**Bond Pricing Calculation Assignment** **Problem Statement:** A 10-year semiannual coupon bond with a coupon rate of 7% per year is selling to yield 6.5% per year compounded semiannually. What is the bond price if the yield changes to: (i) 6% (ii) 6.7% both compounded semiannually? **Instructions:** You should: a) **Use the exact method.** b) **Use the first-order linear approximation based on the modified duration.** c) **Use the first-order approximation based on the Macaulay duration.** --- **Detailed Explanation:** 1. **Exact Method:** - Calculate the bond price using the present value formula, where the bond price is the sum of the present values of all future cash flows. - Use the given yields (6% and 6.7%) to find the present values, considering semiannual compounding. 2. **First-Order Linear Approximation using Modified Duration:** - Modified duration provides an estimate of the bond price sensitivity to changes in yield. - Use the formula: ΔP ≈ -D_mod * Δy, where ΔP is the change in bond price, D_mod is the modified duration, and Δy is the change in yield. - Apply this approximation for both yield changes (from 6.5% to 6% and 6.5% to 6.7%). 3. **First-Order Approximation using Macaulay Duration:** - Macaulay duration also provides an estimate of the interest rate sensitivity and is the weighted average time until cash flows are received. - Use the duration to approximate the new bond price. - Consider the change in yield and apply the Macaulay duration to find the price adjustments. This problem is designed to help students understand the impact of yield changes on bond prices and to practice different methods of bond pricing calculations.
**Bond Pricing Calculation Assignment** **Problem Statement:** A 10-year semiannual coupon bond with a coupon rate of 7% per year is selling to yield 6.5% per year compounded semiannually. What is the bond price if the yield changes to: (i) 6% (ii) 6.7% both compounded semiannually? **Instructions:** You should: a) **Use the exact method.** b) **Use the first-order linear approximation based on the modified duration.** c) **Use the first-order approximation based on the Macaulay duration.** --- **Detailed Explanation:** 1. **Exact Method:** - Calculate the bond price using the present value formula, where the bond price is the sum of the present values of all future cash flows. - Use the given yields (6% and 6.7%) to find the present values, considering semiannual compounding. 2. **First-Order Linear Approximation using Modified Duration:** - Modified duration provides an estimate of the bond price sensitivity to changes in yield. - Use the formula: ΔP ≈ -D_mod * Δy, where ΔP is the change in bond price, D_mod is the modified duration, and Δy is the change in yield. - Apply this approximation for both yield changes (from 6.5% to 6% and 6.5% to 6.7%). 3. **First-Order Approximation using Macaulay Duration:** - Macaulay duration also provides an estimate of the interest rate sensitivity and is the weighted average time until cash flows are received. - Use the duration to approximate the new bond price. - Consider the change in yield and apply the Macaulay duration to find the price adjustments. This problem is designed to help students understand the impact of yield changes on bond prices and to practice different methods of bond pricing calculations.
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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Transcribed Image Text:**Bond Pricing Calculation Assignment**
**Problem Statement:**
A 10-year semiannual coupon bond with a coupon rate of 7% per year is selling to yield 6.5% per year compounded semiannually. What is the bond price if the yield changes to:
(i) 6%
(ii) 6.7%
both compounded semiannually?
**Instructions:**
You should:
a) **Use the exact method.**
b) **Use the first-order linear approximation based on the modified duration.**
c) **Use the first-order approximation based on the Macaulay duration.**
---
**Detailed Explanation:**
1. **Exact Method:**
- Calculate the bond price using the present value formula, where the bond price is the sum of the present values of all future cash flows.
- Use the given yields (6% and 6.7%) to find the present values, considering semiannual compounding.
2. **First-Order Linear Approximation using Modified Duration:**
- Modified duration provides an estimate of the bond price sensitivity to changes in yield.
- Use the formula: ΔP ≈ -D_mod * Δy, where ΔP is the change in bond price, D_mod is the modified duration, and Δy is the change in yield.
- Apply this approximation for both yield changes (from 6.5% to 6% and 6.5% to 6.7%).
3. **First-Order Approximation using Macaulay Duration:**
- Macaulay duration also provides an estimate of the interest rate sensitivity and is the weighted average time until cash flows are received.
- Use the duration to approximate the new bond price.
- Consider the change in yield and apply the Macaulay duration to find the price adjustments.
This problem is designed to help students understand the impact of yield changes on bond prices and to practice different methods of bond pricing calculations.
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