Standard Costing and Cost Variance Analysis: Complete Chapter Notes
Standard costing is one of the most tested topics in Cost and Management Accounting. This post covers the whole chapter in short, exam-ready notes: meaning, features, kinds of standards, setting of standards, advantages and limitations, and every variance (material, labour, overhead and sales) with formulas, causes and checks, followed by 28 solved illustrations that cover every type of numerical question.
Tap a topic below to jump straight to it. Each section is collapsed so you can open only what you need, or use Expand all to read the chapter in one go. The notes are useful for UGC NET Commerce Paper 2, MPPSC, SET, M.Com and CMA/CA foundation-level preparation.
Solved illustrations (28):
Standard Costing Topics and Variance Formulas
Meaning of Standard Cost
A standard is a yardstick: a pre-decided level of performance against which real performance is judged. Standards can be expressed in weight, quantity, quality, time or money.
A standard cost is a scientifically pre-determined estimate of what one unit of product (or one job, process or activity) should cost under stated working conditions and for a stated period. It is built from technical estimates of the material, labour and overhead needed, priced at the rates expected to apply.
- Purpose 1: control costs by comparing actual cost with the standard (variance accounting).
- Purpose 2: value stock and work-in-progress at a uniform, stable rate.
- Purpose 3: help in fixing selling prices.
Writers such as Kohler and the ICMA (London) describe it the same way: a forecast of what cost ought to be, used as a measure of efficiency and as the benchmark against which actual cost is finally compared.
Features of Standard Costs
- It is a pre-determined cost, fixed before production starts.
- It is product specific: set for a particular product, process or job.
- It is determined scientifically using engineering estimates, time and motion study and past data.
- It is fixed for a specified period and is revised when conditions change.
- It rests on the conditions expected in the budget period; past experience is only a guide.
- It is built by combining standard quantities with expected prices, wage rates and overhead rates.
- It is set at an efficient but attainable level, so achieving it needs some effort.
- It is a normal cost: it allows for normal wastage, normal idle time and normal capacity.
- It is set by cost and management accountants together with technical experts and managers.
- It is fixed for each element (material, labour, fixed and variable overhead) and is used for planning, control, correction and motivation.
Meaning of Standard Costing and its Characteristics
Standard costing is a technique of cost control. Costs are worked out in advance, then compared with the actual costs. The gap between the two is a variance; it is analysed by cause and reported so that management can take corrective action and keep actual cost within the pre-determined cost.
In short: standard costing = setting standards + recording actuals + finding variances + analysing causes + acting on them. It is a technique used alongside methods such as job, process or unit costing, not a separate costing method.
Characteristics of a standard costing system
- Careful determination of standard cost for each element: direct material, direct labour and overhead.
- Recording of both standard and actual costs in the books.
- Computation of variances between standard and actual cost.
- Analysis and investigation of the variances.
- Feedback to management with suggestions for correction or revision of standards where needed.
Standard Costing vs Historical Costing
| Basis | Standard costing | Historical costing |
|---|---|---|
| Cost used | Pre-determined (what cost should be) | Actual cost, known only after it is incurred |
| Control | Active control: deviations are spotted early | Little or no control; it only records what happened |
| Comparison | Actual vs standard, with variance analysis | Compared only with past periods, if at all |
| Efficiency measure | Gives a yardstick for efficiency | Carries forward past inefficiency |
| Best suited to | Repetitive, standardised production | Jobbing and one-off work |
| Reports | Management by exception | Detailed post-mortem figures |
Standard Cost vs Estimated Cost
| Basis | Standard cost | Estimated cost |
|---|---|---|
| Nature | What the cost should be | What the cost will probably be |
| Use | Only in a standard costing system | Can be used with historical costing, e.g. for quotations |
| Purpose | Cost control and efficiency measurement | Price fixing and ascertaining probable costs |
| Determination | Scientifically, with technical studies | By adjusting past figures for likely changes |
| Accounts | Usually built into the books | Statistical data only; not entered in the books |
Standard Costing vs Budgetary Control
Both fix pre-determined targets, measure actual performance, compare the two, analyse variances and take corrective steps. They complement each other.
| Basis | Standard costing | Budgetary control |
|---|---|---|
| Scope | Limited to production and production cost | Wider: production, purchase, sales, finance, etc. |
| Concept | Unit concept: cost of one product or unit | Total concept: whole department or concern |
| Based on | Technical estimates of what cost should be | Past figures and expected future changes |
| Emphasis | Achieving the standard | Keeping spending within the budget limit |
| Rigidity | More rigid; targets are fixed | Less rigid; budgets set limits |
| Variance analysis | By element of cost and by cause | By department or for the concern as a whole |
| Dependence | Cannot work well without budgeting | Can work without standard costing |
| Application | Must be applied to all cost elements | Can be applied partly or wholly |
| Relation to accounts | Linked to cost accounts | Linked to financial accounts |
Where Standard Costing Applies
Standard costing is a technique, so it can go with any costing method. It works best where output is uniform and repetitive:
- Mass production of identical products such as cement, steel, bricks and chemicals.
- Industries with repetitive processes.
- Single or output costing, process costing and operation costing.
- Service industries such as transport, power, gas and electricity supply.
- Extractive industries such as mining and quarrying.
- Industries with wide product ranges, e.g. engineering, textiles and automobiles.
- Public utilities and both profit-making and non-profit organisations, in the private or public sector.
Limited use: in jobbing industries (building a boiler, a dam or a ship) each job differs, so a full system is costly and hard to maintain. A partial system may be used instead.
Advantages of Standard Costing
- Basis for evaluating performance: actual cost is compared with a yardstick, so cost centres and workers can be judged fairly.
