Performance Management

Year in, year out, candidates make the same old mistakes when answering questions on limiting factors – and especially those concerning make- versus-buy decisions. It’s time to stop the rot

Every time I mark the Performance Management paper, I constantly find the same errors on certain topics in each sitting, so see many students failing to achieve the mark that their efforts deserve. As a result, I have written an article on liiting factors that I hope will help you to avoid the same mistakes in your P2 exam.

First, let’s work through a simple question where the limiting factor has to be determined. A company manufactures four products: A, B, C and D. Their selling prices and costs are shown in table 1. All products use the same direct material and the same grade of labour. In the year ahead the available supply of material will be restricted to 38,000kg and working time to 21,000 hours. We are required to determine the product mix that would maximise the company’s profit in the coming year.

A first glance at the scenario suggests that there could be two scarce resources: direct material and direct labour. Our first action should be to establish whether there is no limiting factor, one limiting factor or two limiting factors by using table 2. From
 

1: Selling prices and costs of products A, B, C & D
 ABCD
Selling price (£ per unit)44503070
     
Costs (£ per unit)    
Direct material (@ £2 per kg)810610
Direct labour (@ £5 per hour)1010515
Variable overhead88412
Fixedoverhead1010515
     
Profit (£ per unit)8121018
     
Budgeted production/sales (units)2,0002,5002,6003,000


this we can see that direct material is obviously the single limiting factor.

A common error at the start would be to assume that both the supply of material and working hours are limiting factors, and to produce figures accordingly. This practice is both technically incorrect and extremely time-consuming.

Once the limiting factor has been determined, the exercise can follow its usual course. First, we establish the unit contribution per product; then we

2. Determining the limiting factor
 ABCDTotal
Direct material     
Budgeted production (units)2,0002,5002,6003,000 
Kilogramsperunit4535 
Total requirement (kg)8,00012,5007,80015,00043,300
Available (kg)    38,000
Shortfall (kg)    5,300
      
Direct labour     
Budgeted production (units)2,0002,5002,6003,000 
Hours per unit2213 
Total requirement (hours)4,0005,0002,6009,00020,600
Available (hours)    21,000
Surplus (hours)    400


calculate the contribution per unit of limiting factor, ranking each product accordingly (see table 3). Then we allocate what resource is available in a production plan (see table 4). This will leave a shortfall of 2,500 – 1,440 = 1,060 units of product B.

Common errors at this point include ranking the products on their contributions per unit made, which is fundamentally wrong and devalues the rest of the answer. Some candidates forget, or don’t realise, that only the variable costs should be subtracted from the selling price to arrive at the contribution. Again, this is a basic error and produces an incorrect ranking. In real situations this would have disastrous consequences for a company, in that it wouldn’t maximise its profit if it were to rank the products wrongly.

Make-versus-buy decisions In the worked example we have assumed that the company would not be able to meet the full budgeted demand for all four products. But if the company had received definite orders for all the demand figures quoted, it would need to decide which products to make and which to purchase. It must meet the demand – otherwise, it would incur penalty charges and lose the goodwill of its customers. Let’s consider

3: Calculating each product’s contribution per unit of limiting factor
 ABCD
 ABCD
Selling price (£)44503070
Variable costs (£)26281537
Contribution (£)18221533
Limiting factor (kg of material used)4535
Contribution per kg of limiting factor (£)4.54.456.6
Ranking3421


4: Production plan
Available material (kg) 38,000
D3,000 units x 5kg(15,000)
  23,000
   
C2,600 units x 3kg(7,800)
  15,200
   
A2,000 units x 4kg(8,000)
  7,200
B7,200–: 5kg = 1,440 units 


5: Manufacturing data given for products X, Y & Z
 XYZ
Demand (units)4,0005,0007,000
Selling price (£ per unit)455575
Variable production cost (£ per unit)304060
Cost to purchase (£ per unit)385072
Additional cost (£ per unit)81012
Labour hours – the limiting factor – per unit232
Extra variable cost of buying per labour hour saved (£)43.336


a simple example to develop this point. Working time is the limiting factor in this case – only 32,000 direct labour hours are available – and we have been given the data shown in table 5 above.

An analysis of the table shows that if we bought a unit of Z it would release two hours of labour to use, but each of these would cost the company £6. If we bought product X it would also release two hours of direct labour per unit, but the cost would be only £4 per hour of direct labour. Similarly, we can see that Y would be cheaper than X to buy. So the priority for making the components in-house will be Z first, followed by X and then Y. The company will achieve a lower level of contribution by buying the products rather than making them, but it is reducing the impact on its profits by taking this approach.

The final position is shown in table 6 and the final contribution relating to satisfying the total demand for products X, Y and Z is shown in table 7.

