Bond P is a premium bond with a coupon rate of 10 percent. Bond D has a coupon rate of 5 percent and is selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have ten years to maturity.

What is the current yield for Bond P and Bond D?

To calculate the current yield for Bond P and Bond D, we use the following formula:

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

Given:
- Both bonds have 10 years to maturity.
- Yield to Maturity (YTM) for both bonds is 7%.
- Bond P has a coupon rate of 10%.
- Bond D has a coupon rate of 5%.

First, let's determine the current price of each bond using the present value of the bond's cash flows (coupons and face value) discounted at the YTM.

### Price of Bond P
Bond P is a premium bond with a coupon rate of 10% and annual payments. The price of the bond can be calculated using the following formula:

\[ P = \sum_{t=1}^{10} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^{10}} \]

Where:
- \( C = 0.10 \times 1000 = 100 \) (Annual coupon payment)
- \( F = 1000 \) (Face value)
- \( r = 0.07 \) (YTM)

\[ P = \sum_{t=1}^{10} \frac{100}{(1 + 0.07)^t} + \frac{1000}{(1 + 0.07)^{10}} \]

Using a financial calculator or spreadsheet:

\[ P = 100 \left( \frac{1 - (1 + 0.07)^{-10}}{0.07} \right) + \frac{1000}{(1 + 0.07)^{10}} \]
\[ P = 100 \left( 7.0236 \right) + \frac{1000}{1.9672} \]
\[ P = 702.36 + 508.35 \]
\[ P \approx 1210.71 \]

### Price of Bond D
Bond D is a discount bond with a coupon rate of 5% and annual payments. The price of the bond can be calculated similarly:

\[ P = \sum_{t=1}^{10} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^{10}} \]

Where:
- \( C = 0.05 \times 1000 = 50 \) (Annual coupon payment)
- \( F = 1000 \) (Face value)
- \( r = 0.07 \) (YTM)

\[ P = \sum_{t=1}^{10} \frac{50}{(1 + 0.07)^t} + \frac{1000}{(1 + 0.07)^{10}} \]

Using a financial calculator or spreadsheet:

\[ P = 50 \left( \frac{1 - (1 + 0.07)^{-10}}{0.07} \right) + \frac{1000}{(1 + 0.07)^{10}} \]
\[ P = 50 \left( 7.0236 \right) + \frac{1000}{1.9672} \]
\[ P = 351.18 + 508.35 \]
\[ P \approx 859.53 \]

### Current Yield Calculation
Now that we have the prices of the bonds, we can calculate the current yield.

#### Current Yield for Bond P:
\[ \text{Current Yield} = \frac{100}{1210.71} \]
\[ \text{Current Yield} \approx 0.0826 \]
\[ \text{Current Yield} \approx 8.26\% \]

#### Current Yield for Bond D:
\[ \text{Current Yield} = \frac{50}{859.53} \]
\[ \text{Current Yield} \approx 0.0582 \]
\[ \text{Current Yield} \approx 5.82\% \]

### Summary
- **Current Yield for Bond P**: 8.26%
- **Current Yield for Bond D**: 5.82%

Would you like more details on the bond price calculations or further explanations on bond yield concepts?

### Relative Questions
1. What is the difference between current yield and yield to maturity (YTM)?
2. How do changes in market interest rates affect the price of premium and discount bonds?
3. What factors contribute to a bond being sold at a premium or discount?
4. How is the current yield useful for bond investors?
5. What is the relationship between coupon rate, current yield, and YTM for a bond?
6. Can a bond's current yield exceed its coupon rate? If so, under what conditions?
7. How do annual payments versus semiannual payments affect bond pricing and yield calculations?
8. What risks do investors face when purchasing premium bonds compared to discount bonds?

### Tip
When evaluating bonds, it's important to understand that current yield provides a snapshot of the income relative to the bond's price, but it does not account for the total return, including capital gains or losses, which is captured by the yield to maturity (YTM).

Learn how to calculate the current yield for Bond P with a 10% coupon rate and Bond D with a 5% coupon rate. Understand the formula and step-by-step calculation process using the given yield to maturity (YTM) and bond characteristics. Suitable for college-level students and finance professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation