Media Bias, Inc. issued bonds 10 years ago at $1,000 per bond. These bonds had a
ID: 2660097 • Letter: M
Question
Media Bias, Inc. issued bonds 10 years ago at $1,000 per bond. These bonds had a 30-year life when issued and the annual interest payment was then 13 percent. This return was in line with the required returns by bondholders at that point in time as described below:
Assume that 10 years later, due to good publicity, the risk premium is now 2 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 20 years remaining until maturity.
Compute the new price of the bond. Use Appendix B and Appendix D. (Round "PV Factor" to 3 decimal places, intermediate and final answers to 2 decimal places. Omit the "$" sign in your response.)
Explanation / Answer
this is one example how to go through this :
The annual interest payment was at 10% ...10 years ago at $1,000 per bond. These bonds had a 35-year life when issued the annual interest payment was then 10 percent. This return was in line with the required returns by bondholders at that point in time as described below:
Real rate of return
2%
Inflation premium
4?
Risk premium
4?
Total return
10%
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 25 years remaining until maturity. Compute the new price of the bond.
SOLUTION :
Semi-annual coupon: 1,000* (0.10/2) = $50
CF = cash flow
CFs remaining...total: 25 yrs * 2 times per year = 50
CF#1 - 49: $50
CF#50: $1,050
semi-annual discount rate: 0.08/2 = 0.04 (4%)
Price = 50/1.04 + 50/1.04^2 + ...+ 50/1.04^49 + 1050/1.04^50
= $1,214.82