Suppose as an example you intend selling something for $25 and have budgeted that the cost will be $20. Therefore you expect to make a profit of $5 per unit.
However suppose you are not sure of the cost – you just think it will be $20, but you have fixed the selling price and can’t change that. The sensitivity of the cost estimate is what % change would result in zero profit (because any bigger change would mean your decision to produce was wrong because it would be loss making).
You could afford the cost to increase by up to $5 and still be making a profit, so the sensitivity is 5/20 = 25%.