Answers and Solutions
:
23  5
b. The firm would now pay 13 percent on the bonds.
With an 11 percent coupon rate,
the bond issue would bring in only $8,585,447.31:
N = 40; I = 13/2 = 6.5; PMT =
−
0.11/2
×
10,000,000 =
−
550000; FV =
−
10000000;
and solve for PV = $8,585,447.31.
The firm would lose $10,000,000
−
$8,585,447.31= $1,414,552.69 on the bond issue.
However, the firm will make money on its futures contracts. The implied yield at the
time the futures contracts were entered is found by inputting N = 40; PMT = 3000;
FV = 100000; PV = 95531.25; solving for I/YR = 3.199616% per six months.
The
nominal annual yield is 2(3.199616%) = 6.399232%.
(Note that the futures contracts
are on hypothetical 20year, 6 percent semiannual coupon bonds which are yielding
6.399232%.)
Now, if interest rates increased by 200 basis points, to 8.399232%, the value of
each futures contract will drop to $76,945.56, found by inputting N = 40; I =
8.399232/2 = 4.199616; PMT =
−
3000; FV =
−
100000; and solving for PV =
$76,945.56.
The value of all of the futures contracts will drop to $76,945.56(105) = $8,079283.80.
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 Spring '08
 Staff
 Derivative, Underlying, Since Zinn Company

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