# Materials - Standard, Actual, Budgeted; Input, Output, Quantity, Rate, Cost

# Material Cost & Variance

## Material Variance

Material Variance implies the variances in the cost incurred on materials used for obtaining the output.## Material Cost

It is the cost of materials used in the manufacture of a product.In general

Value = Quantity × Price

For materials

Cost of Materials

= | Quantity of Materials × Price of Materials |

From this we can see that the material cost is influenced by two factors,

- The quantity of material used;
- The price at which the materials are acquired.

## Illustration for explanation

Consider the following data relating to the standard costs and the actual costs incurred in relation to the manufacture of a product. This data is referred to in all the explanations below

Standard | Actual | |||||
---|---|---|---|---|---|---|

SQ | SP | SC | AQ | AP | AC | |

Material A Material B Material C | 900 800 200 | 15 45 85 | 13,500 36,000 17,000 | 2,250 1,950 550 | 16 42 90 | 36,000 81,900 41,800 |

Total/Mix | 1,900 | 35 | 66,500 | 4,750 | 35.2421 | 1,67,400 |

Input Loss | 100 | 35 | 3,500 | 430 | ||

Output | 1,800 SO | 4,320 AO |

Output (_O) is in units of measurement of output, Quantities (_Q) are in units of measurement of input, Prices (_P) are in monetary value per unit input and Costs (_C) are in monetary values.

Assuming the input and output are in kgs for the purpose of explanations.

## Note

- The Price in total row is derived using the relation
Value Quantity - Price/unit input (standard)
= 66,500 1,900 kgs = 35/kg - Price/kg (actual)
= 1,67,400 4,750 kgs =

/kg3,348 95 Or = 35.2421/kg In using this in calculations, use fractional value if it is simple. Otherwise use the decimal number with substantial number of digits after the decimal.

## Identities

The data in the above table while being interpreted will be addressed as below.Standard | Actual | |||||
---|---|---|---|---|---|---|

SQ | SP | SC | AQ | AP | AC | |

Material A Material B Material C | SQ_{A}SQ _{B}SQ _{C} | SP_{A}SP _{B}SP _{C} | SC_{A}SC _{B}SC _{C} | AQ_{A}AQ _{B}AQ _{C} | AP_{A}AP _{B}AP _{C} | AC_{A}AC _{B}AC _{C} |

Total/Mix | SQ_{Mix} | SP_{Mix} | SC_{Mix} | AQ_{Mix} | AP_{Mix} | AC_{Mix} |

Input Loss | SQIL_{Mix} | SP_{Mix} | SCIL_{Mix} | AQIL_{Mix} | ||

Output | SO | AO |

SQ_{A} for standard quantity of material A, AQ_{Mix} for total quantity of actual mix (all the materials together) etc.

## Mix

When two or more types of materials are being used in the production process there is a mix. Mix is a term used to indicate all the materials taken together.- Quantity of Mix indicates quantity of all the materials taken together.
- Cost of Mix indicates cost of all the materials taken together.
- Price of Mix indicates the weighted average price of all the material prices taking quantities as weights.

We will go through the explanation for the terms below.

# Standards

## Standard

- A basis for comparison
- The ideal in terms of which something can be judged
- a reference point against which other things can be evaluated
- criterion

The following terms involving standards are relevant to this topic.

## Standard Quantity ~ SQ

The quantity of material required for manufacturing the product.It may be expressed for one or more units of output.

- Standard Material required for producing 1 unit is 10 kg.
- Standard output is 120 units and the material required for the same is 1,200 kg.

### Standard Quantity of Material ~

The quantity of each distinct type of material**SQ**_{Mat}### Standard Quantity of Mix

The quantity of all types of materials together**SQ**_{Mix}= **ΣSQ**_{Mat}Sum of the Standard Quantities of Individual Materials

Where there is only one material SQ

_{Mix}= SQ_{Mat}.

From the data in the illustration

SQ _{A}= 900 kgs SQ _{B}= 800 kgs SQ _{C}= 200 kgs SQ _{Mix}= 1,900 kgs ## Standard Input

The total quantity of materials input as per standards.

