Variance Analyses: formula sheet

Key formulas

General variance rule (cost)

Cost variance = Standard cost for actual output − Actual cost

Positive means Favourable, negative means Adverse. Always use standard for actual output, not budgeted output.

General variance rule (sales/profit)

Sales or profit variance = Actual − Standard (or budgeted)

Positive means Favourable, negative means Adverse. The sign convention is reversed from cost.

Price-type variance

(Standard price − Actual price) × Actual quantity

Applies to material price, labour rate and overhead expenditure style variances.

Quantity-type variance

(Standard quantity for actual output − Actual quantity) × Standard price

Applies to material usage and labour efficiency. Valued at standard price.

Standard cost of a unit

Standard cost = Standard quantity × Standard price (for each element), summed

Prepare a standard cost card for material, labour, variable and fixed overheads.

Standard cost for actual output

Standard cost for actual output = Standard cost per unit × Actual units produced

This is the flexed standard used for comparison.

Material cost variance (MCV)

MCV = (SQ × SP) − (AQ × AP)

SQ is standard quantity for actual output. Positive means favourable, negative means adverse.

Material price variance (MPV)

MPV = (SP − AP) × AQ

AQ is the actual quantity purchased if price is isolated at purchase, or actual quantity used if isolated at consumption. Follow the question.

Material usage variance (MUV)

MUV = (SQ − AQ used) × SP

Valued at standard price. SQ is for actual output.

Revised standard quantity (RSQ)

RSQ of a material = Total actual input of all materials × (Standard quantity of that material ÷ Total standard input)

Same total as actual input, but in the standard ratio.

Material mix variance (MMV)

MMV = (RSQ − AQ) × SP

Calculated material by material. If the total actual input equals the total standard input for the output, this equals (SQ − AQ) × SP.

Material yield variance (MYV)

MYV = (SQ − RSQ) × SP, or (Actual output − Standard output for actual input) × Standard cost per unit of output

Both forms give the same answer.

Identities for checking

MCV = MPV + MUV; MUV = MMV + MYV

Use these to verify the answer. Signs must be added algebraically.

Labour cost variance (LCV)

LCV = (Standard hours for actual output × SR) − (Actual hours paid × AR)

SR = standard rate per hour, AR = actual rate per hour. Positive is favourable, negative is adverse.

Labour rate variance (LRV)

LRV = (SR − AR) × Actual hours paid

Some solutions use hours worked when there is no idle time. With idle time, use hours paid.

Labour efficiency variance (LEV)

LEV = (Standard hours for actual output − Actual hours worked) × SR

Uses hours worked, not hours paid.

Idle time variance

Idle time variance = Idle hours × SR

Always adverse, because idle hours earn no output.

Reconciliation

LCV = LRV + LEV + Idle time variance

Use this to check your answer.

Labour mix variance

Mix variance = (Revised standard hours − Actual hours worked) × SR, for each grade

Revised standard hours = total actual hours worked, shared in the standard ratio of grades.

Labour yield variance

Yield variance = (Standard hours for actual output − Revised standard hours) × SR, for each grade

Overall it equals total hours difference × average standard rate per hour.

Efficiency split

LEV = Mix variance + Yield variance

Holds when idle time is treated separately and hours worked are used.

Standard variable overhead rate

Budgeted variable overhead ÷ Budgeted hours (or units)

Use hours if the question bases absorption on hours; use units if it bases on output.

Standard fixed overhead rate

Budgeted fixed overhead ÷ Budgeted hours (or units)

Use the same base as the variable rate unless told otherwise.

Variable overhead total variance

(Standard hours for actual output × Standard rate) − Actual variable overhead

Positive is favourable. Equals expenditure plus efficiency variance.

Variable overhead expenditure variance

(Actual hours × Standard rate) − Actual variable overhead

Positive is favourable.

Variable overhead efficiency variance

(Standard hours for actual output − Actual hours) × Standard variable rate

Positive is favourable.

Fixed overhead total variance

(Standard hours for actual output × Standard fixed rate) − Actual fixed overhead

Equals expenditure plus volume variance.

