Bond prices and yields   Assume that the Financial Management​ Corporation's

​$1 comma 000

​-par-value 

bond has a

7.600 %
 
​coupon, matures on May​ 15, 2027, has a current price quote of

112.921
 
and a yield to maturity​ (YTM) of

6.618 %

. 

Given this​ information, answer the following​ questions:

a.  What was the dollar price of the​ bond?

b.  What is the ​bond's current​ yield?

c.  Is the bond selling at​ par, at a​ discount, or at a​ premium? ​ Why?

d.  Compare the​ bond's current yield calculated in part b to its YTM and explain why they differ.

Question content area bottom

Part 1

a.  The dollar price of the bond is

​$enter your response here

. 

​(Round to the nearest​ cent.)

Let's go step by step to solve each part of the question. 

### Given:
- **Par value of the bond (Face Value):** $1,000
- **Coupon rate:** 7.600%
- **Current price quote:** 112.921
- **Yield to maturity (YTM):** 6.618%
- **Maturity date:** May 15, 2027

---

### a. Dollar Price of the Bond

The **price quote** is given as 112.921, which means the bond is selling at **112.921%** of its par value.

To find the **dollar price**:

\[
\text{Dollar Price} = \frac{\text{Price Quote}}{100} \times \text{Par Value}
\]

Substitute the values:

\[
\text{Dollar Price} = \frac{112.921}{100} \times 1000 = 1129.21
\]

**Answer:**

The dollar price of the bond is **$1,129.21**.

---

### b. Current Yield

The **current yield** is calculated using the formula:

\[
\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Bond Price}}
\]

The **annual coupon payment** can be found by multiplying the coupon rate by the par value:

\[
\text{Annual Coupon Payment} = \text{Coupon Rate} \times \text{Par Value} = 0.076 \times 1000 = 76
\]

Now, use the dollar price from part a to calculate the current yield:

\[
\text{Current Yield} = \frac{76}{1129.21} \approx 0.0673 = 6.73\%
\]

**Answer:**

The bond's current yield is **6.73%**.

---

### c. Is the bond selling at par, at a discount, or at a premium?

A bond sells at:
- **Par** if its price equals its par value.
- **Discount** if its price is below its par value.
- **Premium** if its price is above its par value.

Since the dollar price of the bond (**$1,129.21**) is greater than the par value (**$1,000**), the bond is selling at a **premium**.

**Answer:**

The bond is selling at a **premium** because its price (**$1,129.21**) is higher than the par value (**$1,000**).

---

### d. Comparison of Current Yield and YTM

- The **current yield** we calculated is **6.73%**.
- The given **YTM** is **6.618%**.

The **current yield** only considers the coupon income relative to the bond's current price, while the **YTM** takes into account both the coupon payments and any capital gain or loss if the bond is held to maturity.

Since the bond is selling at a premium (above par), the **YTM** is slightly lower than the current yield. This is because part of the bond's return comes from the decline in price as it approaches its par value at maturity.

**Answer:**

The bond's **current yield** is **6.73%**, which is higher than its **YTM** of **6.618%** because the bond is selling at a premium, meaning its price will decrease as it nears maturity, reducing the overall return.

---

### Recap:
- **a.** Dollar Price: **$1,129.21**
- **b.** Current Yield: **6.73%**
- **c.** The bond is selling at a **premium**.
- **d.** The **current yield** is higher than the **YTM** because the bond is selling at a premium.

---

Would you like more details or have any questions on any part?

Here are 5 questions to explore related topics:
1. How is the yield to maturity (YTM) different from the coupon rate?
2. What factors influence whether a bond sells at a premium or discount?
3. How do interest rate changes affect bond prices?
4. What is the relationship between bond prices and market interest rates?
5. How can one calculate the yield to maturity (YTM) manually?

**Tip:** The bond's yield to maturity (YTM) is the most comprehensive measure of return as it accounts for all cash flows over the life of the bond, including reinvestment of coupon payments.

Assume that the Financial Management Corporation's $1,000-par-value bond has a 7.600% coupon, matures on May 15, 2027, has a current price quote of 112.921, and a yield to maturity (YTM) of 6.618%. Given this information, answer the following questions: a) What was the dollar price of the bond? b) What is the bond's current yield? c) Is the bond selling at par, at a discount, or at a premium? Why? d) Compare the bond's current yield calculated in part b to its YTM and explain why they differ.

Explore bond pricing and yields for the $1,000-par-value bond with a 7.600% coupon maturing in 2027, including how to calculate the dollar price, current yield, and the difference between current yield and YTM. Suitable for finance students.

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