The Jimmy Corporation issued a new series of bonds on January 1, 1996. The bonds

ID: 2544706 • Letter: T

Question

The Jimmy Corporation issued a new series of bonds on January 1, 1996. The bonds were sold at par ($1,000), have a 12% coupon rate, and mature in 30 years, on December 31, 2025. Coupon interest payments are made semiannually (on June 30 and December 31). (a) What was the yield to maturity (YTM) of the bond on January 1, 1996? (b) Assuming that the level of interest rates had fallen to 9%, what was the price of the bond on January 1, 2001, five years later? (c) On July 1, 2001, the bonds sold for $922.38. What was the YTM at that date? What was the current yield at that date?

Explanation / Answer

Hence YTM will be= Interest rate

Bond Face Value

$1,000

Level of Interest rate fallen to ( Rate= 9%/2)

4.5%

Semi Annual Coupon Rate (12%/2)

PMT (6%*$100)

$60

( nper) (25 *2)

Price of the Bond

PV( Rate, nper,PMT,FV)

PV(4.5%,50,60,1000)

$1296.43

Interest on Bond= ( 6%* $1000*2 )= $120

Price of the Bond= $922.38

Current yield of Bond= Interest/ Price of the bond

= $120/$922.38

=13%

Hence Current Yield of Bond will be 13 % when bond market price is $922.38.

Computation of YTM of Bond

Redeemable Value= $1000

Price of the Bond = $922.38

Remaining Maturity ( N)=25 Year

Interest p.a. = ( $1000*12%)= $120

YTM

Interest+ ( Redeemable Value- Market Price)/N)/ (Market price+ Redeemable value)/2

= [ $120 + ($1000-$922.38)/25] / [ ($1000+$922.38)/2]

= $123.1048/$961.19

= 12.80% or YTM for Semi Annually (12.80%)= 6.40%