Profitability trees and MECE decomposition

When profit falls, don’t guess why — split it into branches until the drop is trapped in exactly one of them.

The idea

Profit is just revenue minus cost, and each of those splits again: revenue into price and volume, cost into variable and fixed. Draw it as a tree and a vague problem — “profit’s down 30%” — becomes a search. Ask for one number per branch until the decline is cornered in a single leaf. Only then do you hypothesise why. The tree is only trustworthy if it’s MECE: the branches don’t overlap, and nothing falls through the gaps.

How it works

Write the identity, then fill the tree with real numbers and watch the pieces sum to the total gap:

Profit  = Revenue - Cost
Revenue = Price x Volume
Cost    = Variable cost + Fixed cost

                  Last year     This year     Change
Price / unit      $50           $50              0%
Volume            100,000       100,000          0%
Variable / unit   $30.00        $31.50          +5%
Fixed cost        $1,500,000    $1,500,000       0%

Revenue           $5,000,000    $5,000,000        $0
Variable cost     $3,000,000    $3,150,000  +$150,000
Fixed cost        $1,500,000    $1,500,000        $0
Profit              $500,000      $350,000  -$150,000  (-30%)

Every branch is flat except one: variable cost per unit rose 5%, and across 100,000 units that is exactly the $150,000 the client lost. The decline is localised — now, and only now, do you ask why the input cost rose.

MECE, in one check

A structure is only as good as its cuts. Pick a way to split revenue and see whether it holds up.

When to use it

Fits	Trade-off
Any “profits are down / costs are up, why?” case; sizing a P&L; before brainstorming causes.	The tree tells you where, never why. You still need hypotheses for the culprit branch — and the whole thing only holds if the cuts are MECE.

Watch out for

• Guessing causes before localising. “Maybe it’s the economy” is a hypothesis with no branch behind it. Reveal the numbers first.
• Overlapping branches. Putting mix beside price double-counts — mix already lives inside blended price. Overlaps inflate or hide the real driver.
• Gaps. Forget a cost line and the pieces won’t sum to the total; the culprit can hide in what you never split.
• Confusing rate with quantity. Variable cost per unit can rise while total variable cost falls if volume dropped. Always separate the rate from the count.
• Stopping at the first branch that moved. Several branches can move and partly cancel. Keep going until the revealed pieces sum to the whole gap.

Worked example

The interviewer says, “A snack maker’s profit fell 30% last year. Where would you look?” You don’t reach for causes. You write Profit = Price × Volume − Variable − Fixed and ask for four numbers. Price flat, volume flat, fixed flat — variable cost per unit up 5% as cocoa prices climbed. The entire decline sits in one branch. In four questions you’ve turned “profit’s down” into a precise, defensible diagnosis, and now you can talk about hedging inputs, reformulating, or repricing.

Check yourself