Contribution margin
Price minus variable cost, per unit, or as a share of sales.
- Formula
- (Sales − variable costs) ÷ sales
- Not
- Revenue, or margin after fixed costs
Unit economics, LTV, CAC and payback, worked
Unit economics asks whether one unit of the business, usually one customer, makes more money than it costs to win. Lifetime value (LTV) is the contribution margin a customer brings over the time they stay, and customer acquisition cost (CAC) is sales and marketing spend divided by new customers won. If LTV is well above CAC and the cost is earned back well before the average customer leaves, growth creates value. Soreno, an AI voice interview practice app for consulting, investment banking and other finance candidates, runs free case math drills with no sign-up for the margin and ratio math, and full mock cases with scored feedback.
Updated
- LTV
- Margin a month × months kept
- Contribution margin, not revenue
- CAC
- Sales and marketing ÷ new customers
- Include discounts paid to win them
- Ratio target
- 3:1 is common, not law
- An HBS note finds the best ratio is often lower
- Worked case
- 0.79 to 2.4
- LTV to CAC, before and after the fix
What are the unit economics formulas?
Harvard Business School's 2022 note on customer unit economics defines unit economics as the ratio of a customer's lifetime value to acquisition costs. Four numbers get you there, and a fifth, payback, tells you how long the cash is tied up. The contribution margin, CAC, churn and lifetime value definitions come from the University of Notre Dame's 2026 Case Book, which lists them for consulting candidates (its lifetime value uses gross margin). Payback and the discounted LTV are added by us.
CAC
What one new customer costs to win.
- Formula
- Sales and marketing ÷ new customers
- Add
- Signup discounts and free trials
Churn and lifetime
How long a customer stays.
- Churn
- Customers lost ÷ total customers
- Lifetime
- About 1 ÷ churn
LTV and payback
Is the customer worth it, and when?
- LTV
- Margin × lifetime
- Payback
- CAC ÷ margin a month
Worked example: Fetchly (ours)6 steps
Fetchly, an invented pet food subscription, ships one box a month and wins 6,000 new customers a month. Sales are growing fast, but the company loses money. The investors ask: does each customer make money, and if not, what would fix it? Fetchly and every figure in it are made up for practice.
Margin per box
$16.20 a month, 27%
A box sells for $60. Food costs $33, shipping and packing $9 and card fees 3% ($1.80). That leaves $16.20 of contribution each month a customer stays.
Lifetime and LTV
About $181.80 a customer
8% of customers cancel each month, so the average customer stays about 1 ÷ 0.08 = 12.5 months, and only 37% are left after a year. The quick LTV is $16.20 × 12.5 = $202.50. Discounting each month's margin at 1% a month gives $181.80, so the quick version is about 11% too high. Use the lower one.
CAC
$230 to win a customer
Marketing spend is $1.2 million a month for 6,000 new customers, $200 each. Add the $30 first-box discount, a cost of winning them, and CAC is $230. By channel: paid social $320, search ads $150, referrals $66.67.
The verdict
LTV to CAC of 0.79
$181.80 ÷ $230 = 0.79. Each customer is worth less than they cost. Payback is $230 ÷ $16.20 = 14.2 months, longer than the 12.5 months the average customer stays. So faster growth means bigger losses: the business has to change before it spends more.
The fix
0.79 to 2.4
Three levers. Raise the price $5 and cut $3 of shipping by consolidating carriers: margin rises to $24.05. Bring churn to 6% with a pause option in place of cancel: lifetime 16.7 months, 48% left after a year. Stop paid social, where a customer costs $320: CAC falls to $144.29, at the price of 2,500 fewer new customers a month. LTV becomes $347.01, the ratio 2.4 and payback 6 months.
