The British government has a consol bond outstanding paying 

pound 300£300 

per year forever. Assume the current interest rate is 

8 %8% 

per year.

**a.** What is the value of the bond immediately after a payment is​ made?

**b.** What is the value of the bond immediately before a payment is​ made?

Question content area bottom

Part 1

**a.** What is the value of the bond immediately after a payment is​ made?

The value of the bond immediately after a payment is made is 

​£enter your response here. 

 ​(Round to two decimal​ places.)

Part 2

**b.** What is the value of the bond immediately before a payment is​ made?

The value of the bond immediately before a payment is made is 

​£enter your response here. 

 ​(Round to two decimal​ places.)

To solve these problems, we are dealing with a type of perpetual bond (consol bond) that pays a fixed annual coupon indefinitely. The value of a consol bond can be calculated using the following formula:

\[
\text{Value of the bond} = \frac{\text{Annual Payment}}{\text{Interest Rate}}
\]

Given:
- Annual Payment (Coupon) = £300
- Interest Rate = 8% or 0.08

### **Part 1: Value of the bond immediately after a payment is made**

Immediately after the payment, there is no upcoming coupon due, so we simply use the present value formula for a perpetual bond.

\[
\text{Value of the bond after payment} = \frac{300}{0.08} = 3750
\]

So, the value of the bond immediately after a payment is made is **£3750.00**.

---

### **Part 2: Value of the bond immediately before a payment is made**

Immediately before a payment is made, the bondholder is entitled to the £300 coupon payment due. Therefore, the value of the bond will be the present value of the perpetual bond **plus** the coupon that is about to be received.

\[
\text{Value of the bond before payment} = \text{Value of the bond after payment} + \text{Coupon Payment}
\]

Using the value from Part 1:

\[
\text{Value of the bond before payment} = 3750 + 300 = 4050
\]

So, the value of the bond immediately before a payment is made is **£4050.00**.

---

Let me know if you need more details or clarifications!

### Related Questions:
1. What happens to the value of the bond if the interest rate increases?
2. How would the value of the bond change if the annual payment increased?
3. What is the significance of a consol bond compared to other types of bonds?
4. How do interest rate changes affect the long-term behavior of perpetual bonds?
5. How would the value change if the interest rate was compounded semi-annually?

**Tip:** For bonds, when interest rates rise, bond prices typically fall, and vice versa.

The British government has a consol bond outstanding paying £300 per year forever. Assume the current interest rate is 8% per year.

**a.** What is the value of the bond immediately after a payment is made?

**b.** What is the value of the bond immediately before a payment is made?

The value of the bond immediately after a payment is made is £enter your response here. (Round to two decimal places.)

The value of the bond immediately before a payment is made is £enter your response here. (Round to two decimal places.)

Learn how to calculate the value of a British consol bond with a £300 annual payment and 8% interest rate. This finance problem explores the valuation of perpetual bonds, including the calculation for the bond's value both before and after a coupon payment. Perfect for students in college-level finance courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation