LIMITING FACTORS LECTURE

Learning ObjectivesStudents should be able to:

(1) Explain and illustrate the impact of limiting factors on the decision making process.

(2) Calculate solutions to problems involving changes to product mix and quantities produced

(3) Specify qualitative factors which are relevant to limiting factors decisions

SCARCE RESOURCES – LIMITING FACTOR

When an organization provides a range of products or services to its markets, but has a limited amount of resources available to it, then it will have to make a decision about what product mix (or mix of services) it will provide. Its volume of output and sales will be constrained by the limited resources rather than by sales demand, and so management faces a decision about how scarce capacity should be best used.

The scarce resource(s) might be any or all of the following:(a) a restricted supply of an item of raw material or components;(b) a maximum capacity of machine time;(c) a limited amount of cash, and a bank overdraft limit;(d) a maximum amount of available labour hours for a particular grade of labour.

A resource is scarce if the organization does not have enough to undertake every available opportunity for making more contribution towards profit. Thus machine time would be scarce if every machine was being operated at a full capacity, without being able to produce enough output to meet sales demand in full.

From a management accounting point of view, the assumption would be that a firm faced with a problem of one or more scarce resources would select a product mix or service mix that would maximize its overall profitability and so maximize its total contribution.

The technique for establishing the contribution- maximizing product mix or service mix differs according to whether there is only one scarce resource or two or more scarce resources. For our purposes we will look at decisions involving only one scarce resource.

Note that the word scarce is potentially misleading, because it does not necessarily mean that there is a worldwide shortage, it simply means that the firm cannot in the short term obtain all the resources it needs to carry out a particular task.

DECISIONS INVOLVING ONE SCARCE RESOURCEWhen there is only one scarce resource, the technique for establishing the contribution-maximising product mix is to rank the products or services in order of contribution per unit of the limiting factor. EXAMPLEBuilders Ltd. makes two products, windows and doors. A door takes 3 hours to make, and has a variable cost of $18 and a sales price of $30. A window takes 2 hours to make, and has a variable cost of $10 and a sales price of $20. Both products use the same type of labour, which is in restricted supply. Which product should be made in order to maximize profits?SOLUTIONThere is no limitation on sales demand, but labour is in restricted supply, and so to determine the profit maximizing production mix, we must rank the products in order of contribution per labour hour.

Doors Windows $ $

Sales 30 20Variable Costs 18 10Contribution 12 10Hours per unit 3 2Contribution per labour hour $4 $5

The ranking is : 2 nd 1 st

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Although Doors have the higher contribution per unit, Windows are more profitable because they make a greater contribution for each hour of labour time worked.Three Windows (with contribution of 3 x $10 = $30) can be made in the same time as two Doors (with contribution of only 2 x $12 = $24)

Other Considerations

The profit- maximizing budget would therefore be to produce Windows only, within the assumptions made. It is important to remember, however, that other considerations, so far excluded from the problem, might alter the decision entirely.

(1) Can the sales price of either product be raised, therefore increasing contribution per unit, and the contribution per labour hour, and also reducing sales demand?

(2) To what extent are sales of each product independent? For example a manufacturer of knives and forks could not expect to cease production of knives without affecting the demand for the forks.

(3) Would a decision to cease production of widgets really have no effect on the fixed costs? The assumption that fixed costs are unaffected by limiting factor decision is not always valid, and closure of either the widgets or splodgets production line might result in fixed costs savings (for example a reduction in production planning costs, product design costs, or equipment depreciation).

Qualitative Factors

There are also qualitative factors to consider.

(1) Would a decision to make and sell just windows have a harmful effect on customer loyalty and sales demand?

(2) Is the decision going to affect the long-term plans of the company as well as the short-term? If widgets are not produced next year, it is likely that competitors will take over the markets vacated by Builders Ltd. Labour skilled in the manufacture of doors will be lost, and a decision in one year’s time to reopen manufacture of doors might not be possible.

(3) Why is there a shortage of labour? Are the skills required difficult to obtain, perhaps because the company is using old-fashioned production methods, or is the company a high-tech new comer located in a low-tech area? Or perhaps the conditions of work are so unappealing that people simply do not want to work for the company.

(4) The same question should be asked whatever the scarce resource. 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?

Example: one scarce resource and limited sales demand

When there is a maximum potential sales demand for an organisation’s products or services, they should be ranked in order of contribution-earning ability per unit of the scarce resource. However, the profit-maximising decision will be to produce the top-ranked products (or to provide the top-ranked services) up to the sales demand limit.

Haydn Ltd. maufactures and sells three products, X, Y and Z, for which budgeted sales demand, unit selling prices and unit variable costs are as follows:

X Y ZBudgeted sales demand 550 units 500 units 400 units

$ $ $ $ $ $Units sales price 16 18 14Variable costs: materials 8 6 2

labour 4 6 9 12 12 11

Unit contribution 4 6 3

The company has existing stocks of 250 units of X and 200 units of Z, which it is quite willing to use up to meet sales demand.

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All three products use the same direct materials and the same type of direct labour. In the next year, the available supply of materials will be restricted to $4,800 (at cost) and the available supply of labour to $6,600 (at cost). What product mix and sales mix would maximize the company’s profits in the next year?

Solution and discussion

There appears to be two scarce resources, direct materials and direct labour. However, this is not certain, and because there is limited sales demand as well it might be that there is:

(a) no limiting factor at all, except sales demand – ie none of these resources is scarce;(b) only one scarce resource that prevents the full potential sales demand being achieved.

When faced with a problem of this kind, you should begin by establishing how many scarce resources there are, and if there are any, which one or which ones are they?

In this example we have: X Y Z

Units Units UnitsBudgeted sales 550 500 400Stock in hand 250 0 200Minimum production to meet demand 300 500 200

Minimum production to meet sales Required materials Required labour at demand at cost cost Units $ $

X 300 2,400 1,200Y 500 3,000 3,000Z 200 400 1,800

Total required 5,800 6,000Total available 4,800 6,600

(1,000) 600

Materials are a limiting factor, but labour is not.

The next step is to rank X, Y and Z in order of contribution earned per $1 of direct materials consumed.

X Y Z$ $ $

Unit contribution 4 6 3Cost of materials 8 6 2Contribution per $1 materials $0.50 $1.00 $1.50Ranking 3rd 2nd 1st

Z should be manufactured up to the limit where units produced plus units in stock will meet sales demand, then Y second and X third, until all the available materials are used up.

Sales demand ProductionRanking Product less units in stock quantity Materials at cost

Units Units $1st Z 200 200 (x $2) 400

2nd Y 500 500 (x $6) 3,0003rd X 300 175 (x $8) *1,400

Total available 4,800

* Balancing amount using up total available.

The profit-maximising budget is as follows:

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X Y Z Units Units Units

Opening stock 250 0 200Add production 175 500 200Sales 425 500 400

X Y Z Total

$ $ $ $Revenue 6,800 9,000 5,600 21,400Variable costs 5,100 6,000 4,400 15,500Contribution 1,700 3,000 1,200 5,900

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Exercise 2What other considerations should be taken into account by Haydn Ltd?

SolutionRefer back to the previous example for suggestions if you cannot think of any for yourself.________________________________________________________________________

Assumptions in limiting factor analysis: one scarce resource

In the previous example, certain assumptions were made. If any of the assumptions are not valid, then the profit-maximizing decision might be different. These assumptions are as follows:

(a) Fixed costs will be the same regardless of the decision that is taken, and so the profit maximizing and contribution-maximizing 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.

(b) The unit variable cost is constant, regardless of the output quantity of a product or service. This implies that:

(i) the price of resources will be unchanged regardless of quantity; for example, there will be no bulk purchase discount of raw materials;

(ii) 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.

(c) The estimate of sales demand for each product, and the resources required to make each product, are known with certainty.

In the previous example, there were estimates of the maximum sales demand for each

of 3 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 stock 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.

(d) Units of output are divisible, and a profit-maximising solution might include fractions of units as the optimum level.

Where fractional answers are not realistic, some rounding of the figures will be necessary.

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Given that these basic assumptions usually apply, a suitable adjustment will have to be made for any problem involving a scarce resource where one (or more) of the assumptions is invalid.

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