You're making a towering, unstated, and very material assumption: SprocketCo can continue to sell the same number of sprockets at $1.25 as it did when the price was $1. In that case, which is your absolute best case scenario, you can completely pay for the increased input cost of the minimum wage with the increased revenue of the now more expensive sprockets. The rise in sprocket prices exactly offsets the increased labor costs making them _exactly equal_; the relative percentage of increase is irrelevant, and that's just your best case scenario.
That won't happen in reality of course. In the real world a 25% increase in sprocket cost is going to reduce the total number of sprockets sold as some portion of worldwide sprocket sales will no longer make financial sense for the sprocket buyers. Now you've got a gap between the cost of providing the minimum wage (increased labor costs) and paying for it (revenue); so who's going to pay for it?
There are lots of different ways to answer that question but the underlying fact remains: someone is going to pay for it. Maybe SprocketCo lays off workers to make up the difference (or simply freezes hiring), maybe SprocketCo reduces their dividend and pays out less to shareholders (or reduces bonuses for your non-minimum wage workers), maybe they start looking to outsource labor to some other country (or invest in more automation), or maybe all of the above.
In any case, you've provided a temporary benefit to a small number of people and permanently harmed some other group or groups. In the end though you've only really made everyone worse off. It feels good but that's just an illusion.