Limited Factor Analysis and Make or Buy Decisions
When one resource – machine hours, labour hours or a material – is in short supply, it is a limiting factor. To make the most profit, rank the products by their contribution per unit of the limiting factor and make the best-ranked product first, up to its demand, then the next, until the resource runs out.
Decisions like this are made using relevant costs – the future cash flows that change because of the decision. The same technique solves make or buy decisions: when a resource is scarce, make the items that save the most (compared with buying them in) per unit of the scarce resource, and buy in the rest.
1 Introduction
In this chapter we will look at how a business should decide what to produce when they have limited resources available. We will also look at how to apply the same technique to the making of decisions as to whether to make products ourselves or buy from others - again, when resources are limited.
2 Limiting factor analysis
In a situation where we are manufacturing several products, all of which use the same limited resource, then we need to decide on how best to use the limited resource in production.
A limiting factor (also called a key factor or scarce resource) is anything that stops a business making and selling as much as it would like – for example a shortage of machine hours, labour hours or a material. To check whether a resource is a limiting factor, work out how much of it would be needed to meet the maximum demand for every product, and compare that with the amount available.
The standard limiting factor (key factor) approach is to rank the products on the basis of the contribution earned per unit of the limiting factor.
Contribution is used, not profit, because the total fixed costs stay the same whatever mix of products is made – only the contribution changes. The steps are:
Calculate the contribution per unit of each product (selling price less variable costs).
Divide by the amount of the limiting factor each unit uses, to give the contribution per unit of the limiting factor (for example, per machine hour).
Rank the products, highest contribution per unit of the limiting factor first.
Make as many units of the first-ranked product as can be sold, then move to the next, until the limiting factor is used up.
Total contribution less the (unchanged) fixed costs = maximum profit.
A ($ per unit) | B ($ per unit) | |
Selling price | 25 | 28 |
Materials | 8 | 20 |
Labour | 5 | 2 |
Other variable costs | 7 | 2 |
Fixed costs | 3 | 2 |
Total cost | 23 | 26 |
Profit | 2 | 2 |
Machine hours per unit | 2 hrs | 1 hr |
Maximum demand | 20,000 units | 10,000 units |
The total hours available are 48,000.
Calculate the optimum production plan and the maximum profit using conventional limiting factor analysis
Show answerHide answer
Notice that A has the higher contribution per unit ($5 against $4), but B earns more for each scarce hour ($4 against $2.50): two hours could make one A ($5) or two Bs ($8).
3 Relevant and irrelevant costs
Limiting factor and make or buy decisions are short-term decisions. Costs are classified for decision-making as relevant or irrelevant.
A relevant cost is a future cash flow that will change as a direct result of the decision being made. Only relevant costs (and revenues) should be considered when making a decision. A cost that will be the same whatever is decided is irrelevant to the decision.
Cost | Relevant? | Why |
Variable costs that change with the decision (materials, labour paid by the hour, variable overheads) | Relevant | Future cash that is spent only if the decision goes ahead |
Fixed costs that stay the same in total | Irrelevant | Paid whatever is decided – this is why limiting factor analysis uses contribution, not profit |
Fixed costs that can be avoided (for example a supervisor hired only for this work) | Relevant | The cash is saved if the decision does not go ahead |
Sunk costs – money already spent (for example the original price of materials bought last year, or market research already paid for) | Irrelevant | Past cost: it cannot be changed by any decision now |
Committed costs – future costs that cannot now be avoided (for example rent under a lease already signed) | Irrelevant | Will be paid whatever is decided |
Depreciation and absorbed fixed overheads | Irrelevant | Not a future cash flow caused by the decision – just a share of costs already incurred or unchanged |
Opportunity cost – the benefit given up by using a resource in this way rather than in its next best use | Relevant | It is a real future cost of the decision |
For materials already held in inventory, the original purchase price is a sunk cost. If the material is in regular use, using it means it must be replaced, so its relevant cost is the current replacement cost. If it is not in regular use, its relevant cost is what it could otherwise be sold for (its opportunity cost).
A business is deciding whether to accept a one-off order. It would need: 100 kg of material M, in regular use, bought last month for $4 per kg and now costing $5 per kg; 50 hours of extra labour hired at $12 an hour; and the use of a machine whose depreciation is $300 a month. Factory rent is $2,000 a month.
Item | Relevant cost ($) | Reason |
Material M: 100 kg × $5 (replacement cost) | 500 | In regular use, so it must be replaced; the $4 paid is sunk |
Labour: 50 hours × $12 | 600 | Extra cash paid only if the order is accepted |
Machine depreciation | – | Not a cash flow caused by the order |
Factory rent | – | Paid whatever is decided |
Total relevant cost | 1,100 |
The order is worth accepting if it brings in more than $1,100.
4 Make or Buy decisions
In order to overcome problems of limited resources, a firm may buy in a product instead of making it itself.
Where incremental costs of manufacture are less than those of buying in, the firm should make – assuming that there are no limited resources.
The comparison uses relevant costs: the variable (incremental) cost of making, plus any fixed costs that would be avoided by buying in, against the price charged by the supplier. Fixed costs that will be paid anyway are irrelevant.
A company can make 5,000 components a year at a variable cost of $8 each. Making them also needs a supervisor costing $15,000 a year, who would not be needed if the components were bought in. A supplier will sell the components for $10 each. General factory overheads of $4 per component are absorbed but would not change.
Relevant cost of making = 5,000 × $8 + $15,000 = $55,000 ($11 per component). Cost of buying = 5,000 × $10 = $50,000. The absorbed overheads are irrelevant. Buy – it saves $5,000 a year.
Where resources are limited, the firm should concentrate on making those products which give the greatest saving (over buying in) per unit of the scarce resource.
To decide which products should be made and which should be bought, we calculate the saving per unit of scarce resource from making the product rather than buying it in.
The availability of Material B is limited to 8,000 kg
Product | X | Y | Z |
Demand (units) | 2,000 | 2,500 | 4,000 |
Variable cost to make ($ per unit) | 10 | 12 | 14 |
Buy-in price ($ per unit) | 13 | 17 | 16 |
Kg of B required per unit (included in variable cost) | 3 | 2 | 1 |
How many units of each product should the company make and how many should it buy?
Show answerHide answer
Near the end of the make or buy lecture the tutor says “third best, Y at $1” – he means X. Y is ranked first ($2.50 per kg) and X third ($1 per kg), as in Answer 2.
The figures are not the only consideration. Before deciding to buy in, a business should also consider:
the quality and reliability of the supplier – will deliveries be on time and to the right standard?
whether the supplier’s price will stay at this level in future
loss of control and confidentiality – a supplier may learn a valuable process or design
the effect on the workforce – buying in may mean redundancies and lower morale, and skills may be lost
whether the capacity freed by buying in can be used for something more profitable
5 Test your knowledge
Two quick checks before you move on: work through the flashcards to fix this chapter’s terms and definitions, then sit the objective questions for exam-style practice. Both mark themselves and explain the answers as you go.
Limited Factor Analysis and Make or Buy Decisions
12 questionsAnswer the questions one at a time. Your progress is saved so you can leave and come back.
Open chapter practice