| Component | Definition |
|---|---|
| Price per Unit | The selling price of a single unit ($) |
| Quantity Sold | Number of units sold in the period |
Interpretation: Total sales dollars generated before any costs are deducted.
Use case: Measuring top-line growth; sizing a product's market potential.
Example:
A SaaS company charges $120/month per seat and has 800 active seats.
$$\text{Revenue} = $120 \times 800 =
| Component | Definition |
|---|---|
| Fixed Costs | Costs unchanged by volume (rent, salaries, insurance) |
| Variable Cost per Unit | Cost incurred for each additional unit (materials, commissions) |
| Quantity Produced | Number of units manufactured or delivered |
Interpretation: The sum of all costs at a specific output level.
Use case: Forecasting operating expenses and identifying cost drivers.
Example:
A factory has $50,000/month in fixed costs, $8 variable cost per unit, and produces 10,000 units.
$$\text{Total Cost} = $50,000 + ($8 \times 10,000) =
| Component | Definition |
|---|---|
| Revenue | Total sales dollars |
| COGS | Direct costs tied to producing the goods sold (materials, direct labor) |
Interpretation: Profit remaining after direct production costs; before operating expenses.
Use case: Assessing product-level profitability.
Example:
Revenue = $96,000; COGS (server costs + direct labor) = $32,000
$$\text{Gross Profit} = $96,000 - $32,000 =
| Component | Definition |
|---|---|
| Revenue | Total sales dollars |
| Operating Costs | COGS + SG&A + R&D — all costs before interest and taxes |
Interpretation: Profit from core business operations, before financing costs and taxes.
Use case: Comparing operational efficiency across companies or time periods.
Example:
Revenue = $96,000; Operating costs (COGS + salaries + marketing) = $74,000
$$\text{Operating Profit} = $96,000 - $74,000 =
| Component | Definition |
|---|---|
| Revenue | Total sales dollars |
| Total Expenses | Operating costs + interest expense + income taxes |
Interpretation: The bottom-line profit belonging to shareholders after every obligation.
Use case: Evaluating overall company profitability; basis for EPS and dividends.
Example:
Revenue = $96,000; Operating costs = $74,000; Interest = $1,500; Taxes = $4,200
$$\text{Net Profit} = $96,000 - ($74,000 + $1,500 + $4,200) =
| Component | Definition |
|---|---|
| Price per Unit | Revenue received for selling one unit |
| Variable Cost per Unit | Cost incurred to produce one additional unit |
Interpretation: The dollar amount each unit sold contributes toward covering fixed costs and generating profit.
Use case: Pricing decisions; understanding how volume changes affect profit.
Example:
A smartphone accessory sells for $25; materials + packaging = $9/unit
$$\text{CM per Unit} = $25 - $9 =
| Component | Definition |
|---|---|
| Numerator | Gross Profit = revenue minus direct production costs |
| Denominator | Revenue = total sales dollars |
Interpretation: What percentage of each sales dollar remains after paying for what was sold.
Use case: Benchmarking product margins against competitors; tracking pricing power.
Example:
Revenue = $96,000; COGS = $32,000
$$\text{Gross Margin %} = \frac{$96,000 - $32,000}{$96,000} = \frac{$64,000}{$96,000} = 66.7%$$
| Component | Definition |
|---|---|
| Numerator | Operating Profit (EBIT) — profit after all operating costs |
| Denominator | Revenue = total sales dollars |
Interpretation: What percentage of each sales dollar remains after all operating costs.
Use case: Comparing cost efficiency across companies regardless of financing choices.
Example:
Operating Profit = $22,000; Revenue = $96,000
$$\text{Operating Margin %} = \frac{$22,000}{$96,000} = 22.9%$$
| Component | Definition |
|---|---|
| Numerator | Net Profit — after all expenses, interest, and taxes |
| Denominator | Revenue = total sales dollars |
Interpretation: Percentage of each sales dollar kept as profit after every cost.
Use case: Comparing overall profitability across industries or time periods.
Example:
Net Profit = $16,300; Revenue = $96,000
$$\text{Net Margin %} = \frac{$16,300}{$96,000} = 17.0%$$
| Component | Definition |
|---|---|
| Numerator | CM per Unit = the portion of the selling price not consumed by variable costs |
| Denominator | Price per Unit = full selling price |
Interpretation: The fraction of every sales dollar available to cover fixed costs and profit.
Use case: Calculating break-even revenue; pricing sensitivity analysis.
Example:
Price = $25; Variable Cost = $9 → CM per Unit = $16
$$\text{CM %} = \frac{$16}{$25} = 64%$$
| Component | Definition |
|---|---|
| Numerator | Total Fixed Costs = costs that must be covered regardless of volume |
| Denominator | CM per Unit = profit contribution from selling one additional unit |
Interpretation: The exact number of units that must be sold so that total contribution equals total fixed costs (profit = $0).
Use case: Setting minimum sales targets; go/no-go decisions for new products.
Example:
Fixed Costs = $80,000/month; CM per Unit = $16
$$\text{Break-Even Units} = \frac{$80,000}{$16} = 5,000 \text{ units}$$
| Component | Definition |
|---|---|
| Numerator | Total Fixed Costs = the dollar amount of overhead to be covered |
| Denominator | CM % = fraction of each revenue dollar that contributes to covering fixed costs |
Interpretation: The total sales dollars required to cover all fixed costs with zero profit remaining.