- Management by exception: attention goes only to areas where actual results depart from the standard.
- Cost control and reduction: constant comparison curbs wastage and losses of material, labour and machine time.
- Fixing responsibility: each variance can be traced to a person or department.
- Early detection of variances: corrective action can be taken quickly.
- Simpler reporting: only the necessary information reaches management.
- Elimination of inefficiency: setting standards forces a study of methods, materials and time.
- Help in decisions: useful for pricing and for handling inflation or rising prices.
- Forward-looking approach: encourages planning and cost consciousness among executives.
- Economical income determination: stock valuation at standard is simpler than at historical cost.
- Motivation: realistic targets encourage workers; incentives can be linked to them.
- Delegation of authority: cost centres with clear responsibility improve co-ordination.
Limitations of Standard Costing
- Unrealistic standards: standards that are too tight demotivate workers; too loose defeat the purpose of control.
- Frequent revision: changing conditions force revisions, which are costly; if standards are not revised they become outdated.
- Difficulty in fixing responsibility: many factors cause a variance, and separating controllable from uncontrollable ones is hard.
- Needs co-operation at all levels: poor co-ordination or departmental rivalry hurts the system.
- Not suitable for small firms: owners already supervise closely and the system is expensive.
- Not suited to non-standard products: made-to-order jobs differ every time.
- Difficult and costly to set up: needs technical skill, time and motion studies, and trained staff.
- Depends on budgetary control: it cannot work well without an effective budgeting system.
Kinds of Standards
| Kind | Meaning |
|---|---|
| Current standard | Set for the current period (normally a year) on the assumption that conditions stay unchanged; revised if prices or methods change. |
| Ideal standard | Also called tight or strict standard. Assumes the best possible conditions: lowest prices, minimum waste and minimum time. Rarely attainable, so it can discourage workers. |
| Expected standard | Realistic and attainable; takes normal difficulties into account. Best for evaluating efficiency. |
| Basic standard | Fixed for a long period and not revised for ordinary changes (also called bogey, fixed or static standard). Used as a base to measure changes in cost over time. |
| Normal standard | Average standard over one trade cycle (about five to ten years). Useful for absorbing overhead over the long run. |
| Lax or loose standard | Deliberately set below attainable level so favourable variances keep morale high. |
| Revised standard | A standard changed from time to time to match new conditions. |
| Historical standard | Based on past performance; easy to set but carries past inefficiency. Sometimes used at the start of a system. |
Setting of Standards (Material, Labour, Overhead)
1. Direct material
Two things are fixed: standard quantity (set by the engineering or production department, allowing for normal wastage) and standard price (set by the purchase department after considering market trends, discounts, transport and storage cost).
2. Direct labour
Two things are fixed: standard time for each operation (from time and motion study and past records) and standard rate per hour for each grade of worker (from wage agreements and expected changes). Where piece rates apply, a standard rate per piece is used.
3. Overhead
The standard overhead rate is found in three steps:
- Estimate overhead for the budget period and divide it into fixed, variable and semi-variable parts.
- Estimate the level of activity (machine hours, labour hours or units).
- Divide budgeted overhead by budgeted activity.
Standard variable overhead rate = Budgeted variable overhead ÷ Budgeted volume
Steps in Introducing a Standard Costing System
- Set standards for each element of cost: neither too tight nor too loose.
- Decide the type of standard (current, basic or normal) based on its value for control and as a measure of efficiency.
- Study technical aspects: plant capacity, product specifications, quality and methods.
- Study the organisation: lines of authority and responsibility, so each cost centre has an owner.
- Review the existing costing system: records, forms, allocation and apportionment of overheads.
- Enlist the co-operation of line managers and factory executives.
- Train the staff who will record standards and actuals.
- Prepare a manual that explains procedures, forms and responsibilities.
- Study labour and machine operations to fix time and cost standards.
- Study market conditions and price trends for material prices, wage rates and overhead levels.
Variance Analysis: Basic Ideas
A variance is the difference between the standard (budgeted) figure and the actual figure for cost or for sales and profit. The purpose is to learn why actual results departed from standard so that action can follow.
- Favourable (F): actual cost is less than standard cost, or actual sales or profit exceed the standard.
- Unfavourable or Adverse (A/U): actual cost is more than standard cost, or sales or profit fall short.
Controllable and uncontrollable variances
A variance is controllable when it can be traced to a particular person or department, for example excess material use due to careless handling, or extra labour hours due to inefficiency. It is uncontrollable when caused by outside factors, for example a market rise in material prices or an industry-wide wage increase. Management should concentrate on controllable variances.
Types of variances
- Material variances
- Labour variances
- Overhead variances: variable and fixed
- Sales variances
Memory aid: for costs the formula is Standard − Actual; for sales and profit it is Actual − Standard. A positive answer is favourable.
Material Variances (Formulas, Causes, Relationships)
Abbreviations: SP = standard price, AP = actual price, SQ = standard quantity for actual output, AQ = actual quantity, RSQ = revised standard quantity.
Material Price Variance (MPV) = AQ × (SP − AP)
Material Usage Variance (MUV) = SP × (SQ − AQ)
MCV = MPV + MUV
Positive result = Favourable, negative = Unfavourable. The price variance is calculated on the quantity actually bought or used; the usage variance is valued at the standard price.
Sub-variances of material usage
MMV = SP × (RSQ − AQ), when the totals differ
RSQ = (Standard quantity of that material ÷ Total standard quantity) × Total actual quantity
Material Revised Usage (Sub-usage) Variance = SP × (SQ − RSQ)
Material Yield Variance (MYV) = Standard rate × (Actual yield − Standard yield)
Standard rate = Standard cost of standard mix ÷ Net standard output
(If actual mix differs, use revised standard mix and revised standard yield.)
