Benson Incorporated has bonds with the following features par value of 1000.00 maturity is 10%. Determine if the bond sells for a premium, par, or discount and explain your answer. Calculate the value of the bond if interest is paid on an annual basis versus a semi annual basis. show the work
To determine if the bond sells for a premium, par, or discount, we need to compare the bond's coupon rate with the prevailing market interest rate. Let's assume that the bond has a coupon rate of 5% (which means it pays 5% of its par value as interest annually) and the prevailing market interest rate is 4%.
If the bond's coupon rate is higher than the prevailing market interest rate, the bond will sell at a premium. If the coupon rate and the market interest rate are the same, the bond will sell at par. If the coupon rate is lower than the market interest rate, the bond will sell at a discount.
In this case, the coupon rate (5%) is higher than the market interest rate (4%), which means the bond will sell at a premium.
To calculate the value of the bond, we'll need to use the present value formula. The formula for a bond with an annual coupon payment is:
Value of the bond = (Coupon payment / (1 + Market interest rate)) + (Coupon payment / (1 + Market interest rate)^2) + ... + (Coupon payment + Par value) / (1 + Market interest rate)^N
Where:
Coupon payment = Annual interest payment on the bond (Par value * Coupon rate)
Market interest rate = Prevailing market interest rate
Par value = Face value or the principal amount ($1000 in this case)
N = Number of years to maturity (10 in this case)
Using the values given, let's calculate the value of the bond if interest is paid on an annual basis:
Coupon payment = $1000 * 0.05 = $50
Value of the bond = ($50 / (1 + 0.04)) + ($50 / (1 + 0.04)^2) + ... + ($50 + $1000) / (1 + 0.04)^10
Simplifying this equation will give you the value of the bond if interest is paid on an annual basis.
To calculate the value of the bond if interest is paid on a semi-annual basis, we'll need to adjust the market interest rate and the number of years to maturity. Since the bond is paid semi-annually, the market interest rate and the maturity need to be divided by 2. After making these adjustments, you can use the same formula mentioned above to calculate the value of the bond.