Cost-Based Pricing: Cost-Plus, Marginal Cost and Relevant Cost Pricing

Most businesses do not price from a demand curve. A building contractor in Port Harcourt adds 25% to what a job costs. A garment factory adds a fixed percentage to the full cost of each style. A distributor adds a standard margin to the invoice price.

This habit is called cost-based pricing. The reason it is so common is that it is quick, it gives a price that covers cost, and everyone in the industry understands it. It also has weaknesses, which the examiner likes to test.

This topic explains cost-plus pricing on full cost and on marginal cost, the difference between a mark-up and a margin, how a change in the way costs are measured, such as a move to activity based costing, changes prices and then sales, and when pricing at relevant cost, which gives a minimum price, is appropriate. It builds on the earlier topic on demand and cost functions. The next topic covers market-based pricing: skimming, penetration and other strategies.

Cost-plus and marginal cost pricing

Full cost-plus pricing

The price is the full cost per unit plus a percentage mark-up. Full cost is direct materials, direct labour, variable overhead and an absorbed share of fixed production overhead (and sometimes a share of administration and selling costs). The mark-up gives the profit and may allow for the risk and capital employed.

• Advantages. It is simple and quick, which suits a business that has many products or must quote often. It ensures that, over time, each product covers its full cost. It is widely accepted: customers and contract partners understand it, and it can be used where the cost is the basis of a contract. Prices are stable, and rivals using the same mark-up may avoid price wars.
• Disadvantages. It ignores demand: the price that covers cost may be more than customers will pay or less than they would. It ignores competitors’ prices. The absorbed fixed overhead depends on the volume assumed and the base used, so the price depends on an arbitrary allocation. Using the budgeted volume can create a circle: a higher price cuts volume, which raises the absorbed cost per unit and calls for a higher price. It rewards inefficiency, since any extra cost is simply passed on. And a standard mark-up for all products ignores differences in elasticity.

Marginal cost-plus pricing

The price is the marginal (variable) cost plus a mark-up that is usually much larger, because it must cover all fixed cost and the profit. It focuses on contribution and avoids the arbitrary absorption of fixed overhead.

It is useful for short-term and special pricing, but the mark-up must be big enough to cover fixed costs over the long run. It may lead to prices that are too low if fixed costs are ignored.

Mark-up and margin

A mark-up is the profit as a percentage of cost. A margin is the profit as a percentage of the selling price. They describe the same profit differently, and a common error is to mix them.

• Margin = mark-up ÷ (1 + mark-up).
  A 25% mark-up gives 0.25 ÷ 1.25 = 20%.
• Mark-up = margin ÷ (1 − margin).
  A 30% margin gives 0.30 ÷ 0.70 = 42.9%.
• Price from cost with a mark-up: cost × (1 + mark-up). Price from cost with a margin: cost ÷ (1 − margin).

Costing methods, elasticity and relevant cost pricing

How a change in costing changes prices and sales

A business that prices at cost plus a standard mark-up lets its costing method set its prices. Moving from absorption by labour hours to activity based costing changes the unit cost of each product: low-volume, complex products usually cost more, and high-volume simple products cost less. With a fixed mark-up, their prices follow. What happens to sales depends on elasticity:

• If the cost, and so price, rises and demand is elastic, volume falls by a larger percentage than the price rise.
• If the price falls and demand is elastic, volume rises by more than the percentage cut.
• If demand is inelastic, volume hardly changes, whichever way the price moves.

This is why a company limited by cost-plus and a standard mark-up may be unable to raise revenue: the method fixes the prices, not the market. A better costing system helps only if prices respond to it intelligently, for example by cutting the price of products found to be over-costed in order to win sales, and raising the price of or dropping those that are under-costed.

Relevant cost pricing

For a one-off order that uses spare capacity, the minimum price is the relevant cost: the extra cash costs of the job, including the opportunity cost of any scarce resource used. At that price the company is no better and no worse off. A quotation should normally be higher, to give a profit, but the relevant cost shows the floor below which the order should not be accepted.

It is not suitable as a long-term price, because it makes no contribution to the fixed cost of the business and no return to investors, and because repeat business at that price would displace better orders.

Return on investment pricing, and why the absorption base changes the price

Return on investment (ROI) pricing is used where an investment centre must earn a target return on its capital. The price is set to cover cost and give that return: price = (budgeted total costs + target ROI × capital employed) ÷ budgeted volume. It is a way of choosing the profit element for cost-plus pricing, and the target can be varied with business risk.

Its weakness is the same as other cost-based methods: it pays no attention to what customers will pay, and the return is reached only if the budgeted volume is sold.

