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Markup and margin

Two percentages of the same money measured against two different things, the price each one gives you, and how to convert between them.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

You will work out the markup and the margin on any sale, convert between them, and set a price that actually hits a margin you have chosen — by dividing rather than by adding. You will also be able to say why a margin can never exceed a hundred percent, how a maker and a shop agree a wholesale price, and why neither percentage tells you what to charge.

2. What you already have

You can say what a unit costs: materials, labor at a costing rate, a share of overhead, all corrected for waste and fees. Everything from here is about what to charge for it, and the first thing to settle is what the percentages people quote mean. Suppliers, shops, accountants and customers all say forty percent and mean different things, and the difference is money.

3. Words this lesson uses

4. Same money, two different divisors

One sale, one amount of profit, two percentages:

$$\text{markup} = \frac{p - c}{c}, \qquad \text{margin} = \frac{p - c}{p}$$

The top is identical. The bottom is cost in one and price in the other, and since price is the larger, the markup is always the bigger number. If your two figures come out the other way round, they are swapped.

Getting a price from each. From a markup, multiply: a 60 percent markup on a cost of 5 is $5 \times 1.6 = 8$. From a margin, divide: a 60 percent margin on a cost of 5 is $5 \div 0.4 = 12.50$. Those are very different prices from the same word sixty, and reaching for the multiplication when the target was a margin is the single most expensive arithmetic error in retail pricing.

Neither percentage tells you what to charge. They are ways of stating a price you have chosen, and what a customer will pay is not in either formula.

5. The method, step by step, and how to check it

Start from the unit cost you trust. Everything in this lesson multiplies or divides the cost, so an error in it is carried into the price at full strength — or larger, when the cost is divided by a small share.

Say which percentage you mean before you use it. Write markup or margin next to every percentage, on quotes, in spreadsheets, in conversations with suppliers. Half the errors in this topic are two people agreeing on a number and disagreeing on what it is of.

To use a markup, multiply. Price = cost × (1 + markup). A 40 percent markup on 30 is 30 × 1.4 = 42.

To reach a margin, divide. Price = cost ÷ (1 − margin). A 40 percent margin on 30 is 30 ÷ 0.6 = 50.

To describe a price you already have, divide the gross profit. By the cost for a markup, by the price for a margin.

Three checks. The markup should always be larger than the margin on the same sale. A margin must be below 100 percent; a markup can be any size. And after setting a price for a target margin, work the margin out again from the answer: if it comes back short, the percentage was added instead of divided.

6. Converting between the two

Because both percentages describe the same gross profit, each can be turned into the other without knowing the cost:

$$\text{margin} = \frac{\text{markup}}{1 + \text{markup}}, \qquad \text{markup} = \frac{\text{margin}}{1 - \text{margin}}$$

A 25 percent markup is 0.25 ÷ 1.25 = 20 percent margin. A 50 percent margin is 0.5 ÷ 0.5 = 100 percent markup. As the margin approaches 100 percent, the markup needed grows without limit: an 80 percent margin needs a 400 percent markup, and a 90 percent margin needs 900.

This matters whenever two businesses meet. A maker selling to a shop quotes a wholesale price; the shop adds its own margin. If the shop needs a 50 percent margin, it must sell at double the wholesale price, and the maker's own retail price has to leave room for that or the shop will not stock the product. Converting both sides into the same measure is the first step of any such negotiation.

7. What a percentage cannot tell you

A margin describes one sale. It says nothing about how many sales there will be, and a business lives on the total. Sixty percent on four sales a month pays for nothing; fifteen percent on four thousand can pay for a great deal. Nor does gross margin include the fixed costs: a gross margin is the price minus the unit cost, and the rent is still to come out of the total.

The percentages also say nothing about the customer. Two cafés with the same coffee cost can charge very different prices because their customers value different things — the view, the speed, the quiet. The margin is an output of a pricing decision, not a way to make one. The next lessons replace it with the numbers that answer the real question: how many sales, at what contribution each, cover the month.

8. Rules of thumb, and what each one assumes

Many trades have a customary markup or margin, and knowing what each one assumes is more useful than knowing the number.

