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Although case interviews do not require any technical math or finance knowledge, there are basic formulas that you should know in order to do well in order to master case interview math.
This article will cover the 26 formulas you should know for case interviews. These formulas are organized into the following categories:
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1. Revenue = Quantity * Price
Revenue is the amount of money a company brings in from selling its products. This can be calculated by taking the number of units sold and multiplying it by the price per unit.
Example: Your company sells shirts for $20 each. Last year, your company sold 1,000 shirts. So, your total revenue last year was 1,000 * $20 = $20,000.
2. Total Variable Costs = Quantity * Variable Costs
Costs are payments that a company needs to make in order to run and operate its business. There are two different types of costs, variable costs and fixed costs.
Variable costs are costs that directly increase for each additional unit of product made. It represents the cost of raw materials needed to make the product.
Total variable costs are calculated by taking the number of units produced or sold and multiplying it by the raw material cost per product.
Example: It costs your company $5 to purchase the raw materials needed to make a shirt. If your company sold 1,000 shirts last year, the total variable costs are 1,000 * $5 = $5,000.
3. Costs = Total Variable Costs + Fixed Costs
Total costs for the company can be calculated by adding total variable costs and fixed costs.
Fixed costs are costs that do not directly increase for each additional unit of product made. They may include costs such as rent for the building or equipment needed to make the product.
Example: Your company pays annual rent of $10,000. It also leases the equipment it needs to make its shirts for $2,000 a year. Therefore, fixed costs are $10,000 + $2,000 = $12,000. Total variable costs were calculated to be $5,000 from the previous example. So, total costs are $12,000 + $5,000 = $17,000.
4. Profit = Revenue – Costs
Profit is the amount of money the company keeps after paying for all of its costs. Profit is calculated by subtracting total costs from total revenue.
Example: Last year, your shirt company generated revenues of $20,000 and had costs of $17,000. The profit last year was $20,000 - $17,000 = $3,000.
5. Profit = (Price – Variable Costs) * Quantity – Fixed Costs
This formula summarizes the previous four formulas into one concise and simplified equation.
6. Contribution Margin = Price – Variable Cost
Contribution margin represents how much money each product sold brings into the company after accounting for the cost of raw materials needed to make the product.
Example: If your company’s shirts sell for $20 and raw materials cost $5, then the contribution margin is $20 - $5 = $15 per shirt.
7. Profit Margin = Profit / Revenue
Profit margin represents the percentage of revenue that a company keeps as profit after taking into account all of its costs.
Example: Last year, your company generated $20,000 in revenue and had $17,000 in costs. Its profit was $3,000. Therefore, your company’s profit margin is $3,000 / $20,000 = 15%.
8. Return on Investment = Profit / Investment Cost
Companies make investments by spending money in the hopes of earning even more money in the future as a result of the investment. Return on investment, or ROI or short, represents how much additional money a company generates relative to the size of its initial investment.
ROI is calculated by taking the profit that the company generated from the investment and dividing it by the investment cost.
Example: Your company spent $5,000 on marketing to advertise its shirts. As a result, the company generated an additional $6,000 in profits from selling shirts. This profit does not yet take into account the costs of the marketing campaign. Therefore, the company has a net increase in profits of $1,000 from its original $5,000 investment. The ROI is $1,000 / $5,000 = 20%.
9. Payback Period = Investment Cost / Profit per Year
Payback period represents how long it would take a company to recoup the money it spent on an investment. It is usually specified in years.
Example: Your company invested in redesigning its shirts for $5,000. As a result, the company expects annual profits to increase by $1,000 for every year going forward. Therefore, the payback period for this investment is $5,000 / $1,000 = 5 years.
10. Output = Rate * Time
The output of production can be calculated by taking the rate of production and multiplying it by time.
Example: The machine that your company uses to produce shirts can produce 5 shirts per hour. If the machine runs for 12 hours, then it will produce 60 shirts.
11. Utilization = Output / Maximum Output
Utilization represents how much a factory or machine is being used relative to its maximum possible output.
Example: The machine that your company uses to produce shirts can produce 5 shirts per hour. Therefore, its maximum capacity in a day is 5 shirts per hour * 24 hours = 120 shirts. If your machine is being used to only produce 60 shirts per day, then it is at 60 / 120 = 50% utilization.
