LIMITING FACTORS
A scarce resource is a resource of which there is a limited supply. Once a scarce resource affects the ability of an organisation to earn profits, a scarce resource becomes known as a limiting factor.
A limiting factor or key factor is ‘Anything which limits the activity of an entity. An entity seeks to optimise the benefit it obtains from the limiting factor’.
Knowledge brought forward from earlier studies
Limiting factor analysis
- An organisation might be faced with just one limiting factor (other than maximum sales demand) but there might also be several scarce resources, with two or more of them putting an effective limit on the level of activity that can be achieved.
- Examples of limiting factors include sales demand and production constraints.
- The limit may be either in terms of total quantity or of particular skills.
- There may be insufficient available materials to produce enough units to satisfy sales demand.
- Manufacturing capacity. There may not be sufficient machine capacity for the production required to meet sales demand.
- It is assumed in limiting factor analysis that management would make a product mix decision or service mix decision based on the option that would maximise profit and that profit is maximised when contribution is maximised (given no change in fixed cost expenditure incurred). In other words, marginal costing ideas are applied.
- Contribution will be maximised by earning the biggest possible contribution per unit of limiting factor. For example if grade A labour is the limiting factor, contribution will be maximised by earning the biggest contribution per hour of grade A labour worked.
- The limiting factor decision therefore involves the determination of the contribution earned per unit of limiting factor by each different product.
- If the sales demand is limited, the profit-maximising decision will be to produce the top-ranked product(s) up to the sales demand limit.
- In limiting factor decisions, we generally assume that fixed costs are the same whatever product or service mix is selected, so that the only relevant costs are variable costs.
- When there is just one limiting factor, the technique for establishing the contributionmaximising product mix or service mix is to rank the products or services in order of contribution-earning ability per unit of limiting factor.
If resources are limiting factors, contribution will be maximised by earning the biggest possible contribution per unit of limiting factor.
Where there is just one limiting factor, the technique for establishing the contributionmaximising product or service mix is to rank the products or services in order of contribution-earning ability per unit of limiting factor.
Two potentially limiting factors
You may be asked to deal with situations where two limiting factors are potentially limiting (and there are also product/service demand limitations). The approach in these situations is to find out which factor (if any) prevents the business from fulfilling maximum demand.
Where there is a maximum potential sales demand for an organisation’s products or services, they should still be ranked in order of contribution-earning ability per unit of the limiting factor. The contribution-maximising decision, however, will be to produce the topranked products (or to provide the top-ranked services) up to the sales demand limit.
LIMITING FACTOR ANALYSIS AND RESTRICTED FREEDOM OF ACTION
In certain circumstances an organisation faced with a limiting factor on production and sales might not be able to produce the profit-maximising product mix because the mix and/or volume of products that can be produced and sold is also restricted by a factor other than a scarce resource.
- A contract to supply a certain number of products to a customer
- Production/sales of a minimum quantity of one or more products to provide a complete product range and/or to maintain customer goodwill
- Maintenance of a certain market share of one or more products
In each of these cases, the organisation might have to produce more of a particular product or products than the level established by ranking according to contribution per unit of limiting factor.
If an organisation has to produce more of a particular product or products than the level established by ranking according to contribution per unit of limiting factor, the products should be ranked in the normal way but the optimum production plan must first take into account the minimum production requirements. The remaining resource must then be allocated according to the ranking.
MAKE OR BUY DECISIONS AND SCARE RESOURCES
An organisation might want to do more things than it has the resources for, and so its alternatives would be as follows.
- Make the best use of the available resources and ignore the opportunities to buy help from outside
- Combine internal resources with buying externally so as to do more and increase profitability
Buying help from outside is justifiable if it adds to profits. A further decision is then required on how to split the work between internal and external effort. What parts of the work should be given to suppliers or sub-contractors so as to maximise profitability?
In a situation where a company must sub-contract work to make up a shortfall in its own in-house capabilities, its total costs will be minimised if those units bought have the lowest extra variable cost of buying per unit of scarce resource saved by buying.
LIMITING FACTORS AND SHADOW PRICES
Whenever there are limiting factors, there will be opportunity costs. As you know, these are the benefits forgone by using a limiting factor in one way instead of in the next most profitable way.
A shadow price is ‘An increase in value which would be created by having available one additional unit of a limiting resource at the original cost’.
Note that the shadow price only applies while the extra unit of resource can be obtained at its normal variable cost. The shadow price also indicates the amount by which contribution could fall if an organisation is deprived of one unit of the resource.
The shadow price of a resource is its internal opportunity cost. This is the marginal contribution towards fixed costs and profit that can be earned for each unit of the limiting factor that is available. A knowledge of the shadow price of a resource will help managers to decide how much it is worth paying to acquire another unit of the resource.
USING LIMITING FACTOR ANALYSIS
Don’t ignore this wordy session – if you were to get a full limiting factor analysis question in the exam there would undoubtedly be marks for discussion of pertinent non-quantifiable issues.
Limiting factor analysis provides us with a profit-maximising product mix, within the assumptions made. It is important to remember, however, that other considerations, so far not fully considered in our examples, might entirely alter the decision reached.
