Let's break this problem down step by step:

Given Information:

• Par value of the bond (Face value): $1,000
• Annual coupon rate: 12%
• Coupon payment: $1,000 * 12% = $120 per year
• Market price of the bond: $1,145
• Market's required yield to maturity (YTM) on comparable-risk bonds: 11%
• Years to maturity: 13 years

a. Compute the bond's yield to maturity (YTM):

The YTM is the interest rate at which the present value of all future cash flows (coupon payments and the face value at maturity) equals the market price of the bond. In this case, we need to solve for the YTM in the following bond price formula:

$\text{Price} = \sum_{t=1}^{13} \frac{C}{(1 + YTM)^t} + \frac{F}{(1 + YTM)^{13}}$ Where:

• $C$ is the annual coupon payment ($120)
• $F$ is the face value ($1,000)
• $YTM$ is the yield to maturity (the rate we need to solve for)
• $t$ is the year of payment
• The bond price is $1,145

This equation requires numerical methods to solve for the YTM, but for simplicity, we can use a financial calculator or Excel's RATE function to solve for YTM.

In Excel:

• Use the formula: =RATE(13, -120, 1145, 1000)

Estimated Yield to Maturity (YTM): Using a financial calculator or Excel, the YTM comes out to approximately 10.15%.

b. Determine the value of the bond to you given the market's required YTM of 11%:

The value of the bond can be computed using the same formula, but now using the market's required YTM of 11%. The formula becomes:

$\text{Value of Bond} = \sum_{t=1}^{13} \frac{120}{(1 + 0.11)^t} + \frac{1,000}{(1 + 0.11)^{13}}$

Breaking it down:

• The coupon payments of $120 are discounted at the rate of 11% for each year.
• The face value of $1,000 is discounted to the present at the 11% rate for 13 years.

Using a financial calculator or Excel:

In Excel:

• Use the formula: =PV(11%, 13, -120, -1000)

Value of the Bond to You: The bond's value, based on a required YTM of 11%, is approximately $1,105.19.

c. Should you purchase the bond?

• The market price of the bond is $1,145.
• The value of the bond, given the required YTM of 11%, is $1,105.19.

Since the bond is priced higher than its calculated value at the market's required YTM, you should not purchase the bond. It is overpriced relative to the required rate of return, and you would be paying more than its intrinsic value based on the market's required YTM.

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Would you like further clarification or additional calculations? Here are some related questions for further learning:

1. How does the bond price change if the YTM increases or decreases?
2. What is the relationship between bond price and interest rates?
3. How can you use the bond price formula to calculate the bond's duration?
4. What other factors influence the price of a bond besides the YTM and coupon rate?
5. How does a bond's credit rating affect its YTM?

Tip: When bond prices and interest rates move in opposite directions, it’s important to remember that a decrease in market interest rates will generally increase the price of a bond, and an increase in rates will reduce its price.