Standard Costing and Variance Analysis: formula sheet

Key formulas

Standard cost per unit

Standard material + Standard labour + Standard overhead (variable and fixed)

Each element is built as standard quantity (or time) × standard price (or rate).

Standard material cost

Standard quantity per unit × Standard price per unit of material

Standard quantity includes normal loss or wastage allowed.

Standard labour cost

Standard hours per unit × Standard wage rate per hour

Standard hours include allowance for normal idle time and fatigue where applicable.

Standard overhead rate

Budgeted overheads ÷ Budgeted base (units or hours)

Calculate separately for variable and fixed overheads.

Standard overhead cost per unit

Standard overhead rate × Standard hours (or units) per unit

Base must be the same one used to compute the rate.

Standard input for given output

Standard input = Standard output ÷ (1 − normal loss %)

Use when the question gives output required and a normal loss percentage on input.

Material cost variance (MCV)

MCV = (SQ × SP) − (AQ × AP)

SQ is the standard quantity for actual output. A positive result is favourable.

Material price variance (MPV)

MPV = AQ × (SP − AP)

Use AQ purchased if the question asks for price variance on purchase, and AQ used if it is on consumption. Read the question.

Material usage variance (MUV)

MUV = SP × (SQ − AQ)

AQ here is the quantity actually used. Valued at standard price.

Material mix variance (MMV)

MMV = SP × (RSQ − AQ), or Standard cost of standard mix for actual input − Standard cost of actual mix

RSQ (revised standard quantity) = total actual input × standard proportion of that material. Applies only when two or more materials are used.

Material yield variance (MYV)

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

Also called sub-usage variance. Adverse when output is lower than the total input should have produced.

Checks

MCV = MPV + MUV, and MUV = MMV + MYV

Use these to verify your answer. Keep the same basis (consumption) for all of them.

Standard hours for actual output (SH)

SH = Actual output × Standard hours per unit

Use actual output, not budgeted output. For several grades, work out SH for each grade.

Labour cost variance (LCV)

LCV = (SH × SR) − (Actual hours paid × AR)

Standard cost of actual output minus actual wages. Positive is F, negative is A.

Labour rate variance

(SR − AR) × Actual hours paid

Use hours paid, not hours worked, because the rate applies to every hour paid.

Labour efficiency variance

(SH − Actual hours worked) × SR

Actual hours worked = hours paid − idle hours. Valued at standard rate.

Idle time variance

Idle hours × SR

Always adverse, because idle hours produce nothing.

Check relationship

LCV = Rate variance + Efficiency variance + Idle time variance

Use this to verify your answer before moving on.

Labour mix variance

(Revised standard hours − Actual hours worked) × SR, grade by grade

Revised standard hours = total actual hours worked × standard proportion of that grade. Also equals standard cost of standard mix minus standard cost of actual mix.

Labour yield variance

(SH − Revised standard hours) × SR, grade by grade

Total can also be worked as (SH total − total actual hours worked) × standard average rate per hour.

Efficiency split

Efficiency variance = Mix variance + Yield variance

Applies when idle time is shown separately and mix and yield use hours worked.

Standard variable overhead for actual output

SVO = Standard hours for actual output × Standard rate per hour

Standard hours for actual output = actual units × standard hours per unit.

Variable overhead cost variance

VOCV = Standard variable overhead for actual output − Actual variable overhead

Positive means Favourable (F), negative means Adverse (A).

Variable overhead expenditure variance

VOEV = (Standard rate × Actual hours) − Actual variable overhead

Also written as (SR − AR) × Actual hours. Use hours actually worked, not paid.

Variable overhead efficiency variance

VOEffV = (Standard hours for actual output − Actual hours) × Standard rate

Fewer actual hours than standard gives Favourable.

Check

VOCV = VOEV + VOEffV

Use this to verify your answer.

Output basis (when rate is per unit)

Efficiency = (Actual units − Standard units for actual hours) × Standard overhead rate per unit

Use this only if the question gives a standard overhead rate per unit and the output expected from the actual hours worked. A higher actual output than standard gives Favourable.

Standard fixed overhead rate

Per unit = Budgeted fixed overhead ÷ Budgeted output; Per hour = Budgeted fixed overhead ÷ Budgeted hours

Use the per hour rate for efficiency, capacity and calendar variances. Use the per unit rate for a quick volume variance.