Check formulas
- MCV = MPV + MUV
- MCV = MPV + MMV + MYV (or MPV + MMV + Revised usage)
- MUV = MMV + MYV (or MMV + Revised usage)
- MPV = MCV − MUV; MUV = MCV − MPV; MMV = MUV − MYV
Common causes
Price variance: change in market price, purchase in uneconomic lot sizes, loss of discounts, change in transport cost, emergency purchases at high prices, wrong grade of supplier, change in excise duty or tax, seasonal buying.
Usage variance: change in design or method, use of non-standard or defective material, careless handling, pilferage, poor workmanship, faulty machines, too rigid inspection, differences in yield.
Labour Variances (Formulas, Causes, Relationships)
Abbreviations: ST = standard time (hours) for actual output, AT = actual time, SR = standard rate per hour, AR = actual rate per hour, IT = idle time, RST = revised standard time.
Labour Rate Variance (LRV) = AT × (SR − AR)
Labour Efficiency Variance (LEV) = SR × (ST − AT worked)
Idle Time Variance (ITV) = Idle hours × SR (always unfavourable)
Labour Mix Variance (LMV) = SR × (ST − AT), when total standard and actual hours are equal
LMV = SR × (RST − AT), when totals differ
RST = (Standard time of the grade ÷ Total standard time) × Total actual time worked
Labour Sub-efficiency (Revised Efficiency) Variance = SR × (ST − RST)
Labour Yield Variance (LYV) = Standard labour cost per unit × (Actual yield − Standard yield)
Rate variance is worked on the hours paid; efficiency variance on the hours worked (idle hours are excluded and shown separately).
Check formulas
- One grade of labour: LCV = LRV + LEV + ITV
- Two or more grades: LCV = LRV + LMV + Sub-efficiency + ITV
- LEV = LMV + Sub-efficiency (+ ITV, if idle time is included in efficiency)
- LRV = LCV − LEV; LEV = LCV − LRV
Common causes
Rate variance: change in basic wage rates, different wage payment method, workers of a different grade, unscheduled overtime, new workers paid below full rate, shortage forcing higher rates.
Efficiency variance: inefficient or untrained workers, wrong grade of labour, poor tools or machines, weak supervision, change in method, bad working conditions (light, ventilation), time wasted.
Idle time: machine breakdown, power failure, strike, waiting for material, tools or instructions.
Variable Overhead Variances
Variable overhead varies in step with output, so its variances resemble labour variances.
Expenditure Variance = Budgeted variable overhead for actual hours (AH × SR) − Actual variable overhead
Efficiency Variance = SR × (SH − AH)
VOV = Expenditure variance + Efficiency variance
- SR = standard variable overhead rate per hour (or per unit); SH = standard hours for actual output; AH = actual hours worked.
- Expenditure variance arises from changes in the price of indirect items. Efficiency variance arises because more or fewer hours were used than planned.
- On a unit basis, use standard rate per unit and compare standard and actual output.
Fixed Overhead Variances
Fixed overhead does not change with output in the short run, so variances arise from over- or under-recovery of the absorbed amount.
Absorbed fixed overhead = Standard hours for actual output × Standard rate per hour (or actual output × rate per unit)
Expenditure (Budget) Variance = Budgeted fixed overhead − Actual fixed overhead
Volume Variance = Standard rate × (Actual output − Budgeted output) [or SR × (SH − BH) on an hours basis]
FOCV = Expenditure variance + Volume variance
Volume variance has three parts (hours basis)
Capacity Variance = SR × (AH − Revised budgeted hours)
Calendar Variance = SR × (Revised budgeted hours − Budgeted hours)
Revised budgeted hours = Budgeted hours × (Actual working days ÷ Budgeted working days)
Volume variance = Efficiency + Capacity + Calendar
- Calendar variance is favourable when actual working days exceed budgeted days.
- Capacity variance measures actual use of capacity against the budgeted level; volume variance measures output against budget.
- Fixed overhead variance (Total) = FOCV; Total Overhead Variance = FOCV + VOV.
Check formulas
- FOCV = Expenditure + Volume
- Volume = Efficiency + Capacity + Calendar
- FOCV = Expenditure + Efficiency + Capacity + Calendar
Sales Variances: Turnover (Sales Value) Method
Sales variances measure how selling performance compares with the budget. Abbreviations: BS = budgeted sales, AS = actual sales, SP = standard (budgeted) price, AP = actual price, BQ = budgeted quantity, AQ = actual quantity, RSQ = revised standard quantity.
Sales Price Variance = AQ × (AP − SP)
Sales Volume Variance = SP × (AQ − BQ)
Sales Mix Variance = SP × (AQ − RSQ)
Sales Quantity Variance = SP × (RSQ − BQ)
RSQ = (Budgeted quantity of the product ÷ Total budgeted quantity) × Total actual quantity
- Positive = Favourable; negative = Adverse.
- Value variance = Price variance + Volume variance.
- Volume variance = Mix variance + Quantity variance.
- With a single product there is no mix variance; for several products compute mix and quantity variances product by product and add them.
Sales Variances: Profit (Sales Margin) Method
Here variances are measured in terms of profit, using standard profit per unit.
Sales Margin Price Variance = AQ × (Actual selling price − Standard selling price)
Cost Variance = AQ × (Standard cost per unit − Actual cost per unit)
Sales Margin Volume Variance = Standard profit per unit × (AQ − BQ)
Sales Margin Mix Variance = Standard profit per unit × (AQ − RSQ)
Sales Margin Quantity Variance = Standard profit per unit × (RSQ − BQ)
- Value variance = Price variance + Cost variance + Volume variance.
