The 11​-year ​$1,000 par bonds of Vail Inc. pay 13 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 $950.
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?

We are asked to evaluate a bond investment with a focus on its yield to maturity (YTM) and whether it is a good purchase at the current market price. Let's go step by step.

### Given Data:
- **Par value (Face value)** = $1,000
- **Coupon rate** = 13% per year
- **Coupon payment** = 13% of $1,000 = $130 annually
- **Time to maturity** = 11 years
- **Market price** = $950
- **Comparable-risk bond's yield to maturity (YTM)** = 15%

### Part (a): Determine the yield to maturity (YTM)
The **Yield to Maturity (YTM)** is the discount rate that equates the present value of the bond's future cash flows (coupon payments and par value repayment) to its current market price.

To calculate YTM, we use the following formula for a bond:

\[
P = \sum_{t=1}^{N} \frac{C}{(1 + YTM)^t} + \frac{F}{(1 + YTM)^N}
\]

Where:
- $P$ = Current market price = $950
- $C$ = Annual coupon payment = $130
- $F$ = Face value = $1,000
- $N$ = Number of years to maturity = 11

There is no simple algebraic solution for YTM, so we will use a numerical method or calculator to find it.

### Part (b): Value of the bonds given the YTM of a comparable-risk bond (15%)
The bond's value can be calculated using the formula for the present value of future cash flows, discounted by the **comparable bond's YTM** of 15%. This is done by computing the present value of the annual coupon payments and the face value repayment at the end of 11 years.

\[
P = \sum_{t=1}^{N} \frac{C}{(1 + YTM_{comp})^t} + \frac{F}{(1 + YTM_{comp})^N}
\]
Where:
- $YTM_{comp} = 15\%$

### Part (c): Should you purchase the bond at the current market price?
To answer this, we compare the bond's **intrinsic value** (from part b) to its **current market price** of $950. If the bond's intrinsic value is higher than the market price, it would be a good purchase; if lower, it would not be a good deal.

Let me calculate the YTM and the value of the bond.### Part (a): Yield to Maturity (YTM)
The calculated **YTM** for the bond is approximately **13.91%**. This is the effective annual return you would earn if you hold the bond to maturity, given its current market price of $950.

### Part (b): Value of the bond given the comparable YTM (15%)
Given the market's required yield of **15%**, the bond's intrinsic value is approximately **$895.33**.

### Part (c): Should you purchase the bond at the current market price?
The bond is currently priced at **$950**, but its intrinsic value based on the comparable bond's YTM is lower at **$895.33**. This suggests that the bond is **overpriced** relative to the market's required return of 15%. Thus, it would not be a good purchase at its current market price unless you are willing to accept a lower return (around 13.91%).

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Would you like further details or explanations? Here are 5 related questions to expand on the topic:
1. What is the difference between yield to maturity (YTM) and current yield?
2. How would rising interest rates affect the value of this bond?
3. What are other factors besides YTM to consider when purchasing bonds?
4. How does bond duration affect its price sensitivity to interest rate changes?
5. What would happen to the bond's price if the market required yield dropped to 12%?

**Tip:** Bond prices and interest rates are inversely related—when interest rates rise, bond prices tend to fall, and vice versa.

The 11​-year ​$1,000 par bonds of Vail Inc. pay 13 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 $950. 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?

Learn how to calculate the yield to maturity (YTM) for Vail Inc.'s 11-year, $1,000 par value bonds paying 13% interest. The problem involves bond valuation concepts, comparing market price to intrinsic value using the market's required YTM of 15%. Suitable for undergraduate finance students.

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