Back to the on-screen lesson ·
A month's profit worked again under fewer sales, a lower price and dearer costs, the change that overturns it, how far each assumption can move, and the volumes at which the month does not lose money.
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 work out a planned month's profit, work it again with one assumption changed at a time, find the change that turns it into a loss, and give the volumes at which the month does not lose money. You will also find how far each assumption can move before the profit is gone.
You can label a forecast's assumptions and measure what rests on each. The next question is which of them could actually change the decision, because a forecast has many assumptions and an owner has time to watch only a few. This lesson tests a plan one assumption at a time, finds the one that could turn a profit into a loss, and turns the test round to say how far each assumption can move before that happens.
| Term | What it means |
|---|---|
| Base case | The result with every assumption as planned. |
| Sensitivity test | Changing one assumption by a stated amount and working the result again. |
| Sensitive | Said of a result whose plausible change in one assumption overturns it. |
| Switch point | How far an assumption can move before the result crosses zero. |
| Break-even volume | Where profit is exactly zero. |
| Scenario | Several assumptions changed together, to describe one coherent bad or good month. |
Corner Bean plans 3000 flat whites a month at 4 dollars, each costing 2 to make, with 5300 of fixed costs.
$$\text{profit} = 3000 \times (4 - 2) - 5300 = 700$$
Now move each assumption on its own, by an amount Alexa thinks could happen:
Only the first turns the month into a loss. So of all the things in the plan, the number of cups is the one Alexa must watch weekly, and the one a buffer should be sized against.
Changing one thing at a time matters. Change everything at once and the result is a gloomy forecast, but not an explanation: nobody can tell which change did the damage, or which to watch.
Another way: steps
Another way: table
Corner Bean's sensitivity test, planned profit 700.
| Change | New figure | Profit | Overturns it? |
|---|---|---|---|
| 15 percent fewer sold | 2550 cups | −200 | Yes |
| 5 percent lower price | 3.80 | 100 | No |
| 10 percent dearer to make | 2.20 | 100 | No |
The same test with other percentages could point elsewhere, which is why each percentage needs a reason.
Work the base case carefully. Every test is measured against it, so an error there runs through all of them.
Choose each change from history. The worst month of sales in the last two years, the biggest supplier rise on the invoices, the deepest discount a competitor has run. A change with a reason is a question about something that has happened; a change without one is a guess.
Change one figure at a time. Keep everything else exactly as planned, including the fixed costs.
Work each result in full. Units times contribution, less fixed costs — not a shortcut that forgets which figure moved.
Name the assumption that crosses zero, and watch it most closely.
Check each test by the size of its fall. A volume change should cost the lost units times the contribution; a price or cost change should cost the change times every unit. If a result falls by more than that, the calculation changed something else too.
Test all three by the same ten percent and a pattern appears. A price that slips ten percent loses that ten percent of revenue on every unit, and all of it comes off profit. Ten percent fewer units lose only the contribution on the lost units. Ten percent dearer materials lose ten percent of the cost, which is smaller than the price.
So a business with a thin contribution is most sensitive to price, and a discount war is most dangerous to it. The size of each test still matters: sales can easily swing by fifteen percent in a wet month while a price rarely slips that far, which is why the café's volume assumption was the one that bit.
So choose each test's size from the business's own history: the worst month of sales in the last two years, the biggest supplier rise on the invoices, the deepest discount a competitor has run. A test sized that way is a question about something that has happened, not a scare.
Instead of asking what a given change does, ask how big a change it takes to wipe out the profit. The planned profit is the room every assumption shares.
Volume can fall by the planned profit over the contribution a unit. Corner Bean's 700 of profit over 2 a cup is 350 cups: the café can sell 2650 and still break even.
Price can fall by the planned profit over the units: 700 over 3000 cups is about 23 cents a cup.
Variable cost can rise by the same: 23 cents a cup, because a cent on the cost comes off every cup just as a cent off the price does.
Switch points are easier to read than sensitivity tests, because they can be set straight against what the owner knows. Could the café lose 350 cups a month? Yes, in a wet March. Could milk rise 23 cents a cup? Not without warning. The assumption whose switch point is within easy reach of normal ups and downs is the one to watch — and to hold a buffer against.
Real bad months rarely change one thing. A rainy week brings fewer customers and more discounting to fill the tables; a supplier's price rise comes with a delivery delay. Once the single tests have shown which assumptions matter, it is worth working one or two scenarios — a coherent bad month with several changes together — to see whether the business survives it.
The single tests stay the foundation, because they explain which change does what. The scenario answers a different question: not which assumption matters? but could we get through a month like that? A plan that survives its worst plausible scenario, with the buffer from an earlier lesson in place, is a plan an owner can sleep on.
A sensitivity test is worth doing only if it changes something. Once the assumption closest to its switch point is known, there are four kinds of response, and most plans use more than one.
Watch it. Put that one figure on the weekly check — cups sold, boxes ordered, the supplier's latest price — so that a slide is seen in the first week, not at the month's end.
Protect against it. A clause that lets a price move with ingredient costs; a minimum order in a contract; a deposit that keeps a cancellation from costing the full amount.
Widen the room. More planned profit moves every switch point further away. A slightly higher price or a slightly lower fixed cost often buys more safety than any amount of forecasting.
Hold a buffer against it. Size it against the scenario the test says is plausible, as the buffer lesson did.
Write the chosen response beside the test, so that the forecast says not only what could go wrong but what has been done about it.
A wedding caterer plans 20 weddings this season at an average of 6,000 dollars each, with food, staff and hire costing about 3,900 a wedding and fixed costs of 36,000 for the season: a planned profit of 20 × 2,100 − 36,000 = 6,000.
She tests three assumptions, each by an amount she has seen before. Two couples canceling, as happened two years ago: 18 × 2,100 − 36,000 = 1,800. Prices 5 percent lower to win bookings against a new competitor, 5,700: 20 × 1,800 − 36,000 = 0. Food costs 8 percent higher, as last year's invoices showed: 3,900 × 1.08 ≈ 4,212, so 20 × 1,788 − 36,000 = −240.
The switch points make the picture sharper. The season can lose 6,000 ÷ 2,100 ≈ 2.9 weddings, and the price or cost per wedding can move by 6,000 ÷ 20 = 300 before the season makes nothing. A 5 percent price cut is exactly 300; an 8 percent food rise is 312.
Food costs are the assumption closest to their switch point, and they have moved that far before. So she puts a food-price clause into her contracts, allowing a menu adjustment if ingredient prices rise by more than 5 percent before the wedding, and she refuses to match the competitor's price, which the tests show would leave no profit at all. A scenario of one cancellation and a 5 percent food rise still leaves about 200.
Banks and large companies run stress tests — the scenario version of this lesson — against sharp falls in sales, prices or asset values, to check that they would still meet their obligations. Regulators often specify the scenarios. The small-business version is the same idea at kitchen-table scale: find what matters, test it against what has happened before, and hold enough back to survive it.
Sensitivity means picking the most optimistic forecast. It means finding which assumption, if wrong, changes the answer.
Test everything at once. Then no one can see which change mattered.
A profitable plan is safe. A profit of 700 on 12000 of sales is one slightly bad month from a loss.
Every assumption deserves the same attention. Only the ones that overturn the result need watching closely.
A price change and a cost change have different switch points. A cent off the price and a cent on the cost both come off every unit, so they share one.
A test is finished when it is worked out. It is finished when the owner has decided what to watch, what to protect and what buffer to hold because of it, and has written those three decisions beside the figures for the next review to check.
Testing one assumption at a time misses nothing. Two small slips together can do more harm than either alone, so the worst case is worth one line of its own.
Work the base case: 100 screens at 80, costing 48, fixed costs 2,800.
$100 \times 32 - 2800 = 400$
The base case first.
Test ten percent fewer screens.
$90 \times 32 - 2800 = 80$
Still a profit.
Test five percent dearer parts, 50.40.
$100 \times 29.60 - 2800 = 160$
Still a profit.
Test a ten percent lower price, 72.
$100 \times 24 - 2800 = -400$
A loss.
Name the assumption that overturns the month.
$\text{price}$
The change that crosses zero is the one to watch.
Work the base case: 3,000 cups at 4, costing 2, fixed 5,300.
$3000 \times 2 - 5300 = 700$
The room every assumption shares.
Find the cups that can be lost.
$700 \div 2 = 350$
Each lost cup takes 2 of contribution.
Find how far the price can fall.
$700 \div 3000 \approx 0.23$
About 23 cents a cup.
Find how far the cost can rise.
$700 \div 3000 \approx 0.23$
The same 23 cents.
Compare with last year's worst month: 400 cups short.
$400 > 350$
Volume is within reach of a normal bad month.
Decide what to watch.
$\text{weekly cups, and a buffer sized on 400 short}$
The assumption whose switch point is closest to ordinary swings.
