A corporate bond with a face value of $100,000 was issued six years ago and there are nine years remaining until maturity. The bond pays semi-annual coupon payments of $4500, the coupon rate is 9% pa paid twice yearly and rates in the marketplace are 9.4% pa compounded semi-annually. What is the value of the bond today? Group of answer choices $98,975.05 $97,606.30 $71,095.02 $100,000.00 $98,196.97
Question
A corporate bond with a face value of 4500, the coupon rate is 9% pa paid twice yearly and rates in the marketplace are 9.4% pa compounded semi-annually. What is the value of the bond today?
Group of answer choices
$98,975.05
$97,606.30
$71,095.02
$100,000.00
$98,196.97
Solution
To find the value of the bond today, we need to calculate the present value of the future cash flows, which are the semi-annual coupon payments and the face value of the bond at maturity.
Step 1: Calculate the present value of the semi-annual coupon payments.
The bond pays semi-annual coupon payments of $4500 for the next 9 years, which is 18 periods. The discount rate is 9.4% per annum compounded semi-annually, so the discount rate per period is 9.4%/2 = 4.7%.
Using the formula for the present value of an annuity:
PV = C * [(1 - (1 + r)^-n) / r]
where: C = coupon payment = $4500 r = discount rate per period = 4.7% = 0.047 n = number of periods = 18
PV = 60,606.30
Step 2: Calculate the present value of the face value of the bond at maturity.
The face value of the bond is $100,000, which will be received in 18 periods. Using the formula for the present value of a single sum:
PV = FV / (1 + r)^n
where: FV = future value = $100,000 r = discount rate per period = 4.7% = 0.047 n = number of periods = 18
PV = 37,000
Step 3: Add the present values calculated in steps 1 and 2 to find the value of the bond today.
Value of bond = PV of coupon payments + PV of face value Value of bond = 37,000 = $97,606.30
So, the value of the bond today is 97,606.30.
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