- Volume variance = Mix variance + Quantity variance.
- Use this method when management cares about contribution or profit more than turnover.
Quick Revision Table: All Variances and Checks
| Area | Main variance | Formula | Check |
|---|---|---|---|
| Material | Cost (MCV) | (SQ × SP) − (AQ × AP) | MCV = MPV + MUV |
| Price (MPV) | AQ (SP − AP) | ||
| Usage (MUV) | SP (SQ − AQ) | ||
| Labour | Cost (LCV) | (ST × SR) − (AT × AR) | LCV = LRV + LEV + ITV |
| Rate (LRV) | AT (SR − AR) | ||
| Efficiency (LEV) | SR (ST − AT worked) | ||
| Variable OH | Expenditure | (AH × SR) − Actual VOH | VOV = Exp + Eff |
| Efficiency | SR (SH − AH) | ||
| Fixed OH | Expenditure | Budgeted FOH − Actual FOH | FOCV = Exp + Volume |
| Volume | SR (AQ − BQ) | ||
| Sales (value) | Value | AS − BS | Value = Price + Volume |
| Price | AQ (AP − SP) | ||
| Volume | SP (AQ − BQ) |
Sign rule: for costs, Standard − Actual; for sales and profit, Actual − Standard. Positive = Favourable.
Practice Questions for Exams
Long answer questions
- What is standard costing? Explain its objectives, merits and demerits.
- Define standard costing and explain its main characteristics.
- How does standard costing differ from budgetary control? How does it differ from historical costing?
- Explain the conditions of an effective standard cost system and the preliminaries to setting it up.
- Explain the methods of determining standards for material, labour and overhead.
- What is variance analysis? Distinguish between controllable and uncontrollable variances.
- Explain the causes of the different types of variances.
- Explain the managerial uses of variance analysis. Is a favourable variance always an indicator of efficiency?
Short notes
- Cost variance analysis
- Controllable and uncontrollable variances
- Material variances
- Labour variances
- Fixed overhead variances
- Sales variances
- Kinds of standards
- Standard cost vs estimated cost
Numerical practice
- Compute material cost, price, usage, mix and yield variances for a given standard mix and actual mix.
- Compute labour cost, rate, efficiency, idle time and mix variances for two grades of workers.
- Compute variable and fixed overhead variances, including calendar and capacity variances.
- Compute sales variances by the value method and the profit method.
Standard Costing Illustrations with Solutions
Each illustration states the question, shows the working step by step and ends with a check using the variance relationships. Open the one you want to practise.
Material variance illustrations
Illustration M1: Material cost, price and usage variances (basic)
Question. Standard: 40 kg at ₹12 per kg. Actual: 45 kg at ₹11 per kg. Calculate material cost, price and usage variances.
Solution.
MPV = AQ × (SP − AP) = 45 × (12 − 11) = ₹45 (F)
MUV = SP × (SQ − AQ) = 12 × (40 − 45) = ₹60 (A)
Check: MPV + MUV = ₹45 (F) + ₹60 (A) = ₹15 (A) = MCV.
Illustration M2: Favourable usage with adverse price
Question. Standard quantity for the output is 120 kg at ₹8 per kg. The firm actually used 110 kg bought at ₹8.50 per kg. Find the material variances and comment.
Solution.
MPV = 110 × (8 − 8.50) = ₹55 (A)
MUV = 8 × (120 − 110) = ₹80 (F)
Check: ₹55 (A) + ₹80 (F) = ₹25 (F). Comment: saving in usage more than offset the dearer purchase, so the net result is favourable.
Illustration M3: Standard quantity from a per-unit norm
Question. Each unit of a product needs 6 kg of material at a standard price of ₹5 per kg. In a month 2,000 units were produced. The material actually used was 11,500 kg, costing ₹63,250. Calculate the material variances.
Solution.
Actual price (AP) = 63,250 ÷ 11,500 = ₹5.50 per kg
MCV = 60,000 − 63,250 = ₹3,250 (A)
MPV = AQ × (SP − AP) = 11,500 × (5 − 5.50) = ₹5,750 (A)
MUV = SP × (SQ − AQ) = 5 × (12,000 − 11,500) = ₹2,500 (F)
Check: ₹5,750 (A) + ₹2,500 (F) = ₹3,250 (A).
Illustration M4: Two materials, cost, price and usage variances
Question. Standard for the output: Material A 50 kg at ₹4, Material B 30 kg at ₹6. Actual: Material A 55 kg at ₹4.20, Material B 28 kg at ₹6.50. Analyse the material cost variance.
Solution.
Material B: MCV = (30×6) − (28×6.5) = ₹2 (A); MPV = 28 × (6 − 6.5) = ₹14 (A); MUV = 6 × (30 − 28) = ₹12 (F)
Total: MCV = ₹33 (A); MPV = ₹25 (A); MUV = ₹8 (A)
Check: ₹25 (A) + ₹8 (A) = ₹33 (A).
Illustration M5: Material mix variance (equal total weight)
Question. Standard mix for 100 kg of output: X 60 kg at ₹5, Y 40 kg at ₹10. Actual input: X 50 kg at ₹5.20 and Y 50 kg at ₹9.50, giving 100 kg of output. Find the price, usage and mix variances.
Solution.
MCV = 700 − 735 = ₹35 (A)
MPV: X = 50 × (5 − 5.20) = ₹10 (A); Y = 50 × (10 − 9.50) = ₹25 (F); total = ₹15 (F)
MUV: X = 5 × (60 − 50) = ₹50 (F); Y = 10 × (40 − 50) = ₹100 (A); total = ₹50 (A)
Total actual weight (100 kg) equals total standard weight (100 kg), so RSQ = SQ and there is no yield variance.
