What's the value to you of a $1,000 face-value bond with an 8% coupon rate when your required rate of return is 15 percent?
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A. B. C. D.B
To determine the value of a bond, we need to calculate its present value. The present value of a bond is the sum of the present values of all its future cash flows, which include the coupon payments and the face value payment at maturity.
The formula to calculate the present value of a bond is:
PV = C/(1+r)^1 + C/(1+r)^2 + ... + C/(1+r)^n + F/(1+r)^n
Where: C = Coupon payment r = Required rate of return n = Number of periods F = Face value payment at maturity
In this case, the bond has a face value of $1,000 and a coupon rate of 8%, which means that it pays $80 in annual coupon payments (8% of $1,000). The bond's required rate of return is 15%.
Let's assume that the bond has a remaining term of 5 years, which means that it will pay 5 more annual coupon payments of $80 and a final face value payment of $1,000 at maturity.
Using the formula above, we can calculate the present value of the bond:
PV = $80/(1+0.15)^1 + $80/(1+0.15)^2 + $80/(1+0.15)^3 + $80/(1+0.15)^4 + $80/(1+0.15)^5 + $1,000/(1+0.15)^5
PV = $63.16 + $54.92 + $47.77 + $41.50 + $35.96 + $497.18
PV = $740.49
Therefore, the value of the bond to you is $740.49, which is less than its face value of $1,000.
So the correct answer is B. Less than its face value.