Standard Costing and Variance Analysis (Management Accounting): formula sheet

Key formulas

Standard material cost per unit

Standard quantity per unit × Standard price per unit of material

Standard quantity includes normal wastage or normal loss. Use gross input if output is net of loss.

Standard labour cost per unit

Standard hours per unit × Standard rate per hour

Standard hours include allowance for normal idle time. Compute the rate from wage rate and any fixed allowances.

Standard overhead absorption rate

Budgeted overhead ÷ Budgeted base (units or standard hours)

Compute separately for variable and fixed overhead. Use the same base for both.

Standard overhead cost per unit

Standard overhead rate × Standard base per unit

For a per-unit rate use units as the base. For an hourly rate multiply by standard hours per unit.

Standard cost per unit

Standard material + Standard labour + Standard variable overhead + Standard fixed overhead

Add standard profit to get standard selling price.

Standard cost for actual output

Standard cost per unit × Actual output

This is the base for comparing actual cost. Never use budgeted output unless asked.

Standard quantity (SQ)

SQ = standard quantity per unit of output × actual output

This is the quantity allowed for the actual output. It is the base for every usage-type variance.

Material cost variance (MCV)

MCV = (SQ × SP) − (AQ × AP)

Positive is favourable. It equals MPV + MUV.

Material price variance (MPV)

MPV = AQ × (SP − AP)

AQ is the actual quantity used. If the question asks for price variance on purchases, use the quantity purchased.

Material usage variance (MUV)

MUV = SP × (SQ − AQ)

Valued at standard price. It equals MMV + MYV when there is more than one material.

Revised standard quantity (RSQ)

RSQ of a material = total actual input of all materials × its standard mix proportion

It is the actual total input re-divided in the standard ratio.

Material mix variance (MMV)

MMV = SP × (RSQ − AQ), summed over all materials

It equals the standard cost of the revised standard mix minus the standard cost of the actual mix.

Material yield variance (MYV)

MYV = SP × (SQ − RSQ), summed over all materials

Equivalent form: standard cost per unit of output × (actual output − standard output for actual input).

Check relationships

MCV = MPV + MUV; MUV = MMV + MYV

Use these to check your answer before you write it.

Labour Cost Variance (LCV)

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

Positive means favourable, negative means adverse. SR = standard rate, AR = actual rate.

Labour Rate Variance (LRV)

LRV = Actual hours paid × (SR − AR)

Use hours paid, which includes idle hours.

Labour Efficiency Variance (LEV)

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

Use hours worked, which excludes idle hours.

Idle Time Variance (LITV)

LITV = Idle hours × SR

Adverse whenever idle hours exist, because paid hours produced nothing. If there is no idle time, the variance is nil.

Total check

LCV = LRV + LEV + LITV

Use this to verify your answer before moving on.

Labour Mix Variance (LMV)

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

Revised standard hours = total actual hours worked shared in the standard mix ratio.

Labour Yield (Sub-efficiency) Variance

LYV = SR × (Standard hours for actual output − Revised standard hours), grade by grade

Equals the standard average cost per hour × (standard hours for actual output − total actual hours worked).

Mix and yield link

LEV = LMV + LYV

Holds on hours worked, after removing idle time.

Standard variable overhead rate

SR = Budgeted variable overhead ÷ Budgeted hours (or standard rate per hour given)

Rate per labour hour or machine hour, as the question states.

Standard hours for actual output (SH)

SH = Actual output × Standard hours per unit

This is the flexing step. It is the hours allowed for what you actually produced.

Standard variable overhead for actual output

SH × SR

What the output should have absorbed.

Variable overhead cost variance

(SH × SR) − Actual variable overhead

Positive is favourable. Negative is adverse.

Variable overhead expenditure variance

(AH × SR) − Actual variable overhead

AH is actual hours worked. Also written as AH × (SR − AR), where AR is actual rate per hour.

Variable overhead efficiency variance

(SH − AH) × SR

Favourable if actual hours are less than standard hours.

Check

Cost variance = Expenditure variance + Efficiency variance

Use this to verify your answer. The signs must agree.

Standard fixed overhead rate

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

Use the per-hour rate when you need efficiency, capacity and calendar variances.

Absorbed (standard) fixed overhead

Actual output × Standard rate per unit = Standard hours for actual output × Standard rate per hour

This is the amount charged to production at standard.

Fixed overhead cost variance

Absorbed fixed overhead − Actual fixed overhead

Positive is favourable, negative is adverse. It equals expenditure variance + volume variance.

Expenditure variance

Budgeted fixed overhead − Actual fixed overhead

Compares spending with the budget. Output does not affect it.

Volume variance

Absorbed fixed overhead − Budgeted fixed overhead

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

Efficiency variance

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

Favourable when actual hours are fewer than standard hours for the output.

Capacity variance

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

Revised budgeted hours = Budgeted hours × Actual days ÷ Budgeted days. With no calendar split, use budgeted hours instead.

Calendar variance

Standard rate per hour × (Revised budgeted hours − Budgeted hours)

Same as standard rate per day × (Actual days − Budgeted days). Favourable when more days are worked.

Volume variance check

Volume = Efficiency + Capacity + Calendar

Use this to check your arithmetic. Also Cost = Expenditure + Volume.

Sales value variance (turnover)

Actual sales − Budgeted sales = (AQ × AP) − (BQ × SP)

Positive is favourable. Equals price variance + volume variance.

Sales price variance

AQ × (AP − SP)

Same under both methods. AQ is actual quantity, AP actual price, SP standard price.

Sales volume variance (turnover)

SP × (AQ − BQ)

BQ is budgeted quantity. Equals mix + quantity variance.

