Question

At one point, some Treasury bonds were callable. Consider the prices on the following three Treasury issues as of May 15, 2016:

7.05		May	20	n		110.31250		110.37500		−	.37500		5.39
8.80		May	20			107.43750		107.50000		−	.12500		5.35
12.55		May	20			145.93750		146.12500		−	.43750		5.43

The bond in the middle is callable in February 2017. 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.)

Calculate Call value $ ________

Answer 1

ANSWER:

As the hint implies, we will first look at the coupon rates. Imagine that we have money to invest, and we want a 8.80% return, but we cannot invest in Bond 2. The other option is to invest part of our money into Bond 1 and part into Bond 3, so that the average rate of return is 8.80%

Formula: Rate 2 = Rate 1 * (X) + Rate 3 * (1-X)

8.80 = 7.05 X + 12.55(1 -X)

8.80 = 7.05 X + 12.55 - 12.55 X

12.55 X - 7.05 X = 12.55 - 8.80

5.50 X = 3.75

X = 3.75 / 5.50

X = 0.681818

Expected Price of Bond 2:

Price 2 = (Price 1 * 0.681818) + (Price 3 * 0.31819)

Price 2 = (110.37500 * 0.681818) + (146.12500 * 0.31819)

Price 2 = (75.25566) + (46.49551)

Price 2 = 121.75117

NOW EXPECTED PRICE - GIVEN PRICE 2:

121.75117 - 107.50000

= 14.25117

ASSUMING BOND VALUES IS $1000

CALL FEATURE IS $ 142.5117