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Waste, spoilage and fees

Two leaks that never appear on a receipt: stock that cannot be sold, and the cut a processor takes from each sale.

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 spread the cost of stock that cannot be sold over the units that can, work out what a payment fee takes off a sale, and say which of the two belongs on the cost side and which on the price side. You will also find what one sale keeps once both are counted, and say how much a loss that happens every batch adds to every unit you sell.

2. What you already have

You can total a batch and divide by what you can sell. This lesson is about the two leaks either side of that division, and both are invisible on a receipt: stock that was paid for and never sold, and the slice of each sale that a payment processor keeps before the money reaches you. Neither arrives as a bill, which is exactly why they are so often left out of a price.

3. Words this lesson uses

4. One leak shrinks the count, the other shrinks the price

They feel like the same thing — money going missing — and they enter the arithmetic at opposite ends.

Loss shrinks the count. The money is already spent. Buy 200 mangoes for 180 dollars and bruise 20, and you have not saved anything: you have 180 dollars of cost sitting on 180 mangoes instead of 200. The cost per sellable mango goes from 0.90 to 1.00, and the 0.10 is the waste, paid for by the ones that survived.

The fee shrinks the price. A 2 percent card fee on a 2 dollar sale is 4 cents, so 1.96 arrives. It never shows up as a bill, because it is deducted before the money reaches you — which is exactly why it goes uncounted for years.

Do them in that order, and use the two results where they belong: the loss figure everywhere you would use cost, the fee figure everywhere you would use price.

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

Measure the loss, do not guess it. Count what was bought and what was sold, and the difference is the loss — whatever the cause. Owners who guess usually guess low, because the bruised fruit thrown away at six o'clock is not remembered the way the sale at noon is. Keep a count for a few weeks and use the typical rate.

Divide the cost by what survives. The whole cost of the lot, divided by the units fit to sell. The money was spent on all of them, and only the survivors can bring it back.

Find the fee from the contract. Card and online processors charge a percentage of each sale, sometimes plus a fixed amount per transaction. The rate is a term of your own contract, so read it from the statement, not from an advert. Multiply the rate by the price.

Take the fee off the price. What arrives is the price minus the fee. Use that figure wherever you would have used the price.

Subtract to find what a sale keeps. Net receipt minus the cost of a sellable unit.

Two checks. Multiply the corrected unit cost by the survivors: you should get the whole cost back, not less. And the fee should be small beside the price — a few percent — but compare it with the margin, not with the price: a fee that is 2 percent of the price can be a fifth of what the sale keeps.

6. Why the fee is measured against the margin

A percentage is only meaningful beside the thing it is a percentage of. A 3 percent fee on a 10-dollar sale is 30 cents. If the item cost 5 dollars, the sale keeps 4.70 instead of 5.00, and the fee has taken 6 percent of the margin. If the item cost 9 dollars, the sale keeps 0.70 instead of 1.00, and the fee has taken 30 percent of it.

So low-margin businesses — grocers, resellers, market stalls — feel payment fees far more than high-margin ones like a consultant or a craftsperson. This is why some small shops set a minimum card spend or add a small surcharge where the rules allow it: on a one-dollar sale, a fixed per-transaction fee can take most of the margin. Whether to do that is a decision about customers, not arithmetic; the arithmetic only tells you how much is at stake.

7. Reducing waste, and when not to

Once waste is costed it becomes something with a price, and the price tells you what reducing it is worth. The kitchen that throws away 15 of 120 boxes pays 4.00 a sellable box; at 5 thrown away it would pay 420 ÷ 115 ≈ 3.65. That 35 cents on every box is the value of better forecasting.

But zero waste is rarely the right target. Making fewer boxes cuts waste and also means running out at 12:40 and turning customers away, and a customer turned away may not come back. The right amount of waste balances the cost of the leftovers against the sales lost by running out, and it is usually more than zero. Cost what actually happens, and treat the waste rate as a number to manage, not a failure to hide.

8. Other leaks that behave the same way

Once the two leaks are clear, others turn out to be one or the other in disguise, and the same question sorts them: does this shrink the count I divide the cost by, or the price that arrives?

