ABC Health Med, has a $1,000 par value bond with an 8 percent rate outstanding. The bond has 12 years remaining to it maturity date.
If interest is paid semiannual interest, what is the value of the bond when the required return is 8 percent. Show all work.
To find the value of the bond, we need to calculate the present value of all future cash flows, which include the periodic interest payments and the bond's face value at maturity.
Step 1: Calculate the number of periods:
Since the bond pays semiannual interest, we need to double the number of years remaining to maturity. Therefore, the number of periods is 12 * 2 = 24.
Step 2: Determine the periodic interest payment:
The annual interest payment is calculated as a percentage of the par value of the bond. In this case, the annual interest payment is $1,000 * 8% = $80. As there are two interest payments per year, the semiannual interest payment is $80 / 2 = $40.
Step 3: Determine the required rate of return:
The question states that the required return is 8 percent.
Step 4: Calculate the present value of future cash flows:
To calculate the present value of the bond, we will use the formula for the present value of an annuity. The formula is:
PV = CF * [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value
CF = Cash Flow per period (semiannual interest payment)
r = Required rate of return per period (half of the annual required return)
n = Number of periods
In this case:
PV = $40 * [1 - (1 + 0.08/2)^(-24)] / (0.08/2)
Simplifying the formula:
PV = $40 * [1 - (1.04)^(-24)] / 0.04
Calculating the present value:
PV = $40 * [1 - 0.4564] / 0.04
PV = $40 * (0.5436) / 0.04
PV = $21.744 / 0.04
PV = $543.60
Therefore, the value of the bond, when the required return is 8 percent, is $543.60.