Consider a Treasury Bond with a 1000 face value 15 years to

Consider a Treasury Bond with a $1000 face value, 15 years to maturity and an annual coupon of 6% which means a 3% coupon payment every six months suppose current market interest rates are 5% per year (2.5% per six months). the first cou on payment s six months today) 2 S Find the price of the bond. 12 16 18 19 20 28

Solution

Price of a bond is the present value of all future cash flows receivable from the bond discounted at current market interest rates

Cash flows from bond are periodic interest and maturity value

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

Periodic interest

= Principal x Rate x Time / 12 months

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

= $30 every 6 months

Present value factor

= 1 / (1 + r) ^ n

Where,

r = Market rate of interest every 6 month = Annual rate / 2 = 5 / 2 = 2.5% or 0.025

n = Time period = Number of years x 2 = 15 x 2 = 30 semi-annual periods

So, PV Factor for n = 2 will be

= 1 / (1.025) ^ 2

= 1 / 1.050625

= 0.951814

Similarly, other calculations are shown in the following table

So, the price of the bond is $ 1,104.65

Calculations	A	B	C = A x B
Period	Cash Flow	PV Factor	Present value
1	30	0.975610	29.27
2	30	0.951814	28.55
3	30	0.928599	27.86
4	30	0.905951	27.18
5	30	0.883854	26.52
6	30	0.862297	25.87
7	30	0.841265	25.24
8	30	0.820747	24.62
9	30	0.800728	24.02
10	30	0.781198	23.44
11	30	0.762145	22.86
12	30	0.743556	22.31
13	30	0.725420	21.76
14	30	0.707727	21.23
15	30	0.690466	20.71
16	30	0.673625	20.21
17	30	0.657195	19.72
18	30	0.641166	19.23
19	30	0.625528	18.77
20	30	0.610271	18.31
21	30	0.595386	17.86
22	30	0.580865	17.43
23	30	0.566697	17.00
24	30	0.552875	16.59
25	30	0.539391	16.18
26	30	0.526235	15.79
27	30	0.513400	15.40
28	30	0.500878	15.03
29	30	0.488661	14.66
30	30	0.476743	14.30
30	1000	0.476743	476.74
		Total	1104.65