Delivery apps and online marketplaces deserve a special mention because their cut is large. A food-delivery platform keeping 25 to 30 percent of the order is not a small fee on top of a price built for the counter; it is a different price. A restaurant that charges the same on the app as at the counter is selling the same meal for about three-quarters of the money, and the arithmetic in this lesson is how it finds out whether that still leaves anything once the ingredients are paid for.

The discipline is the same for every row: name the leak, say which side it is on, and put a number on it before setting a price that assumes it away.

9. In the world: a greengrocer's week

A greengrocer buys 1,400 dollars of fruit and vegetables for the week. From past counts she knows about 12 percent by value is thrown away or given to a food charity: soft tomatoes, yellowing greens, split bags. So 1,400 of cost sits on stock that sells for what 88 percent of it would have: the cost of what she sells is 1,400 ÷ 0.88 ≈ 1,591 at purchase prices, which means every dollar of produce she sells cost her not 1.00 but about 1.14 in purchases.

About 70 percent of her takings arrive by card at 1.75 percent. On a week of 2,600 dollars in sales, 1,820 is by card and the processor keeps 0.0175 × 1,820 ≈ 32 dollars. That sounds trivial until it is set against the week's margin: 2,600 − 32 − 1,400 = 1,168 before rent and wages, and against that the 32 dollars of fees and the 168 dollars of waste together take about 15 percent of what the week would otherwise have kept.

With both leaks costed, she can put a value on each fix. Cutting waste from 12 to 8 percent is worth about 56 dollars a week — more than a new display fridge costs to run. Moving card customers to another processor at 1.4 percent is worth about 6. The second is easier to arrange; the first is worth ten times as much.

10. In the world: shrinkage in large retail

Big retailers report shrinkage — stock that disappears through theft, damage and miscounts — as a percentage of sales, and it commonly runs between 1 and 2 percent. For a supermarket whose net margin is only a few percent, that is a large share of the profit, which is why shops spend heavily on stock counts, security tags and cameras: every point of shrinkage recovered goes straight to the bottom line.

11. Where this goes wrong

Waste is a separate problem, not a cost. If it happens every batch it is a cost, and a price that does not carry it is short every time. Reduce it by all means; cost it in the meantime.

The fee comes off the profit. It comes off the price, before anything is profit. A business quoting margins on the list price is overstating every one of them by the fee.

It is only two percent. Two percent of price on a product carrying a ten percent margin is a fifth of the margin. Percentages are only comparable when they are percentages of the same thing.

The fee is a percentage of the cost. It is a percentage of what the customer paid.

Unsold is not lost. Stock that is still there tomorrow is not lost. Stock that cannot be sold tomorrow — the unsold lunches, the wilted flowers — is, and the difference is whether the thing keeps.

12. Mangoes at Monica's Market Stall

1. Write the lot: 200 mangoes bought for 180 dollars.

   $180 \div 200 = 0.90 \text{ if all sell}$

   Start from the optimistic figure so the leak can be measured.

2. Count the mangoes fit to sell: 20 were bruised.

   $200 - 20 = 180$

   Bruised fruit cannot be sold at the stall's price.

3. Spread the cost over the survivors.

   $180 \div 180 = 1.00$

   The same 180 dollars sits on fewer mangoes.

4. Find the card fee on a 2-dollar sale at 2 percent.

   $0.02 \times 2 = 0.04; \quad 2 - 0.04 = 1.96$

   The fee comes off the price before the money arrives.

5. Find what one sale keeps.

   $1.96 - 1.00 = 0.96$

   Both corrected figures, one subtraction.

13. A tray of pastries

1. Cost the tray as if every pastry sells.

   $300 \div 250 = 1.20$

   The optimistic figure, before the day happens.

2. Count the pastries sold: fifty were thrown out at closing.

   $250 - 50 = 200$

   The money for the fifty did not come back.

3. Spread the cost over those sold.

   $300 \div 200 = 1.50$

   A quarter more than the optimistic figure.

4. Measure the waste as a cost on each pastry sold.

   $1.50 - 1.20 = 0.30$

   This is what the fifty unsold pastries add to each one that sold.

5. Find the waste rate.

   $50 \div 250 = 20\%$

   A fifth of the tray was thrown away.

6. Decide which cost to price from.

   $\text{price from } 1.50$

   Baking fewer would cut the cost, but until that decision is taken, cost what happens.

