Question

Problem 10-15 (Algo) Effect of yield to maturity on bond price [LO10-2, 10-3] Media Bias Incorporated issued bonds 10 years ago at $1,000 per bond. These bonds had a 40 -year life when issued and the annual interest payment was then 13 percent. This return was in line with the required returns by bondholders at that point in time as described below: Assume that 10 years later. due to good publicity, the risk premium is now 2 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 30 years remaining until maturity. Compute the new price of the bond. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.

Answer 1

The new price of the bond, considering the change in yield to maturity, is approximately $1,781.71.

To compute the new price of the bond, we need to consider the effect of the change in yield to maturity on the bond price. The yield to maturity is the required return or discount rate that investors expect to earn on the bond.

Here's how we can calculate the new price of the bond:

1. Determine the bond's annual interest payment: The annual interest payment is given as 13 percent of the bond's face value. Since the face value of the bond is $1,000, the annual interest payment is $1,000 * 0.13 = $130.

2. Calculate the new yield to maturity: The risk premium has decreased by 2 percent. Therefore, the new yield to maturity is the required return at that point in time minus the risk-free rate. Let's assume the risk-free rate is 4 percent. So, the new yield to maturity is 13 percent - 2 percent - 4 percent = 7 percent.

3. Determine the number of years remaining until maturity: The bonds were issued 10 years ago and had a 40-year life when issued. Therefore, there are 30 years remaining until maturity.

4. Calculate the present value of the bond's cash flows: To calculate the present value of the bond's cash flows, we need to discount the annual interest payment and the bond's face value at the new yield to maturity. We can use the present value formula or a financial calculator for this calculation.

Using the present value formula, the present value of the annual interest payments can be calculated as follows:
PV = (Annual interest payment) * [(1 - (1 + r)^(-n)) / r],
where PV is the present value, r is the discount rate (yield to maturity), and n is the number of periods (years remaining until maturity).

For the present value of the bond's face value, we can simply divide the face value by (1 + r)^n.

5. Calculate the new price of the bond: The new price of the bond is the sum of the present value of the bond's cash flows.

Using the formula or financial calculator, the present value of the bond's cash flows can be calculated as follows:
PV of annual interest payments = $130 * [(1 - (1 + 0.07)^(-30)) / 0.07] ≈ $1,613.27
PV of bond's face value = $1,000 / (1 + 0.07)^30 ≈ $168.44

The new price of the bond is the sum of the present values:
New bond price = PV of annual interest payments + PV of bond's face value
≈ $1,613.27 + $168.44 ≈ $1,781.71