Fingen's 13​-year, ​$1 comma 000 par value bonds pay 15 percent interest annually.  The market price of the bonds is ​$1 comma 140 and the​ market's required yield to maturity on a​ comparable-risk bond is 11 percent.
a.  Compute the​ bond's yield to maturity.
b.  Determine the value of the bond to​ you, given your required rate of return.
c.  Should you purchase the​ bond?

Let's proceed step-by-step to answer each part of the question.

### Part (a): Compute the Bond's Yield to Maturity (YTM)

The **Yield to Maturity (YTM)** is the discount rate at which the present value of all future cash flows (coupon payments and the par value at maturity) equals the current market price of the bond. Since it's not easy to solve the YTM directly through a formula, it is typically found using a financial calculator or iteratively.

The formula for calculating YTM is:

\[
P = \frac{C}{(1+YTM)^1} + \frac{C}{(1+YTM)^2} + \ldots + \frac{C + F}{(1+YTM)^n}
\]

Where:
- $ P $ = Current market price of the bond ($1,140)
- $ C $ = Annual coupon payment = 15% of $1,000 = $150
- $ F $ = Face value of the bond ($1,000)
- $ n $ = Number of years to maturity (13)
- $ YTM $ = Yield to Maturity (the rate we need to find)

Let's calculate this.

Using a financial calculator or iterative approach, the YTM can be approximated to be **12.89%**.

### Part (b): Determine the Value of the Bond to You, Given Your Required Rate of Return

To determine the value of the bond based on your required rate of return (11%), we use the **Present Value of Cash Flows** formula:

\[
\text{Value of Bond} = \frac{C}{(1+r)^1} + \frac{C}{(1+r)^2} + \ldots + \frac{C + F}{(1+r)^n}
\]

Where:
- $ r $ = Required rate of return (11% or 0.11)

The bond's value can be found by summing the present values of all future coupon payments and the face value. Using the formula, we get:

\[
\text{Value} = \sum_{t=1}^{13} \frac{150}{(1+0.11)^t} + \frac{1000}{(1+0.11)^{13}}
\]

After calculating the present value of all these cash flows, the bond's value based on an 11% required return is approximately **$1,184.22**.

### Part (c): Should You Purchase the Bond?

To decide whether to purchase the bond, compare the **calculated value** of the bond (based on your required rate of return) with the **current market price**:

- **Calculated Value**: $1,184.22
- **Market Price**: $1,140

Since the bond's calculated value ($1,184.22) is **greater than** the market price ($1,140), the bond is **undervalued** and **should be purchased**. This is because it offers a higher yield than your required rate of return.

### Conclusion:
- **(a)** The bond's YTM is approximately **12.89%**.
- **(b)** The bond's value to you, given a required return of 11%, is **$1,184.22**.
- **(c)** Since the bond is undervalued (calculated value > market price), **you should purchase the bond**.

Would you like more details on any part of the solution or have other questions?

Here are 5 related questions to consider:
1. What is the formula to calculate the present value of an annuity?
2. How does the YTM change if the bond price increases?
3. Can YTM be greater than the coupon rate? Why?
4. How do market interest rates affect bond prices?
5. What are other methods to determine if a bond is worth purchasing?

**Tip:** YTM is an effective way to compare the returns of different bonds, as it considers all future cash flows and the time value of money.

Fingen's 13-year, $1,000 par value bonds pay 15 percent interest annually. The market price of the bonds is $1,140 and the market's required yield to maturity on a comparable-risk bond is 11 percent.
a. Compute the bond's yield to maturity.
b. Determine the value of the bond to you, given your required rate of return.
c. Should you purchase the bond?

Explore how to calculate the yield to maturity (YTM) for Fingen's 13-year, $1,000 par value bond with a 15% annual coupon, currently priced at $1,140. This solution covers key finance concepts like bond valuation and the present value of cash flows. Suitable for undergraduate finance students.

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