Question

1. Gabriele Enterprises has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and selling for $810. At this price, the bonds yield 10 percent. What must the coupon rate be on the bonds?

2. Chamberlain Co. wants to issue new 13-year bonds for some much-needed expansion projects. The company currently has 12.0 percent coupon bonds on the market that sell for $1,112.67, make semiannual payments, and mature in 13 years. What coupon rate should the company set on its new bonds if it wants them to sell at par? Assume a par value of $1,000.

Answer 1

Bond Price = PV Of Cash flows from it.

Let X be the Coupon amount.

Year	CF	PVF @10%	Disc CF
1	X	0.9091	0.9090X
2	X	0.8264	0.8264X
3	X	0.7513	0.7513X
4	X	0.6830	0.6830X
5	X	0.6209	0.6209X
6	X	0.5645	0.5644X
7	X	0.5132	0.5131X
8	X	0.4665	0.4665X
9	X	0.4241	0.4240X
10	X	0.3855	0.3855X
11	X	0.3505	0.3504X
12	X	0.3186	0.3186X
13	X	0.2897	0.2896X
14	X	0.2633	0.2633X
15	X	0.2394	0.2393X
16	X	0.2176	0.2176X
17	X	0.1978	0.1978X
17	$ 1,000.00	0.1978	$               197.84
price of Bond			8.0216X+197.84

Thus

8.0216X + 197.84 = 810

8.0216X = 810 - 197.84

= 612.16

X = 612.16 / 8.0216

= 76.31

Coupon Rate = Coupon amount / Face Value

= $ 76.31 / $ 1000

= 0.07631 i.e 7.63%

Part B:

If coupon rate and YTM are same, Bind will be sold at Par. Thus identify the YTM of existing Bond and issue bond with same coupon Rate.

YTM is the rate at which PV of Cash Inflows are equal to Bond Price.

Period	CF	PVF @5%	Disc CF	PVF @5.5%	Disc CF
1-26	$      60.00	14.3752	$    862.51	13.6625	$    819.75
26	$ 1,000.00	0.2812	$    281.24	0.2486	$    248.56
PV of Cash Inflows			$1,143.75		$ 1,068.31
Bond Price			$1,112.67		$ 1,112.67
NPV			$      31.08		$     -44.36

YTM per 6 Months = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 0.5% inc in Disc Rate ] * 0.5%

= 5% + [ 31.08 / 75.44 ] * 0.5%

= 5% + [ 0.41 * 0.5% ]

= 5% +0.21%

= 5.21%

YTM poer anum = YTM per 6 Months * 12/ 6

= 5.21% * 12 / 6

= 10.41%

If the Coupon Rate of new bind is 10.41%, Bond will be sold at Par.