I think it's best to be concerned with the effect your marginal donation would have. If they already have so much money that they buy $0.07 packets for everybo

I think it's best to be concerned with the effect your marginal donation would have. If they already have so much money that they buy $0.07 packets for everybody that needs them, then your additional donation won't pay for any additional packets, and you can leave it out of your analysis. Donating won't affect the packets. But if they don't have enough money to vaccinate everyone, and they're putting as much money into that as they can, then the effect of donating $50 is that three more children are vaccinated. On the third hand, if they already have enough funding for everything they want to do then your donation is not useful, even if they have low administrative overhead. It won't lead to any extra packets or vaccinations compared to if you didn't donate. Administrative overhead is good to take into account - if it's very high then something fishy could be going on - but the main thing is the effect of your donation.