Assume WhirledCom has an issue of 15 year $1000 par value bonds that pay 6% interest, semiannually Futher asssume that today's required rate of return on htese bonds is 9% How much would these bonds be worth today? Round off to the nearest $1
$1,000. @ 9% for 15 years, compounded sem0-annually.
Pt = Po(1+r)^n.
r = (9% / 2) /100% = 0.045 = S-APR expressed a a decimal.
n = 2comp./yr * 15yrs = 30 Compounding periods.
Pt = $1000(1.045)^30 = $3745.
To calculate the present value of the bonds, we need to use the formula for the present value of a bond:
PV = C * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
C = Periodic interest payment (in this case, semiannually)
r = Required rate of return per period
n = Number of periods until maturity
In this case, the periodic interest payment is $1000 * 6% / 2 = $30, because the 6% interest is paid semiannually.
The required rate of return is given as 9% per year, so we need to use 4.5% per semiannual period, which is 9% / 2.
The bonds have a 15-year maturity, which means there will be 15 * 2 = 30 semiannual periods.
Now we can substitute these values into the formula:
PV = $30 * (1 - (1 + 4.5%)^(-30)) / 4.5%
Calculating this expression will give us the present value of the bonds. Rounding off to the nearest $1 will give us the final answer.
Please note that the percentage values should be converted to decimal form before calculating.