Use case: Revenue planning and scenario analysis when unit prices vary.
Example:
Fixed Costs = $80,000; CM % = 64%
$$\text{Break-Even Revenue} = \frac{$80,000}{0.64} =
| Component | Definition |
|---|---|
| Numerator | Sum of each value multiplied by its weight |
| Denominator | Sum of all weights |
| Weight of item |
|
| Value of item |
Interpretation: An average that accounts for the relative size or importance of each observation — larger weights pull the result closer to their value.
Use case: Calculating a blended interest rate across loans of different sizes; portfolio return.
Example:
A company has two loans: $200K at 5% and $800K at 8%.
| Component | Definition |
|---|---|
| Probability of outcome |
|
| Payoff or value of outcome |
Interpretation: The probability-weighted average outcome across all scenarios.
Use case: Deciding between business options when outcomes are uncertain.
Example:
A new product launch has three scenarios:
| Scenario | Probability | Profit |
|---|---|---|
| Strong market | 40% | +$500K |
| Moderate market | 45% | +$150K |
| Weak market | 15% | −$200K |
| Component | Definition |
|---|---|
| Numerator | New Value − Old Value = the absolute change |
| Denominator | Old Value = the baseline or starting point |
Interpretation: Relative change expressed as a percentage of the starting value.
Use case: Calculating revenue growth, price changes, or volume shifts.
Example:
Units sold went from 4,000 to 4,600.
| Component | Definition |
|---|---|
| Numerator | % change in quantity demanded — how much demand shifted |
| Denominator | % change in price — what caused the demand shift |
Interpretation:
-
$|\text{PED}| > 1$ → Elastic — demand is sensitive to price; raising price reduces total revenue -
$|\text{PED}| < 1$ → Inelastic — demand is insensitive to price; raising price increases total revenue - The result is normally negative (price up → demand down)
Use case: Setting prices to maximize revenue; predicting volume impact of price changes.
Example:
Price raised from $10 → $11 (+10%). Demand fell from 1,000 → 850 units (−15%).
| Component | Definition |
|---|---|
| Principal — the original amount borrowed or invested | |
| Annual interest rate (as a decimal, e.g., 6% = 0.06) | |
| Time in years |
Interpretation: Interest earned only on the original principal; no compounding.
Use case: Short-term loans, trade credit, or simple savings instruments.
Example:
A $5,000 short-term loan at 6% per year for 9 months (
$$\text{Interest} = $5,000 \times 0.06 \times 0.75 =
| Component | Definition |
|---|---|
| Principal — initial amount | |
| Annual interest rate (decimal) | |
| Number of compounding periods (years) |
Interpretation: The value your money grows to when interest is earned on both the principal and all previously accumulated interest.
Use case: Projecting investment or savings account balances over time.
Example:
$10,000 invested at 7% per year for 5 years.
$$\text{FV} = $10,000 \times (1.07)^5 = $10,000 \times 1.4026 =
| Component | Definition |
|---|---|
| Numerator | Future Value — the cash amount expected to be received |
| Denominator |
|
| Discount rate (opportunity cost of capital) | |
| Number of years until the cash is received |
Interpretation: What a future cash amount is worth in today's dollars — accounts for the fact that money available now is more valuable than money received later.
Use case: Valuing a future payment; comparing investment options on a like-for-like basis.
Example:
You will receive $14,026 in 5 years. Your discount rate is 7%.
$$\text{PV} = \frac{$14,026}{(1.07)^5} = \frac{$14,026}{1.4026} =
(Same mechanics as Compound Interest — see above.)
Use case: Planning how much a current savings balance will grow to at a future date.
Example:
You invest $20,000 today at 8% for 10 years.
$$\text{FV} = $20,000 \times (1.08)^{10} = $20,000 \times 2.1589 =
| Component | Definition |
|---|---|
| PMT | Fixed payment amount per period |
| Numerator |
|
| Denominator |
|
| Number of periods |
Interpretation: The lump-sum value today of a fixed stream of future payments.
Use case: Pricing a loan, valuing a lease, determining how much a pension is worth today.
Example:
A 5-year lease pays $12,000/year. Discount rate = 8%.
$$\text{Annuity PV} = $12,000 \times \frac{1 - (1.08)^{-5}}{0.08} = $12,000 \times \frac{1 - 0.6806}{0.08} = $12,000 \times 3.993 =
| Component | Definition |
|---|---|
| PMT | Fixed payment amount per period |
| Numerator |
|
| Denominator |
|
| Number of periods |
Interpretation: The total value accumulated at the end of the period if you make equal payments each period and they earn compound interest.
Use case: Calculating the balance of a savings plan or pension fund at maturity.
Example:
You save $500/month for 10 years at 6% annual rate → 0.5%/month,
$$\text{Annuity FV} = $500 \times \frac{(1.005)^{120} - 1}{0.005} = $500 \times \frac{0.8194}{0.005} = $500 \times 163.88 =
| Component | Definition |
|---|---|
| Numerator | Net Gain = final value minus what you originally paid |
| Denominator | Initial Investment = the total upfront capital outlay |
Interpretation: The percentage return earned relative to what was invested.
