Question 1197302: Hi, please help me solve this problem
1.If the coupon rate of USD 1000 is 6%, the coupon rate is semiannual, the yield is 5%, and the maturity is 9 years, what is the price?
2.If the yield rises to 7%, what will the bond price be?
3.If the yield to maturity is 7%, what is the current bond yield?
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **1. Calculate Bond Price with 5% Yield**
* **Calculate Semiannual Coupon Payment:**
* Annual Coupon Payment = $1000 * 6% = $60
* Semiannual Coupon Payment = $60 / 2 = $30
* **Determine Number of Periods:**
* Number of Periods = 9 years * 2 (semiannual) = 18 periods
* **Calculate Semiannual Yield:**
* Semiannual Yield = 5% / 2 = 2.5%
* **Use the Bond Pricing Formula:**
* Bond Price =
* (Coupon Payment * [1 - (1 + Semiannual Yield)^-Number of Periods]) / Semiannual Yield
* +
* (Face Value / (1 + Semiannual Yield)^Number of Periods)
* Bond Price =
* ($30 * [1 - (1 + 0.025)^-18]) / 0.025
* +
* ($1000 / (1 + 0.025)^18)
* Bond Price ≈ $30 * 13.7908 + $1000 * 0.6036
* Bond Price ≈ $393.72 + $603.60
* Bond Price ≈ $997.32
**2. Calculate Bond Price with 7% Yield**
* **Calculate Semiannual Yield:**
* Semiannual Yield = 7% / 2 = 3.5%
* **Use the Bond Pricing Formula (with the new yield):**
* Bond Price =
* ($30 * [1 - (1 + 0.035)^-18]) / 0.035
* +
* ($1000 / (1 + 0.035)^18)
* Bond Price ≈ $30 * 11.9464 + $1000 * 0.4604
* Bond Price ≈ $358.39 + $460.40
* Bond Price ≈ $818.79
**3. Calculate Current Bond Yield**
* **Current Bond Yield = (Annual Coupon Payment / Bond Price) * 100%**
* **Using the original bond price (from part 1):**
* Current Bond Yield = ($60 / $997.32) * 100% ≈ 6.01%
* **Using the bond price with the 7% yield (from part 2):**
* Current Bond Yield = ($60 / $818.79) * 100% ≈ 7.32%
**Key Points:**
* **Bond Prices and Yields:** Bond prices and yields have an inverse relationship. When yields rise, bond prices fall, and vice versa.
* **Current Yield:** The current yield only considers the annual coupon payment relative to the current bond price. It doesn't account for the time value of money or the bond's maturity.
* **Yield to Maturity (YTM):** YTM is the overall return anticipated on a bond if it is held until maturity. It considers all future cash flows (coupon payments and principal repayment) and discounts them back to their present value.
**Disclaimer:**
* This is a simplified explanation for illustrative purposes.
* Bond pricing can be complex and may involve other factors like credit risk, liquidity, and market conditions.
* It's always recommended to consult with a financial professional for investment advice.
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