BASIC MANAGEMENT ACCOUNTING TECHNIQUES
7 Limiting factors
Introduction
A limiting factor is anything that is in scarce supply and therefore limits the activities that a business can carry out.
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. Examples are a shortage of supply of a resource or a restriction on sales demand at an particular price'. (CIMA Official Terminology) A limiting factor could be sales if there is a limit to sales demand but any one of the organisation's resources (labour, materials and so on) may be insufficient to meet the level of production demanded.
It is assumed in limiting factor analysis that management wishes to maximise profit and that profit will be maximised when contribution is maximised (given no change in fixed costs expenditure incurred).
A company manufactures three products, details of which are as follows.
Product J Product K Product L
$ per unit $ per unit $ per unit
Selling price 140 122 134
Direct materials ($2/kg) 22 14 26
Other variable cost 84 72 51
Fixed cost 20 26 40
Example: Limiting factor
KEY TERM
In a period when direct material is restricted in supply, what is the ranking of the products in terms of the most profitable use of the material?
1st K, 2nd L, 3rd J.
Product J Product K Product L $ per unit $ per unit $ per unit
Selling price 140 122 134
Variable cost 106 86 77
Contribution 34 36 57
Kg of material 11 7 13
Contribution per kg $3.09 $5.14 $4.38
Ranking 3 1 2
Section summary
In a limiting factor situation, contribution will be maximised by earning the biggest possible contribution per unit of limiting factor.
Solution
Costs which are not affected by the level of activity are fixed costs or period costs.
A step cost is a cost which is fixed in nature but only within certain levels of activity.
Variable costs increase or decrease with the level of activity.
Semi-variable/semi-fixed or mixed costs are costs which are part-fixed and part-variable and which are thus partly affected by a change in the level of activity.
The high-low method or the scattergraph method can be used to determine the fixed and variable elements of semi-variable costs.
Margin of safety = Budgeted sales volume – breakeven sales volume.
Margin of safety % =
The target profit is achieved when sales revenue equals variable costs plus fixed costs plus profit.
Therefore the total contribution required for a target profit = fixed costs + required profit.
Relevant costs are future cash flows arising as a direct consequence of a decision. Relevant costs are:
– Future costs – Differential costs
– Cash flows – Avoidable costs
– Incremental costs – Opportunity costs
A sunk cost is a past cost which is not directly relevant in decision making.
The principle underlying decision accounting is that management decisions can only affect the future. In decision making, managers therefore require information about future costs and revenues which would be affected by the decision under review, and they must not be misled by events, costs and revenues in the past, about which they can do nothing.
Qualitative factors should always be considered alongside the quantitative data in any management accounting situation.
In a limiting factor situation, contribution will be maximised by earning the biggest possible contribution per unit of limiting factor.
Chapter Roundup
1 The costs of operating the canteen at 'Eat a lot Company' for the past three months is as follows.
Month Cost Employees
£
1 72,500 1,250
2 75,000 1,300
3 68,750 1,175
Variable cost (per employee per month) = Fixed cost per month =
2 Use the following to make up four formulae which can be used to calculate the breakeven point.
Contribution per unit Contribution required to break even Contribution per unit Contribution required to break even
Fixed costs C/S ratio
Fixed costs C/S ratio
(a) Breakeven point (sales units) =
or
(b) Breakeven point (sales revenue) =
or
3 The P/V ratio is a measure of how much profit is earned from each £1 of sales.
True False
4 Profits are maximised at the breakeven point.
True False
5 At the breakeven point, total contribution = ………. .
6 The total contribution required for a target profit = ……….. . 7 Name six types of relevant costs
8 A sunk cost is:
A a cost committed to be spent in the current period B a cost which is irrelevant for decision making
C a cost connected with oil exploration in the North Sea D a cost unaffected by fluctuations in the level of activity
Quick Quiz
9 Select the correct word in the following sentences.
(a) For a material item that is regularly used, the relevant cost of using it for a particular order is its original purchase price/current replacement cost.
(b) For a material item that has already been purchased and would not be replaced once used, the relevant cost of using it for a particular order is the higher/lower of its current resale value and its value if put to an alternative use.
1 Variable cost = £50 per employee per month Fixed costs = £10,000 per month
Activity Cost
No employees £
High 1,300 75,000
Low 1,175 68,750
125 6,250
Variable cost per employee = £6,250/125 = £50 For 1,175 employees, total cost = £68,750 Total cost = variable cost + fixed cost
£68,750 = (1,175 × £50) + fixed cost
or Contributionper unit
even
(b) Breakeven point (sales revenue) =
ratio
3 False. The P/V ratio is a measure of how much contribution is earned from each £1 of sales.
4 False. At the breakeven point there is no profit.
5 At the breakeven point, total contribution = fixed costs 6 Fixed costs + required profit
7 (a) Future costs
8 B A sunk cost is a cost which is irrelevant for decision making.
9 (a) current replacement cost (b) higher
Answers to Quick Quiz
6a.1 Activity levels (a) Rise (b) Stay the same (c) Fall (d) Fall
6a.2 Cost behaviour graphs
(e)
Answers to Questions
6a.3 High-low method
Although we only have two activity levels in this question we can still apply the high-low method.
Valuations Total cost
V £
Period 2 515 90,275
Period 1 420 82,200
Change due to variable cost 95 8,075
∴Variable cost per valuation = £8,075/95 = £85.
Period 2: fixed cost = £90,275 – (515 × £85) = £46,500
The variable cost of £85 per valuation must be added to the fixed cost.
Therefore Total Costs (TC) = Fixed costs + Variable costs = £46,500 + £85V
6a.4 C/S ratio
ratio C/S
on contributi
Required =
20%
£50,000 = £250,000
∴ Number of units = £250,000 ÷ £10 = 25,000.
6a.5 Target profits
Required contribution = fixed costs plus profit
= £47,000 + £23,000
= £70,000
Required sales = 14,000 units
£
Required contribution per unit sold (£70,000/14,000) 5
Variable cost per unit 15
Required sales price per unit 20
6a.6 Relevant cost of materials
(a) Material A is not yet owned. It would have to be bought in full at the replacement cost of £6 per unit.
(b) Material B is used regularly by the company. There are existing stocks (600 units) but if these are used on the contract under review a further 600 units would be bought to replace them. Relevant costs are therefore 1,000 units at the replacement cost of £5 per unit.
(c) 1,000 units of material C are needed and 700 are already in stock. If used for the contract, a further 300 units must be bought at £4 each. The existing stocks of 700 will not be replaced. If they are used for the contract, they could not be sold at £2.50 each. The realisable value of these 700 units is an opportunity cost of sales revenue forgone.
(d) The required units of material D are already in stock and will not be replaced. There is an opportunity cost of using D in the contract because there are alternative opportunities either to sell the existing stocks for £6 per unit (£1,200 in total) or avoid other purchases (of material E), which would cost 300 × £5 =
£1,500. Since substitution for E is more beneficial, £1,500 is the opportunity cost.
(e) Summary of relevant costs
£
Material A (1,000 × £6) 6,000
Material B (1,000 × £5) 5,000
Material C (300 × £4) plus (700 × £2.50) 2,950
Material D 1,500
Total 15,450
159
6b
topic list learning outcomes syllabus references ability required
1 The principles of marginal costing A1(a) A1(i) analysis
2 The principles of absorption costing A1(a) A1(i) analysis
3 The effect of marginal costing and absorption costing on reported profit and inventory valuation
A1(a), A1(b) A1(i) analysis
4 Marginal costing and absorption costing compared
A1(a), A1(b) A1(i) analysis