Budgeting & debt
When does annual prepayment actually help a household budget?
Compare a subscription's annual discount with cash timing, expected use, cancellation terms, and the cost of making the commitment harder to reverse.
Definitions & calculations
Finance, defined and calculated
Explore financial terms through definitions, formulas, original USD examples and the limits of each measure.
Definitions are more useful when the units, time horizon and exclusions stay visible. Each entry includes an original example, its arithmetic and one reason the result should not be overinterpreted.
All monetary examples use hypothetical U.S. dollars (USD), not current product prices, yields or tax rules. Ratios, days, months and percentages retain their stated units.
36 of 36 definitions · prepared 2026-10-29
Cash & obligations
Cash flowCash flow records money received and paid during a stated period. It is a movement measure, whereas a bank balance is measured at a particular time.
Work through an example
A hypothetical household opens a month with USD 1,200, receives USD 3,000 and pays USD 3,400. Closing cash is USD 800. The month used USD 400 of its opening reserve despite receiving more than USD 3,000 of income. Record the dates as well as the total: a payment before payday can produce an earlier shortfall.
What this does not establish: A positive month-end balance does not establish that every earlier payment was funded on time.
Net worthNet worth is the difference between the assets and liabilities included in a dated personal balance sheet. It is not the same as spendable cash.
Work through an example
Suppose included assets are USD 250,000 and liabilities are USD 170,000. Net worth is USD 80,000. If most of the assets are a home and the bank account holds USD 1,000, the household cannot assume USD 80,000 is available for an immediate invoice. State the valuation basis for assets that have no ready market.
What this does not establish: An estimated asset value can be uncertain, costly to realize or unavailable before a bill is due.
LiquidityLiquidity concerns the ability to obtain usable cash when it is needed, including the delay and value loss that conversion may involve.
Work through an example
An asset notionally valued at USD 10,000 might produce a USD 9,600 sale and incur USD 100 of costs when cash is needed quickly. Usable proceeds would be USD 9,500. The USD 500 difference from the displayed value is relevant even though the seller still owns an asset until settlement. Availability and valuation answer different questions.
What this does not establish: This is an invented execution scenario, not an estimate of a particular security’s spread or settlement time.
Working capitalIn its basic balance-sheet form, working capital equals current assets less current liabilities. Its usefulness depends on what those categories contain.
Work through an example
A simplified business reports USD 40,000 of current assets and USD 25,000 of current liabilities, giving USD 15,000 of working capital. If USD 30,000 of the assets are slow inventory, that result is not a cash reserve. Follow collections, stock usability and payment dates rather than treating the difference as money in the bank.
What this does not establish: Current classification, restricted balances and doubtful collections can make two equal totals economically different.
Cash runwayCash runway expresses how long an available reserve covers a recurring funding gap under an explicitly constant-spending scenario.
Work through an example
With USD 9,000 available and a monthly gap of USD 1,500 after reliable income, the simple runway is six months. Dividing by gross expenses of USD 3,000 instead would answer a different question. If costs rise or income disappears, calculate the new net gap and reduce the available reserve for already committed payments first.
What this does not establish: The ratio is undefined as a depletion measure when there is no positive funding gap; payment dates can shorten usable runway.
Sinking fundA sinking fund assigns periodic savings to a known future expense rather than treating that predictable payment as an emergency.
Work through an example
An invented USD 2,400 payment is due after ten more monthly contributions. USD 400 is already reserved, leaving USD 2,000 to fund. At zero interest the required monthly saving is USD 200. Starting with twelve months instead of the ten actually available would understate what the payment schedule requires.
What this does not establish: The example assumes equal month-end contributions, a fixed USD bill and no earnings or withdrawals.
Rates & time
PrincipalPrincipal is the base amount borrowed or invested before the particular interest amount being measured. The relevant balance can change over time.
Work through an example
For a hypothetical USD 5,000 balance at a stated 4% annual simple-interest rate for one year, interest is USD 200. The example does not apply interest on earlier interest. For a loan with repayments during the year, using the opening USD 5,000 for the whole year would not model a reducing balance accurately.
What this does not establish: The principal basis and accrual interval must be stated; a headline rate alone is insufficient.
CompoundingCompounding adds an earning period’s growth to the base used for the next period. Constant rates are a modeling assumption, not a prediction.
Work through an example
USD 1,000 growing at an assumed 5% once a year becomes USD 1,102.50 after two years with no deposits or charges. The second year earns on USD 1,050, not just the original USD 1,000. If the second year instead loses value, multiplying the actual sequence of growth factors is necessary; the constant-rate example no longer describes it.
What this does not establish: No investment, savings rate or two-year outcome is promised by this arithmetic.
Effective annual yieldAn effective annual yield expresses the one-year growth factor after compounding at the stated frequency, before any omitted costs.
