Why it multiplies
Some losses come off the total once and are done. Others divide everything that depended on them. The books record both the same way, as one line. Here is how to tell which one you are looking at before it happens.
One question sorts them
If all of it disappeared tomorrow, would anything else stop or slow down? If nothing would, the loss is its own size and no more: a subtraction. If something would, the loss is passed along, and that is where multiplying starts.
It stands alone. Cancel a magazine nobody reads and you lose a magazine nobody reads.
Other things need it, one after another. The baker, the oven and the van: lose any one and no bread arrives.
One thing affects several, and each of those affects several more. One late supplier, five late products, every customer waiting on each.
Each step gains less than the last. Past a certain step you pay full price for almost nothing.
Each step costs more than the last. It never levels off; it has to be stopped.
The result goes below zero. The climb back is steeper than the fall, and whatever compounds now compounds against you.
The multiple: links in a chain
A cost is taken off once. An input is different: each step of the work can only pass on what it was given. Take a tenth away at one step and the next step starts with nine tenths, then passes on nine tenths of that.
The cascade: one thing touching many
A chain passes a loss along a line. A cascade passes it outward. If one thing affects three others, and each of those affects three more, the count does not add, it multiplies at every layer. This is the one place the word exponential is exact: the number touched is a power of how many layers it spreads through. The separate parts of a business it reaches (the work, the know-how, the selling, the customers) are its dimensions, and the loss multiplies across those as well.
The climb back is steeper than the fall
A loss is measured against what you had. The gain that repairs it is measured against what is left, which is smaller. So the two percentages are never the same, and the gap opens fast.
| You lose | Left | Gain needed to get back |
|---|
Below zero, the multiplier turns on you
Above zero, anything that compounds is a friend: 10% a year on what you have makes it grow. Below zero the same 10% is applied to what you owe, and makes that grow. Nothing about the multiplier changed. The number it is applied to changed sign.
That is why a loss that pushes a result negative is the worst of the four. Getting back takes more than stopping the fall: you have to outrun the hole while it deepens.
Two ways it runs away: the rabbit hole and the runaway
Picture a spiral of squares. Follow it inward and each square is smaller than the last. Follow it outward and each is bigger. Those are the two ways a cost can get away from you.
Running smoothly is the spiral itself. Each new square is exactly as long as the two before it put together, so nothing grows faster than what is already there to support it, and the shape keeps the same proportions at every size. Trouble is leaving that balance in either direction: sinking effort into ever smaller squares, or adding squares bigger than anything behind them can carry.
This is a Fibonacci spiral, where each square is about 1.618 times the one before. It is a picture of balance, steady shrinking and steady growing. It is not a claim that money follows that number: real costs shrink or grow at their own rate, which is what the sliders below are for.
Inward: the rabbit hole
Each step gains less than the one before, so the gains add up toward a ceiling they never reach. If every step costs about the same, there is a last step worth taking. Past it, you are paying full price to fill a smaller and smaller gap: one more fix, one more revision, one more feature.
Outward: the runaway
Each step costs more than the one before. It does not level off, and the latest step is always a large share of everything spent so far, which is why it seems to come from nowhere. This is the fix that needs a bigger fix. It has to be stopped early, because waiting only makes the next step larger.
Why the books do not show it
Nobody is doing anything wrong. Companies report what the rules require, and the rules require bad news as well as good: write-downs, lawsuits and doubtful debts all have to be disclosed. What the rules do not require is tracing cause and effect from a decision to everything it later touches. That analysis is optional, internal, and rarely done in full.
Four things follow from that:
- The books record transactions. Income that a decision prevented was never a transaction, so it appears nowhere.
- Spending on people is recorded as a cost with no lasting value. Wages, training and most research are charged in the year they are paid and never appear as an asset. Cut them and profit rises at once. What they were building was never on the balance sheet, so its loss never shows either.
- The saving and its effects arrive apart. The saving shows this quarter on one line. The lost sales, overtime and rework show in later quarters under other headings. No line joins them.
- People are judged on what the books show. In a 2005 survey of about 400 finance executives, roughly four in five said they would cut spending such as research, advertising or maintenance to meet an earnings target, and more than half said they would delay a worthwhile new project.
So a cut that harms the business can raise reported profit, every figure can be correct, and nothing in the statements will connect the two. Filling that gap is the purpose of the calculator.
Survey: Graham, Harvey and Rajgopal, "The Economic Implications of Corporate Financial Reporting", Journal of Accounting and Economics, 2005.
When it really is only a subtraction
Not everything multiplies, and treating every cut as a disaster is its own mistake. A saving is just a saving when:
- Nothing else needed it. It was spare, idle or duplicated.
- Something else can do the same job at once, so the chain is not broken.
- What it affects stops there and does not pass anything on.
- The result stays above zero either way.
- It can be undone cheaply if you turn out to be wrong.