Use case: Quickly comparing two investments or marketing campaigns on a common scale.
Example:
You spend $8,000 on a marketing campaign. It generates $11,200 in attributable revenue.
$$\text{ROI} = \frac{$11,200 - $8,000}{$8,000} = \frac{$3,200}{$8,000} = 40%$$
| Component | Definition |
|---|---|
| Numerator | Ending Value — value at the end of the period |
| Denominator | Beginning Value — value at the start of the period |
| Exponent |
Converts total growth into a per-year rate over |
Interpretation: The constant annual growth rate that would take the beginning value to the ending value over
Use case: Comparing investments or business metrics (revenue, users) that span different time horizons.
Example:
A company's revenue grew from $2.0M to $3.5M over 4 years.
| Component | Definition |
|---|---|
| Numerator | Initial Investment = total upfront capital outlay |
| Denominator | Annual Net Cash Inflow = net cash generated per year from the investment |
Interpretation: The number of years required to recover the initial investment through operating cash flows.
Use case: Quick liquidity screening — preferred when capital recovery speed matters more than total return.
Example:
A machine costs $120,000 and generates $30,000 net cash/year.
$$\text{Payback Period} = \frac{$120,000}{$30,000} = 4.0 \text{ years}$$
| Component | Definition |
|---|---|
| Numerator | Cash Flow$_t$ = net cash inflow in year |
| Denominator |
|
| Discount rate (cost of capital / hurdle rate) | |
| Initial Investment | Upfront cost at time 0 (subtracted because it is a cash outflow) |
Interpretation:
- NPV > 0 → The project creates value; accept.
- NPV < 0 → The project destroys value; reject.
- NPV = 0 → The project exactly meets the required return.
Use case: Capital budgeting — deciding whether a project, acquisition, or expansion is financially worthwhile.
Example:
A $100,000 machine generates $45,000/year for 3 years. Discount rate = 10%.
| Year | Cash Flow | Discount Factor | PV of Cash Flow |
|---|---|---|---|
| 1 | $45,000 | ÷ 1.10¹ = 1.100 | $40,909 |
| 2 | $45,000 | ÷ 1.10² = 1.210 | $37,190 |
| 3 | $45,000 | ÷ 1.10³ = 1.331 | $33,809 |
| Sum of PVs | $111,908 |
Interpretation: The annualized return the project generates — the discount rate that makes NPV exactly zero.
Decision rule: Accept if IRR > Hurdle Rate (cost of capital).
Use case: Ranking competing projects; comparing project return against the cost of borrowing.
Example (same project as NPV above):
Initial Investment = $100,000; Cash flows = $45,000/year × 3 years.
Solving iteratively: NPV = 0 at r ≈ 16.7%.
Hurdle rate = 10% → IRR (16.7%) > Hurdle Rate → Accept the project.
| Component | Definition |
|---|---|
| Market value of equity | |
| Market value of debt | |
| Total firm value | |
| Equity weight — fraction of financing from equity | |
| Debt weight — fraction of financing from debt | |
| Cost of equity (return required by shareholders) | |
| Pre-tax cost of debt (interest rate on borrowing) | |
| Corporate tax rate (interest is tax-deductible, so after-tax debt cost = $R_d \times (1-T)$) |
Interpretation: The blended minimum return the company must earn on its assets to satisfy all investors (both debt and equity holders).
Use case: Discount rate for NPV/DCF valuations; hurdle rate for capital budgeting.
Example:
Capital structure: 70% equity at 12% cost; 30% debt at 6% pre-tax; tax rate = 25%.
| Component | Definition |
|---|---|
| Risk-free rate (e.g., 10-year government bond yield) | |
| Beta — the stock's sensitivity to market movements ( |
|
| Expected market return (e.g., long-run S&P 500 average ≈ 10%) | |
| Market risk premium — extra return demanded for bearing market risk |
Interpretation: The return equity investors require, compensating them for the risk-free rate plus a premium proportional to how volatile the stock is relative to the broader market.
Use case: Estimating cost of equity for WACC; valuing equities in DCF models.
Example:
Risk-free rate = 4%; Expected market return = 10%; Beta = 1.3
| Component | Definition |
|---|---|
| Numerator | Current Assets — cash, receivables, inventory; assets convertible to cash within 12 months |
| Denominator | Current Liabilities — obligations due within 12 months |
Interpretation:
- > 1.0 → Short-term assets exceed short-term obligations (liquid)
- < 1.0 → Potential liquidity problem
Use case: Lender covenant checks; quick assessment of short-term financial health.
Example:
Current Assets = $850,000 (cash $300K + receivables $250K + inventory $300K); Current Liabilities = $400,000
$$\text{Current Ratio} = \frac{$850,000}{$400,000} = 2.1$$
| Component | Definition |
|---|---|
| Numerator | Current Assets minus Inventory — excludes the least liquid current asset |
| Denominator | Current Liabilities — obligations due within 12 months |
Interpretation: A stricter liquidity test — can the company meet near-term obligations without relying on selling inventory?
