# There is no advanced math required in case interviews, but calculating quickly is a real challenge

Nearly all the math required in case interviews is arithmetic: addition, subtraction, multiplication and division. You will likely need to perform these calculations with percentages, decimals or fractions, and calculate a percentage value (which requires division). Most candidates understand these math concepts; the **challenge** for many people is performing multiple calculations with large numbers **quickly and without calculators** or spreadsheets, in a high-pressure environment with a six-figure salary and your future career on the line.

## Case numbers are “round” with few significant digits

The good news is that most of the numbers you encounter in case interviews (what we call “**Case** **Numbers**”) are “round” numbers and have only a few **significant** **digits** (i.e. only a few digits are non-zero), but may be in the Millions or Billions. For example, the number 200 Thousand, which is 200,000 in long form, has a single digit that is not zero (“2”), and so has one **significant digit.** The number 2.5 Million, which is 2,500,000 in long form, has two non-zero digits (“2” and “5”), and therefore has two **significant digits.** Case numbers frequently have only one or two significant digits, less frequently three significant digits, and in rare cases four or more significant digits. The term "**Case** **Calculation**" refers to a calculation required in a case interview, and may provide specific Case Numbers or refer to a general calculation without specifying the numbers involved, such as calculating Revenue, given Price and Quantity.

## Addition and Subtraction

Most of the Case Numbers you need to add and subtract will have only a few significant digits. If they have more than one significant digit, the last or “trailing” significant digits will often be “5” or “25,” which makes them easier to add/subtract.

**Example 1:** Add 250 Million, 300 Million, and 150 Million.

**Answer: **700 Million

In this addition example, the leading digits (prior to the Million) are: 250, 300 and 150. These numbers have either one significant digit (300) or two significant digits, where the last significant digit is a “5,” which makes addition easier.

When you need to add Case Numbers with three significant digits, the last two significant digits are often “25” or “75,” which are also easy to calculate with.

**Example 2:** Add 225 Million, 375 Million and 200 Million.

**Answer: **800 Million

You may need to add some Case Numbers with three significant digits that don’t end in “25” or “75,” but they most likely end in “5.” For example, you might need to add numbers like 115 and 165. Since these numbers both end in “5”, they are relatively easy to add without a calculator, and the answer is 280.

It is highly **unlikely** you will need to add or subtract a series of numbers with three or more significant digits, where all the digits are effectively random, such as: 147, 368 and 434 (where the last significant digits are **not** “25” or “75”).

## Multiplication and Division

As you can see from the prior examples, candidates need to perform multiplication and division calculations using numbers in the thousands, millions or even billions (but with a limited number of significant digits). In case interviews, candidates often need to perform multiplication and/or division with percentages, decimals and fractions. For example, you might need to multiply a number by a percentage (e.g., calculate 25% of $500 Million), or divide two numbers and express the result as a percentage (e.g. what percentage of $80 Million does $16 Million represent?). Similar operations using fractions instead of percentages are also frequently required.

Most of the Case Numbers you need to multiply or divide will be round numbers with only a few significant digits. For instance, numbers of units sold for each product could be 5 Million, 10 Million, and 12.5 Million. In a case interview, you are unlikely to receive a similar problem where the number of units sold is something like 9,618,493, which has many significant digits that appear random. The percentage values you need to multiply/divide within case interviews will also usually have only a few significant digits. A typical Case Calculation would be calculating 20% or 25% of another number. It is **unlikely** you would need to calculate 23.7% of a value in a Case Calculation.

**Example 3:** Calculate $120 Million times 250.

**Answer: **$30 Billion

## Compounded Growth

Candidates also need to understand compound percentage growth and how to make approximations with compound growth. It is a very common Case Calculation to be given a firm’s revenue (or another metric), and the associated Compounded Annual Growth Rate (CAGR), and be asked to estimate that value at some point in the future.

## Net Present Value (NPV)

Another common Case Calculation involves assigning a financial value to monetary payments that will occur in the future. Management Consultants usually determine the current value of future payments using a financial method called Net Present Value or** NPV.** Hence, candidates need to be able to calculate the NPV under a variety of scenarios.

**NPV Example 1:** How much would your company be willing to pay for another company that generates $20 Million in profit annually, if your firm requires an annual Return on Investment of 10%?

**Answer: **$200 Million

**NPV Example 2:** A real estate development firm is evaluating a project that involves buying a parcel of land and building condominiums on that parcel. The company forecasts they can sell the condominiums for a total of $250 Million **six years **in the future.

What is the maximum the real estate company would be willing to spend **now** to buy the land and develop the condominiums, if all the associated costs for the project would be incurred today, and they require a 12% annual return on invested capital?

**Answer: **$125 Million

Is it correct that the article equates the ROI and the discount rate in the following example: "How much would your company be willing to pay for another company that generates $20 Million in profit annually, if your firm requires an annual Return on Investment of 10%?"

In my understanding, one would have to calculate first the NPV using the actual discount rate (say 3/4%) - and then compute NPV+10% to get the target ROI.