# Case Interview Formulas: 6 Concepts You Need to Know

- Last Updated May, 2023

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- Last Updated May, 2023

Consulting case formulas are the quantitative frameworks used to evaluate real-world business problems. Testing these concepts in your case interview helps your interviewer assess your ability to think critically, analyze data, and communicate effectively. Applying these formulas can help you solve consulting cases, such as market sizing or cost savings.

Here’s the good news: Consulting case interview formulas aren’t like the boring math you learned in school. Instead, it’s all about getting insights that guide business decisions rather than calculating the correct answer to the 4th decimal point. So don’t worry if you weren’t the math whiz in your calculus class!

While the concepts are not particularly complex, you’ll need to be able to do the math calculations efficiently without a calculator or computer. You don’t want your interviewer to wait while you struggle to divide 1000 by 7!

A consultant often works against the clock, juggling multiple tasks and competing deadlines. In such a fast-paced environment, mental math is a skill that can help you estimate the answer, avoid wasting time on low-value work, and, ultimately, solve your client’s problems!

Being able to do mental math isn’t just about efficiency – it’s also about looking competent in front of clients and having productive conversations. After all, clients are paying a lot for your team’s expertise. When a client asks a basic question, you don’t want to frantically search for your calculator or fumble on Excel.

Another reason why this skill is important in consulting is that it allows you to sense-check your answers. Excel formulas can break, databases may be incomplete, and mistakes can happen. By having a solid understanding of mental math and case interview formulas, you can spot errors before they lead you down the wrong path.

Mastering the case interview formula skill also frees up your brain power to focus on the broader answer. Instead of being bogged down by tedious calculations, you can devote more mental bandwidth to analyzing the problem, identifying key insights, and providing recommendations for the client. In other words, developing this skillset allows you to focus on what you enjoy about consulting: problem-solving for real business challenges!

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Let’s dive into the 6 case interview formulas that are common in consulting interviews and how to use them effectively.

Keep in mind that this list is not exhaustive, but it is a good foundation. During the interview, you’ll need to apply these formulas strategically and may need to combine them to solve the client’s problem.

To illustrate the following case interview formulas, we’ll use this problem:

*Our client, SweetCo, is a candy company that manufactures gummies and hard candies. Over the past five years, they’ve noticed a decrease in profitability and have hired us to help them understand what’s wrong and how to fix it.*

One of the most common case interview questions revolves around a company’s profitability. The goal is to figure out whether a company is making money or not, and what it can do to increase its bottom line.

Profit is the amount of money left over after a company has paid all its expenses and collected its revenue. It’s typically calculated over a set period, such as a quarter or a year. The formula is:

**Profit = Revenues – Cost**.

There are two main ways for companies to increase their profits: by bringing in more revenue or by cutting costs.

In the case of SweetCo, their profits have gone down in the last 5 years. To figure out why, we’d need to take a closer look at both their revenues and their costs and see which one is driving the problem.

Revenue, also known as sales, is the total amount of money a company receives from selling its products or services. It’s always measured in terms of currency, such as U.S. dollars or European euros.

To calculate revenue, you’ll need to know the volume of products sold and the price at which they are sold. Depending on what data you have, you can use the formula:

**Revenue = Volume x Price**.

There are 2 types of costs: fixed and variable costs.

**Fixed costs** are expenses that do not change regardless of how much product or service is produced. Examples of SweetCo’s fixed costs include rent and management salaries. These costs do not change if SweetCo increases its candy production (unless it needs a whole new factory).

On the other hand, **variable costs** are expenses that increase with higher sales or production. For SweetCo, these could include costs for sugar, flavoring, and production labor.

To calculate the total cost, you add all costs together:

**Total Cost = Fixed Costs + Variable Costs**.

We recommend reading about the Profitability Framework If you want to learn more.

Profit margin is a metric used to measure how much profit the company makes as a percentage of its revenue:

**Profit Margin % = Profit / Revenue** ** x 100**

This is an essential metric for businesses because it helps them determine their pricing strategies and evaluate their financial health.

SweetCo’s profit margin decreased from 25% to 15% over the last 5 years. This indicates that the company is not operating as efficiently as it could be or that competition in their market is getting more intense. The profit margin is a useful tool to identify areas where the company could potentially improve its profitability.

There are 3 types of profit margins:

**Net profit margin**measures the company’s overall profitability after all expenses, including taxes and interest, have been deducted from the revenue. This is the most common profit margin case interview formula you will use.**Gross profit margin**gives an idea of the profitability of the company’s core operations. It only considers the revenue and the cost of goods sold, which are the expenses incurred to produce the company’s product or service.**Operating profit margin**takes it one step further from the gross profit margin. It also takes into account other operating expenses, such as rent, utilities, etc. It excludes taxes and interest expenses.

Each of these types of profit margins provides a different perspective on a company’s financial performance. For example, if SweetCo’s gross profit margin is decreasing more than the operating profit margin, it may indicate that the costs of candy ingredients are driving the overall profitability problem, rather than fixed costs.

Breakeven, also known as the payback period, is a financial metric that helps companies determine how long it would take to recover their initial investment in a new project or investment. It is usually measured in years and is calculated by:

**Breakeven or Payback Period = Initial Investment / Annual Profit**.

For example, let’s say SweetCo is considering expanding into the chocolate market and building a new factory that costs $2 million. This factory is projected to generate an additional $250,000 in annual profit. Using the breakeven formula, we can calculate that it would take SweetCo 8 years to recoup its initial investment.

It’s important to note that breakeven analysis should not be the only factor considered when making business decisions. Other factors, such as market competition and potential future growth, should also be considered.

In the SweetCo case, improving operating efficiency to lower costs in the existing candy category could be a more feasible option for increasing profits than waiting 8 years to pay back the chocolate factory.