Work the base case: 150 boxes at 24, costing 9, fixed 2,100.
$150 \times 15 - 2100 = 150$
A thin planned profit.
Test ten percent fewer boxes.
$135 \times 15 - 2100 = -75$
A loss on volume alone.
Test a 2.5 percent lower price, 23.40.
$150 \times 14.40 - 2100 = 60$
Still a profit.
Test ten percent dearer boxes, 9.90.
$150 \times 14.10 - 2100 = 15$
Only just a profit.
Find the volume switch point.
$150 \div 15 = 10$
Losing just 10 boxes wipes out the month's profit.
Work a scenario: 10 percent fewer and 10 percent dearer together.
$135 \times 14.10 - 2100 = -196.50$
A coherent bad month.
Read what the tests say.
$\text{volume first, cost second}$
Tomasz watches box orders weekly and holds a buffer for a month like the scenario.
Work the base profit.
$60 \times 20 - 1100 = 100$
Contribution for the month less fixed costs.
Test ten percent fewer.
$54 \times 20 - 1100 = -20$
A loss on volume.
Find the volume switch point.
Corner Bean plans to sell $3000$ flat whites this month at $4$ dollars, each costing $2.00$ to make, with fixed costs of $5300$ dollars. Complete the sentence about the plan, in dollars.
The month's units contribute w dollars, which leaves a planned profit of p dollars.
Complete the worked solution: a shop plans to sell $240$ units at $30$ dollars, each costing $19$, with fixed costs of $528$ dollars. Find the planned profit and the profit if ten percent fewer sell.
Find the contribution a unit.
$30 - 19 =$ u
Price less variable cost.
Find the month's contribution.
$240 \times (\text{contribution}) =$ m
Every planned unit.
Take off the fixed costs.
$(\text{month's contribution}) - 528 =$ p
The base case.
Work the month with a tenth fewer units.
$216 \times (\text{contribution}) - 528 =$ a
One assumption changed; the rest as planned.
Read the test.
$\text{profit falls by a tenth of the contribution}$
Only the lost units' contribution goes.
Corner Bean plans to sell $800$ sandwiches this month at $8$ dollars, each costing $4.80$ to make, with fixed costs of $2400$ dollars. Three things could go wrong, one at a time: selling $5$ percent fewer, getting $2$ percent less for each, or paying $10$ percent more to make each. Which one on its own would turn the month's profit into a loss?
Corner Bean plans to sell $3000$ flat whites this month at $4$ dollars, each costing $2.00$ to make, with fixed costs of $5300$ dollars. Test two assumptions, one at a time: selling $15$ percent fewer, and paying $10$ percent more to make each one. Fill in the changed figure and the month's profit in each case, in dollars, with a minus sign for a loss.
| Changed figure: units, or cost a unit | Profit | |
|---|---|---|
| $15$ percent fewer sold | ||
| $10$ percent more to make each |
Corner Bean plans to sell $800$ sandwiches this month at $8$ dollars, each costing $4.80$ to make, with fixed costs of $2400$ dollars. Keeping the price and costs as planned, for which monthly volumes $n$ does the month not lose money?
This task has no paper form; do it on a device.
A bakery plans to sell $100$ cakes this month at $20$ dollars, each costing $11$ to make, with fixed costs of $720$ dollars: a planned profit of $180$. Fill in how far each assumption can move before the month loses money.
| Amount | |
|---|---|
| Cakes that can be lost | |
| Dollars the price can fall | |
| Dollars the making cost can rise | |
| Break-even volume |
A food truck plans $800$ meals a month at $10$ dollars, each costing $4$ to make, with fixed costs of $3200$: a profit of $1600$. Fill in the month's profit under each of three slips of ten percent, taken one at a time.
| Amount | |
|---|---|
| Profit with the price ten percent lower | |
| Profit with ten percent fewer meals | |
| Profit with making ten percent dearer |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Fixit Mobile plans to sell $100$ screen replacements this month at $80$ dollars, each costing $48.00$ to make, with fixed costs of $2800$ dollars. If it gets $10$ percent less for each one and nothing else changes, what is the month's profit in dollars? Write a loss with a minus sign.
Answer:
You can test a plan one assumption at a time, name the one that could overturn it, and find each assumption's switch point. Tell someone why a small slip in price usually hurts more than the same slip in costs. Next: what borrowing does to cash, now and later.
16. Your turn: 60 units at 50, costing 30, fixed costs 1100, step 3
$100 \div 20 = 5$
Five fewer units and the month breaks even.