Benson Incorporated has bonds with the following features: Par value of 1,000, maturity of 12 years, and a coupon rate of 8%.The yield to maturity is 10%. Pleases determine if the bond sells for 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 your work?
To determine if the bond sells at a premium, par, or discount, we compare the coupon rate to the yield to maturity (YTM).
If the coupon rate is higher than the yield to maturity, the bond sells at a premium. This means that investors are willing to pay more than the face value of the bond because the coupon rate is higher than the market interest rate.
If the coupon rate is equal to the yield to maturity, the bond sells at par. This means that the bond is priced exactly at its face value, and the coupon rate is equal to the market interest rate.
If the coupon rate is lower than the yield to maturity, the bond sells at a discount. This means that investors are not willing to pay the full face value of the bond because the coupon rate is lower than the market interest rate.
In this case, the coupon rate is 8% and the yield to maturity is 10%. Since the yield to maturity is higher than the coupon rate, the bond sells at a discount.
To calculate the value of the bond, we need to determine the present value of its cash flows. With an annual coupon payment and a semi-annual payment, the cash flows are as follows:
- Annual payment: $80 (8% of $1,000 face value)
- Semi-annual payment: $40 (8% of $1,000 face value divided by 2)
To calculate the value of the bond with an annual payment, we use the formula:
Bond value = [C x (1 - (1+r)^-n)]/r + FV/(1+r)^n
Where:
C = Coupon payment
r = Yield to maturity
n = Number of periods until maturity (in this case, 12 years)
Substituting the values, we get:
Bond value = [80 x (1 - (1+0.10)^-12)]/0.10 + 1000/(1+0.10)^12
= 584.45 + 321.97
= $906.42
Therefore, the value of the bond with annual payments is $906.42.
To calculate the value of the bond with semi-annual payments, we use the same formula, but adjust the values of C and n:
C = $40 (semi-annual payment)
n = 24 (2 payments per year for 12 years)
Substituting the values, we get:
Bond value = [40 x (1 - (1+0.10)^-24)]/0.10 + 1000/(1+0.10)^24
= 434.96 + 256.73
= $691.69
Therefore, the value of the bond with semi-annual payments is $691.69.