Question

Compute the price of a 6.1 percent coupon bond with fifteen years left to maturity and a market interest rate of 9.0 percent. (Assume interest payments are semiannual.) (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Price of a bond is the present value of all future cash payments receivable from the bond discounted at required rate of return

Future cash flows are interest payments and maturity value

Semi-annual interest

= Face Value of the bond x Interest rate on the bond x 6 / 12

= $1,000 x 6.1% x 6 / 12

= $ 30.5

When interest is paid semi-annually, interest rate of discounting is divided by 2 and time period is multiplied by 2

So, interest rate = 9 / 2 = 4.5%

Time = 15 x 2 = 30 semi-annual periods

Present value factor

= 1 / (1 + r) ^ n

So, PV Factor for year 2 will be

= 1 / (1.045) ^ 2

= 1 / 1.092025

= 0.915730

The following table shows the calculations :

Calculations	A	B	C = A x B
Period	Cash Flow	PV Factor	Present Value
1	30.5	0.956938	29.18660287
2	30.5	0.91573	27.92976351
3	30.5	0.876297	26.72704642
4	30.5	0.838561	25.57612098
5	30.5	0.802451	24.47475692
6	30.5	0.767896	23.42082002
7	30.5	0.734828	22.41226796
8	30.5	0.703185	21.44714637
9	30.5	0.672904	20.52358505
10	30.5	0.643928	19.6397943
11	30.5	0.616199	18.79406153
12	30.5	0.589664	17.98474788
13	30.5	0.564272	17.21028505
14	30.5	0.539973	16.4691723
15	30.5	0.51672	15.75997349
16	30.5	0.494469	15.08131435
17	30.5	0.473176	14.43187976
18	30.5	0.4528	13.81041125
19	30.5	0.433302	13.21570455
20	30.5	0.414643	12.64660722
21	30.5	0.396787	12.10201648
22	30.5	0.379701	11.58087701
23	30.5	0.36335	11.08217896
24	30.5	0.347703	10.60495594
25	30.5	0.332731	10.1482832
26	30.5	0.318402	9.711275788
27	30.5	0.304691	9.293086879
28	30.5	0.291571	8.892906104
29	30.5	0.279015	8.509957994
30	30.5	0.267	8.143500473
30	1000	0.267	267.0000155
		Price	763.81

So, as per above calculations, the price of the bond is $763.81