Hung convertibles, also known as busted convertibles, are a type of convertible securities where the share price of the underlying security is significantly lower than the conversion price, therefore making it unlikely that the securities will be converted into common stock. Although they can be redeemed in money or in the stock of the issuing company, depending on the certain conditions stated in the agreement, investors prefer them as they provide a steady fixed income and greater administrative flexibility.

Hung convertibles are a concern for companies, because they present both an immediate and long-term challenge. In the short-term, companies face the problem of redeeming their convertibles in cash or in stock, should the underlying share price remain well below the conversion price. This, in turn, increases the financial burden on the company, as it has to pay out the amount to the investors in cash.

In the long-term, companies must look for ways to attract more investors, preferably institutional investors, as large investors are more likely to want to convert their convertibles into common stock. Some companies can use the prospect of stock appreciation to attract investors, yet for some, this strategy does not always bring the desired results. As such, companies must devise a long-term strategy that ensures that the share price of the underlying security rises enough to meet the conversion price, so that the hung convertibles may be converted into common stock. This could involve improving the company fundamentals, such as increasing earnings, reducing debt, and improving the quality of the management team and board of directors.

In conclusion, hung convertibles represent a challenge for companies due to the both immediate and long-term implications that come with them. Companies must work on both a short-term and long-term financial strategy to ensure that they can redeem the securities in cash or in the underlying stock, as well as attract more investors to the stock. To achieve this, companies must focus on improving their fundamentals to spur their share price high enough to meet the conversion price.