Wayne has convinced me that the fraction of people who become vegetarian because of receiving a brochure is probably much much lower than estimated below. The evidence Vegan Outreach provides on this is very weak, and you shouldn't expect 1% of people to make a large change to their behavior in response to a leaflet.

Alan Dwarst calculates that preventing a year of direct suffering on factory farms costs between $0.02 and $3.65 (pdf) via Vegan Outreach. [1] While I don't (currently) believe we should value animal suffering, I was curious about his calculation. The main part that seemed high was his estimate of how cheaply Vegan Outreach 'makes' vegetarians. His calculation was:

b = the number of people who receive a brochure per dollar donated = 4.7 to 8.0 people

v = the fraction of b who become vegetarian or vegan who wouldn't otherwise have done so = 0.43% to 2.5%

s = the fraction of v who stay vegetarian or vegan = 30% to 100%

t = years those people would otherwise have eaten factory-farmed meat = 10 to 56 years

vegetarian-years per dollar = b*v*s*t = 0.06 to 11
cost of a vegetarian-year = 1/(b*v*s*t) = $16.5 to $0.09

details on these estimates (pdf)

I decided to try and get an alternate estimate, calculating through Vegan Outreach's revenue and the number of vegetarians.

There are around 7M vegetarians in the US and 10% say "animal rights" is their main reason (wikipedia). At the high end, I would put Vegan Outreach's work at being responsible for 1/4 of these people, and at the low end I'd say maybe around 1/500.

n = number of US vegetarians = 7M people

a = fraction of n who are primarily concerned with animal rights = 10%

r = fraction of a that Vegan Outreach is responsible for = 1/4 to 1/500

m = annual budget of Vegan Outreach = ~$750K

vegan outreach caused vegetarian years = n*a*r = 175K to 1.4K
cost of a vegetarian year = m/(n*a*r) = $4.29 to $536

I think the main reason my cost estimate comes out much higher is Alan's estimate for s, the fraction of people who stay vegetarian. I know more lapsed vegetarians than vegetarians, so I think 100% is definitely too high, but 30% may also be. I'm also not so sure about v. They seem amenable to measurement, but I don't think anyone's done that.

[1] His goal is reducing suffering, including wild animal suffering, which would put him at odds with many vegans. He also is not coming at this from an environmental angle, so he advocates eating beef over chicken or eggs if you are going to eat animal protein.