Standard Costing - Material Variances

COST AND MANAGEMENT ACCOUNTING

STANDARD COSTING (VARIANCE ANALYSIS)

MATERIAL VARIANCES

 

Part A: Discussion of basic theories including various formulas for computing different variances

Part B: 7 illustrations with solutions

Part A

Definition of Standard Costing

Standard Costing is a method of costing where actual costs/revenues are compared with pre-determined standard costs/revenues in order to:-

1.  Calculate different variances (namely Material Variances, Labour Variances, Overhead Variances and Sales Variances);

2.  Analyse the reasons for the variances, which may be positive as well as negative;

3.  Identify the concerned departments or departmental heads responsible for such variances;

4.  Fix responsibilities for the concerned departmental heads towards achieving   certain standards in the future; and

5.  Take necessary steps wherever required either for achieving the standards or for modifying the standards.

 

Therefore, in standard costing the most important pre-requisite is ‘fixing the standards’ which is actually carried out by the technical persons. Once the standards are determined, then only different variances can be calculated by comparing the actual results with the pre-determined standards. The variances are basically of two types: (a) Cost Variances and (b) Sales Variances.

 

Cost Variances may be of the following four types:

1.  Material Variances

2.  Labour Variances

3.  Variable Overhead Variances

4.  Fixed Overhead Variances

 

Sales Variances may be of the following two types:

1.  Sales Turnover Variances

2.  Sales Margin Variances

 

Standard Costing is also termed as Variance Analysis because the whole of the Standard Costing System revolves around calculating the variances and analysing them in order to control different costs and operations of the business.

 

Material Variances

1	Material Cost Variance	= M4 – M1
2	Material Price Variance	= M2 – M1
3	Material Usage Variance	= M4 – M2
4	Material Mix Variance	= M3 – M2
5	Material Yield / Sub-Usage Variance	= M4 – M3

 

Where,

M1	= AP x AQ
M2	= SP x AQ
M3	= SP x AQ in SP
M4	= SP × SQ for AO
AP	= Actual Price
AQ	= Actual Quantity Consumed
SP	= Standard Price
AQ in SP	= Actual Quantities of the mix in Standard Proportion
SQ for AO	= Standard Quantities of the mix for Actual Output

 

Note A:

When Price Variance is required to be calculated at the point of purchase, the purchased quantity itself is considered as the Actual Quantity (AQ) consumed.

 

Note B:

When there is no mix of materials in the actual input i.e. when the direct material consists of only one material, then

1.   Do not calculate M₃;

2.   Do not calculate material mix variance;

3.   Do not calculate material yield variance.

 

Note C:

Negative variances are adverse variances and positive variances are favourable variances.

Check:

1.   Material Cost Variance (M₄ – M₁)

= Material Price Variance (M₂ – M₁) + Material Usage Variance (M₄ – M₂)

2.   Material Usage Variance (M₄ – M₂)

= Material Mix Variance (M₃ – M₂) + Material Yield Variance (M₄ – M₃)

Part B 

Illustration: 1

The standard and actual figures of product “Z” are as under:

Particulars	Standard	Actual
Material quantity	50 units	45 units
Material price p.u.	Rs 1.00	Rs 0.80

 

Calculate:

1.   Material Cost Variance

2.   Material Price Variance

3.   Material Usage Variance

 

Solution: 1

M1	= AP x AQ	= Rs 0.80 × 45 units	= Rs 36
M2	= SP x AQ	= Rs 1.00 × 45 units	= Rs 45
M4	= SP × SQ for AO	= Rs 1.00 × 50 units	= Rs 50

 

Variances:

Material Cost Variance	=M4 – M1	= Rs 50 – Rs 36	= Rs 14	F
Material Price Variance	=M2 – M1	= Rs 45 – Rs 36	= Rs 9	F
Material Usage Variance	=M4 – M2	= Rs 50 – Rs 45	= Rs 5	F

 

Note: “F” stands for Favourable Variance, and “A” stands for Adverse Variance.

