Profit Margin Calculator

Background

Two worksheets that answer one question

Every price is an argument about two things at once: how much you keep on each sale, and how many sales it takes before keeping anything matters. The BA II Plus splits that argument across two worksheets. PROFIT handles the first — cost, selling price and margin, any one of them from the other two. BRKEVN handles the second — how many units the contribution from each sale has to cover the fixed cost.

They are separate on the hardware, and that separation is the source of most of the errors people make with them. A price that looks healthy on a 40% margin is a bad price if the fixed cost needs 1,250 units to clear and you can only sell 900. The two answers only mean something together, which is why this page runs them as one calculation: the price PROFIT solves becomes BRKEVN's P, the cost becomes VC, and the only figure you enter twice is nothing at all.

Neither worksheet involves time. There is no interest rate and no discounting, so nothing here competes with the TVM calculator — if the profit stream runs for years and you want its present value, that is the tool for it, and the NPV calculator if the cash flows are uneven.

The formulas

One triangle, one division, and the mistake in between

PROFIT is built on a single identity. Gross profit is the price less the cost, and margin is that profit expressed as a share of the price.

Rearranged, that gives the other two directions. Note which one divides and which one multiplies — this is the step that goes wrong most often.

Markup measures the identical profit against the cost instead of the price, which is why it is always the larger number and why the two are not interchangeable. A 60 item sold for 100 carries 40 of profit: a 40% margin, and a 66.667% markup.

BRKEVN starts from the same profit per unit under a different name. Contribution margin is the price less the variable cost, and the whole worksheet is one identity solved five ways.

Set PFT to zero and the second line is the breakeven volume: 50,000 of fixed cost divided by 40 of contribution is 1,250 units, or 125,000 of revenue. Leave PFT at 20,000 and the same division gives 1,750 units. Everything else on this page — the margin of safety, the operating leverage, the profit at a planned volume — is arithmetic on those two lines.

1. Margin is measured against the price

   Which is why solving the price divides by (1 − margin) rather than multiplying. Dividing by the margin itself, or multiplying by (1 + margin), are the two classic wrong answers.

2. Markup is measured against the cost

   Suppliers and retail buyers usually quote markup; accounts and analysts usually quote margin. Convert before comparing, or you will compare 40 with 66.667 and think something changed.

3. Contribution, not margin, drives breakeven

   Breakeven divides a currency amount by a currency amount. A percentage margin only helps once it has been turned back into money per unit.

4. A negative contribution has no breakeven

   If the price is at or below the variable cost, every extra unit widens the loss and no volume will cover the fixed cost. The division is undefined and the worksheet says so.

Margin against markup

The conversion table worth memorising

Five pairs cover most conversations, and knowing them stops the argument before it starts. A third off the price is a half on the cost; a half off the price is a doubling of it.

The gap widens as the numbers rise, which is what makes the confusion expensive. At a 20% margin the two figures differ by five points. At a 66.667% margin they differ by more than a hundred and thirty. Anyone who reads a 200% markup as a 200% margin has mispriced by a factor that no volume will rescue.

The BA II Plus only speaks margin. There is no markup field in PROFIT, so a markup quote has to be converted on the way in — either with the formula above, or by simply multiplying the cost by one plus the markup and entering the result as SEL, which is what the markup option on this page does for you.

On the hardware

Three fields, then five, and CPT does the rest

Both worksheets behave the same way, and once you have the habit neither takes more than twenty seconds.

1. 2ND 3 opens PROFIT

   The display shows CST with whatever was left in it. Press 2ND CLR WORK to zero all three fields before you start — a stale SEL is the single most common cause of a nonsense margin.

2. Enter the two you know, leave the third alone

   Type a value and press ENTER to store it, then ↓ to move on. The order is CST, SEL, MAR, and it wraps, so ↓ from MAR returns to CST.

3. Scroll to the missing one and press CPT

   The worksheet solves whichever field the cursor is on. Nothing is computed until you press CPT, so a field you have not asked about keeps showing whatever you last stored in it.

4. 2ND 6 opens BRKEVN

   Five fields in the order FC, VC, P, PFT, Q. The price you just solved goes into P and the unit cost into VC, so PROFIT has effectively filled in two of them already. Clear the worksheet first here too.

5. PFT is an input, not just an output

   Leave it at zero for a plain breakeven, or enter a target and compute Q for the volume that reaches it. You can also fix Q and compute P to find the price a given volume needs, or compute VC to find the most a unit may cost.

Two habits are worth building. Press 2ND CLR WORK every single time you enter either worksheet, because both keep their values through a CE/C and even through switching the calculator off. And set the display to more decimals than you think you need — 2ND FORMAT, then 4 or higher — because a margin rounded to two places will not reproduce the price it came from. The on-screen emulator has both worksheets on the same keys if you want to rehearse the sequence.