A related concept to breakeven is the return on investment (ROI). This metric helps companies measure their investment’s effectiveness in generating additional profit.

Return on investment helps businesses determine whether or not an investment is worth the resources or to choose between alternative investments. A higher ROI means a better return on the investment, while a lower ROI means less profit generated relative to the investment cost.

SweetCo is considering investing $500,000 in a new packaging machine for their gummy candies. The machine will help reduce costs and increase efficiency. The expected annual savings from this investment is $75,000.

We would use the case interview formula:

**Return on Investment % = (Profit from Investment / Investment Cost) x 100**

= ($75,000 / $500,000) x 100% = 15%

This means that for every dollar SweetCo invests in the new packaging machine, they can expect to earn an additional 15 cents in profit. This ROI calculation can help SweetCo determine whether the new machine is worth pursuing, as they can compare the ROI to their desired return rate or compare it to other uses for their resources.

Market size determines the number of potential customers for a product or service, as well as the revenue potential that comes with it. It helps businesses determine if investing in a new product or service is worth the costs. Additionally, market sizing helps businesses understand their target audience and their needs.

If SweetCo is considering expanding its product offerings to include chocolate, they need to determine the potential market size for chocolate to see if there are enough customers.

There are two ways to determine market size: the top-down and bottom-up approaches.

**The top-down approach: **We first look at the total number of households in our target market, the U.S. in this example. Our research finds there are 125 million households in the country. We estimate that about 70% of households are chocolate consumers.

125 million households x 70% = 87.5 million potential chocolate-consuming households in the U.S.

**The bottom-up approach: **SweetCo plans to introduce its chocolate products in five major cities in the United States: New York, Los Angeles, Chicago, Houston, and Philadelphia.

After research and analysis, we estimate about 3 million households in these 5 cities are chocolate consumers. A preliminary market survey suggests households spend an average of $50 a year on chocolate.

3 million households in target cities x $50 spent on chocolate per household per year = $150 million potential revenue in target cities.

Both approaches have pros and cons, but combining the two can lead to the most accurate estimate of market size. By using market size calculations, SweetCo can make informed decisions about whether to expand into the chocolate market and what resources to allocate to this new category.

We dive deep into How to Ace Market Sizing for more examples.

Market share is the percentage of the total sales in a specific market the company makes. This metric can vary from 0%, which means the company has no presence in the market, to 100%, which signifies the company has complete dominance in the market.

Calculating market share can also provide insights into potential challenges and opportunities for a company within the market. For example, if the company already has a high market share, it suggests there is limited room to grow in that market. Factors that impact market share include brand recognition, distribution, and pricing strategy.

**Company’s Market Share = Company’s Revenue in the Market / Total Market Revenue**

For example, if the chocolate market is worth $150 million and SweetCo believes it can generate $15 million in revenue, its market share would be 10%.

Growth rate tells us how much a company’s revenue (or other metric) has increased or decreased over a period of time. We calculate it by comparing the current year’s revenue to the previous year’s. The formula is:

**Growth Rate % = (New – Old) / Old**** x 100**

For example, let’s say SweetCo had $100 million in revenue this year and $120 million in revenue last year. To calculate the revenue growth rate, we would use the formula:

Growth rate = ($100 million – $120 million) / $120 million = -0.17 ** **x 100 = -17%

This means that SweetCo’s revenue has decreased by 17% from last year to this year.

The growth rate can be positive or negative. A negative growth rate would indicate a decrease in revenue, which is the problem SweetCo has noticed in the last 5 years.

If you are just starting to practice cases, we recommend printing this cheat sheet as a reference. Once you get comfortable, you should know the formulas by memory.

Refresh your knowledge of basic multiplication, division, addition, and subtraction. Know key fractions, such as ⅛ being equal to 0.125.

Review and know how to use the six most common case interview formulas we covered in the previous section.

Remember that you are not allowed a calculator in most interviews, so you will have to rely on pen and paper.

Practice consistently! Other than case mock interviews, there are online resources for mental math drills. You can also practice in everyday life situations, such as calculating bills or grocery expenses without a calculator.

Ask your interviewer to clarify any confusing case contexts or concepts. For example, if it is a utility client, you can confirm how the company generates revenue.

At the beginning of your analysis, ask for permission to round numbers. Most interviewers will allow you to do this.

Experiment with different mental math methods to make calculations easier for you. Use simple numbers (e.g., rounding to the nearest 1000) or scientific notations to visualize numbers. For example, if you need to divide 60,000,000 by 3,000,000, you can use the scientific notation method. First, rewrite it as (6 x 10^7) x (3 x 10^6). You can easily multiply the single digits (6 / 3 = 2). You can then subtract the exponents (7 – 6 = 1). Therefore, you are left with 2 x 10^1, which is 20.

Try different methods during your practice case interviews to find what works best for you.

Focus on the insights you can draw from the numbers and how they relate to the business problem you’re trying to solve. Explain what that number means in the context of the business problem and recommend a solution.

You can impress your interviewer by knowing the nuances of the industry. For example, if the client is in mining, it’s typically important to know your return on investment on the heavy machinery.

With consistent practice, you can master case interview formulas and land your dream consulting job! If you need more help, check out Our Ultimate Guide to Case Interview Prep.

**– – – – –**

In this article, we’ve covered:

- Understanding what case interview formulas are and their importance in consulting interviews
- Learning the top 6 concepts and formulas that you need to know, including a bonus cheat sheet
- 5 tips on how to master case interview math formulas

If you have more questions about case interview formulas, leave them in the comments below. One of My Consulting Offer’s case coaches will answer them.

Other people prepping on case interview formulas found the following pages helpful:

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