**SI**= **ΣSQ**_{Mat}= **SQ**_{Mix}From the data in the illustration

SI = SQ _{Mix}= 1,900 kgs ## Standard Mix Ratio

Where there are two or more materials involved in the production process, Standard Mix Ratio indicates the ratio in which the component materials are to be mixed if the production process is carried on according to plans.This ratio can be for the quantities or for costs of materials used.

### Standard Quantity Mix Ratio

**SQMR**= **SQ**_{Mat1}: SQ_{Mat2}: ...Ratio of Standard Quantities of Individual Materials

### Standard Cost Mix Ratio

**SCMR**= **SC**_{Mat1}: SC_{Mat2}: ...Or = **SQ**_{Mat1}× SP_{Mat1}: SQ_{Mat2}× SP_{Mat2}: ...Ratio of Standard Costs of Individual Materials From the data in the illustration,

SQMR = SQ _{A}: SQ_{B}: SQ_{C}= 900 kgs : 800 kgs : 200 kgs = 9 : 8 : 2 SCMR = SC _{A}: SC_{B}: SC_{C}= 13,500 : 36,000 : 17,000 = 27 : 72 : 34 ## Standard Price

The price at which the materials used in the production process are to be acquired.### Standard Price of Material ~

The price of each type of material**SP**_{Mat}### Standard Price of Mix

The weighted average standard price of all types of materials taking quantities as weights.**SP**_{Mix}= SQ _{Mat1}× SP_{Mat1}+ SQ_{Mat2}× SP_{Mat2}+ ...SQ _{Mat1}+ SQ_{Mat2}+ ...= Σ(SQ _{Mat}× SP_{Mat})ΣSQ _{Mat}= ΣSC _{Mat}ΣSQ _{Mat}= **SC**_{Mix}**SQ**_{Mix}Where there is only one material SP

_{Mix}= SP_{Mat}.From the data in the illustration

SP

_{A}= 15/kg

SP_{B}= 45/kg

SP_{C}= 85/kgSP _{Mix}= 66,500 1,900 kg = 35/kg

## Standard Cost of Materials

The cost of materials to be incurred on manufacturing the standard output.It is the value of standard quantity of materials taken at the standard price.

**SC**= **SQ × SP**Standard Quantity × Standard Price

### Standard Cost of Material

The cost of each type of material distinctly**SC**_{Mat}= **SQ**_{Mat}× SP_{Mat}### Standard Cost of Mix

The standard cost of all types of materials together**SC**_{Mix}= **SQ**_{Mix}× SP_{Mix}Standard Quantity of Mix × Standard Price of Mix

Or = **ΣSC**_{Mat}Sum of the Standard Costs of Individual Materials

Where there is only one material SC

_{Mix}= SC_{Mat}.

From the data in the illustration

SC _{A}= SQ _{A}× SP_{A}= 900 kgs × 15/kg = 13,500 SC _{B}= SQ _{B}× SP_{B}= 800 kgs × 45/kg = 36,000 SC _{C}= SQ _{C}× SP_{C}= 200 kgs × 85/kg = 17,000 SC _{Mix}= 66,500 SC _{Mix}= SQ _{Mix}× SP_{Mix}= 1,900 kgs × 35/kg = 66,500 ## Standard Output/Production ~ SO

It is the output to be achieved using the standard quantity of materials.From the data in the illustration

SO = 1,800 kgs

## Input and Output need not be in the same terms

The input and output may or may not be in the same units.### Different Units

The Standard Quantity of Materials required for producing 1 unit of DEXAR are 20 tons of AMY and 15 tons of TRE.Here the input (in tons) and output (in units) are in different terms.

### Same Units

The Actual Quantity of Materials used for producing 9 tons of SUFTRA is 12 tons comprising of 5 tons of Chemical A, 4 tons of Chemical B and 3 tons of Material Z.Here the input (in tons) and the output (in tons) are in the same terms.

## Standard Cost for Unit Output/Yield

The standard cost incurred per unit output= Standard Cost Standard Output ⇒ **SC/UO**= **SC****SO**SC/UO ≡ SC/UY. Output is also addressed to as yield.

