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What one unit costs

Totaling a batch — materials, hours at a rate, a share of overhead — and dividing by the units that can actually be sold.

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 build the cost of one unit from a batch: total the materials, the hours worked at an hourly rate and the batch's share of the indirect costs, then divide by the units good enough to sell. You will also say how much the units that could not be sold add to the cost of the ones that could, and check a unit cost by multiplying it back.

2. What you already have

You can sort costs two ways: direct or indirect, fixed or variable. Now the two cuts are put to work on one batch, and the result is the first number in this course you could put a price beside. Everything from markup to break-even starts from the unit cost you build here, so a mistake in it travels into every later figure.

3. Words this lesson uses

4. Total the batch, then divide by what you can sell

Unit cost is one division, and both of its numbers are easy to get wrong.

$$\text{unit cost} = \frac{\text{everything the batch cost}}{\text{units good enough to sell}}$$

The top has three lines, and small businesses reliably write down one of them. Materials get counted. The owner's own hours usually do not, and the batch's share of rent and power almost never does. A unit cost built from materials alone is not a small underestimate; it is often half.

The bottom is the count of units a customer could pay for. Some of what you made cannot be sold — broken, spoiled, unsold at closing. Those units cost money and earn none, so their cost has to be carried by the ones that do sell. Dividing by the units you started with hands that cost to nobody, and nobody does not pay.

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

Choose a normal batch. A batch is a sample of how the business works. Pick one that is typical, or average three, and say which. A batch with a freak kiln failure gives a unit cost that is true of that day and false of the business.

Line one: materials. Everything the batch consumed, at what it cost you: the clay and glaze, the ingredients and boxes, the crates bought in. Count what was used, including the offcuts and the extra you always make, not the amount in the recipe.

Line two: labor. Hours worked on the batch times an hourly rate. The owner's hours count. If the owner is paid nothing, the rate is still what those hours are worth — lesson 5 separates the senses of that — because a unit cost without them describes a business that only works while someone works for free.

Line three: overhead share. The batch's share of rent, power, insurance and the other shared costs. Lesson 7 shows how to choose the share; for now it is given to you.

Count the sellable units and divide once. Add the three lines, count what a customer could buy, and divide.

Then check. Multiply the unit cost back by the sellable units: you should get the batch total exactly. Compare the unit cost with materials alone: if they are almost the same, one of the other two lines is missing. And compare it with the price: a unit cost above the price means the business loses on every sale, and it is better to find that out on paper.

6. Why the divisor matters as much as the total

Losses are not an accident on top of the cost; they are part of it. A baker who throws away one loaf in ten is really paying for ten loaves to sell nine, and the price of each of the nine has to carry the tenth. If she divides by ten, her unit cost is ten percent low; if the losses are one in four, as they can be for fresh food at a market, it is a quarter low.

Nothing here is wasted twice. The money for the lost units was spent once; dividing by the sellable units simply shares that same money among the units that bring money back. The difference between the two unit costs is exactly the batch's losses spread over what sold, which makes it a useful number in its own right: it is what reducing waste is worth, on every unit, for as long as the improvement lasts.

7. A unit cost that has not been checked is a guess

The most common unit-cost error is not arithmetic; it is a missing line. Materials are visible because they arrive with a receipt. Hours are invisible because the owner does them, and the overhead share is invisible because it is paid monthly, not by the batch.

A simple habit catches both: write the three line names first, before any numbers, and do not divide until each has a figure. A zero is allowed if it is true — a reseller buying finished goods may have almost no labor on a batch — but it should be written down as a zero, not left out.

8. The same three lines in a shop and in a service

The batch looks different in each trade, and the three lines do not change.

For a reseller the materials line is usually the largest, because the goods arrive finished; labor is small but not zero. For a service the materials line is small and labor is almost everything, so leaving out the owner's hours does not make the unit cost a little low — it makes it nearly nothing. A cleaner who costs a clean at the price of the cloths and fuel has costed the van ride and forgotten the job.

The divisor needs the same care in a service. A booked clean that is canceled on the doorstep still used fuel and an hour, and earns nothing unless a cancellation fee is charged. A week of 30 bookings with 3 cancellations is a batch of 27 sellable cleans, and the unit cost has to be the week's total divided by 27.

