BUSI 103 - Introduction to Business (Chapter 5)
July 30, 2026
You already know how to compute a margin and a break-even - the question now is whether you can use one to make a call: which costs count for the decision in front of you, and what do the numbers say to do?
Read time ~24 min - ~3,637 words - problems ~50 min
Why this matters. Every operating decision - take the discounted order or pass, commit to the lease or stay flexible, spend more to acquire customers or fix retention first - lands on next quarter’s profit. The tools from the last two chapters stop being definitions here and start driving choices.
What you’ll be able to do.
The big ideas.
Key terms. relevant cost, sunk cost, avoidable cost, differential cost, unit economics, unit profit, customer acquisition cost (CAC).
A caterer charges $50 a person, pays about $30 a plate in variable costs - food, disposables, staff time - and carries $4,000 a month in fixed costs for the kitchen and equipment. One afternoon a corporate client calls about next month’s event: they want to add 50 more guests, but at $45 a head instead of $50. Taking it feels wrong - it is below the price everyone else pays, and the whole point of a price is to hold it.
Should the caterer say yes? Hold that question - by the end of the chapter, the answer takes about a minute of arithmetic, and the reasoning behind it is the whole lesson.
Profit is not just a result you look back on - it responds to what you do, and the job is to make today’s choices with tomorrow’s profit in view.
Profitability is shaped by the decisions you make. It’s not just something that we put after the fact. Lots of times we’re profitable and sometimes we’re not - there is some uncertainty around this - but there’s a way to intentionally raise the chances of you making profits, and it’s based on the decisions you make.
Looking backwards you can say, “Hey, are we profitable?” Every manager asks that. What I want to do is not take that question but think about today’s choices: how do today’s choices change tomorrow’s profit? Profits are always something that people see looking in the rearview mirror - a general performance of the past. We need to ask: how are our decisions today going to change that? Will these decisions improve or destroy profitability? How does our size affect our margins - does growth affect that a lot or a little, how much, and why? What costs are going to change if we take a different action, and which ones won’t? We always want to focus on what’s going to change versus stay the same based on actions we take.
We’ve talked about these concepts in the past - margins, break-evens, cost behavior - and now we want to be really explicit: how do we take what we know about these techniques and apply them in a certain context to make a decision? There’s no template or formula that works for every situation. You need to understand enough of the context and how to apply these tools. Each tool answers a different question:
Bottom line: the tools are the ones you already have - what changes in this chapter is that each one gets pointed at a decision.
There is no universally correct classification of a cost - the decision you are making picks the classification you need.
First: there is no universal correct classification of a cost. You need to know something about the context. Is something fixed or variable? Well, it changes with volume - and, more nuanced, it changes with volume in the time horizon we’re talking about. John Maynard Keynes was famous for saying that in the long run we’re all dead. Another thing about the long run: everything is mutable. Everything can change.
If you think about it for the next month, I have some employees and they’re expecting paychecks. Whether we have volume or not in the next week or the next month, we’re going to have to pay these guys. These people seem very fixed. But if you think about what our business is going to be in 10 or 15 years, we can make changes with the number of people we hire over that longer time horizon - we have the time to ease into that or make a fast change. Things that seem very fixed might not seem fixed if we have a long enough time horizon. Fixed or variable is always with respect to what time horizon. The faster we can change things, the more nimble we are. We can just decide whether or not to buy more, say, raw cloth if we’re making jeans, right away. If we made big volume commitments to get discounts, maybe those things aren’t so easy to change, because we’re contractually obliged to do it. Understanding fixed and variable isn’t just understanding what line item sits where on the income statement. It’s about understanding the context of our relationships with our suppliers and who we’re working with.
Then there is avoidable versus sunk. There are some costs that, by the way, don’t matter. What we’ve prepaid for - “don’t cry over spilled milk” - those are the things where we’ve incurred the cost and there’s no way to reverse it. It doesn’t change no matter what we do. Avoidable costs, on the other hand, are those where we could make a decision that allows us to turn that cost off. Some people just don’t think about it this way. They make this big investment and it’s irreversible: “I spent this money and I need to make my money back, because I’ve made this bad decision.” Now, I know that you’d like to - because you’d like to not make a loss - but it doesn’t matter whether you make the money back or don’t make the money back. This cost is going to be there. Rather than being locked into a behavior around a cost that you can do nothing about, you just need to acknowledge there’s nothing we can do about this either way. Sometimes trying to assuage the regrets we might have in the future can lead us to making bad choices, and we shouldn’t do that.
