**Some tips to help alleviate students' fears of variance analysis**

Since long ago, variance analysis has been an area that evokes fear in students worldwide. Students enter the exam hall, desperately running through the formulae used to calculate all the different variances, fearful of forgetting them before they have managed to put pen to paper. Then the inevitable happens: they turn over the exam paper and a variance question stares back at them. Frantically, they scribble down all the formulae before they are lost forever. Alas, they can’t remember it quite accurately enough. Is it actual quantity x standard price or standard quantity x actual price? Panic grips them. Logic flies out of the window. They move desperately on to the next question.

Does this sound like a familiar story to you? If it does, carry on reading. This article might help you. Many articles have been written about variance analysis over the years, but the purpose of this one is to cover the area of calculating materials mix and yield variances. While the calculation of a mix variance can also be done for sales, this is not covered by the Paper F5 syllabus at present.Therefore, I shall concentrate purely on the materials variance here.

**Material usage variance
**Most students have relatively little difficulty in calculating a straightforward material usage variance. As a reminder, let’s recap on what the material usage variance is and how it is calculated. The material usage variance analyses the difference between how much actual material we used for our production relative to how much we expected to use, based on standard usage levels. So, for example, if we made 5,000 items using 11,000kg of material A and our standard material usage is only 2kg per item, then we clearly used 1,000kg of material more than we expected to (11,000kg – [2 kg x 5,000 items]). In terms of how we value this difference, it must be at standard cost. Any difference between standard and actual cost would be dealt with by the material price variance.

There can be many reasons for an adverse material usage variance. It may be that inferior quality material have been purchased, perhaps at a lower price. This may be reflected in a favourable material price variance: the materials were cheaper but as a result there was perhaps more waste.

On the other hand, it may be that changes to the production process have been made, or that increased quality controls have been introduced, resulting in more items being rejected. Whatever the cause, it can only be investigated after separate material usage variances have been calculated for each type of material used and then allocated to a responsibility centre.

**Further variance analysis where several materials are used
**The fact that most products will be comprised of several, or sometimes hundreds of different materials, leads us back to the more detailed materials mix and yield variances that can be calculated in these instances. In many industries, particularly where the product being made undergoes a chemical process, it may be possible to combine different levels of the component materials to make the same product. This, in turn, may result in differing yields, dependent on the mix of materials that has been used. Note, when we talk about the materials ‘mix’ we are referring to the quantity of each material that is used to make our product ie we are referring to our inputs. When we talk about ‘yield’, on the other hand, we are talking about how much of our product is produced, ie our output.

**Materials mix variance
**In any process, much time and money will have been spent ascertaining the exact optimum mix of materials. The optimum mix of materials will be the one that balances the cost of each of the materials with the yield that they generate. The yield must also reach certain quality standards. Let us take the example of a chemical, C, that uses both chemicals A and B to make it. Chemical A has a standard cost of $20 per litre and chemical B has a standard cost of $25 per litre. Research has shown that various combinations of chemicals A and B can be used to make C, which has a standard selling price of $30 per litre. The best two of these combinations have been established as:

Mix 1: 10 litres of A and 10 litres of B will yield 18 litres of C; and

Mix 2: 8 litres of A and 12 litres of B will yield 19 litres of C.

Assuming that the quality of C produced is exactly the same in both instances, the optimum mix of materials A and B can be decided by looking at the cost of materials A and B relative to the yield of C.

Mix 1: (18 x $30) – (10 x $20) – (10 x $25) = $90 contribution

Mix 2: (19 x $30) – (8 x $20) – (12 x $25) = $110 contribution

Therefore, the optimum mix that minimises the cost of the inputs compared to the value of the outputs is mix 2: 8/20 material A and 12/20 material B. The standard cost per unit of C is (8 x $20)/19 + (12 x $25)/19 = $24.21. However, if the cost of materials A and B changes or the selling price for C changes, production managers may deviate from the standard mix. This would, in these circumstances, be a deliberate act and would result in a materials mix variance arising. It may be, on the other hand, that the materials mix changes simply because managers fail to adhere to the standard mix, for whatever reason.

