Case Interview Business Terms and Formulas

Revenue

Revenue = price × volume

Money earned from selling goods or services.

ExampleA cafe sells 20,000 drinks at $5 each, producing $100,000 in revenue.

Cost of goods sold (COGS)

Gross profit = revenue − COGS

Direct costs assigned to the goods or services sold.

ExampleA manufacturer earns $1 million and spends $600,000 on materials and factory labor, so COGS is $600,000.

Gross profit

Gross profit = revenue − COGS

Revenue remaining after COGS.

ExampleA retailer with $2 million in sales and $1.2 million in COGS earns $800,000 in gross profit.

Gross margin

Gross margin = gross profit ÷ revenue

Gross profit expressed as a share of revenue.

ExampleThe retailer earns $800,000 in gross profit on $2 million of sales, giving it a 40% gross margin.

Operating expenses (OpEx)

Operating profit = gross profit − OpEx

Costs of running the business outside COGS.

ExampleA software company has $5 million in gross profit and spends $2 million on sales and administration, leaving $3 million in operating profit.

Fixed cost

Total cost = fixed cost + variable cost

A cost that does not change with short-term volume.

ExampleA gym pays $100,000 in annual rent whether it serves 1,000 or 2,000 members.

Variable cost

Total variable cost = unit cost × volume

A cost that changes with units or activity.

ExampleDelivery costs are $3 per order, so 10,000 orders create $30,000 in variable cost.

Operating profit or EBIT

EBIT = revenue − COGS − OpEx

Profit from operations before interest and taxes.

ExampleA business with $10 million in revenue, $6 million in COGS, and $2 million in OpEx has $2 million in EBIT.

EBITDA

EBITDA = EBIT + depreciation + amortization

EBIT before depreciation and amortization.

ExampleIf EBIT is $2 million and depreciation is $500,000, EBITDA is $2.5 million.

Net income

Net income = revenue − all recognized expenses

Profit after operating costs, interest, taxes, and other items.

ExampleStarting with $2 million in EBIT, then paying $300,000 in interest and $400,000 in tax, leaves $1.3 million in net income.

Contribution per unit

Contribution per unit = price − variable cost per unit

The amount one unit contributes after its variable cost.

ExampleA meal sells for $15 and costs $9 to prepare and deliver, so it contributes $6 toward fixed costs and profit.

Contribution margin

Contribution margin ratio = contribution ÷ revenue

Revenue remaining after all variable costs.

ExampleA product earns $100,000 in revenue with $60,000 in variable costs, creating a $40,000 contribution and a 40% margin.

Break-even volume

Break-even volume = fixed costs ÷ contribution per unit

Units required for contribution to cover fixed costs.

ExampleWith $120,000 in fixed costs and $6 contribution per meal, the business breaks even at 20,000 meals.

Unit economics

Unit profit = unit revenue − unit cost

Revenue and cost measured for one useful unit.

ExampleA ride generates a $20 fare and $15 in driver and payment costs, leaving $5 per ride.

Marginal cost

Marginal profit = marginal revenue − marginal cost

The cost of producing or serving one additional unit.

ExampleFilling an empty airline seat may cost only $30 in food and handling even when the average cost per seat is much higher.

Willingness to pay

The maximum price a customer would accept.

ExampleCustomers accept a software plan at $180 a month but reject it at $200, suggesting willingness to pay is near $180.

Price elasticity of demand

Elasticity = % change in quantity ÷ % change in price

How strongly demand responds to a price change.

ExampleIf price rises 10% and volume falls 20%, elasticity is −2, so demand is relatively sensitive.

Cannibalization

Net new sales = new sales − displaced existing sales

Sales of one offer that replace sales of another company offer.

ExampleA new snack earns $1 million but displaces $300,000 of existing sales, so net new sales are $700,000.

Percentage change

% change = (new − old) ÷ old

Relative movement from an old value to a new value.

ExampleRevenue rising from $80 million to $100 million is a 25% increase because the $20 million gain is divided by the original $80 million.

Compound annual growth rate (CAGR)

CAGR = (ending ÷ beginning)^(1 ÷ years) − 1

The smoothed annual growth rate between two values.

ExampleRevenue growing from $100 million to $121 million over two years has a 10% CAGR.

Percentage point

25% − 20% = 5 percentage points

The arithmetic difference between two percentages.

ExampleA margin moving from 30% to 34% increases by 4 percentage points, not 4%.

Basis point

100 basis points = 1 percentage point

One hundredth of one percentage point.

ExampleAn interest rate rising from 5.00% to 5.25% has increased by 25 basis points.

Weighted average

Weighted average = Σ(value × weight)

An average that reflects the size of each segment.

ExampleIf 80% of units sell for $10 and 20% sell for $20, the weighted average price is $12.

Mix shift

Total result = Σ(segment result × segment mix)

A change in the share of sales from segments with different economics.

ExampleAverage price rises when premium products grow from 20% to 40% of sales even if every product price stays unchanged.

TAM, SAM, and SOM

SOM ≤ SAM ≤ TAM

Total demand, the serviceable portion, and the realistically obtainable share.