We’re always worried about, when we make choices, what changes - what’s different about the different choices? If nothing changes across the choices, that factor is irrelevant. A cost that does differ across the alternatives is a differential cost, and those are the relevant costs for the decision. We’re always wondering which costs and revenues will change because of a decision.
Bottom line: before you compute anything, ask which costs and revenues will change because of this decision - for this choice, everything else is noise.
When the fixed costs are already covered, any deal with positive contribution can add profit - even one below your usual price.
You know contribution margin from the cost behavior lens (Chapter 4): price minus variable cost, what every unit puts in our hands. Once fixed costs are covered, this contribution margin is what contributes to profit. We want to use this whole concept when we’re thinking about a deal - whether we should give some discounts, or whether we can produce more volume for somebody.
So, in my example, imagine we’re that caterer. Our price is 50 and our variable costs per plate are 30, so every single person that comes in here is a $20 contribution margin. The fixed cost that we’ve incurred - the kitchen and all that stuff - is 4,000, so to break even we have to have 200 guests. Now, what if somebody comes and says, “Hey, I have this event. Can I add some more guests?” We’ve already incurred this fixed cost. We would love to have more guests, because that’s going to help cover it. And then: “I’d like to have a discount. Instead of a price at 50, can we make it 45?”
Here’s the thing: if we’re already making this money, but volume is really going to help us, then even at a price of 45 we’re going to have positive contribution margin. We still have this fixed cost. We might be able to justify a lower price, or a discount on additional guests, or allowing a certain number of guests to come free - because if that’s going to win the deal, that’s going to be better. That’s one way where the insight in contribution margin helps us make a decision, often in the face of negotiating with a client.
Bottom line: judge a discounted deal by its contribution, and by whether winning it beats losing it.
Unit economics tests whether the business works one customer at a time - including what it costs to get that customer in the door.
Unit economics is another way of looking at it. We always try to simplify things, so instead of thinking about the whole business, we just ask: are we making money on this single customer? Because we do a lot of things with this customer the way we do for every customer - it’s a repeat process. If we’re making money at the customer level, that’s probably good at the business level, and if we’re not, we need to think about that more carefully. Unit profit is the revenue per unit we sell; we subtract off variable costs, and then we subtract off the share of fixed cost per unit.
And when we think about it, not only is there the cost of producing - there’s also the cost of selling. We might make a product, but we also have to find a customer, get the customer to come into the store, service that customer, and get them to buy it. That takes some cost too, and that’s what we call the cost of acquiring customers - customer acquisition cost, CAC - and that’s like a variable cost. For every business, we’re not just in the business of making things. We have to sell it too, and that comes with a cost.
This is why we’re not just chasing revenue. It could be that you’ve earned this dollar from a customer - congratulations - but you end up making a loss, because the cost to get that dollar could be higher. In that case you have negative contribution. That’s bad. We always want to know that if we’re doing extra effort, we are creating more value, and we’re capturing some of that value.
Here’s a mini example. Let’s imagine the price of what we sell is $35 a month and the variable cost is $20. It seems like we’re making $15 - but the cost of acquiring a customer is like $40. Customers stick around for three months, so we’ve got three runs at them.
\[ \text{Total CM per customer} = (\$35 - \$20) \times 3 = \$45 \]
Three months of contribution adds up to $45 per customer. Now subtract what it cost to get them:
\[ \text{Unit contribution after CAC} = \$45 - \$40 = \$5 \]
We’re only making $5 per person. It’s barely a positive contribution - and if people don’t stay for three months, something shorter, then we actually didn’t make money on that customer at all. We’re very vulnerable to people who don’t stay around long enough.
What we need to do is focus on how we can translate this insight into specific action. Maybe we really need to focus on retention of customers. Maybe we really need to focus on lowering what it takes to get customers in the first place - are there lower-cost channels to get in front of customers and give them our message? That kind of thing, in addition to the lever of whether we can raise price or lower variable costs. Breaking the business down this way tells us where we’re making money, where we’re not, and what kind of decisions are going to help turn this business from an unprofitable one into a profitable one. And it’s good to know all of this before you start investing a lot in scaling - if you scale something that’s unprofitable, you’re just going to make less profit at a bigger scale.
Bottom line: a model that loses money per customer does not get fixed by growth - find the losing lever first, then scale.
Break-even anchors feasibility - it names the volume you would have to believe in for the business to work.