Work through an example
A nominal 12% annual rate compounded monthly implies a 1% monthly rate. On an unchanged principal, twelve monthly periods produce an effective annual yield of about 12.68%. A separately quoted 12% effective annual yield has a smaller monthly equivalent. The two labels therefore cannot be compared as if they described identical growth.
What this does not establish: Withdrawal restrictions, fees, changing rates and special product conventions can change the realized result.
Present valuePresent value expresses a future cash amount at a selected valuation date using a specified discount-rate convention.
Work through an example
A hypothetical USD 1,100 due in one year has a present value of USD 1,000 at a 10% one-year discount rate. That is a valuation relationship, not a guaranteed account balance or an offer to buy the payment. A higher selected discount rate gives a lower present value for the same future receipt.
What this does not establish: The chosen discount rate does not remove default risk, uncertainty about receipt or liquidity constraints.
Real returnA real return measures growth relative to a stated price change, separating a larger nominal balance from a larger command over goods.
Work through an example
Under invented annual growth of 5% and price inflation of 3%, the exact real return is about 1.94%, rather than exactly 2%. A USD 1,000 nominal base becomes USD 1,050, while a USD 1,000 starting basket costs USD 1,030. Dividing the two growth factors keeps the measurement base consistent.
What this does not establish: The assumed inflation rate is not observed CPI and may differ from the prices relevant to a specific household.
Basis pointOne basis point is one hundredth of a percentage point. It describes an absolute change in a quoted percentage rate.
Work through an example
An assumed rate moves from 5.00% to 5.25%. The increase is 0.25 percentage points, or 25 basis points. It is also a 5% relative increase in the rate itself, because 0.25 divided by 5.00 equals 5%. These are different descriptions of the same change, not interchangeable units.
What this does not establish: A basis-point rate change is not automatically an equal percentage price change in an asset.
Business performance
Gross marginGross margin expresses revenue remaining after the stated cost-of-sales measure as a proportion of the same revenue.
Work through an example
Hypothetical revenue of USD 20,000 and cost of sales of USD 12,000 leave USD 8,000 of gross profit, or a 40% gross margin. That USD 8,000 still has to cover the operating costs excluded from cost of sales. Compare both the percentage and total dollars when product mix or revenue changes.
What this does not establish: Classification differences and business mix can prevent direct comparison between two companies’ reported margins.
Operating marginOperating margin relates a defined operating-profit measure to revenue over the same reporting period.
Work through an example
Assume USD 20,000 of revenue, USD 12,000 of cost of sales and USD 5,000 of other operating expense. Operating profit is USD 3,000 and operating margin is 15%. Borrowing costs and taxes are excluded in this deliberately simplified setup. A gross margin of 40% would not describe this narrower residual.
What this does not establish: Specify which adjustments and costs are included before comparing the margin with another business.
Contribution per unitContribution per unit is a product’s selling price less the variable cost assigned to supplying one additional unit in the model.
Work through an example
An invented USD 50 sale with USD 30 of variable cost contributes USD 20 toward fixed costs and then operating profit. Selling one more unit is helpful only if the relevant costs and available capacity match that assumption. A step-up in staffing or a displaced higher-value order can change the incremental decision.
What this does not establish: A positive contribution is not the same as positive total profit after fixed costs.
Break-even volumeBreak-even volume is the sales quantity at which modeled revenue equals the included operating costs. Whole-unit models round a fractional requirement upward.
Work through an example
With USD 5,000 of fixed costs, a USD 50 price and USD 30 variable unit cost, the exact requirement is 250 units. At 200 units, the same assumptions leave USD 1,000 of operating loss. At 300 units, operating profit is USD 1,000. The threshold does not say that customers will actually buy that volume.
What this does not establish: This is a single-product, constant-price and constant-variable-cost model without capacity changes.
Free cash flowFree cash flow needs an explicit definition. Here it means operating cash flow less cash capital expenditure for the same period.
Work through an example
A hypothetical USD 12,000 of operating cash flow minus USD 7,000 of cash capital spending leaves USD 5,000 under this definition. A debt repayment of USD 4,000 is a separate claim on that amount. Calling all USD 5,000 distributable would ignore financing obligations and other uses of cash.
What this does not establish: Other definitions exist; a positive result does not establish sustainable earnings or unrestricted cash.
Enterprise valueEnterprise value is a bridge between equity value and other included financial claims, using explicitly selected debt and cash amounts.
Work through an example
An invented equity value of USD 100,000 plus USD 30,000 of debt less USD 10,000 of included cash produces USD 120,000. If some cash is restricted or needed for operations, the subtraction needs reconsideration. The definition must also say whether leases, minority claims or other financing items enter the bridge.
