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It balances because you are essentially taking the debt out of the liabilities section and moving it to the equity section. To take sharpie's example further:

I'm going to assume that the convertible bond's face value is $100. When you exercise the conversion, you have to take into account the par value of the stock. Let's say it's $2. So when you convert 19 shares you increase (credit) common stock by $38. Then you need a plug figure to balance out the transaction. In this case you would credit Paid in Capital in Excess of Par (an equity account) for $62. So you can see that you are simply moving around the source of capital within the L+SE section of the balance sheet.

I may have messed up a couple details because it's late, but it looks right to me. Let me know if the explanation doesn't make sense.

 

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