Limiting Factors and Make-or-Buy Decisions

In the budget, sales demand is normally what limits a business. In the real world, something else often gets in the way first: not enough skilled workers, a machine that runs only so many hours, a material that cannot be imported in full, or simply not enough cash. When that happens, making more of everything is impossible and the question becomes which products deserve the scarce resource.

The answer is not the product with the biggest profit, or even the biggest contribution per unit. It is the product with the biggest contribution for each unit of the scarce resource.

This topic covers the types of limiting factor, how to identify the factor that binds, how to build the profit-maximising production plan for a single limiting factor (including cases with minimum and maximum output levels, and where the scarce resource is money), and make-or-buy decisions, including those where in-house capacity is scarce and some work must be outsourced.

These are very frequently examined: both of the newest diets set a 20-mark limiting factor question.

What a limiting factor is

A limiting factor (also called a scarce or key factor) is any resource or condition that restricts an organisation’s ability to meet its objectives or maximise profit. Budgets usually assume that the company can produce as much as demand requires, so sales demand is the normal limit.

But sometimes a key resource is in short supply, and then the availability of that resource sets the limit on output, sales and profit. If a company makes one product, profit is maximised by making as many as the resource allows. If it makes several using the same scarce resource, it must decide how many of each to make.

Types of limiting factor

Effects on decisions

When resources are constrained, management must decide how to use them. It may concentrate on the most profitable products, postpone or reject less profitable work, outsource, raise prices to reflect scarcity, or invest to relieve the constraint (more machines, more staff). Recognising the limiting factor and responding to it helps the business optimise profit and manage risk.

Identifying the limiting factor

A question may say that a resource is restricted without saying which. Work it out: calculate the amount of each resource needed to meet the full sales demand and compare with the amount available. The resource for which the need exceeds the availability is the limiting factor.

Example. A company makes products X and Y on two machines. Demand is 14,000 units of X and 12,000 of Y.

Machine 1 is the limiting factor. Machine 2 has enough time and does not restrict the plan.

Maximising profit with one limiting factor

When there is one limiting factor (other than sales demand), total profit is maximised by maximising total contribution from the scarce resource. Select products by the contribution per unit of scarce resource, not by contribution per unit of product.

1. Calculate the contribution per unit for each product.
2. Identify the scarce resource.
3. Calculate how much of the scarce resource each product uses.
4. Divide the contribution per unit by the resource used per unit.
5. Rank the products: highest contribution per unit of resource first.
6. Build the plan: make each product in rank order up to its maximum demand until the resource is used up.

Example (continued). Contribution per unit: X ₦90, Y ₦70. Machine 1 hours per unit: X = 12 minutes = 0.2 hours; Y = 8 minutes = 0.1333 hours.

Y has the lower contribution per unit but earns more per scarce hour. Only 6,000 of the 14,000 units of X can be made. Check: making only X (all 2,800 hours) gives 14,000 units × ₦90 = ₦1,260,000, which is less than ₦1,380,000. ✓

Why not rank on profit per unit?

Full cost and profit per unit include fixed overhead apportioned to units. Fixed costs do not change with the plan, so profit per unit can point to the wrong product. Example. A company makes four products using labour at ₦12 an hour. Demand and unit data:

Labour is limited to 14,000 hours, while full demand needs 21,000 hours (6,000 + 6,000 + 4,000 + 5,000). Ranking on profit per unit would put B first. Ranking on contribution per hour puts C first and B third.

(Two hours are left over because only whole units are made. If part units were allowed, B would be 1,666.67 units and total contribution ₦324,166.67.)

Variations that appear in examinations

Minimum and maximum output levels

Recent papers add limits: a minimum quantity of each product that must be made (to keep customers or contracts), or a maximum production capacity. Method: first make the minimum quantities of all products and deduct the resource used. Then allocate the balance in rank order, up to each product’s maximum.

Example. A company makes J, K and L and is able to sell all that it makes. Labour hours available: 19,500. Labour per unit and contribution per unit: J 1.5 hours, ₦90 (₦60 per hour); K 2.0 hours, ₦100 (₦50 per hour); L 3.0 hours, ₦210 (₦70 per hour). Maximum production possible: J 6,000, K 7,000, L 4,500. Current production: J 3,000, K 4,000, L 2,000.