12. Market Share = Company Revenue in the Market / Total Market Revenue
Market share measures the percentage of total market sales a particular company has. Market shares can range from 0%, no presence in the market, to 100%, complete dominance in the market.
Example: Your company sells shirts and generates $100M in annual revenues. The market size of shirts is $500M. Therefore, your company has a market share of $100M / $500M = 20%.
13. Relative Market Share = Company Market Share / Largest Competitor’s Market Share
Relative market share compares a company’s market share to the largest competitor’s market share. It measures how strong of a presence a company has relative to the market leader. If the company is the market leader, relative market share measures how much of a lead they have over the next largest player.
Instead of using company market share and the largest competitor’s market share, you can use company revenue and the largest competitor’s revenue. This will give you the same answer.
Example: Your company has a 20% market share in the shirts market. Your largest competitor has a 50% market share. Therefore, your relative market share is 20% / 50% = 0.4.
Example 2: Your company is the market leader and has a 50% market share in the shirts market. Your largest competitor has a 25% market share. Therefore, your relative market share is 50% / 25% = 2.
These formulas are much less commonly seen in case interviews than the previous formulas. You likely won’t need to use these formulas since they require more technical knowledge of accounting, finance, and economics.
However, you should still be familiar with these formulas in the small chance that one of these concepts shows up in your case interview.
14. Gross Profit = Sales – Cost of Goods Sold
Gross profit is a measure of how much money a company makes from selling its product after taking into account the costs associated with making and sellings its product. These costs are often called the cost of goods sold.
Compared to the previous profit formula, which was simply revenue minus costs, gross profit is always higher since it does not take into account all of the costs of the business.
Example: Your company sold $20,000 of shirts last year. The cost to produce these shirts was $5,000. Therefore, your gross profit is $20,000 - $5,000 = $15,000.
15. Operating Profit = Gross Profit – Operating Expenses – Depreciation – Amortization
Operating profit is calculated by taking gross profit and subtracting all operating expenses and depreciation and amortization.
Operating expenses may include rent, utilities, maintenance and repairs, advertising and marketing, insurance, and salaries and wages. So, operating profit is always less than gross profit.
Depreciation is the spreading of a fixed asset’s cost over its useful lifetime.
For example, let’s say that a company purchases a new machine for $10,000 that it expects to last for 5 years. Instead of stating that it incurred $10,000 in costs in its first year, the company may choose to state that the new machine costs $2,000 per year for the next five years.
Amortization is the spreading of an intangible asset’s cost over its useful lifetime. It is the exact same principle as depreciation except that it deals with intangible assets, or assets that aren’t physical.
For example, let’s say that a company purchases a patent for $10,000 and expects the benefits of the patent to last for 20 years. Instead of stating that it incurred $10,000 in costs in its first year, the company may choose to state that the patent costs $500 per year for the next twenty years.
Example: You sold $20,000 of shirts last year. Cost of goods is $5,000, operating expenses are $10,000, depreciation of a machine is $2,000, and amortization of a patent is $500. Therefore, your operating profit is $20,000 - $5,000 - $10,000 - $2,000 - $500 = $2,500.
16. Gross Profit Margin = Gross Profit / Revenue
This is the exact same formula as the profit margin formula except that gross profit is used. Gross profit margin measures how much money a company keeps from selling its products after taking into account cost of goods sold.
Example: Your company has a gross profit of $15,000 from $20,000 of revenue. Therefore, your gross profit margin is $15,000 / $20,000 = 75%.
17. Operating Profit Margin = Operating Profit / Revenue
This is the exact same formula as the profit margin formula except that operating profit is used. Operating profit margin measures how much money a company keeps from sellings its products after cost of goods sold, operating expenses, depreciation, and amortization is taken into account.
Example: Your company has an operating profit of $2,500 from $20,000 of revenue. Therefore, your operating profit margin is $2,500 / $20,000 = 12.5%.
18. EBITDA = Operating Profit + Depreciation + Amortization
EBITDA stands for earnings before interest, taxes, depreciation, and amortization. It is a financial metric used to measure a company’s cash flow or the amount of cash that a company has generated in a period of time.
To calculate EBITDA, start with operating profit and add back depreciation and amortization expenses.
