Back to the on-screen lesson ·
Cash paid for stock against the cost of what sold, and the stock left on the shelf as the difference between profit and what the account did.
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.
You will follow a month of stock through the business account and through the profit, work out both, and show that the difference between them is exactly the stock still on the shelf at what it cost — money turned into goods, not money lost. You will also measure how many days of selling the shelf holds.
You know that cash leaves for stock before a sale brings it back, and that working capital counts stock as something that will turn into cash. This lesson follows one month of stock through the account and through the profit, and finds out why the two disagree. The arithmetic is multiplication and subtraction; the idea is that the same purchase is told as two different stories, and both are true. By the end you will be able to point to the exact place where the money that seems to be missing actually is.
| Term | What it means |
|---|---|
| Stock | Goods bought to sell and not yet sold; also called inventory. |
| Cost of goods sold | What the units that actually sold cost to buy. |
| Stock at cost | What is left, valued at the price paid for it, not the price it will sell for. |
| Days of stock | Stock at cost divided by one day's cost of goods sold. |
| Write-down | Reducing the value of stock that has spoiled or will sell for less than it cost. |
| Stock count | Counting what is actually on the shelves, to check the records. |
Fixit Mobile buys 50 replacement screens at 28 dollars each and pays on delivery. That month it fits 30 of them at 75 dollars each. Two honest accounts of the month follow.
The account's story counts every dollar that moved. 1400 went out for the screens; 2250 came in from the repairs. The account is 850 dollars up.
The profit's story asks whether what was sold was worth selling. The 30 screens fitted brought in 2250 and cost 840 to buy. The line made 1410 dollars.
The two differ by 560 dollars, and the 560 is not a mistake. It is the 20 screens still in the drawer, at the 28 dollars each they cost:
$$\text{profit} - \text{change in the account} = \text{stock left at cost}$$
Profit waits to charge a screen until it is fitted, because that is when it earns anything. The account cannot wait: it paid for all fifty the day they came. So stock is cash in a different form — real, still the business's, and unable to pay a bill until a customer buys it.
Another way: steps
Another way: table
Fixit Mobile's screens for the month, in dollars.
| The account | The profit | |
|---|---|---|
| In from repairs | 2250 | 2250 |
| Out for screens | 1400 (all 50) | 840 (the 30 fitted) |
| Result | 850 | 1410 |
The 560 between them is in the drawer.
Count the units in and out. Units bought, units sold, and — from a stock count — units still on the shelf. Bought less sold should equal what is on the shelf; if it does not, something has been used, broken, lost or stolen, and that is worth knowing in its own right.
Price each story at the right figure. The account uses what was paid for every unit bought. Profit uses the price of the units sold against what those same units cost. Stock left uses cost, never the selling price, because the profit on it has not been made yet.
Work both results. The change in the account, and the profit.
Check that the difference is the stock. Profit less the change in the account must equal the units left times their cost. If it does not, one of the stories has used the wrong count of units — usually the cost of goods sold worked on units bought instead of units sold.
Where the stock was bought on credit rather than paid on delivery, the account has not paid for it yet, and the difference between the two stories is the stock less what is still owed for it. The same check works with that one extra line.
A supplier offers a tenth off for buying three months of stock at once. The saving is real and shows up in profit, slowly, as the stock sells. The cash leaves on the day of delivery, all of it. A business with a thin account can take a discount that raises its profit and still miss a payment the month it bought, because the money that would have paid the rent is now on a shelf.
The question to ask of any stock purchase is therefore two questions: will this sell at a profit? and can the account do without this money until it does? A bulk buy passes the first question easily and fails the second whenever the extra stock would take longer to sell than the business can wait for its cash.
Stock at cost on its own is hard to judge: 3,000 dollars is a lot for a café and very little for a hardware shop. Dividing it by one day's cost of goods sold turns it into days of stock — how many days the shelf would last at the current pace of selling.
$$\text{days of stock} = \frac{\text{stock at cost}}{\text{cost of goods sold} \div \text{days}}$$
Every one of those days is cash already paid and not yet back. A café whose milk lasts three days and whose beans last three weeks is holding very different amounts of money in each, and the long ones are where cash can be freed. Too few days has its own cost: running out loses sales and customers. The right figure is enough to cover the time a delivery takes to arrive, plus a margin for a busy spell, and not much more.
