Back to the on-screen lesson ·
Two options laid out line by line, the lines that are the same either way struck out, the contribution given up counted, and the choice settled on what is left.
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 lay two options out line by line, strike every cost that is the same under both or already spent, and settle the choice on the costs that are left — including the case of a product line that shows a loss only because of a share of costs its closing would not remove. You will also count the contribution given up when a full resource is moved to other work.
You have compared two options on their figures, and you can tell a fixed cost from a variable or mixed one. This lesson asks which of an option's costs are allowed into the comparison at all. The answer is simpler than the arithmetic that usually surrounds it — only the costs the choice changes — and harder to hold on to, because the biggest numbers on the page are often the ones that should be struck out first.
| Term | What it means |
|---|---|
| Relevant cost | A cost that would be different depending on which option is chosen. |
| Shared cost | A cost the same under every option; not relevant to the choice. |
| Sunk cost | Money already spent, the same under every option; not relevant either. |
| Opportunity cost | The contribution given up by using a resource for one thing instead of another. |
| Price floor | The lowest price at which taking an order leaves the business no worse off. |
| Make or buy | The choice between producing something yourself and paying another business for it. |
Corner Bean is deciding whether to bake its pastries or buy them in. Alexa lists the monthly costs of each:
| Line | Bake in-house | Buy in |
|---|---|---|
| Ingredients or purchase price | 800 | 1500 |
| Extra kitchen hours | 500 | 0 |
| Oven power | 120 | 0 |
| Rent on the kitchen | 1400 | 1400 |
The rent is 1400 whichever she chooses. It is the biggest number on the page and it cannot tell the two options apart, so it is struck out. What is left: baking 1420, buying 1500. Baking saves 80 a month.
That is the whole method: a choice is decided by the costs that differ between the options. Strike every line that is the same either way, strike money already spent, and compare what remains.
Striking a shared line does not change the difference — 2820 against 2900 is still 80 apart. What it prevents is the step that usually follows: dividing the shared cost between the options by some rule, and then treating each option's share as a cost that choosing the other would save.
Another way: steps
Name the options exactly, and the period. Bake the pastries ourselves for the next twelve months against buy them from the bakery on the corner for the same twelve months. A comparison without a period cannot say whether a one-off cost matters.
List every cost of each option. Every line either option would have, even the obvious ones. Listing the rent under both, and then striking it, is clearer than leaving it off and wondering later whether it was forgotten.
Strike what cannot differ. Lines the same under both, and money already spent. Neither can make one option cheaper than the other.
Add what is not on any bill. If an option uses a resource that is already fully used — the only oven, the owner's last free hours — the contribution of the work it pushes out is a cost of that option.
Total what is left and compare. The difference is the saving, and the option with the smaller relevant total is the cheaper one.
Check by working the full totals too, every line included: the gap between them must be the same as the gap between the relevant totals. If it is not, a struck line was not really the same under both.
The costliest form of the mistake is closing something because of a cost it does not cause. A bakery charges each product line a share of the rent. The pie line sells 2500 a month, its own ingredients and hours cost 1800, and its share of the rent is 1000: on paper it loses 300.
Close it, and the 2500 of sales go, the 1800 of own costs go — and the 1000 of rent stays, paid now by the other lines. Profit falls by 700. The question is never does this line show a loss after its share? It is what would be different if it were gone?
Some relevant costs never arrive as an invoice. When a resource is already full, using it for one thing means not using it for another, and the contribution the other thing would have made is lost. That lost contribution is the opportunity cost of the choice, and it belongs in the comparison as surely as the timber does.
A workshop that is fully booked and asked to make a special table must count the table's timber and hours, and also the contribution of the stools it would have to turn away to make room. A price that covers the timber and hours but not the stools leaves the workshop worse off than if it had said no.
When the resource is not full — the joiner has idle hours this month — there is no work pushed out, and the opportunity cost is nothing. The same special order can therefore have a different price floor in a quiet month and a busy one, and both are right. What decides it is whether anything is given up.
A cost can be shared over one period and different over another. The kitchen rent is the same whether Corner Bean bakes or buys this month; if buying in for good would let Alexa give up the kitchen when its lease ends, then over the years after that the rent is a relevant cost of baking.
So the period named at the start matters. For a decision about the next month, the lease is shared. For a decision about the next five years, it may not be. Ask of every struck line whether it would still be the same under both options over the whole period — and if the answer changes partway through, split the period and compare each part.
