Question

Consider a bond that has a par value of $1,000, pays a coupon rate of 10% at the end of each year, and has three years remaining until maturity. Assume that the prevailing annualized yield for a bond order requested and indicate the number of the question: 1. Determine the appropriate value of the bond. Show the formula, do the math step by step until the final result, and indicate the unit of measurement. 2. Is the bond traded at a discount, premium, or at par value? Explain.

Answer 1

The present value of the bond is approximately $1,198.86, indicating that the bond is traded at a premium.

Step-by-step explanation:

To calculate the value of the bond, we can use the formula for present value of a bond:

Present Value = Coupon Payment x (1 - (1 / (1 + Yield Rate)^Number of Periods)) / Yield Rate + Face Value / (1 + Yield Rate)^Number of Periods

In this case, the par value is $1,000, the coupon rate is 10% (which means the coupon payment is $100), and there are three years remaining until maturity. Let's assume the annualized yield rate is 8%. Plugging in these values into the formula, we get:

Present Value = $100 x (1 - (1 / (1 + 0.08)^3)) / 0.08 + $1,000 / (1 + 0.08)^3

Simplifying the equation, we find that the appropriate value of the bond is approximately $1,198.86. The unit of measurement is in dollars ($).

To determine if the bond is traded at a discount, premium, or at par value, we can compare the value of the bond to its par value. In this case, since the value of the bond is higher than its par value ($1,198.86 > $1,000), the bond is traded at a premium.