ExampleA $1 billion global market may become a $300 million target-city SAM and a realistic $15 million SOM.

Market share

Market share = company sales ÷ market sales

The company portion of total market sales or units.

ExampleA company selling $50 million in a $500 million market holds 10% market share.

Conversion rate

Conversion rate = conversions ÷ eligible prospects

The share of eligible people completing a target action.

ExampleIf 50 of 1,000 website visitors buy, the conversion rate is 5%.

Customer acquisition cost (CAC)

CAC = acquisition spend ÷ new customers

Acquisition spending per new paying customer.

ExampleSpending $20,000 to acquire 200 paying customers produces a CAC of $100.

Retention and churn

Retention ≈ 1 − churn when definitions match

Retention measures customers kept; churn measures customers lost.

ExampleIf 900 of 1,000 starting customers remain, retention is 90% and churn is 10%.

Customer lifetime value (LTV)

Simple LTV = ARPU × margin ÷ churn

Expected contribution generated over a customer relationship.

ExampleWith $50 monthly ARPU, a 60% margin, and 5% monthly churn, simple LTV is about $600.

LTV to CAC ratio

LTV:CAC = LTV ÷ CAC

Customer value compared with acquisition cost.

ExampleAn LTV of $600 and CAC of $200 produce a 3:1 LTV to CAC ratio.

Average revenue per user (ARPU)

ARPU = revenue ÷ average active users

Revenue generated per active user or customer.

ExampleA subscription business earning $120,000 from 2,000 active users has monthly ARPU of $60.

Average order value (AOV)

AOV = revenue ÷ orders

Revenue generated per order.

ExampleAn online store earning $90,000 from 3,000 orders has a $30 AOV.

Share of wallet

Share of wallet = company spend ÷ total category spend

The company share of a customer’s category spending.

ExampleA client spending $4,000 with your firm out of a $10,000 category budget gives you 40% share of wallet.

Working capital

Working capital = receivables + inventory − payables

Short-term operating assets minus short-term operating liabilities.

ExampleA business with $10 million in receivables, $6 million in inventory, and $4 million in payables has $12 million in working capital.

Receivables, payables, and inventory

Cash cycle depends on collection, stock, and payment timing

Cash tied up in customer credit and stock, offset by supplier credit.

ExampleIf customers begin paying in 60 days instead of 30, roughly one extra month of sales may be tied up in receivables.

Operating cash flow

Operating cash flow ≈ profit + noncash items − working-capital investment

Cash generated by core operations.

ExampleA company with $5 million in profit, $1 million in depreciation, and a $3 million working-capital increase generates about $3 million in operating cash flow.

Capital expenditure (capex)

Cash spent on long-lived operating assets.

ExampleBuying a $2 million machine is capex because the asset will support operations for several years.

Free cash flow (FCF)

FCF = operating cash flow − capex

Cash left after operations and capital investment.

ExampleIf operating cash flow is $5 million and capex is $2 million, free cash flow is $3 million.

Return on investment (ROI)

ROI = net gain ÷ investment

Gain from an investment relative to its cost.

ExampleA $100,000 project that creates $30,000 in net gain has a 30% ROI.

Payback period

Payback = investment ÷ annual cash benefit

Time required to recover the initial investment.

ExampleA $500,000 investment producing $125,000 of annual cash benefit pays back in four years.

Net present value (NPV)

NPV = discounted future cash flows − investment

Present value of future cash flows minus the initial investment.

ExampleIf discounted future cash flows total $1.2 million against a $1 million investment, NPV is $200,000.

Capacity

Capacity = output per resource × available resources

Maximum sustainable output in a stated period.

ExampleFour machines that each produce 100 units per hour provide 400 units of hourly capacity.

Utilization

Utilization = actual output ÷ available capacity

The share of available capacity currently used.

ExampleA plant producing 320 units against capacity of 400 units is running at 80% utilization.

Throughput

Throughput = completed units ÷ time

Finished saleable output completed per period.

ExampleA line completing 2,400 units in an eight-hour shift has throughput of 300 units per hour.

Bottleneck

Process capacity = bottleneck capacity

The step with the least effective capacity relative to demand.

ExampleIf cutting handles 500 units per hour, assembly 350, and packing 450, assembly is the bottleneck.

Cycle time and lead time

Lead time ≥ cycle time

Cycle time is processing time; lead time includes waiting and handoffs.

ExampleAn order may require 10 minutes of actual work but take two days to reach the customer because it waits between steps.

Yield and defect rate

Yield = good units ÷ total units

Yield measures good output; defect rate measures failed output.

ExampleProducing 950 good units from 1,000 total units gives 95% yield and a 5% defect rate.

Productivity

Productivity = output ÷ input

Output generated for each unit of input.

ExampleA team processing 240 orders in eight labor hours delivers 30 orders per labor hour.

Economies of scale

Average cost = total cost ÷ volume

Average cost falls as volume grows.

ExampleSpreading a $200,000 warehouse cost over 100,000 orders instead of 50,000 cuts fixed cost per order from $4 to $2.