Jackson Corporation’s Bonds Have 10 Years Remaining To Matur ✓ Solved
Jackson Corporation’s bonds have 10 years remaining to maturity.
1. Jackson Corporation’s bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%. The bonds have a yield to maturity of 10%. What is the current market price of these bonds?
2. Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 10 years, have a face value of $1,000, and a yield to maturity of 9%. What is the price of the bonds?
3. Wilson Wonders’s bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $900. What is their yield to maturity?
4. Heath Foods’s bonds have 10 years remaining to maturity. The bonds have a face value of $1,000 and a yield to maturity of 9%. They pay interest annually and have a 10% coupon rate. What is their current yield?
5. Suppose Hillard Manufacturing sold an issue of bonds with a 12-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 5%. At what price would the bonds sell? Suppose that 2 years after the initial offering, the going interest rate had risen to 11%. At what price would the bonds sell? Suppose that 2 years after the issue date (as in part a) interest rates fell to 5%. Suppose further that the interest rate remained at 6% for the next 10 years. What would happen to the price of the bonds over time?
Paper For Above Instructions
In the world of finance, understanding bond pricing and yields is crucial for investors. This paper will examine the various bond pricing scenarios presented in the assignment for Jackson Corporation, Renfro Rentals, Wilson Wonders, Heath Foods, and Hillard Manufacturing.
1. Current Market Price of Jackson Corporation's Bonds
Jackson Corporation's bonds have a par value of $1,000, a coupon rate of 9%, and they yield to maturity (YTM) at 10%. To calculate the current market price of the bonds, we can use the present value formula for bonds:
The price of the bond can be calculated as:
Current Price = C * [1 - (1 + r)^-n] / r + F / (1 + r)^n
Where:
- C = annual coupon payment = $1,000 * 0.09 = $90
- r = yield to maturity = 0.10
- n = number of years to maturity = 10
- F = par value = $1,000
Plugging in the numbers:
Current Price = $90 * [1 - (1 + 0.10)^-10] / 0.10 + $1,000 / (1 + 0.10)^10
Calculating this gives:
Current Price = $90 * [1 - 0.42241] / 0.10 + $1,000 / 2.59374
Current Price = $90 * 5.578 = $501.62 + $386.44
Current Price ≈ $888.06
2. Price of Renfro Rentals' Bonds
For Renfro Rentals, the bonds have a coupon rate of 10%, a face value of $1,000, and a yield to maturity of 9%. The coupon payments are semiannual, so we need to adjust the numbers:
- C = semiannual coupon payment = $1,000 * 0.10 / 2 = $50
- r = semiannual yield = 0.09 / 2 = 0.045
- n = total number of periods = 10 * 2 = 20
- F = par value = $1,000
Using the bond pricing formula:
Current Price = $50 * [1 - (1 + 0.045)^-20] / 0.045 + $1,000 / (1 + 0.045)^20
Current Price = $50 * 13.595 + $1,000 / 2.48759
Current Price = $679.75 + $402.02
Current Price ≈ $1,081.77
3. Yield to Maturity of Wilson Wonders' Bonds
Wilson Wonders' bonds are selling for $900 with a coupon rate of 10% and a face value of $1,000. To find the yield to maturity, we will use trial and error or a financial calculator that iteratively calculates the YTM since it cannot be isolated algebraically. We know:
- C = $100 (annual coupon payment from $1,000 * 10%)
- Current Price = $900
- n = 10 years
- F = $1,000
By inputting these values into a financial calculator, we find that the approximate yield to maturity is about 11.10%.
4. Current Yield of Heath Foods' Bonds
The current yield can be calculated as follows:
Current Yield = Annual Coupon Payment / Current Market Price
Annual Coupon Payment = $1,000 * 0.10 = $100
Price = $1,000 / (1 + 0.09)^10 = $422.41 (from above calculations, using discount)
Current Yield = $100 / $422.41 ≈ 23.65%
5. Pricing of Hillard Manufacturing's Bonds after Interest Rate Changes
Initially, the bonds have a face value of $1,000 and a coupon rate of 10%. If interest rates fall to 5%, we will use the bond pricing formula similarly by adjusting the yield:
- New C = $50 (every 6 months for a semiannual bond)
- New r = 0.025 (5% yield)/2
- n = 20 periods for 12 years
Calculating gives:
Price = $50 * [1 - (1 + 0.025)^-20] / 0.025 + $1,000 / (1 + 0.025)^20 ≈ $1,230.20
If interest rates increase to 11%, then:
Price = $50 * [1 - (1 + 0.055)^-20] / 0.055 + $1,000 / (1 + 0.055)^20 which comes to about $785.40.
Conclusion
Understanding how various factors influence the pricing and yields of bonds is essential for investors. By evaluating specific cases such as those presented above, one can analyze market conditions, interest rate fluctuations, and their impact on bond pricing.
References
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