Question

1. The semi-annual bond for Williams Co. matures in 13 years, has a yield to maturity of 5.4%, and is trading at 96.815% of par. (To get the Price of the bond, take the 96.815% and multiply it by its par value of $1000. Use $1,000 as the future value)
   1. What is the coupon rate for the Williams Co. bond? Give your answer as a coupon percent.

Answer 1

Let x be the Semi annual coupon amount.

Bond Price = PV of CFs fromit.

Period	Cash flow	[email protected]%	PV of CFs
1-26	x	18.5101	18.5101x
26	1000	0.5002	500.23
Price of Bond			18.5101x + 500.23

Thus 18.5101x + 500.23 = 968.15

18.5101x = 968.15 - 500.23

= 467.92

x = 467.92 / 18.5101

= 25.28

Annual couponamount = 25.28 * 2

= 50.56

Coupon Rate = Annual couponamount / Face Value

= 50.56 / 1000

= 0.0506 I.e 5.06%

Coupon Rate is 5.06%

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods