Answer:
To calculate the maximum price you should be willing to pay for the bond, you can use the formula for the present value of a bond. Here's how you can do it step by step:
1. Identify the relevant information:
- Face value of the bond (FV) = $1,000
- Annual coupon rate (CR) = 9.5%
- Number of years to maturity (N) = 15 years
- Semiannual interest payments (since it makes semiannual payments, you need to adjust the annual coupon rate and the number of years accordingly)
- Nominal yield to maturity (YTM) = 12.6%
2. Calculate the semiannual coupon payment:
- Semiannual coupon rate = Annual coupon rate / 2 = 9.5% / 2 = 4.75%
- Semiannual coupon payment = Face value * Semiannual coupon rate = $1,000 * 4.75% = $47.50
3. Determine the number of periods:
- Since it's a 15-year bond with semiannual payments, the total number of periods will be 15 years * 2 = 30 periods
4. Calculate the present value of the bond:
- Using the formula for the present value of a bond:
PV = (C / r) * (1 - 1 / (1 + r)^N) + FV / (1 + r)^N
where:
PV = Present value
C = Coupon payment
r = Yield to maturity per period
N = Total number of periods
FV = Face value
5. Plug in the values and solve for the present value:
- PV = ($47.50 / 0.063) * (1 - 1 / (1 + 0.063)^30) + $1,000 / (1 + 0.063)^30
- PV ≈ $760.96
Therefore, the maximum price you should be willing to pay for the bond is approximately $760.96, which corresponds to option c.
