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.