Percentages, margins and growth
“Revenue went from $100 to $144 in two years. What's the growth rate?”
Interviewers expect quick, clean mental math. Mixing up points and percent, or forgetting compounding, is an easy way to lose credibility.
A margin is profit ÷ revenue. Growth is change ÷ starting value. And growth compounds: each year grows on the year before.
The handful of calculations
Margin: what share of each dollar of revenue becomes profit. $60 of operating income on $400 of revenue is a 15% operating margin. Growth: change divided by where you started. $250 to $300 is 20% growth.
Points vs percent: a margin moving from 10% to 12% is up 2 percentage points, which is a 20% relative increase. Say which one you mean.
- 1$100 growing 20% a year: $100 × 1.2 = $120 after year 1.
- 2Then $120 × 1.2 = $144 after year 2, not $140.
- 3So growth from $100 to $144 over two years is a 20% compound annual growth rate (CAGR).
Dashed: cash flow that year. Filled: what it's worth today. The further out, the more it shrinks.
Try dragging FCF growth and watch EV.
A multiple is just value ÷ a measure of profit. A company worth $600 earning $50 trades at 12x. You'll use multiples constantly in valuation.
Say it like this
Margins are profit divided by revenue, and growth rates are the change divided by the starting value. Growth compounds, so 20% a year for two years turns $100 into $144, not $140, and that's a 20% compound annual growth rate. I'm also careful to separate percentage points from percent: a margin going from 10% to 12% is up two points, or 20%.
Traps to avoid
- ✕Adding growth rates instead of compounding them.
- ✕Mixing up percentage points and percent.
- ✕Dividing by the ending value instead of the starting value when computing growth.
What they'll ask next
›Roughly how long does money take to double at 9% a year?
About 8 years, by the rule of 72: 72 ÷ 9.
›If revenue grows 10% and costs grow 5%, what happens to the margin?
It widens, because profit grows faster than revenue.
›What's a P/E multiple?
Share price ÷ earnings per share, or equity value ÷ net income: how many years of profit the market is paying for.
Check yourself
Revenue is $400 and operating income is $60. What's the operating margin?