What is the value of a $1000 bond if the investors' required rate of return is 11.5%, and it has 7 years until maturity. The coupon rate is 8%. (Please round your answer to the nearest dollar but exclude the $ sign and , when typing your answer.)
Question
What is the value of a sign and , when typing your answer.)
Solution 1
The value of a bond is calculated by discounting the future cash flows (coupon payments and the face value at maturity) to the present using the required rate of return as the discount rate.
The bond in question pays annual coupons of 8% * 80 and has a face value of $1000 that will be paid back at maturity.
The present value (PV) of the coupon payments is calculated as follows:
PV(coupons) = 380.68 (rounded to the nearest dollar)
The present value of the face value is calculated as follows:
PV(face value) = 513.16 (rounded to the nearest dollar)
Adding these two present values together gives the value of the bond:
Value of bond = PV(coupons) + PV(face value) = 513 = $893
So, the value of the bond is $893 when rounded to the nearest dollar.
Solution 2
The value of a bond is calculated by discounting the future cash flows (coupon payments and the face value at maturity) to the present using the required rate of return as the discount rate.
The bond in question pays annual coupons of 8% * 80 and has a face value of $1000 that will be paid back at maturity.
The present value (PV) of the coupon payments is calculated as follows:
PV(coupons) = 380.68 (rounded to the nearest dollar)
The present value of the face value is calculated as follows:
PV(face value) = 513.16 (rounded to the nearest dollar)
Adding these two present values together gives the value of the bond:
Value of bond = PV(coupons) + PV(face value) = 513 = $893
So, the value of the bond is $893 when rounded to the nearest dollar.
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