Question

Qantas is planning to issue 15-year bonds. The going market rate for such bonds is 8.2%. Assume that
coupon payments will be semiannual. The company is trying to decide between issuing an 7.5% coupon bond or a zero coupon bond. The company needs to
raise $1 million.
a. What will be the price of the 7.5% coupon bonds?
b. How many coupon bonds would have to be issued?
c. What will be the price of the zero coupon bonds?
d. How many zero coupon bonds will have to be issued?

Answer 1

Answer : (a.) Calculation of Price of the 7.5% coupon Bonds :

Price of the bond can be alculated using PV function of Excel :

=PV(rate,nper,pmt,fv)

where

rate is the going market rate i.e 8.2% / 2 = 4.1% (As the coupons are paid semiannually therefore divided by 2)

nper is the number of years to maturity = 15 * 2 = 30 (As the coupons are paid semiannually therefore multiplied by 2)

pmt is the coupon payment = 1000 * 7.5% = 75/ 2 = 37.5 (As the coupons are paid semiannually therefore divided by 2)

fv is the face value = 1000

==PV(4.1%,30,-37.5,-1000)

This gives the current market price of 7.5% coupon bonds as 940.21

(b.) Number of 7.5% bonds to be raised = Amount to be raised / Current Market Price

= 1,000,000 / 940.21

= 1063.60 or 1064 bonds

(c.) Calculation of Price of the Zero coupon Bonds :

Price of the bond can be alculated using PV function of Excel :

=PV(rate,nper,pmt,fv)

where

rate is the going market rate i.e 8.2% / 2 = 4.1% (As rates are compounded semiannually)

nper is the number of years to maturity = 15 * 2 = 30 (As rates are compounded semiannually)

pmt is the coupon payment = 0

fv is the face value = 1000

==PV(4.1%,30,0,-1000)

This gives the current market price of zero coupon bonds as 299.56

(d.) Number of Zero coupon  bonds to be raised = Amount to be raised / Current Market Price

= 1,000,000 / 299.56

= 3338.27 or 3338 bonds