Mini Case: 23 – 12
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Answer: If TS waits until June to issue its bonds, and if interest rates rise, then TS will have to
pay a higher interest rate on its debt. How much does that cost TS? One way to
calculate the cost is to see how much the 20-year 7 percent semi-annual bonds that it
intended to issue would be worth at the new discount rate of 8%. Input N = 40, I/YR
= 8/2, PMT = -5,000,000(7%/2) = 175,000, FV = -5,000,000 and solve for PV =
$4,505,181.
Since they were going to be worth $5 million if they were issued immediately, then
this represents a loss of $5,000,000 – $4,505,181 = $494,819. TS can hedge this risk
by selling T-bond futures contracts.
T-bond futures contracts are priced off of a hypothetical 20–year, 6 percent coupon,
semiannual payment bond, and the 111’25 futures price translates to a $1,117.81 for
each $1000 face value bond. The implied yield can be caluclated with a financial
calculator to be (N = 40; Pmt = 30; FV = 1000; PV = -1117.81; calculate I/Y =
2.5284% semi-annually, which is an annual rate of about 5.057%. If interest rates
represents a decrease of $111,781 – $99,344 = $12,437 for each contract. Since TS
has sold futures contracts, this represents a profit to TS. The total profit from the
futures contracts is 45($12,437) = $559,665.
TS will lose $494,819 on the bonds it issues but gain $559,665 on its futures