Question

Your company currently has $1,000 ​par,

6.75% coupon bonds with 10 years to maturity and a price of

$1,083. If you want to issue new​ 10-year coupon bonds at​ par, what coupon rate do you need to​ set? Assume that for both​ bonds, the next coupon payment is due in exactly six months.

Answer 1

If the Coupon and YTM are same, Bond will trade at par.

Hence fin the YTM of earlier bond.

YTM :

YTM is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till maturity.
Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures.
Yield to maturity is considered a long-term bond yield but is expressed as an annual rate

Period	Cash Flow	PVF/PVAF @ 2.5 %	PV of Cash Flows	PVF/ PVAF @3 %	PV of Cash Flows
1-20	$                 33.75	15.5892	$               526.13	14.8775	$                   502.11
20	$           1,000.00	0.6103	$               610.27	0.5537	$                   553.68
PV of Cash Inflows			$            1,136.41		$                1,055.79
PV of Cash Oiutflows			$            1,083.00		$                1,083.00
NPV			$                  53.41		$                    -27.21

YTM per six months = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 0.5% in Int Rate ] * 0.5%
= 2.5 % + [53.41 / 80.61 ] * 0.5%
= 2.5 % + [0.66 * 0.5% ]
= 2.5 % + [0.3312 % ]
= 2.83 %

YTM Per anum = IRR per six months * 12 / 6
= 2.8312 % * 2
= 5.6625 %
i.e 5.66 %

Hence coupon Rate of new Bond shall be 5.66% per anum