Recommend
Fix the unit, then grow
Pause paid social now, test the price rise and the pause option on new customers, and renegotiate shipping. Alone, each lever lifts the ratio to 1.17 (margin), 1.02 (churn) or 1.26 (CAC), so no single fix is enough. Restart paid social only if its CAC falls well below what one customer is now worth ($347.01), with payback well inside the 16.7-month lifetime. The main risk: the price rise pushes churn up and undoes the gain.
The formulas, one at a time6 formulas
Contribution margin
(Sales − variable costs) ÷ sales
Notre Dame's Case Book gives this formula and says it is used to decide break-even and pricing. Variable costs are the ones each unit adds: goods, delivery, payment fees, per-order support.
CAC
Sales and marketing ÷ new customers
The Case Book's formula. In a case, ask whether the spend includes salaries, discounts and free trials, and whether it is blended across channels or split by channel. Split CAC tells you which channel to cut.
Churn
Customers lost ÷ total customers
Also from the Case Book. Expected lifetime is about 1 ÷ churn in the same period: 5% a month means about 20 months.
LTV
Margin × lifetime, then discount
The Case Book defines customer lifetime value as average revenue per user × gross margin × customer lifetime. With a constant retention rate r and a discount rate i, the discounted version is margin × (1 + i) ÷ (1 + i − r) when margin arrives from the first period.
Payback
CAC ÷ margin per month
How many months until a customer has repaid what it cost to win them. It needs to be well inside the expected lifetime, and short enough for the company's cash to carry.
LTV to CAC
Value ÷ cost to win
Above 1, each customer is worth more than they cost. How far above depends on the business, which is why we compare it with payback and cash rather than a single target.
What the research says3 papers
Academic work on customer value warns against the shortcuts most case math uses. Use them anyway, but know the direction of the error.
HBS, 2022
3:1 is a common target, not the optimum
Ofek, Libai and Muller's note says a common target for unit economics, advocated by many VCs and analysts, is 3:1. Their analysis, which maximizes customer equity and allows for decreasing returns to marketing, finds the optimal ratio is often lower than 3:1, giving firms more leeway to grow.
Gupta et al., 2003
Lifetime from retention overstates value
Gupta, Lehmann and Stuart's paper in the Journal of Marketing Research says turning a retention rate into an expected lifetime and valuing that fixed period overestimates lifetime value. Their example: $100 of yearly margin, 80% retention and a 12% discount rate give $250 (margin counted from the end of the first year), against $360 by the five-year shortcut, about 44% too high.
Wharton, 2007
Retention rises with cohort age
Fader and Hardie show that a cohort's retention rate can rise over time even when each customer's own churn is constant, because the customers likely to leave go first. They call it the well-known ruse of heterogeneity and say it is often overlooked. Ask for churn by cohort age, not one average.
From HBS: On CUE, The Quest for Optimal Customer Unit Economics (2022), University of Notre Dame: 2026 Case Book (PDF), Gupta, Lehmann and Stuart: Valuing Customers (JMR, 2003, PDF) and Fader and Hardie: How to Project Customer Retention (2007, PDF).
What do interviewers listen for in unit economics?
In our experience, the math is easy and the definitions are where candidates slip. These are the moves we listen for.
Pick the unit out loud
A customer, an order, a store, a vehicle or a ride. The right unit is the one that repeats and drives the cost.
Margin, not revenue
LTV built on revenue makes almost any customer look profitable. Take off every cost the unit adds.
A full CAC
Include discounts, free trials and sales salaries, and split by channel when you can. Blended CAC hides the channel that loses money.
Payback against lifetime
Say how many months to earn back CAC and compare it with how long customers stay. That is the clearest yes or no.
Turn the ratio into a decision
Grow, fix the unit first, or cut a channel, with the lever that moves the ratio most.
7 practice questions with unit economics
Each one turns on what one unit earns against what it costs. Under each is what a strong answer does.
Customer economics
Is a customer worth what it costs to win?
A software company is growing 40% a year and still losing money. How would you assess whether that is a problem?
