Yes, it is possible for a business to be solvent but not profitable because the profits that the business makes can be used to pay off any debt obligations when they are due. Those businesses are smart because if they don't take the time to pay those debts off then they will increase and be more and more each month. And eventually they will just be paying off the minimum amount. If they do that then they can be profitable but they will have more liabilities to pay off the next month. But if they pay those debts off before they get out of hand then they will be profitable the next month when they don't have that debt to pay back.
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