 

Illustration: 2

NEXT Manufacturing Concern furnishes the following information:

Particulars	Standard	Actual
Output	70 kg	2,10,000 kg
Material quantity	100 kg	2,80,000 kg
Material price p.u.	Rs 1.00
Total material cost		Rs 2,52,000

 

Calculate:

4.   Material Cost Variance

5.   Material Price Variance

6.   Material Usage Variance

 

Solution: 2

M1	= AP x AQ		= Rs 2,52,000
M2	= SP x AQ	= Rs 1.00 × 2,80,000 kg	= Rs 2,80,000
M4	= SP × SQ for AO	= Rs 1.00 × 3,00,000 kg	= Rs 3,00,000

 

Variances:

Mat. Cost Variance	=M4 – M1	=3,00,000 – 2,52,000	= Rs 48,000	F
Mat. Price Variance	=M2 – M1	=2,80,000 – 2,52,000	= Rs 28,000	F
Mat. Usage Variance	=M4 – M2	=3,00,000 – 2,80,000	= Rs 20,000	F

 

Note: “F” stands for Favourable Variance, and “A” stands for Adverse Variance.

 

Workings:

SQ for AO

= (100 kg ÷ 70 kg) × 2,10,000 kg

= 3,00,000 kg

 

Illustration: 3

The standard cost of a chemical mixture is as follows:

Standard total material input is 200 kg

40% material A at Rs 200 per kg

60% material B at Rs 300 per kg

A standard loss of 10% of input is expected in production.

 

The cost records for a period showed the following usage:

90 kg material A at a cost of Rs 180 per kg

110 kg material B at a cost of Rs 340 per kg

The quantity produced was 182 kg of good product.

 

Calculate all the material variances.

 

Solution: 3

Analytical Arrangement of Given Data

Material	Standard			Actual
	Quantity (kg)	Price (Rs)	Value (Rs)	Quantity (kg)	Price (Rs)	Value (Rs)
A	80	200	16,000	90	180	16,200
B	120	300	36,000	110	340	37,400
Total	200		52,000	200		53,600
Less: Loss	20			18 (b/f)
	180		52,000	182		53,600

M₁ = AP x AQ

Material	AP (Rs)	AQ (Kg)	M1 (Rs)
A	180	90	16,200
B	340	110	37,400
TOTAL			53,600

 

M₂ = SP x AQ

Material	SP (Rs)	AQ (Kg)	M2 (Rs)
A	200	90	18,000
B	300	110	33,000
TOTAL			51,000

 

M₃ = SP x AQ of input in Standard Proportion

Material	SP (Rs)	AQSP (Kg)	M3 (Rs)
A	200	200 × 40% = 80	16,000
B	300	200 × 60% = 120	36,000
TOTAL			52,000

 

M₄ = SP x SQ of input for Actual Output

Material	SP (Rs)	SQAO (Kg)	M4 (Rs)
A	200	80.89	16,178
B	300	121.33	36,399
TOTAL			52,577

 

Workings:

Standard quantity of input for actual output (SQAO):

Material A	= (80 ÷ 180) × 182	= 80.89 kg
Material B	= (120 ÷ 180) × 182	= 121.33 kg

 

VARIANCES:

Variances	Details	Rs	F / A
Material price variance	M2 − M1
A	18,000 – 16,200	1,800	F
B	33,000 – 37,400	4,400	A
		2,600	A
Material usage variance	M4 − M2
A	16,178 – 18,000	1,822	A
B	36,399 – 33,000	3,399	F
		1,577	F
Material mix variance	M3 – M2
A	16,000 – 18,000	2,000	A
B	36,000 – 33,000	3,000	F
		1,000	F
Material yield variance	M4 – M3
A	16,178 – 16,000	178	F
B	36,399 – 36,000	399	F
		577	F
Material cost variance	M4 – M1
A	16,178 – 16,200	22	A
B	36,399 – 37,400	1,001	A
		1,023	A

 

Illustration: 4

SV Ltd. manufactures BXE by mixing 3 raw materials. For every batch of 100 kg of BXE, 125 kg of raw materials are used. In April 2012, 60 batches were prepared to produce an output of 5600 kg of BXE. The standard and actual particulars for April, 2012 are as under:

	Standard		Actual
Raw material	Mix (%)-age	Price per kg (Rs)	Mix (%)-age	Price per kg (Rs)	Quantity of raw materials purchased (kg)
A	50	20	60	21	5,000
B	30	10	20	8	2,000
C	20	5	20	6	1,000

 Calculate all the material variances.