1. Full cost.
   Fixed 1,200,000 ÷ 50,000 = ₦24
   full cost = 80 + 24 = ₦104.
   Full cost plus 20% = ₦124.80.
2. Marginal cost plus 50%.
   80 × 1.5 = ₦120.
3. ROI price.
   Capital 7,000,000 × 12% = 840,000
   per unit 840,000 ÷ 50,000 = ₦16.80
   price = 104 + 16.80 = ₦120.80.
4. Volume shortfall.
   At 40,000 units: revenue 4,832,000; costs 80 × 40,000 + 1,200,000 = 4,400,000; profit ₦432,000, a return of 6.2% on ₦7,000,000, about half the target.
   A cost-based price protects the target only if the volume is achieved.

1. Labour hour basis. 5,000 hours; rate ₦240. X overhead 480, Y 720.
   Prices: X (300 + 480) × 1.2 = ₦936
   Y (350 + 720) × 1.2 = ₦1,284.
2. Machine hour basis. 3,000 hours; rate ₦400. X overhead 400, Y 800.
   Prices: X (300 + 400) × 1.2 = ₦840
   Y (350 + 800) × 1.2 = ₦1,380.
3. Lesson. The same mark-up gives different prices (X ₦96 lower, Y ₦96 higher) merely because the base changes, which shows that the choice of mark-up and of absorption method is arbitrary.

Layouts for cost-based prices

1. Full cost per unit. Direct materials + direct labour + variable overhead + fixed overhead absorbed (budgeted fixed overhead ÷ budgeted units).
2. Price with a mark-up. Cost × (1 + mark-up %).
3. Margin on sales. (Price − cost) ÷ price.
4. Price on marginal cost. Variable cost × (1 + mark-up %).
5. Effect of a price change on volume. % change in price × elasticity = % change in volume.
6. New revenue. New price × new volume.

Money is in naira and each answer is rounded once, at the end.

Worked examples

1. Full cost.
   300 + 120 + 80 = ₦500.
2. Price.
   500 × 1.25 = ₦625.
3. Margin.
   (625 − 500) ÷ 625 = 20.0% of sales.
4. Mark-up for a 30% margin.
   0.30 ÷ 0.70 = 42.9% of cost, giving a price of 500 ÷ 0.70 = ₦714.29.

1. Old prices.
   A 400 × 1.2 = ₦480
   B 600 × 1.2 = ₦720
   C 500 × 1.2 = ₦600.
   Old revenue: ₦4.8m, ₦7.2m and ₦6.0m.
2. New prices.
   A 460 × 1.2 = ₦552 (up 15%)
   B 540 × 1.2 = ₦648 (down 10%)
   C 520 × 1.2 = ₦624 (up 4%).
3. Volume changes.
   A: 15% × 1.5 = −22.5%, so 7,750 units.
   B: 10% × 1.5 = +15%, so 11,500 units.
   C: 4% × 0.2 = −0.8%, so 9,920 units.
4. New revenue.
   A 552 × 7,750 = ₦4,278,000.
   B 648 × 11,500 = ₦7,452,000.
   C 624 × 9,920 = ₦6,190,080.
5. Comment. A loses revenue, because its price rises when its demand is elastic; B gains because its price falls; C gains slightly because demand is inelastic. A company should price A with care and consider cutting B further, rather than just applying the mark-up.

Expect variants: a different base for the mark-up, marginal cost-plus, a question that asks for the effect on volume only, or a discussion of the method.

Common mistakes

• Mixing mark-up and margin. State which one is used.
• Adding the mark-up to the wrong cost. Full-cost pricing uses full cost; marginal pricing uses variable cost.
• Ignoring elasticity when asked about the effect on sales.
• Treating relevant cost as a selling price. It is the minimum.
• Listing advantages only. The weaknesses carry as many marks.
• Forgetting that absorbed overhead depends on volume.

Quick revision

• Price = cost × (1 + mark-up).
  Margin = mark-up ÷ (1 + mark-up)
  mark-up = margin ÷ (1 − margin).
• Full cost-plus: simple, covers cost; ignores demand and competition; overhead absorption arbitrary.
• Marginal cost-plus: large mark-up on variable cost; focuses on contribution.
• Costing change alters prices; elasticity decides the effect on sales.
• Relevant cost pricing gives the minimum price for a one-off order.

How the marks are earned

• Calculate: full cost, price, margin, with the layout.
• Discuss: advantages and disadvantages, with the product in the question.
• Apply elasticity: price change, volume change and revenue.

Practice questions

These are original questions, written in the style of the Skills examination. Work each one before you open the answer.

Recall check: multiple choice

Section B style: written questions

Model answers

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