American Bearer Bonds are a debt security issued by a business entity, such as a corporation, or by a government. It differs from the more common types of debt securities in that it is unregistered – no records are kept of the owner (i.e. Joe Takagi), or the transactions involving ownership. In Die Hard, Hans Gruber's reasoning for taking over Nakatomi in the first place was to steal $640 million in bearer bonds from the vault.
The bearer bonds are physically shown near the end of the film. When Theo manages to break six of the seven locks leading to the vault carrying the bonds, only the FBI inadvertently unlocked the seventh lock, opening the vault. The alarm sounds and Hans, Theo, Eddie and Kristoff steal the bonds, putting them in bags. While Hans is packing the bag with bearer bonds inside, Holly calls him "nothing but a common thief". Kristoff runs with one bag before he is knocked out by John McClane, and Hans and Eddie stop packing their bags of bearer bonds to deal with McClane. But this would be the last time they touch the bonds as both men were shot and killed by McClane, foiling their plot.
Bearer bonds, because they are unregistered, are technically owned by whoever is holding them. Because they were produced in denominations higher than common currency ($640,000,000 issues in the Nakatomi vault), they were often used to more easily transfer exorbitant sums of money. Near the end of the 1970s, the parties most using these types of bonds were primarily engaged in illegal activities. Following the passage of The Tax Equity and Fiscal Responsibility Act in 1982, neither the interest distributed by issuers of bearer bonds, nor the income reported by bondholders, received any type of favorable tax treatment, specifically for new issues. This made new issues of bearer bonds an unattractive income investment as compared to other debt offerings.
Why Nakatomi holds bearer bonds
With the bonds in question having been issued in 1979, it is possible that the Nakatomi Corporation could have been continuing to hold them solely for favorable tax treatment. However, in 1988, bearer bonds were widely considered a questionable form of investment. Furthermore, whomever Nakatomi Corp received these funds from would not need to have been recorded in any type of tax ledger. So while it is pure speculation, it brings into question what type of business Nakatomi Corp may have been involved in, such that they would have received bearer bonds as a form of payment and in such a high $640 million dollar sum. Lastly, were anyone (Hans Gruber) to find out that these bonds were being held in the vault, they would be an obvious target for theft. The US government has to honor the issues regardless of who is holding them. One could easily question the Nakatomi Corporation's motives for holding and/or using bearer bonds during the course of regular business. Thus, though it is never explored in the film, the presence of such a large number of bearer bonds could hint at criminal (or at least questionable) activity on the part of Nakatomi, which could explain how a criminal such as Gruber became aware of them in the first place.