Consider the prices of the following three Treasury issues as of February 24, 20

Question

Consider the prices of the following three Treasury issues as of February 24, 2012:   

  

The bond in the middle is callable in February 2013. What is the implied value of the call feature? (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 and round your final answer to 2 decimal places. (e.g., 32.16))

   7.100 May 17 112.34375 112.40625 13 5.40 7.990 May 17 109.46875 109.53125 5 5.36 11.740 May 17 146.62500 146.81250 15 5.44

Explanation / Answer

Answer:

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

C2 = C1 X + C3(1 – X)

7.990 = 7.100 X + 11.740 (1 – X)

7.990 = 7.100 X + 11.740 – 11.740 X

X = 0.8082

So, we invest about 80.82% percent of our money in Bond 1, and about 19.18% percent in Bond 3. This combination of bonds should have the same value as the callable bond, excluding the value of the call. So:

P2 = 0.8082 P1 + 0.1918103 P3

P2 = 0.8082 (112.34375) + 0.1918103(146.81250)

P2 = 90.79621875+28.1601496

=118.96

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

Call value = 118.95636– 109.5= 9.456

Assuming $1,000 par value, the call value is $94.56.

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