A bond with a par value of £1,000 makes annual coupon payments of 6%. If investors holding the bonds require an 8% rate of return, and the bond has 5 years left to maturity what is the current bond price, to the nearest whole pound?£681£1,084£1,123£920£870
Question
A bond with a par value of £1,000 makes annual coupon payments of 6%. If investors holding the bonds require an 8% rate of return, and the bond has 5 years left to maturity what is the current bond price, to the nearest whole pound?£681£1,084£1,123£920£870
Solution
To calculate the current bond price, we need to calculate the present value of the bond's future cash flows, which include the annual coupon payments and the par value at maturity.
Step 1: Calculate the present value of the coupon payments.
The bond makes annual coupon payments of 6% of the par value, which is £1,000 * 6% = £60.
The present value of these payments is calculated as an annuity. The formula for the present value of an annuity is:
PVA = PMT * [(1 - (1 + r)^-n) / r]
where: PMT = annual payment = £60 r = required rate of return = 8% = 0.08 n = number of years = 5
So, the present value of the coupon payments is:
PVA = £60 * [(1 - (1 + 0.08)^-5) / 0.08] = £248.69
Step 2: Calculate the present value of the par value at maturity.
The present value of the par value is calculated as a single sum. The formula for the present value of a single sum is:
PV = FV / (1 + r)^n
where: FV = future value = par value = £1,000 r = required rate of return = 8% = 0.08 n = number of years = 5
So, the present value of the par value is:
PV = £1,000 / (1 + 0.08)^5 = £680.58
Step 3: Add the present values from steps 1 and 2 to get the current bond price.
Current bond price = PVA + PV = £248.69 + £680.58 = £929.27
Rounding to the nearest whole pound, the current bond price is £929. So, the closest answer is £920.
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