This question can be answered in terms of movie budgets, or estimated fictional costs where Matt Damon has been sent on extended "business trips". See detailed estimates below.
Movie Budgets Courage under Fire: $46m Saving Private Ryan: $70m Titan AE: $75m Syriana: $50m Green Zone: $100m Elysium: $115m Interstellar: $165m The Martian: $108m TOTAL: $729m
Fictional Costs My estimates, costs are in 2015 currency Courage Under Fire (Gulf War 1 helicopter rescue): $300k Saving Private Ryan (WW2 Europe search party): $100k Titan AE (Earth evacuation spaceship): $200B Syriana (Middle East private security return flight): $50k Green Zone (US Army transport from Middle East): $50k Elysium (Space station security deployment and damages): $100m Interstellar (Interstellar spaceship): $500B The Martian (Mars mission): $200B TOTAL: $900B plus change
Notes
Movie marketing costs are not included
Only movies where Matt Damon acted are included
Making the Matt Damon movies has cost about 0.1% of the "real" cost to actually send him on all of these business trips
His movie gross takings so far are about $2.7B, which is about 40% of the cheapest proposed trip to Mars, as proposed by the Mars One team.
Send me corrections if you know of actual costs mentioned in the movies, or if you know of other movies where he had to endure significantly dangerous travel. Edits from comments:
I think Ocean's Eleven (suggested by Madalyn Zimbric) doesn't count, as Matt Damon is not being explicitly sent somewhere even though he does travel to take up the job.
I think Courage Under Fire (suggested by Kurt Scholz) does count as a Matt Damon rescue, even though it's not the main topic of the film.
Does the Bourne series count? No, because Matt Damon does lots of travel at his own expense (he might have lots of frequent flyer points under different identities). Or maybe it's yes, because plenty of money is spent trying to "bring him back" - but the people looking for him don't seem to be very concerned about his safety.
Does Team America: World Police count? I'm not sure. It includes a parody of Matt Damon as "himself" (at least a puppet version). He is sent to North Korea on a business trip of sorts.
Jamie Folsom has pointed out that the ratio of fictional/real costs indicated above is 1234.5679. You couldn't make it up. (Actually the fictional costs were rounded off to $900B so the ratio is slightly different, but let's not let details get in the way...)
The real question is why after so many failed attempts do we continue to send Matt Damon into outrageous scenarios which inevitably require hundreds of millions of dollars simply to rescue him only so he can undo all our efforts by getting stuck in another equally or more absurd situation. $1Bn minimum. Which, while I don't believe in putting a price on human life, is too high even for Matt Damon.
Also how many lives were lost along the way - several were killed in Saving Private Ryan. So $729m (as calculated by Kynan Eng.) plus the priceless lives that were lost.