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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

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All CPA BAR Formulas

Business Analysis 30 items

Economic value added (EVA)

EVA = NOPAT - (WACC \times Invested Capital)

NOPAT

= Net Operating Profit After Tax. Positive EVA = value creation.

Sales volume variance

Sales Volume Variance = (Actual Units - Budgeted Units) \times Budgeted CM per Unit

Favorable if actual units > budgeted units.

Direct labor variances

Rate Var=(AR−SR)×AH
Efficiency Var=(AH−SHallowed​)×SR
AR/SR=actual/standard rate; AH/SH=actual/standard hours.

CAPM cost of equity

r_{e} = r_{f} + β (r_{m} - r_{f})

Used to estimate required return on equity for WACC.

β

reflects systematic risk of the firm/division.

Degree of operating leverage (DOL) and financial leverage (DFL)

DOL=%ΔSales%ΔEBIT​=EBITCM​
DFL=%ΔEBIT%ΔEPS​=EBIT−IEBIT​
DCL = DOL × DFL.

Operating Income vs Free Cash Flow forecasting

O I = S a l es - O pE x

;

F C F F = O I \times (1 - t) + D & A - C a pE x - Δ N W C

— t = tax rate, D&A = depreciation/amortization, ΔNWC = change in net working capital. Used in DCF valuation.

Activity-Based Costing (ABC) — overhead rate

A c t i v i t y R a t e = E s t . O H C os t_{a c t i v i t y} / E s t . A c t i v i t y D r i v er

;

C os t_{p r o d u c t} = A c t i v i t y R a t e \times D r i v er C o n s u m e d

— traces OH to specific drivers; better than plant-wide for diverse product lines.

Economic Order Quantity (EOQ)

E O Q = \frac{2 D S}{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)

E U_{F I F O} = (B e g W I P \times % T o C o m pl e t e) + S t a r t e d A n d C o m pl e t e d + (E n d W I P \times % C o m pl e t e)

— separates prior-period beginning WIP work from current-period effort, yielding a pure current-period cost per equivalent unit.

Reorder Point (with safety stock)

R O P = (L T \times D U) + S S

— LT = lead time, DU = daily usage (LT×DU = expected usage during lead time), SS = safety stock buffering demand/lead-time variability.

Profitability Index (PI)

P I = P V_{f u t u r e C F} / I ni t ia l I n v es t m e n t = 1 + (N P V / I ni t ia l I n v es t m e n t)

— accept if PI ≥ 1; rank projects by PI under capital rationing.

Cost of equity — Dividend Discount Model (Gordon Growth)

R_{e} = \frac{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

D P B = years until \sum \frac{C F _{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 = (F C + T P) / C M_{u}

; $ sales:

(F C + T P) / C M %

. After-tax:

T P_{p r e} = T P_{p os t} / (1 - t)

. FC = fixed costs, TP = target profit, CM_u = CM/unit, CM% = CM ratio, t = tax rate.

Variable Overhead spending and efficiency variances

S p e n d in g = A V O H - (A H \times S R)

;

E f f i c i e n cy = (A H - S H) \times S R

— AVOH = actual VOH, AH = actual hours, SH = standard hours allowed, SR = standard VOH rate.

Process costing — equivalent units (weighted-average)

E U = U C + (E W I P \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)

N P V = \sum_{t = 1}^{n} \frac{C F _{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:

\sum_{t = 0}^{n} \frac{C F _{t}}{( 1 + I R R ) ^{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)

M I R R = (T V_{in f l o w s} / P V_{o u t f l o w s})^{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

M o S = A c t u a l S a l es - B E S a l es

;

M o S % = M o S / A c t u a l S a l es

— BE = break-even; shows how far sales can fall before hitting break-even.

