Consider the prices in the following three Treasury issues as of May 15, 2014: T

Question

Consider the prices in the following three Treasury issues as of May 15, 2014:

The bond in the middle is callable in February 2015. What is the implied value of the call feature? Assume a par value of $1,000. (Hint: Is there a way to combine the two noncallable issues to create an issue that has the same coupon as the callable bond?) (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)

   05/15/2020 7.00 108.62500 108.68750 .31250 5.910 05/15/2020 8.25 105.75000 105.81250 .09375 7.050 05/15/2020 12.50 144.90625 145.09375 .46875 3.980

Explanation / Answer

Answer: To calculate this, we need to set up an equation with tha callable bond equal to the weighted average of the noncallable bonds.We will invest X% of our money in the first noncallable bond, which means our investment in bond 3(the other non callable bond) will be (1-X). The equation is:

C2=C1X+C3(1-X)

8.25=7.00X+12.50(1-X)

8.25=7.00+12.50-12.50X

X=0.9

So, we invest about 90% of our money in bond 1 and about 10% in Bond 3.This combinations of bonds should have same value as the callable bonds,excluding the value of call,So:

P2=0.9 P1+0.1P3

=0.9(108.375)+0.1(144.96875)

=112.034375

The call value is the difference between this implied bond value and the actual bond price. So, the call value is:

Call value = 112.034375 – 105.5 = 6.534375

Assuming $1,000 par value, the call value is $65.34.

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