On December 15, the company borrows at 8.6 percent. The sum that it would receive for
the face value of DM 2.5 million is found by the price yield formula:
Yield X N
Bond price = Face value [1 - --------- ]
360
where N is the borrowing period in days.
0.086 X 90
So the sum realized is 2.5 [1 - ------------- ] = DM 2.44625 million.
360
But the sum that would have been realized at the yield rate of 7.5 percent is
0.075 X 90
2.5 [ 1 - -------------- ] = DM 2.453125 million
360
So shortfall = DM 2.453125 - DM 2.44625 = DM 6,875
Now the company buys back the future contracts. The gain is equal to 100 ticks (=
92.5 - 91.5). So the gain is
3 X 100 X 25 = DM 7,500Thus, shortfall is more than made up through the hedging operation.
Illustration
Problem 13
A company plans to borrow $ 20 million by issuing a 90 days commercial paper in
August. The yield rate of the CP is 10.5 percent at the moment, i.e. the month of March.
Interest rates are anticipated to rise. Since no future contracts are available in CP, the
company can resort to T-bill futures. September T-bill futures are being quoted at 90.20.
Assume that on August 15, the CP yield has risen to 11 percent and T-bill future contract
is quoting at 89.60. What is the company expected to do?
Solution 13
In March, at the yield rate of 10.5 percent, the CP issue will result into a realization of
0.105 X 90
20 [ 1 - -------------] = $ 19.475 million
360