### for each Material separately

SC/UO _{Mat}= SC _{Mat}SO Since after mixing up the input materials, each material loses its individual identity, measuring SC/UO

_{Mat}is not rational.### for all Materials together

The standard cost incurred per unit output over all the materials taken together.SC/UO _{Mix}= SC _{Mix}SO

From the data in the illustration,

SC/UO _{A}= SC _{A}SO = 13,500 1,800 kgs =

/kg27 19 SC/UO _{B}= SC _{B}SO = 36,000 1,800 kgs =

/kg72 19 SC/UO _{C}= SC _{C}SO = 17,000 1,800 kgs =

/kg34 19 SC/UO _{Mix}= SC _{Mix}SO = 66,500 1,800 kgs = 7/kg

## When there are losses

## Standard Quantity of Input Loss ~ SQIL

It is the inupt lost in achieving the output. It may be expressed as an absolute figure of as a % of input.- Of the total input of 4,000 kgs, 250 kgs will be lost in achieving the output.
- 10% of the input would be lost in processing.

## Loss of Mix

In dealing with losses in calculating material variances we consider loss of mix and not of individual materials. This amounts to assuming that the losses are being ascertained after the materials are mixed up for the purposes of production.For being capable of identifying the loss for individual materials, the production process should be such that the materials are processed individually till the point where the losses are ascertained. Losses should be ascertained and then the net quantities are to be combined to form the material mix.

## Standard Output (from loss data)

Where input and output are expressed in the same units and loss is expressed in input terms, we will be able to calculate the output.Standard Output ~

**SO**= **SI − SQIL**Standard Input − Standard Quantity of Input Loss

**SI = SQ**_{Mix}## Standard Cost of Input Loss

It is the cost incurred on the input loss quantity.It is obtained by valuing the input loss quantity at the standard price.

**SCIL**= **SQIL × SP**Standard Quantity of Input Loss × Standard Price

For the mix of materials

SCIL

_{Mix}= SQIL

_{Mix}× SP_{Mix}

# Actuals

## Actual Quantity of Materials ~ AQ

The quantity of material actually used in the manufacture of the product.It may be expressed for one or more units of output.

- Actual Material used for producing 1 kg of the product is 18 units.
- 2,450 tons of the material have been used in producing an output of 8 million units.

### Actual Quantity of Material ~ AQ

The quantity of each type of material_{Mat}### Actual Quantity of Mix

The quantity of all types of materials together**AQ**_{Mix}= **ΣAQ**_{Mat}Sum of the Actual Quantities of Individual Materials

Where there is only one material AQ

_{Mix}= AQ_{Mat}.

From the data in the illustration

AQ _{A}= 2,250 kgs AQ _{B}= 1,950 kgs AQ _{C}= 550 kgs AQ _{Mix}= 4,750 kgs ## Actual Input

The total quantity of materials actually input.

**AI**= **ΣAQ**_{Mat}= **AQ**_{Mix}From the data in the illustration

AI = AQ _{Mix}= 4,750 kgs ## Actual Mix Ratios

Where there are two or more materials involved in the production process, Actual Mix Ratio indicates the ratio in which the component materials are actually mixed.This ratio can be for the quantities or for costs of materials used.

### Actual Quantity Mix Ratio

**AQMR**= **AQ**_{Mat1}: AQ_{Mat2}: ...Ratio of Actual Quantities of Individual Materials

### Actual Cost Mix Ratio

**ACMR**= **AC**_{Mat1}: AC_{Mat2}: ...Or = **AQ**_{Mat1}× AP_{Mat1}: AQ_{Mat2}× AP_{Mat2}: ...Ratio of Actual Costs of Individual Materials From the data in the illustration,

AQMR = AQ _{A}: AQ_{B}: AQ_{C}= 2,250 kgs : 1,950 kgs : 550 kgs = 45 : 39 : 11 ACMR = AC _{A}: AC_{B}: AC_{C}= 36,000 : 81,900 : 41,800 = 40 : 91 : 55 ## Actual Price (of Materials Input) ~ AP

The price at which the materials used in the production process are acquired.### Cost and Value

By Price we mean price based on the value of materials used and not just the cost of purchase. Value would also include the direct expenses incurred before bringing the material into the store or more specifically to the production area.Where there are no direct expenses relating to materials, value would be the purchase price itself.

