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. 61 formulas across 3 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

61 Formulas
3 Topics
2026 Syllabus
Free Forever
Print-ready PDF: 1080x1350 portrait, math pre-rendered, fonts embedded. Download once, study anywhere.
Download PDF →

All CPA BAR Formulas

Business Analysis 30 items
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.
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 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.
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.
Operating Income vs Free Cash Flow forecasting
OI=Sales−OpExOI = Sales - OpEx; FCFF=OI×(1−t)+D&A−CapEx−ΔNWCFCFF = OI \times (1-t) + D\&A - CapEx - \Delta NWC — t = tax rate, D&A = depreciation/amortization, ΔNWC = change in net working capital. Used in DCF valuation.
Activity-Based Costing (ABC) — overhead rate
Activity Rate=Est. OH Costactivity/Est. Activity DriverActivity\ Rate = Est.\ OH\ Cost_{activity} / Est.\ Activity\ Driver; Costproduct=Activity Rate×Driver ConsumedCost_{product} = Activity\ Rate \times Driver\ Consumed — traces OH to specific drivers; better than plant-wide for diverse product lines.
Economic Order Quantity (EOQ)
EOQ=2DSHEOQ = \sqrt{\dfrac{2DS}{H}} — D = annual demand (units), S = cost per order, H = carrying cost per unit/yr. Minimizes total ordering + carrying cost; assumes constant demand, constant lead time, no stockouts.
Process costing — equivalent units (FIFO)
EUFIFO=(BegWIP×%ToComplete)+StartedAndCompleted+(EndWIP×%Complete)EU_{FIFO} = (BegWIP \times \%ToComplete) + StartedAndCompleted + (EndWIP \times \%Complete) — separates prior-period beginning WIP work from current-period effort, yielding a pure current-period cost per equivalent unit.
Reorder Point (with safety stock)
ROP=(LT×DU)+SSROP = (LT \times DU) + SS — LT = lead time, DU = daily usage (LT×DU = expected usage during lead time), SS = safety stock buffering demand/lead-time variability.
Profitability Index (PI)
PI=PVfuture CF/Initial Investment=1+(NPV/Initial Investment)PI = PV_{future\ CF} / Initial\ Investment = 1 + (NPV / Initial\ Investment) — accept if PI ≥ 1; rank projects by PI under capital rationing.
Cost of equity — Dividend Discount Model (Gordon Growth)
Re=D1P0+gR_e = \dfrac{D_1}{P_0} + g — D1 = next year's expected dividend, P0 = current stock price, g = constant perpetual dividend growth rate. Assumes g < Re.
Discounted Payback Period
DPB=years until ∑CFt(1+r)t≥C0DPB = \text{years until } \sum \frac{CF_t}{(1+r)^t} \geq C_0 — CF_t = cash flow in year t, r = discount rate, C_0 = initial investment. Ignores CFs after payback.
CVP — Target profit units
Q=(FC+TP)/CMuQ = (FC + TP) / CM_u; $ sales: (FC+TP)/CM%(FC + TP)/CM\%. After-tax: TPpre=TPpost/(1−t)TP_{pre} = TP_{post}/(1-t). FC = fixed costs, TP = target profit, CM_u = CM/unit, CM% = CM ratio, t = tax rate.
Variable Overhead spending and efficiency variances
Spending=AVOH−(AH×SR)Spending = AVOH - (AH \times SR); Efficiency=(AH−SH)×SREfficiency = (AH - SH) \times SR — AVOH = actual VOH, AH = actual hours, SH = standard hours allowed, SR = standard VOH rate.
Process costing — equivalent units (weighted-average)
EU=UC+(EWIP×%C)EU = UC + (EWIP \times \%C) — EU = equivalent units, UC = units completed & transferred out, EWIP = ending WIP units, %C = % complete in EWIP. Beg WIP costs lumped with current-period costs (no separation).
Net Present Value (NPV)
NPV=∑t=1nCFt(1+r)t−C0NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - C_0 — CF_t = cash flow in period t, r = required return/WACC, C_0 = initial outlay. Accept project if NPV ≥ 0.
Internal Rate of Return (IRR)
IRR = discount rate where NPV = 0: ∑t=0nCFt(1+IRR)t=0\sum_{t=0}^{n} \frac{CF_t}{(1+IRR)^t} = 0. Accept project if IRR ≥ hurdle rate. Assumes cash flows reinvested at IRR (often unrealistic vs. NPV's WACC assumption).