Non-quantifiable factors
Non-quantifiable factors, such as effect on customer goodwill, ability to restart production and reasons for a resource being a limiting factor, should also be borne in mind in product mix decisions.
| Factor | Examples |
| Demand | Will the decision reached (perhaps to make and sell just one product rather than two) have a harmful effect on customer loyalty and sales demand? For example, a manufacturer of knives and forks could not expect to cease production of knives without affecting sales demand for the forks. |
| Longterm
effects |
Is the decision going to affect the long-term as well as the short-term plans of the organisation? If a particular product is not produced, or produced at a level below sales demand, is it likely that competitors will take over vacated markets? Labour skilled in the manufacture of the product may be lost and a decision to reopen or expand production of the product in the future may not be possible. |
| Labour | If labour is a limiting factor, is it because the skills required are difficult to obtain, perhaps because the organisation is using very old-fashioned production methods, or is the organisation a high-tech newcomer in a low-tech area? Or perhaps the conditions of work are so unappealing that people simply do not want to work for the organisation. |
| Other limiting factors | The same sort of questions should be asked whatever the limiting factor. If machine hours are in short supply is this because more machines are needed, or newer, more reliable and efficient machines? If materials are in short supply, what are competitors doing? Have they found an equivalent or better substitute? Is it time to redesign the product? |
Assumptions in limiting factor analysis
Various assumptions are made in limiting factor analysis.
- Fixed costs remain the same regardless of the decision taken.
- Unit variable cost is constant regardless of the decision taken.
- Estimates of sales demand and resources required are known with certainty. – Units of output are divisible.
In the examples covered in the chapter, certain assumptions were made. If any of the assumptions are not valid, then the profit-maximising decision might be different. These assumptions are as follows.
Fixed costs will be the same regardless of the decision that is taken, and so the profit-maximising and contribution-maximising output level will be the same.
This will not necessarily be true, since some fixed costs might be directly attributable to a product or service. A decision to reduce or cease altogether activity on a product or service might therefore result in some fixed cost savings, which would have to be taken into account.
The unit variable cost is constant, regardless of the output quantity of a product or service. This implies the following.
-
- The price of resources will be unchanged regardless of quantity; for example, there will be no bulk purchase discount of raw materials.
- Efficiency and productivity levels will be unchanged; regardless of output quantity the direct labour productivity, the machine time per unit, and the materials consumption per unit will remain the same.
The estimates of sales demand for each product, and the resources required to make each product, are known with certainty.
In the example in Section 1.2.1, there were estimates of the budgeted sales demand for each of three products, and these estimates were used to establish the profit-maximising product mix. Suppose the estimates were wrong? The product mix finally chosen would then either mean that some sales demand of the most profitable item would be unsatisfied, or that production would exceed sales demand, leaving some inventory unsold. Clearly, once a profit-maximising output decision is reached, management will have to keep their decision under continual review, and adjust their decision as appropriate in the light of actual results.
Units of output are divisible, and a profit-maximising solution might include fractions of units as the optimum output level.
Where fractional answers are not realistic, some rounding of the figures will be necessary.
Exam Focus Point
An examination problem might present you with a situation in which there is a limiting factor, without specifically stating that this is so, and you will have the task of recognising what the situation is. You may be given a hint with the wording of the question.
It is possible that the main raw material used in manufacturing the products will be difficult to obtain in the next year.’
The company employs a fixed number of employees who work a maximum overtime of eight hours on top of the basic 36 hour week. The company has also agreed that no more staff will be recruited next year.’
In (a) there is a hint that raw materials might be a limiting factor. In (b), perhaps less obviously, a maximum limit is placed on the available labour hours, and so the possibility should occur to you that perhaps labour is a limiting factor.
If you suspect the existence of a limiting factor, some quick computations should confirm your suspicions.
- Calculate the amount of the scarce resource (material quantities, labour hours, machine hours and so on) needed to meet the potential sales demand.
- Calculate the amount of the scarce resource available (for example number of employees multiplied by maximum working hours per employee).
- Compare the two figures. Obviously, if the resources needed exceed the resources available, there is a limiting factor on output and sales.
CHAPTER ROUNDUP
- A scarce resource is a resource of which there is a limited supply. Once a scarce resource affects the ability of an organisation to earn profits, a scarce resource becomes known as a limiting factor.
- If resources are limiting factors, contribution will be maximised by earning the biggest possible contribution per unit of limiting factor.
- Where there is just one limiting factor, the technique for establishing the contribution-maximising product or service mix is to rank the products or services in order of contribution-earning ability per unit of limiting factor.
- Where there is a maximum potential sales demand for an organisation’s products or services, they should still be ranked in order of contribution-earning ability per unit of the limiting factor. The contribution-maximising decision, however, will be to produce the top-ranked products (or to provide the top-ranked services) up to the sales demand limit.
- If an organisation has to produce more of a particular product or products than the level established by ranking according to contribution per unit of limiting factor, the products should be ranked in the normal way but the optimum production plan must first take into account the minimum production requirements. The remaining resource must then be allocated according to the ranking.
- In a situation where an organisation must subcontract work to make up a shortfall in its own in-house capabilities, its total costs will be minimised if the units bought have the lowest extra variable cost of buying per unit of scarce resource saved by buying.
- The shadow price or dual price of a limiting factor is the increase in value which would be created by having one additional unit of the limiting factor at the original cost.
- Non-quantifiable factors, such as the effect on customer goodwill, ability to restart production and reasons for a resource being a limiting factor, should also be borne in mind in product mix decisions.
- Various assumptions are made in limiting factor analysis.
− Fixed costs remain the same regardless of the decision taken.
− Unit variable cost is constant regardless of the decision taken.
− Estimates of sales demand and resources required are known with certainty.
− Units of output are divisible
