Question

An 8^1/2 30-year US corporate bond is callable in 12 years. It is currently sold at a price of $960. The call premium is 10 percent. The prevailing market interest rate at the call date is 8 percent.

a. What is the yield to call to an investor who does not reinvest the call price at the prevailing interest rate at the call date?

b. What is the yield to call to an investor who reinvests the call price at the prevailing interest rate at the call date?

Answer 1

(a) The bond pays semiannual coupon = 81/2 = 40.5 dollars.

The current price = 960, that is the out flow at time 0 (today) = 960

The bond will be called at a price of 1100 ( 10% premium over face value ) after 12 years. We can arrange the cash flows neatly and calculate the IRR for those cash flows through a spreadsheet. IRR will be the yield to that bond. We have a total 24 payments for 12 years. Note that the last csh flow will consist of the coupon plus the call payment (1100 )

Cash flows are :

Period	Cash flow
0	-1175
1	40.5
2	40.5
3	40.5
4	40.5
5	40.5
6	40.5
7	40.5
8	40.5
9	40.5
10	40.5
11	40.5
12	40.5
13	40.5
14	40.5
15	40.5
16	40.5
17	40.5
18	40.5
19	40.5
20	40.5
21	40.5
22	40.5
23	40.5
24	1140.5

The IRR from these cash flows = 3.268%

Note that this is a semi annual yield as the coupons were semi annual.

The annual Yield = 3.268% * 2 = 6.535%

Thus, Yield to Call = 6.535%

(b)

If the call price (1100 ) is reinvested at 8% for semi annual coupons, we need to calculate the cash flows for full 30 years period to calculate the yield. We have the following cash flows

Period	Cash flow
0	-1175
1	40.5
2	40.5
3	40.5
4	40.5
5	40.5
6	40.5
7	40.5
8	40.5
9	40.5
10	40.5
11	40.5
12	40.5
13	40.5
14	40.5
15	40.5
16	40.5
17	40.5
18	40.5
19	40.5
20	40.5
21	40.5
22	40.5
23	40.5
24	40.5
25	44
26	44
27	44
28	44
29	44
30	44
31	44
32	44
33	44
34	44
35	44
36	44
37	44
38	44
39	44
40	44
41	44
42	44
43	44
44	44
45	44
46	44
47	44
48	44
49	44
50	44
51	44
52	44
53	44
54	44
55	44
56	44
57	44
58	44
59	44
60	1144

Note that in this case we won’t consider the 1100 cash flow at period 24 and will only consider 40.5 dollars. From period 25 onwards the payment amount will simply change to 44 ( 4% of 1100 ) and at the end we’ll get 1100 + 44 = 1144

Semiannual yield = 3.52%

Annual yield = 7.0406%