Question

Your company issues a 5-year bond with a face value of $10,000 and a stated interest rate of 7%. the market interest rate is 5%. the issue price of the bond is calculated as the:_____.

Answer 1

The issue price of the bond is calculated using the present value of its future cash flows, discounted at the market interest rate. Since the bond's stated interest rate of 7% is higher than the market interest rate of 5%, it will be issued at a premium. If the discount rate increases, the present value, and thus the price of the bond, will decrease.

Step-by-step explanation:

The issue price of a bond when the stated interest rate is less than the market interest rate can be calculated using the present value of the bond's future cash flows, discounted at the market interest rate. Since the bond's stated interest rate is 7% but the market interest rate is 5%, the bond will be issued at a premium because its coupon payments are more attractive compared to the market rate.

For example, a $10,000 bond with a 7% interest rate would pay $700 annually. To find the present value of these payments, each payment is divided by (1 + market interest rate) raised to the number of years until the payment is received. The face value payment at maturity is also discounted back to the present using the same method. Summing these present values provides the bond's issue price, which in this case would be higher than the face value due to the premium.

Calculating Bond Price with a Discount Rate

When recalculating the bond's price with a higher discount rate than the bond's interest rate, for example, a discount rate of 12% versus an 8% interest rate, the bond's present value would decrease. This is because the future cash flows are discounted more heavily, reflecting the higher opportunity cost of not investing in an alternative investment with a higher return. Therefore, with a higher discount rate, the bond's price will be less.

Answer 2

The issue price of the bond can be found by calculating the present value of its cash flows discounted at the market interest rate, which is higher than the bond's stated interest rate. The bond will be issued at a premium, and the two main components to consider for the issue price calculation are the present value of the bond's coupon payments and the present value of its face value at maturity.

Step-by-step explanation:

The issue price of a bond when the bond's interest rate is less than the market interest rate can be calculated by finding the present value of the bond's cash flows discounted at the market interest rate. Since the bond's stated interest rate (7%) is lower than the market interest rate (5%), the bond will be issued at a premium.

To calculate the issue price, we would first calculate the present value of the bond's annual coupon payments, which would be $700 ($10,000 x 7%), and then discount them at the market interest rate of 5% over the 5-year term. Additionally, we calculate the present value of the $10,000 face value, which is repaid at the end of the bond's term, and also discount this at the market interest rate of 5%. Adding these two present values together gives us the issue price of the bond.

Using an example similar to the one provided, if the market interest rates are now 12%, and you could invest $964 to receive $1,080 in a year, then you would not pay more than $964 for a bond paying $1,000 at maturity plus the final interest payment. This is because the discounted value of this bond's expected payments at the prevailing market interest rate determines its fair market price.