Free CFA Level 1 formula sheet
Find the equation, check the units, then solve a worked example. Start with 12 foundational formulas.
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Try 3 exercises12 of 12 selected formulas
Quantitative methods
Compound future value
FV = PV × (1 + r)^n
Calculator check
1,000 × 1.05^3 = 1157.625 currency units.
Variables, assumptions & common error
- Variables and units
- PV: currency today; FV: currency at period n; r: return per period; n: number of periods.
- When it applies
- A constant periodic rate; no deposits or withdrawals between the endpoints.
- Common error
- Match the rate period to n. A quoted annual rate is not automatically a monthly rate.
Quantitative methods
Present value of a single payment
PV = FV / (1 + r)^n
Calculator check
1,210 / 1.10^2 = 1000 currency units.
Variables, assumptions & common error
- Variables and units
- FV: future currency payment; r: discount rate per period; n: periods until payment.
- When it applies
- A single certain cash flow at the end of period n and a rate appropriate to its risk.
- Common error
- Discounting moves a payment backwards in time; multiplying moves it forwards.
Quantitative methods
Ordinary-annuity present value
PV = PMT × [1 - (1 + r)^(-n)] / r
Calculator check
100 × (1 - 1.10^(-3)) / 0.10 = 248.6852 currency units.
Variables, assumptions & common error
- Variables and units
- PMT: equal currency payment; r: rate per payment period; n: payment count.
- When it applies
- Payments arrive at each period end. For an annuity due, multiply this PV by (1 + r).
- Common error
- At r = 0 the present value is PMT × n; do not divide by zero.
Quantitative methods
Holding-period return
HPR = (P1 - P0 + income) / P0
Calculator check
(106 - 100 + 2) / 100 × 100 = 8 %.
Variables, assumptions & common error
- Variables and units
- P0/P1: beginning/ending price per unit; income: distributions during the holding period.
- When it applies
- No additional external cash flows; a one-period total return before tax and costs.
- Common error
- This is the holding-period return, not an annualized return unless the period is one year.
Economics
Exact real return
r_real = (1 + r_nominal) / (1 + inflation) - 1
Calculator check
(1.08 / 1.03 - 1) × 100 = 4.8544 %.
Variables, assumptions & common error
- Variables and units
- Both nominal return and inflation are decimals for the same period.
- When it applies
- Compare purchasing power over one common period; exclude taxes unless already reflected.
- Common error
- Subtracting inflation is an approximation, not this exact result.
Corporate issuers
Net present value
NPV = Σ CFt / (1 + r)^t, including CF0
Calculator check
-100 + 60 / 1.10 + 60 / 1.10^2 = 4.1322 currency units.
Variables, assumptions & common error
- Variables and units
- CFt: signed currency cash flow at date t; r: risk-appropriate rate per period.
- When it applies
- Cash flows and discount rates use the same currency and nominal/real basis.
- Common error
- The initial outlay is already at time zero and must not be discounted again.
Corporate issuers
After-tax weighted average cost of capital
WACC = we × re + wd × rd × (1 - T)
Calculator check
(0.60 × 0.10 + 0.40 × 0.05 × 0.75) × 100 = 7.5 %.
Variables, assumptions & common error
- Variables and units
- we/wd: market-value equity/debt weights; re/rd: costs of equity/debt; T: applicable tax rate.
- When it applies
- A simple debt/equity capital structure, deductible interest, and weights summing to one.
- Common error
- Do not tax-adjust the equity cost or silently substitute book-value weights.
Financial statement analysis
Current ratio
Current ratio = Current assets / Current liabilities
Calculator check
360 / 240 = 1.5 times.
Variables, assumptions & common error
- Variables and units
- Current assets and liabilities: currency balances from the same reporting date.
- When it applies
- Use consistent classifications; the ratio is a liquidity indicator, not a cash forecast.
- Common error
- Receivables and inventory may not convert to cash when liabilities fall due.
Portfolio management
CAPM required return
E(Ri) = Rf + βi × [E(Rm) - Rf]
Calculator check
(0.03 + 1.2 × (0.08 - 0.03)) × 100 = 9 %.
Variables, assumptions & common error
- Variables and units
- Rf: risk-free return; βi: market beta; E(Rm): expected market return, on a consistent horizon.
