Question

Exactly, eight years ago, Milfred, Inc. issued some $15,000 par value bonds. When issued, the bonds had a life of 30 years, paid coupon interest semiannually, and sold at par value. Today, the bonds sell for a price equal to 92 percent of par value (i.e., 92% of $15,000) and the yield to maturity on these bonds is 7.1%. What is the coupon rate of these bonds?

Answer 1

Let the coupon rate be "x"%. Thus semiannual coupon payments = x/(100*2)*$15,000

= 75x

Now n = (30-8)*2 = 44 and YTM = 7.1% annual or 7.1%/2 = 3.55% semi-annual.

Thus the present value of all future cash flows discounted using the YTM of 3.55% (semi-annual) will be = 92% of 15,000 = 13,800

Or 13,800 = 75x/1.0355 + 75x/1.0355^2+.......75x/1.0355^44 + 15000/1.0355^44

Solving the above we get x = 6.3760%.

Thus the coupon rate is 6.3760% (4 decimal places) or 6.38% (2 decimal places)

N	Coupon	1+r	PV
1	478.20	1.0355	461.81
2	478.20		445.97
3	478.20		430.68
4	478.20		415.92
5	478.20		401.66
6	478.20		387.89
7	478.20		374.59
8	478.20		361.75
9	478.20		349.35
10	478.20		337.37
11	478.20		325.81
12	478.20		314.64
13	478.20		303.85
14	478.20		293.43
15	478.20		283.37
16	478.20		273.66
17	478.20		264.28
18	478.20		255.22
19	478.20		246.47
20	478.20		238.02
21	478.20		229.86
22	478.20		221.98
23	478.20		214.37
24	478.20		207.02
25	478.20		199.92
26	478.20		193.07
27	478.20		186.45
28	478.20		180.06
29	478.20		173.88
30	478.20		167.92
31	478.20		162.16
32	478.20		156.61
33	478.20		151.24
34	478.20		146.05
35	478.20		141.04
36	478.20		136.21
37	478.20		131.54
38	478.20		127.03
39	478.20		122.67
40	478.20		118.47
41	478.20		114.41
42	478.20		110.49
43	478.20		106.70
44	478.20		103.04
44	15,000.00		3,232.11
		Total	13,800.00