### Actual Price of Material ~ AP

The price of each type of material_{Mat}### Actual Price of Mix

The weighted average actual price of all types of materials taking quantities as weights.**AP**_{Mix}= AQ _{Mat1}× AP_{Mat1}+ AQ_{Mat2}× AP_{Mat2}+ ...AQ _{Mat1}+ AQ_{Mat2}+ ...= Σ(AQ _{Mat}× AP_{Mat})ΣAQ _{Mat}= ΣAC _{Mat}ΣAQ _{Mat}= **AC**_{Mix}**AQ**_{Mix}Where there is only one material AP

_{Mix}= AP_{Mat}.

From the data in the illustration

AP

_{A}= 15/kg

AP_{B}= 45/kg

AP_{C}= 85/kgAR _{Mix}= AC _{Mix}AQ _{Mix}= 1,67,400 4,750 kg =

/kg (Or) 35.2421/kg3,348 95 ## Actual Cost

The actual cost of materials incurred for manufacturing the actual output.It is the value of actual quantity of materials taken at the actual price.

**AC**= **AQ × AP**Actual Quantity × Actual Price

### Actual Cost of Material

The cost of each type of material distinctly.**AC**_{Mat}= AQ _{Mat}× AP_{Mat}### Actual Cost of Mix

The actual cost of all types of materials together**AC**_{Mix}= **AQ**_{Mix}× AP_{Mix}Actual Quantity of Mix × Actual Price of Mix

Or = **ΣAC**_{Mat}Sum of the Actual Costs of Individual Materials

Where there is only one material AC

_{Mix}= AC_{Mat}.

From the data in the illustration

AC _{A}= AQ _{A}× AP_{A}= 2,250 kgs × 16/kg = 36,000 AC _{B}= AQ _{B}× AP_{B}= 1,950 kgs × 42/kg = 81,900 AC _{C}= AQ _{C}× AP_{C}= 550 kgs × 90/kg = 41,800 AC _{Mix}= 1,67,400 AC _{Mix}= AQ _{Mix}× AP_{Mix}= 4,750 kgs ×

/kg3,348 95 = 1,67,400 ### Note

In calculations use fractions where it is a simple one to reduce the need for corrections on account of approximations. Alternatively take more digits after the decimal.35.2421 × 4,750 = 1,67,399.975

## Actual Output/Production ~ AO

It is the output achieved using the actual quantity of materials.From the data in the illustration

AO = 4,320 kgs

## Input and Output need not be in the same terms

The input and output may or may not be in the same units.### Different Units

The Actual Quantity of Materials required for producing 1 unit of DEXAR are 20 tons of AMY and 15 tons of TRE.Here the input (in tons) and output (in units) are in different terms.

### Same Units

The Actual Quantity of Materials used for producing 9 tons of SUFTRA is 12 tons comprising of 5 tons of Chemical A, 4 tons of Chemical B and 3 tons of Material Z.Here the input (in tons) and the output (in tons) are in the same terms.

## Actual Cost of Output/Yield per unit

The actual cost incurred per unit output.**AC/UO**= Actual Cost Actual Output = **AC****AO**Output is also addressed to as yield. As such ACY/U ≡ AC/UO.

### for each Material separately

AC/UO _{Mat}= AC _{Mat}AO Since after mixing up the input materials, each material loses its individual identity, measuring AC/UO

_{Mat}is not rational.### for all Materials together

The actual cost incurred per unit output over all the materials taken together.AC/UO _{Mix}= AC _{Mix}AO From the data in the illustration,

AC/UO _{Mix}= AC _{Mix}AO = 1,67,400 4,320 kgs =

/kg837 114 Or = 7.342/kg

## When there are losses

## Actual Quantity of Input Loss ~ AQIL

It is the inupt lost in achieving the output. It may be expressed as an absolute figure of as a % of input.- Of the total input of 5,000 kgs, 350 kgs are lost in achieving the output.
- 8% of the input is lost in processing.

