficult to compare results across different periods.

Thirdly, vertical analysis does not account for external factors that may be affecting the company’s performance. Economic conditions, industry trends, and competitive pressures can all have a significant impact on a company’s financial results, and these factors are not explicitly considered in vertical analysis.

Finally, vertical analysis is most effective when used in conjunction with other analytical techniques, such as horizontal analysis, ratio analysis, and industry comparisons. By combining different analytical approaches, you can gain a more comprehensive and nuanced understanding of a company’s financial performance and position.

Combining Horizontal and Vertical Analysis: A Powerful Approach

Individually, horizontal and vertical analysis offer valuable insights into a company’s financial standing. However, their true power is unlocked when used in tandem. By weaving together the insights from both techniques, analysts can achieve a far more comprehensive understanding of a company’s financial performance and trajectory. This holistic approach allows for more informed decision-making and a sharper focus on both potential risks and promising opportunities.

Creating a Holistic View of Financial Performance

Combining horizontal and vertical analysis provides a richer, more nuanced perspective than either technique can offer alone. Horizontal analysis highlights trends over time, revealing whether specific line items are increasing or decreasing.

Vertical analysis, on the other hand, reveals the internal structure of a financial statement at a specific point in time, showing the relative importance of different items. By integrating these two perspectives, analysts can answer critical questions.

For example, is an increase in revenue reflected in a corresponding increase in net income, or are rising costs eating into profits? Is a growth in assets funded by increasing debt or by equity? These are the types of critical questions that can be easily answered by using both.

This integrated approach goes beyond simply identifying changes; it helps to explain why those changes are occurring and their impact on the company’s overall financial health.

Identifying Potential Red Flags and Opportunities

The synergy of horizontal and vertical analysis is particularly useful for spotting both red flags and opportunities that might be missed when using the techniques in isolation.

For example, a company might show consistent revenue growth (as revealed by horizontal analysis), which initially appears positive. However, vertical analysis might reveal that the cost of goods sold is increasing as a percentage of revenue, squeezing profit margins.

This combined insight suggests a potential problem with the company’s cost management or pricing strategy.

Conversely, a company might appear to have stagnant revenue growth. But a simultaneous vertical analysis could reveal that the company has significantly reduced its operating expenses as a percentage of revenue.

This could indicate improved efficiency and potentially higher profitability in the future. Such a finding can reveal a hidden opportunity that a simple horizontal analysis might have overlooked.

Enhancing Financial Forecasting and Decision-Making

The enhanced understanding gained from combining horizontal and vertical analysis directly translates into better financial forecasting and more informed decision-making.

By understanding both the trends (horizontal) and the structural relationships (vertical), analysts can create more accurate projections of future performance. For instance, forecasts might incorporate assumptions about revenue growth, cost of goods sold as a percentage of revenue, and the impact of changes in capital structure.

This more detailed analysis enables management to make better strategic decisions. It can inform decisions related to investments, cost control, pricing, and capital allocation.

Investors and creditors, armed with this comprehensive view, can also make more informed judgments about the company’s prospects and risk profile.

Leveraging Trend Analysis

Trend analysis involves examining data patterns over time to predict future outcomes. When horizontal and vertical analyses are combined, trend analysis becomes much more powerful.

By tracking changes in both absolute amounts (horizontal analysis) and proportional relationships (vertical analysis) over several periods, analysts can identify consistent patterns and deviations.

For example, consistently increasing debt-to-equity ratio (identified via vertical analysis) coupled with increasing interest expense (identified via horizontal analysis) could indicate a dangerous trend towards higher financial risk.

Conversely, a consistent improvement in gross profit margin (vertical analysis) combined with steady revenue growth (horizontal analysis) may point to a strong and sustainable competitive advantage. Identifying these trends early allows for proactive decision-making and risk mitigation.

Complementing with Ratio Analysis

While horizontal and vertical analyses provide a broad overview of financial performance, they can be further enhanced by incorporating ratio analysis. Ratio analysis involves calculating and interpreting various financial ratios that provide insights into a company’s profitability, liquidity, solvency, and efficiency.

For example, vertical analysis might reveal that a company’s inventory constitutes a large percentage of its total assets. Combining this with ratio analysis by calculating the inventory turnover ratio, you can assess how efficiently the company is managing its inventory.

Similarly, horizontal analysis might show a significant increase in accounts receivable. By calculating the accounts receivable turnover ratio and days sales outstanding, you can determine whether the company is collecting its receivables in a timely manner.