Whatever the trade, write down what the batch was, which three figures went into its total, and what you divided by. Those three statements turn a unit cost from a number someone remembers into one somebody else can check, and they are the first thing to look at when a price that should have worked does not.

9. In the world: a bakery's sourdough

A neighborhood bakery bakes 120 sourdough loaves on a Saturday. Flour, salt, the starter's feed and the paper bags come to 66 dollars. The baker and one helper spend 7 hours each on the dough, shaping and the bake, costed at 22 an hour: 7 × 2 × 22 = 308. The bakery assigns 70 dollars of the week's rent, oven gas and insurance to the Saturday bake. The batch total is 66 + 308 + 70 = 444 dollars.

Six loaves come out misshapen and are sold off at a discount to a café, and 14 are unsold at closing and given to a food bank. So 100 loaves are sold at full price. The unit cost is 444 ÷ 100 = 4.44 dollars a loaf. Divided by the 120 baked it would have been 3.70, and a price of 5 dollars would have looked like a 26 percent margin when it was really 11 percent.

Two things follow. The bakery now knows what cutting the unsold loaves from 14 to 4 is worth: 444 ÷ 110 = 4.04, forty cents off every loaf. And it sees that materials are only 15 percent of the cost, so haggling with the flour mill matters far less than planning the bake to match the Saturday crowd.

10. In the world: yield in a factory

Manufacturers call the share of started units that come out good the yield. A chip factory whose yield rises from 70 to 90 percent has not made its materials any cheaper, but its cost per good chip falls by more than a fifth, because the same batch total is now carried by 90 units instead of 70. That is why plants report yield alongside cost: it is the divisor in this lesson, measured every day.

11. Where this goes wrong

Materials are the cost. They are one of three lines. The owner's hours and the share of overhead are the two that get left out, and together they are usually the larger half.

Divide by what you made. Divide by what you can sell. The gap is small on good batches and enormous on bad ones, and it is exactly the cost of the losses.

Divide early. Work out a cost per unit for materials, then another for labor, then forget the third — it happens constantly. One total, one division, at the end.

The losses are counted twice. They are not: the batch total is the same money either way, shared among fewer units.

One batch is the truth. A batch with an unusually bad firing gives an unusually high unit cost. Use a normal batch, or average several, and say which you did.

12. Crates at Monica's Market Stall

1. Add the materials: 25 crates bought at 2.40 each.

   $25 \times 2.40 = 60$

   The crates are what the batch consumed.

2. Cost Monica's hours: 5 hours at 16 an hour.

   $5 \times 16 = 80$

   Her time loading, setting out and selling is part of the batch.

3. Add the stall's share of overhead and total the batch.

   $60 + 80 + 20 = 160$

   All three lines are in the total before anything is divided.

4. Count the crates good to sell: 5 were bruised.

   $25 - 5 = 20$

   A bruised crate cannot be sold at full price.

5. Divide the batch total once.

   $160 \div 20 = 8$

   Each sellable crate carries 8 dollars, including its share of the bruised ones.

13. A morning of lunch boxes

1. Add the ingredients and packaging for 50 boxes.

   $\text{materials} = 135$

   Line one, the easy one.

2. Cost the owner's nine hours of prep and service at 20.

   $9 \times 20 = 180$

   Line two, the one usually missing.

3. Add the kitchen's share of rent and power.

   $\text{overhead share} = 45$

   Line three, the one almost never there.

4. Total the batch.

   $135 + 180 + 45 = 360$

   One total before any division.

5. Count what sold: five boxes were left at closing.

   $50 - 5 = 45$

   Unsold food is a loss like a broken mug.

6. Divide once, and check by multiplying back.

   $360 \div 45 = 8; \quad 8 \times 45 = 360$

   The check returns the batch total exactly.

14. The same batch costed badly, and what it hides

1. Cost the boxes from ingredients alone, divided by the boxes made.

   $135 \div 50 = 2.70$

   This is the number most owners would give.

