A government bond with a face value of $1,000 was issued eight years ago and there are twelve years remaining until maturity. The bond pays annual coupon payments of $90, the coupon rate is 9% pa and rates in the marketplace are 9.5% p.a. What is the value of the bond today?Group of answer choices$965.08$931.86$1,600.97$1,040.05$1,000.00
Question
A government bond with a face value of 90, the coupon rate is 9% pa and rates in the marketplace are 9.5% p.a. What is the value of the bond today?Group of answer choices931.861,040.05$1,000.00
Solution
To calculate the value of the bond today, we need to calculate the present value of the future cash flows. The cash flows consist of the annual coupon payments and the face value of the bond at maturity.
Step 1: Calculate the present value of the coupon payments.
The bond pays annual coupon payments of $90 for the next 12 years. The present value of these payments can be calculated using the formula for the present value of an annuity:
PV = C * [(1 - (1 + r)^-n) / r]
where: C = annual coupon payment = $90 r = discount rate = 9.5% = 0.095 n = number of years = 12
PV = 690.08
Step 2: Calculate the present value of the face value.
The face value of the bond is $1,000, which will be received at the end of 12 years. The present value of this amount can be calculated using the formula for the present value of a single sum:
PV = FV / (1 + r)^n
where: FV = face value = $1,000 r = discount rate = 9.5% = 0.095 n = number of years = 12
PV = 275
Step 3: Add the present values.
The value of the bond today is the sum of the present values of the future cash flows:
Value = PV of coupon payments + PV of face value = 275 = $965.08
So, the value of the bond today is $965.08.
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