Question

A five year bond, face value of 1,000 with a 6% semi-annual coupon is yielding 5.6%. It amortizes by paying 10% at the end of each year. Produce a table of cash flows for each payment date, showing coupon and principal separately. III The thirty-year US Treasury bond has a 2.5% coupon and yields 3.3%. What is its price?

A thirty-year corporate bond with a 4% coupon is priced at par. Is it possible for the corporate bond to have a higher price than the Treasury? How is the corporate bond’s “spread” quoted? Both bonds are 100 face and semi-annual

Answer 1

2 & 3

Treasury Bond

Price=PV of the $ 100 FV Treasury bond=PV of the future 60 semi-annual coupons+PV of Face value $ 100 to be recd. Along with the 60 th coupon(both discounted at the semi-annual yield.

ie.PV of the $ 100 FV Treasury bond=((1.25%*100)*(1-1.0165^-60)/0.0165))+(100/1.0165^60)

84.84

Corporate Bond

PV of the $ 100 FV Corporate bond=PV of the future 60 semi-annual coupons+PV of Face value $ 100 to be recd. Along with the 60 th coupon(both discounted at the semi-annual yield.

PV of the $ 100 FV Corporate bond=((1.25%*100)+(1-1.0165^-60)/0.0165))+(100/1.0165^30)

100=((2%*100)*(1-(1+r)^-60)/r))+(100/(1+r)^60)

Yield ,r = 2%

Price=Par when the yield is same as the coupon rate, as in the above case.

Price< Par when the yield is greater than the coupon rate.

Price > Par when the yield is less than the coupon rate, as in the above case.

So, given , the same Face values,

It is possible for the corporate bond to have a higher price than the Treasury ,when its yield is lower than that on Treasury bonds

The SPREAD is the difference between the yields of the corporate bond & treasury bond

ie. The additional yield by holding the corporate bond as against the cprporate bond

so, the spread here is

2%-1.65%=

0.35%

semi-annual

OR

4%-3.3%=

0.70%

Annual

1…

Price=PV of the $ 1000 FV Treasury bond=PV of the future 10 semi-annual coupons+PV of Face value $ 100 paid with each coupon

ie.PV of the $ 1000 FV bond=((3%*1000)*(1-1.028^-10)/0.028))+(100*8.61793)-----(PV F 2.8%,10 yrs.)

((3%*1000)*(1-1.028^-10)/0.028)+(100*8.61793)

1120.33