I'd be interested if you have done any analysis on the topic.
I haven't, because it seems obviously false to me. Africa's population has been growing exponentially over the 20-21st centuries, aid to Africa has not, as far as I know. If conditions in Africa were so bad that aid contributed only a fixed number of life-days - if it only saved people to die another day, then I would not expect to see continued exponential growth but rather, re-hitting the Malthusian ceiling and quickly.
(One could try to explain this by saying the life expectancies and public health changes are thanks to non-aid Western inputs like regular commercial goods, but this strikes as an ad hoc explanation to try to deny the value of aid.)
Latest in an irregular series, some of whose previous entries were Edge.org and the Girl Scouts...
I examine the Folding@home distributed computing project with reference to the costs (electricity resulting in air pollution causing deaths) and benefits (some papers): http://www.gwern.net/Charity is not about helping. Additional data on either side of the cost-benefit is welcome.
(I also recently split out my essay describing things I have changed my mind on.)