Let's work through each part of this bond analysis step-by-step.

Given Data

• Par Value ($FV$) = $1,000
• Coupon Rate = 15% (Annual Coupon Payment of $0.15 \times 1000 = 150$)
• Years to Maturity ($N$) = 13
• Market Price ($P_0$) = $1,140
• Market's Required Yield to Maturity ($r$) = 11%

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

The yield to maturity (YTM) is the rate of return expected on a bond if held until it matures. To find YTM, we can use the following equation:

$P_0 = \sum_{t=1}^{N} \frac{C}{(1 + \text{YTM})^t} + \frac{FV}{(1 + \text{YTM})^N}$

where:

• $P_0$ is the bond's current price
• $C$ is the annual coupon payment ($150 in this case)
• $FV$ is the bond's face value at maturity ($1,000)
• $N$ is the number of years to maturity (13 years)

This equation can be solved for YTM using financial calculators or iterative techniques, since it's difficult to rearrange analytically. Plugging in the values, the approximate solution gives us:

Yield to Maturity (YTM) ≈ 12.74%

Part (b): Determine the Value of the Bond Given Your Required Rate of Return

Given your required rate of return of 11%, the value of the bond to you can be calculated by discounting the cash flows at this rate:

$\text{Bond Value} = \sum_{t=1}^{N} \frac{C}{(1 + r)^t} + \frac{FV}{(1 + r)^N}$

Plugging in:

• $C = 150$
• $FV = 1000$
• $r = 0.11$
• $N = 13$

Using these inputs, the calculated present value of this bond would be approximately $1,180.54.

Part (c): Should You Purchase the Bond?

To decide if you should purchase the bond, compare the bond’s market price with the value to you at your required return rate (11%).

• Calculated Bond Value ($1,180.54) > Market Price ($1,140)

Since the bond’s value based on your required return rate of 11% is higher than its market price, it would be a good investment if you're satisfied with a yield close to 12.74%.

Summary of Results:

1. Yield to Maturity (YTM): 12.74%
2. Value of Bond at 11% Required Rate of Return: $1,180.54
3. Decision to Purchase: Yes, as it is priced lower than its value to you.

Would you like further details or clarifications on any part of this solution?

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Related Questions

1. How would the bond value change if the market interest rates rose to 13%?
2. What effect would a lower market price have on the bond’s YTM?
3. How does the bond’s duration affect its sensitivity to interest rate changes?
4. What is the relationship between bond price and yield to maturity?
5. How does a higher coupon rate influence the value of bonds with similar risks?

Tip

Remember, when interest rates in the market rise, bond prices typically fall. This inverse relationship is fundamental in bond investment decisions.