Modified Internal Rate of Return (MIRR)
MIRR=(TVinflows/PVoutflows)1/n−1MIRR = (TV_{inflows} / PV_{outflows})^{1/n} - 1 — TV = terminal value of inflows reinvested at cost of capital, PV = present value of outflows, n = project life. Avoids IRR's multiple-rate problem.
Margin of Safety
MoS=Actual Sales−BE SalesMoS = Actual\ Sales - BE\ Sales; MoS%=MoS/Actual SalesMoS\% = MoS / Actual\ Sales — BE = break-even; shows how far sales can fall before hitting break-even.
Cost of debt and cost of preferred equity
Kd=YTM×(1−T)K_d = YTM \times (1 - T); Kp=Dp/PnetK_p = D_p / P_{net} — YTM = yield to maturity, T = tax rate, DpD_p = annual preferred dividend, PnetP_{net} = net issue price (no tax adj; pref divs not deductible)
Cost-Volume-Profit (CVP) — Break-Even in units
BEunits=FC/(P−V)BE_{units} = FC / (P - V) — FC = total fixed costs, P = selling price/unit, V = variable cost/unit; denominator is contribution margin per unit. Assumes linear cost/revenue within relevant range.
Fixed Overhead budget and volume variances
Budget Var=Actual FOH−Budgeted FOH\text{Budget Var} = \text{Actual FOH} - \text{Budgeted FOH}; Volume Var=Budgeted FOH−Applied FOH\text{Volume Var} = \text{Budgeted FOH} - \text{Applied FOH}, where Applied FOH = Std Hours Allowed × Std FOH Rate. Volume var = under/over capacity utilization.
Return on Investment (ROI)
ROI=Operating IncomeAvg Operating Assets=Margin×TurnoverROI = \frac{Operating\ Income}{Avg\ Operating\ Assets} = Margin \times Turnover; Margin = Op Inc/Sales, Turnover = Sales/Avg Op Assets. Used for divisional performance.
High-Low method (cost estimation)
VC/unit=(High Cost−Low Cost)/(High Act−Low Act)VC/unit = (High\ Cost - Low\ Cost)/(High\ Act - Low\ Act); FC=Total Cost−(VC/unit×Activity)FC = Total\ Cost - (VC/unit \times Activity). Uses only extreme observations — sensitive to outliers.
Weighted Average Cost of Capital (WACC)
WACC=(E/V)⋅Re+(D/V)⋅Rd⋅(1−t)WACC = (E/V) \cdot R_e + (D/V) \cdot R_d \cdot (1 - t) — E = mkt value equity, D = mkt value debt, V = E + D, R_e = cost of equity, R_d = pretax cost of debt, t = tax rate
Cost-Volume-Profit (CVP) — Break-Even in dollars
BE$=Fixed CostsCM RatioBE_\$ = \dfrac{Fixed\ Costs}{CM\ Ratio}, where CM Ratio=Sales−Variable CostsSalesCM\ Ratio = \dfrac{Sales - Variable\ Costs}{Sales}. Use when product mix or per-unit data unavailable.
Direct Materials price and quantity variances
DM Price Var=(AP−SP)×AQpDM\ Price\ Var = (AP - SP) \times AQ_p; DM Qty Var=(AQu−SQ)×SPDM\ Qty\ Var = (AQ_u - SQ) \times SP — AP/SP = actual/standard price, AQ_p = actual qty purchased, AQ_u = actual qty used, SQ = standard qty allowed; negative = favorable.
Payback Period
Payback=Initial Investment/Annual Cash FlowPayback = Initial\ Investment / Annual\ Cash\ Flow (uniform CF); else count years until cumulative CF ≥ initial investment. Ignores TVM and post-payback cash flows; liquidity proxy only.
Residual Income (RI)
RI=Operating Income−(Required Rate of Return×Avg Operating Assets)RI = Operating\ Income - (Required\ Rate\ of\ Return \times Avg\ Operating\ Assets) — positive RI means division earned above its cost of capital; avoids ROI's underinvestment problem.
Technical Accounting and Reporting 16 items
Software costs — capitalize vs expense (internal-use)
Internal-use software (ASC 350-40): 1) Preliminary stage = expense. 2) Application Development = capitalize direct costs (coding, config, testing); expense training. 3) Post-Implementation = expense. Amortize capitalized cost straight-line over useful life.
Franchise revenue recognition
1) Initial fee: recognize when performance obligations satisfied (training, site selection substantially performed). 2) Continuing royalties: recognize over time as franchisee operates (sales-based royalty exception). 3) Pre-opening services: recognize as each PO is met.
Non-controlling interest — full vs partial goodwill