Cost of debt and cost of preferred equity

K_{d} = Y T M \times (1 - T)

;

K_{p} = D_{p} / P_{n e t}

— YTM = yield to maturity, T = tax rate,

D_{p}

= annual preferred dividend,

P_{n e t}

= net issue price (no tax adj; pref divs not deductible)

Cost-Volume-Profit (CVP) — Break-Even in units

B E_{u ni t s} = F C / (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

;

Volume Var = Budgeted FOH - Applied FOH

, where Applied FOH = Std Hours Allowed × Std FOH Rate. Volume var = under/over capacity utilization.

Return on Investment (ROI)

R O I = \frac{O p er a t in g I n co m e}{A v g O p er a t in g A sse t s} = M a r g in \times T u r n o v er

; Margin = Op Inc/Sales, Turnover = Sales/Avg Op Assets. Used for divisional performance.

High-Low method (cost estimation)

V C / u ni t = (H i g h C os t - L o w C os t) / (H i g h A c t - L o w A c t)

;

F C = T o t a l C os t - (V C / u ni t \times A c t i v i t y)

. Uses only extreme observations — sensitive to outliers.

Weighted Average Cost of Capital (WACC)

W A C C = (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

B E_{$} = \frac{F i x e d C os t s}{C M R a t i o}

, where

C M R a t i o = \frac{S a l es - V a r iab l e C os t s}{S a l es}

. Use when product mix or per-unit data unavailable.

Direct Materials price and quantity variances

D M P r i ce V a r = (A P - S P) \times A Q_{p}

;

D M Qt y V a r = (A Q_{u} - S Q) \times S P

— AP/SP = actual/standard price, AQ_p = actual qty purchased, AQ_u = actual qty used, SQ = standard qty allowed; negative = favorable.

Payback Period

P a y ba c k = I ni t ia l I n v es t m e n t / A nn u a l C a s h F l o w

(uniform CF); else count years until cumulative CF ≥ initial investment. Ignores TVM and post-payback cash flows; liquidity proxy only.

Residual Income (RI)

R I = O p er a t in g I n co m e - (R e q u i r e d R a t e o f R e t u r n \times A v g O p er a t in g A sse t s)

— 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):

G W = (F V_{co n s i d} + F V_{N C I}) - F V_{n e t a sse t s}

; NCI at FV. Partial (IFRS only):

G W = F V_{co n s i d} - %_{p a r e n t} \times F V_{n e t a sse t s}

; 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

G W = C T + F V_{N C I} + F V_{P H I} - F V_{I N A}

— 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

C o m p E x p e n s e_{p er i o d} = (T o t a l G r an t - D a t e F V \div V es t in g P er i o d)

— 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)

C T A = Σ (A sse t s_{C R} - L ia b_{C R}) - E q u i t y_{H R} - N I_{A R}

— 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:

R e v e n u e = 0, P r o f i t = 0

; accumulate CIP & billings 2) At completion:

P r o f i t = C o n t r a c t P r i ce - T o t a l C os t s

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)

C u r r e n t R e v / T o t a l E x p ec t e d R e v

Derivative — net investment hedge (foreign subsidiary)

Effective portion → OCI (Cumulative Translation Adjustment); Ineffective portion → NI.

Δ F V_{h e d g e} = E f f ec t i v e_{O C I / C T A} + I n e f f ec t i v e_{N I}

. Released to NI on sale/substantial liquidation of foreign sub.

Long-term construction contract — % completion (cost-to-cost)

% C o m p = C os t s T oD a t e / T o t a l E s tC os t

;

R e v = % C o m p \times P r i ce

;

GP = % C o m p \times E s tP r o f i t

. 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

Fund balance classifications (lowest to highest restriction): Nonspendable, Restricted, Committed, Assigned, Unassigned.

Government-wide net position

Net Position=Assets+Def. Outflows−Liab.−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)

R e v e n u e = L e v y - U n co l l ec t ib l e A l l o w an ce - D e f er r e d I n f l o w s

. 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

= P V

of min lease payments; CR Other Financing Source–Lease

= P V

. 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.

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