Use case: Assessing liquidity in industries where inventory is slow to convert to cash (manufacturing, retail).
Example:
Using same data: Current Assets = $850,000; Inventory = $300,000; Current Liabilities = $400,000
$$\text{Quick Ratio} = \frac{$850,000 - $300,000}{$400,000} = \frac{$550,000}{$400,000} = 1.4$$
| Component | Definition |
|---|---|
| Numerator | Total Debt = all interest-bearing liabilities (short-term + long-term) |
| Denominator | Total Shareholders' Equity = total assets minus total liabilities |
Interpretation: How many dollars of debt exist for every dollar of equity. Higher = more financial leverage and risk.
Use case: Credit analysis; evaluating capital structure risk; comparing leverage across peers.
Example:
Total Debt = $1,200,000 (bank loans + bonds); Equity = $800,000
$$\text{D/E} = \frac{$1,200,000}{$800,000} = 1.5$$
There is $1.50 of debt for every $1 of equity.
| Component | Definition |
|---|---|
| Numerator | EBIT = Earnings Before Interest and Taxes (operating profit) |
| Denominator | Interest Expense = annual interest owed on all outstanding debt |
Interpretation: How many times over the company can pay its interest bill from operating profit.
- > 3× is generally considered safe
- < 1.5× is a warning sign
Use case: Bond analysis; credit risk assessment; covenant monitoring.
Example:
EBIT = $500,000; Annual interest expense = $80,000
$$\text{Interest Coverage} = \frac{$500,000}{$80,000} = 6.25\times \quad \Rightarrow \text{Operating profit covers interest 6.25 times}$$
| Component | Definition |
|---|---|
| Avg. Revenue per Period | Average monthly (or annual) revenue from one customer |
| Gross Margin % | Fraction of revenue remaining after variable delivery costs |
| Avg. Customer Lifetime | Expected number of periods before the customer churns |
Interpretation: The total gross profit a typical customer generates over their entire relationship with the company.
Use case: Setting maximum allowable customer acquisition cost (CAC); justifying retention spend.
Example:
A subscription app earns $15/month per user; gross margin = 75%; average customer stays 28 months.
$$\text{CLV} = $15 \times 75% \times 28 =
| Component | Definition |
|---|---|
| Numerator | CAC = total sales & marketing spend ÷ number of new customers acquired |
| Denominator | Gross Profit per Period = Revenue per customer × Gross Margin % |
Interpretation: How many periods it takes to recover the cost of acquiring one customer from the gross profit that customer generates.
Use case: Assessing growth efficiency; ensuring acquisition cost is justified by lifetime value.
Example:
CAC = $180; Monthly gross profit per customer = $15 × 75% = $11.25
$$\text{CAC Payback} = \frac{$180}{$11.25} = 16 \text{ months}$$
Sanity check: CLV ($315) >> CAC ($180) → healthy unit economics.
| Component | Definition |
|---|---|
| Numerator | Cost − Salvage Value = the total amount to be depreciated (the "depreciable base") |
| Denominator | Useful Life = how many years the asset is expected to be used |
| Salvage Value | Estimated resale or scrap value at the end of the asset's useful life |
Interpretation: Allocates the depreciable cost evenly across each year of the asset's useful life.
Use case: Forecasting D&A expense on the income statement; calculating EBITDA.
Example:
A delivery van costs $48,000, has a salvage value of $6,000, and a useful life of 6 years.
$$\text{Annual Depreciation} = \frac{$48,000 - $6,000}{6} = \frac{$42,000}{6} =
| Component | Definition |
|---|---|
| Original Cost | Purchase price of the asset |
| Accumulated Depreciation | Total depreciation charged since purchase = Annual Depreciation × years elapsed |
Interpretation: The remaining accounting value of the asset carried on the balance sheet.
Use case: Balance sheet reporting; calculating gain or loss on asset disposal.
Example:
After 3 years: Accumulated Depreciation = $7,000 × 3 = $21,000
$$\text{Book Value} = $48,000 - $21,000 =
| Driver | What it measures | How to improve |
|---|---|---|
| Net Margin | Profitability — profit kept per sales dollar | Cut costs or raise prices |
| Asset Turnover | Efficiency — sales generated per dollar of assets | Increase revenue or reduce assets |
| Equity Multiplier | Leverage — assets funded per dollar of equity | Take on more debt (increases risk) |
Interpretation: Decomposes ROE into three levers so management can diagnose why ROE is high or low.
Use case: Identifying whether ROE improvements come from better margins, better asset use, or higher leverage.
Example:
Net Margin = 8%; Asset Turnover = 1.6×; Equity Multiplier = 2.5×
| Component | Definition |
|---|---|
| Numerator | Revenue = total annual sales |
| Denominator | Average Total Assets = (Opening assets + Closing assets) ÷ 2 |
Interpretation: How many dollars of revenue are generated for every dollar of assets held.
Example:
Revenue = $4.8M; Beginning assets = $2.8M; Ending assets = $3.2M → Average = $3.0M
$$\text{Asset Turnover} = \frac{$4.8M}{$3.0M} = 1.6\times$$
| Component | Definition |
|---|---|
| Numerator | Average Total Assets = total assets the business controls |
| Denominator | Average Shareholders' Equity = net assets funded by owners |
Interpretation: How many dollars of assets exist per dollar of equity — measures balance-sheet leverage.
