The Altoona Company issued a 25-year bond 5 years ago with a face value of $1,00
ID: 2759027 • Letter: T
Question
The Altoona Company issued a 25-year bond 5 years ago with a face value of $1,000. The bond pays interest semiannually at a 10.6% annual rate. a. What is the bond's price today if the interest rate on comparable new issues is 12%? Round the answer to the nearest cent. What is the price today if the interest rate is 8%? Round the answer to the nearest cent. What is the price today if the interest rate is 10.6%? Round the answer to the nearest cent. Calculate the market price of a $1,000 face value bond under the following conditions. Assume interest is paid semiannually. Round the answers to the nearest cent.Explanation / Answer
P= PMT [PVFAK,n] + FV [PVFK,n) ]
A
n = 20 *2
2 = 40k = 12/2 = 6
PMT = $1,000
.10.6/2 = $53
FV = $1,000
Pb= = $53 [PVFA6,40] + $1,000 [PVF6,40]
= $53 (15.0463) + $1,000 (.0972)
= $894.65
B
k = 8/2 = 4
= $53 [PVFA4,40] + $1,000 [PVF4,40]
= $53 (19.7928) + $1,000 (.2083)
= $1257.3184
C
c. In part a the interest rate has risen above the coupon rate. Therefore an investment equal to the bond's face value would earn more if placed in newly issued bonds. That means the bond's price has to decrease below face value to keep its yield competitive with new issues. In part b the bond offers more than new issues costing $1,000. Therefore, its price can increase above $1,000 and still remain competitive.
A
PB = PMT [PVFAK.n ] + FV [PVFk.n)
65 [PVFA5,30] + $1,000 [PVF5,30]
= $65 (15.3725) + $1,000 (.2314)
= $1230.6125
B
.PB= $30 [PVFA6,10] + $1,000 [PVF6,10]
= $30 (7.3601) + $1,000 (.5584)
= $779.203.
C
PB= $50 [PVFA3,50] + $1,000 [PVF3,50]
= $50 (25.7298) + $1,000 (.2281)
= $1,514.59
D
.PB= $70 [PVFA4.5,60] + $1,000 [PVF4.5,60]
= $70 (20.638) + $1,000 (.0713)
== $1,515.96
E
PB= $1,515.964,12] + $1,000 [PVF4,12]
= $25 (9.3851) + $1,000 (.6246)
= $859.23
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