Final answer:
The price of a $518,000 bond issue when the market interest rate is 12%, and the bond's coupon rate is 8%, is calculated to be $499,152. This is based on the market principle that investors will not pay more for a bond than what they could earn from an alternative investment at the current market interest rate.
Step-by-step explanation:
To determine the price of a $518,000 bond issue when the market interest rate is higher than the bond's coupon rate, we must look at the expected payments and the current market interest rate. If the bond is paying 8% annually but the market rate is 12%, investors will prefer the bond that yields the higher rate. Therefore, the price of the 8% bond must be discounted to make it an attractive investment relative to the 12% market rate.
Using the provided example, assume we have an individual $1,000 bond paying $80 per year. If there's only one year left until maturity, the bond will pay a total of $1,080 that year. Given a market rate of 12%, an investment of $964 today would grow to $1,080 in one year ($964 x 1.12). Hence, an investor would not pay more than $964 for the bond that is expected to pay $1,080 in a year. Following this logic for the entire bond issue:
- The price of each individual $1,000 bond is $964.
- Since the total bond issue is $518,000, we calculate the price by ($964/$1,000) times the total bond issue.
- The discounted price of the $518,000 bond issue is ($964/$1,000) * $518,000 = $499,152.