Each rule is a shortcut for a full costing that somebody once did for a typical business in that trade. It works when your business looks like that typical one and fails quietly when it does not. A potter whose pieces take far longer than average will lose money on three times materials, because the rule assumed an average amount of labor in each piece. A café in an expensive street will lose money on a standard food-cost percentage, because its rent takes more of each sale than the rule allowed for.

So use a rule of thumb as a first guess and a check, never as the price. Cost the unit properly, find the margin your business actually needs to cover its fixed costs at a realistic volume, and then compare with the trade's rule. If your figure is far from it, one of the two is telling you something: either your costs are unusual, or your costing has missed a line. Both are worth knowing before a customer finds out for you. Write down which rule you compared against and why your own figure differs from it.

9. In the world: a bookshop's discount

Publishers sell books to bookshops at a discount off the cover price, and the discount is the bookshop's margin. A novel with a cover price of 20 dollars, sold to a shop at a 40 percent discount, costs the shop 12. The shop's margin is 8 ÷ 20 = 40 percent; its markup on cost is 8 ÷ 12 ≈ 67 percent.

From that 8 dollars the shop has to pay its rent, its staff and its card fees. If a customer asks for 10 percent off, the price falls to 18, and the gross profit falls from 8 to 6 — a quarter of the margin gone for a tenth off the price. That is why small bookshops are wary of discounting: a price cut comes entirely out of the margin, and at a 40 percent margin every percentage point off the price is two and a half percent of the gross profit.

Online sellers who can negotiate a 50 percent discount have a margin of 10 on the same book, which is why they can afford to cut the price and still keep as much as the main street shop does at full price.

10. In the world: supermarket margins

Supermarkets run on thin margins — often a gross margin of around 25 percent and a net margin, after all costs, of a few percent. Fresh produce and own-brand goods usually carry higher margins than branded staples, and shops arrange their aisles and promotions with that in mind. The percentages only work because of the volume: a few cents on millions of items a week.

11. Where this goes wrong

Adding the margin to cost. Want 40 percent margin on a cost of 60? The price is $60 \div 0.6 = 100$, not $60 \times 1.4 = 84$. At 84 the margin is 28.6 percent, and the business is short on every sale it makes.

Taking a supplier's markup as your margin. They are quoting against their cost. Convert before comparing.

Margins above 100 percent. There are none. A quoted 200 percent is a markup being called the wrong thing.

The margin is smaller, so it is the worse number. It is the same money; only the divisor differs.

Margin as proof of health. It is one sale's percentage. A 60 percent margin on four sales a month pays for nothing, and the next lessons are about the number that actually answers the question: how many.

A 50 percent markup and a 50 percent margin are the same price. A cost of 10 with a 50 percent markup sells at 15, a margin of one third; a 50 percent margin needs a price of 20. Say which one is meant, every time, and check it by working the other.

12. A mug at Maya's

1. Find the gross profit on a mug costing 16 and selling for 25.

   $25 - 16 = 9$

   The money first; both percentages share it.

2. Divide by the cost for the markup.

   $9 \div 16 = 56.25\%$

   Markup is over cost.

3. Divide by the price for the margin.

   $9 \div 25 = 36\%$

   Margin is over price.

4. Check the markup is the larger.

   $56.25 > 36$

   The smaller divisor always gives the larger percentage.

5. Convert the markup to a margin to confirm.

   $0.5625 \div 1.5625 = 0.36$

   The conversion gives the same margin without the price.

13. The addition mistake, costed

1. A kitchen wants a 75 percent margin on a box costing 5 dollars. Find the cost's share of the price.

   $100\% - 75\% = 25\%$

   The margin is the rest of the price.

2. Divide the cost by that share.

   $5 \div 0.25 = 20$

   The right price.

3. Now price by adding 75 percent to the cost.

   $5 \times 1.75 = 8.75$

   The wrong method, and a very common one.

4. Find the margin the wrong price actually gives.

   $(8.75 - 5) \div 8.75 \approx 42.9\%$

   Far short of 75.

5. Find the shortfall on one box.

   $20 - 8.75 = 11.25$

   Each box is under-priced by more than twice its cost.