MMV = MUV = ₹50 (A); MYV = Nil
Check: MPV + MUV = ₹15 (F) + ₹50 (A) = ₹35 (A) = MCV.
Illustration M6: Mix and yield variances with 20% process loss
Question. Standard mix for 100 kg of input: X 60 kg at ₹5 and Y 40 kg at ₹10; standard loss is 20% of input. In the period, actual input was X 80 kg at ₹5.50 and Y 50 kg at ₹9.50, and actual output was 96 kg. Calculate all material variances.
Solution.
Standard input = 100 kg; standard output = 80 kg; standard cost = ₹700; standard rate per unit of output = ₹700 ÷ 80 = ₹8.75
SQ for actual output: X = 72 kg; Y = 48 kg
Total actual input = 130 kg; RSQ: X = 60 ÷ 100 × 130 = 78 kg; Y = 40 ÷ 100 × 130 = 52 kg
Standard yield on actual input = 130 × 80% = 104 units
Standard cost of actual output = ₹840; actual cost = ₹915
Variances
MCV = 840 − 915 = ₹75 (A)
MPV = AQ × (SP − AP): X = 80 × (5 − 5.50) = ₹40 (A); Y = 50 × (10 − 9.50) = ₹25 (F). Total = ₹15 (A)
MUV = SP × (SQ − AQ): X = 5 × (72 − 80) = ₹40 (A); Y = 10 × (48 − 50) = ₹20 (A). Total = ₹60 (A)
MMV = SP × (RSQ − AQ): X = 5 × (78 − 80) = ₹10 (A); Y = 10 × (52 − 50) = ₹20 (F). Total = ₹10 (F)
MYV = SR × (AY − SY) = 8.75 × (96 − 104) = ₹70 (A)
Revised usage (sub-usage) variance = SP × (SQ − RSQ): X = ₹30 (A); Y = ₹40 (A). Total = ₹70 (A)
Check: MCV ₹75 (A) = MPV ₹15 (A) + MMV ₹10 (F) + MYV ₹70 (A); MUV ₹60 (A) = MMV ₹10 (F) + MYV ₹70 (A).
Illustration M7: Three materials, mix, yield and revised usage
Question. Standard mix for 100 kg of input: P 50 kg at ₹8, Q 30 kg at ₹12, R 20 kg at ₹20; standard loss is 10%. Actual input: P 60 kg at ₹8.50, Q 28 kg at ₹11.50, R 22 kg at ₹19; actual output 100 kg. Calculate the material variances.
Solution.
Standard input = 100 kg; standard output = 90 kg; standard cost = ₹1,160; standard rate per unit of output = ₹1,160 ÷ 90 = ₹12.89
SQ for actual output: P = 55.56 kg; Q = 33.33 kg; R = 22.22 kg
Total actual input = 110 kg; RSQ: P = 50 ÷ 100 × 110 = 55 kg; Q = 30 ÷ 100 × 110 = 33 kg; R = 20 ÷ 100 × 110 = 22 kg
Standard yield on actual input = 110 × 90% = 99 units
Standard cost of actual output = ₹1,288.89; actual cost = ₹1,250
Variances
MCV = 1,288.89 − 1,250 = ₹38.89 (F)
MPV = AQ × (SP − AP): P = 60 × (8 − 8.50) = ₹30 (A); Q = 28 × (12 − 11.50) = ₹14 (F); R = 22 × (20 − 19) = ₹22 (F). Total = ₹6 (F)
MUV = SP × (SQ − AQ): P = 8 × (55.56 − 60) = ₹35.56 (A); Q = 12 × (33.33 − 28) = ₹64 (F); R = 20 × (22.22 − 22) = ₹4.44 (F). Total = ₹32.89 (F)
MMV = SP × (RSQ − AQ): P = 8 × (55 − 60) = ₹40 (A); Q = 12 × (33 − 28) = ₹60 (F); R = 20 × (22 − 22) = Nil. Total = ₹20 (F)
MYV = SR × (AY − SY) = 12.89 × (100 − 99) = ₹12.89 (F)
Revised usage (sub-usage) variance = SP × (SQ − RSQ): P = ₹4.44 (F); Q = ₹4 (F); R = ₹4.44 (F). Total = ₹12.89 (F)
Check: MCV ₹38.89 (F) = MPV ₹6 (F) + MMV ₹20 (F) + MYV ₹12.89 (F); MUV ₹32.89 (F) = MMV ₹20 (F) + MYV ₹12.89 (F).
Illustration M8: Finding a missing material variance
Question. Material cost variance is ₹1,200 (A) and material price variance is ₹800 (F). Standard price is ₹10 per kg. Find the usage variance and the excess quantity used.
Solution.
MUV = SP × (SQ − AQ), so AQ − SQ = 2,000 ÷ 10 = 200 kg
Actual consumption exceeded the standard quantity by 200 kg.
Labour variance illustrations
Illustration L1: Labour cost, rate and efficiency variances (basic)
Question. Standard: 90 hours at ₹6 per hour. Actual: 100 hours at ₹5.80 per hour, with no idle time. Find the labour variances.
Solution.
LRV = AT × (SR − AR) = 100 × (6 − 5.80) = ₹20 (F)
LEV = SR × (ST − AT) = 6 × (90 − 100) = ₹60 (A)
Check: ₹20 (F) + ₹60 (A) = ₹40 (A) = LCV.
Illustration L2: Labour variances with idle time
Question. Standard: 400 hours at ₹7.50 per hour. Workers were paid for 450 hours at ₹7.80 per hour, of which 20 hours were idle because of a power failure. Calculate the labour variances.
