Should we run the discount?

Kestrel Tools makes one product: a benchtop clamp. The founder wants to grow, marketing wants a discount, finance wants to refuse an order, and the factory is nearly full. Everything you need is in this table.

And the one thing they have measured — how each type of customer reacts to price:

Start with the profit, because every answer will be measured against it:

A distributor offers to buy 100 units at $30 each, one-off, in a market Kestrel does not currently sell to — so it will not affect any other sale. Finance objects: each unit cost us $36 last month, so this loses $6 a unit.

Accept or refuse?

Accept — it adds $600.

Finance's $36 is real but irrelevant. It is $18,000 of total cost ÷ 500 units, and it contains the $6,000 of fixed cost that gets paid whether or not this order happens. The only cost this decision causes is the $24 of materials and labour for 100 more clamps.

Check the factory before saying yes: 500 + 100 = 600 units, against a capacity of 650. It fits, with 50 to spare. What does one more cost?'s rule holds because the fixed cost genuinely is fixed here — hold on to that, because Question 5 is where it stops being true.

Marketing proposes 20% off for everyone, for a quarter. "We'll more than make it up on volume." How much volume would "making it up" actually take — and will the discount deliver it?

It would take double the sales. The discount delivers a loss of $816 a month.

Take the two halves separately. First, what the discount does to each sale:

Kestrel needs $8,000 of margin just to stand still. At $8 a unit that means 1,000 units — exactly double today's 500. So marketing is not asking for "some" extra volume; they are asking sales to double, to earn precisely what the company earns now.

Second: will it? Doubling volume from a 20% price cut means a 100% quantity response to a 20% price move — an elasticity of 5. Kestrel's most price-sensitive customers sit at 2.5. Nothing in the business is close to 5.

Here is what the discount really produces, segment by segment:

Against $6,000 of fixed cost, $5,184 of contribution is a loss of $816 a month. The company goes from making $2,000 to losing $816 while selling 148 more units.

That was not bad luck with the numbers. Any discount has a volume it must produce, and it is fixed by two things only — how deep the discount is, and how much margin you started with:

Drag the discount, then drag the margin, and watch how quickly this stops being survivable.

Two things fall out of that shape. A discount deeper than your margin can never break even, at any volume — the curve simply leaves the page. And the thinner your margin, the more violent the whole picture: at a 25% margin, a 20% discount needs 400% more volume.

Kestrel charges everyone $40, but trade buyers and individuals are not the same customer. Should each segment have its own price — and which way should each one move?

Raise trade by 10%. Leave retail exactly where it is.

Trade first. Elasticity 0.8, so a 10% price rise costs only 8% of them:

Now retail, and this is where instinct fails. They are elastic at 2.5, so the received wisdom is that they are the ones to discount — cut 10% and volume jumps 25%.

Read the discount column again. Revenue up $1,000, volume up 25%, profit down $200. Every dashboard in the company would show that quarter as a success.

And because the price rise loses exactly as much, retail is already priced correctly. Both directions being worse is what "you are at the top of the hill" looks like from the ground — the same peak Where the money peaks drew from above.

Three decisions are now made. Assemble them, check the factory, and compare against marketing's plan.

$3,320 a month — a 66% increase — from selling 72 fewer units than the discount would have.

Subtract the $6,000 of fixed cost and set the three plans side by side:

That row is the whole hour. Volume is not the goal, revenue is not the goal, and the two plans that look most different on a sales dashboard are ranked in the opposite order by the bank. $3,320 against −$816 — a swing of over $4,100 a month, from arithmetic that took ten minutes and no new customers, no new product and no new spending.

With 74 units of headroom left, the founder asks about a second shift: $3,000 a month of extra fixed cost, raising capacity from 650 to 1,000. The only demand Kestrel can reach at short notice is more bulk business at $30. Worth it?

No — it falls $456 short. But the reason is a pricing problem, not a capacity one.

Question 1's rule does not apply here, and spotting that is the point of this question. There, the fixed cost was untouched by the decision. Here the decision creates $3,000 of new fixed cost, so it belongs in the arithmetic.

So: no. And notice how thin it is — the plan fails even at perfect execution, which means it fails badly at realistic execution.

But turn the question around. What bulk price would justify the shift?

At $32 the shift returns 424 × $8 = $3,392 against $3,000 — it makes $392 and buys room to grow. A dollar and change on the bulk price turns the answer from no to yes.

None of this needed calculus, a model, or data the company did not already have. It needed five questions asked in the right order — and the discipline to check what a plan assumes before checking whether you like it.