2027 CFA® Level 1 formula sheet

Move a single amount forward through time. Each year's interest becomes part of the next year's starting amount.

When to use itAnnual compounding, a constant annual rate, and no additional deposits. Enter 6 for 6% in the example fields.

Translate a future amount into today's money using a discount rate.

When to use itA single future payment and annual compounding. The result is the positive value today.

Find the constant yearly rate that connects a beginning value to an ending value.

When to use itPositive starting and ending values; no intermediate cash flows. This is not the arithmetic mean of annual returns.

Include compounding within the year when comparing stated annual interest rates.

When to use itThe stated rate is nominal. Compounding periods must be a positive whole number.

Measure the constant per-period return with the same compounded outcome as two actual returns.

When to use itEqual-length periods, no external cash flows, and each return greater than −100%.

Average the returns observed in two equally weighted periods.

When to use itThis average does not describe the compound growth of an investment.

Compare how strongly quantity demanded responds to a change in the good's own price.

When to use itUse compatible percentage-change conventions. This example supplies the changes directly and holds other demand factors constant.

Add final spending on domestic production, including net exports.

When to use itAll components cover the same period and currency units. Investment includes gross capital formation.

Compare near-term assets with near-term obligations at a balance-sheet date.

When to use itUse matching dates and units. A high ratio alone does not establish the quality or liquidity of the assets.

Relate a period's earnings to the equity supporting those earnings.

When to use itThis example uses total net income and average total shareholders' equity consistently. Negative equity makes the conventional ratio difficult to interpret.

Separate profitability, asset efficiency, and financial leverage to explain ROE.

When to use itUse consistent income, sales, average assets, and average equity across the three ratios.

Express the inventory balance as the number of days of annual cost of goods sold it represents.

When to use itA 365-day year, annual COGS, and average inventory. Use a different day count if a question specifies one.

Subtract the investment outlay from the present value of its expected cash inflows.

When to use itThe initial outlay is entered as a positive amount; C1 and C2 arrive at each year-end. Use a discount rate appropriate to the cash flows.

Combine the required returns on debt and equity, allowing for the debt interest tax shield.

When to use itDebt and equity only; market-value weights total 100%. Interest is fully tax-deductible at the stated tax rate.

Value a stream of dividends growing at a constant rate indefinitely.

When to use itD1 is next period's dividend, not the dividend just paid. The required return must exceed perpetual growth.

Estimate a required return using exposure to market risk.

When to use itThe equity risk premium is the expected market return minus the risk-free rate. It is not the market return itself.

Express the share price as a multiple of earnings attributable to one share.

When to use itState whether EPS is trailing or forward. This example uses positive trailing EPS.

Combine downside, base, and upside valuation scenarios instead of relying on one outcome.

When to use itValues are measured at the same date. The three scenario probabilities are non-negative and sum to 100%.

Discount the only cash flow of a zero-coupon bond: its payment at maturity.

When to use itAnnual effective yield, no interim coupons, and the stated maturity payment is received.

Translate cash-flow timing into first-order sensitivity to a change in yield.

When to use itMacaulay duration is in years; y is nominal annual yield compounded m times. Use the same yield convention throughout.

Approximate a bond's percentage price move for a small yield change.

When to use itIgnores convexity and assumes unchanged cash flows. One basis point is 0.0001 in decimal yield.

Compare annual coupon income with the amount paid for the bond.

When to use itPrice and coupon refer to the same face amount. This omits reinvestment and any gain or loss at maturity.

Grow the spot price by the financing cost to obtain the no-arbitrage delivery price.

When to use itAnnual effective compounding, no income or storage cost, and frictionless borrowing and lending at the same rate.

A call holder uses the right to buy only when the asset is worth more than the strike.

When to use itPayoff per unit of underlying at expiration. Subtract the premium separately to find profit.

A put holder uses the right to sell only when the strike exceeds the asset's market price.

When to use itPayoff per unit of underlying at expiration. This is before the option premium.

Turn one year's stabilized property income into an estimated property value.

When to use itUse forward stabilized NOI before financing and income taxes, paired with a comparable capitalization rate.

Measure how borrowed funds amplify the spread between asset performance and financing cost.

When to use itOne period; fixed beginning debt, no taxes, fees, or interim cash flows. Losses can also be amplified.

Average expected returns using the share of capital allocated to each asset.

When to use itA fully invested, long-only two-asset portfolio. Weights refer to the start of the return period.

Include both individual volatility and how the two assets move together.

When to use itLong-only weights sum to 100%; both standard deviations use the same time horizon; correlation lies between −1 and 1.

Measure excess return relative to total return variability.

When to use itReturn, risk-free rate, and volatility use the same time horizon and compatible annualization. Positive standard deviation is required.