# Paper P2 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 limiting 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.
```1: SELLING PRICES AND COSTS OF PRODUCTS A, B, C & D

A      B      C      D

Selling price        44     50     30     70
([pounds
sterling] per
unit)

Costs ([pounds
sterling] per
unit)

Direct material       8     10      6     10
(@[pounds
sterling]2 per
kg)

Direct labour        10     10      5     15
(@ [pounds
sterling]5 per
hour)

Variable              8      8      4     12

Fixed overhead       10     10      5     15

Profit ([pounds       8     12     10     18
sterling] per
unit)

Budgeted          2,000  2,500  2,600  3,000
production/sales
(units)
```

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 this we can see that direct material is obviously the single limiting factor.
```2: DETERMINING THE LIMITING FACTOR

A      B       C      D     Total
Direct material

Budgeted production (units)  2,000   2,500  2,600   3,000

Kilograms per unit               4       5      3       5

Total requirement (kg)       8,000  12,500  7,800  15,000  43,300

Available (kg)                                             38,000

Shortfall (kg)                                              5,300

Direct labour

Budgeted production (units)  2,000   2,500  2,600   3,000

Hours per unit                   2       2      1       3

Total requirement (hours)    4,000   5,000  2,600   9,000  20,600

Available (hours)                                          21,000

Surplus (hours)                                               400
```

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 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.
```3: CALCULATING EACH PRODUCT'S CONTRIBUTION PER UNIT OF LIMITING FACTOR

A    B   C    D

Selling price   44   50  30   70
([pounds
sterling])

Variable        26   28  15   37
costs
([pounds
sterling])

Contribution    18   22  15   33
([pounds
sterling])

Limiting         4    5   3    5
factor (kg of
material
used)

Contribution   4.5  4.4   5  6.6
per kg of
limiting
factor
([pounds
sterling])

Ranking          3    4   2    1

4: PRODUCTION PLAN

D        3,000 units x 5kg  (15,000)
23,000

C        2,600 units x 3kg   (7,800)
15,200

A        2,000 units x 4kg   (8,000)
7,200

B  7,200/5kg = 1,440 units
```

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.

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 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.
```5: MANUFACTURING DATA GIVEN FOR PRODUCTS X, Y & Z

X      Y      Z
Demand       4,000  5,000  7,000
(units)

Selling         45     55     75
price
([pounds
sterling]
per unit)

Variable        30     40     60
production
cost
([pounds
sterling]
per unit)

Cost to         38     50     72
purchase
([pounds
sterling]
per unit)

cost
([pounds
sterling]
per unit)

Labour           2      3      2
hours - the
limiting
factor -
per unit

Extra            4   3.33      6
variable
cost of
labour hour
saved
([pounds
sterling])
```

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 [pounds sterling]6. If we bought product X it would also release two hours of direct labour per unit, but the cost would be only [pounds sterling]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

z               7,000 x 2 hours  (14,000)
18,000

X               4,000 x 2 hours   (8,000)
10,000

Y  10,000/3 hours = 3,333 units

7: TOTAL CONTRIBUTION

Z: make 7,000                 105,000
units x
([pounds
sterling]75 -
[pounds
sterling]60)
per unit

X: make 4,000                  60,000
units x
([pounds
sterling]45 -
[pounds
sterling]30)
per unit

Y: make 3,333                  49,995
units x
([pounds
sterling]55 -
[pounds sterling]40) per
unit

units x ([pounds sterling]55
- [pounds sterling]50) per
unit

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.
```8: MANUFACTURING DATA GIVEN FOR PRODUCTSR,S&T

R      S      T

Selling         72     64    139
price
([pounds
sterling]
per unit)

Cost
([pounds
sterling]
per unit)

Direct          24     20     32
material A
([congruent
to] [pounds
sterling]4
per kg)

Special          0      0     35
component
XX

Direct          10     12     14
labour

Variable         6      8     12

Total           40     40     93
variable
cost

Demand per   1,800  3,000  4,200
week
(units)
```

Beta buys in a special component XX from a supplier called Gamma that it uses in making product T at [pounds sterling]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 ([pounds sterling]12) + direct labour ([pounds sterling]8) + variable overhead ([pounds sterling]6) = [pounds sterling]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.

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 [pounds sterling]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.
```9: CALCULATING WHRTHER BETA SHOULD CONTINUE TO PURCHASE
COMPONENT XX OR PRODUCE IT IN-HOUSE

R     S    T     XX
per   per   per   per
unit  unit  unit  unit

Selling price    72    64   139    35
cost ([pounds
sterling])

Direct           24    20    32    12
material A
([pounds
sterling])

Special           0     0    35     0
component XX
([pounds
sterling])

Direct labour    10    12    14     8
([pounds
sterling])

Variable          6     8    12     6
([pounds
sterling])

Contribution     32    24    46     9
([pounds
sterling])

Limiting          6     5     8     3
factor (kg of
material A
used)

Contribution   5.33  4.80  5.75  3.00
per kg of
material A
([pounds
sterling])

Ranking           2     3     1     4

10: PRODUCTION PLAN

T         4,200 units x 8kg  (33,600)
23,400

R         1,800 units x 6kg  (10,800)
12,600

S  12,600/5kg = 2,520 units
```

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 [pounds sterling]4.80 per kg of direct material A. This is [pounds sterling]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 [pounds sterling]1.80 = [pounds sterling]5.40 per unit higher than it is at present. It would then have the same contribution per unit of limiting factor, and ranking, as product S. So the purchase price of XX at which Beta's decision could change is [pounds sterling]35 + [pound sterling]5.40 = [pound sterling]40.40 per unit.

If such a situation did actually arise and raw materials 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 contribution 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.

By Norwood Whittle

Lead marker for the P2 paper
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