What this does not establish: The simplified bridge is not an appraisal and does not establish an executable purchase price.
Portfolio measures
Coupon rateA fixed coupon rate expresses the contractual annual coupon amount relative to the bond’s stated face value, not its current trading price.
Work through an example
An invented bond with USD 1,000 face value and USD 40 of annual coupon payments has a 4% coupon rate. A purchase price of USD 800 does not change that contractual ratio, although it changes other return measures. Payment frequency and any conditions in the contract still matter to the cash-flow schedule.
What this does not establish: A coupon rate is neither a yield-to-maturity calculation nor a guarantee of payment.
Current yieldCurrent yield compares a bond’s stated annual coupon amount with a selected current price, omitting redemption gains and losses.
Work through an example
A hypothetical USD 40 annual coupon divided by a USD 800 price gives a 5% current yield. The same bond has a 4% coupon rate on USD 1,000 face value. Neither number by itself incorporates the time to redemption, accrued interest, trading charges or the consequences of a missed payment.
What this does not establish: Current yield is not total return and does not value all remaining cash flows.
Modified durationModified duration summarizes approximate price sensitivity to a small yield change under a specified bond-pricing convention.
Work through an example
For an invented USD 10,000 holding with modified duration 5, a 0.50 percentage-point yield increase implies an approximate USD 250 price decline. The decimal yield change is 0.005. Using 0.50 in its place would exaggerate the modeled change one hundredfold. The approximation is local and ignores any cash income during the interval.
What this does not establish: Large or nonparallel yield moves, option effects, spread changes and convexity can materially alter the result.
DiversificationDiversification concerns the distribution of economically different exposures. A longer list of holdings can still share the same underlying risk.
Work through an example
Assume USD 10,000 of portfolio value, with 60% linked to one company. A 20% loss in that exposure removes USD 1,200 if everything else stays unchanged. Owning that company through two overlapping funds does not split the underlying risk into two independent exposures. Map economic holdings before counting account names.
What this does not establish: The unchanged-other-assets assumption is illustrative; diversification does not eliminate common shocks or guarantee protection.
Total returnA period’s total return includes the change in value and the distributions included by the stated measurement method.
Work through an example
An invented USD 1,000 investment ends at USD 1,040 and pays USD 40 of cash distributions during the period. Without reinvestment, fees or new contributions, the total holding-period return is 8%. Looking only at the price change would show 4%. A return calculation must explain how any intermediate contributions or reinvestment are treated.
What this does not establish: Do not count a distribution twice by adding it to a return series that already includes it.
DrawdownA drawdown measures the decline from an identified previous peak to a later value, using a stated valuation series.
Work through an example
A hypothetical portfolio falls from USD 10,000 to USD 8,000, a 20% drawdown. Returning from USD 8,000 to USD 10,000 requires a 25% gain on the smaller base. Neither percentage says how long recovery will take or whether a future recovery will occur. The chosen observations can miss a larger intraperiod decline.
What this does not establish: Contribution changes, withdrawals and valuation frequency must be handled consistently before interpreting an investor’s loss.
Funding decisions
Loan amortizationLoan amortization describes the scheduled reduction of principal through payments that may also cover interest and other included charges.
Work through an example
At a hypothetical USD 10,000 opening balance and 0.5% monthly rate, the month’s interest is USD 50. A USD 200 payment therefore reduces principal by USD 150 if there are no fees or other adjustments. The next opening principal would be USD 9,850, not USD 9,800. Actual statement allocation and rounding must be checked separately.
What this does not establish: This example does not model daily accrual, additional fees, delinquency or special lender allocation rules.
Loan-to-value ratioLoan-to-value relates an included loan balance to a selected collateral valuation. The numerator, denominator and valuation date need to be clear.
Work through an example
An invented USD 180,000 loan against a USD 240,000 value produces 75% loan-to-value. If that value falls to USD 200,000 without principal reduction, the ratio rises to 90%. The household’s monthly payment need not change at the same moment. The ratio and the household budget measure different constraints.
What this does not establish: This is arithmetic, not a lending eligibility threshold, valuation opinion or refinancing offer.
Debt-service coverageDebt-service coverage compares a defined cash-availability measure with the principal and interest obligations included for the same period.
Work through an example
Suppose an invented business has USD 120,000 of defined cash available and USD 100,000 of scheduled debt service for a year. Coverage is 1.20 times, leaving USD 20,000 before any uses excluded from that definition. Replacing cash available with EBITDA without explanation can change what the ratio actually says.
What this does not establish: Contract definitions vary. This illustration establishes neither covenant compliance nor creditworthiness.
Opportunity costOpportunity cost is the value of the best alternative given up when the same scarce resource is committed to one choice.
