The market price of a semi-annual pay bond is $994.96. It has 17.00 years to maturity and a coupon rate of 6.00%. Par value is $1,000. What is the effective annual yield?

Answer 1

To calculate the effective annual yield (EAY) of the bond, we first need to determine several key components, including the semi-annual coupon payment, the number of periods until maturity, and the yield to maturity (YTM).

1. Calculate the semi-annual coupon payment:

   • The bond has a par value of $1,000 and a coupon rate of 6.00%.
   • Semi-annual coupon payment = \( \frac{6% \times 1000}{2} = \frac{60}{2} = 30 \).

2. Determine the number of periods until maturity:

   • The bond has 17.00 years to maturity and pays interest semi-annually.
   • Total number of periods = \( 17 \times 2 = 34 \).

3. Set up the cash flow equation for YTM: The bond price can be expressed with the following formula: \[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \] Where:

   • \( P \) = market price of the bond = $994.96,
   • \( C \) = semi-annual coupon payment = $30,
   • \( F \) = face value of the bond = $1,000,
   • \( n \) = total number of periods = 34,
   • \( r \) = semi-annual YTM (yield per period).

   This is an equation we need to solve for \( r \).

4. Using trial and error or a financial calculator: You might typically use a financial calculator or Excel to find \( r \). For simplicity, let’s start with estimating YTM using bond formulas and approximation.

   A good approximation for YTM, especially using \( P, C,\) and \( F \), can be: \[ r \approx \frac{C + \frac{F - P}{n}}{\frac{F + P}{2}} \]

   Plugging in the values: \[ r \approx \frac{30 + \frac{1000 - 994.96}{34}}{\frac{1000 + 994.96}{2}} = \frac{30 + \frac{5.04}{34}}{\frac{1994.96}{2}} = \frac{30 + 0.14824}{997.48} = \frac{30.14824}{997.48} \approx 0.03024 \text{ or } 3.024% \]

5. Convert to effective annual yield (EAY): Since this is a semi-annual coupon bond, the effective annual yield can be calculated by: \[ \text{EAY} = \left(1 + r\right)^2 - 1 \] Substituting in our semi-annual yield: \[ \text{EAY} = (1 + 0.03024)^2 - 1 \approx 1.03024^2 - 1 \approx 1.06168 - 1 \approx 0.06168 \]

   Converting to percentage: \[ \text{EAY} \approx 6.168% \]

Conclusion: The effective annual yield (EAY) of the bond is approximately 6.17%.