The Zinn Company plans to issue $10,000,000 of 20-year bonds in June to help fin

Question

The Zinn Company plans to issue $10,000,000 of 20-year bonds in June to help finance a new research and development laboratory. The bonds will pay interest semiannually. It is now November, and the current cost of debt to the high-risk biotech company is 11%. However, the firm's financial manager is concerned that interest rates will climb even higher in coming months. The following data are available:
Future prices: Treasury Bonds - $100,000; Pts 32nds of 100%

Delivery month Open High Low Settle Change Open interest
December 94'28 95'13 94'22 95'05 +0'07 591,944
March 96'03 96'03 95'13 95'25 +0'08 120,353
June 95'03 95'17 95'03 95'17 +0'08 13,597

a. Use the given data to create a hedge against rising interest rates

b. Assume that interest rates in general increase by 200 basis points. How well did your hedge perform?

The answers are: a) 105 contracts b) bond = -$1414552.69 futures = $1951497.45 net = +$436944.76  

Tell me how to get the answers.

Explanation / Answer

Solution:

a.

Futures maturing in June =95'17 is the highest= 95 17/32*100,000= $95,531.25

If Zinn plans to issue 10,000,000 of 20 year bonds then:

Needs to sell:10,000,000/ $95,531.25=104.67779=105 rounded up to cover the $10,000,000 planned June bond issue

b.

New interest rate:200 basis points =2%= 11 + 2= 13%

At 11% coupon rate:N =40

I= (13/2) =6.5

PMT=-0.11/2*10,000,000= -550,000

FV=-10,000,000

PV=?

Plug in to calculator to get:= $8,585,447.31

Subtract from bond issue:= $10,000,000-$8,585,447.31=$1,414,552.69 is the amount Zinn would lose on the bond issue.

Futures Contracts:First find implied yield:

N=40

PMT=3000

FV=10,000,000

PV=-95,531.25

I/yr=?

Plug into calculator to get:

= 3.199616%per 6 months

= 3.199616%*2

= 6.399232%

200 basis points =2%

= 6.399232%+2

= 8.399232%/2

Semi annual rate= 4.199616%

N=40

I=4.199611

PMT=-3000

FV=-10,000,000

PV=?

Plug into calculator to get:PV=$76,945.56

Drop in value of futures contracts:= $76,945.56*105 contracts=$8,079,283.80

Original value when sold:= 95,531.25*105 contracts=$10,030,781.25

Difference in futures contracts after Zinn buys back:

= $10,030,781.25 -$8,079,283.80

=$1,951,497.45 is the amount Zinn would make after buying them back

Net=$1,951,497.45-$1,414,552.69=$536,944.76

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