With each passing day, the future looks brighter for Boeing (NYSE:BA) ... in South Korea.

Last week, Boeing received official confirmation from the Pentagon that it's won the contract to supply 36 AH-64E Apache attack helicopters to the Republic of Korea, beating out rival Textron (NYSE:TXT) for the contract. That sale's expected to net Boeing anywhere from $904 million to $1.6 billion, depending on whose figures you believe. (And maybe even more than that. Boeing also won a 30-Apache sale to Taiwan earlier this month, and a Congressional research report estimated that the smaller Taiwanese contract could ultimately generate as much as $2.5 billion for Boeing.)

Apache helicopters in flight. Source: Boeing.

Boeing also appears to have grabbed the pole position for an even bigger South Korean defense contract. Dubbed "F-X III," this is a contract to continue modernizing the Asian nation's aging air force of F-4 Phantoms with new, stealth-technology fighter jets. According to published reports, South Korea is holding tight to its intention to pay no more than $7.4 billion to acquire 60 new fighter jets.

But here's the problem: When the U.S. Defense Security Cooperation Agency notified Congress of the potential sales of both Lockheed Martin (NYSE:LMT) and Boeing fighters to South Korea (to clear the way for a speedy sale, in the event either defense contractor wins the contract), DSCA quoted Lockheed's price at "$10.8 billion."

That's way, way out of line with South Korea's stated budget, and it suggests that Lockheed may have priced itself out of this competition. Meanwhile, Boeing lowballed the competition with an estimated price of only $2.4 billion for five dozen of its new F-15SE "Silent Eagle" fighter jets.

Boeing's F-15SE. Source: Boeing Korea.

A couple of weeks ago, South Korea's Defense Acquisition Program Administration confirmed that of the three companies bidding for FX-III, at least one came in below the $7.4 billion cutoff. Knowing what we know about Boeing's offer -- it's pretty much a given that that company's name was "Boeing."

Side note: Sources say that Eurofighter still has hopes it will steal away the contract, stressing that South Korean pilots have not yet had a chance to test-fly either the F-35 or F-15SE, but have flown the Typhoon. However, the Typhoon is not a true stealth fighter like the F-35. And at a price tag estimated to range from $6.1 billion to $8.1 billion for five dozen planes, it appears to cost significantly more than the F-15SE.

Foolish final thought
One final factor in Boeing's favor: In the first two rounds of "FX" fighter-jet buying that have already taken place, Boeing already swept the field, winning contracts to sell the South Koreans a total of 60 F-15K fighter jets. So we already know that the South Koreans like one flavor of the F-15. Odds are, given the opportunity to buy an even more advanced version, and at a price well under-budget, they'll jump at the chance.

A decision is expected next month. Stay tuned.

Editor's note: A previous version of this article incorrectly stated that Boeing won a contract to sell F-16K, rather than F-15K, fighter jets. The Fool regrets the error.