Full (US GAAP req'd): GW=(FVconsid+FVNCI)−FVnet assetsGW = (FV_{consid} + FV_{NCI}) - FV_{net\,assets}; NCI at FV. Partial (IFRS only): GW=FVconsid−%parent×FVnet assetsGW = FV_{consid} - \%_{parent} \times FV_{net\,assets}; NCI = \%_{NCI} × FV net assets.
Derivative — cash flow hedge
Hedges forecasted txn. 1) Effective portion of FV change → OCI (deferred) 2) Reclassify from AOCI → NI when hedged item affects earnings 3) Ineffective portion → NI immediately 4) Requires formal designation + effectiveness testing.
Derivative — fair value hedge
FV hedge: 1) Hedged item ΔFV → Net Income (adjust carrying amount). 2) Derivative ΔFV → Net Income. 3) Net P&L impact = ineffective portion only (effective portions offset in NI).
Acquisition method — goodwill calculation
GW=CT+FVNCI+FVPHI−FVINAGW = CT + FV_{NCI} + FV_{PHI} - FV_{INA} — CT = consideration transferred, FV_NCI = FV of noncontrolling interest, FV_PHI = acquisition-date FV of previously held interest, FV_INA = FV of identifiable net assets. If negative → bargain purchase gain to NI.
Software revenue recognition (post-ASC 606)
ASC 606 software: 1) Identify POs: license, implementation, PCS, training. 2) License = functional (point-in-time at delivery) or symbolic/access (over time). 3) Allocate price by relative SSP. 4) PCS recognized ratably over support period.
IFRS vs GAAP — inventory and impairment
IFRS: LIFO prohibited (FIFO/WA only); inventory at lower of cost or NRV; impairment reversal allowed (except goodwill). GAAP: LIFO permitted (uses LCM with ceiling/floor); FIFO/WA uses LCNRV; NO impairment reversal.
Stock-based compensation — fair-value method
Comp Expenseperiod=(Total Grant-Date FV÷Vesting Period)Comp\ Expense_{period} = (Total\ Grant\text{-}Date\ FV \div Vesting\ Period) — FV from option-pricing model (Black-Scholes/binomial) at grant; not remeasured for stock-price changes; true-up only for forfeitures.
Foreign currency translation — Cumulative Translation Adjustment (CTA)
CTA=Σ (AssetsCR−LiabCR)−EquityHR−NIARCTA = \Sigma\,(Assets_{CR} - Liab_{CR}) - Equity_{HR} - NI_{AR} — CR=current rate, HR=historical rate, AR=avg rate. Recorded in OCI/Equity; reclassified to NI upon sale or substantial liquidation of foreign sub.
R&D costs — capitalize vs expense
ASC 730 default: expense as incurred. Capitalize when: 1) tangible asset with alternative future use (capitalize, then depreciate to R&D); 2) software costs after technological feasibility (ASC 985-20); 3) IPR&D in business combination (indefinite-life intangible until project completes).
Long-term construction — completed-contract method (rare under ASC 606)
Defer all revenue & profit until completion: 1) During: Revenue=0, Profit=0Revenue=0,\ Profit=0; accumulate CIP & billings 2) At completion: Profit=Contract Price−Total CostsProfit=Contract\ Price-Total\ Costs 3) Losses: recognize immediately when probable. ASC 606: only if control transfers at a point in time.
Software costs — capitalize vs expense (sale to others)
Pre-tech feasibility: expense as R&D. Post-tech feasibility (working model): capitalize. Post-release: amortize at greater of (a) SL over economic life or (b) Current Rev/Total Expected RevCurrent\ Rev / Total\ Expected\ Rev.
Derivative — net investment hedge (foreign subsidiary)
Effective portion → OCI (Cumulative Translation Adjustment); Ineffective portion → NI. ΔFVhedge=EffectiveOCI/CTA+IneffectiveNI\Delta FV_{hedge} = Effective_{OCI/CTA} + Ineffective_{NI}. Released to NI on sale/substantial liquidation of foreign sub.
Long-term construction contract — % completion (cost-to-cost)
%Comp=CostsToDate/TotalEstCost\%Comp = CostsToDate / TotalEstCost; Rev=%Comp×PriceRev = \%Comp \times Price; GP=%Comp×EstProfitGP = \%Comp \times EstProfit. Any expected total loss recognized in full immediately.
Convertible debt — bifurcation (post-ASU 2020-06)
