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The British government has a consol bond outstanding paying per year forever. Assume the
current interest rate is 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?
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
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 . (Round to the nearest pound.)
nearest pound.)
v

Ask by Griffiths Potter. in the United States
Jan 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

  • a. The bond is worth £833 immediately after a payment.
  • b. The bond is worth £933 immediately before a payment.

Solution

Certainly! Let’s solve both parts of the problem step by step.

Given:

  • Consol Bond Payment ©: £100 per year (forever)
  • Interest Rate ®: 12% per year

a. Value of the Bond Immediately After a Payment is Made

Understanding the Scenario:
  • Immediately after a payment is made, the next payment is one year away.
  • The bond is essentially a perpetuity, meaning it will pay £100 every year indefinitely.
Valuation Formula for a Perpetuity:
where:
  • = Annual payment (£100)
  • = Interest rate (0.12)
Calculations:
Rounded to the Nearest Pound:
Answer:
  • a. The value of the bond immediately after a payment is made is £833.

b. Value of the Bond Immediately Before a Payment is Made

Understanding the Scenario:
  • Immediately before a payment is made, you are about to receive the £100 payment.
  • Additionally, the bond still has all future payments to offer, starting from the next year onward.
Valuation Approach:
  1. Immediate Payment: You receive £100 right now.
  2. Present Value of Remaining Payments: The value of the bond after this payment is made (which we’ve already calculated as £833).
Total Value:
Rounded to the Nearest Pound:
Answer:
  • b. The value of the bond immediately before a payment is made is £933.

Summary of Answers:

  • a. £833
  • b. £933

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Bonus Knowledge

To determine the values, we can use the formula for a consol bond, which is a type of perpetuity. The value of a consol can be calculated using the following formula:
where is the annual payment and is the interest rate.
  1. Immediately after a payment is made: The bond has just paid , which means the next payment will occur at the end of the year. The value immediately after the payment is made is:
Rounded to the nearest pound, this is .
  1. Immediately before a payment is made: This is just the value we computed, but since the next payment is approaching, we don’t have that payment included in this valuation. Thus, the value immediately before the payment is made would be:
But since we haven’t received that payment yet, we must account for one less payment till the next one is made, thus evaluating:
Final rounded values are:
a. The value of the bond immediately after a payment is made is .
b. The value of the bond immediately before a payment is made is .

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