 The 

1818​-year, 

​$1 comma 0001,000 

par value bonds of Waco Industries pay 

1111 

percent interest annually.  The market price of the bond is 

​$855855​, 

and the​ market's required yield to maturity on a​ comparable-risk bond is 

1515 

percent.

**a.**  Compute the​ bond's yield to maturity.

**b.**  Determine the value of the bond to you given the​ market's required yield to maturity on a​ comparable-risk bond.

**c.**  Should you purchase the​ bond?

Let's solve this step-by-step:

### **Part (a): Compute the bond's yield to maturity (YTM)**

Yield to maturity (YTM) is the internal rate of return (IRR) of the bond, considering its current market price, par value, coupon interest rate, and time to maturity. The formula for YTM is given by:

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

Where:
- $C$ = Annual coupon payment
- $F$ = Face value of the bond
- $P$ = Price of the bond
- $n$ = Number of years to maturity

Given values:
- Par value ($F$) = $1,000
- Annual coupon rate = 11%
- Coupon payment ($C$) = 11% of $1,000 = $110
- Current market price ($P$) = $855
- Maturity ($n$) = 18 years

Let's calculate the YTM using the above values.

### **Part (b): Determine the value of the bond given the market's required yield to maturity (15%)**

The value of the bond can be found using the present value formula of the bond, which is the sum of the present value of the coupon payments and the present value of the face value of the bond:

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

Where:
- $r$ = Market's required yield to maturity (15%)
  
Let's calculate the bond value using the given 15% yield.

### **Part (c): Should you purchase the bond?**

To decide whether to purchase the bond, compare the YTM calculated in part (a) with the market's required yield (15%).

If the bond's YTM is higher than the market's required yield, it is a good investment as it offers a higher return. If it is lower, then it's not a good buy.

Now, let's calculate:

1. **Yield to Maturity (YTM)**
2. **Bond Value based on 15% required yield**### Calculation Results:

**(a) Yield to Maturity (YTM):** Approximately 12.73%

**(b) Value of the bond given the market's required yield (15%):** Approximately $754.88

### **(c) Should you purchase the bond?**

To decide whether to purchase the bond:

- The bond's YTM (12.73%) is lower than the market's required yield (15%). 
- Since the YTM is less than the required rate of return, this bond is not a good investment, and you should **not** purchase it.

Would you like further details or have any questions?

Here are some related questions you might consider:

1. How does the coupon rate impact the bond's value compared to the required yield?
2. What is the relationship between bond prices and interest rates?
3. How do changes in market conditions affect the yield to maturity of bonds?
4. How would the value of the bond change if the yield to maturity increases?
5. What other factors should be considered when investing in bonds?

**Tip:** A bond's price moves inversely with changes in the market's required yield to maturity. When required yields rise, bond prices fall, and vice versa.

Learn how to compute a bond's yield to maturity (YTM) and determine its value based on market conditions. This problem involves calculating YTM, bond valuation, and deciding on investment based on required yields. Suitable for higher education and financial analysis.

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