 

Solution: 4

For a standard batch of 100 kg of output (BXE), standard quantity of raw materials required is 125 kg. Therefor, for 60 standard batches of output, standard raw materials required = 125 × 60 = 7,500 kg.

 

Analytical Arrangement of Given Data

Material	Standard			Actual
	Quantity	Price (Rs)	Value (Rs)	Quantity	Price (Rs)	Value (Rs)
A	3,750	20	75,000	4,500	21	94,500
B	2,250	10	22,500	1,500	8	12,000
C	1,500	5	7,500	1,500	6	9,000
Total	7,500		1,05,000	7,500		1,15,500
Less: Loss	1,500			1,900
Output	6,000		1,05,000	5,600		1,15,500

 

M₁ = AP x AQ

Material	AP (Rs)	AQ (Kg)	M1 (Rs)
A	21	4,500	94,500
B	8	1,500	12,000
C	6	1,500	9,000
TOTAL			1,15,500

 

M₂ = SP x AQ

Material	SP (Rs)	AQ (Kg)	M2 (Rs)
A	20	4,500	90,000
B	10	1,500	15,000
C	5	1,500	7,500
TOTAL			1,12,500

 

M₃ = SP x AQ of input in Standard Proportion

Material	SP (Rs)	AQSP (Kg)	M2 (Rs)
A	20	3,750	75,000
B	10	2,250	22,500
C	5	1,500	7,500
TOTAL			1,05,000

 

M₄ = SP x SQ of input for Actual Output

Material	SP (Rs)	SQAO (Kg)	M4 (Rs)
A	20	3,500	70,000
B	10	2,100	21,000
C	5	1,400	7,000
TOTAL			98,000

Working:

Standard quantity of input for actual output (SQAO):

Material A	= (3,750 ÷ 6,000) × 5,600	= 3,500 kg
Material B	= (2,250 ÷ 6,000) × 5,600	= 2,100 kg
Material C	= (1,500 ÷ 6,000) × 5,600	= 1,400 kg

 

VARIANCES:

Variances	Details	Rs	F / A
Material price variance	M2 − M1
A	90,000 – 94,500	4,500	A
B	15,000 – 12,000	3,000	F
C	7,500 – 9,000	1,500	A
		3,000	A
Material usage variance	M4 − M2
A	70,000 – 90,000	20,000	A
B	21,000 – 15,000	6,000	F
C	7,000 – 7,500	500	A
		14,500	A
Material mix variance	M3 – M2
A	75,000 – 90,000	15,000	A
B	22,500 – 15,000	7,500	F
C	7,500 – 7,500	-	-
		7,500	A
Material yield variance	M4 – M3
A	70,000 – 75,000	5,000	A
B	21,000 – 22,500	1,500	A
C	7,000 – 7,500	500	A
		7,000	A
Material cost variance	M4 – M1
A	70,000 – 94,500	24,500	A
B	21,000 – 12,000	9,000	F
C	7,000 – 9,000	2,000	A
		17,500	A

 

Illustration: 5

A brass foundry making castings which are transferred to the machine shop of the company at standard price uses a standard costing system. Standards in regard to the input materials stocks of which are kept at standard prices are as follows:

Standard Mixture: 70% Copper and 30% Zinc

Standard Price: Copper Rs 2,400 per ton and Zinc Rs 650 per ton

Standard loss in melt: 5% of input

 

Actual figures in respect of a costing period are as follows:

Commencing stocks: Copper 100 tons and Zinc 60 tons

Finished stock: Copper 110 tons and Zinc 50 tons

Purchases during the period:

Copper 300 tons costing Rs 7, 32,500

Zinc 100 tons costing Rs 62,500

Metal melted 400 tons.

Casting produced 375 tons.

 

Calculate all the material variances.

