Respond To The Questions And Complete The Problems ✓ Solved
Respond to the questions and complete the problems.
Respond to the questions and complete the problems. Number your responses 1–4. Explain what a call provision enables bond issuers to do. Why would bond issuers exercise a call provision?
Define a discount bond and a premium bond. Provide examples of each. Describe the relationship between interest rates and bond prices. Describe the differences between a coupon bond and a zero coupon bond. Use references to support your responses as needed.
Be sure to cite all references using correct APA style. Your responses should be free of grammar and spelling errors, demonstrating strong written communication skills.
Problems: Compute the following: Assuming semi-annual compounding, what is the price of a zero coupon bond that matures in 3 years if the market interest rate is 5.5 percent? Assume par value is $1000. Using semi-annual compounding, what is the price of a 5 percent coupon bond with 10 years left to maturity and a market interest rate of 7.2 percent? Assume that interest payments are paid semi-annually and that par value is $1000. Using semi-annual compounding, what is the yield to maturity on a 4.65 percent coupon bond with 18 years left to maturity that is offered for sale at $1,025.95? Assume par value is $1000.
Paper For Above Instructions
In the realm of finance, understanding bonds is crucial for both investors and issuers. This paper systematically addresses the questions regarding bond provisions, types, market relationships, and specific computational problems using given financial metrics.
1. Call Provision in Bonds
A call provision is a feature embedded in a bond, which permits the issuer to redeem the bond before its maturity date at specified call prices. This means that if interest rates drop significantly, the bond issuer has the flexibility to refinance its debt at lower rates by calling back the bonds. For example, if an organization issues bonds with a 6% interest rate and the market rate drops to 4%, the company can call in the existing bonds to reissue new ones at the lower rate, effectively reducing the interest payments. This flexibility can be advantageous for issuers, especially in a fluctuating interest rate environment (Fabozzi, 2018).
2. Discount Bonds vs. Premium Bonds
A discount bond is sold for less than its face (par) value, typically because its interest rate is lower than the current market rates. An example of a discount bond is a bond with a face value of $1,000 that sells for $950. Conversely, a premium bond is sold above its par value because its interest rate is higher than the prevailing market rates. For instance, a bond with a face value of $1,000 may sell for $1,050. The relationship between these two types of bonds largely hinges on interest rates: as market interest rates rise, the prices of existing bonds tend to fall, making discount bonds more common, while premium bonds emerge when market rates fall (Mishkin & Eakins, 2018).
3. Interest Rates and Bond Prices
The relationship between interest rates and bond prices is inversely proportional. When interest rates rise, the market value of existing bonds tends to decrease, as newer bonds are likely to be issued with higher rates of return, making the older bonds with lower rates less desirable. Conversely, if interest rates fall, the prices of existing bonds rise because they become more sought after. This phenomenon is crucial for investors looking to understand market trends and make informed investment choices (Bodie, Kane, & Marcus, 2018).
4. Coupon Bonds vs. Zero Coupon Bonds
A coupon bond pays interest (coupon payments) periodically, typically twice a year, until maturity, at which point the face value is returned. For instance, a bond with a 5% coupon rate will pay $50 annually for a $1,000 bond. In contrast, a zero-coupon bond does not make periodic interest payments; instead, it is issued at a discount to its face value and matures at par value. For example, a zero-coupon bond priced at $700 will pay $1,000 at maturity. Understanding these differences is essential for investors when considering their options in fixed-income investments (Luenberger, 2014).
Computational Problems
Problem 1: Price of a Zero Coupon Bond
To compute the price of a zero coupon bond maturing in 3 years with a market interest rate of 5.5%, we can use the present value formula:
Price = Par Value / (1 + r)^n
Where:
- Par Value = $1,000
- r = 0.055 / 2 = 0.0275 (semi-annual)
- n = 3 * 2 = 6 (total compounding periods)
Thus, the calculation becomes:
Price = 1000 / (1 + 0.0275)^6 = 1000 / (1.175206) ≈ $850.58
Problem 2: Price of a Coupon Bond
To find the price of a 5% coupon bond with 10 years to maturity and a market interest rate of 7.2%, we use the formula for the present value of a bond:
Price = C * [1 - (1 + r)^-n]/r + F/(1 + r)^n
Where:
- C = Coupon Payment = 1000 * 0.05 / 2 = $25
- r = 0.072 / 2 = 0.036 (semi-annual)
- n = 10 * 2 = 20 (total compounding periods)
- F = Face Value = $1000
Applying the formula:
Price = 25 * [1 - (1 + 0.036)^-20]/0.036 + 1000/(1 + 0.036)^20 ≈ $818.66
Problem 3: Yield to Maturity for a Coupon Bond
To compute the yield to maturity (YTM) for a bond priced at $1,025.95 with a coupon rate of 4.65% and 18 years to maturity, we can use an iterative method or financial calculator. For simplicity, let’s assume a financial calculator is used. Input values:
- N = 36 (number of periods)
- P = -1025.95 (current price)
- C = 23.25 (semi-annual coupon payment, 1000*0.0465/2)
- F = 1000 (face value)
Using these, we find that YTM ≈ 4.50% (annualized).
In conclusion, understanding bond provisions, classifications, and their computations can significantly impact investment decisions and financial strategy.
References
- Bodie, Z., Kane, A., & Marcus, A. J. (2018). Investments (11th ed.). McGraw-Hill Education.
- Fabozzi, F. J. (2018). Bond Markets, Analysis, and Strategies (9th ed.). Pearson.
- Luenberger, D. G. (2014). Investment Science (2nd ed.). Oxford University Press.
- Mishkin, F. S., & Eakins, S. G. (2018). Financial Markets and Institutions (8th ed.). Pearson.