The next one is a bit of a repeat from past lessons. Managers do this a lot, and the basic question is: how many units do we need to sell in order to cover our fixed costs? You have the formula from the cost behavior lens (Chapter 4) - fixed cost divided by contribution margin. An example: we have fixed costs of 10,000 a month, a price of 40, and variable costs of 20. We’re making $20 per unit, and that means we need to sell 500 just to cover our fixed cost. After that, every single subscriber pays us $40, costs us $20, and we’re making $20 on every customer after the 500th.
What that gives us is an anchor for feasibility. If this is what the business needs - 500 customers a month just to make nothing at all - then we can ask: do we think we can get 500 customers? And we can ask more concrete tactical questions: where would that volume come from? What basically has to be true to be successful, on some combination of price, cost, and volume?
It’s not that we ever have a goal of just breaking even. We obviously want to make a lot of profits. But this helps us understand what we would have to believe for this to work. Is our aspiration much further beyond that number, or do we feel that getting there would be risky?
Bottom line: break-even converts “is this viable?” into a concrete claim about volume that you can argue with.
Leverage tells you where profit is most sensitive to volume - and margin of safety tells you how much analysis the decision even deserves.
A sophisticated way of looking at this is operating leverage - the risk-and-reward view of break-even and scale. You know the idea from the operating leverage discussion (Chapter 4): when we have a lot of fixed costs, we have a lot of operating leverage, and profit becomes very sensitive to sales volume. Here the point is to read the number as a statement about your position. I worked through an example: if we have fixed costs of 200 and a contribution margin of just 4, and the quantity is around 80, our profits are going to be 4 times 80 minus the 200 in fixed costs:
\[ \pi = (4 \times 80) - 200 = 120 \]
The degree of operating leverage is the total contribution margin over that profit:
\[ \text{DOL} = \frac{4 \times 80}{120} = 2.67 \]
That means a 10% volume increase is going to be a 26.7% profit increase - volume moves up 10%, profit moves up more than 20%. Now, if the quantity is 30, profit is going to be 4 times 30 minus 200: negative. It’s a loss, and DOL is undefined below break-even. What that tells us, as we’ve talked about before, is that the degree of operating leverage is highest when we’re just above break-even, and small changes are going to change profits a lot. As the volume grows, the degree of operating leverage tapers off - and we can shift. We no longer worry about making that volume; we can shift to, “Hey, at this next level of volume, how do we get efficiency in the mix?”
The same math carries a decision-process point. We’re always getting information and good predictions and good data, especially about uncertain things, which is always costly and difficult in business - and you don’t want to waste your time doing that. If you’re saying, “Look, this is a situation of making a lot of money or a lot, a lot, a lot - like three times a lot of money,” then instead of trying to analyze which one, just take the step, because there’s very little risk of downside. We have a very large margin of safety. On the other hand, we spend a lot of time before making a move - or perhaps don’t make it at all - when we think it’s too difficult and too risky: a very slim margin of safety.
Bottom line: read DOL and margin of safety together as your risk posture - they tell you where you’re vulnerable, and how much the analysis itself is worth.
Each tool answers one question well - the craft is matching the tool to the decision, and then actually running the numbers.
These are all tools, and you’ve got to choose the right tool for the question you’re answering and the context you’re working in. Why do we want contribution margin? We want to evaluate whether this incremental deal or discount is going to actually add profits or not. When we’ve got fixed costs: this next order - should we take it? Should we not? What are the terms that would make it attractive? Unit economics: we can test whether the general business model is making money at the customer-and-product level. Break-even is when you’re getting in there and trying to say: do we have the volume in the future to justify our fixed costs? If you’re going to make another investment in more fixed cost, what volume do we need where we’re going to look back and say this was a good idea? That helps us get more comfortable with our decision. Then we can blend this all into a perspective on risk and reward by understanding: what’s our operating leverage? Where will we be most sensitive and most vulnerable? Where are we going to see profits really change? Depending on the question you’re trying to answer, you choose the right tool.
| Tool | The decision it serves |
|---|---|
| Contribution margin | Is this incremental deal, discount, or order worth taking? |
| Unit economics | Does the model create value per customer, before we scale it? |
| Break-even | Is the volume this business needs realistic - what has to be true? |
| Operating leverage | How hard will volume swings hit us, and how much risk are we carrying? |
Worked example: two ways into the coffee business. Two setups for the same idea. A coffee cart rents for $240 a day, pays $1 a cup in variable costs, and sells at $4. A pop-up table has no rent at all, but without the cart’s efficiency the variable cost is $2.50 a cup, selling at the same $4. Which one do you choose?
