Question

(Bond Valuation) Hamilton, Inc. bonds have a coupon rate of 12 percent. The interest is paid semiannually, and the bonds mature in 14 years. Their par value is $1,000. If your required rate of return is 9 percent, what is the value of the bond? What is the value if the interest is paid annually?

a. If the interest is paid semiannually, the value of the bond is $_____

Answer 1

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

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

Future cash flows are semi-annual coupons and maturity value

Semi-annual coupons

= Principal x Rate x Time / 12

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

= $60

Discount rate = 9 / 2 = 4.5% per 6 months

Time = 14 x 2 = 28 semi-annual periods

Present value factor

= 1 / (1 + r)^n

Where,

r = Required rate of return

n = Time period

So, PV Factor for n = 2 will be

= 1 / (1.045)^2

= 1 / 1.092025

= 0.915730

Similarly, other values are calculated in the following table

Calculations	A	B	C = A x B
Period (n)	Cash Flows	PV Factor	Present Value
1	60	0.956938	57.42
2	60	0.915730	54.94
3	60	0.876297	52.58
4	60	0.838561	50.31
5	60	0.802451	48.15
6	60	0.767896	46.07
7	60	0.734828	44.09
8	60	0.703185	42.19
9	60	0.672904	40.37
10	60	0.643928	38.64
11	60	0.616199	36.97
12	60	0.589664	35.38
13	60	0.564272	33.86
14	60	0.539973	32.40
15	60	0.516720	31.00
16	60	0.494469	29.67
17	60	0.473176	28.39
18	60	0.452800	27.17
19	60	0.433302	26.00
20	60	0.414643	24.88
21	60	0.396787	23.81
22	60	0.379701	22.78
23	60	0.363350	21.80
24	60	0.347703	20.86
25	60	0.332731	19.96
26	60	0.318402	19.10
27	60	0.304691	18.28
28	60	0.291571	17.49
28	1000	0.291571	291.57
		Price	1236.14

So, the price of the bond as per semi-annual coupon payments is $1,236.14

When interest is paid annually,

Discount rate = 9 %

Time = 14 years

Present value factor

= 1 / (1 + r)^n

Where,

r = Required rate of return

n = Time period

So, PV Factor for n = 2 will be

= 1 / (1.09)^2

= 1 / 1.1881

= 0.841680

Similarly, other values are calculated in the following table

Annual coupons

= $1,000 x 12%

= $120

Calculations	A	B	C = A x B
Period (n)	Cash Flows	PV Factor	Present Value
1	120	0.917431	110.09
2	120	0.841680	101.00
3	120	0.772183	92.66
4	120	0.708425	85.01
5	120	0.649931	77.99
6	120	0.596267	71.55
7	120	0.547034	65.64
8	120	0.501866	60.22
9	120	0.460428	55.25
10	120	0.422411	50.69
11	120	0.387533	46.50
12	120	0.355535	42.66
13	120	0.326179	39.14
14	120	0.299246	35.91
14	1000	0.299246	299.25
		Price	1233.58

So, the price with annual compounding will be $1,233.58