Consider three bonds with 6.1% coupon rates, all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.
a. What will be the price of each bond if their yields increase to 7.1%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
4 Years :
8 Years:
30 Years:
b. What will be the price of each bond if their yields decrease to 5.1%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
4 Years:
8 Years :
30 Years :
Please show work!
The price of a bond is the PV of the expected | ||
cash flows from the bond discounted at the | ||
market rate of interest. | ||
The expected cash flows in the case are: | ||
*The maturity value of $1000, and | ||
*The annual interest of $61, which is an annuity. | ||
The calculations are made below: | ||
a] | Maturity of 4 Years = 1000/1.071^4+61*(1.071^4-1)/(0.071*1.071^4) = | $ 966.20 |
Maturity of 8 Years = 1000/1.071^8+61*(1.071^8-1)/(0.071*1.071^8) = | $ 940.52 | |
Maturity of 30 Years = 1000/1.071^30+61*(1.071^30-1)/(0.071*1.071^30) = | $ 877.15 | |
b] | Maturity of 4 Years = 1000/1.051^4+61*(1.051^4-1)/(0.051*1.051^4) = | $ 1,035.38 |
Maturity of 8 Years = 1000/1.051^8+61*(1.051^8-1)/(0.051*1.051^8) = | $ 1,064.37 | |
Maturity of 30 Years = 1000/1.051^30+61*(1.051^30-1)/(0.051*1.051^30) = | $ 1,151.99 |
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