Step 1 - what does each cup contribute? Take price minus variable cost for each setup:
\[ CM_{cart} = \$4.00 - \$1.00 = \$3.00 \qquad CM_{popup} = \$4.00 - \$2.50 = \$1.50 \]
The cart makes twice as much on every cup - but its contributions have a $240 hole to climb out of first.
Step 2 - break-even. For the cart, we have to cover the rent:
\[ Q_{BE} = \frac{\$240}{\$3.00} = 80 \text{ cups} \]
Gotta sell 80 cups just to make nothing at all. In the pop-up there is no fixed cost to cover, so we are breaking even if we sell nothing. From the very first unit we sell, we’re going to be making some money - albeit less money, because the contribution margin is less.
Step 3 - profit at different volumes. At 60 cups the cart earns \(3(60) - 240 = -\$60\) - a loss - while the pop-up earns \(1.50(60) = \$90\). At 240 cups the cart makes $480 to the pop-up’s $360.
Step 4 - the crossover. Set the two profit equations equal:
\[ 3Q - 240 = 1.5Q \quad \Rightarrow \quad Q = 160 \text{ cups} \]
At 160 cups it kind of doesn’t matter which way you organize the business - same profit either way. Beyond it, which one is actually turning out the higher profit? The cart - because at that point it has covered all its fixed costs, and every single cup it sells, it sells at a higher contribution margin than the pop-up. If you think you’re going to sell a lot of volume - beyond 160 cups - you’d rather have the cart. Less than 160, you’d rather have the pop-up.
What choice do we make when we do the structure of this math? We have very good cut points: what do we need to expect about the future to make a good decision about how we want to get into the coffee business?
Bottom line: the toolkit doesn’t make the decision for you - it converts the decision into numbers you can hold your beliefs up against.
So does the caterer take the call? Run the toolkit. The relevant costs are the ones that change with the decision: 50 more plates at $30 each - the kitchen is already paid for, and nothing about the $4,000 changes. At $45 a head, each added guest still contributes $15, so the deal adds $750 of contribution. We’re already making this money, but volume is really going to help us cover that fixed cost - and if a discount on additional guests is what’s going to win the deal, that’s going to be better than losing it. The one thing to check is the relevance test from 5.2: would 50 more guests force a cost that doesn’t yet exist - another cook, rented equipment - and would the discounted price leak into what other clients expect to pay? If the answer to both is no, the caterer says yes. That is profit-informed thinking: start with what changes, price the contribution, check what has to be true, and know your risk posture before you commit.
5-1 The Band’s Venue Choice. [LO2, LO4] A band can play a bar for a flat $450, no costs, any turnout. Or it can rent a hall for $600, sell tickets at $25, and pay $3 per ticket in variable costs. (a) Compute the hall’s contribution margin per ticket and its break-even attendance. (b) Compute profit for both options at 30, 50, and 80 tickets. (c) Find the attendance at which the two options tie. (d) The band expects somewhere between 45 and 55 people. Use the margin-of-safety idea to advise them - and say what additional information would change your advice.
5-2 The Merch Table. [LO2] At the show, the band sells four items: a hoodie at $45 (cost $38), a T-shirt at $20 (cost $9), a poster at $12 (cost $4), and a sticker at $3 (cost $1). (a) Compute the contribution margin per unit for each item. (b) The lead singer wants to push the hoodie hardest “because it’s the most expensive thing on the table.” What would you push instead, and why? (c) State the general lesson about price versus margin in one sentence.
5-3 The Snack-Box Model. [LO3] A snack-box subscription charges $28 a month with $16 of variable cost per box. Acquiring a subscriber costs $54, and the average subscriber stays 5 months. (a) Compute the total contribution per customer and the unit contribution after CAC. (b) Recompute if average tenure slips to 4 months, and interpret. (c) Name three levers that could fix the model, and argue for which one you would prioritize.
5-4 The Studio’s Discount Ask. [LO1, LO2] A photography studio charges $900 per event, with about $300 of variable cost per event, and carries $2,500 a month in fixed studio costs against six typical bookings. A nonprofit asks for three events next month at $450 each. (a) Compute the contribution of the discounted work. (b) List the conditions under which the studio should say yes. (c) Identify one cost in this story that is irrelevant to the decision and explain why.
© 2026 Eric Lin. All rights reserved. This chapter is provided for students in BUSI 103 - please do not repost or redistribute without permission.