14. A repair paid two ways, with a fixed fee

1. Write the sale: a 50-dollar repair using 25 dollars of parts.

   $50 - 25 = 25 \text{ kept if paid in cash}$

   Cash arrives whole.

2. The card contract charges 1.6 percent plus 0.20 a transaction. Find the percentage part.

   $0.016 \times 50 = 0.80$

   The percentage part grows with the price.

3. Add the fixed part.

   $0.80 + 0.20 = 1.00$

   The fixed part is the same on every transaction.

4. Take the fee off the price.

   $50 - 1.00 = 49.00$

   This is what arrives from a card payment.

5. Find what the card sale keeps.

   $49.00 - 25 = 24.00$

   The fee took 4 percent of the margin.

6. Do the same for a 5-dollar screen-wipe sale that cost 3.

   $0.016 \times 5 + 0.20 = 0.28; \quad 5 - 0.28 - 3 = 1.72$

   On a small sale the fixed part dominates.

7. Compare the fee's share of each margin.

   $1.00 \div 25 = 4\%; \quad 0.28 \div 2 = 14\%$

   The same contract takes a far bigger share of a small sale's margin.

15. Your turn: 50 mugs fired, 10 broken

1. The batch cost 200 dollars. Find the cost of a mug if all 50 sell.

   $200 \div 50 = 4$

   Start from the optimistic figure.

2. Ten broke. Count the mugs that carry the 200.

   $50 - 10 = 40$

   Broken mugs cannot be sold.

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

   Spread the cost over the survivors.

16. Guided practice

Neighborhood Kitchen loses about $50$ pastries in every $250$ to unsold at closing time — it happens every time, not just this once. Which cost per pastry should the price be built on?

• $1.5$ — the cost spread over the pastries that can be sold
• $1.2$ — the cost spread over every pastry bought
• $1.2$, because the loss is a separate problem to fix rather than a cost
• $3$ — the price already covers it

17. Guided practice

Complete the worked solution: a stall buys $96$ units for $243$ dollars and $15$ spoil. Each sells for $17$ dollars, paid by card at a fee of 5 percent. What does a sellable unit cost, and what does one sale keep?

1. Count the units left to sell.

   $96 - 15 =$ _s

   Spoiled units cost money and cannot be sold.

2. Spread the cost over the survivors.

   $243 \div (\text{left}) =$ _c

   The money is spent; only the units that sell can carry it.

3. Find the fee on one sale.

   $5\% \times 17 =$ _f

   The fee is a share of the price.

4. Take the fee off the price.

   $17 - (\text{fee}) = 16.15$

   This is the cash that arrives from one sale.

5. Subtract the true cost from the cash that arrives.

   $16.15 - (\text{cost}) =$ _k

   What one sale keeps uses both corrected figures.

18. Guided practice

Neighborhood Kitchen pays $420$ dollars for $120$ lunch boxes, and $15$ of them are unsold at closing time. What does one lunch box that can be sold actually cost, in dollars?

Answer:

19. Practice

A lunch box sells for $8$ dollars, and the card processor Neighborhood Kitchen uses takes $2.5$ percent of each sale under its contract. How many dollars reach the account?

Answer:

20. Practice

Maya's Ceramics pays $200$ dollars for $50$ mugs, of which $10$ are broken in the firing. It sells at $25$ dollars, and its processor keeps $1.6$ percent of each sale. How many dollars does one sale keep once both are counted?

Answer:

21. Practice

Monica's Market Stall buys in a lot of mangoes and sells them at $2$ dollars each. Fill in the missing lines.

22. Somewhere new

A flower stall buys $89$ bunches for a market day and sells at $9$ dollars a bunch, taking card only, on a contract that costs 2 percent of each sale. $14$ bunches wilt before the stall opens. Fill in the day.

23. Lesson test

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

24. Test question

Neighborhood Kitchen buys in a lot of pastries and sells them at $3$ dollars each. Fill in the missing lines.

25. What you can do now

You can recost a batch for its losses, take a payment fee off a price, and find what one sale keeps. Tell someone why a two percent fee can be a fifth of a margin. Next: the biggest missing cost of all — the owner's own work.

Working for the steps left to you

15. Your turn: 50 mugs fired, 10 broken, step 3