Math Problem Statement
he 13-year $1 comma 000 par bonds of Vail Inc. pay 14 percent interest. The market's required yield to maturity on a comparable-risk bond is 15 percent. The current market price for the bond is $ 850. a. Determine the yield to maturity. b. What is the value of the bonds to you given the yield to maturity on a comparable-risk bond? c. Should you purchase the bond at the current market price? Question content area top Part 1 (Related to Checkpoint 9.2 and Checkpoint 9.3) (Bond valuation) The 13-year $1 comma 000 par bonds of Vail Inc. pay 14 percent interest. The market's required yield to maturity on a comparable-risk bond is 15 percent. The current market price for the bond is $ 850. a. Determine the yield to maturity. b. What is the value of the bonds to you given the yield to maturity on a comparable-risk bond? c. Should you purchase the bond at the current market price? Question content area bottom Part 1 a. What is your yield to maturity on the Vail bonds given the current market price of the bonds?
enter your response here% (Round to two decimal places.)
Solution
Part a: Determine the Yield to Maturity (YTM)
The Yield to Maturity (YTM) can be calculated using the following formula:
Where:
- = current market price of the bond = $850
- = annual coupon payment = 14% of $1,000 = $140
- = face value of the bond (par value) = $1,000
- = number of years to maturity = 13
- = yield to maturity (which we need to solve for)
Since this equation is complex and solving directly requires iterative or numerical methods, the YTM can be found using either a financial calculator or software by solving iteratively.
Let's use an approximation method to estimate .
The approximate YTM formula is:
Substitute the given values:
Let's compute this.The approximate Yield to Maturity (YTM) for the Vail Inc. bond is 16.38%.
Part b: Value of the Bonds
To calculate the value of the bond given the market's required yield to maturity (15%), we use the bond valuation formula:
Where:
- or 0.15,
- ,
- ,
- .
Let's calculate this next.The value of the bond, given the market's required yield to maturity of 15%, is approximately $944.17.
Part c: Should you purchase the bond at the current market price?
- The bond is currently priced at $850.
- The value of the bond given the required yield to maturity is $944.17.
Since the bond's current market price ($850) is lower than its calculated value ($944.17), it is undervalued. Therefore, it would be a good investment to purchase the bond at the current market price.
Do you want more details on any part of this? Here are some additional questions to consider:
- How does the yield to maturity change with the bond's price?
- What happens to the bond value if the market interest rate decreases?
- How do bond ratings affect the required yield to maturity?
- Can you explain how the coupon rate compares to the YTM for this bond?
- What is the difference between YTM and current yield in bond valuation?
Tip: Always compare the market price with the intrinsic value of a bond before making an investment decision.
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Math Problem Analysis
Mathematical Concepts
Bond Valuation
Yield to Maturity
Financial Mathematics
Formulas
Bond Valuation Formula: P = (C × (1 - (1 + r)^-n)/r) + F/(1 + r)^n
Approximate Yield to Maturity Formula: YTM ≈ (C + (F - P)/n) / ((F + P)/2)
Theorems
Yield to Maturity Approximation
Suitable Grade Level
Undergraduate Finance
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