Example:
Avg Total Assets = $3.0M; Avg Equity = $1.2M
$$\text{Equity Multiplier} = \frac{$3.0M}{$1.2M} = 2.5\times$$
| Component | Definition |
|---|---|
| Numerator | COGS = cost of inventory actually sold during the period |
| Denominator | Average Inventory = (Opening inventory + Closing inventory) ÷ 2 |
Interpretation: How many times inventory is fully sold and replaced during the year. Higher = leaner operations.
Use case: Identifying slow-moving stock; comparing supply chain efficiency with peers.
Example:
Annual COGS = $1,800,000; Beginning inventory = $300,000; Ending inventory = $420,000 → Average = $360,000
$$\text{Inventory Turnover} = \frac{$1,800,000}{$360,000} = 5.0\times$$
| Component | Definition |
|---|---|
| Numerator | 365 — days in a year |
| Denominator | Inventory Turnover — how many full cycles occur per year |
Interpretation: The average number of days inventory sits on the shelf before being sold.
Use case: Working capital optimization; identifying excess or obsolete stock.
Example:
| Component | Definition |
|---|---|
| Numerator | Accounts Receivable = money owed by customers at period end |
| Denominator | Annual Revenue ÷ 365 = average daily revenue (dividing AR by this gives days outstanding) |
Interpretation: The average number of days it takes to collect cash after making a sale.
Use case: Managing credit policy; identifying collection problems; cash flow forecasting.
Example:
Accounts Receivable = $180,000; Annual Revenue = $1,800,000
$$\text{DSO} = \frac{$180,000}{$1,800,000} \times 365 = 0.10 \times 365 = 36.5 \text{ days}$$
| Component | Definition |
|---|---|
| Numerator | Accounts Payable = money owed to suppliers at period end |
| Denominator | COGS ÷ 365 = average daily purchases from suppliers |
Interpretation: The average number of days the company takes to pay its suppliers. Higher DPO = company holds cash longer (favorable for liquidity).
Use case: Supplier negotiation; cash management strategy.
Example:
Accounts Payable = $180,000; Annual COGS = $1,800,000
$$\text{DPO} = \frac{$180,000}{$1,800,000} \times 365 = 36.5 \text{ days}$$
| Component | Definition |
|---|---|
| DIO | Days inventory is held before being sold |
| DSO | Days to collect cash from customers after the sale |
| DPO | Days taken to pay suppliers — subtracted because it delays the cash outflow |
Interpretation: The number of days cash is tied up in operations from the moment you pay for inventory to the moment you collect from customers. Lower CCC = better cash efficiency.
Use case: Working capital management; identifying cash flow bottlenecks.
Example:
DIO = 73 days; DSO = 36.5 days; DPO = 36.5 days
| Component | Definition |
|---|---|
| Product Mix % | Share of total unit sales each product represents (all must sum to 100%) |
| CM per Unit | Contribution margin of each individual product |
Interpretation: The average contribution per unit sold across the entire product portfolio, weighted by sales mix.
Use case: Break-even analysis when a company sells more than one product.
Example:
Product A: 60% of sales, CM = $20/unit. Product B: 40% of sales, CM = $8/unit.
$$\text{Weighted CM} = (0.60 \times $20) + (0.40 \times $8) = $12.00 + $3.20 =
| Component | Definition |
|---|---|
| Numerator | Total Fixed Costs = overhead that must be covered |
| Denominator | Weighted CM per Unit = blended average contribution across the product mix |
Use case: Planning total output required across a product portfolio to reach break-even.
Example:
Fixed Costs = $76,000; Weighted CM = $15.20
$$\text{Break-Even Units (total)} = \frac{$76,000}{$15.20} = 5,000 \text{ units}$$
Split by mix: 5,000 × 60% = 3,000 units of A; 5,000 × 40% = 2,000 units of B.
| Component | Definition |
|---|---|
| Coupon Payment | Fixed periodic cash interest = Face Value × Coupon Rate |
| Face Value | Par value of the bond, repaid in full at maturity (typically $1,000) |
| Numerator (coupons) | The cash interest received each period |
| Numerator (final term) | The face value received at maturity |
| Denominator |
|
| Total number of periods until maturity |
Interpretation: A bond's price equals the present value of all future cash flows discounted at the market yield.
- Market yield rises → Bond price falls (inverse relationship)
- Market yield falls → Bond price rises
Use case: Valuing bonds; understanding the price-yield relationship.
Example:
3-year bond; Face = $1,000; Coupon = 5% ($50/year); Market yield = 7%
| Year | Cash Flow | Discount Factor | PV of Cash Flow |
|---|---|---|---|
| 1 | $50 | ÷ 1.07¹ = 1.070 | $46.73 |
| 2 | $50 | ÷ 1.07² = 1.145 | $43.67 |
| 3 | $1,050 | ÷ 1.07³ = 1.225 | $857.96 |
$$\text{Bond Price} = $46.73 + $43.67 + $857.96 =
| Component | Definition |
|---|---|
| Numerator |
Next year's expected dividend per share = |
| Denominator |
Required return minus the perpetual dividend growth rate |
| Investor's required rate of return (cost of equity) | |
| Constant annual growth rate of dividends (must be |
Interpretation: The fair value of a stock equals the present value of its dividends growing at a constant rate forever.