Single-instrument: 1) Record full proceeds as debt at face. 2) Amortize using stated rate (no BCF, no cash-conversion bifurcation). 3) Bifurcate ONLY if conversion feature is a derivative under ASC 815 or substantial premium exists. Eff: PBE 2022, others 2024.
State and Local Governments 15 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).
Government-wide vs fund-level reconciliation
GW Net Position = Fund Balance + Capital Assets (net of A/D) − LT Debt + Deferred Inflows/Outflows adj + ISF Net Position. Converts modified accrual (current resources) to full accrual (economic resources). Shown at bottom of fund B/S and Stmt of Rev/Exp/Changes.
Five governmental fund types (GRaSPP)
GRaSPP (modified accrual, current financial resources): 1) General — ordinary ops 2) Special Revenue — earmarked 3) Debt Service — LT debt P&I 4) Capital Projects — major construction 5) Permanent — corpus restricted, only income spendable.
Four fiduciary fund types (PAPI)
PAPI fiduciary funds: 1) Pension (and OPEB) trust 2) Agency/Custodial (temporary holdings for others) 3) Private-purpose trust (non-investment assets for individuals/private orgs) 4) Investment trust (external pools). All use full accrual + economic resources measurement.
Fund balance classifications (NRSCAU)
Governmental fund balance hierarchy: 1) **N**onspendable (inventory, prepaids, permanent fund principal); 2) **R**estricted (external constraints); 3) **C**ommitted (highest-level formal vote); 4) **A**ssigned (intended use, lower-level); 5) **U**nassigned (residual; only General Fund can be positive).
Property tax revenue (modified accrual)
Revenue=Levy−Uncollectible Allowance−Deferred InflowsRevenue = Levy - Uncollectible\ Allowance - Deferred\ Inflows. Recognize when LEVIED if measurable AND available (collectible within current period or ≤60 days after year-end). Collections >60 days post year-end = Deferred Inflows of Resources.
MD&A required content (GASB 34)
MD&A (RSI, before basic F/S): 1) brief F/S overview 2) condensed prior-year comparison 3) analysis of overall financial position & results 4) discussion of significant variations 5) capital asset & long-term debt activity 6) currently known facts/decisions affecting future.
Two proprietary fund types (SE)
Proprietary funds (full accrual, economic resources): 1) Internal Service Fund — serves internal govt customers on cost-reimbursement basis. 2) Enterprise Fund — serves external customers; required if debt is fee-secured, fees legally recover costs, or pricing targets cost recovery.
NFP vs governmental — when which framework applies
GASB if ANY: 1) majority of governing body appointed by govt 2) unilateral dissolution with assets to govt 3) power to enact/enforce a tax levy. Else FASB ASC 958 (NFP). Most public hospitals/universities/museums = GASB.
Encumbrance accounting (governmental funds only)
PO issued: DR Encumbrances / CR Reserve for Encumbrances. Goods received: 1) DR Reserve for Encumbrances / CR Encumbrances 2) DR Expenditures / CR Vouchers Payable. Year-end open encumbrances reduce unassigned fund balance.
Capital lease (government) — JE at inception
Fund level (modified accrual): DR Expenditure–Capital Outlay =PV= PV of min lease payments; CR Other Financing Source–Lease =PV= PV. Government-wide: DR Capital Asset; CR Lease Liability (ASC 842/GASB 87). Reconciled in gov't-wide statements.
Special items vs extraordinary items (governmental)
Special: unusual OR infrequent AND within mgmt control (e.g., land sale gain). Extraordinary: unusual AND infrequent AND outside mgmt control (e.g., natural disaster). Both shown separately at bottom of gov-wide Statement of Activities (GASB 34).
Component units — discretely vs blended presentation
Discrete: separate column on gov-wide F/S (default). Blended if ANY: 1) governing body substantively the same; 2) services almost exclusively to primary gov; 3) debt expected to be repaid by primary gov.