Most of this lesson compares costs, because most small choices — make or buy, van or courier, print in-house or outside — leave the sales the same. When the options also change what comes in, the revenue that differs belongs in the comparison, and the rule is exactly the same: count what differs, strike what does not.
Opening on Saturdays brings Saturday sales as well as a Saturday wage. Buying pastries in rather than baking them may change what customers buy, if the bought ones are better or worse. A courier may deliver earlier in the morning and win an extra restaurant. In each case the comparison is no longer cost against cost but result against result: relevant revenue less relevant cost, for each option.
The mistake to avoid is the mirror image of the shared cost. Revenue the business will earn whichever option it chooses — the weekday takings, the restaurants that stay either way — is struck out just as the rent was. Only the sales the choice creates or loses decide it. Written as one line: the better option is the one with the larger relevant revenue less relevant cost, over the period named at the start.
A print shop with two presses runs them about 70 percent of the time. A school offers an order for 5,000 yearbooks at 6 dollars each, 30,000 dollars, spread over two weeks in May. The shop's usual costing, which adds a share of rent, rates, the presses' depreciation and the office to every job, puts the cost at 6.40 a yearbook, and the manager's first instinct is to decline.
The owner lists what would actually change. Paper and ink: 2.10 a book, 10,500. Binding, sent out: 1.20 a book, 6,000. Overtime for two press operators to fit it round the regular work: 1,600. Delivery: 400. The rent, rates, depreciation and office are the same whether or not the yearbooks are printed, so they are struck. Relevant cost: 18,500.
One more line. In the second week of May the presses would be full, and the shop would have to turn away about 2,000 dollars of contribution from regular customers' jobs — unless those customers can wait a week, which three of the four say they can. The opportunity cost is about 500.
Against 30,000 of revenue, the relevant costs of about 19,000 leave 11,000 toward the shop's fixed costs and profit. The share-of-overheads costing had turned a good order into an apparent loss. The owner accepts, confirms the delay with the three customers in writing, and schedules the fourth customer's job first.
Organizations that outsource cleaning, catering, payroll or IT are making the make-or-buy choice of this lesson. The careful ones compare the contractor's fee with the costs that would actually stop — not with a full-cost figure that includes a share of buildings and management that stay whatever is decided — and name the period, because a building or a manager freed in two years' time is relevant to a five-year decision and not to a one-year one.
Every cost of an option decides the choice. Only the costs that differ between the options do.
The biggest cost matters most. A large cost the same under both options matters not at all to the choice.
A shared cost must be split before choosing. Splitting adds the same total to the options and invites counting each share as a saving.
Money already spent must be counted. It is gone under every option; the next lesson is about exactly that.
A cost has to be on a bill to count. The contribution given up when a full resource is moved to other work is a relevant cost too.
Only costs are relevant. Revenue that differs between the options belongs in the comparison as well; revenue earned either way is struck, like the rent.
A wage is always a relevant cost. Not when the person is paid the same whichever option is chosen; then it is shared, and only overtime or new hours that one option needs are relevant.
List the van's costs: fuel 250, driving hours 450, servicing 120, lease 600.
$250 + 450 + 120 + 600 = 1420$
Every line of the first option.
List the courier's costs: fee 780, and the same lease of 600.
$780 + 600 = 1380$
Every line of the second.
Strike the lease.
$600 \text{ under both}$
It cannot decide the choice.
Total what is left for each.
$\text{van } 820; \quad \text{courier } 780$
The relevant totals.
Subtract the relevant totals.
$820 - 780 = 40$
The courier is 40 a month cheaper, the same gap as 1420 − 1380.
Read the line's report: sales 2,500, own costs 1,800, rent share 1,000.
$2500 - 1800 - 1000 = -300$
On paper, a loss of 300.
List what closing it would remove: the sales.
$-2500$
Customers who bought pies stop paying for them.
List what closing it would save: its own costs.
$+1800$
Pastry, fillings, the baker's extra hours.
Check the rent share.
$1000 \text{ still paid}$
The rent is the same with or without pies.
Find the change in profit.
$-2500 + 1800 = -700$
Profit falls by 700.
Say what the report should have shown.
$2500 - 1800 = 700 \text{ contribution}$
The line pays 700 toward the rent; the rest of the bakery would have to find it.
Cost the job's own parts: a board at 90.
$90$
Exists only because of this job.
Cost the technician's hours: 3 at 30.
$3 \times 30 = 90$
Paid for these hours whatever he works on.
Check whether the hours are free this week.