Absorbed (standard) fixed overhead

Standard rate × Actual output (or Standard hours for actual output)

This is the amount charged to production at standard.

Fixed overhead cost variance

Absorbed fixed overhead − Actual fixed overhead

Positive is F, negative is A. It equals expenditure variance + volume variance.

Expenditure (budget) variance

Budgeted fixed overhead − Actual fixed overhead

Uses the budget for the full period, not a flexed figure, because fixed overhead does not flex.

Volume variance

Absorbed fixed overhead − Budgeted fixed overhead = Std rate per unit × (Actual output − Budgeted output)

It equals efficiency + capacity + calendar variances.

Efficiency variance

Std rate per hour × (Standard hours for actual output − Actual hours worked)

Positive means actual output took fewer hours than standard.

Capacity variance

Std rate per hour × (Actual hours worked − Revised budgeted hours)

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

Calendar variance

Std rate per hour × (Revised budgeted hours − Budgeted hours) = Std rate per day × (Actual days − Budgeted days)

More working days than budget is F, fewer is A.

Check relationships

Volume = Efficiency + Capacity + Calendar; Cost = Expenditure + Volume

Use these as a quick arithmetic check in the exam.

Sales Value Variance (turnover)

(AQ × AP) − (BQ × BP)

Actual sales minus budgeted sales. Favourable if actual sales are higher. AQ = actual quantity, AP = actual price, BQ = budgeted quantity, BP = budgeted price.

Sales Price Variance

(AP − BP) × AQ

Same in both methods. Favourable if actual price is higher than budgeted price.

Sales Volume Variance (turnover)

(AQ − BQ) × BP

Product by product. Favourable if actual units exceed budgeted units.

Check: turnover method

Sales Value Variance = Sales Price Variance + Sales Volume Variance

Use this to check your answer before moving on.

Revised Standard Quantity (RSQ)

RSQ of a product = Total AQ of all products × (BQ of the product ÷ Total BQ)

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

Sales Mix Variance (turnover)

(AQ − RSQ) × BP

Product by product, then add. Mixed at budgeted price.

Sales Quantity Variance (turnover)

(RSQ − BQ) × BP

Equivalently (Total AQ − Total BQ) × budgeted price per unit of the budget mix. Volume = Mix + Quantity.

Budgeted margin per unit

BP − Standard cost per unit

Used in the margin method for volume, mix and quantity.

Sales Margin Variance

Actual profit − Budgeted profit

Actual profit = AQ × (AP − standard cost). Budgeted profit = BQ × (BP − standard cost).

Sales Margin Volume Variance

(AQ − BQ) × budgeted margin per unit

Price variance (AP − BP) × AQ is unchanged. Margin variance = Price + Volume.

Sales Margin Mix and Quantity Variances

Mix = (AQ − RSQ) × budgeted margin per unit; Quantity = (RSQ − BQ) × budgeted margin per unit

Margin Volume = Mix + Quantity.

Profit reconciliation

Actual profit = Standard (budgeted) profit + Favourable variances − Adverse variances

Use the same costing basis throughout. Check that the closing figure equals the given actual profit.

Total cost variance

Cost variance = Standard cost of actual output − Actual cost

Positive is favourable and negative is adverse. So an adverse variance means Actual cost = Standard cost + the variance amount. For sales and profit, the sign logic is reversed: higher actual gives F.

Material variances

MCV = SC − AC; MPV = (SP − AP) × AQ; MUV = (SQ − AQ) × SP; MCV = MPV + MUV

SQ is the standard quantity for actual output. MUV = Mix variance + Yield variance when there is a mix.

Labour variances

LCV = LRV + LEV + Idle time variance; LRV = (SR − AR) × Actual hours paid; LEV = (SH − Actual hours worked) × SR; Idle time variance = Idle hours × SR (always A)

SH is the standard hours for actual output.

Variable overhead variances

VOH cost variance = Standard VOH for actual output − Actual VOH; Expenditure = (Std rate × Actual hours) − Actual VOH; Efficiency = (SH − Actual hours) × Std rate

Expenditure plus efficiency gives the cost variance.

