Question

NBCUniversal Media has a bond outstanding that matures in 22 years. If its market price is $1,153.87 and it yields 3.64%, what is the bond's coupon rate? Step by step answer pls.

Answer 1

Price of Bond = PV of Cash Flows from it.

Let "X" be the coupon amount.

Year	CF	PVF @3.64%	Disc CF
1	X	0.9649	0.9648X
2	X	0.9310	0.9309X
3	X	0.8983	0.8982X
4	X	0.8667	0.8667X
5	X	0.8363	0.8363X
6	X	0.8069	0.8069X
7	X	0.7786	0.7785X
8	X	0.7512	0.7512X
9	X	0.7249	0.7248X
10	X	0.6994	0.6994X
11	X	0.6748	0.6748X
12	X	0.6511	0.6511X
13	X	0.6283	0.6282X
14	X	0.6062	0.6062X
15	X	0.5849	0.5849X
16	X	0.5644	0.5643X
17	X	0.5445	0.5445X
18	X	0.5254	0.5254X
19	X	0.5070	0.5069X
20	X	0.4892	0.4891X
21	X	0.4720	0.4719X
22	X	0.4554	0.4554X
22	$ 1,000.00	0.4554	$                  455.40
Price of Bond			14.9614X + 455.40

Thus 14.9614X + 455.40 = 1153.87

14.9614X = 1153.87 - 455.40

= 698.47

X = 698.47 / 14.9614

= 46.68

Coupon Rate = Coupon amount / Face Value

= $ 46.68 / $ 1000

= 0.0467 i.e 4.67%