Splits the loss into what each new customer costs now and what each one earns over its life, then checks payback against churn. Practice it, see a model answer
A streaming service's monthly churn has doubled in a year. How would you find out why?
Converts churn into lifetime and LTV to show what is at stake, then splits churn by cohort, plan and channel to find the cause. Practice it, see a model answer
A meal kit company spends $150 to win a customer who orders five times at $12 of contribution each. Is that a good business?
Computes LTV of $60 against CAC of $150, says each customer loses $90, and asks what would have to change: retention, margin or CAC.
A regional bank's customer growth has stalled. How would you structure the problem?
Looks at new customers by channel and what each costs to win, alongside how many existing customers leave. Practice it, see a model answer
When the unit is not a customer
An order, a store or a vehicle.
A scooter-sharing company makes $1.20 per ride after variable costs. Each scooter costs $500 and lasts nine months. Does it pay back?
Needs about 417 rides per scooter, or about 1.5 rides a day over nine months, then compares that with the rides scooters actually get.
A coffee chain is opening a new store. How many cups a day does it need to sell to break even?
Uses the store as the unit: margin per cup against the store's fixed costs, then cups a day. Practice it, see a model answer
An airline is thinking about raising its checked bag fee. How would you decide?
Works out margin per bag before and after, how many passengers stop checking bags or switch airlines, and the net per flight. Practice it, see a model answer
Common unit economics mistakes in case interviews
These are the ones we hear most in practice cases.
Using revenue in LTV
At Fetchly, revenue over a lifetime is $750 against a margin LTV of $181.80. One looks like a great business, the other is losing money.
Leaving discounts out of CAC
A free first month or half-price first box is part of the cost of winning a customer. Leave it out and CAC looks smaller than it is.
Blended CAC only
Cheap referrals can hide an expensive paid channel. Ask for spend and customers by channel.
Mixing periods
Monthly margin with yearly churn, or the reverse, gives nonsense. Put everything in the same period first.
Treating 3:1 as a pass mark
A ratio is only as good as its inputs, and research finds the best ratio for growth is often below 3:1. Check payback and cash too.
Forcing customer LTV on every case
For a store, a factory or a scooter, the unit is the asset: what it earns per period against what it cost.
Run the numbers out loud
Soreno's AI interviewer runs a full case, gives you margin, churn and spend data when you ask, checks your LTV and CAC and scores the session. Start your free week.
Questions people ask
What is unit economics?
The profit or loss of one unit of a business, usually one customer: what it brings in over its life after variable costs, against what it costs to win. An HBS note defines it as the ratio of a customer's lifetime value to acquisition costs.
How do you calculate LTV?
Contribution margin per period times expected lifetime, where lifetime is about 1 ÷ churn. For a more accurate number, discount future margin: with retention r and a rate i per period, LTV = margin × (1 + i) ÷ (1 + i − r).
How do you calculate CAC?
Sales and marketing spend in a period divided by the new customers won in that period. Include discounts and free trials given to win them, and split by channel when you can.
What is a good LTV to CAC ratio?
3:1 is a common target among VCs and analysts, according to an HBS note, but the same note finds the best ratio is often lower. In a case, pair the ratio with payback and the company's cash.
What is CAC payback?
CAC divided by contribution margin per month: how many months a customer takes to repay what it cost to win them. It should be well inside the expected lifetime.
Should LTV use revenue or margin?
Margin. Notre Dame's Case Book builds customer lifetime value from revenue per user times gross margin times lifetime. Revenue alone makes customers look far more valuable than they are.
How do you get lifetime from churn?
Divide 1 by the churn rate for the same period: 8% a month gives 12.5 months. Gupta, Lehmann and Stuart show that turning retention into a fixed lifetime overstates value even after discounting that period, so treat the quick number as an upper bound.
Do unit economics come up in consulting case interviews?
Yes, in subscription, e-commerce, marketplace and growth cases, and any time a client is growing but losing money. The unit is not always a customer: it can be a store, a vehicle or an order.