This question assumes that I am an individual working for a company in a perfectly competitive market.  I know the secret of the new method but I do not benefit from it.  Therefore, I want to sell my secret to some number of other firms in the market.

In this case, I am essentially a monopolist.  Only I have the information  and I can sell it to whoever I want.  If I am in a monopoly, I will want to sell the secret up to the point where my marginal revenues equal my marginal costs.  This is the profit maximization point.  Of course, I essentially have no marginal costs for selling this secret.  Therefore, I will sell the secret until my marginal revenue is essentially zero.  This would mean that I would sell it to every firm in the market because they will all need it.  I will only stop selling when no one is willing to pay me anything for the secret.