Question

1. A GM bond carries a coupon rate of 8%, has 9 year until maturity, and sells at a yield to maturity of 7%.

   1. At what price does the bond sell assuming annual interest payments?

   2. At what price does the bond sell assuming semiannual interest payments?

   3. Recalculate (a) and (b) if the yield to maturity increases to 10%.

Answer 1

Solution:

Coupon rate = 8%

Years to maturity(nper) = 9 years

Yield to maturity (Rate)= 7%

Price of bond (PV) =?

a) Assumption :annual interest payment and face value ( FV) =$100

Coupon payment ( PMT) = 100*8%= $8

PV ( Rate, nper, pmt, FV)

Price ( 7%, 9, 8, 100) = $106.52

b) Assumption: Semi annual interest payment

Coupon rate = 8%/2=4%

Coupon payment ( PMT) =4%*100= $4

Nper = 9*2= 18

Yield to maturity ( Rate) =7%/2=3.5%

PV (3.5%,18,4,100)= $106.59

a) if yield to maturity (rate) increases to 10%

Price (10%,9,8,100)= $88.48

b ) if yield to maturity increases to 10% and if there is semi annual payment then rate = 10%/2=5%

Price ( 5%, 18,4,100)= $88.31