$\text{fully booked}$
The rush job would push out three screen repairs.
Cost the work pushed out.
$3 \times 45 = 135$
Each screen repair contributes 45.
Decide whether the wage is relevant.
$\text{paid either way} \Rightarrow \text{strike}$
The technician is paid whether he does the rush job or the screens.
Add the relevant costs.
$90 + 135 = 225$
The board and the contribution given up.
Read the price floor.
$225$
Charge less and the shop is worse off than doing the screens; in a quiet week the floor would be 90.
Strike the shared line.
$900 \text{ under both}$
The same under both options.
Total what is left.
$A: 300 + 200 = 500; \quad B: 450$
The relevant totals.
Subtract the relevant totals.
Corner Bean must decide whether to bake the pastries in-house or buy them in. The monthly costs of the two options, in dollars, are below. Fill in each line's difference (the second option less the first, with a minus sign where it is below zero), and total only the lines that differ.
| bake in-house | buy in | Difference | |
|---|---|---|---|
| Ingredients or purchase price | 900 | 1700 | |
| Extra kitchen hours | 600 | 0 | |
| Oven power | 100 | 0 | |
| Rent on the kitchen | 1500 | 1500 | |
| Total of the lines that differ |
Complete the worked solution: to print its own menus a café would pay $430$ dollars for paper and ink, $300$ for staff time and $70$ for printer servicing a month; a print shop would charge $880$. The café's rent of $850$ is the same either way. Which option costs less, and by how much?
Strike the rent.
$850 \text{ under both options}$
A cost the same either way cannot decide the choice.
Total the lines for printing in-house.
$430 + 300 + 70 =$ m
Only the costs that exist because of printing in-house.
Write the print shop's total.
$(\text{print shop}) =$ p
Its charge is the only line that differs on that side.
Subtract the in-house total from the print shop's.
$(\text{print shop}) - (\text{in-house}) =$ n
Above zero, printing in-house is cheaper by that much.
Check that the rent changes nothing.
$\text{adding it to both leaves the gap the same}$
A shared line adds the same to each side.
Corner Bean must decide whether to keep the printed loyalty card or move to an app. printed cards: Printing or subscription $120$, Staff time stamping cards $90$, Spoilt and lost cards $30$, Counter rent $1500$ dollars a month. the app: $260$, $0$, $0$ and $1500$ on the same lines. Which option costs less a month?
Dan is deciding whether Fixit Mobile should open on Saturdays. Mark every cost on his list that should play no part in the decision.
This task has no paper form; do it on a device.
A bakery's pie line sells $3300$ dollars a month. Its own costs — pastry, fillings and the extra baker's hours, all of which stop if the line stops — come to $2200$ dollars. It is also charged $1800$ dollars as its share of the rent and insurance, which the bakery pays whatever it bakes. On that basis the line shows a loss. If the pie line is dropped, by how many dollars a month does the bakery's profit change?
Answer:
A furniture workshop is fully booked. A customer asks for a one-off table needing $280$ dollars of timber and $7$ hours of the joiner's time, paid at $30$ dollars an hour. To make it, the workshop would have to turn away $6$ stools it would otherwise sell, each contributing $33$ dollars. What is the lowest price for the table that leaves the workshop no worse off?
Answer:
A caterer can make its desserts or buy them from a patisserie. Making them costs $600$ dollars of ingredients, $220$ of a pastry cook's extra hours and $50$ of gas a month; buying costs $610$ a month. The kitchen rent of $1800$ is paid either way. Fill in the comparison, in dollars a month.
| Amount | |
|---|---|
| Relevant cost of making | |
| Relevant cost of buying | |
| Buying less making | |
| What the rent adds to the gap |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Corner Bean is deciding whether to bake the pastries in-house or buy them in. bake in-house costs a month: Ingredients or purchase price $900$, Extra kitchen hours $600$, Oven power $100$ and Rent on the kitchen $1500$ dollars. buy in costs $1700$, $0$, $0$ and $1500$ on the same lines. How many dollars a month does choosing bake in-house save compared with buy in? If it costs more, write the saving with a minus sign.
Answer:
You can compare two options on their relevant costs, say what dropping a line would really change, and set a price floor that counts the work pushed out. Tell someone why the biggest cost on the page can have nothing to do with the choice. Next: money already spent, and why no choice can bring it back.
16. Your turn: option A costs 300, 200 and a shared 900; option B costs 450, 0 and the same 900, step 3
$500 - 450 = 50$
B is 50 cheaper.