Worked example

A 60 unit cost, a 40% margin, and 50,000 to cover

Take a product that costs 60 a unit to make. You want a 40% gross margin, and the operation carries 50,000 of fixed cost for the period. Start in PROFIT: enter 60 in CST, 40 in MAR, and compute SEL. Because margin is a share of the price, the calculation is 60 ÷ 0.60, and the price is 100.00. Profit per unit is 40.00 — which is a 66.667% markup on the cost, the figure a buyer would quote back at you.

Now move to BRKEVN with those two numbers. P is 100, VC is 60, so contribution is 40 a unit. With PFT at zero, computing Q gives 1,250 units. That is 125,000 of revenue, and it is also exactly 125,000 of total cost: 50,000 fixed plus 60 × 1,250 variable. The point where the two lines cross on the chart above is this number.

Ask for a profit and the answer moves in a straight line. Enter 20,000 in PFT and compute Q again: (50,000 + 20,000) ÷ 40 = 1,750 units, or 175,000 of revenue against 155,000 of cost. Every extra 40 of target profit adds one unit, which is the most useful intuition the worksheet gives you — the contribution is the exchange rate between profit and volume.

Finally, test a plan. If you expect to sell 2,000 units, set Q to 2,000 and compute PFT: revenue of 200,000 less total cost of 170,000 leaves 30,000. The margin of safety is 2,000 − 1,250 = 750 units, or 37.5% of the plan, so sales could fall by more than a third before the operation stopped covering its costs. Operating leverage at that volume is 80,000 of contribution over 30,000 of profit, or 2.667× — a 1% change in volume moves profit about 2.7%.

One last comparison shows how sharp the fixed cost makes things. Suppose a buyer pushes the price to 95 and you still plan on 2,000 units. Contribution falls to 35, breakeven rises from 1,250 units to 1,428.57, and profit at 2,000 units drops from 30,000 to 20,000. A 5% price cut cost a third of the profit, because the fixed cost did not move.

Troubleshooting

Six ways a margin calculation goes wrong

1. A markup was entered as a margin

   The tell is that the price comes out lower than expected. Entering 66.667 in MAR when you meant a 66.667% markup gives a price of 180 on a 60 cost instead of 100. If the number came from a supplier or a buyer, assume markup until told otherwise.

2. The margin was applied by multiplying

   60 × 1.40 = 84 is not a 40% margin; it is a 40% markup, and the margin is 28.571%. The correct step divides: 60 ÷ 0.60 = 100.

3. A margin of 100% or more was requested

   There is no such price. Margin is a share of the selling price, so 100% implies a cost of zero and anything above implies a negative cost. What people usually mean is a 100% markup, which is a 50% margin.

4. The worksheet still held old values

   Both PROFIT and BRKEVN keep their contents indefinitely, and CPT only recomputes the field you are standing on. A leftover PFT will quietly inflate every breakeven you calculate afterwards. 2ND CLR WORK on entry, every time.

5. Fixed cost was mixed into the unit cost

   VC is the cost of one more unit and nothing else. Allocating a share of rent into it makes the contribution too small and the breakeven too high, and the fixed cost then gets counted twice. Keep FC whole and per-period.

6. Total revenue was entered where a unit price belongs

   P and VC are per unit; FC and PFT are for the whole period; Q is a count. Mixing the scales produces answers that are wrong by a factor of the volume, which is usually large enough to spot but not always.

A last sanity check that costs nothing: multiply the breakeven volume by the price and confirm it equals the fixed cost plus the variable cost at that volume. If those two figures do not match, one of the five BRKEVN fields is not what you think it is.

Where to go next

Related worksheets and pages

• The BA II Plus emulator — press 2ND 3 for PROFIT or 2ND 6 for BRKEVN and walk either worksheet yourself, with the display showing exactly what the hardware would.
• TVM calculator — a margin is a single period. Once the profit repeats for years, this is where it gets a present value and a required return.
• NPV calculator — for a product decision rather than a price: the launch cost against the contribution stream it buys, discounted.
• IRR calculator — the return implied by those same flows, when the question is whether the product clears a hurdle rate rather than what it is worth.
• Depreciation calculator — the fixed cost in a breakeven usually includes a depreciation charge. DEPR is where that number comes from.
• Statistics calculator — if the volume in Q is an estimate rather than a commitment, the DATA and STAT worksheets will tell you how much it has moved in the past.

Keep going

Related calculators

Same engine, same sign convention — pick the worksheet that matches your problem.