To start, all of this is conceptually tricky, and you should talk to an economist or policy analyst with expertise in CBA if this ends up being a crux.

That said, in cost benefit/effectiveness analysis, the perspective EA usually takes is to consider public benefit per EA dollar spent, whereas policy analysts typically consider total social benefit per total dollar spent, which is slightly different. Either way, if government forces businesses to spend money, that's a cost to society, and if government spending replaces private spending, it's not a benefit. (EA funders should consider that as well - forcing others to spend money isn't a benefit.) Overall, the total public benefit perspective makes sense, because the costs and benefit to people and companies needs to be compared to the costs to government or to the EA funder. 

In the case you're discussing, the cost to government is negative, so the Benefit-to-cost ratio is negative - which happens sometimes^[1]. If we spend $1m to get the government to save $5m and create a benefit of $5m, we would have total social cost-benefit ratio of -0.8. It's good to note that, and then we also probably want to do the cost-benefit analysis from the perspective of EA spending, so it can be compared to other interventions, and we would say it cost $1m to generate $10m in total public benefit.

A key caveat for actual analysis, however, is that if we shift government spending, it might not save anything! For instance, if the budget for the government spending on healthcare is set by Congress, and not impacted by costs, then "saving" $5m in transplant costs is actually just shifting that spending to a different place - which has benefits, but it's hard to estimate them, so we often just assume the benefit from marginal spending is a wash, and call it savings. This is hard to justify, but doing anything else is often infeasible.

On the other hand, if the savings are real, there is another small but often important caveat, which is that we often want to account for the overhead and deadweight costs of taxation. It's plausible^[2] that every dollar the government spends costs the economy $1.20. That is, if the government were to only get $1 in benefit for doing something, it's a net loss for the country because they damage the economy via taxes more than they benefit it. If that is the case, saving $5m in government spending might actually be worth $6m - and so it cost the EA funder $1m to generate $11m in benefit. But if you do this, be really careful to note exactly what you're doing - otherwise, it can be very misleading.

1. ^{^}

   There are two ways this happens, and you need to know which it is - it's either really good, or really bad. If cost is negative but benefit is positive, as in the transplant case, it's great. If cost is positive but benefit is negative, it's very bad. If both are negative, it's easily compared to other positive numbers; spending $X less causes $Y in harm is equivalent to saying that we're currently spending $X to benefit, i.e. avoid the harm of, $Y, and consdiering if we should stop.

2. ^{^}

   The 20% figure isn't sourced anywhere I've seen it used, but I have seen it used and mentioned more than once as the typical value for deadweight loss for taxation.

Nice question!

Firstly I would challenge your assumptions in using "lives saved"  as currency in your very brief final estimate. Depending on your moral basis, the lives of people in need of a kidney transplant are probably less valuable than those typically saved by malaria interventions:

• they probably gain less extra lifetime
• they are probably more likely to have health problems that diminish their quality of life
• they probably have less productivity and more healthcare costs ahead of them for the previous two reasons

Consider using DALYs instead.

I think you are right to think about considering government funding. It seems plausible that transplants would save govt money compared to dialysis. But transplant recipients also live longer (that's the point of this) and will incur healthcare costs for a longer time.

If you do come up with a figure for "costs saved" you could try to convert govt spending into DALYs or similar. Some countries' healthcare systems evaluate treatments based on the cost per QALY (in the UK publicly-funded drugs are supposed to cost less than £30,000 per QALY).  If you assume that any money the system saves is invested in DALYs at the threshold rate, converting is simple. I don't think this applies in the US, where costs are split between private and public sources in a confusing way.

All of this brings me back to broad agreement with your instinct to count the health gains as "free", because it's quite complicated to do otherwise. But I would caution about complexity. Objections to the buying/selling of organs are partly based on notions of sanctity that we might see as stupid (much like the fear of GM crops that is blocking Golden Rice) but also partly on valid concerns about the hard-to-predict secondary effects of an organ trade (exploitation, decreased concern for the poor who "can always sell a kidney if they are truly struggling").