Question

Titania Inc. is issuing bonds to finance the construction of a new plant in Wisconsin. These bonds are being offered with a face value of $1000, a coupon rate of 9% (paid annually), and a maturity of 18 years. The current market interest rate for similar financial assets is 7% per year (compounded annually). a. Find the pure/fair price of each bond at the time of issuance. b. Find the fair price of each bond if purchase ends up being made right before the 4th coupon payment. c. Find the fair price of each bond if purchase ends up being made after before the 4th coupon payment.

Answer 1

Please see table below.

Time	Cash Flow	PV = CF / 1.07^Time
0		-
1	90.00	84.11
2	90.00	78.61
3	90.00	73.47
4	90.00	68.66
5	90.00	64.17
6	90.00	59.97
7	90.00	56.05
8	90.00	52.38
9	90.00	48.95
10	90.00	45.75
11	90.00	42.76
12	90.00	39.96
13	90.00	37.35
14	90.00	34.90
15	90.00	32.62
16	90.00	30.49
17	90.00	28.49
18	1,090.00	322.49
	a. Total PV = Price at the time of issuance	1,201.18

b. $1264.91 (pls see table below (right hand side columns) for calculations)

Time	Cash Flow	PV = CF / 1.07^Time
0		-
1	90.00	84.11
2	90.00	78.61
3	90.00	73.47		Time	Cash Flow	PV = CF / 1.07^Time
4	90.00	68.66	b. if bought right before 4th coupon payment	0	90.00	90.00
5	90.00	64.17		1	90.00	84.11
6	90.00	59.97		2	90.00	78.61
7	90.00	56.05		3	90.00	73.47
8	90.00	52.38		4	90.00	68.66
9	90.00	48.95		5	90.00	64.17
10	90.00	45.75		6	90.00	59.97
11	90.00	42.76		7	90.00	56.05
12	90.00	39.96		8	90.00	52.38
13	90.00	37.35		9	90.00	48.95
14	90.00	34.90		10	90.00	45.75
15	90.00	32.62		11	90.00	42.76
16	90.00	30.49		12	90.00	39.96
17	90.00	28.49		13	90.00	37.35
18	1,090.00	322.49		14	1,090.00	422.72
	a. Total PV = Price at the time of issuance	1,201.18				1,264.91

c. If purchase is right after the 4th coupon is paid, then we subtract the first term $90 and the price would be $1,264.91. There will be practically no change to time (right before is almost the same as right after except that teh coupon goes to someone else)