Wine and Roses, Incorporated, offers a bond with a coupon of 6.0 percent with semiannual payments and a yield to maturity of 6.91 percent. The bonds mature in 12 years. What is the market price of a $1,000 face value bond?

multiple choice
$1,410.62
$1,484.04
$1,442.55
$926.59
$1,023.89

To find the market price of the bond, we can use the **present value of cash flows** formula for a bond, which consists of two parts: the **present value of the coupon payments** and the **present value of the face value**.

The bond provides **semiannual payments**, so we will adjust the coupon rate, yield to maturity, and the number of periods accordingly. Here’s how to approach it:

1. **Coupon payment (C):**
   \[
   C = \left( \frac{\text{Coupon Rate}}{2} \right) \times \text{Face Value} = \left( \frac{6.0\%}{2} \right) \times 1000 = 0.03 \times 1000 = 30
   \]
   So, the semiannual coupon payment is **$30**.

2. **Number of periods (N):**
   Since the bond matures in 12 years and pays semiannually:
   \[
   N = 12 \times 2 = 24 \text{ periods}
   \]

3. **Yield to maturity per period (r):**
   The yield to maturity is 6.91% annually, so the semiannual yield is:
   \[
   r = \frac{6.91\%}{2} = 0.03455 = 3.455\%
   \]

4. **Present Value of Coupons:**
   The present value of the coupon payments is the present value of an annuity:
   \[
   PV_{\text{coupons}} = C \times \left( 1 - \left( 1 + r \right)^{-N} \right) \div r
   \]

5. **Present Value of Face Value:**
   The present value of the $1,000 face value paid at the end is:
   \[
   PV_{\text{face value}} = \frac{1000}{(1 + r)^N}
   \]

Let me calculate this now.The market price of the bond is approximately **$926.59**, which matches the closest option:

**$926.59**

Would you like further details or explanations?

Here are 5 related questions for further exploration:
1. How does the coupon rate affect the bond price if the yield to maturity changes?
2. What happens to bond prices when interest rates increase?
3. How does the number of periods (time to maturity) influence the bond’s market price?
4. What is the relationship between the yield to maturity and the current bond price?
5. How is the price of a zero-coupon bond calculated?

**Tip:** When bond prices fall below face value, the bond is said to be trading at a **discount**.

Wine and Roses, Incorporated, offers a bond with a coupon of 6.0 percent with semiannual payments and a yield to maturity of 6.91 percent. The bonds mature in 12 years. What is the market price of a $1,000 face value bond?

Learn how to calculate the market price of a $1,000 face value bond with a 6.0% coupon rate and 6.91% yield to maturity, using present value formulas for coupon payments and face value. Suitable for finance students and bond market enthusiasts.

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