Business math cases

For consultants, being able to quickly and accurately assess a company's financial health is essential. A solid analysis of the financial situation enables well-informed decisions and strategic recommendations. Accounting, in particular, serves as a crucial tool, providing a clear overview of the company's assets and funding.Unlike the income statement, the balance sheet is a snapshot of the company’s status at a specific point in time. It consists of two sides: assets on one side and liabilities on the other. The asset side shows what the company owns, while the liability side reveals how these assets are funded—either through equity or debt (liabilities). These two sides must always balance: equity + debt (liabilities) = assets (or liabilities = assets). The General Structure of a Balance SheetLet’s take a closer look at the components of a company’s balance sheet:AssetsAssets include all tangible and intangible items a company owns and are listed in the balance sheet by liquidity—how quickly they can be converted to cash.Current Assets: Current assets are cash and other assets that can quickly become cash, like receivables and inventory.Fixed Assets (Long-term Assets): Fixed assets includes both tangible and intangible assets, such as buildings, machinery, trademarks, or patents. These are often long-term investments and less liquid but essential for daily operations.Liabilities and EquityLiabilities and equity show how a company’s assets are funded.Short-term Liabilities: These are obligations, such as supplier payments, due within a short period.Long-term Liabilities: Typically loans or other long-term debts with more favorable terms.Equity: This represents the owners’ capital, including the initial investment and retained earnings.Sample Balance Sheet: AssetsAmountLiabilities & EquityAmountCurrent Assets Liabilities Cash$100,000Accounts Payable$200,000Accounts Receivable$200,000Short-term Debt$400,000Inventory$1,500,000Long-term Loans$500,000Prepaid Expenses$50,000  Fixed Assets Equity Equipment$500,000Share Capital$1,500,000Land$50,000Retained Earnings$100,000Property$250,000  Goodwill$50,000  Total Assets$2,700,000Total Liabilities & Equity$2,700,000 Both sides of the sheet must balance, with assets equaling the total of liabilities and equity at $2,700,000. This balance sheet example gives a clear view of a company’s financial position at a specific point in time.A company’s assets are listed on the left side, while liabilities and equity are on the right. Both sides must balance, meaning the total assets should equal the total of liabilities and equity. This structure is the foundation of double-entry bookkeeping, where every transaction requires two entries—one on the asset side and a corresponding one on the liability/equity side. This ensures the balance sheet always stays balanced and every financial movement is accurately recorded. Cash Flow Statement and Income StatementTo get a complete view of a company’s financial health, the balance sheet is analyzed alongside the cash flow statement and income statement. While the balance sheet provides a snapshot of assets and funding, the income statement reveals profitability, and the cash flow statement gives insight into actual cash movements. Using relevant KPIs (Key Performance Indicators), these data points can be structured and compared against similar companies, providing valuable insights into financial performance and efficiency. This process, known as benchmarking, highlights strengths and weaknesses in a competitive context. Key Financial Analysis Ratios1. Liquidity Ratios: Liquidity Ratios indicate whether a company can reliably meet its short-term liabilities. Strong liquidity suggests financial stability and reduces the risk of cash flow shortages—a critical factor for investors and lenders. Cash Ratio: This ratio shows if cash and easily liquidated securities are sufficient to cover short-term liabilities. It is calculated by dividing cash and liquid securities by short-term liabilities. A ratio of 1 or higher is considered good, as it indicates the company can fully cover its short-term debt with immediately available funds. Quick Ratio: The Quick Ratio is calculated by dividing current assets—excluding inventory—by short-term liabilities. This ratio considers only assets that can be quickly converted to cash, such as receivables and cash equivalents, as inventory is often harder to liquidate in the short term. An ideal Quick Ratio is 1 or higher, indicating that the company can cover its short-term debts without relying on inventory sales. Working Capital Ratio: The Working Capital Ratio is calculated by dividing current assets by short-term liabilities. It indicates whether the company has enough short-term assets to cover its short-term debts. A ratio above 1 is seen as positive, as it shows the company has more current assets than short-term liabilities, indicating good financial health and sufficient liquidity to meet ongoing obligations. 2. Debt-to-Equity Ratios: The Debt-to-Equity Ratio measures the proportion of debt to equity, indicating how heavily a company is financed through debt. A high Debt-to-Equity Ratio suggests a stronger reliance on debt financing, which can mean higher risks but also greater financial leverage for growth projects.Debt Ratio: The Debt Ratio is calculated by dividing total debt by total assets and expressing the result as a percentage. This ratio shows the extent to which the company relies on debt to finance its assets. A lower Debt Ratio is generally viewed positively, as it suggests a greater portion of assets is financed through equity, indicating a more stable financial foundation. Leverage Ratio: Leverage represents the ratio of liabilities to equity and reflects how much the company relies on borrowed capital to finance its growth. High leverage can increase potential returns but also raises risk, as the company becomes more dependent on creditors. Price-to-Book (P/B) Ratio: The Price-to-Book Ratio indicates whether the company is over- or undervalued by the market. A P/B Ratio above 1 suggests that the market values the company higher than its book value, which could imply a positive outlook or strong investor confidence. Balance Sheet Analysis and Interpretation in Case InterviewsIn consulting case interviews, a solid understanding of balance sheet analysis is essential. You’ll need to quickly assess a company’s financial strengths and weaknesses to provide strategic recommendations based on the balance sheet and other financial data. Key balance sheet items can offer valuable insights into a company.What You Can Read from the Assets:Cash: A high cash balance may indicate strong financial performance, but can also suggest the company is waiting for the right investment opportunities.Inventory: Large inventories can tie up capital and increase storage costs. Growing inventory levels may also signal declining sales.Accounts Receivable: The faster a company collects receivables, the better, as this minimizes the risk of bad debts.Long-term Assets: This includes assets like property and machinery, which are often essential for operations but harder to liquidate. The level of long-term assets varies significantly across industries.What You Can Read from the Liabilities and Equity:Short-term Liabilities: These are usually manageable, but they can pose a risk during cash flow shortages if the company struggles to meet them on time.Long-term Liabilities: Loans and debt can offer tax benefits, but high interest costs and debt levels may threaten financial stability.A balance sheet should always be analyzed in the context of the industry and company strategy, as asset and financing structures can vary greatly. Capital-intensive industries, like manufacturing, often have high levels of long-term assets, while service companies typically have a lighter balance sheet structure. The level of debt also depends on the industry: Companies with stable cash flows often use more debt, while those in volatile industries rely more on equity to maintain flexibility. Key Takeaways for Balance Sheet AnalysisFundamental Importance: The balance sheet provides a snapshot of a company’s financial position and forms the basis for strategic consulting decisions.Asset and Liability Analysis: Assets (cash, inventory, long-term investments) and liabilities (short- and long-term debt) offer insights into a company’s liquidity and financing structure.Key Ratios for Evaluation: Ratios like the Cash Ratio, Quick Ratio, and Debt Ratio help assess financial stability and compare the company to its peers (benchmarking).Role of Equity: Equity reflects financial independence and shows how well a company is protected against risks.Relevance in Case Interviews: In case interviews, you must be able to quickly and accurately analyze balance sheets to assess a company’s financial strength and make informed recommendations.