Using ratio analysis in conjunction with horizontal and vertical analysis allows for a more in-depth and nuanced evaluation of a company’s financial condition and performance. It provides a deeper understanding of the underlying drivers of financial results and helps to identify potential areas of concern or opportunity.

Practical Applications and Real-World Examples

The true value of horizontal and vertical analysis lies in their application to real-world financial scenarios. These techniques aren’t just theoretical exercises; they are practical tools used daily by investors, analysts, and lenders to make informed decisions and assess financial health. Let’s explore some concrete examples of how these methods are employed in various contexts.

Investment Decisions: Making Informed Choices

Investors constantly seek an edge in understanding a company’s prospects. Horizontal and vertical analysis provide critical insights that go beyond simple net income figures. By examining trends in revenue, expenses, and asset allocation, investors can gain a deeper understanding of a company’s operational efficiency and future growth potential.

For example, an investor might use horizontal analysis to track revenue growth over the past five years. A consistent upward trend could signal a healthy, expanding business.

However, vertical analysis is then used to examine the cost of goods sold (COGS) as a percentage of revenue. If COGS is increasing as a percentage of revenue, it might indicate that the company is losing pricing power or facing rising input costs.

This combination of insights helps the investor evaluate the sustainability of the company’s profitability.

Furthermore, investors use these analyses to assess a company’s debt levels and ability to manage its financial obligations. Examining the balance sheet through both horizontal (changes in debt levels) and vertical (debt as a percentage of total assets) analysis reveals whether the company is becoming overly leveraged, which could increase its risk profile.

Financial Analyst’s Toolkit: Evaluating Company Health

Financial analysts are at the forefront of evaluating the financial health of companies. These professionals use horizontal and vertical analysis extensively to dissect financial statements and provide comprehensive assessments to clients.

These analyses form the bedrock of their evaluation process, providing a structured framework for understanding a company’s performance and position.

By applying these techniques across multiple periods and against industry benchmarks, analysts can uncover key insights into a company’s profitability, efficiency, and solvency.

Vertical analysis is instrumental in comparing a company’s financial structure to its peers. For instance, an analyst might compare a company’s R&D expenditure as a percentage of revenue against the industry average. A significantly higher percentage might indicate a strong focus on innovation.

Conversely, a lower percentage could suggest underinvestment in future growth. Horizontal analysis complements this by revealing how these key ratios have changed over time, providing a view into the company’s strategic priorities and operational effectiveness.

Credit Risk Assessment: Evaluating Creditworthiness

Lenders rely heavily on financial analysis to assess the creditworthiness of potential borrowers. Horizontal and vertical analysis are essential tools in this process, helping lenders understand a company’s ability to repay its debts.

By reviewing the income statement and balance sheet using these techniques, lenders can assess the borrower’s profitability, cash flow generation, and leverage.

For example, a lender will examine the trend in a company’s net income (horizontal analysis) to assess its ability to generate sufficient profits to cover debt payments. At the same time, they’ll analyze the company’s debt-to-equity ratio (vertical analysis) to gauge its financial leverage and risk of default.

Significant increases in debt levels or declining profitability trends could raise red flags and prompt further investigation.

Lenders also use these analyses to identify potential early warning signs of financial distress. A sudden increase in accounts receivable as a percentage of revenue, coupled with a slowdown in inventory turnover, could indicate that the company is struggling to collect payments from customers or is facing difficulties selling its products.

Comparative Company Analysis: Benchmarking Performance

Horizontal and vertical analysis are also invaluable tools for comparing companies within the same industry. By standardizing financial data using vertical analysis, analysts can compare the relative performance and financial structure of different companies, regardless of their size.

For instance, an analyst might compare the gross profit margins of several companies in the retail sector using vertical analysis (gross profit as a percentage of revenue). This allows for a direct comparison of their profitability, even if the companies have vastly different revenue levels.

Horizontal analysis can then be applied to identify which companies are improving their margins over time and which are lagging behind.

This comparative approach helps investors identify undervalued or overvalued companies within an industry. It also provides insights into best practices and potential areas for improvement for companies looking to enhance their financial performance.

By comparing key financial metrics across different companies, analysts can gain a deeper understanding of the competitive landscape and identify which companies are best positioned for future success.

So, that’s the lowdown on horizontal vertical analysis! Hopefully, you’ve got a solid grasp on the basics and are ready to start putting it to use. Good luck analyzing, and remember to always double-check your numbers!