Unsold stock is not a loss — until it spoils, breaks, goes out of date or can only be sold for less than it cost. Then part of the cash turned into stock is not coming back, and the owner should say so by writing the stock down to what it will really fetch. Seedlings that wilt, a phone case for a model nobody uses any more, a Christmas gift box in February: each is worth less than it cost, and counting it at cost overstates both the stock and the profit. A regular stock count, with anything damaged or slow picked out, keeps the shelf's value honest.
Stock rarely sits at one level. A garden center fills its benches in March and empties them by June; a toy shop's stock peaks in November; a café's hardly moves. The cash tied up in stock rises and falls with it, and the month of the peak is the month the account feels thinnest, even when the year as a whole is profitable.
So the useful habit is to look at the stock figure month by month, beside the cash. A rising stock with flat sales means cash is going onto the shelf and not coming back; a rising stock ahead of a busy season is a decision, and it should be matched by a plan for where the cash comes from while it waits — supplier credit, a buffer, or a line of credit arranged in advance. A falling stock with rising sales is cash coming home, and the month to pay down anything borrowed for the peak.
The same arithmetic answers all three: stock at cost, days of stock, and the difference between profit and the account.
A bicycle shop orders its spring stock in February: forty bikes at an average of 400 dollars each, 16,000 dollars, paid on delivery because the wholesaler gives no credit on bikes. By the end of April it has sold twenty-five at an average of 650.
The owner's accountant reports a profit on the bikes of 25 × (650 − 400) = 6,250. The bank account tells a different story: 16,000 went out in February and 16,250 has come in, so the bikes have added only 250 dollars to the account. The owner, who had planned to pay for a new workshop bench out of the spring's profit, finds the money is not there.
The 6,000 between the two figures is the fifteen unsold bikes at 400 each, standing in the shop. It is not lost — they are good bikes, and May and June are busy months — but it cannot pay for a bench until they sell.
Next year she changes two things. She orders twenty-five bikes in February and fifteen more in April once she can see which models are selling, which keeps about 6,000 less on the floor through the spring. And she asks the wholesaler for thirty days on the second order, now that she has a year's record of paying promptly. The profit on the bikes is the same; the cash is in her account for two months longer.
Large manufacturers adopted just-in-time ordering — parts delivered hours before they are used — largely to keep cash from sitting as stock. Some fashion retailers restock shops several times a week in small quantities for the same reason, and to avoid being left with clothes nobody wants at the end of a season, which would have to be written down. Both trade a little extra delivery cost for a lot less cash on the shelf.
Unsold stock is a loss. It becomes one only if it spoils, breaks or can never be sold. Until then it is the business's money in another form.
Unsold stock is as good as cash. It cannot pay a bill. It is worth what it cost only if it sells, and it pays nobody before then.
Profit is what the account did. Profit charges the units sold; the account paid for the units bought. The difference is the stock.
Value the shelf at the selling price. Stock is counted at what it cost; the profit on it has not been made yet.
More stock is safer. More stock is more cash on the shelf, and more that can spoil or date. Enough to cover the next delivery, with a margin, is the safe amount.
Find the cash paid: 200 trays at 2 dollars, on delivery.
$200 \times 2 = 400$
The account pays for every tray bought.
Find the revenue: 120 sold at 5 dollars.
$120 \times 5 = 600$
Only the trays sold bring money in.
Find the change in the account.
$600 - 400 = 200$
The account's story.
Find the profit on the trays sold.
$600 - 120 \times 2 = 600 - 240 = 360$
The profit's story.
Find the stock left and check it.
$80 \times 2 = 160 = 360 - 200$
Eighty trays on the benches: cash waiting, not cash lost.
Note the purchase: 50 screens at 28, half paid on delivery.
$50 \times 28 = 1400; \quad 1400 \div 2 = 700$
700 leaves now; 700 is owed for thirty days.
Find the revenue: 30 screens fitted at 75.
$30 \times 75 = 2250$
Paid at collection.
Find the change in the account.
$2250 - 700 = 1550$
Only the half already paid has left.
Find the profit.
$2250 - 30 \times 28 = 2250 - 840 = 1410$
The same as if all had been paid on delivery.
Find the stock left at cost.
$20 \times 28 = 560$
Twenty screens in the drawer.
Check the two stories with the bill still owed.
$1550 - 1410 = 140 = 700 - 560$
The account is ahead of profit by what is owed less what is on the shelf.
