Solution 12/8/2012
Chapter: 23
Problem: 6
Problem Inputs:
Size of planned debt offering = $20,000,000
Anticipated rate on debt offering = 10%
Value of each T-bond futures contract = 94,781.25$
Change in interest rate on debt offering (basis points) = -300
New interest rate on debt = 7.0%
Value of issuing at new rate interest = $26,406,522
Dollar value savings or cost from issuing debt at the new rate = $6,406,522
New yield on futures contract = 3.469%
New value of each futures contract $136,289.74
Value of all fo the futures contract at new yield = $28,757,134
Dollar change in value of the futures position = ($8,758,290)
Total dollar value change of hedge = ($2,351,769)
Change in
rate
Dollar
change in
cost/saving
s of issue
Dollar
change in
value of
futures
Total dollar
value change of
hedge
Base -300 $6,406,522 -$8,758,290 -$2,351,769
-300 $6,406,522 -$8,758,290 -$2,351,769
a. Create a hedge with the futures contract for F Pierce’s planned March debt offering of $20
million. What is the implied yield on the bond underlying the future’s contract?
b. Suppose interest rates fall 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?
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.
F. Pierce Products Inc. is financing a new manufacturing facility with the issue in March of
$20,000,000 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:
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
Size of futures contract (dollars) = $100,000
-200 $3,958,555 -$5,343,806 -$1,385,251
-100 $1,840,158 -$2,453,960 -$613,801
$2,000,000
$4,000,000
$6,000,000
$8,000,000
Effectiveness of Hedge
Bond