The income statement, also known as the profit and loss statement (P&L), provides a summary of a company's annual revenues, costs, and profits/losses. It is one of the three key financial documents, alongside the balance sheet and cash flow statement.The income statement records revenues and expenses at the time they are incurred (accrual accounting). For example, an invoice appears in a company's income statement on the day it is generated, regardless of when the payment is made. In contrast, in the cash flow statement, an expense is recorded only when the payment is actually made.Example:Suppose a company sells products worth €100,000 and receives a bill for material costs of €40,000. In the income statement, the revenue of €100,000 is recorded at the time of the sale, and the material costs of €40,000 appear simultaneously. Key Terms in the Income StatementOperating revenue: All revenue generated from the regular business operations of a company.Operating costs: These are subdivided into:COGS (Cost of Goods Sold): Costs directly incurred from producing goods, such as material and labor costs.SGA (selling, general and administrative costs): Costs that cannot be easily attributed to a single product, such as general advertising expenses.Gross profit: Operating revenue minus operating costs.Non-operating revenue and costs: Income and expenses not related to the main business activity, such as revenue from selling real estate or legal costs.Depreciation: The reduction in value of assets, such as outdated machinery.Interest: Costs of debt, which are listed on the balance sheet.Taxes: Taxes paid on EBT (Earnings Before Tax).💡Prep tip: Need to freshen up your mental math skills? Try out our Mental Math Tool. Role of the Income Statement in Consulting and Case InterviewsThe income statement is an important tool for analyzing a company’s profitability. In consulting projects and case interviews, various financial ratios play a crucial role in gaining deeper insights into a company's financial condition and performance.Analysis of Financial Ratios:Gross profit margin: This metric indicates the profitability of the core business by considering only operating revenue, COGS, and SGA. A high gross profit margin suggests that the company produces efficiently and manages its costs well.Operating margin: This includes non-operating costs and revenues, as well as depreciation. This metric provides a more comprehensive view of the company’s profitability.Net profit margin: This metric takes into account all costs, including interest and taxes, and is an indicator of the overall profitability of the company.By comparing the gross margin and the net profit margin, consultants can draw conclusions about the causes of variations. If the net profit margin differs while the operating margin remains stable, this indicates that differences in tax and interest payments are the cause. Case Example💡To make the whole process of presenting the income statement and its relevance for case interviews clearer, we illustrate this calculation using an example case from Oliver Wyman.Case PromptTrainCo is a manufacturer of rolling stock, or trains, with production sites in three European countries. The company has seen declining profitability over the past years; however, they are currently in a very good position to bid for and win a big contract for regional trains for a Swiss national rail company. They have asked you advise to them on whether they should place a bid for the contract. Given InformationSelling price per train: €21.0 millionVariable costs per train:Material costs: €15.2 millionLabor costs: €3.9 millionFixed costs for the facility in Switzerland:Re-tooling investment: €16.0 millionAnnual fixed costs (20% of the investment): €3.2 million per yearDismantling costs: €2.0 millionProduction: 30 trains over 6 years (5 trains per year)Variable profit margin per train: €1.9 millionNow, let’s create an Income Statement for the entire project duration to calculate the total profit.Calculations1. Total Revenue:Revenue per train = €21.0 millionTotal revenue for 30 trains = 30 * €21.0 million = €630.0 million2. Total Costs:a. Variable Costs:Material costs for 30 trains = 30 * €15.2 million = €456.0 millionLabor costs for 30 trains = 30 * €3.9 million = €117.0 millionTotal variable costs = €456.0 million + €117.0 million = €573.0 millionb. Fixed Costs:Re-tooling investment = €16.0 million (one-time)Fixed costs per year for 6 years = 6 * €3.2 million = €19.2 millionDismantling costs = €2.0 million (one-time)Total fixed costs = €16.0 million + €19.2 million + €2.0 million = €37.2 million3. Total Costs (Variable + Fixed Costs):Total costs = €573.0 million + €37.2 million = €610.2 million4. Profit:Total Revenue = €630.0 millionTotal Costs = €610.2 millionTotal Profit = €630.0 million - €610.2 million = €19.8 million5. Profit Margin:Profit Margin = (Total Profit / Total Revenue) * 100 = (€19.8 million / €630.0 million) * 100 = 3.1%ResultThe calculated profit margin is 3.1%. However, the case specifies a minimum margin of 10%, which means that the current plan for production in Switzerland does not meet the profitability requirements.The company must therefore reduce costs or increase revenue to achieve the 10% profit margin.⚠️ We have simplified the case to illustrate the scheme. In the real case, other factors, such as the possibility of changing location, are also taken into account. Can you solve the entire case? Find out here! Key TakeawaysThe income statement summarizes a company's revenues and expenses over a specific period, using accrual accounting to record transactions when incurred.Key components include operating revenue, operating costs (COGS and SGA), gross profit, and net profit, which together inform financial health and performance.Financial ratios derived from the income statement, such as gross profit margin and net profit margin, are critical for analyzing profitability and operational efficiency.Variations in these margins can indicate underlying issues, such as changes in tax strategies or interest expenses, making the income statement essential for strategic decision-making in consulting and case interviews.