Question

Assets, Inc., plans to issue $8 million of bonds with a coupon rate of 6 percent, a par value of $1,000, semiannual coupons, and 30 years to maturity. The current market interest rate on these bonds is 10 percent. In one year, the interest rate on the bonds will be either 10 percent or 4 percent with equal probability.

Assume investors are risk-neutral. a. If the bonds are noncallable, what is the price of the bonds today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Price of Bonds = ______

Answer 1

To solve such types of questions, it is best to calculate price of bonds in the given two scenarios of interest rate and take a weighted average price. Since, investor is risk-neutral, we need to give equal weight to both the prices

Cashflows for this bond would be as below:

CF1 @ T = 0.5, $1000*0.06/2=$30 (coupon)
CF2 @ T = 1, $1000*0.06/2 = $30 (coupon)
.
.
CF59, @ T = 29.5, $1000*0.06/2= $30 (coupon)
CF60, @ T = 30, $1000*0.06/2 (coupon) + $1000 (principal) = $1030

To calculate price of the bond, we simply need to discount these cashflows to present using interest rates as per the scenarios given

Calculation of prices in both scenarios is shown below, pl note till year 1 discounting for both the scenarios is at 10% since interest rates change after year 1

period	CF,i	int rate	discount factor	PV		int rate	discount factor	PV
0.5	30	10%	0.95	28.60		10%	0.98	28.6
1	30	10%	0.91	27.27		10%	0.96	27.3
1.5	30	10%	0.87	26.00		4%	0.94	28.29
2	30	10%	0.83	24.79		4%	0.92	27.74
2.5	30	10%	0.79	23.64		4%	0.91	27.20
3	30	10%	0.75	22.54		4%	0.89	26.67
3.5	30	10%	0.72	21.49		4%	0.87	26.15
4	30	10%	0.68	20.49		4%	0.85	25.64
4.5	30	10%	0.65	19.54		4%	0.84	25.15
5	30	10%	0.62	18.63		4%	0.82	24.66
5.5	30	10%	0.59	17.76		4%	0.81	24.18
6	30	10%	0.56	16.93		4%	0.79	23.71
6.5	30	10%	0.54	16.15		4%	0.77	23.25
7	30	10%	0.51	15.39		4%	0.76	22.80
7.5	30	10%	0.49	14.68		4%	0.75	22.35
8	30	10%	0.47	14.00		4%	0.73	21.92
8.5	30	10%	0.44	13.34		4%	0.72	21.50
9	30	10%	0.42	12.72		4%	0.70	21.08
9.5	30	10%	0.40	12.13		4%	0.69	20.67
10	30	10%	0.39	11.57		4%	0.68	20.27
10.5	30	10%	0.37	11.03		4%	0.66	19.87
11	30	10%	0.35	10.51		4%	0.65	19.49
11.5	30	10%	0.33	10.03		4%	0.64	19.11
12	30	10%	0.32	9.56		4%	0.62	18.74
12.5	30	10%	0.30	9.11		4%	0.61	18.37
13	30	10%	0.29	8.69		4%	0.60	18.02
13.5	30	10%	0.28	8.29		4%	0.59	17.67
14	30	10%	0.26	7.90		4%	0.58	17.32
14.5	30	10%	0.25	7.53		4%	0.57	16.99
15	30	10%	0.24	7.18		4%	0.56	16.66
15.5	30	10%	0.23	6.85		4%	0.54	16.33
16	30	10%	0.22	6.53		4%	0.53	16.02
16.5	30	10%	0.21	6.23		4%	0.52	15.71
17	30	10%	0.20	5.94		4%	0.51	15.40
17.5	30	10%	0.19	5.66		4%	0.50	15.10
18	30	10%	0.18	5.40		4%	0.49	14.81
18.5	30	10%	0.17	5.14		4%	0.48	14.52
19	30	10%	0.16	4.91		4%	0.47	14.24
19.5	30	10%	0.16	4.68		4%	0.47	13.96
20	30	10%	0.15	4.46		4%	0.46	13.69
20.5	30	10%	0.14	4.25		4%	0.45	13.43
21	30	10%	0.14	4.05		4%	0.44	13.17
21.5	30	10%	0.13	3.87		4%	0.43	12.91
22	30	10%	0.12	3.69		4%	0.42	12.66
22.5	30	10%	0.12	3.51		4%	0.41	12.41
23	30	10%	0.11	3.35		4%	0.41	12.17
23.5	30	10%	0.11	3.19		4%	0.40	11.94
24	30	10%	0.10	3.05		4%	0.39	11.70
24.5	30	10%	0.10	2.90		4%	0.38	11.48
25	30	10%	0.09	2.77		4%	0.38	11.25
25.5	30	10%	0.09	2.64		4%	0.37	11.03
26	30	10%	0.08	2.52		4%	0.36	10.82
26.5	30	10%	0.08	2.40		4%	0.35	10.61
27	30	10%	0.08	2.29		4%	0.35	10.40
27.5	30	10%	0.07	2.18		4%	0.34	10.20
28	30	10%	0.07	2.08		4%	0.33	10.00
28.5	30	10%	0.07	1.98		4%	0.33	9.81
29	30	10%	0.06	1.89		4%	0.32	9.62
29.5	30	10%	0.06	1.80		4%	0.31	9.43
30	1030	10%	0.06	59.03		4%	0.31	317.57
Total Price				636.73				1353.73

Thus, for a risk neutral investor, price of the bond = (636.73+1353.73)/2 = $995.23