Calculating quantities of material and the cost of manufacture, including material and component costs, waste and yield, fixed and variable costs, unit cost, percentage profit and markup, break-even quantity, value added tax (VAT) and how costing informs pricing and the choice of process and scale.

What this dot point is asking

Edexcel wants you to calculate quantities of material and the cost of manufacture: material and component costs, waste and yield, fixed and variable costs, unit cost, percentage profit and markup, break-even quantity and VAT, and to explain how costing informs pricing and the choice of process and scale.

The answer

Quantities of material, waste and yield

To cost materials, find the quantity used per unit (length, area, volume or mass) and multiply by the price, then allow for waste. Yield is the proportion of material that ends up in the product; the rest is offcut or scrap, so the material you must buy is more than the part itself.

Fixed and variable costs and unit cost

Profit, markup and selling price

Markup is profit expressed as a percentage of the cost. The selling price $= \text{cost} + \text{profit}$, where profit $= \text{markup} \times \text{cost}$. (Profit margin, by contrast, is profit as a percentage of the selling price.)

Break-even quantity

VAT and how costing informs decisions

Value added tax (VAT), commonly 20 per cent in the UK, is added to the selling price (multiply by $1.20$). Costing informs pricing (covering cost plus profit at a price the market accepts), viability (through break-even), and the choice of process and scale (expensive tooling is only worth it once volume spreads the fixed cost, linking to scales of production).

Examples in context

A furniture maker costs a table by the timber used plus an allowance for offcuts (yield), then adds labour and a share of workshop fixed costs to get the unit cost, and applies a markup to set the price. A start-up uses break-even to decide how many units it must sell to recover its tooling investment before it profits, which also guides whether to choose cheap low-volume tooling or expensive high-volume tooling. Retail prices then have VAT added. Calculating material quantities with waste, unit cost, markup, break-even and VAT, and using them to justify a price and a production scale, are exactly the maths-in-context skills Edexcel rewards.

Try this

Q1. A part contains $150$ g of plastic but the process has a $75\%$ yield. How much plastic must be bought per part? [2 marks]

• Cue. $\dfrac{150}{0.75} = 200$ g per part.

Q2. Fixed costs are 3000 pounds, the contribution per unit is 6 pounds. Find the break-even quantity. [1 mark]

• Cue. $\dfrac{3000}{6} = 500$ units.

Q3. A product costs 4.00 pounds and is sold with a 100 per cent markup. Find the price before and after 20 per cent VAT. [2 marks]

• Cue. Before VAT: $4.00 + 4.00 = 8.00$ pounds; after VAT: $8.00 \times 1.20 = 9.60$ pounds.