• Ranking: L (₦70), then J (₦60), then K (₦50).
• Optimal plan: L at its maximum, 4,500 units, uses 13,500 hours.
  Balance = 6,000 hours.
  J: 6,000 ÷ 1.5 = 4,000 units (below its maximum of 6,000).
  K: nil.
• Contribution:
  L 4,500 × ₦210 = ₦945,000.
  J 4,000 × ₦90 = ₦360,000.
  Total ₦1,305,000.
• Current production:
  J 3,000 × ₦90 = ₦270,000
  K 4,000 × ₦100 = ₦400,000
  L 2,000 × ₦210 = ₦420,000.
  Total ₦1,090,000 (using 3,000 × 1.5 + 4,000 × 2 + 2,000 × 3 = 18,500 hours).
• Improvement.
  ₦1,305,000 − ₦1,090,000 = ₦215,000.

If management insisted on a minimum of 2,000 units of K, K would be made first (2,000 × 2 = 4,000 hours), leaving 15,500 hours: L 4,500 units (13,500 hours), then J 2,000/1.5 = 1,333 units. The minimum lowers contribution by the amount K’s hours would have earned in J and L: that is the cost of the commitment.

When the scarce resource is money

If the limit is a sum of money available to buy a material (for example, imports limited to a naira amount), rank on contribution per ₦1 of the material. Example. Only ₦600,000 can be spent on a material. Product P: contribution ₦40, material cost ₦10 per unit, giving ₦4 per ₦1 of material. Q: contribution ₦60, material ₦20, giving ₦3. R: contribution ₦30, material ₦5, giving ₦6.

Rank: R, P, Q. If demand is R 40,000, P 30,000 and Q 20,000 units, R uses ₦200,000 (40,000 × ₦5), P uses ₦300,000 (30,000 × ₦10), leaving ₦100,000 for Q: 5,000 units (₦100,000 ÷ ₦20). The same method applies when a question gives the value of the material and not the quantity.

When there is more than one limiting factor

If two or more resources are scarce, the ranking method does not work in general. Specialised methods (such as linear programming) are needed. At Foundation level, questions have one limiting factor, so check the identification step first.

Make-or-buy decisions

A make-or-buy decision asks whether to make an item or do work internally, or to buy it from or contract it to an outsider. It is a short-term relevant costing decision: the financially preferred option has the lower relevant cost. Compare the costs saved by outsourcing with the incremental costs of buying.

Example. A company makes 5,000 components a year with a variable cost of ₦240 each. A supplier offers to sell at ₦270. If the company stops making the component, it will save ₦200,000 a year in avoidable fixed overhead.

On financial grounds, buy. If the fixed overhead saving were only ₦100,000, buying would lose ₦50,000 and the company should make. Only avoidable fixed costs matter; absorbed fixed overhead that continues is irrelevant.

Make or buy with scarce capacity

When in-house capacity is limited, the company may outsource some work to use the capacity more profitably. The profit-maximising choice is to outsource the items where the extra cost of outsourcing per unit of scarce resource saved is lowest. Steps:

1. For each item, calculate the extra cost of buying = external price − in-house variable cost.
2. Divide by the scarce resource used per unit in-house, to give the extra cost per hour saved.
3. Rank: outsource first the item with the lowest extra cost per hour; make in-house the items with the highest.
4. Fill the in-house capacity in order of priority and outsource the rest.

Example. Three components, with 3,000 machine hours available in-house.

Full demand would need 1,000 + 2,400 + 1,800 = 5,200 hours. Only 3,000 are available, so 2,200 hours of work must be outsourced.

Check that every item is cheaper to buy than to leave unmade, that is, that the selling price exceeds the outsourcing cost per unit. If it does not, a product should be dropped rather than bought.

Non-financial factors in make-or-buy

• Quality and reliability of the supplier, and the risk of late delivery.
• Control over specification, design secrecy and intellectual property.
• Capacity use. Idle capacity after outsourcing may have no alternative use, and skilled staff may leave.
• Dependence on one supplier, and the cost of switching back.
• Long-term strategy, since short-term relevant costing ignores the time value of money and long-term investment effects.

The ideas in more depth

Why contribution per unit of resource?

A product with a high contribution per unit may use up so much of the scarce resource that the resource earns less per hour than on a lower-contribution product. The scarce resource is the money-maker. Each hour or kilogram should go where it earns the most.

Short-term versus long-term

Limiting factor analysis is a short-term tool. If a resource is permanently scarce, the better question is whether to relieve the constraint: hire and train staff, buy another machine, or find new suppliers. The value of one extra hour of the scarce resource is the contribution per hour of the lowest-ranked product being made, the “shadow price”.

