What to charge
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Soap has cheap materials and expensive time, which is the trap in pricing it.
The cost that gets missed
Oils, lye, fragrance, color and packaging are easy to add up, and they are a minority of the real cost.
What gets missed is the six weeks of cure: shelving, space, and capital sitting in bars that cannot be sold.
And the time. Weighing, mixing, pouring, cutting, planing, bevelling, wrapping, labeling. A batch is several hours spread over six weeks, and almost none of it is the mixing.
Building the number up
Materials per bar, from the actual batch: batch material cost divided by sellable bars, not bars cut.
Packaging per bar, including the label.
Labor at a real rate, with the whole process timed once honestly.
Overhead: space, insurance, market fees, card fees, website.
Then a margin on top of all of that, because the sum so far is break-even and not a business.
The wholesale problem
A shop expects roughly half of retail, which means your retail price has to work at half.
Set retail first with wholesale in mind, rather than setting a retail price and discovering wholesale is below cost.
And hold the retail price yourself: undercutting your stockists on your own website is the fastest way to lose them.
What the market bears
Handmade bar soap sits in a fairly narrow band and customers know it.
Being at the bottom of that band does not win, because the supermarket is far below it anyway and nobody buying handmade is buying on price.
If your honest cost puts you above the band, the answer is usually batch size or process rather than a lower price.
And if it puts you far below, you have forgotten the labor.