15.1 Why Case Math Is Different from Academic Math
Academic math often rewards reaching the correct numerical answer. Case math requires an additional step: using the number to make a business decision.
Case-math process: Define what you need to calculate, establish the equation, perform the arithmetic, check the result, and interpret its business meaning.
15.2 Arithmetic Accuracy Versus Analytical Insight
Accuracy matters, but a correct calculation without interpretation is incomplete.
If you calculate that a proposed initiative generates $20 million in annual profit, explain whether that is large enough to meet the client’s objective.
Remember: Every important number should lead to a “so what?”
15.3 Addition and Subtraction
Basic addition and subtraction appear frequently when combining revenue streams, calculating cost savings, or comparing periods.
Write large numbers clearly and keep track of units.
Common mistake: Mixing thousands, millions, and billions during a calculation.
15.4 Multiplication and Division
Multiplication and division appear throughout cases: price times volume, revenue per customer, productivity per worker, and costs per unit.
Break difficult numbers into simpler components and estimate the approximate answer beforehand so you can detect major errors.
15.5 Percentages
Percentages are among the most common case calculations.
Percentage = Part ÷ Total × 100%
Learn common conversions such as 10%, 20%, 25%, 33%, and 50% so that straightforward calculations become automatic.
15.6 Percentage-Point Changes
Percentage changes and percentage-point changes are different.
If market share rises from 20% to 25%, it increases by 5 percentage points, but by 25% relative to its original level.
Use the correct terminology when interpreting exhibits or business performance.
15.7 Growth Rates
To calculate growth from an old value to a new value:
Growth Rate = (New Value − Old Value) ÷ Old Value
Always use the original value as the denominator.
15.8 Weighted Averages
Weighted averages are useful when different segments have different sizes.
Multiply each value by its share of the total and add the results.
Example: If 70% of sales have a 20% margin and 30% have a 40% margin, the overall margin is 26%.
15.9 Ratios
Ratios compare two quantities. Common examples include customers per employee, debt to equity, inventory turnover, and revenue per store.
Practical point: Define what the numerator and denominator represent before calculating.
15.10 Breakeven Calculations
Breakeven analysis determines how much must be sold before an investment or activity covers its fixed costs.
Breakeven Volume = Fixed Costs ÷ (Price per Unit − Variable Cost per Unit)
After calculating breakeven, compare it with realistic expected demand.
15.11 Contribution Margin
Contribution margin measures how much each sale contributes toward fixed costs and profit after variable costs.
Contribution Margin per Unit = Price − Variable Cost per Unit
This is especially useful in pricing, breakeven, and product-mix cases.
15.12 Profit Margins
Profit margin expresses profit as a percentage of revenue.
Profit Margin = Profit ÷ Revenue
Be careful about which profit measure is being used, such as gross, operating, or net profit.
15.13 Market Share
Market share measures the client’s sales relative to the total market.
Market Share = Company Sales ÷ Total Market Sales
Clarify whether the case measures share by revenue, units, customers, or another metric.
15.14 CAGR
Compound annual growth rate describes the constant annual rate that would take a starting value to an ending value over multiple periods.
CAGR = (Ending Value ÷ Starting Value)1 ÷ Number of Years − 1
In many cases, reasonable estimation is sufficient unless precise calculation is requested.
15.15 Expected Values
Expected value combines possible outcomes with their probabilities.
Expected Value = Sum of (Outcome × Probability)
This can help compare decisions involving uncertainty, such as product launches or investments.
15.16 Basic Probability
You may occasionally need simple probability concepts. Probabilities range from 0% to 100%, and mutually exclusive outcomes can often be added.
Case focus: Understand how probability affects the expected business outcome rather than treating it as an abstract mathematical exercise.
15.17 Capacity and Utilization
Capacity is the maximum output a system can produce, while utilization measures how much of that capacity is being used.
Utilization = Actual Output ÷ Maximum Capacity
High utilization may signal the need for additional capacity or process improvements.
15.18 Productivity
Productivity compares output with the resources required to generate it.
Productivity = Output ÷ Input
Examples include units per employee, customers served per hour, or revenue per salesperson.
15.19 Return on Investment
Return on investment compares the economic benefit generated with the investment required.
ROI = Return or Gain ÷ Investment
Make sure you understand exactly how “return” is defined in the case before calculating.
15.20 Payback Periods
The payback period estimates how long it takes for an investment’s benefits to recover its initial cost.
Simple Payback Period = Initial Investment ÷ Annual Cash Benefit
This shortcut works when annual benefits are relatively constant.
15.21 Basic Present-Value Concepts
Money received in the future is generally worth less than the same amount received today. Present-value analysis accounts for timing by discounting future cash flows.
You usually do not need advanced finance calculations unless the interviewer specifically requests them.
Core concept: When comparing investments with cash flows occurring at different times, both the amount and timing of those cash flows matter.
The formulas in this chapter are useful, but memorizing them is not enough. Case math is ultimately a problem-solving skill. Define the question before calculating, keep units organized, estimate your expected answer, check whether the result is reasonable, and always explain what the number means for the client.