Let us assume now that the standard mix has been set (mix 2) and production of C commences. 1,850kg of C is produced, using a total of 900kg of material A and 1,100kg of material B (2,000kg in total). The actual costs of materials A and B were at the standard costs of $20 and $25 per kg respectively. How do we calculate the materials mix variance?

The variance is worked out by first calculating what the standard cost of our 1,850kg worth of C would have been if the standard mix had been adhered to, and comparing that figure to the standard cost of our actual production, using our actual quantities. My preferred approach has always been to present this information in a table as shown in **Table 1** below. The materials mix variance will be $46,000 – $45,500 = $500 favourable.

Remember: it is essential that, for every variance you calculate, you state whether it is favourable or adverse. These can be denoted by a clear ‘A’ or ‘F’ but avoid showing an adverse variance by simply using brackets. This leads to mistakes.

The formula for this is shown below, but if you were to use it, the variance for each type of material must be calculated separately.

(Actual quantity in standard mix proportions – actual quantity used) x standard cost

As a student, I was never a person to blindly learn formulae and rely on these to get me through. I truly believe that the key to variance analysis is to understand what is actually happening. If you understand what the materials mix variance is trying to show, you will work out how to calculate it. However, for those of you who do prefer to use formulae, the workings would be as follows:

**Material A**: (800kg – 900kg) x $20 = $2,000 Adverse

**Material B:** (1,200kg – 1,100kg) x $25 = $2,500 Favourable

**Net variance** = $500 favourable

In this particular example, I have kept things simple by keeping all actual costs in line with the standards. The reality is that, in the real world, actual costs will often vary from standards. Why haven’t I covered this above? Because any variance in materials price is always dealt with by the materials price variance. If we try and bring this into our mix variance, we begin distorting the one thing that we are trying to understand – how the difference in materials mix has affected our cost, rather than how the difference in price has affected our cost.

Why haven’t I considered the fact that although our materials mix variance is $500 favourable, our changed materials mix may have produced less of C than the standard mix? Because this, of course, is where the materials yield variance comes into play.

The materials mix variance focuses on inputs, irrespective of outputs. The materials yield variance, on the other hand, focuses on outputs, taking into account inputs.

**Material usage variance
**Most students have relatively little difficulty in calculating a straightforward material usage variance. As a reminder, let’s recap on what the material usage variance is and how it is calculated. The material usage variance analyses the difference between how much actual material we used for our production relative to how much we expected to use, based on standard usage levels. So, for example, if we made 5,000 items using 11,000kg of material A and our standard material usage is only 2kg per item, then we clearly used 1,000kg of material more than we expected to (11,000kg – [2 kg x 5,000 items]). In terms of how we value this difference, it must be at standard cost. Any difference between standard and actual cost would be dealt with by the material price variance.

There can be many reasons for an adverse material usage variance. It may be that inferior quality material have been purchased, perhaps at a lower price. This may be reflected in a favourable material price variance: the materials were cheaper but as a result there was perhaps more waste.

On the other hand, it may be that changes to the production process have been made, or that increased quality controls have been introduced, resulting in more items being rejected.

Whatever the cause, it can only be investigated after separate material usage variances have been calculated for each type of material used and then allocated to a responsibility centre.

**Further variance analysis where several materials are used
**The fact that most products will be comprised of several, or sometimes hundreds of different materials, leads us back to the more detailed materials mix and yield variances that can be calculated in these instances. In many industries, particularly where the product being made undergoes a chemical process, it may be possible to combine different levels of the component materials to make the same product. This, in turn, may result in differing yields, dependent on the mix of materials that has been used. Note, when we talk about the materials ‘mix’ we are referring to the quantity of each material that is used to make our product ie we are referring to our inputs. When we talk about ‘yield’, on the other hand, we are talking about how much of our product is produced, ie our output.

