Break-even analysis: 2 worked cases from finance interviews

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Break-even analysis finds the point where revenue covers every cost.

In a finance interview, getting that number is the easy part, and what gets scored is what you do after it: which cost you forgot, and who would have bought anyway.

I've had both of those turn a case around in real finance manager interviews. Below are the same two shapes with new numbers, so you can practise the turn.

It's part of our guide to finance interviews.

What is break-even analysis?

Break-even analysis finds the volume, price or rate where revenue exactly covers cost, so you make no profit and take no loss. The U.S. Small Business Administration gives it in units: take fixed costs and divide by what's left of the price after variable cost.

The piece that matters is the bottom of that fraction: price minus variable cost, the contribution margin, what each sale leaves over to pay for rent, salaries and anything else fixed.

When variable cost is a share of revenue, divide by the share you keep, so if 25 percent of every dollar goes to variable costs, each dollar covers 75 cents of fixed cost.

That last step is where finance interviews live, and the simple case on the financial analyst page walks the one-product version through in three numbers.

Case 1: the bike rental where maintenance flipped the answer

This looks like a pricing question until maintenance goes in and flips the answer. A bike rental business has 80 bikes and $8,000 a month of fixed cost, including $800 of depreciation. Variable costs run 25 percent of revenue, and bikes rent 4 times a month for 4 days, which is 1,280 rental days.

The break-even price. Divide $8,000 by the 75 percent you keep and spread it over 1,280 rental days, and you need $8.33 a day to cover everything.

Two options. The owner is comparing pay-per-use at $10 a day with a $30 monthly membership, and expects to sign 500 members.

On those numbers membership wins by $1,650 a month, and most people stop here.

In the real case I sat, this is where the interviewer added maintenance, and before I compared anything I worked out "how much it's going to cost us for light service and then how much it's going to cost us for heavy service".

That split is the whole case.

Say light service costs $2.50 every time a bike changes hands, and heavy service costs $4 for every 10 days a bike is ridden.

Members don't rent for 4 days at a time. They take short rides, say 3 a month, one day each, which is 1,500 handoffs a month against 320 for pay-per-use.

Membership goes from $1,650 ahead to a loss, and handoffs drove most of that cost.

The Corporate Finance Institute puts it plainly: when variable costs rise and demand doesn't, the break-even point goes up with them.

With maintenance in, membership needs about $32.93 a month to break even. At $30 it's priced too low for how members actually ride.

What to say after the number

Once you have the number, the interviewer wants to hear what could break it and how you'd find out cheaply. In my case I named the risks in the membership plan: whether that many members was realistic, churn, and "a little bit of seasonality".

Then I said the plan needs "the base case. Bull case as well as like bear case", and I'd start with a pilot and pre-signups before anything scales.

I learned that the hard way, which is the story on the FP&A interview page.

Case 2: the incentive that only looked cheap

This one looks cheap until you count who would have acted anyway. A company wants customers to switch from paper bills to email. Each paper bill costs $0.80 a month to print and mail, and a customer stays about 4 years, so every switch saves $38.40. The plan is to email non-switchers a $15 credit for going paperless, at 5 cents an email.

The first break-even. Each switch nets $38.40 minus the $15 credit, or $23.40. Divide the 5-cent email cost by $23.40, and the campaign breaks even if about 0.2 percent of people switch.

That looks like an easy yes.

The test. The company emails 4,000 customers and holds back a control group that gets nothing. In the test group 11 percent switch, and in the control group 9 percent switch anyway.

This is where I slipped in the real version.

I charged the incentive only to the extra switchers, the 2 percent lift, and the interviewer pointed out that the credit goes to every switcher in the test group, not just the new ones.

Once I saw it, I named it: the real issue was "incentive leakage". We were paying people who "would switch anyway without the actual campaign."

That's what a control group is for. Google's Conversion Lift does the same for ads, comparing people who saw them with people who didn't and counting only the increase the ad caused.

The real break-even. As I put it then, "we basically have to take that as like our baseline." Benefit comes only from switchers above 9 percent, but cost comes from every switcher, so break-even moves from about 0.2 percent to about 15 percent.

What I'd change before testing again

I wouldn't launch that campaign as designed. The test group switched at 11 percent against a break-even of about 15 percent, so it loses money and the honest answer is no. What I'd do instead is test a better version before anyone pays for a full rollout.

The fix is targeting.

The credit leaks to people who were going to switch anyway, so aim it at the ones who weren't.

In the case, I suggested splitting the list and starting with customers who are "less digitally active".

Break-even outside the interview room

Outside the interview room, the break-even question is rarely a unit count. It's usually whether the customers you'd need exist. I once worked on a pricing idea to offer a fixed price next to the variable one, to smooth out revenue.

The problem was that if everyone went for fixed price, "we'd actually have to sign up more people", and the market had no room for that many more, so we didn't do it.

If pricing work like that appeals to you, what an FP&A manager does shows where it sits in the week.

How to walk an interviewer through a break-even case

Walking an interviewer through a break-even case comes down to order. Read the inputs back before you touch the math, and say how you'll set it up. Then get the number and say out loud what drives each cost, because the first number is where the conversation starts.

Both cases I sat turned on something the first number left out, a cost driver in one and a baseline in the other.

Find the missing piece before the interviewer hands it over.

The other case that turns up often hands you a plan and an actual instead. Variance analysis interview questions works one miss through to a bridge that ties.