Business math cases

This type of case can either be a subset of an M&A case, in which you need to know a company's worth before purchasing, or a standalone case (rare). For instance, “How much is Pfizer worth today?” In strategy consulting, these questions are rather rarely seen. However, cases where you do need to value something usually start with “How much would you pay for company XY?” The Most Common Methods of Valuing Are the Discounted Cash Flow (DCF) and the Industry Multiple MethodAs these are still case studies meant to fit in an interview round, the interviewer will very likely not ask you to perform an exact and comprehensive valuation analysis. Instead, you may be required to estimate the worth of a product, patent, or a service. You may also have to judge if an offered price is reasonable. Discounted Cash Flow methodThe first valuation method is the Discounted Cash Flow method. This method shows how much money you would have in your savings account at a certain interest rate in order to provide you with the same annual cash flow generated by the company that is being evaluated.Here, you simply divide projected annual cash flows by a discounted rate (or interest rate). Of course, the discount rate of your savings account will be much lower than that of an investment in a company. This is so because the risk you take putting your money in a savings account is much lower than the risk of investing in a company.👉 For more details on how to use the Discounted Cash Flow (DCF) method, have a look at our Net Present Value (NPV) lesson Industry Multiple MethodThe DCF method is limited since it does not take into account additional dimensions other than money (unless you quantify those dimensions into the future cash flows).Football teams, for instance, are often overvalued compared to their generated returns. For such cases, there is another method called the industry multiple method.This method allows you to value a firm by using a metric known of this company and multiplying it by the associated industry multiple. This can be done for similar players in the industry to assess their relative valuations using benchmarking.An example of a multiple ratio is the price-to-book ratio (P/B). This multiple is the ratio of the actual firm valuation (based for example on M&A deals) and the book value of the same firm (value of its assets, which can be found in the balance sheet). If a firm’s assets added up to 200 million, and it was sold for 100 million, the ratio is 0.5 (100 million/200 million).Do this for a set of representative industry players, take the average and you get the average industry multiple. Finally, you multiply the industry multiple with the value of the assets.Other commonly used ratios are the price-earnings ratio (P/E ratio or PER) and the EBITDA ratio.Since you will not be required to calculate the value of an investment on too high a level of detail, it is not necessary to learn values for different interest rates or industry multiples by heart. However, to give you an idea about orders of magnitude:A good guess for an industry multiple is EBITDA*10.Good guesses for interest rates would range from 3% (inflation) to up to 20% for highly speculative investments. Key takeawaysUse the Discounted Cash Flow (DCF) method to value a firm based solely on its expected profits.Use the industry multiple method to double-check if the DCF valuation is reasonable. Sometimes other aspects need to be factored in like brand value, customer loyalty, liabilities, etc.There are several types of industry multiples to choose from. For more precise valuation, choose more types of industry multiples. Practice M&A cases to optimize your valuation-techniques:👉 tkMC Case: Portfolio optimization of a holding company👉 Bain Case: Old Winery

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.