Fixed overhead variances

FOH cost variance = Absorbed FOH − Actual FOH; Expenditure = Budgeted FOH − Actual FOH; Volume = Absorbed FOH − Budgeted FOH

Cost variance = expenditure + volume. Volume can be split into efficiency, capacity and calendar variances.

Sales margin variances

Sales margin variance = Actual profit − Budgeted profit; Price = (AP − SP) × AQ; Volume = (AQ − BQ) × Standard profit per unit

Price plus volume gives the margin variance. Under the margin method, volume is valued at standard profit per unit.

Disposal rule of thumb

Small variance: Costing P&L A/c. Significant variance from wrong standards: prorate to WIP, finished goods and cost of sales. Abnormal variance: P&L A/c

This is accepted practice, not a fixed formula. State your assumption when the question does not say.

Quick revision

• Variance = difference between standard and actual; mark it Favourable (F) or Adverse (A).
• For costs, actual cost lower than standard is F; for sales and profit, actual higher than standard is F.
• Material Cost Variance = Standard cost for actual output − Actual cost.
• Material Price Variance = Actual Quantity × (Standard Price − Actual Price).
• Material Usage Variance = Standard Price × (Standard Quantity for actual output − Actual Quantity).
• Labour Rate Variance = Actual Hours Paid × (Standard Rate − Actual Rate).
• Labour Efficiency Variance = Standard Rate × (Standard Hours for actual output − Actual Hours Worked).
• Idle Time Variance = Idle Hours × Standard Rate; it is adverse (a loss), shown separately from efficiency variance.
• Fixed Overhead Cost Variance = Absorbed fixed overhead − Actual fixed overhead.
• Fixed Overhead Expenditure Variance = Budgeted fixed overhead − Actual fixed overhead.
• Sales Value (Turnover) Variance = Actual sales − Budgeted sales; split into Sales Price Variance and Sales Volume Variance. Under the margin method, use profit (margin) instead of sales value.
• In reconciliation, the sum of the variances must equal the gap between standard and actual figures; if not, recheck.

Common mistakes

• Calling ideal and current standards the same. Fix: Ideal assumes perfect conditions with no loss. Current is attainable with reasonable effort and allows for normal loss and idle time.
• Ignoring normal loss when fixing standard material quantity. Fix: Divide required output by (1 − normal loss %) to get the input, then price the input.
• Using budgeted quantity instead of standard quantity for actual output Fix: Always start with: actual output × standard input per unit. Write SQ before anything else.
• Getting the sign wrong, especially in price variance Fix: Use the forms SP − AP and SQ − AQ. A positive answer is favourable and a negative answer is adverse. Think in terms of 'should have cost' minus 'did cost'.
• Calculating the rate variance on hours worked instead of hours paid Fix: Remember that you pay for every hour on the clock. Rate variance always uses hours paid.
• Using budgeted output to get standard hours Fix: Underline actual output and use only that for SH.
• Using hours paid instead of hours worked for expenditure variance. Fix: Variable overhead normally uses hours actually worked unless the question says otherwise. Check for idle time.
• Valuing efficiency variance at the actual rate. Fix: Efficiency variance is always at the standard rate.
• Flexing the fixed overhead budget for actual output when finding expenditure variance. Fix: Fixed overhead does not flex. Expenditure = Budgeted FO − Actual FO, using the full period budget.
• Using standard hours for actual output in the capacity variance. Fix: Capacity compares actual hours with revised budgeted hours. Efficiency compares standard hours for actual output with actual hours.

Exam tips

• In theory answers, write each type of standard as a separate point with a one-line definition; this earns step marks.
• For MCQs, link keywords: 'perfect conditions' means ideal, 'not revised' means basic, 'present conditions' means current, 'average over cycle' means normal.
• In setting-standard problems, always show normal loss working separately before pricing material.
• For the comparison question, give at least four points of difference in a two-column style written as lines, with a heading for each.
• Show the overhead rate calculation on its own line; examiners award marks for the rate even if later arithmetic slips.
• Write the formula and the working for each variance, with F or A next to every answer. Step marks are given even if one number goes wrong.
• Read whether the question wants price variance on purchase or on usage. This changes the quantity you use and is a common trap.
• In mix and yield problems, show the RSQ calculation clearly. Check that total RSQ equals total AQ.