Question

Complete Auto Inc. sold a $375 million bond issue to finance the purchase of new jet airliners. These bonds were issued at par with an original maturity of 15 years and a coupon rate of 9% paid semiannually. Determine the value today of one of these bonds to an investor who requires a 7% rate of return on these securities. Is it a discount or premium bond and why?

Answer 1

Bond price calculation (Assuming Face value of one bond = $ 1000)	#
F = Face value =	$1,000.00
C = Coupon = Semi-annual (Coupon Rate /2) =	4.5000%
Required Rate = Yield /2 =	3.5000%
Number of coupon payments = N =	30
PV or Price of Bond = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)
Price of the bond = (4.5%*1000*((1-((1+3.5%)^-30))/3.5%)+(1000/(1+3.5%)^30))
Price of the bond =	$1,183.92

When bond gets issued the; coupon = required rate of return (yield).

Bond is selling at premium because the yield or required rate return of the bond decreased to 7% from 9%. As we can see in formula of bond price the yield is denominator, lower the number (yield) in denominator higher the value of the bond.

As yield increases the value of the bond decreases and as the yield decreases the value of the bond increases. In our case the value of the bond has increased as yield has gone down.