Question

Two 1000 dollar face value bonds are both redeemable at par, with the first having a redemption date 3 years prior to the redemption date of the second. Both are bought to yield 12 percent convertible semiannually. The first bond sells for 813.04 dollars and pays coupons at 8.3 precent convertible semiannually. The second bond pays coupons at 5.3 percent per half year. What is the price of the second bond

Answer 1

Answer:

$915.71  

Explanation:

Price of the bond is determined by calculating the present value of all cash flows.

We will use following formula in Excel

=nper(rate,pmt.-pv,fv)

rate = Interest rate = 12% x 6/12 = 6%

pmt = Coupon Payment=$1000 x 8.3% x 6/12=$41.50  

pv = Price of first coupon = $813.04

fv = Face value = $1000

Placinf all the values in the formula

=nper(6%,41.50,-813.04,1000)= 16.00  

Years to maturity=16/2=8 years

The years to maturity of second bond=8+3=11 years

price of second bond=-pv(rate,nper,pmt,fv)

rate = 6%

nper = 11 years x 2= 22

pmt =5.3% x $1000=$53

fv = $1000

Placing values in the formula

=-pv(6%,22,53,1000)=$915.71  

Answer 2

Answer:

$ 915.71  

Explanation:

In order to determine the second bond price we need to determine the number of years to maturity of the first bond using nper formula in excel.

=nper(rate,pmt.-pv,fv)

rate is the semiannual interest rate of 6% (12%*6/12)

pmt is the semiannual interest=$1000*8.3%*6/12=$41.50  

pv is the current price at $813.04

fv is the face value of $1000

=nper(6%,41.50,-813.04,1000)= 16.00  

The years to maturity=16/2=8 years

The years to maturity of second bond=8+3=11 years

price of second bond=-pv(rate,nper,pmt,fv)

rate is 6%

nper is 11 years multiplied by 2= 22

pmt =5.3%*$1000=$53

fv is $1000

=-pv(6%,22,53,1000)=$915.71