It assumes that 100% of the funding went to treating children with malnutrition. First of all its doubtful that even the intent of the program was to spend 100% of the money on that in particular. And even if it was, this is clearly false because even a super efficiently run program to help starving children is going to have massive overhead, so not even close to 100% of the funding would be spent that way. It's not like starving children of the world are located around major logistics hubs, so I would be absolutely shocked if they could even get close to 50% here. It also assumes that you only have to treat each child once. So ok, you treat a child for malnutrition and then what? You send him back out into the same place where he couldn't get food in the first place? There's just so much wrong with this number that I have a hard time believing you are even asking in good faith.
If you look at the sources for the $100-200 figure, she's looking at a particular form of humanitarian aid - community-based therapeutic care for children with severe acute malnutrition. There are other models like inpatient programs that are more expensive, but also reach fewer children, and then if you're supporting people who don't have severe acute malnutrition it's presumably much less expensive because you don't have to include the healthcare costs.
If you look at the papers that are being cited, these programs are incredibly effective:
> A total of 328 patient cards/records of children treated in the programs were reviewed; out of which 306 (157 CTC and 149 TFC) were traced back to their households to interview their caretakers. The cure rate in TFC was 95.36% compared to 94.30% in CTC. The death rate in TFC was 0% and in CTC 1.2%. The mean cost per child treated was $284.56 in TFC and $134.88 in CTC.
If you look at what they mean by CTC program, it's ongoing support in addition to the treatment for acute malnutrition, so it's not just throwing a child back into the same environment:
> CTC programs use decentralized networks of outpatient treatment sites (usually located at existing primary health-care facilities), small inpatient units (usually located in existing local hospital facilities), and large numbers of community-based volunteers to provide case detection and some follow-up of patients in their home environments. Patients with severe malnutrition, with good appetite, and without medical complications are treated in an outpatient therapeutic program (OTP) that provides ready-to-use therapeutic food (RUTF) and medicines to treat simple medical conditions. The food and medicines are taken at home, and the patient attends an OTP site weekly or fortnightly for monitoring and resupply.
In terms of overhead, the overhead for the organization providing care is already accounted for in the $100-200 figure, including the costs of managing the program from the capital. Presumably Save The Children takes a chunk of the grant for its own overhead but I believe these costs are typically capped by the US government at something like 10%. Similarly, USAID has its own costs but I'm not sure if those are accounted for in the $168m line item or if they're accounted for elsewhere.
So, sure, Nichols' paper is using a cost estimate that's based on specific types of programs and generalizing that. Given the number of countries and organizations involved, I'm not sure how much more accurate you could get.
But your cynicism is also pretty unfounded. The sources take into account the organization's overhead, the logistics of reaching remote areas (the Ethiopia paper points out that much of the overhead goes to vehicle rental and gives a distribution of patients by how far they have to walk to get to the treatment center). It accounts for ongoing vs acute care.
So I wouldn't take 168,000 number especially seriously - and I would note that the author adds some very large error bars - but I also wouldn't dismiss it as a complete fiction.