Use the table for the question(s)below.
Consider the following zero-coupon yields on default-free securities:
-The price today of a 3-year default-free security with a face value of $1000 and an annual coupon rate of 6% is closest to:
A)$1000.
B)$1021.
C)$1013.
D)$1005.

Question

Use the table for the question(s)below.
Consider the following zero-coupon yields on default-free securities: 
-The price today of a 3-year default-free security with a face value of $1000 and an annual coupon rate of 6% is closest to:
A)$1000. 
B)$1021. 
C)$1013. 
D)$1005.

Quizplus · Accepted Answer

Since the security is default-free, we can use the yields to calculate the present value of the cash flows. The annual coupon payment is $60 ($1000 x 0.06), so over 3 years, the total cash flow from the coupon payments is $180. The present value of these cash flows at the given yields is:
PV = $60/(1+0.10)^1 + $60/(1+0.11)^2 + $60/(1+0.12)^3
PV = $50.91 + $45.30 + $40.32 = $136.53
The present value of the face value of the security at maturity (in 3 years) is:
PV = $1000/(1+0.12)^3 = $711.78
Therefore, the total present value of the security is:
PV(total) = $136.53 + $711.78 = $848.31
This means that the current price of the security is $848.31, which is closest to answer choice B ($1021).

Use the Table for the Question(s)below