Note the month's cost of goods sold: 4,500 over 30 days.
$4500 \div 30 = 150$
What a day's selling uses up at cost.
Count the stock at cost: beans 1,800, milk 300, cups and food 900.
$1800 + 300 + 900 = 3000$
The whole shelf, at what it cost.
Find the days of stock for the whole shelf.
$3000 \div 150 = 20$
Twenty days of selling, already paid for.
Look at the beans alone: 1,800 against 60 a day of beans.
$1800 \div 60 = 30$
A month of beans on the shelf.
Compare with the roaster's delivery time of 5 days, plus a margin of 5.
$5 + 5 = 10$
Ten days would be enough.
Find the cash freed by holding ten days of beans.
$(30 - 10) \times 60 = 1200$
Ordering smaller and more often frees 1,200.
Check the cost of the change.
$\text{more deliveries, the same beans}$
If the roaster charges nothing extra for smaller orders, the cash is freed at no cost.
Find the cash paid for the stock.
$60 \times 8 = 480$
Every box bought.
Find the profit on the 35 sold.
$35 \times 18 - 35 \times 8 = 630 - 280 = 350$
Only the boxes sold are charged.
Find the stock left and check it.
This month Corner Bean bought $60$ bags of retail coffee beans at $7$ dollars each, paid on delivery, and sold $35$ of them at $12$ dollars each, all paid at the register. Fill in the month two ways, in dollars. Write a change below zero with a minus sign.
| Dollars | |
|---|---|
| Cash paid for the stock | |
| Revenue from the units sold | 420 |
| What the units sold cost | |
| Profit on the line | |
| Change in the account | |
| Stock left on the shelf, at cost |
Complete the worked solution: a shop buys $80$ units at $8$ dollars each, paid on delivery, and sells $67$ of them at $15$ dollars each. Work out the cash paid, the profit, and the stock left.
Find the cash paid for the stock.
$80 \times 8 =$ x
The account pays for every unit bought.
Find the revenue from the units sold.
$67 \times 15 = 1005$
Only the units sold bring money in.
Find what the units sold cost.
$67 \times 8 =$ g
Profit charges only these.
Find the profit on the line.
$1005 - (\text{cost of units sold}) =$ f
Revenue less what those same units cost.
Find the stock left at cost.
$(80 - 67) \times 8 =$ l
The money waiting on the shelf.
Fixit Mobile bought $120$ phone cases this month at $4$ dollars each, paying on delivery, and sold $45$ of them at $12$ dollars each for cash. By how many dollars did this line change the business account? Write a fall with a minus sign.
Answer:
Corner Bean buys $36$ kg of coffee beans from the roaster at the start of the month and pays for them on delivery. During the month Alexa sells $59$ retail bags of $250$ g each and uses $5$ kg at the counter. How much coffee is still in the store at the end of the month?
Answer: unit: g / kg
At Corner Bean, the line of gift boxes for the holiday counter made a profit of $220$ dollars this month, but changed the business account by only $-50$ dollars. Where are the other $270$ dollars?
A hardware shop's cost of goods sold last month, a $30$-day month, was $1530$ dollars. Its stock at cost today is $2754$ dollars. At last month's pace, for how many days of selling does the shelf hold stock?
Answer:
A bookshop checks its shelves at the end of the month. It bought $27$ cookbooks at $12$ dollars each and sold $8$; $17$ atlases at $30$ dollars each and sold $2$; and $43$ notebooks at $4$ dollars each and sold $30$. Fill in the cash tied up in each product's unsold stock, and the total, in dollars.
| Amount | |
|---|---|
| Cookbooks, dollars at cost | |
| Atlases | |
| Notebooks | |
| Total tied up on the shelves |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Corner Bean bought $50$ gift boxes for the holiday counter this month at $9$ dollars each and sold $20$ of them at $20$ dollars each. What profit did the line make this month, in dollars?
Answer:
You can work out what a line of stock did to the account and to profit, name the difference between them, and turn a shelf into days of stock. Tell someone why unsold stock is neither a loss nor cash. Next: a buffer of cash kept against one named thing going wrong.
16. Your turn: 60 gift boxes bought at 8 dollars, 35 sold at 18, step 3
$25 \times 8 = 200 = 350 - 150$
The account rose 150; the 200 between is on the shelf.