Sales mix variance (turnover)

SP × (AQ − RSQ)

Worked product by product, then added.

Sales quantity variance (turnover)

SP × (RSQ − BQ)

Also called sales sub-volume variance.

Revised standard quantity (RSQ)

Total actual quantity × (Budgeted quantity of the product ÷ Total budgeted quantity)

Actual total quantity in the budgeted ratio.

Sales margin value variance

Actual profit − Budgeted profit

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

Sales margin volume variance

Standard margin per unit × (AQ − BQ)

Equals margin mix + margin quantity variance.

Sales margin mix variance

Standard margin per unit × (AQ − RSQ)

Use the standard margin of each product.

Sales margin quantity variance

Standard margin per unit × (RSQ − BQ)

Total-quantity effect on profit.

Link between the two methods

Margin volume variance of a product = Turnover volume variance × (Standard margin ÷ Standard price)

Holds product by product for volume, mix and quantity.

Reconciliation of profit

Actual profit = Budgeted (standard) profit ± Sales variances ± Cost variances

Add favourable variances and subtract adverse ones. The result must equal the actual profit.

Material cost variance

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

SQ is standard quantity for actual output. Positive means favourable.

Material price and usage

MPV = AQ × (SP − AP); MUV = SP × (SQ − AQ)

Price variance uses the quantity actually purchased or used, as the question states.

Labour cost variance

LCV = (SH × SR) − (Hours paid × AR) = Rate + Idle time + Efficiency

SH is standard hours for actual output. Use this form when idle time exists.

Labour rate, idle time and efficiency

LRV = Hours paid × (SR − AR); Idle time variance = Idle hours × SR (adverse); LEV = SR × (SH − Hours worked)

Hours paid = hours worked + idle hours.

Fixed overhead variances

FOH cost variance = Absorbed FOH − Actual FOH = Expenditure variance + Volume variance

Volume variance = (Actual output − Budgeted output) × standard rate per unit.

Sales variances (margin method)

Sales price variance = Actual qty × (Actual price − Standard price); Sales volume variance = (Actual qty − Budgeted qty) × Standard margin per unit

Standard margin is contribution under marginal costing and profit under absorption costing.

Investigation rule of thumb

Investigate when expected benefit of correction > cost of investigation

Also consider size, trend and controllability. This is a guide, not a fixed law.

Quick revision

• Standard quantity is always for actual output, not budgeted output.
• Material price variance = (SP − AP) × Actual quantity purchased or used, as the question states.
• Material usage variance = (SQ − AQ) × SP.
• Material cost variance = Standard cost for actual output − Actual cost.
• Labour rate variance = (SR − AR) × Actual hours paid.
• Labour efficiency variance = (SH for actual output − Actual hours worked) × SR.
• Idle time variance = Idle hours × Standard rate, normally Adverse (it is a loss of paid but unproductive time).
• Fixed overhead volume variance = Absorbed (standard) fixed overhead for actual output − Budgeted fixed overhead.
• Fixed overhead expenditure variance = Budgeted overhead − Actual overhead.
• Sales price variance = (Actual price − Standard price) × Actual quantity sold.
• Favourable means higher profit; Adverse means lower profit.
• Reconcile by starting from standard profit and adjusting each variance with its sign.

Common mistakes

• Treating ideal standard as the one used for control. Fix: Remember that ideal standards ignore normal losses and are rarely attainable. Current or normal standards are preferred for control.
• Ignoring normal loss when setting the material quantity. Fix: Divide net output by (1 − loss %) or add the normal loss to get standard input. Only normal loss is included, not abnormal loss.
• Using budgeted output instead of actual output to find the standard quantity. Fix: Always multiply the standard per unit by the actual output. Flexing the standard to actual output comes first.
• Valuing the usage variance at actual price. Fix: Price variance uses actual quantity. Usage, mix and yield variances use standard price. Remember: price on AQ, quantity at SP.
• Using hours worked for the rate variance. Fix: Rate variance uses hours paid, because you pay for idle hours too. Efficiency uses hours worked.
• Showing idle time variance as favourable. Fix: Paid hours with no output are a loss, so idle time variance is adverse whenever idle hours exist. If there is no idle time, it is nil.
• Using actual output hours instead of standard hours for actual output in the efficiency variance. Fix: Always compute SH = actual units × standard hours per unit first.
• Calculating the standard rate using actual hours or actual overhead. Fix: Standard rate comes only from budgeted overhead ÷ budgeted hours, or is given directly.
• Using actual fixed overhead to compute the volume variance. Fix: Volume = Absorbed − Budgeted. Actual fixed overhead appears only in cost and expenditure variances.
• Using budgeted hours instead of revised budgeted hours when days differ. Fix: When actual and budgeted days differ, compute revised budgeted hours = budgeted hours × actual days ÷ budgeted days. Use it for capacity and calendar.

Exam tips

• Theory questions on types of standards often ask you to distinguish them. Give one line each and one point on usefulness.
• In cost sheets, show the adjustment for normal loss and idle time as a separate line so you get step marks.
• Write the formula before each computation, then the numbers, then the answer with a unit.
• For MCQs, watch for words like ideal, attainable, long period and short period. They point to the type of standard.
• When asked to compare standard costing and budgetary control, answer in a two-column format with at least five points.
• In the MCQ section, most questions ask for one variance with its sign. Compute only that variance and check F or A by asking whether actual cost is below standard.
• In written answers, show SQ, RSQ and AQ in a small table first. Step marks are given for correct quantities even if a later sign is wrong.
• Always label F or A and show the check MCV = MPV + MUV. Examiners reward the reconciliation.