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Total contribution under each, the fixed costs that differ, the gap between them, and the switch point that would overturn the answer.
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 compare two options by totaling the contribution each one makes, take off only the fixed costs that differ, and report the gap and which option it favors. You will also find the switch point for the estimate the answer rests on, and name what the arithmetic cannot see.
Dilla sells soup from a market stall. A cup goes for 6 dollars, and the soup, cup and lid in it cost her 2 dollars 40.
The pitch, the license and the insurance come to 1,080 dollars a month whatever she sells.
A depot has offered to take 200 cups a month at 4 dollars each, collected at closing time.
The pan holds them and the order costs her no market hours.
Her brother says 4 dollars is under what a cup costs once the pitch is counted in, so she should refuse.
March has 24 trading days, and Dilla needs 1,440 dollars of takings in the month to come out even.
Nine days in, the tin holds 460 dollars.
Two of those nine were the wettest days of the year and the market was half empty.
Her market pitch costs 1,080 dollars a month and sold 900 cups in a good month.
A pitch outside the station costs 1,400 a month, and last year's trader there sold about 1,200 cups.
Nobody has counted this year.
Everything in this course so far: contribution, volume, fixed cost, break-even and the minimum sustainable price. This lesson uses them together on the kind of decision owners actually face — this pitch or that one, this price or that one, this line or that one — and adds one habit: saying what the arithmetic did not settle, and how wrong an estimate would have to be before the answer changed.
| Term | What it means |
|---|---|
| Option | One of the courses of action being compared. |
| Differential comparison | A comparison that looks only at what differs between the options. |
| Relevant cost | A cost that changes depending on which option is chosen; the others cancel. |
| Total contribution | Contribution per sale times the volume, for one option. |
| Switch point | The volume at which two options give the same result, so the choice flips. |
| Sensitivity | How much the answer moves when an estimate moves. |
Read the two pitches. April's rent goes to one of them.
The station costs more and is said to sell more. Both halves of that are numbers, so the comparison can be done. What cannot be done is the last line: nobody has counted this year, and the answer turns on the figure nobody has.
So work out which pitch wins, and then how wrong the 1,200 would have to be before that changed.
A choice between two options is settled in two steps, and the second is the one people skip.
One: total contribution under each, less any fixed cost that differs. Not the price, not the contribution per sale, not the volume — the product of the last two:
$$(\text{price} - \text{variable cost}) \times \text{volume}$$
Any cost that is the same under both options drops out. If the rent is 900 either way, the 900 changes neither column's ranking and only gives you two more chances to subtract it wrongly. A cost that differs — a dearer pitch, a new machine for one option only — is taken off that option's total.
Two: name what would change the answer. Every one of these comparisons rests on a volume somebody estimated. Say which number you are least sure of and what it would take to overturn the result. The park wins by 350 dollars a month, assuming 400 cups; below 330 cups the station wins is a far more useful sentence than the first half alone.
This is how to work the number out and read it, not a recommendation about what to charge. What any particular business should do depends on a market nobody here can see, and on rules that differ from place to place.
Another way: steps
Another way: table
Two options at a kitchen, in dollars.
| Keep the price | Raise the price | |
|---|---|---|
| Price | 8 | 9 |
| Variable cost | 5 | 5 |
| Contribution | 3 | 4 |
| Boxes | 600 | 500 |
| Total | 1800 | 2000 |
A hundred customers lost, and the month is 200 dollars better. The arithmetic is clear and it is not the whole answer: whether those hundred were also buying coffee is a fact nobody has looked up.
Write each option down in the same form. Price, variable cost, volume, and any fixed cost that belongs to it alone. Options described differently — one as a price, the other as about 20 percent more sales — cannot be compared until both are turned into the same four figures.
Total each option's contribution. Contribution per sale times that option's own volume. Never compare per-sale figures or volumes on their own.
Take off only the fixed costs that differ. A dearer rent, an extra lease, a hired helper needed for one option only. Costs the same under both options cancel, and leaving them out keeps the comparison small and clear.
Subtract, and say which way. Option B by 740 a month is an answer; 740 is not.
Find the switch point. Take the estimate you trust least — usually one option's volume — and work out the value at which the two options tie. For a volume, that is the other option's net total, plus this option's extra fixed cost, divided by this option's contribution per sale.
Check the arithmetic by working each option's profit in full — total contribution minus all fixed costs — and confirming the difference between the two profits equals the gap you found. Then check the judgment: is the estimated figure comfortably beyond the switch point, or close to it?
A comparison on contribution sees money that changes with the choice this month. Several things that matter are invisible to it.
Effects on other sales. Raising a price may lose customers who were also buying something else; moving pitch may lose regulars who will not follow. Effects over time. A new pitch may start slowly and grow; a price rise may cost little now and more once competitors notice. Effects on the owner. An option that wins by 200 a month but adds ten hours a week may not be worth it at the owner's costing rate, and the comparison should include those hours if they are real. Risk. An option that wins on the expected volume but loses badly if the volume disappoints may be worse than a steadier one that wins by less.
None of these is a reason to ignore the arithmetic. Each is a reason to name it beside the arithmetic, so that the decision is made with the gap, the switch point and the unknowns in view together.
A short written note does this well: one line for the winner and the gap, one for the switch point and how close the estimate is to it, and one for each effect the arithmetic could not see, with a word on whether it points toward or away from the winner. Four or five lines are enough, and they make the decision easy to revisit when the facts change.
In most real comparisons, one estimate matters far more than the others. The way to find it is to change each estimate a little and see which one moves the answer most. In a pitch comparison it is nearly always the new pitch's volume; in a price rise it is how many customers stay; in a bulk-buy decision it is how much of the extra stock can be sold.
Once that figure is found, the useful next step is often not more arithmetic but a small, cheap test that measures it: a trial day at the new pitch, a price rise on one line for two weeks, a smaller bulk order first. A test that costs little and pins down the deciding figure is usually worth more than any amount of calculation on a guess.
Write the result of the test beside the comparison and redo the arithmetic with the measured figure in place of the estimate. If the answer holds, the decision is now made on evidence; if it flips, the test has just saved the cost of the wrong choice. Either way, the owner knows which figure mattered, and can keep measuring it after the decision — a new pitch that wins in its first month still needs its volume watched in its third, because the comparison was only ever as good as that one number.
A food truck owner currently parks outside an office park on weekdays, selling about 1,100 meals a month at a contribution of 5.50 each, with a pitch fee of 600 dollars. A brewery offers her its parking lot on Thursday to Sunday evenings for a fee of 1,000 a month. Its owners expect about 900 meals a month, and because people buy drinks from the brewery, not from her, her contribution per meal there would be the same 5.50.
The office park gives 1,100 × 5.50 − 600 = 5,450. The brewery gives 900 × 5.50 − 1,000 = 3,950. On the figures the office park wins by 1,500 a month. But the question she is really asking is whether to add the brewery evenings on top of her weekdays, not instead of them. Then the comparison is weekdays only against weekdays plus evenings, and the evenings add 3,950 − (her extra hours at her costing rate). At about 60 extra hours a month and a costing rate of 30, that is 3,950 − 1,800 = 2,150 better off.
The switch point matters too: the evenings stop paying once 5.50 × meals < 1,000 + 1,800, which is below about 509 meals a month. The brewery's estimate of 900 is well above that, so she agrees to a three-month trial with a monthly fee, not a year's contract — and counts meals from the first night.
Manufacturers regularly decide whether to make a part themselves or buy it in. The comparison is exactly this lesson's: the relevant costs of each option, with shared costs canceled, and a switch point at the volume where the two tie. Firms usually add the things the arithmetic cannot see — quality, reliability of supply, and what they would do with the freed capacity — before deciding.
Comparing per-sale figures. A 50 dollar contribution on 30 sales loses to a 32 dollar one on 70. Per-sale is half the answer.
Comparing volumes. Selling more is not earning more, and every lesson in this unit has been a way of saying so.
Carrying the identical costs through. They cancel. Including them is not wrong, only slower and more error-prone — and it hides how small the real difference between the options is.
Forgetting the shared constraint. If both options want the same bench, the same oven or the same Saturday, you cannot have both, and the comparison should be per hour of the thing that is scarce.
Presenting the winner without the assumption. The number that decided it was usually an estimated volume. Say so, and say how far it could move before the answer flips.
Total the screens: 50 dollars, 18 variable, 70 a month.
$(50 - 18) \times 70 = 32 \times 70 = 2240$
Contribution per sale times its own volume.
Total the boards: 90 dollars, 40 variable, 30 a month.
$(90 - 40) \times 30 = 50 \times 30 = 1500$
Better per job, fewer jobs.
Subtract the smaller total.
$2240 - 1500 = 740$
Screens win by 740 a month on a job that earns less than half as much each.
Find the switch point for the screens' volume.
$1500 \div 32 \approx 47$
Below about 47 screens a month, boards would win.
Name the unknown.
$\text{whether 70 screens hold up without advertising boards}$
It is comfortably above 47, but it is the figure to go and check.
Total the current plan: crates at 20, 180 sold at 25.
$(25 - 20) \times 180 = 900$
As she is.
Cost the bulk offer: 250 crates at 18.
$250 \times 18 = 4500$
The price list looks cheaper.
She can only sell 200. Find the cost of each crate sold.
$4500 \div 200 = 22.50$
Waste changed the variable cost.
Total the bulk plan.
$(25 - 22.50) \times 200 = 500$
More sales, less contribution.
Subtract the smaller total.
$900 - 500 = 400$
The discount costs her 400 a month.
Find how many she would need to sell for the bulk plan to tie.
$(25 \times x - 4500) = 900 \Rightarrow x = 216$
Only if she could sell 216 of the 250 would the discount break even.
Write each cup's contribution from the earlier reading: 6 less 2.40.
$6 - 2.40 = 3.60$
The same at either pitch.
Total the market pitch at 900 cups.
$3.60 \times 900 = 3240$
Its contribution in a good month.
Take off its rent of 1080.
$3240 - 1080 = 2160$
The rents differ, so each comes off its own option.
Total the station at 1200 cups and take off its rent of 1400.
$3.60 \times 1200 - 1400 = 4320 - 1400 = 2920$
Its result on last year's trader's figure.
Subtract the smaller total.
$2920 - 2160 = 760$
The station wins by 760 a month on those figures.
Find the station volume at which the two tie.
$(2160 + 1400) \div 3.60 \approx 989$
Below about 989 cups the market is better.
Say how wrong the 1200 would have to be.
$(1200 - 989) \div 1200 \approx 18\%$
An uncounted estimate 18 percent too high overturns it; a day of counting is worth doing first.
Total the mug option.
$140 \times 12 = 1680$
Per sale times volume.
Total the bowl option.
$80 \times 23 = 1840$
The same for bowls.
Subtract, and name what is missing.
Four figures from this course, and four questions an owner asks. Match each figure to the question it answers.
| Contribution per sale | Break-even in units | The contribution margin ratio | The margin of safety | |
|---|---|---|---|---|
| How much does one more sale add? | ||||
| How many sales does the month need? | ||||
| What share of each dollar taken survives the variable cost? | ||||
| How far above break-even are we trading? |
Complete the worked solution: option A contributes $3$ dollars a sale on $186$ sales. Option B contributes $5$ a sale on $196$ sales but costs $131$ dollars a month more in rent. Everything else is the same. Which is better, and by how much?
Total option A's contribution.
$3 \times 186 =$ a
Contribution per sale times its own volume.
Total option B's contribution.
$5 \times 196 =$ b
The same for the other option.
Take off the rent that differs.
$(\text{B's total}) - 131 =$ m
Only the fixed cost that differs between the options enters the comparison.
Subtract option A's total.
$(\text{B after rent}) - (\text{A's total}) =$ d
The gap in favor of option B.
Name the figure the answer rests on.
$\text{B's volume of } 196$
An estimated volume usually decides it, and should be said.
At Neighborhood Kitchen, option A is keep the box at 8 dollars and sell 600 a month and option B is raise the box to 9 dollars and sell 500 a month. Variable costs are $5$ and $5$ a sale. How many dollars a month separate the two, in total contribution?
Answer:
The numbers at Bright Home Cleaning favor the standard cleans by $198$ dollars a month. Which further figure would most change that conclusion?
Option A contributes $5$ dollars a sale on $1099$ sales a month. Option B contributes $7$ dollars a sale, at the same fixed costs, but its volume is only an estimate. Below how many sales a month does option B stop being the better choice?
Answer:
Northside Repairs is choosing between two options, with the same fixed costs either way. Option A: 70 screen replacements a month at 50 dollars, 18 of it variable, at $50$ dollars with $18$ of variable cost and $70$ sales. Option B: 30 board repairs a month at 90 dollars, 40 of it variable, at $90$ with $40$ and $30$. Work out what each contributes.
| Dollars | |
|---|---|
| Option A: contribution per sale, dollars | |
| Option A: total for the month, dollars | |
| Option B: contribution per sale, dollars | |
| Option B: total for the month, dollars | |
| Difference between the two, dollars |
A coffee cart can take one of two pitches, at the same rent. The station sells $743$ cups a month at a contribution of $3$ dollars; the park sells $425$ cups at $7$ dollars, because people buy pastries with them. By how many dollars a month does the better pitch win?
| Amount | |
|---|---|
| The station's contribution a month, dollars | |
| The park's contribution a month, dollars | |
| How much the park wins by, dollars |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Northside Repairs is choosing between two options, with the same fixed costs either way. Option A: 70 screen replacements a month at 50 dollars, 18 of it variable, at $50$ dollars with $18$ of variable cost and $70$ sales. Option B: 30 board repairs a month at 90 dollars, 40 of it variable, at $90$ with $40$ and $30$. Work out what each contributes.
| Dollars | |
|---|---|
| Option A: contribution per sale, dollars | |
| Option A: total for the month, dollars | |
| Option B: contribution per sale, dollars | |
| Option B: total for the month, dollars | |
| Difference between the two, dollars |
You can settle a choice between two options on total contribution, find the volume at which it flips, and name what the numbers did not settle. Tell someone why the option earning more on each sale can still be the worse of the two. That is the pricing unit: you can cost a unit, price it, find break-even, set a daily target and compare two plans on the figures.
16. Your turn: 140 mugs at 12 contribution, or 80 bowls at 23, step 3
$1840 - 1680 = 160$
Bowls win by 160, but only if the kiln can fire 80 bowls.