A company issues its shares at a premium when the price at which it sells the shares is higher than their par value. This is quite common, since the par value is typically set at a minimal value, such as $0.01 per share. The amount of the premium is the difference between the par value and the selling price. If shares do not have a par value, then there is no premium. In this case, the entire amount paid is recorded in the common stock account (if the payment is for common stock, rather than for some form of preferred stock). For example, if ABC Company sells a share of common stock to an investor for $10, and the stock has a par value of $0.01, then it has issued the share at a premium of $9.99.
This premium is rarely recorded in an account having that name. Instead, it is more commonly recorded in an account called Paid-In Capital In Excess of Par Value. It may also be recorded in an account called Additional Paid-In Capital. The account appears in the shareholders' equity section of the balance sheet. It does not appear in the income statement. Other than the use of two accounts to record the separate elements of the price at which a share is sold, there is no particular relevance to the concept of a premium.
Share issuance at a premium is also known as capital surplus.