Answers and Solutions:23 - 5b. 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 20-year, 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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