Free CPA BAR (Business Analysis & Reporting) Formula Sheet (2026)

Every CPA BAR formula you need on the test, grouped by topic, rendered with full math notation. 19 formulas across 2 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

19 Formulas
2 Topics
2026 Syllabus
Free Forever
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All CPA BAR Formulas

Business Analysis 16 items
Return on investment (ROI)
ROI=Operating IncomeInvested Assets (Average)\text{ROI} = \frac{\text{Operating Income}}{\text{Invested Assets (Average)}}
Alternatively: ROI=Profit Margin×Asset Turnover\text{ROI} = \text{Profit Margin} \times \text{Asset Turnover} (DuPont decomposition).
Residual income
RI=Operating Income−(Required Rate of Return×Invested Assets)\text{RI} = \text{Operating Income} - (\text{Required Rate of Return} \times \text{Invested Assets})
Positive RI = earns above minimum required return. Used in decentralized performance evaluation.
Economic value added (EVA)
EVA=NOPAT−(WACC×Invested Capital)\text{EVA} = \text{NOPAT} - (\text{WACC} \times \text{Invested Capital})
NOPAT\text{NOPAT} = Net Operating Profit After Tax. Positive EVA = value creation.
Breakeven: units and dollars
BEPunits=FCCM per unit\text{BEP}_{units} = \frac{FC}{\text{CM per unit}}
BEP$=FCCM ratio\text{BEP}_{\$} = \frac{FC}{\text{CM ratio}}
CM ratio=CM per unitPrice per unit\text{CM ratio} = \frac{\text{CM per unit}}{\text{Price per unit}}
Contribution margin
CM=Sales Revenue−Variable Costs\text{CM} = \text{Sales Revenue} - \text{Variable Costs}
CM per Unit=Selling Price−Variable Cost per Unit\text{CM per Unit} = \text{Selling Price} - \text{Variable Cost per Unit}
Fixed costs are excluded; CM covers fixed costs first, remainder is operating income.
Sales volume variance
Sales Volume Variance=(Actual Units−Budgeted Units)×Budgeted CM per Unit\text{Sales Volume Variance} = (\text{Actual Units} - \text{Budgeted Units}) \times \text{Budgeted CM per Unit}
Favorable if actual units > budgeted units.
Direct materials variances
Price Var=(AP−SP)×AQpurchased\text{Price Var} = (AP - SP) \times AQ_{purchased}
Quantity Var=(AQused−SQallowed)×SP\text{Quantity Var} = (AQ_{used} - SQ_{allowed}) \times SP
AP/SP=actual/standard price; AQ/SQ=actual/standard qty.
Direct labor variances
Rate Var=(AR−SR)×AH\text{Rate Var} = (AR - SR) \times AH
Efficiency Var=(AH−SHallowed)×SR\text{Efficiency Var} = (AH - SH_{allowed}) \times SR
AR/SR=actual/standard rate; AH/SH=actual/standard hours.
Net present value (NPV)
NPV=∑t=0nCFt(1+r)t\text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}
Accept project if NPV ≥0\geq 0. NPV uses WACC as discount rate. Accounts for time value of money and all cash flows.
Internal rate of return (IRR)
Rate r∗r^* such that NPV = 0. Accept if IRR ≥\geq required rate of return (hurdle rate).
For non-normal cash flows (multiple sign changes), multiple IRRs possible — use NPV instead.
Payback period
Payback=Initial InvestmentAnnual Net Cash Inflows\text{Payback} = \frac{\text{Initial Investment}}{\text{Annual Net Cash Inflows}} (even flows)
For uneven flows: cumulate cash flows until initial investment recovered.
Ignores time value and post-payback cash flows.
Weighted average cost of capital (WACC)
WACC=wdrd(1−T)+wprp+were\text{WACC} = w_d r_d(1-T) + w_p r_p + w_e r_e
ww = weight (market value), rdr_d = pre-tax cost of debt, TT = tax rate, rpr_p = cost of preferred, rer_e = cost of equity.
CAPM cost of equity
re=rf+β(rm−rf)r_e = r_f + \beta(r_m - r_f)
Used to estimate required return on equity for WACC. β\beta reflects systematic risk of the firm/division.
Degree of operating leverage (DOL) and financial leverage (DFL)
DOL=%ΔEBIT%ΔSales=CMEBITDOL = \frac{\%\Delta EBIT}{\%\Delta Sales} = \frac{CM}{EBIT}
DFL=%ΔEPS%ΔEBIT=EBITEBIT−IDFL = \frac{\%\Delta EPS}{\%\Delta EBIT} = \frac{EBIT}{EBIT - I}
DCL = DOL × DFL.
Overhead variances (2-variance method)
Budget Var=Actual OH−Flex Budget OH\text{Budget Var} = \text{Actual OH} - \text{Flex Budget OH}
Volume Var=Flex Budget OH−OH Applied\text{Volume Var} = \text{Flex Budget OH} - \text{OH Applied}
=Fixed OH Rate×(Denom Hrs−SHallowed)= \text{Fixed OH Rate} \times (\text{Denom Hrs} - SH_{allowed})
Profitability index (PI)
PI=PV of Future Cash InflowsInitial Investment\text{PI} = \frac{\text{PV of Future Cash Inflows}}{\text{Initial Investment}}
Accept if PI ≥1\geq 1 (equivalent to NPV ≥0\geq 0). Useful for ranking projects under capital rationing.
State and Local Governments 3 items
Governmental fund balance equation
Fund Balance=Assets+Deferred Outflows−Liabilities−Deferred Inflows\text{Fund Balance} = \text{Assets} + \text{Deferred Outflows} - \text{Liabilities} - \text{Deferred Inflows}
Fund balance classifications (lowest to highest restriction): Nonspendable, Restricted, Committed, Assigned, Unassigned.
Government-wide net position
Net Position=Assets+Def. Outflows−Liab.−Def. Inflows\text{Net Position} = \text{Assets} + \text{Def. Outflows} - \text{Liab.} - \text{Def. Inflows}
Categories: Net investment in capital assets; Restricted; Unrestricted.
Full accrual basis (economic resources focus).
Modified accrual revenue recognition
Revenues recognized when measurable AND available.
Available = collectible within current period or within 60 days after year-end (commonly).
Expenditures recognized when liability incurred (except debt service, long-term liabilities).

Frequently Asked Questions

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Yes. The full CPA BAR formula sheet is free, with no signup, no email, and no credit card required. 19 formulas across 2 topics, all rendered with the same KaTeX math notation used in the FreeFellow study app.
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What's covered on the CPA BAR formula sheet?
Every formula is grouped by official syllabus topic, with the formula in math notation plus a one-line note on when to use it (or a watch-out from CAIA, CFA, or other prep-provider commentary). Coverage is calibrated to the 2026 syllabus and refreshed when the corpus changes.
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