Solution.
LCV = (400 × 7.50) − (450 × 7.80) = 3,000 − 3,510 = ₹510 (A)
LRV = 450 × (7.50 − 7.80) = ₹135 (A)
Idle time variance = 20 × 7.50 = ₹150 (A)
LEV = 7.50 × (400 − 430) = ₹225 (A)
Check: ₹135 (A) + ₹150 (A) + ₹225 (A) = ₹510 (A) = LCV.
Illustration L3: Standard hours from a per-unit norm
Question. A product needs 3 standard labour hours per unit at ₹8 per hour. In a month 500 units were made. Workers were paid ₹12,636 for 1,560 hours; there was no idle time. Calculate the labour variances.
Solution.
Actual rate = 12,636 ÷ 1,560 = ₹8.10 per hour
LCV = 12,000 − 12,636 = ₹636 (A)
LRV = 1,560 × (8 − 8.10) = ₹156 (A)
LEV = 8 × (1,500 − 1,560) = ₹480 (A)
Check: ₹156 (A) + ₹480 (A) = ₹636 (A) = LCV.
Illustration L4: Two grades of labour, mix variance (equal hours)
Question. Standard for the output: skilled 60 hours at ₹10, semi-skilled 40 hours at ₹6. Actual: skilled 50 hours at ₹10.50, semi-skilled 50 hours at ₹5.80. No idle time. Calculate cost, rate and mix variances.
Solution.
Semi-skilled: LCV = (40×6) − (50×5.8) = ₹50 (A); LRV = 50 × (6 − 5.8) = ₹10 (F); LMV = 6 × (40 − 50) = ₹60 (A)
Total: LCV = ₹25 (F); LRV = ₹15 (A); LMV = ₹40 (F); no sub-efficiency variance because total standard and actual hours are equal (100 each).
Check: LRV + LMV = ₹15 (A) + ₹40 (F) = ₹25 (F) = LCV.
Illustration L5: Mix, sub-efficiency and idle time (unequal hours)
Question. Standard for the output: skilled 120 hours at ₹8, semi-skilled 80 hours at ₹5. Actual hours paid: skilled 130 at ₹8.40 (10 hours idle), semi-skilled 100 at ₹5.50. Calculate all labour variances.
Solution.
Total standard hours = 200. RST: Skilled = 120 ÷ 200 × 220 = 132; Semi-skilled = 80 ÷ 200 × 220 = 88
LCV = (120×8 + 80×5) − (130×8.40 + 100×5.50) = 1,360 − 1,642 = ₹282 (A)
LRV = AT paid × (SR − AR): Skilled = ₹52 (A); Semi-skilled = ₹50 (A); total = ₹102 (A)
Idle time variance = idle hours × SR: Skilled = 10 × 8 = ₹80 (A); total = ₹80 (A)
LMV = SR × (RST − AT worked): Skilled = ₹96 (F); Semi-skilled = ₹60 (A); total = ₹36 (F)
Sub-efficiency = SR × (ST − RST): Skilled = ₹96 (A); Semi-skilled = ₹40 (A); total = ₹136 (A)
LEV = SR × (ST − AT worked): total = ₹100 (A)
Check: LCV ₹282 (A) = LRV ₹102 (A) + LMV ₹36 (F) + Sub-efficiency ₹136 (A) + Idle time ₹80 (A); also LEV ₹100 (A) = LMV + Sub-efficiency.
Illustration L6: Gang labour yield variance
Question. A gang of workers has a standard cost of ₹200 per gang hour and a standard output of 40 units per gang hour. In a week the gang worked 100 hours at an actual cost of ₹205 per hour and produced 3,900 units. Calculate the labour variances.
Solution.
LCV = (3,900 × 5) − (100 × 205) = 19,500 − 20,500 = ₹1,000 (A)
LRV = 100 × (200 − 205) = ₹500 (A)
LEV = 200 × (97.50 − 100) = ₹500 (A)
Labour yield variance = Standard cost per unit × (AY − SY) = 5 × (3,900 − 4,000) = ₹500 (A)
Check: LRV + LEV = ₹1,000 (A) = LCV. With one gang, yield variance equals efficiency variance.
Illustration L7: Department-wise labour variances
Question. Data for two departments:
| Dept A | Dept B | |
|---|---|---|
| Standard hours for output | 800 | 500 |
| Standard rate per hour | ₹6 | ₹8 |
| Actual hours worked | 850 | 480 |
| Gross wages paid | ₹5,525 | ₹3,984 |
Calculate labour cost, rate and efficiency variances for each department and in total.
Solution.
Dept B: standard cost = 500 × 8 = 4,000; actual rate = 3,984 ÷ 480 = ₹8.30; LCV = 4,000 − 3,984 = ₹16 (F); LRV = 480 × (8 − 8.30) = ₹144 (A); LEV = 8 × (500 − 480) = ₹160 (F)
Total: LCV = ₹709 (A); LRV = ₹569 (A); LEV = ₹140 (A)
Check: LRV + LEV = ₹709 (A) = LCV (₹709 (A)).
Illustration L8: Finding a missing labour variance
Question. Labour cost variance is ₹900 (A) and labour rate variance is ₹350 (F). The standard rate is ₹5 per hour and there was no idle time. Find the efficiency variance and the excess hours worked.
Solution.
LEV = SR × (ST − AT), so AT − ST = 1,250 ÷ 5 = 250 hours
Workers took 250 hours more than the standard hours.
Overhead variance illustrations
Illustration O1: Variable overhead variances
Question. Budgeted variable overhead ₹30,000 for 6,000 hours. In the period, standard hours for the actual output were 5,400, actual hours worked 5,600 and actual variable overhead ₹29,400. Calculate the variable overhead variances.
