When market interest rates rise to 12%, the value of a convertible bond will typically decrease below its par value. Hence, one would expect to pay less than $10,000 for a bond with a par value of $10,000 under these circumstances.
Given the scenario where increased expectations concerning inflation cause the yield on straight debt of equivalent risk and maturity to reach 12 percent, the value of a convertible bond will generally be affected negatively. This is because bonds have an inverse relationship with interest rates.
Specifically, if the market interest rate rises above the bond's coupon rate, the bond's price will decrease to offer a yield attractive enough to match the market rate.
When calculating a bond's price under these conditions, we must consider the future payments the bond will generate. For instance, if a bond has a face value of $1,000, and it's the last year before maturity, then the expected payments from the bond would be $1,080 ($1,000 face value + $80 last year's interest). If the current market interest rate is 12%, an investor would not pay more than $964 for the bond since investing $964 at a 12% rate would also yield $1,080 after one year.
Therefore, one would expect to pay less than $10,000 for a convertible bond with a par value of $10,000 when the yield on straight debt reaches 12%.