## Loss of Mix

In dealing with losses in calculating material variances we consider loss of mix and not of individual materials. This amounts to assuming that the losses are being ascertained after the materials are mixed up for the purposes of production.## Actual Output (from loss data)

Where input and output are expressed in the same units and loss is expressed in input terms, we will be able to calculate the output.Actual Output ~

**AO**= **AI − AQIL**Actual Input − Actual Quantity of Input Loss

**AI = AQ**_{Mix}## Standard Cost of Input Loss

It is the standard cost of actual input loss quantity.It is obtained by valuing the actual input loss quantity at the standard price.

**SC(ACIL)**= **AQIL × SP**Actual Quantity of Input Loss × Standard Price

For the mix of materials

ACIL _{Mix}= AQIL _{Mix}× SP_{Mix}

# Budget/Budgeted

## Budget

- a depiction of a future activity in quantitative terms.

### Production Budget

A Production Budget indicates the production that is planned to be achieved over a future period through a production process.### Material Budget

A Material Budget indicates the quantity of materials required for the production that is planned to be achieved over a future period through a production process.### Cash Budget

A cash budget indicates the inflow and outflow of cash over a certain future period.### Expenditure Budget

An expenditure budget indicates the expenditure that is to be incurred over the budget period.

## Budgeted

- relates to a budget

By the term Budgeted Data in this topic, we mean the data pertaining to a specified budget indicating a level of activity that has been planned to be achieved.

The following terms involving budgets are relevant to this topic.

## Budgeted Output/Production ~ BO

The output that is planned to be achieved during a period through the production process.## Budgeted Quantity

The standard quantity of materials to be input into the production process for achieving the budgeted output.**BQ**= **SQ/UO × BO**Standard Quantity of Materials for unit output × Budgeted Output

## Budgeted Price

Budgets are prepared as per standards. As such Budgeted Price is nothing but standard price.**BP = SP**## Budgeted Cost

The cost of materials to be incurred for manufacturing the budgeted output. It is the value of budgeted quantity of materials taken at the standard price.**BC**= **BQ × SP**Budgeted Quantity × Standard Price

# Budgeted vs Standard

## Examples

- Budgeted Output is the output that is planned to be achieved by the organisation in a given period/process and Standard Output is that output for which the standards are expressed.
- Standard Cost gives an idea of how much each unit of the product should cost under normal circumstances. Budget Cost gives an idea of the cost that should be incurred for bringing out the budget quantity of output (over a certain period or in a certain process) under normal circumstances.

We use the terms Budgeted and Standard synonymously at times, but they would not be the same in all cases.

## For analysing material variances, we need standards

In analysing variances we need the data relating to the standards, i.e. data relating to the standard quantity (SQ), price (SP) and output (SO).## Budgets are always as per the standard

It should be noted that the budgeted data is always based on standards. Standards are fixed for each unit of production and budgeted data is relevant to a particular production level. Standards may be expressed for any production level (1 unit, 2 units, 10 units, ...).Since budgeted data is standard data for a particular production level we do not need separate data for the standard when the budgeted data is known.

## SO = BO

The standard output and the budgeted output are the same.Standard | Budgeted | Actual | |||||||
---|---|---|---|---|---|---|---|---|---|

SQ | SP | SC | BQ | BP | BC | AQ | AP | AC | |

Material | 20 | 10 | 200 | 20 | 10 | 200 | 20 | 10 | 200 |

Output | 12 units SO | 12 units BO | 12 units AO |

## SO ≠ BO

The standard output and the budgeted output are not the same.Standard | Budgeted | Actual | |||||||
---|---|---|---|---|---|---|---|---|---|

SQ | SP | SC | BQ | BP | BC | AQ | AP | AC | |

Material | 200 | 10 | 2,000 | 500 | 10 | 5,000 | 524 | 10 | 5,240 |

Output | 10 units SO | 25 units BO | 24 units AO |