A corporate bond with a face value of $100,000 was issued six years ago and there are four 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 8% pa compounded semi-annually. What is the value of the bond today? Group of answer choices $88,407.56 $102,621.07 $104,692.54 $103,366.37 $100,000.00
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 8% pa compounded semi-annually. What is the value of the bond today?
Group of answer choices
$88,407.56
$102,621.07
$104,692.54
$103,366.37
$100,000.00
Solution
To calculate 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 4 years, which is 8 periods (4 years * 2). The market interest rate is 8% per annum compounded semi-annually, so the rate per period is 4% (8% / 2).
The present value of an annuity formula is:
PV = C * [(1 - (1 + r)^-n) / r]
where: C = cash flow per period ($4500) r = interest rate per period (4% or 0.04) n = number of periods (8)
PV = 30,621.07
Step 2: Calculate the present value of the face value of the bond at maturity.
The face value of the bond is $100,000 and it will be paid back at the end of 4 years (8 periods). The present value of a single sum formula is:
PV = FV / (1 + r)^n
where: FV = future value ($100,000) r = interest rate per period (4% or 0.04) n = number of periods (8)
PV = 72,000
Step 3: Add the present values calculated in step 1 and step 2 to get the value of the bond today.
Value of bond = PV of coupon payments + PV of face value Value of bond = 72,000 = $102,621.07
So, the value of the bond today is 102,621.07.
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