Work through an example
Committing USD 1,000 to an expense instead of leaving it in a hypothetical account earning 3% simple interest for one year forgoes USD 30 of modeled interest. That is only one part of the decision: the purchase might provide benefits, save costs or preserve time. Comparing alternatives requires a common horizon and a clear risk assumption.
What this does not establish: The 3% rate is invented; forgone modeled earnings are not a guaranteed loss.
Expected valueExpected value is a probability-weighted average of possible outcomes under a specified model. It is not the most likely result or a promised payoff.
Work through an example
An invented two-outcome model assigns a 25% chance to net USD 80 and a 75% chance to net negative USD 20. Expected value is USD 5. A single trial can still lose USD 20, and a household may be unable to absorb that loss. The probabilities are assumptions, not estimates from a financial product.
What this does not establish: Model quality depends on the outcome set and probabilities; an average cannot establish affordability or suitability.
Operating margin of safetyIn this operating-cost convention, a margin of safety measures how far modeled sales exceed break-even volume relative to the selected sales volume.
Work through an example
An invented business sells 400 units while its simplified break-even requirement is 250 units. The unit cushion is 150 and the margin of safety is 37.5%. It is not a cash reserve: customers may pay later, while suppliers may need cash first. A price change or fixed-cost step also changes the threshold.
What this does not establish: This is an operating break-even measure, not a statement that a stock is undervalued or that a business is safe.
Analytical checks
Asset turnoverAsset turnover compares a period’s revenue with the average included asset base, not merely the closing asset balance.
Work through an example
A simplified business earns USD 120,000 of annual revenue with USD 60,000 of average included assets, producing turnover of 2.0 times. A large equipment purchase on the final reporting date can distort a ratio using closing assets only. The numerator and asset definition should match the business question being asked.
What this does not establish: Higher turnover does not automatically mean better margins, lower risk or more cash generated.
Days sales outstandingDays sales outstanding scales a defined receivables balance against credit sales over a consistent reporting period to approximate collection intensity.
Work through an example
With USD 15,000 of average trade receivables, USD 90,000 of credit sales and a 90-day quarter, simplified DSO is 15 days. Using all revenue when some sales are cash sales changes the interpretation. A surge in sales near period end can also create a misleading result if only closing receivables are used.
What this does not establish: DSO is not an aging schedule and does not prove that a particular invoice will be paid.
Cash conversion cycleThe cash conversion cycle combines selected inventory, collection and supplier-payment intervals to describe operating funding timing.
Work through an example
Assume 45 inventory days, 30 receivable days and 40 payable days on consistent operating definitions. The modeled cash conversion cycle is 35 days. Those intervals summarize turnover patterns; they do not give the exact dates of every purchase, sale or settlement. Investigate a changing component before attributing the total to improved management.
What this does not establish: Seasonality, averaging choices and non-trade balances can undermine comparisons.
Ownership dilutionOwnership dilution reduces an existing holder’s percentage claim when the included share count grows and that holder does not participate proportionately.
Work through an example
A holder with 10 of 100 shares owns 10%. If 25 new shares are issued and the holder keeps 10, the claim becomes 10/125, or 8%. The change is two percentage points, a 20% relative decline in ownership percentage. The company may also receive resources for the new shares, so the percentage change alone does not determine the holder’s economic gain or loss.
What this does not establish: Issue price, use of proceeds and other claims matter; lower percentage ownership is not automatically lower dollar value.
Discount rateA discount rate is a selected conversion convention for valuing future cash flows at an earlier date. It should match the cash stream and period.
Work through an example
At a hypothetical 8% annual discount rate, USD 1,200 expected in one year has a present value of about USD 1,111.11. That calculation does not establish the right rate for a risky business or the probability of receiving the payment. Separating the selected rate from the cash-flow assumption makes a sensitivity table interpretable.
What this does not establish: Do not combine an annual rate with monthly periods without an explicit conversion convention.
Sensitivity analysisSensitivity analysis changes specified inputs to show how a model responds while identifying which assumptions remain fixed.
Work through an example
On an invented USD 10,000 unchanged balance under simple one-year interest, moving the annual rate assumption from 5% to 6% increases modeled interest by USD 100. The calculation shows a response to a chosen input change. It does not establish that either rate will occur, or that another variable would stay unchanged in practice.
What this does not establish: A sensitivity table is not a probability distribution or a forecast.
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Further reading
Savings & financial mathematics
Fixed Savings Fees: Why Small Balances Feel a Larger Percentage Drag
Translate a fixed account charge into a balance-based percentage, compare net hypothetical interest, and understand why advertised yield does not tell the whole story.
Small business operating decisions
Accept a Wholesale Order Only After Charging for Bottleneck Capacity
Evaluate a discounted wholesale order using contribution per unit, displaced retail work, setup, and scarce production hours.