**Materials mix variance
**In any process, much time and money will have been spent ascertaining the exact optimum mix of materials. The optimum mix of materials will be the one that balances the cost of each of the materials with the yield that they generate. The yield must also reach certain quality standards. Let us take the example of a chemical, C, that uses both chemicals A and B to make it. Chemical A has a standard cost of $20 per litre and chemical B has a standard cost of $25 per litre. Research has shown that various combinations of chemicals A and B can be used to make C, which has a standard selling price of $30 per litre. The best two of these combinations have been established as:

Mix 1: 10 litres of A and 10 litres of B will yield 18 litres of C; and

Mix 2: 8 litres of A and 12 litres of B will yield 19 litres of C.

Assuming that the quality of C produced is exactly the same in both instances, the optimum mix of materials A and B can be decided by looking at the cost of materials A and B relative to the yield of C.

Mix 1: (18 x $30) – (10 x $20) – (10 x $25) = $90 contribution

Mix 2: (19 x $30) – (8 x $20) – (12 x $25) = $110 contribution

Therefore, the optimum mix that minimises the cost of the inputs compared to the value of the outputs is mix 2: 8/20 material A and 12/20 material B. The standard cost per unit of C is (8 x $20)/19 + (12 x $25)/19 = $24.21. However, if the cost of materials A and B changes or the selling price for C changes, production managers may deviate from the standard mix. This would, in these circumstances, be a deliberate act and would result in a materials mix variance arising. It may be, on the other hand, that the materials mix changes simply because managers fail to adhere to the standard mix, for whatever reason.

Let us assume now that the standard mix has been set (mix 2) and production of C commences. 1,850kg of C is produced, using a total of 900kg of material A and 1,100kg of material B (2,000kg in total). The actual costs of materials A and B were at the standard costs of $20 and $25 per kg respectively. How do we calculate the materials mix variance?

The variance is worked out by first calculating what the standard cost of our 1,850kg worth of C would have been if the standard mix had been adhered to, and comparing that figure to the standard cost of our actual production, using our actual quantities. My preferred approach has always been to present this information in a table as shown in **Table 1** below. The materials mix variance will be $46,000 – $45,500 = $500 favourable.

Remember: it is essential that, for every variance you calculate, you state whether it is favourable or adverse. These can be denoted by a clear ‘A’ or ‘F’ but avoid showing an adverse variance by simply using brackets. This leads to mistakes.

The formula for this is shown below, but if you were to use it, the variance for each type of material must be calculated separately.

(Actual quantity in standard mix proportions – actual quantity used) x standard cost

As a student, I was never a person to blindly learn formulae and rely on these to get me through. I truly believe that the key to variance analysis is to understand what is actually happening. If you understand what the materials mix variance is trying to show, you will work out how to calculate it. However, for those of you who do prefer to use formulae, the workings would be as follows:

**Material A**: (800kg – 900kg) x $20 = $2,000 Adverse

**Material B:** (1,200kg – 1,100kg) x $25 = $2,500 Favourable

**Net variance** = $500 favourable

In this particular example, I have kept things simple by keeping all actual costs in line with the standards. The reality is that, in the real world, actual costs will often vary from standards. Why haven’t I covered this above? Because any variance in materials price is always dealt with by the materials price variance. If we try and bring this into our mix variance, we begin distorting the one thing that we are trying to understand – how the difference in materials mix has affected our cost, rather than how the difference in price has affected our cost.

Why haven’t I considered the fact that although our materials mix variance is $500 favourable, our changed materials mix may have produced less of C than the standard mix? Because this, of course, is where the materials yield variance comes into play.

The materials mix variance focuses on inputs, irrespective of outputs. The materials yield variance, on the other hand, focuses on outputs, taking into account inputs.