Please Show Work Step By Step, NO Excel. Thank you!

Duke Power plans to issue $100 million of bonds. It needs one month to prepare the documentation. It is concerned that interest rates might rise before it can sell the issue. its current new-issue rate is 9% for 30 year bonds.

a) the yield on 8% 20 year Treasury bonds is 7.5%. The yield on these bonds will rise to 8.5% if Duke's borrowing cost rises to 10%. Calculate the hedge ratio:

b) calculate the number of Treasury bond futures contracts Duke should sell to hedge its risk:

c) calculate Duke's missed issuance opportunity cost and its profit on the futures contracts if interest rates rise by 1%: