Standard Costing: formula sheet

Key formulas

Standard cost of an element

Standard cost = Standard quantity (or time) × Standard price (or rate)

Applies to material and labour. Quantity is for actual output, adjusted for normal loss.

Standard overhead rate

Standard overhead rate = Budgeted overhead ÷ Budgeted base (units or hours)

Compute separately for variable and fixed overheads when asked.

Variance

Variance = Standard cost for actual output − Actual cost

For cost items, a positive result is favourable and a negative result is adverse. Always state F or A.

Standard cost of one unit

Standard cost per unit = Material + Labour + Variable overhead + Fixed overhead (per unit)

Prepared as a standard cost card.

Material cost variance (MCV)

MCV = (SQ × SP) − (AQ × AP)

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

Material price variance (MPV)

MPV = AQ × (SP − AP)

Use quantity purchased if price variance is isolated at purchase. Use quantity consumed if isolated at consumption.

Material usage variance (MUV)

MUV = SP × (SQ − AQ)

AQ is the quantity actually used in production. It is always valued at standard price.

Material mix variance (MMV)

MMV = SP × (RSQ − AQ)

Equivalent: standard cost of RSQ − standard cost of AQ. Applies only when two or more materials are used.

Revised standard quantity (RSQ)

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

Total of RSQ equals total of AQ. Only the proportions differ.

Material yield variance (MYV)

MYV = SP × (SQ − RSQ)

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

Relationships

MCV = MPV + MUV; MUV = MMV + MYV

Use these as a check. Add signs algebraically, treating F as + and A as −.

Labour Cost Variance (LCV)

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

Positive = favourable, negative = adverse. LCV = Rate + Idle time + Efficiency variance.

Labour Rate Variance (LRV)

LRV = (Standard rate − Actual rate) × Actual hours paid

Use hours paid, which include idle hours.

Labour Efficiency Variance (LEV)

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

Use hours actually worked, not hours paid.

Idle Time Variance

Idle time variance = Idle hours × Standard rate

Always adverse. Idle hours = hours paid − hours worked. Abnormal idle time goes to Costing P&L.

Standard hours for actual output

SH = Actual output × Standard hours per unit

Calculate this first. It is the base for every variance.

Revised Standard Hours (RSH)

RSH of a grade = Total actual hours worked × (Standard hours of that grade ÷ Total standard hours)

Actual total hours spread in the standard mix.

Labour Mix Variance

Mix = (Revised standard hours − Actual hours worked) × Standard rate, for each grade

Total of mix across grades shows the cost effect of changing the grade proportion.

Labour Yield (Sub-Efficiency) Variance

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

Equals (Total SH − Total actual hours worked) × average standard rate per hour of the standard mix (total standard cost ÷ total standard hours).

Check relationships

Efficiency = Mix + Yield; LCV = Rate + Idle time + Efficiency

Use these to verify your answer before moving on.

Standard rate (fixed overhead)

Standard rate per hour = Budgeted fixed overhead ÷ Budgeted hours; Standard rate per unit = Budgeted fixed overhead ÷ Budgeted output

Use the rate that matches the base given in the question (hours or units).

Standard hours for actual output

SH = Actual output × Standard hours per unit

Needed for every efficiency variance and to find absorbed overhead.

Variable overhead cost variance

Standard VOH for actual output − Actual VOH, where Standard VOH = SH × Standard rate per hour

Equals expenditure variance + efficiency variance.

Variable overhead expenditure variance

(Actual hours × Standard rate per hour) − Actual VOH

Also called budget variance. Positive means F.

Variable overhead efficiency variance

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

Fewer actual hours than standard means F.

Fixed overhead cost variance

Absorbed FOH − Actual FOH, where Absorbed FOH = Actual output × Standard rate per unit (or SH × rate per hour)

Equals expenditure variance + volume variance.

Fixed overhead expenditure variance

Budgeted FOH − Actual FOH

Uses the budget, not the absorbed amount.

Fixed overhead volume variance

Absorbed FOH − Budgeted FOH = Standard rate per unit × (Actual output − Budgeted output)

Equals efficiency + capacity + calendar variances.

Fixed overhead efficiency variance

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

Same form as the variable overhead efficiency variance.

Fixed overhead capacity variance

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

Without calendar data, use budgeted hours instead of revised budgeted hours.

Fixed overhead calendar variance

Standard rate per hour × (Revised budgeted hours − Budgeted hours), where Revised budgeted hours = Budgeted hours × Actual days ÷ Budgeted days

More actual days than budgeted gives F; fewer gives A.

Sales value variance (turnover)

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

Equals price variance + volume variance. Favourable if actual sales exceed budget.

Sales price variance

AQ × (AP − BP)

Same in both methods. AQ is actual quantity sold, AP actual price, BP budgeted price.

Sales volume variance (value)

BP × (AQ − BQ)

Uses budgeted selling price. Equals mix variance + quantity variance.

Sales mix variance (value)

BP × (AQ − RAQ)

RAQ is actual total quantity split in the budgeted ratio. Calculated product by product, then added.

Sales quantity variance (value)

BP × (RAQ − BQ)

Effect of total units differing from budget at the budgeted mix.

Revised actual quantity (RAQ)

RAQ of a product = Total actual quantity × (BQ of that product ÷ Total BQ)

Total of RAQ equals total of AQ.

Total sales margin variance

Actual profit − Budgeted profit, where actual profit = Actual sales − Standard cost of actual sales

Equals margin price variance + margin volume variance.

Sales margin volume variance

Budgeted margin per unit × (AQ − BQ)

Budgeted margin per unit = BP − standard cost per unit.

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. Mix + quantity = margin volume variance.

Basic reconciliation

Actual profit = Budgeted profit + Favourable variances − Adverse variances

The closing figure must match actual profit from the accounts. This is your check.

Sales price variance

(Actual price − Standard price) × Actual quantity sold

Positive means favourable.

Sales volume (margin) variance

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

Under absorption costing use standard profit per unit. Under marginal costing use standard contribution per unit.

Material price variance

(Standard price − Actual price) × Actual quantity

Use quantity purchased or quantity used as the question states. Be consistent.

Material usage variance

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

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

Labour rate variance

(Standard rate − Actual rate) × Actual hours paid

Positive means favourable.

Labour efficiency variance

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

Idle time is a separate variance if hours paid exceed hours worked.

Investigation rule

Investigate if variance is material, recurring, adverse in trend, and benefit of correction > cost of investigation

Firms set their own limits, often a percentage of standard. It is a management judgement, not a fixed legal rule.

Quick revision

• For cost variances, Standard cost − Actual cost: a positive result is F and a negative result is A. For sales and profit variances, Actual − Standard: a positive result is F. Either way, state each answer as F or A: lower cost than standard is F, higher is A.
• Material price variance = (Standard price − Actual price) × Actual quantity.
• Material usage variance = (Standard quantity for actual output − Actual quantity) × Standard price.
• Material mix variance = (Standard quantity in standard mix for actual total input − Actual quantity) × Standard price of that material. Compute it material by material, using each material's own standard price, and add the results. Material yield variance = (Actual yield − Standard yield for actual input) × Standard cost per unit of output, where standard cost per unit of output = standard cost of standard input ÷ standard output. Material usage variance = Material mix variance + Material yield variance.
• Labour rate variance = (Standard rate − Actual rate) × Actual hours paid.
• Labour efficiency variance = (Standard hours for actual output − Actual hours worked) × Standard rate.
• Idle time variance = Idle hours × Standard rate, and it is normally Adverse.
• Variable overhead expenditure variance = Standard variable overhead for actual hours worked − Actual variable overhead, where standard variable overhead for actual hours worked = Standard variable overhead rate × Actual hours worked; positive is F.
• Fixed overhead total variance = Absorbed overhead − Actual overhead; positive is F. Here absorbed overhead means standard overhead for actual output (standard rate × actual output).
• Fixed overhead volume variance = (Actual output − Budgeted output) × Standard rate per unit = Absorbed overhead (standard rate × actual output) − Budgeted overhead; positive is F. It is the combined gap from budgeted overhead to absorbed overhead: calendar variance + capacity variance (excluding calendar) + efficiency variance. Calendar variance is nil if actual working days equal budgeted working days. Capacity variance (excluding calendar) is measured from revised budgeted hours to actual hours: Capacity variance = (Actual hours − Revised budgeted hours) × Standard rate per hour.
• Sales price variance = (Actual price − Standard price) × Actual quantity; higher price is F.
• In profit reconciliation, add F variances and deduct A variances starting from standard profit to reach actual profit.

Common mistakes

• Treating ideal and attainable standards as the same. Fix: Remember ideal assumes perfect conditions with no loss. Attainable allows normal waste, idle time and delays.
• Saying standard costing and budgetary control are identical. Fix: State the difference: standards are unit-level cost targets for a product or operation, while budgets are total-level plans for a function or the whole business over a period. Standards are used mainly for cost control, budgets for overall planning and control of expenses and revenue.
• Using budgeted output instead of actual output to find SQ Fix: Always compute SQ = standard quantity per unit × actual output. The comparison must be at the actual level of activity.
• Valuing the usage, mix or yield variance at actual price Fix: Price variance uses AQ and the price difference. All quantity variances (usage, mix, yield) use standard price only.
• Using hours worked for the rate variance Fix: Rate variance is on hours paid. Efficiency is on hours worked. Keep both columns in your table.
• Including idle time in the efficiency variance Fix: Subtract idle hours from hours paid to get hours worked. Show idle time as its own variance.
• Using absorbed overhead instead of budgeted overhead in the fixed overhead expenditure variance. Fix: Fixed expenditure variance = Budgeted FOH − Actual FOH. Absorbed overhead appears only in cost and volume variances.
• Using actual hours at the standard rate as the base for the variable expenditure variance but forgetting it in the efficiency variance, or mixing the two. Fix: Expenditure uses actual hours (AH × rate − actual VOH). Efficiency uses the difference between standard hours for actual output and actual hours.
• Using actual price in the volume or mix variance. Fix: Price variance uses AP − BP. Volume, mix and quantity always use the budgeted price (or budgeted margin per unit).
• Using selling price instead of margin per unit in the margin method. Fix: In margin variances, use budgeted profit per unit = BP − standard cost. Underline 'profit' in the question to remind yourself.

Exam tips

• For a long theory question, write numbered points with bold keywords. Examiners give marks per point, so use clear headings you can scan.
• Learn the four types of standards with one trigger phrase each. MCQs usually test these phrases.
• Practise the standard cost card. Quantity × price and time × rate are the base of all later variance work.
• In distinction questions, use at least four parallel points and keep them in the same order on both sides.
• Since there is no negative marking, attempt every MCQ. Eliminate overstatements such as always or never first.
• Write SQ, RSQ and AQ in a small table before any formula. Most errors start with a wrong SQ or RSQ.
• Always run the two checks: MPV + MUV = MCV and MMV + MYV = MUV. If a check fails, fix it before moving on.
• In MCQs, work out the sign first. Many options differ only in F or A, so you can eliminate half of them quickly. There is no negative marking, so always attempt every MCQ.