 

Solution: 5

            Computation of Actual Quantity (AQ) and Actual Cost (M₁)

Particulars	Copper		Zinc
	Quantity (tons)	Value (Rs)	Quantity (tons)	Value (Rs)
Opening stock	100	2,40,000	60	39,000
ADD: Purchases	300	7,32,500	100	62,500
	400	9,72,500	160	1,01,500
LESS: Closing stock	110	2,64,000	50	32,500
Actual quantity (AQ)	290	7,08,500	110	69,000

 

Analytical Arrangement of Given Data

Material	Standard			Actual
	Quantity (tons)	Price (Rs)	Value (Rs)	Quantity (tons)	Price (Rs)	Value (Rs)
Copper	280	2,400	6,72,000	290		7,08,500
Zinc	120	650	78,000	110		69,000
Total	400		7,50,000	400		7,77,500
Less: Loss	20			25 (b/f)
	380		7,50,000	375		7,77,500

 

M₁ = AP x AQ

Material	AP (Rs)	AQ (tons)	M1 (Rs)
Copper			7,08,500
Zinc			69,000
TOTAL			7,77,500

 

M₂ = SP x AQ

Material	SP (Rs)	AQ (tons)	M2 (Rs)
Copper	2,400	290	6,96,000
Zinc	650	110	71,500
TOTAL			7,67,500

 

M₃ = SP x AQ of input in Standard Proportion

Material	SP (Rs)	AQSP (tons)	M2 (Rs)
Copper	2,400	280	6,72,000
Zinc	650	120	78,000
TOTAL			7,50,000

 

M₄ = SP x SQ of input for Actual Output

Material	SP (Rs)	SQAO (tons)	M4 (Rs)
Copper	2,400	276.32	6,63,168
Zinc	650	118.42	76,973
TOTAL			7,40,141

 

Workings:

Standard quantity of input for actual output (SQAO):

Copper	= (280 ÷ 380) × 375	= 276.32 tons
Zinc	= (120 ÷ 380) × 375	= 118.42 tons

 

VARIANCES:

Variances	Details	Rs	F / A
Material price variance	M2 − M1
Copper	6,96,000 – 7,08,500	12,500	A
Zinc	71,500 – 69,000	2,500	F
		10,000	A
Material usage variance	M4 − M2
Copper	6,63,168 – 6,96,000	32,832	A
Zinc	76,973 – 71,500	5,473	F
		27,359	A
Material mix variance	M3 – M2
Copper	6,72,000 – 6,96,000	24,000	A
Zinc	78,000 – 71,500	6,500	F
		17,500	A
Material yield variance	M4 – M3
Copper	6,63,168 – 6,72,000	8,832	A
Zinc	76,973 – 78,000	1,027	A
		9,859	A
Material cost variance	M4 – M1
Copper	6,63,168 – 7,08,500	45,332	A
Zinc	76,973 – 69,000	7,973	F
		37,359	A

 

Illustration: 6

A company manufacturing a special type of fencing tile of dimensions 12” X 8” X 1/2” used a system of standard costing. The standard mix of the compound used for making the tiles is:

1,200 kg of Material A @ Rs 0.30 per kg

500 kg of Material B @ Rs 0.60 per kg

800 kg of Material C @ Rs 0.70 per kg

The compound should produce 12,000 square feet of tiles of 1/2” thickness.

 

During a period in which 1, 00,000 tiles of the standard size were produced, the material usage was:

Material	Quantity (kg)	Price per kg (Rs)	Value (Rs)
A	7,000	0.32	2,240
B	3,000	0.65	1,950
C	5,000	0.75	3,750
Total	15,000		7,940

 

Present the cost figures for the period showing Material Price, Mixture, and Sub-usage Variance.

 

Solution: 6

Standard size of a tile	= 12” × 8” × ½”
	= 96 square inch of area × ½” of thickness
	= (96 ÷ 144) square feet of area × ½” of thickness
	= 2/3 square feet of area × ½” of thickness

 

Therefore, number of tiles for an area of (12,000 square feet × ½” of thickness)

= 12,000 ÷ 2/3 = 12,000 × 3/2 = 18,000

 

Therefore, standards for 18,000 tiles:

Material	Quantity (kg)	Price per kg (Rs)
A	1,200	0.30
B	500	0.60
C	800	0.70

 

Therefore, standards for 1, 00,000 tiles:

Material	Quantity (kg)	Price per kg (Rs)	Value (Rs)
A	6,667	0.30	2,000
B	2,778	0.60	1,667
C	4,444	0.70	3,111
Total	13,889		6,778

 

M₁ = AP x AQ

Material	AP (Rs)	AQ (Kg)	M1 (Rs)
A	0.32	7,000	2,240
B	0.65	3,000	1,950
C	0.75	5,000	3,750
TOTAL			7,940

 