Solution.
Standard VOH for actual output = 5,400 × 5 = ₹27,000
VOV = 27,000 − 29,400 = ₹2,400 (A)
Expenditure variance = (5,600 × 5) − 29,400 = 28,000 − 29,400 = ₹1,400 (A)
Efficiency variance = 5 × (5,400 − 5,600) = ₹1,000 (A)
Check: ₹1,400 (A) + ₹1,000 (A) = ₹2,400 (A) = VOV.
Illustration O2: Variable overhead with a rate per hour of ₹2.50
Question. Variable overhead is absorbed at ₹2.50 per hour on a budget of 10,000 hours. Standard hours for the actual output were 9,000, actual hours 9,400 and actual variable overhead ₹24,100. Find the variable overhead variances.
Solution.
VOV = 22,500 − 24,100 = ₹1,600 (A)
Expenditure variance = (9,400 × 2.50) − 24,100 = 23,500 − 24,100 = ₹600 (A)
Efficiency variance = 2.50 × (9,000 − 9,400) = ₹1,000 (A)
Check: ₹600 (A) + ₹1,000 (A) = ₹1,600 (A) = VOV.
Illustration O3: Fixed overhead cost, expenditure and volume variances
Question. Budgeted fixed overhead ₹50,000 for an output of 5,000 units. Actual output was 4,600 units and actual fixed overhead ₹49,000. Calculate the fixed overhead variances.
Solution.
FOCV = 46,000 − 49,000 = ₹3,000 (A)
Expenditure variance = 50,000 − 49,000 = ₹1,000 (F)
Volume variance = 10 × (4,600 − 5,000) = ₹4,000 (A)
Check: ₹1,000 (F) + ₹4,000 (A) = ₹3,000 (A) = FOCV.
Illustration O4: Fixed overhead with efficiency, capacity and calendar variances
Question. Budgeted fixed overhead ₹1,20,000 for 12,000 hours in 24 working days. Actual: 26 working days, 12,900 hours worked, standard hours for actual output 12,500 and actual fixed overhead ₹1,22,500. Calculate all fixed overhead variances.
Solution.
FOCV = (12,500 × 10) − 122,500 = 125,000 − 122,500 = ₹2,500 (F)
Expenditure variance = 120,000 − 122,500 = ₹2,500 (A)
Volume variance = 10 × (12,500 − 12,000) = ₹5,000 (F)
Efficiency variance = 10 × (12,500 − 12,900) = ₹4,000 (A)
Capacity variance = 10 × (12,900 − 13,000) = ₹1,000 (A)
Calendar variance = 10 × (13,000 − 12,000) = ₹10,000 (F)
Check: Volume ₹5,000 (F) = Efficiency ₹4,000 (A) + Capacity ₹1,000 (A) + Calendar ₹10,000 (F); FOCV ₹2,500 (F) = Expenditure ₹2,500 (A) + Volume ₹5,000 (F).
Illustration O6: Fixed overhead when fewer days were worked
Question. Budgeted fixed overhead ₹80,000 for 8,000 hours in 20 working days. Actual: 18 working days, 7,300 hours worked, standard hours for actual output 7,500 and actual fixed overhead ₹79,000. Find the fixed overhead variances and explain the calendar variance.
Solution.
FOCV = (7,500 × 10) − 79,000 = 75,000 − 79,000 = ₹4,000 (A)
Expenditure variance = 80,000 − 79,000 = ₹1,000 (F)
Volume variance = 10 × (7,500 − 8,000) = ₹5,000 (A)
Efficiency variance = 10 × (7,500 − 7,300) = ₹2,000 (F)
Capacity variance = 10 × (7,300 − 7,200) = ₹1,000 (F)
Calendar variance = 10 × (7,200 − 8,000) = ₹8,000 (A)
Check: Volume ₹5,000 (A) = Efficiency ₹2,000 (F) + Capacity ₹1,000 (F) + Calendar ₹8,000 (A); FOCV ₹4,000 (A) = Expenditure ₹1,000 (F) + Volume ₹5,000 (A).
Illustration O5: Total overhead variance (fixed and variable)
Question. Budget for the period: fixed overhead ₹60,000, variable overhead ₹30,000, 6,000 hours. Actual: standard hours for actual output 5,400, actual hours 5,600, actual fixed overhead ₹59,000, actual variable overhead ₹29,400. Calculate the total overhead variance and its parts.
Solution.
FOCV = (5,400 × 10) − 59,000 = ₹5,000 (A) = Expenditure ₹1,000 (F) + Volume ₹6,000 (A)
VOV = (5,400 × 5) − 29,400 = ₹2,400 (A) = Expenditure ₹1,400 (A) + Efficiency ₹1,000 (A)
Total overhead variance = FOCV + VOV = ₹5,000 (A) + ₹2,400 (A) = ₹7,400 (A)
Check: Absorbed overhead = 5,400 × 15 = ₹81,000; actual overhead = ₹88,400; difference = ₹7,400 (A).
Sales variance illustrations
Illustration S1: Sales value, price and volume variances (one product)
Question. Budgeted sales: 2,000 units at ₹25. Actual sales: 2,200 units at ₹24. Calculate the sales variances by the turnover method.
Solution.
Value variance = 52,800 − 50,000 = ₹2,800 (F)
Price variance = AQ × (AP − SP) = 2,200 × (24 − 25) = ₹2,200 (A)
Volume variance = SP × (AQ − BQ) = 25 × (2,200 − 2,000) = ₹5,000 (F)
Check: ₹2,200 (A) + ₹5,000 (F) = ₹2,800 (F) = Value variance.