6: Production plan
Available direct labour (hours)32,000
Z7,000 x 2 hours(14,000)
  18,000
   
X4,000 x 2 hours(8,000)
  10,000
   
Y10,000 –: 3 hours = 3,333 units 


7: Total contribution
Z: make 7,000 units x (£75 - £60) per unit105,000
X: make 4,000 units x (£45 - £30) per unit60,000
Y: make 3,333 units x (£55 - £40) per unit49,995
Y: buy 1,667 units x (£55 - £50) per unit8,335
 223,330


A common error on such questions is to rank the products incorrectly. The rule here is to minimise the extra variable costs of subcontracting per unit of scarce resource saved. In this case, it means minimising the cost per direct labour hour saved.

Combining the two techniques In the past few years the P2 paper has included questions that combine a limiting-factor situation with a make-versus-buy decision. Let’s consider a simple question that is not complicated by the requirement to identify which cost item is the limiting factor but does feature the need to fulfil a one-off contract. Beta Manufacturing is a company that produces three products – R, S and T – using different quantities of the same resources. Information about the three products is shown in table 8.

Beta buys in a special component XX from a supplier called Gamma that it uses in making product T at £35 per unit. It is considering manufacturing this component in-house and has established that the total cost per unit of doing so would be as follows: direct material at 3kg per unit (£12) + direct labour (£8) + variable overhead (£6) = £26. The material used to produce component XX is the same material A that’s used in making products R, S and T. The quantity of output for component XX will relate directly to that of product T. Beta has also established that it can obtain only 57,000kg of direct material A per week for the foreseeable future.

You are required to:
1. Calculate whether the company should continue to purchase component XX from Gamma or whether it should manufacture this internally.

8: Manufacturing data given for products R, S & T
 RST
Selling price (£ per unit)7264139
    
Cost (£ per unit)   
Direct material A (@ £4 per kg)242032
Special component XX0035
Direct labour101214
Variable overhead6812
Total variable cost404093
    
Demand per week (units)1,8003,0004,200


9: Calculating whether Beta should continue to purchase component XX or produce it in-house
 RSTXX
 per unitper unitper unitper unit
Selling price / buying-in cost (£)726413935
Direct material A (£)24203212
Special component XX (£)00350
Direct labour (£)1012148
Variable overhead (£)68126
Contribution (£)3224469
Limiting factor (kg of material A used)6583
Contribution per kg of material A (£)5.334.805.753.00
Ranking2314


10: Production plan
T 57,000
T4,200 units x 8kg(33,600)
  23,400
   
R1,800 units x 6kg(10,800)
  12,600
   
S12,600 –: 5kg = 2,520 units 


2. Prepare a statement to show the optimum weekly output based on your decision for requirement 1.
3. Explain any non-financial factors that Beta should consider before it decides whether or not to make component XX itself.

An analysis of table 9 shows that if the company manufactures component XX internally it will consume 3kg of direct material A per unit and each unit of XX will generate £3 per kg of this limiting factor. This figure is lower than those earned by any of Beta’s three existing products. Therefore, since component XX has the lowest rank, the company should continue to buy in XX so that the resources available can be used to manufacture products R, S and T. The resulting production plan (see table 10) indicates that Beta’s optimum weekly output would be 4,200 units of T, 1,800 units of R and 2,520 units of S.

We now need to calculate the purchase price of component XX at which Beta would manufacture it internally as opposed to buying it. This type of situation has featured in several recent P2 papers. The decision concerning the purchase of component XX would change if the contribution earned from manufacturing it equalled that of the lowest- contributing product of the other three. In this case it’s product S, which has a contribution of £4.80 per kg of direct material A. This is £1.80 higher than that from component XX. Because each unit of XX requires 3kg of direct material A, the buying price would have to be 3 x £1.80 = £5.40 per unit higher than it is at present. It would then have the same contribution per unit of limiting factor, and rank- ing, as product S. So the purchase price of XX at which Beta’s decision could change is £35 + £5.40 = £40.40 per unit.

If such a situation did actually arise and raw mate- rials were still in short supply, this would obviously open the door to another set of questions relating to the manufacture and supply of product S. I’ll discuss these points in the last part of the answer.

Common errors here include failing to realise that component XX is comparable with products R, S and T in arriving at a decision and, again, ranking a product on its contribution rather than on its con- tribution per unit of limiting factor.

The most relevant non-financial factors associated with this scenario are as follows:

Does Beta’s workforce possess the requisite skills to produce component XX?
Would Beta be able to manufacture component XX to the same standard as that achieved by Gamma – ie, would quality be compromised?
Does Beta have sufficient resources to manufacture component XX? Is special machinery needed, for example?
If Beta manufactures component XX internally, more of product S would have to be sacrificed. How might this affect the sales of products R and T?
How would Gamma react to losing its business with Delta? Could it jeopardise the relationship?

A typical error at this point would be to cite non-financial factors that do not relate to the scenario. I hope that this article has clarified any misunderstandings associated with questions on limiting factors and make-versus-buy decisions. My advice to P2 candidates would be to:
Review the past papers and practise answering questions relating to this topic.
When attempting these questions, you should make every effort to lay out your answers clearly and also apply proper exam technique by completing them in the time allowed.
Visit CIMA’s website and read the post-exam guide relating to the past few sittings. This will give details of all common mistakes to avoid.

 

 

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