Use case: Valuing mature, dividend-paying companies with stable growth (utilities, blue-chip stocks).
Example:
Last dividend paid $D_0 =
$$D_1 = $2.00 \times 1.04 =
| Sign | Revenue line | Cost line |
|---|---|---|
| Positive | Favorable — actual > budget | Unfavorable — actual > budget |
| Negative | Unfavorable — actual < budget | Favorable — actual < budget |
Use case: Monthly management reporting; identifying over- and under-performing areas.
Example:
Budgeted revenue: $500,000; Actual revenue: $470,000
$$\text{Revenue Variance} = $470,000 - $500,000 = -$30,000 \quad \text{(Unfavorable)}$$
| Component | Definition |
|---|---|
| Numerator | Absolute Variance = Actual minus Budget |
| Denominator | Budget = the planned or reference amount |
Interpretation: Expresses the variance as a percentage of the plan — useful for scaling comparisons across line items of very different sizes.
Example:
$$\text{Variance %} = \frac{$470,000 - $500,000}{$500,000} = \frac{-$30,000}{$500,000} = -6.0%$$
| Component | Definition |
|---|---|
| CM per Unit | Profit added (or lost) for each additional (or fewer) unit sold |
| ΔVolume | Increase or decrease in units sold |
Interpretation: Fixed costs do not change with volume, so every unit above break-even adds exactly CM per unit to profit — and every unit below subtracts it.
Use case: Scenario analysis ("what if sales drop 10%?"); quantifying downside risk quickly.
Example:
CM per Unit = $16; A supply disruption cuts volume by 800 units.
$$\Delta\text{Profit} = $16 \times (-800) = -$12,800$$
The profit impact is an immediate $12,800 decline with no offset from fixed cost savings.
All examples within each section use consistent numbers so the formulas can be traced and cross-referenced easily.
| Component | Definition |
|---|---|
| Numerator | Actual Output = units (or hours) actually produced in the period |
| Denominator | Maximum Possible Output = theoretical maximum at full capacity |
Interpretation: What percentage of total available capacity is being used.
- < 70% → Significant idle capacity; fixed costs are spread over fewer units, raising unit cost
- 70–85% → Typical efficient operating range
- > 90% → Risk of bottlenecks, quality issues, and inability to handle demand spikes
Use case: Identifying whether a capacity investment is needed; diagnosing high unit costs in a manufacturing case.
Example:
A factory can produce 20,000 units/month at full capacity. It currently produces 14,000.
| Component | Definition |
|---|---|
| Numerator | Fixed Costs = costs unchanged regardless of output (rent, depreciation, salaried staff) |
| Denominator | Actual Output = units actually produced |
| Variable Cost per Unit | Costs that scale directly with output (materials, direct labor) |
Interpretation: As output rises, fixed costs are spread over more units, so unit cost falls — this is operating leverage. Conversely, underutilization inflates unit cost.
Use case: Explaining why a plant running at 50% utilization has uncompetitively high unit costs; pricing decisions.
Example:
Fixed Costs = $200,000/month; Variable Cost = $8/unit.
| Utilization | Units Produced | Fixed Cost per Unit | Variable Cost | Unit Cost |
|---|---|---|---|---|
| 50% | 10,000 | $20.00 | $8.00 | $28.00 |
| 70% | 14,000 | $14.29 | $8.00 | $22.29 |
| 100% | 20,000 | $10.00 | $8.00 | $18.00 |
Running at 70% vs 100% costs an extra $4.29 per unit — purely due to underutilization.
| Component | Definition |
|---|---|
| Bottleneck | The single process step with the lowest capacity — it limits the entire system |
| Demand Rate | Volume of orders or jobs arriving per period |
Interpretation: The output of an entire operation is capped by its slowest step. No amount of improvement elsewhere increases total throughput unless the bottleneck is addressed.
Use case: Operations cases involving queues, factory floor redesign, or service capacity.
Example:
A 3-step assembly line: Step A = 500 units/hr; Step B = 320 units/hr; Step C = 450 units/hr.
Bottleneck = Step B (320 units/hr) → System output is capped at 320 units/hr regardless of Steps A and C.
If demand = 400 units/hr:
| Component | Definition |
|---|---|
| Numerator | Company Revenue = the firm's sales in a defined market and period |
| Denominator | Total Market Revenue = all sales by all competitors in that same market |
Interpretation: The fraction of total market spending captured by the company.
Use case: Competitive benchmarking; tracking whether growth is coming from market expansion or share gains.
Example:
The company earns $48M; total market = $320M.
$$\text{Market Share} = \frac{$48M}{$320M} = 15%$$
Interpretation: Share based on units rather than dollars. Comparing value share vs volume share reveals whether the company sells at a premium (value share > volume share) or a discount (volume share > value share).