- When it applies
- A single market-risk-factor equilibrium model; the premium is expected, not guaranteed.
- Common error
- Multiply beta by the market premium, not by the entire market return.
Equity investments
Constant-growth dividend value
V0 = D1 / (r - g)
Calculator check
3 / (0.09 - 0.03) = 50 currency units per share.
Variables, assumptions & common error
- Variables and units
- D1: next-period dividend per share; r: required equity return; g: constant dividend growth.
- When it applies
- A sustainable perpetual growth rate with r > g and a stable payout policy.
- Common error
- If given D0, grow it once first. A denominator at or below zero invalidates this model.
Fixed income
Coupon-bond present value
P = Σ C / (1 + y)^t + F / (1 + y)^n
Calculator check
50 / 1.05 + 1,050 / 1.05^2 = 1000 currency units.
Variables, assumptions & common error
- Variables and units
- C: coupon per period; F: redemption amount; y: yield per coupon period; n: periods.
- When it applies
- Fixed promised cash flows, no embedded options, valuation on a coupon date.
- Common error
- With semiannual coupons use half the annual coupon, half a bond-equivalent yield and twice the years.
Fixed income
Modified-duration price approximation
ΔP / P ≈ -Dmod × Δy
Calculator check
-5 × 0.002 × 100 = -1 %.
Variables, assumptions & common error
- Variables and units
- Dmod: modified duration in years; Δy: absolute yield change as a decimal.
- When it applies
- A small parallel yield move with unchanged cash flows; ignores convexity.
- Common error
- 20 basis points is 0.002, not 0.20. Price and yield generally move in opposite directions.
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Three worked practice exercises
Three original exercises, separate from the level samples. Open explanations freely; written answers are self-reviewed, not graded.
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- Question 1 of 3Cash-flow timingMultiple choice
Case facts
A payment of 500 arrives two years from now. The annual effective discount rate is 8%.
Which operation places the payment at time zero?
Answer and explanations
PV = 500 / 1.08² = 428.67 approximately. Draw the time line before selecting a calculator operation.
- A: Multiplication takes the payment further forwards.
- B - correct: Two annual discount periods bring it to today.
- C: This treats a single payment as a perpetuity.
- Question 2 of 3Growth-model inputsMultiple choice
Case facts
The most recent dividend is 2. A stable firm grows dividends at 3% with a 9% required equity return.
Which dividend belongs in the Gordon numerator?
Answer and explanations
First grow D0 to D1 = 2.06. Then V0 = 2.06 / (0.09 - 0.03) = 34.33 approximately, under perpetual-growth assumptions.
- A: This is D0, not the next payment.
- B: This is the increase in the dividend, not the dividend itself.
- C - correct: D1 = 2 × 1.03 is the next payment.
- Question 3 of 3Rate unitsMultiple choice
Case facts
A bond has modified duration 7 and its yield falls by 10 basis points. Ignore convexity.
What is the approximate percentage price change?
Answer and explanations
Ten basis points is 0.001. The duration approximation is -7 × (-0.001) = +0.007, or +0.7%.
- A - correct: -7 × (-0.001) gives a positive 0.7% price change.
- B: This reverses the effect of a yield decline.
- C: This uses a yield move ten times too large.
Keep this checklist handy
What to do, at a glance
01Check the model
- Match the formula to the requested output.
- Read its assumptions before substituting numbers.
- Use your official exam-year outline for full coverage.
02Check the inputs
- Use decimal rates: 25 bp = 0.0025.
- Match rate periods, currencies and cash-flow dates.
- Round the final result, not intermediate steps.
03Use the reference
- Selected 2026 coverage; not a complete syllabus.
- Free HTML: no separate downloadable formula-sheet PDF.
- Browser printing is available for personal reference.
Put one idea into practice.
Try it first. Check the reasoning. Pick your next task.
Quick answers
Does this replace the official curriculum?
No. This is selected independent practice, not a complete syllabus or official exam. Check your exam-year outline.
Are these the official CFA formula sheets?
No. These are independent selected equations with original examples. The linked official outlines establish study scope, not endorsement or verification of these examples.
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Sources
Selected 2026 teaching content. Official sources do not endorse or verify these examples.
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