Foundations of Financial Management (Block, Hirt, Danielsen, 16th Ed.)Chap. 10 - Problem 13Effect of yield to maturity on bond price Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point as described next: Real rate of return 4% Inflation premium 6 Risk premium 5 Total return 15% Assume that five years later the inflation premium is only 3 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.

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Asked Mar 22, 2019
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Foundations of Financial Management (Block, Hirt, Danielsen, 16th Ed.)

Chap. 10 - Problem 13

Effect of yield to maturity on bond price Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point as described next:

Real rate of return 4%
Inflation premium 6
Risk premium 5
Total return 15%

Assume that five years later the inflation premium is only 3 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.

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Step 1

Real rate of return = 4% 
Inflation premium = 3% 
Risk premium = 5%
Hence, required return (or yield to maturity) of the bonds, y = 4% + 3% + 5% = 12%

Step 2

Please note that the coupon rate will still remain the same as 15% as before.

Face Value, FV = $ 1,000

Annual Coupon, C = Coupon rate x FV = 15% x 1,000 = $ 150

Time to maturity, N = 20 years

Step 3

Price of the bond = PV of all the future copupon payments + PV of FV received at the time of maturity = C / y x [1 - (1 + y)-N] + FV ...

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