6. Find the shortfall over 600 boxes a month.

   $600 \times 11.25 = 6750$

   The same word, two prices, and a large monthly gap.

14. Wholesale to a shop

1. Maya's bowl costs 18 to make. A shop wants to stock it and needs a 50 percent margin. She wants a 40 percent margin on wholesale. Find her wholesale price.

   $18 \div 0.6 = 30$

   Her margin is on her own price, the wholesale one.

2. Find the shop's retail price from its margin.

   $30 \div 0.5 = 60$

   The shop's cost is her wholesale price.

3. Find the shop's markup on her price.

   $(60 - 30) \div 30 = 100\%$

   A 50 percent margin is a 100 percent markup.

4. Compare with the price she charges direct: 45.

   $60 > 45$

   The shop would sell her bowl for more than she does.

5. Find her margin on a direct sale at 45.

   $(45 - 18) \div 45 = 60\%$

   Direct sales keep more of the price.

6. Find the retail price that would match her direct price.

   $45 \times 0.5 = 22.50 \text{ wholesale}$

   To sell at 45 in the shop, she would have to wholesale at 22.50.

7. Find her margin at that wholesale price.

   $(22.50 - 18) \div 22.50 = 20\%$

   Matching prices would halve her margin, so the two channels need different retail prices or different costs.

15. Your turn: a crate costs 20 and sells for 25

1. Find the gross profit.

   $25 - 20 = 5$

   Price minus cost.

2. Find the markup.

   $5 \div 20 = 25\%$

   Profit over cost.

3. Your turn: work this step out. Its working is at the end of the packet.

   Find the margin.

16. Guided practice

A crate of mangoes at Monica's Market Stall costs $20$ dollars and sells for $25$. Somebody says the business makes $25$ percent on it and somebody else says $20$ percent. Which is true?

• Both — $25$ percent is the markup on cost and $20$ percent the margin on price
• Only $25$ percent, because profit is measured against what you spent
• Only $20$ percent, because percentages always go over the price
• Neither — one of them must be an arithmetic error

17. Guided practice

Complete the worked solution: a unit costs $28$ dollars and the business wants a margin of $20$ percent on price. What must the price be?

1. Find the share of the price the cost must be.

   $100\% - 20\% =$ _c $\%$

   A margin is the part of the price left after the cost.

2. Write that share as a decimal.

   $(\text{that share}) \div 100 = 0.8$

   Dividing by a percentage means dividing by its decimal.

3. Divide the cost by that share.

   $28 \div 0.8 =$ _p

   If the cost is that share of the price, the price is the cost over the share.

4. Find the gross profit.

   $(\text{price}) - 28 =$ _g

   Price minus cost.

5. Check the margin on the new price.

   $(\text{gross profit}) \div (\text{price}) = 20\%$

   Checking the target on the answer catches the addition mistake.

18. Guided practice

Neighborhood Kitchen wants a margin of $75$ percent on a lunch box that costs $5$ dollars. What must the price be, in dollars?

Answer:

19. Practice

Northside Repairs prices a screen replacement costing $25$ dollars with a markup of $100$ percent on cost. What is the price, in dollars?

Answer:

20. Practice

A wholesaler quotes markups and a shop thinks in margins. Match each markup on cost to the margin on price it produces, for a unit costing $60$ dollars.

21. Practice

At Northside Repairs, one screen replacement costs $25$ dollars and sells for $50$. Fill in the gross profit and both percentages.

22. Somewhere new

A bicycle shop buys a service kit for $64$ dollars and sells the service that uses it for $80$ dollars, with no other cost. What margin on price is it making, in percent?

23. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

24. Test question

At Bright Home Cleaning, one standard clean costs $40$ dollars and sells for $64$. Fill in the gross profit and both percentages.

25. What you can do now

You can compute both percentages, convert one into the other, and price to a target margin. Tell someone why adding forty percent to your cost does not give a forty percent margin. Next: the number that says what one sale is actually worth to the business.

Working for the steps left to you

15. Your turn: a crate costs 20 and sells for 25, step 3