M₂ = SP x AQ

Material	SP (Rs)	AQ (Kg)	M2 (Rs)
A	0.30	7,000	2,100
B	0.60	3,000	1,800
C	0.70	5,000	3,500
TOTAL			7,400

 

M₃ = SP x AQ of input in Standard Proportion

Material	SP (Rs)	AQSP (Kg)	M2 (Rs)
A	0.30	7,200	2,160
B	0.60	3,000	1,800
C	0.70	4,800	3,360
TOTAL			7,320

 

M₄ = SP x SQ of input for Actual Output

Material	SP (Rs)	SQAO (Kg)	M4 (Rs)
A	0.30	6,667	2,000
B	0.60	2,778	1,667
C	0.70	4,444	3,111
TOTAL			6,778

 

Workings:

Actual Quantity of input in Standard Proportion (AQSP):

Material A	= (6,667 ÷ 13,889) × 15,000	= 7,200 kg
Material B	= (2,778 ÷ 13,889) × 15,000	= 3,000 kg
Material C	= (4,444 ÷ 13,889) × 15,000	= 4,800 kg

 

Standard quantity of input for actual output (SQAO):

Material A		6,667 kg
Material B		2,778 kg
Material C		4,444 kg

 

VARIANCES:

Variances	Details	Rs	F / A
Material price variance	M2 − M1
A	2,100 – 2,240	140	A
B	1,800 – 1,950	150	A
C	3,500 – 3,750	250	A
		540	A
Material usage variance	M4 − M2
A	2,000 – 2,100	100	A
B	1,667 – 1,800	133	A
C	3,111 – 3,500	389	A
		622	A
Material mix variance	M3 – M2
A	2,160 – 2,100	60	F
B	1,800 – 1,800	-	-
C	3,360 – 3,500	140	A
		80	A
Material yield variance	M4 – M3
A	2,000 – 2,160	160	A
B	1,667 – 1,800	133	A
C	3,111 – 3,360	249	A
		542	A
Material cost variance	M4 – M1
A	2,000 – 2,240	240	A
B	1,667 – 1,950	283	A
C	3,111 – 3,750	639	A
		1,162	A

 

Illustration: 7

The standard set for material consumption was 100 kg. @ Rs 2.25 per kg.

In a cost period:

Opening stock was 100 kg. @ Rs 2.25 per kg.

Purchases made 500 kg. @ Rs 2.15 per kg.

Consumption: 110 kg

 

Calculate: (a) Usage, and (b) Price Variances

1)   When variance is calculated at point of purchase

2)   When variance is calculated at point of issue on FIFO basis

3)   When variance is calculated at point of issue on LIFO basis

 

Solution: 7

1.   When variance is calculated at point of purchase

M1	= AP × AQ	= 2.15 × 500	= 1,075
M2 (For Price V.)	= SP × AQ	= 2.25 × 500	= 1,125
M2 (For Usage V.)	= SP × AQ	= 2.25 × 110	= 247.50
M4	= SP × SQAO	= 2.25 × 100	= 225
Mat. Price V.	= M2 – M1	= 1,125 – 1,075	= 50 (F)
Mat. Usage V.	= M4 – M2	= 225 – 247.50	= 22.50 (A)

 

2.   When variance is calculated at point of issue on FIFO basis

M1	= AP × AQ	= 2.25 × 100 + 2.15 × 10	= 246.50
M2	= SP × AQ	= 2.25 × 110	= 247.50
M4	= SP × SQAO	= 2.25 × 100	= 225
Mat. Price V.	= M2 – M1	= 247.50 – 246.50	= 1 (F)
Mat. Usage V.	= M4 – M2	= 225 – 247.50	= 22.50 (A)

 

3.   When variance is calculated at point of issue on LIFO basis

M1	= AP × AQ	= 2.15 × 110	= 236.50
M2	= SP × AQ	= 2.25 × 110	= 247.50
M4	= SP × SQAO	= 2.25 × 100	= 225
Mat. Price V.	= M2 – M1	= 247.50 – 236.50	= 11 (F)
Mat. Usage V.	= M4 – M2	= 225 – 247.50	= 22.50 (A)

 

Important note:

When Price Variance is required to be calculated at the point of purchase, the purchased quantity itself is considered as the Actual Quantity (AQ) consumed.