Consider the prices in the following three Treasury issues as of May 15, 2011: 6

Question

Consider the prices in the following three Treasury issues as of May 15, 2011:

6.800 May 17 n 118:16 118:18 15 5.34

8.550 May 17 115:20 115:22 7 5.30

12.300 May 17 140:25 140:31 17 5.38

The bond in the middle is callable in February 2012. 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?) (Round your answer to the nearest whole dollar amount and round your final answer to 2 decimal places. (e.g., 32.16)) Call value $

Explanation / 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:

8.55 = 6.8 X + 12.30(1 – X)

8.55 = 6.8 X + 12.30 – 12 .30X

8.55 = -5.5x+12.30

5.50x = 12.30-8.55

X = 0.6818

So, we invest about 68 percent of our money in Bond 1, and about 32 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 = 0.6818 P1 + 0.31819 P3

P2 = 0.68181(106.375) + 0.3182(134.96875)

P2= 115.4730

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

Call value = 115.4730103.50 = 11.9730

Assuming $1,000 par value, the call value is $119.73.

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