4.3 Pricing with Cost Information: Full-Cost-Plus, Marginal-Cost-Plus, Mark-Ups, Margins and Return Targets

Why this topic is examined

Syllabus area B2(e) asks you to apply cost information in pricing decisions: "marginal cost pricing and full-cost pricing to achieve specified targets (return on sales, return on investment, mark-up and margins)". Questions are almost always calculations. The common traps are confusing mark-up with margin, forgetting that a return on investment is based on capital employed rather than on cost, and using the wrong cost base.

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Two cost bases for pricing

Full-cost-plus pricing

The price is set by adding a percentage mark-up to the full cost per unit:

$$\text{Price} = \text{Full cost per unit} \times (1 + \text{mark-up \%})$$

"Full cost" may mean full production cost (variable production cost plus absorbed fixed production overhead) or total cost (also including a share of administration, selling and distribution costs). A question will say which to use; read it carefully.

Marginal-cost-plus pricing

The price is set by adding a mark-up to the marginal (variable) cost per unit:

$$\text{Price} = \text{Marginal cost per unit} \times (1 + \text{mark-up \%})$$

Because variable cost is smaller than full cost, the mark-up percentage must be much larger to produce the same price. The mark-up has to cover all fixed costs and the profit.

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Mark-up versus margin

Converting between them:

$$m = \frac{k}{1 + k} \qquad k = \frac{m}{1 - m}$$

A return on sales target is simply a margin: profit as a percentage of revenue.

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Pricing to achieve a return on investment (ROI)

A return on investment (return on capital employed) target relates profit to the capital employed in the product or business, not to cost or revenue.

1. Required annual profit = target ROI % × capital employed.
2. Required profit per unit = required annual profit ÷ budgeted units.
3. Price = cost per unit + required profit per unit.

Worked example

Castell Ltd is setting the price of a new product:

• Variable cost: $24 per unit
• Fixed costs attributed to the product: $180,000 per year
• Budgeted sales: 20,000 units per year
• Capital employed in the product: $500,000
• Target return on investment: 18% per year

Full cost per unit:

$$\text{Fixed cost per unit} = \frac{\text{\textdollar}180{,}000}{20{,}000} = \text{\textdollar}9.00 \qquad \text{Full cost} = \text{\textdollar}24.00 + \text{\textdollar}9.00 = \text{\textdollar}33.00$$

Required profit:

$$0.18 \times \text{\textdollar}500{,}000 = \text{\textdollar}90{,}000 \qquad \frac{\text{\textdollar}90{,}000}{20{,}000} = \text{\textdollar}4.50 \text{ per unit}$$

Price:

$$\text{\textdollar}33.00 + \text{\textdollar}4.50 = \text{\textdollar}37.50$$

The same price expressed three ways:

The marginal-cost mark-up is 56.25% because it must cover $9.00 of fixed cost as well as $4.50 of profit: ($9.00 + $4.50) ÷ $24.00 = 56.25%.

Check the ROI: 20,000 units × ($37.50 − $33.00) = $90,000 profit, and $90,000 ÷ $500,000 = 18%.

If a return on sales target is set instead

If Castell wanted a 20% return on sales on full cost:

$$\text{Price} = \frac{\text{\textdollar}33.00}{1 - 0.20} = \text{\textdollar}41.25$$

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The volume problem in full-cost pricing

The fixed cost per unit depends on the budgeted volume. If Castell had budgeted 15,000 units, fixed cost per unit would be $12.00 and full cost $36.00, pushing the price up. A higher price may reduce demand, which pushes the fixed cost per unit higher still. Full-cost-plus pricing can therefore price a product out of the market when demand is weak. Pricing decisions should always be checked against what customers will pay and what competitors charge.

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Advantages and disadvantages