In countries which use a central bank system:
When people speak about the 'interest rates', they mean interest to which the central bank (whatever it is) lends money to other banks, which in turn will lend money to corporates and individuals. (correct?)
However, can a company issue bonds at any interest rate (regardless of the central bank policy), or is this enforced by law? What about banks?
There may be some country out there that has that control of the corporate economy, but in the developed world, corporate bond rates are NOT set by the government. They are set by the corporation when they issue the bond, and are based on market interest rates for companies with similar default risk.
The higher the interest rate of a bond, the higher the market price, so setting the price of a bond is a trade-off between getting the most money upfront (higher price) versus higher interest payments going forward. They (with the help of an underwriter) set as low an interest rate as they can and still be able to sell the bonds at their par rate.
Bonds don't pay interest, they pay a "coupon".
The value of the coupon of a corporate bond is set by the corporation which issues the bond. They are free to pick any value they want (including zero). But if they set the coupon too high, they will pay more capital acquisition cost than they have to. If they set the coupon too low, they won't find any investors willing to buy their bonds. So they will usually set it at the lowest value they still expect to be high enough to attract investors.
While the central bank interest rate doesn't directly affect the coupons of private and public bonds, it does so indirectly. Bonds compete with other forms of financial investment. When the interest rate is high, then bonds might have to increase their coupons in order to still be an attractive option for investors compared to just parking their money on a bank account.
