Fingen's 14​-year, ​$1 comma 000 par value bonds pay 14 percent interest annually.  The market price of the bonds is ​$890 and the​ market's required yield to maturity on a​ comparable-risk bond is 15 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?a.  What is your yield to maturity on the Fingen bonds given the market price of the​ bonds?

enter your response here​%  ​(Round to two decimal​ places.)

To solve this problem, we will calculate the **Yield to Maturity (YTM)**, **value of the bond** given your required return, and finally, determine whether you should purchase the bond. 

Let's break this down step-by-step:

### a. Compute the Bond's Yield to Maturity (YTM)
The **YTM** is the rate of return expected on a bond if held until maturity. Since it's a 14-year bond paying 14% annually, we need to calculate the YTM using the following formula for bonds:

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

Where:
- $ P $ = current bond price ($890)
- $ C $ = annual coupon payment ($ 14\% \times 1000 = 140 $)
- $ F $ = face value of the bond (\$1000)
- $ n $ = number of years to maturity (14)
- $ YTM $ = yield to maturity (which we solve for)

Given that this is a difficult equation to solve directly, we can use a financial calculator or an iterative method (trial and error) to solve for the YTM. I'll calculate this now.

### b. Determine the Value of the Bond to You
To find the **value of the bond to you**, we'll use the **Present Value (PV)** of future cash flows formula:

\[
PV = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n}
\]

Where:
- $ r $ = your required rate of return (15%)
- All other variables remain the same.

I will calculate both parts now to find the YTM and value of the bond.### a. Yield to Maturity (YTM):
The YTM on Fingen's bonds, given the market price of $890, is approximately **16.01%** (rounded to two decimal places).

### b. Value of the Bond to You:
Given your required rate of return of 15%, the value of the bond to you is approximately **$942.76**.

### c. Should You Purchase the Bond?
Since the value of the bond to you ($942.76) is higher than the current market price ($890), it would be a good investment opportunity. You would likely want to purchase the bond because it is underpriced relative to your required return.

Let me know if you want more details or further clarification. Here are some related questions you could explore:

1. What happens to the bond price if the market yield increases?
2. How is the duration of a bond related to its sensitivity to interest rates?
3. How does coupon frequency affect the calculation of YTM?
4. What are the risks associated with purchasing a bond below its par value?
5. How would inflation expectations affect the yield of the bond?

**Tip:** Always compare a bond's yield to your required return to decide if it's worth purchasing, especially when market conditions fluctuate.

Fingen's 14-year, $1,000 par value bonds pay 14 percent interest annually. The market price of the bonds is $890 and the market's required yield to maturity on a comparable-risk bond is 15 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?

Learn how to calculate the yield to maturity (YTM) of Fingen's 14-year bond, determine its value based on a required return of 15%, and assess whether it's a good investment. This guide covers key concepts such as bond valuation, YTM calculation, and present value of cash flows.

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