Question

Mobius is issuing 16-year, semiannual coupon, bonds for $994 to fund new projects. The expected yield to maturity on these bonds is 9%. What is the coupon rate on these bonds. Show your answer to the nearest .01%. Do not use the % sign in your answer.

Answer 1

Let us assume the coupon payment to be "x".
The bond is assumed to be redeembed at par upon maturity.
The coupon payments are made annually

Years	Cash flows	Disount Factor @ 9%	Present Value
1	x	0.9174	0.9174x
2	x	0.8417	0.8417x
3	x	0.7722	0.7722x
4	x	0.7084	0.7084x
5	x	0.6499	0.6499x
6	x	0.5963	0.5963x
7	x	0.5470	0.5470x
8	x	0.5019	0.5019x
9	x	0.4604	0.4604x
10	x	0.4224	0.4224x
11	x	0.3875	0.3875x
12	x	0.3555	0.3555x
13	x	0.3262	0.3262x
14	x	0.2992	0.2992x
15	x	0.2745	0.2745x
16	x+$1000	0.2519	0.2519x+251.9
		8.3126	8.3126x+251.9

Clearly,

8.3126x+$251.9=$994

8.3126x=$742.1

x= $89.27

Coupon rate = $89.27/$1000

= 0.0893 or 8.93%