Consider the reverse direction: if a company can decrease costs, they will usually pocket the extra profit, not reduce the price they charge. Price cuts usually only happen for one of two reasons: 1) to avoid losing customers to another company that is charging less (or to entice customers of another company that's charging the same), or 2) to capture more profit if they'll earn more customers at a lower price than they'll lose due to the lower per-unit profit. (Yes, there are other reasons, but these seem to be the main ones.
For goods that are not essential to life, prices are set based on what people are willing to pay vs. how many units can be sold at that price, with the cost as a floor (absent a policy of using a product as a loss leader).
I am no expert in BoM and margins, but that seems like a wild claim to me. Could you explain your math?