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.)

### Part a: Determine the Yield to Maturity (YTM)
The Yield to Maturity (YTM) can be calculated using the following formula:

\[
P = \frac{C \times (1 - (1 + r)^{-n})}{r} + \frac{F}{(1 + r)^n}
\]

Where:
- $ P $ = current market price of the bond = $850
- $ C $ = annual coupon payment = 14% of $1,000 = $140
- $ F $ = face value of the bond (par value) = $1,000
- $ n $ = number of years to maturity = 13
- $ r $ = 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 $r$.

The approximate YTM formula is:

\[
YTM \approx \frac{C + \frac{F - P}{n}}{\frac{F + P}{2}}
\]

Substitute the given values:

\[
YTM \approx \frac{140 + \frac{1,000 - 850}{13}}{\frac{1,000 + 850}{2}}
\]

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:

\[
P = \frac{C \times (1 - (1 + r)^{-n})}{r} + \frac{F}{(1 + r)^n}
\]

Where:
- $r = 15\%$ or 0.15,
- $C = 140$,
- $F = 1,000$,
- $n = 13$.

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:

1. How does the yield to maturity change with the bond's price?
2. What happens to the bond value if the market interest rate decreases?
3. How do bond ratings affect the required yield to maturity?
4. Can you explain how the coupon rate compares to the YTM for this bond?
5. 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.

The 13-year $1,000 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?

Calculate the yield to maturity and value of Vail Inc.'s 13-year $1,000 par bonds with a 14% coupon rate. Learn whether purchasing at the market price of $850 is a good investment. Detailed step-by-step solution provided, covering bond valuation formulas and financial mathematics.

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