If an extra machine hour would earn ₦450 (the marginal product’s rate) and a machine hour costs ₦200 to hire, hiring pays.

Checking the plan

After building the plan, check:

• (1) total resource used does not exceed the amount available
• (2) no product exceeds its demand or maximum production
• (3) any left-over resource is explained (usually rounding to whole units)

Then calculate total contribution and, if fixed costs are given, profit.

Presenting advice

An examiner wants a recommendation, not just numbers. State the limiting factor, the ranking, the plan, the total contribution, and any risk (for example, that the plan stops production of a product some customers need).

Worked example: a full limiting factor question

1. Hours needed for full demand:
   G 4,000 + E 4,000 + P 3,000 = 11,000.
   Available 9,000.
   Machine time is the limiting factor (short by 2,000 hours).
2. Contribution per tin: G ₦400, E ₦300, P ₦200.
3. Per machine hour:
   G ₦400 ÷ 0.8 = ₦500.
   E ₦300 ÷ 0.5 = ₦600.
   P ₦200 ÷ 0.25 = ₦800.
   Rank: P, E, G.
4. Plan: P 12,000 tins (3,000 hours). E 8,000 tins (4,000 hours).
   G with the balance of 2,000 hours: 2,000 ÷ 0.8 = 2,500 tins.
5. Contribution:
   P 12,000 × ₦200 = ₦2,400,000.
   E 8,000 × ₦300 = ₦2,400,000.
   G 2,500 × ₦400 = ₦1,000,000.
   Total ₦5,800,000.
6. Profit.
   ₦5,800,000 − ₦3,000,000 = ₦2,800,000.
7. Advice: gloss has the highest contribution per tin but the lowest per machine hour, so only 2,500 of 5,000 tins are made. Each extra machine hour would earn ₦500 (the rate on the marginal product G), so extra hours costing less than ₦500 each, up to 2,000 hours, would add to profit.

The value of extra capacity

A limiting factor analysis also tells you what extra capacity is worth. The marginal product is the last one in the rank order that is limited by the resource (not by demand). Each extra hour of the scarce resource would be used to make more of that product, so it is worth that product’s contribution per hour. In the Warri example it is ₦500 per machine hour.

If the firm can hire machines at ₦350 an hour, it gains ₦150 an hour on up to 2,000 hours: a gain of ₦300,000. If hiring costs ₦550 an hour, it should not. Once all gloss demand is met (2,500 more tins using 2,000 hours), the constraint is no longer the machines, and sales demand becomes the limit.

Special cases

• Products with equal contribution per unit of resource. The order does not change total contribution. Use other criteria such as strategic importance or customer commitments.
• Products that cannot be dropped. If a customer contract requires a product, make the contract quantity first even though it ranks low. The cost of this commitment is the extra contribution that the resource would have earned elsewhere.
• Resources shared between products. If a product uses two scarce resources, only one can be the single limiting factor at a time. Test each resource and see which is exhausted first.
• Fractional units. If the balance of the resource does not make a whole unit, state whether you round down (whole units only) or allow part units. Say what you assumed.

Common mistakes in the exam

• Ranking on contribution per unit, or profit per unit, instead of contribution per unit of the scarce resource.
• Including fixed overhead (absorbed) in the contribution.
• Not checking which resource is the limiting factor when more than one is given.
• Making more than the demand or maximum production for the top-ranked product.
• Forgetting to deduct minimum production quantities first.
• Dividing the hours left by the wrong hours per unit.
• In outsourcing, ranking on the cost of buying instead of the extra cost per hour saved.
• Ignoring avoidable fixed costs in a make-or-buy decision.

Quick revision

• Limiting factor: the resource that restricts output. Identify it by comparing hours needed for full demand with hours available.
• Single limiting factor: rank on contribution per unit of scarce resource. Make in rank order up to demand.
• Money as the limit: rank on contribution per ₦1 of the material.
• Minimums first, maximums as caps.
• Make or buy: buy if price is less than avoidable cost of making. With scarce capacity, outsource first the lowest extra cost per hour saved.
• Ignore apportioned fixed overhead and sunk costs.

Practice questions

These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer.

Section A style: multiple choice

Section B style: written questions

A further written question

Model answers

Spotted a mistake? Tell us and we will check it.