Illustration S2: Two products, value, price, volume, mix and quantity
Question. Budgeted sales: A 1,200 units at ₹10, B 800 units at ₹15. Actual sales: A 1,300 units at ₹10.50, B 900 units at ₹14.50. Calculate all sales variances by the turnover method.
Solution.
RSQ = BQ ÷ total BQ × total AQ: A = 1,200 ÷ 2,000 × 2,200 = 1,320; B = 800 ÷ 2,000 × 2,200 = 880
Value variance = 26,700 − 24,000 = ₹2,700 (F)
Price = AQ × (AP − SP): A = ₹650 (F); B = ₹450 (A). Total = ₹200 (F)
Volume = SP × (AQ − BQ): A = ₹1,000 (F); B = ₹1,500 (F). Total = ₹2,500 (F)
Mix = SP × (AQ − RSQ): A = ₹200 (A); B = ₹300 (F). Total = ₹100 (F)
Quantity = SP × (RSQ − BQ): A = ₹1,200 (F); B = ₹1,200 (F). Total = ₹2,400 (F)
Check: Value ₹2,700 (F) = Price ₹200 (F) + Volume ₹2,500 (F); Volume ₹2,500 (F) = Mix ₹100 (F) + Quantity ₹2,400 (F).
Illustration S3: Three products, sales mix and quantity variances
Question. Budgeted sales: A 500 units at ₹20, B 300 units at ₹30, C 200 units at ₹40. Actual sales: A 450 units at ₹21, B 400 units at ₹29, C 250 units at ₹41. Calculate the sales variances.
Solution.
RSQ = BQ ÷ total BQ × total AQ: A = 500 ÷ 1,000 × 1,100 = 550; B = 300 ÷ 1,000 × 1,100 = 330; C = 200 ÷ 1,000 × 1,100 = 220
Value variance = 31,300 − 27,000 = ₹4,300 (F)
Price = AQ × (AP − SP): A = ₹450 (F); B = ₹400 (A); C = ₹250 (F). Total = ₹300 (F)
Volume = SP × (AQ − BQ): A = ₹1,000 (A); B = ₹3,000 (F); C = ₹2,000 (F). Total = ₹4,000 (F)
Mix = SP × (AQ − RSQ): A = ₹2,000 (A); B = ₹2,100 (F); C = ₹1,200 (F). Total = ₹1,300 (F)
Quantity = SP × (RSQ − BQ): A = ₹1,000 (F); B = ₹900 (F); C = ₹800 (F). Total = ₹2,700 (F)
Check: Value ₹4,300 (F) = Price ₹300 (F) + Volume ₹4,000 (F); Volume ₹4,000 (F) = Mix ₹1,300 (F) + Quantity ₹2,700 (F).
Illustration S4: Sales margin (profit) method, one product
Question. Standard selling price ₹50 and standard cost ₹35 per unit; budget 1,000 units. Actual: 1,100 units sold at ₹49 with actual cost ₹36 per unit. Calculate the sales margin variances.
Solution.
Value variance = 14,300 − 15,000 = ₹700 (A)
Price variance = 1,100 × (49 − 50) = ₹1,100 (A)
Cost variance = 1,100 × (35 − 36) = ₹1,100 (A)
Volume variance = 15 × (1,100 − 1,000) = ₹1,500 (F)
Check: ₹1,100 (A) + ₹1,100 (A) + ₹1,500 (F) = ₹700 (A) = Value variance.
Illustration S5: Sales margin method, two products
Question. Standard selling price and cost per unit: A ₹30 and ₹22; B ₹50 and ₹35. Budgeted sales: A 400 units, B 600 units. Actual: A 500 units sold at ₹31 (cost ₹23), B 600 units sold at ₹49 (cost ₹36). Calculate all sales margin variances.
Solution.
Actual profit = 500 × (31 − 23) + 600 × (49 − 36) = 4,000 + 7,800 = ₹11,800
RSQ: A = 400 ÷ 1,000 × 1,100 = 440; B = 600 ÷ 1,000 × 1,100 = 660
Value variance = 11,800 − 12,200 = ₹400 (A)
Price = AQ × (AP − SP): A = ₹500 (F); B = ₹600 (A). Total = ₹100 (A)
Cost = AQ × (Std cost − Actual cost): A = ₹500 (A); B = ₹600 (A). Total = ₹1,100 (A)
Volume = Std margin × (AQ − BQ): A = ₹800 (F); B = Nil. Total = ₹800 (F)
Mix = Std margin × (AQ − RSQ): A = ₹480 (F); B = ₹900 (A). Total = ₹420 (A)
Quantity = Std margin × (RSQ − BQ): A = ₹320 (F); B = ₹900 (F). Total = ₹1,220 (F)
Check: Value ₹400 (A) = Price ₹100 (A) + Cost ₹1,100 (A) + Volume ₹800 (F); Volume = Mix ₹420 (A) + Quantity ₹1,220 (F).
Illustration S6: Finding a missing sales variance
Question. Sales value variance is ₹6,000 (F) and sales price variance is ₹2,500 (A). Standard price is ₹20 per unit. Find the sales volume variance and the extra units sold over budget.
Solution.
Volume = SP × (AQ − BQ), so AQ − BQ = 8,500 ÷ 20 = 425 units
The firm sold 425 units more than budgeted, but at lower prices.
Revise standard costing by first learning the definitions and comparisons, then practising each variance with a small numerical, using the check formulas to confirm your answers. Practise with real exam questions too: see the Unit 2 Accounting and Auditing PYQs and the Paper 2 Commerce PYQs on webcomm.in.
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