Fixed overhead expenditure variance

Budgeted fixed overhead − Actual fixed overhead

Positive is favourable.

Fixed overhead volume variance

(Standard hours for actual output × Standard fixed rate) − Budgeted fixed overhead

Equivalent to (Actual output − Budgeted output) × Standard rate per unit.

Fixed overhead efficiency variance

(Standard hours for actual output − Actual hours) × Standard fixed rate

Positive is favourable.

Fixed overhead capacity variance

(Actual hours − Revised budgeted hours) × Standard fixed rate

Revised budgeted hours = budgeted hours × actual days ÷ budgeted days. If no calendar data is given, use budgeted hours.

Fixed overhead calendar variance

(Revised budgeted hours − Budgeted hours) × Standard fixed rate

Favourable if more working days than budget.

Volume variance check

Volume = Efficiency + Capacity + Calendar

Use this to verify your workings.

Sales value variance (turnover)

(AQ × AP) − (BQ × BP)

AQ = actual quantity, AP = actual price, BQ = budgeted quantity, BP = budgeted price. Favourable if actual sales exceed budget.

Sales price variance

AQ × (AP − BP)

Same figure under both methods. Favourable if actual price is higher.

Sales volume variance (turnover)

BP × (AQ − BQ)

Always at budgeted price. Equals mix variance + quantity variance.

Revised actual quantity (RAQ)

Total actual units × (BQ of the product ÷ Total BQ)

Actual total units spread in the budgeted proportion. Needed for mix and quantity variances.

Sales mix variance (turnover)

BP × (AQ − RAQ)

Sum over all products. Compares actual mix with budgeted mix for the same total units.

Sales quantity variance (turnover)

BP × (RAQ − BQ)

Sum over all products. Shortcut: (Total AQ − Total BQ) × average budgeted price per unit.

Total sales margin variance (profit)

Actual profit − Budgeted profit

Actual profit here is sales less standard cost of the actual units sold.

Sales margin volume variance

Budgeted margin per unit × (AQ − BQ)

Budgeted margin per unit = BP − standard cost per unit. Equals margin mix + margin quantity variance.

Sales margin mix variance

Budgeted margin per unit × (AQ − RAQ)

Sum over all products.

Sales margin quantity variance

Budgeted margin per unit × (RAQ − BQ)

Sum over all products. Shortcut: (Total AQ − Total BQ) × average budgeted margin per unit.

Reconciliation checks

Value variance = Price + Volume; Volume = Mix + Quantity

The same holds for margin variances. Use these to verify your answer.

Reconciliation identity

Actual profit = Budgeted profit + Σ Favourable variances − Σ Adverse variances

Use this as the spine of the statement. Always check it against actual sales less actual costs.

Sales price variance

(Actual price − Standard price) × Actual quantity sold

Positive means favourable.

Sales volume variance (absorption)

(Actual quantity sold − Budgeted quantity) × Standard profit per unit

Favourable if actual sales exceed budget.

Sales volume variance (marginal)

(Actual quantity sold − Budgeted quantity) × Standard contribution per unit

Use contribution, not profit, in marginal costing.

Material price and usage variances

Price = (Standard price − Actual price) × Actual quantity; Usage = (Standard quantity for actual output − Actual quantity) × Standard price

Standard quantity is based on actual output, not budgeted output.

Labour rate and efficiency variances

Rate = (Standard rate − Actual rate) × Actual hours; Efficiency = (Standard hours for actual output − Actual hours) × Standard rate

Add an idle time variance if idle hours are given: Idle hours × Standard rate, adverse.

Variable overhead variances

Expenditure = (Standard rate × Actual hours) − Actual variable overhead; Efficiency = (Standard hours for actual output − Actual hours) × Standard rate

Standard rate is per hour of the chosen base.

Fixed overhead variances

Expenditure = Budgeted fixed overhead − Actual fixed overhead; Volume = (Actual output − Budgeted output) × Standard fixed overhead rate per unit

Volume variance appears only in absorption costing.

Planning variance (material price)

(Original standard price − Revised standard price) × Actual quantity

Positive means favourable. Use the same logic for any element: original standard minus revised standard.