2. Set a price on that figure with a comfortable markup.

   $2.70 \times 1.5 \approx 4.00$

   The price looks like a 48 percent margin on paper.

3. Compare the price with the true unit cost.

   $4.00 - 8.00 = -4.00$

   The kitchen loses four dollars on every box it sells.

4. Find how much of the gap is the missing labor.

   $180 \div 45 = 4.00$

   The owner's hours alone are four dollars a box.

5. Find how much is the overhead share.

   $45 \div 45 = 1.00$

   The rent and power are another dollar a box.

6. Find how much is the wrong divisor.

   $135 \div 45 - 135 \div 50 = 3.00 - 2.70 = 0.30$

   The unsold boxes add thirty cents of materials to each box sold.

7. Add the three gaps to the bad figure.

   $2.70 + 4.00 + 1.00 + 0.30 = 8.00$

   Two missing lines and one wrong divisor account for the whole difference.

15. Your turn: a firing of 40 mugs at Maya's Ceramics

1. Cost Maya's 6 hours at 15 an hour.

   $6 \times 15 = 90$

   The labor line is hours times the rate.

2. Add clay and glaze of 72 and a kiln share of 18.

   $72 + 90 + 18 = 180$

   All three lines in one total.

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

   Four broke in the firing. Count the mugs good to sell and divide.

16. Guided practice

Put the four steps of costing a batch of $32$ units into the order you do them.

Number the steps in order (write the number in the box):

• Add up the materials the batch used
• Add the owner's hours on the batch at an hourly rate
• Add the batch's share of the indirect costs
• Divide the total by the units good enough to sell

17. Guided practice

Complete the worked solution: a batch of $24$ units uses $49$ dollars of materials and $6$ hours of the owner's time at $13$ dollars an hour, and carries $137$ dollars of overhead. $2$ units are spoiled. What does one sellable unit cost?

1. Cost the owner's hours.

   $6 \times 13 =$ _l

   The owner's time is a line of the batch cost, at an hourly rate.

2. Add materials, labor and overhead.

   $49 + (\text{labor}) + 137 =$ _t

   Every cost goes into one total before anything is divided.

3. Count the units good to sell.

   $24 - 2 =$ _s

   Spoiled units cost money and earn none.

4. Divide the total by the sellable units.

   $(\text{total}) \div (\text{sellable}) =$ _c

   The units that sell carry the cost of the ones that did not.

5. Check the answer by multiplying back.

   $(\text{unit cost}) \times (\text{sellable}) = (\text{total})$

   A division is checked by the multiplication it undoes.

18. Guided practice

Neighborhood Kitchen makes a batch of $50$ lunch boxes. Materials cost $135$ dollars, the owner's $9$ hours are costed at $20$ dollars an hour, and the batch carries $45$ dollars of overhead. $5$ were left unsold at closing time. What does one sellable lunch box cost, in dollars?

Answer:

19. Practice

At Neighborhood Kitchen the batch of $30$ cost $120$ dollars and $6$ were left unsold at closing time. How many dollars does the loss add to the cost of each pastry that is left?

Answer:

20. Practice

A batch at Neighborhood Kitchen, in dollars. Fill in the missing lines and give the cost of one pastry that can actually be sold.

21. Practice

Put the four steps of costing a batch of $56$ units into the order you do them.

Number the steps in order (write the number in the box):

• Add up the materials the batch used
• Add the owner's hours on the batch at an hourly rate
• Add the batch's share of the indirect costs
• Divide the total by the units good enough to sell

22. Somewhere new

A print shop runs $447$ flyers for a customer at a total cost of $287$ dollars, and $37$ of them come out misaligned and are binned. What does each flyer the shop can deliver cost, in dollars?

23. Lesson test

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

24. Test question

A batch at Monica's Market Stall, in dollars. Fill in the missing lines and give the cost of one crate of mangoes that can actually be sold.

25. What you can do now

You can cost a batch on three lines and divide by the units that can be sold. Tell someone what happens to your unit cost if you divide by the units you started with instead. Next: the losses and the fees, counted properly.

Working for the steps left to you

15. Your turn: a firing of 40 mugs at Maya's Ceramics, step 3