ROI vs break-even vs payback: what each one hides

ROI, break-even and payback are the three numbers people reach for when deciding whether something is worth doing: a marketing campaign, a coffee machine for the office, a new product line. Each answers a different question, and each can make a bad decision look good if you read it alone. This article works through one example of each with our ROI and break-even calculator, then lists the traps. It is arithmetic, not financial advice.

Three questions, three numbers

• ROI asks: how much did it return, relative to what it cost?
• Break-even asks: how much do I need to sell before I stop losing money?
• Payback asks: how long until I have my money back?

None of them answers "should I do it?" on its own. Together they cover size, risk and time.

ROI, and why "per year" needs care

You invest 10,000 and two years later it is worth 12,500. ROI = (12,500 − 10,000) ÷ 10,000 = 25%.

Is that good? It depends on time. Split evenly, it is 12.5% a year, but that is not how growth works: the second year earns on the first year's gain. The rate that, compounded, turns 10,000 into 12,500 in two years is (12,500 ÷ 10,000)^(1/2) − 1 = 11.80% a year. That is the number to compare with a savings account or a loan rate. Over 18 months, 1,000 growing to 1,210 is a 21% ROI but 13.55% a year.

The gap between the simple and compound figures grows with time and with the size of the return. For a 100% ROI over 5 years, the simple figure is 20% a year; the compound one is 14.87%.

Break-even, worked through

A small shop sells a product at 20. Each unit costs 12 to make and deliver (variable cost). Rent, salaries and software cost 30,000 a month whatever happens (fixed costs).

1. Contribution margin per unit = 20 − 12 = 8. Each sale pays 8 toward fixed costs.
2. Contribution margin ratio = 8 ÷ 20 = 40%.
3. Break-even units = 30,000 ÷ 8 = 3,750 units.
4. Break-even revenue = 30,000 ÷ 40% = 75,000.

To earn a profit of 10,000 on top: (30,000 + 10,000) ÷ 8 = 5,000 units. At those 5,000 units, the margin of safety is (5,000 − 3,750) ÷ 5,000 = 25%: sales can fall a quarter before the month makes a loss. Operating leverage is contribution ÷ profit = 40,000 ÷ 10,000 = 4: a 10% fall in sales cuts profit by 40%. That is the number that tells you how fragile the plan is.

Margin and markup: the same profit, two percentages

The product above costs 12 and sells for 20, a profit of 8. As a share of the price, that is a 40% margin. As a share of the cost, it is a 66.67% markup. Both are correct; they divide by different things.

The trap is pricing with one and reporting with the other. A buyer who wants a 40% margin and adds 40% to a cost of 60 sets a price of 84. The profit is 24, and 24 ÷ 84 is a 28.6% margin, not 40%. To hit a 40% margin you divide: 60 ÷ (1 − 0.40) = 100. The conversions are markup = margin ÷ (1 − margin) and margin = markup ÷ (1 + markup).

Payback, simple and discounted

A machine costs 10,000 and saves 3,000, 4,000, 5,000 and 2,000 over four years.

• After year 1: −7,000. After year 2: −3,000. Year 3 brings 5,000, so the remaining 3,000 is recovered 3,000 ÷ 5,000 = 0.6 of the way through: payback = 2.6 years.
• With an even 3,000 a year it would be 10,000 ÷ 3,000 = 3 years 4 months.

Money received in year 3 is worth less than money today. Discounted payback divides each year's cash by (1 + rate)^year first. At 10%, year 1's 3,000 is worth 2,727.27 today, year 2's 4,000 is 3,305.79 and year 3's 5,000 is 3,756.57. After three years 210.37 is still missing; year 4's 2,000 is worth 1,366.03, so discounted payback is 3 + 210.37 ÷ 1,366.03 = 3.154 years, more than half a year later than the simple figure.

The traps

• Comparing ROIs over different periods. 25% in two years and 15% in one year are not comparable until both are annualised (11.80% and 15%).
• Dividing ROI by years. Simple averaging overstates the yearly rate of anything that compounds.
• Treating break-even units as a fraction. With fixed costs of 10,000 and a margin of 3 per unit, break-even is 3,333.33 units. You cannot sell a third of a unit: the real answer is 3,334.
• Forgetting that a price below the variable cost has no break-even. If each sale loses money, more sales lose more; the formula would return a negative number of units.
• Calling fixed costs fixed forever. They are fixed within a range. Double the volume and you may need a second shift or a bigger warehouse, which moves the break-even point.
• Mixing up margin and markup, as above. Agree which one a target means before anyone sets a price.
• Choosing by payback alone. Payback ignores everything after the recovery point. A project that repays in two years and then stops is ranked above one that repays in three years and earns for ten more.
• Ignoring the time value of money. Simple payback and simple ROI treat a dollar in year five like a dollar today. For anything longer than a year or two, use the discounted versions, and say which rate you used.

Using the three together

Start with break-even and the margin of safety to see how risky the plan is. Use ROI, annualised, to compare it with alternatives, including leaving the money in a savings account (the compound interest calculator shows what that would earn). Use discounted payback to see how long your cash is tied up. If all three look acceptable under pessimistic numbers, not just the expected ones, the plan is probably sound; if one looks good only under optimistic assumptions, that is the one to investigate.