Frequently Asked Questions

Is the CPA BAR formula sheet free?
Yes. The full CPA BAR formula sheet is free, with no signup, no email, and no credit card required. 61 formulas across 3 topics, all rendered with the same KaTeX math notation used in the FreeFellow study app.
Can I download the CPA BAR formula sheet as a printable PDF?
Yes. A 1080x1350 portrait PDF (Instagram and LinkedIn carousel native size, also great for tablet study) is linked at the top of this page. The PDF is fully self-contained: math is pre-rendered, fonts are embedded, no internet connection needed once downloaded.
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.
What is FreeFellow's relationship with CPA?
No. FreeFellow is not affiliated with the CPA or any examination body. This is an independent study aid covering the published syllabus.
What else is free at FreeFellow for CPA BAR candidates?
The full question bank with detailed solutions, mixed practice, readiness tracking, lessons (where available), and the formula sheet are all free forever. Fellow ($59/quarter or $149/year per track) unlocks timed mock exams, spaced-repetition flashcards, performance analytics, AI essay grading, and a personalized study plan.
Practice CPA BAR questions free →

Formula sheets for other exams

Exam P Exam FM Exam FAM Exam SRM Exam ALTAM Exam ASTAM CFA Level I CFA Level II CFA L3 Portfolio Mgmt CFA L3 Private Wealth CFA L3 Private Markets CFP

About FreeFellow

FreeFellow is an AI-native exam prep platform for actuarial (SOA & CAS), CFA, CFP, CPA, CAIA, GARP FRM, IRS Enrolled Agent, IMA CMA, and FINRA / NASAA securities licensing candidates — built around modern AI as a core capability rather than as a bolt-on. Every lesson ships with AI-narrated audio. Every constructed-response item has a copy-to-AI prompt builder so candidates can paste their answer into their own ChatGPT or Claude for self-graded feedback. Fellow members get instant AI grading on essays against the official rubric (currently CFA Level III, expanding to other essay-bearing sections).

The 70% you need to pass — question bank, written solutions, lessons, formula sheet, mixed practice, readiness tracking — is free forever, with no trial period and no credit card. Become a Fellow ($59/quarter or $149/year per track) to unlock mock exams, flashcards with spaced repetition, performance analytics, AI essay grading, and a personalized study plan.