F. Pierce Products Inc. is financing a new manufacturing facility with the issue in March of $25,000,000 of 20-year bond

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F. Pierce Products Inc. is financing a new manufacturing
facility with the issue in March of $25,000,000 of 20-year bonds
with semiannual interest payments. It is now October, and if Pierce
were to issue the bonds now, the yield would be 10% because of
Pierce’s high risk. Pierce’s CFO is concerned that interest rates
will climb even higher in coming months and is considering hedging
the bond issue. The following data are available:
Problem Inputs:
Size of planned debt offering = $25,000,000
Anticipated rate on debt offering = 10%
Maturity of planned debt offering = 20
Number of months until debt offering = 5
Settle price on futures contract (% of par) = 94.78125%
Maturity of bond underlying futures contract = 20
Coupon rate on bond underlying futures contract = 6%
Size of futures contract (dollars) = $100,000
a. Create a hedge with the futures contract for F Pierce's
planned March debt offering of $25 million. What is the implied
yield on the bond underlying the future’s contract? Value of each
T-bond futures contract = Number of contracts needed for hedge =
rounding = Value of contracts in hedge = Implied semi-annual yield
= Implied annual yield =
b. Suppose interest rates increase by 300 basis points. What is
the dollar savings from issuing the debt at the new interest rate?
What is the dollar change in value of the futures position? What is
the total dollar value change of the hedged position?
Change in interest rate on debt offering (basis points) =
300
New interest rate on debt =
Value of issuing at new rate interest =
Dollar value savings or cost from issuing debt at the new rate
=
New yield on futures contract =
New value of each futures contract Value of all fo the futures
contract at new yield =
Dollar change in value of the futures position =
Total dollar value change of hedge =
c. Create a graph showing the effectiveness of the hedge if the
change in interest rates, in basis points, is: -300, -200, -100, 0,
100, 200, or 300. Show the dollar cost (or savings) from issuing
the debt at the new interest rates, the dollar change in value of
the futures position, and the total dollar value change.