Example:
Company sells 90,000 units; total market = 750,000 units.
| Component | Definition |
|---|---|
| Numerator | The company's own market share |
| Denominator | The market share of the single largest competitor |
Interpretation: A ratio > 1.0 means the company is the market leader. Used in BCG matrix analysis: a relative share > 1× confers scale advantages in cost and brand.
Use case: Competitive position assessment; portfolio strategy (Stars, Cash Cows, etc.).
Example:
Company share = 15%; Largest competitor = 25%.
| Component | Definition |
|---|---|
| Numerator | Absolute growth in total market size (revenue or units) year-over-year |
| Denominator | Prior year market size = the baseline |
Interpretation: How fast the overall market is expanding or contracting — distinct from the company's own revenue growth.
Use case: Distinguishing organic growth from share gains; market attractiveness screening.
Example:
Market was $300M last year; it is $324M this year.
$$\text{Market Growth} = \frac{$324M - $300M}{$300M} = 8%$$
If the company's revenue grew 15%, it outpaced the market by 7pp → it gained share.
| Component | Definition |
|---|---|
| Number of Potential Customers | Everyone who could plausibly buy the product (segment the population if needed) |
| Avg. Annual Spend per Customer | Average dollars spent on this category per year |
Interpretation: The maximum revenue opportunity if the company captured 100% of the market.
Use case: Market entry decisions; investor pitch sizing; setting growth ambition.
Example:
Target segment: 4 million small businesses in the country. Each spends ~$600/year on the software category.
$$\text{TAM} = 4{,}000{,}000 \times $600 =
| Component | Definition |
|---|---|
| Price effect | Revenue change caused solely by the price change, holding volume constant |
| Volume effect | Revenue change caused by the volume change at the new price |
Interpretation: Any revenue movement can be split into what was driven by pricing versus what was driven by volume. This is the first diagnostic in any profitability case.
Use case: Diagnosing a revenue decline — is it a pricing problem, a volume problem, or both?
Example:
Last year: 10,000 units at $30 = $300,000. This year: 8,500 units at $32 = $272,000 (−$28,000).
| Effect | Calculation | Amount |
|---|---|---|
| Price effect | +$2 × 10,000 units | +$20,000 |
| Volume effect | −1,500 units × $32 | −$48,000 |
| Net change | −$28,000 |
The price increase added $20K but volume loss cost $48K — the net effect is negative, so the price increase was not worth it.
| Driver | Definition |
|---|---|
| Price Growth | Change in average selling price, holding mix and volume constant |
| Volume Growth | Change in total units sold, holding price and mix constant |
| Mix Shift | Revenue change from selling proportionally more high-price vs low-price products |
Interpretation: Revenue growth comes from three levers simultaneously; isolating each reveals which lever is driving (or dragging) performance.
Use case: Explaining to an interviewer why revenue grew despite a price cut, or why it fell despite volume gains.
Example:
Revenue grew 6%. Breakdown: Average price −2% (competitive pressure); Volume +5%; Mix +3% (shift toward premium SKUs).
The company is growing despite price erosion — it compensates through volume and premiumization.
| Component | Definition |
|---|---|
| Numerator |
|
| Denominator | CM per Unit + ΔP = the new contribution per unit after the price change |
Interpretation: If you cut the price by
Use case: Deciding whether a price cut or promotional discount is financially justified.
Example:
Current price = $25; Variable cost = $9; CM = $16. Considering a $3 price cut → new price $22, new CM = $13.
$$\Delta Q_{\text{break-even}} = \frac{-(-$3)}{$16 + (-$3)} = \frac{$3}{$13} = 23.1%$$
You must sell at least 23.1% more units just to break even on profit. If PED = −1.5 and the price cut is −12%, expected volume gain ≈ +18% — which falls short of 23.1%, so the price cut destroys profit.
For a linear demand curve
Interpretation: Revenue is maximized at the price point where elasticity = −1 (unit elastic). Above this price, the % volume loss exceeds the % price gain; below it, the opposite is true.
Use case: Setting an initial price for a new product; quick-check in pricing strategy cases.
| Component | Definition |
|---|---|
| Numerator | Net incremental profit = gross profit attributable to the campaign minus what was spent |
| Denominator | Marketing Spend = total campaign cost |
Interpretation: The profit return generated for every dollar spent on marketing. Unlike simple revenue ROI, this uses gross profit because the cost of goods must be subtracted first.
Use case: Evaluating whether a campaign, channel, or promotion should be continued or scaled.
Example:
A digital campaign costs $50,000 and drives 2,000 incremental units sold. Price = $25; Variable cost = $9 → Gross profit/unit = $16.
$$\text{Incremental Gross Profit} = 2,000 \times $16 =
| Component | Definition |
|---|---|
| Numerator | Revenue (not profit) directly driven by the advertising |
| Denominator | Total advertising spend in the same period |
Interpretation: How many dollars of revenue are generated per dollar of advertising. Note: ROAS uses revenue, not profit — a high ROAS can still be unprofitable if margins are thin.
Use case: Comparing efficiency across ad channels (search, social, display).
Example:
Ad spend = $50,000; Attributed revenue = $200,000.
$$\text{ROAS} = \frac{$200,000}{$50,000} = 4.0\times$$
Every $1 of ad spend returns $4 in revenue. But if gross margin is only 20%, gross profit = $40,000 < ad spend ($50,000) → still unprofitable.
| Component | Definition |
|---|---|
| Numerator | Incremental sales = actual sales minus what would have been sold without the promotion |
| Denominator | Baseline Sales = expected sales in the same period absent any promotion |
Interpretation: How much extra volume (%) the promotion generated above the normal run-rate.
Use case: Measuring whether a promotion actually drove incremental demand or simply pulled forward future purchases.
Example:
Baseline weekly sales = 5,000 units. During the promotion = 6,800 units.
| Component | Definition |
|---|---|
| Numerator |
|
| Denominator | New CM per Unit = contribution margin after the discount is applied |
Interpretation: The minimum percentage volume increase the promotion must generate for total profit to remain unchanged.
Use case: Deciding whether to run a price promotion; evaluating trade deal terms from a retailer.
Example:
Normal price $25; Variable cost $9; CM = $16. Promotion offers $4 off → new price $21; new CM = $12.
$$\text{Required Lift} = \frac{$4}{$12} = 33.3%$$
The promotion must drive at least 33.3% more volume to break even on profit. Pair this with your PED estimate to judge feasibility.
| Component | Definition |
|---|---|
| Market share of firm |
|
| Number of firms in the market |
Interpretation:
- HHI < 1,500 → Competitive (unconcentrated) market
- 1,500–2,500 → Moderately concentrated
- > 2,500 → Highly concentrated / near-monopoly
Use case: Assessing competitive intensity in an industry case; understanding M&A regulatory risk.
Example:
Four firms with shares of 40%, 30%, 20%, 10%:
| Component | Definition |
|---|---|
| Numerator | The absolute price difference between the company and the reference competitor |
| Denominator | Competitor Price = the benchmark (usually the market average or the largest rival) |
Interpretation: How much more (or less) the company charges relative to the competition. A positive premium is only sustainable if backed by differentiation customers value.
Use case: Pricing strategy; diagnosing volume share loss; brand positioning analysis.
Example:
Company price = $32; main competitor = $27.
$$\text{Price Premium} = \frac{$32 - $27}{$27} = 18.5%$$
If volume share is declining, ask: has the premium grown (price-driven loss) or has perceived differentiation eroded (brand-driven loss)?
Interpretation: When a competitor cuts price, you face two options — do nothing (lose volume) or match (keep volume but at lower margin). Quantifying both is the first step in a competitive response analysis.
Use case: Competitive dynamics cases; deciding whether to start or join a price war.
Example:
A competitor cuts price by $3. You estimate you'll lose 1,200 units/month if you don't respond.
Current CM = $16/unit.
$$\text{Profit impact of doing nothing} = -1,200 \times $16 = -$19,200/\text{month}$$
If matching the cut reduces CM from $16 to $13 but retains all 8,000 units:
$$\text{Profit impact of matching} = 8,000 \times ($13 - $16) = -$24,000/\text{month}$$
In this case, not responding is less costly — unless the volume loss compounds over time.
| Component | Definition |
|---|---|
| Numerator | Contribution Margin = Revenue − Total Variable Costs |
| Denominator | Operating Profit (EBIT) = Contribution Margin − Fixed Costs |
Interpretation: How many times larger the contribution margin is relative to operating profit — tells you how sensitive profit is to a change in revenue.
Use case: Assessing profit sensitivity in scenario analysis; explaining why a business is risky in a downturn.
Example:
Revenue = $96,000; Variable costs = $32,000; Fixed costs = $52,000.
CM = $64,000; EBIT = $12,000.
$$\text{Operating Leverage} = \frac{$64,000}{$12,000} = 5.3\times$$
If revenue falls 10%:
| Component | Definition |
|---|---|
| Numerator | Fixed Costs = costs that do not change with output level |
| Denominator | Total Costs = Fixed Costs + Total Variable Costs |
Interpretation: Businesses with a high fixed cost ratio have high operating leverage — profitable when running near capacity, but vulnerable in downturns. Businesses with a high variable cost ratio are more resilient but have lower upside.
Use case: Quickly characterizing a business model's risk profile in an industry case.
Example:
Fixed costs = $200,000; Variable costs at current volume = $80,000; Total costs = $280,000.
$$\text{Fixed Cost Ratio} = \frac{$200,000}{$280,000} = 71.4%$$
This is a high fixed-cost business (e.g., manufacturing, hospitality) — profits are highly sensitive to volume changes.
| Component | Definition |
|---|---|
| ΔCost per Unit | Change in variable cost per unit (positive = cost increase, negative = saving) |
| Volume | Current units sold |
Interpretation: A variable cost saving flows directly to profit (dollar for dollar) across all units sold. Fixed cost changes flow to profit in full regardless of volume.
Use case: Quantifying the profit impact of a supplier price increase, wage change, or efficiency improvement.
Example:
A $1.50/unit increase in raw material costs; current volume = 80,000 units/year.
$$\Delta\text{Profit} = -$1.50 \times 80,000 = -$120,000/\text{year}$$
To offset this, the company must either raise prices, cut other costs, or grow volume.
Sections 16–21 cover the quantitative tools most commonly tested in case interviews beyond standard financial statements.