Example: Your company has an annual operating profit of $2,500. Depreciation expenses are $2,000 and amortization expenses are $500. Therefore, your EBITDA is $2,500 + $2,000 + $500 = $5,000.
19. CAGR = (Ending Value / Beginning Value)^(1/Time Period) – 1
CAGR stands for compounded annual growth rate. It measures how quickly something is growing year after year.
Example: Your company generates $144M in annual revenue. Two years ago, your company only generated $100M. Over this time period, your CAGR was ($144M / $100M)^(1/2) - 1= 20%. In other words, your company grew by 20% each year for two years.
20. Rule of 72
The Rule of 72 is a shortcut used to estimate how long a market, company, or investment would take to double in size. To use it, simply divide 72 by the annual growth rate to get an estimate for the number of years needed to double in size.
Example: Your company is growing steadily at 9% per year. Using the Rule of 72, we’d expect it to take 72 / 9 = 8 years for your company to double in size if it maintains its current growth rate.
21. NPV = Cash Flow / [(1 + Discount Rate)^(Time Period)]
NPV stands for net present value. It measures how much future cash flow is worth today.
Receiving $1,000 right now is not the same as receiving $1,000 five years from now. If you received $1,000 right now, you could invest it and grow your money. Therefore, it is better to receive $1,000 right now than to receive the same amount in the future.
Net present value takes this into account.
Cash flow is the amount of money you expect to receive in the future. Time period is how many years in the future you will receive that amount of money. The discount rate is the return you expect to get from investing your money.
Example: You expect to receive $1,000 five years from now. You expect that you will be able to get 8% annual returns by investing in the stock market. Therefore, the net present value of your future cash flow is $1,000 / [(1 + 0.08)^5] = $680.58. In other words, receiving $680.58 today would give you the same value as receiving $1,000 five years from now.
22. Perpetuity Formula: Present Value = Cash Flow / Discount Rate
An annuity is a fixed sum of money paid at regular intervals such as every year. Perpetuity is an annuity that lasts forever.
The present value of a perpetuity is calculated by taking the cash flow of each payment and dividing it by the discount rate.
Example: You are expecting to receive $1,000 per year for the rest of your life. You expect that you will be able to get 8% annual returns by investing in the stock market. Therefore, the present value of this perpetuity is $1,000 / 0.08 = $12,500. In other words, receiving $12,500 today would give you the same value as receiving $1,000 each year for the rest of your life.
23. Return on Equity = Profit / Shareholder Equity
Return on equity, or ROE for shirt, measures how effectively a company is using its assets to create profits. It is calculated by taking profit and dividing by shareholder equity, which represents the net worth of a company.
In other words, shareholder equity is the value of a company’s total assets minus its total liabilities.
Example: Your company’s profit this year is $100M. Shareholder equity, or the net worth of the company is $1B. Your company has a ROE of $100M / $1B = 10%.
24. Return on Assets = Profit / Total Assets
Return on assets, or ROA for short, measures how profitable a company is relative to its total assets. In other words, it shows how efficiently a company is using its assets to generate income.
Assets can be anything that has value that can be converted into cash. This includes cash, property, equipment, inventory, and investments.
Example: Your company’s profit this year is $100M. Your company as $400M worth of assets. Your company has a ROA of $100M / $400M = 25%.
25. Price Elasticity of Demand = (% Change in Quantity) / (% Change in Price)
Elasticity is a measure of how much customer demand changes for a product given a change in the product’s price. In almost all cases, an increase in a product’s price results in a decrease in customer demand. Therefore, price elasticity of demand is usually negative.
Example: Your company has decreased its product’s price by 10%. As a result, the number of units sold has increased by 20%. Therefore, the price elasticity of demand is 20% / -10% = -2.
26. Cross Elasticity of Demand = (% Change in Quantity for Good #1) / (% Change in Price for Good #2)
Cross elasticity of demand measures how much customer demand changes for a product given a change in price of a different product.
If two products are complements, an increase in price of one product will result in a decrease in demand of the other product. Complementary products have a negative cross elasticity of demand.
If two products are substitutes, an increase in price of one product will result in an increase in demand of the other product. Substitute products have a positive cross elasticity of demand.
Example: A competitor has decreased the price of a competing product by 20%. As a result, the demand for your product has dropped by 10%. The cross elasticity of demand is -10% / -20% = 0.5.
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