Operational variance (material price)

(Revised standard price − Actual price) × Actual quantity

Positive means favourable. Measures performance against the revised standard.

Total price variance check

Planning variance + Operational variance = Variance on original standard

Use this to check your split.

Revised standard cost for actual output

Revised standard quantity for actual output × Revised standard price

Base for operational usage and efficiency variances.

Operational usage variance

(Revised standard quantity for actual output − Actual quantity) × Revised standard price

Positive means favourable.

Investigation rule of thumb

Investigate if expected benefit of correction > cost of investigation

Also consider size, trend, controllability and whether it is within tolerance limits.

Standard costing entries (adverse variance)

Dr Variance A/c, Cr Material/Wages/Overhead control A/c

Favourable variance is the reverse: Dr control account, Cr Variance A/c.

Quick revision

• Variance = standard (or budget) figure minus actual figure for costs; the reverse for revenue and profit. Favourable means profit goes up.
• Always compute standard cost for actual output, not for budgeted output, when measuring cost variances.
• Material price variance = (standard price − actual price) × actual quantity purchased or used, as the question's basis states.
• Material usage variance = (standard quantity for actual output − actual quantity) × standard price.
• Material mix variance plus yield variance equals the usage variance.
• Labour rate variance uses actual hours paid; efficiency variance uses standard hours for actual output against actual hours worked.
• Idle time variance = idle hours × standard rate and is always adverse.
• Fixed overhead volume variance splits into capacity and efficiency, with calendar variance where the question gives days.
• Sales volume variance on a profit basis uses standard profit per unit; sales price variance compares actual and standard selling price on actual units.
• In reconciliation, favourable variances add to budgeted profit and adverse ones are deducted.
• Investigate a variance by size, trend, controllability and cost of investigation, not only because it is adverse.
• Check that sub-variances add to the total before you write the final answer.

Common mistakes

• Comparing actual cost with standard cost of budgeted output Fix: Always flex the standard to actual output before comparing.
• Marking a variance F or A by the sign of the number alone Fix: Ask whether profit rises or falls. Higher cost is A; higher sales or profit is F.
• Using actual price to value usage, mix or yield variances. Fix: Value every quantity variance at standard price. Actual price appears only in the price variance.
• Calculating RSQ with the standard total instead of the actual total input. Fix: RSQ always sums to the actual total input. Only the ratio comes from the standard.
• Using hours worked for the rate variance when idle time exists. Fix: Wages are paid for all hours paid. Compute rate variance on hours paid, and efficiency on hours worked.
• Valuing idle time at the actual rate. Fix: Idle time variance is idle hours × standard rate. The rate difference on those hours is already inside the rate variance.
• Using actual hours instead of standard hours for actual output when computing absorbed overhead. Fix: Always compute standard hours for actual output first: actual units × standard hours per unit.
• Mixing up the sign convention for fixed overhead expenditure variance. Fix: Use Budgeted − Actual. If you spent less than budget, it is favourable.
• Using actual price to value volume, mix or quantity variances Fix: Only the price variance uses AP. Volume, mix and quantity use budgeted price (turnover) or budgeted margin per unit (profit).
• Using selling price instead of margin in the profit method Fix: In the profit method, replace BP with budgeted profit per unit (BP − standard cost). Calculate it in a separate column first.

Exam tips

• Practise the F/A label until it is automatic. Many marks in MCQs are lost on direction, not calculation.
• For theory answers, list the types of standards with a one-line distinction each, then add attainability and motivation.
• In a case-based question, state the standard cost card first. It anchors every later variance.
• Write a short interpretation for each variance in descriptive questions, naming the likely cause and the responsible manager.
• When asked to differentiate standard costing and budgetary control, use points like unit versus total level, cost versus overall plan, and use for pricing and valuation.
• In MCQs, first decide whether the question wants a total or a material-wise variance, and whether it is favourable or adverse. Options often differ only in sign.
• With a single material, mix variance does not exist. Usage variance is the whole quantity variance.
• Check the wording on normal loss. If the standard has a normal loss, yield variance usually appears in the question.