Question

a) Consider the following, a AAA rated Treasury bond with a face value of $1000, maturing in 20 years and paying 14.00 per cent per annum coupons semi-annually. If current market yields for this type of security are 12.00 per cent per annum, what price would you pay for the instrument?  

b) What will happen to the price of the bond if yields adjust from
12.00 to 10.00 percent per annum?

c) Consider now the bonds noted above in (a) and (b). What generalisation emerges from the examples concerning the response of prices of bond market instruments when there is a change in yields?

d) What implications do the coupon size and term to maturity have for the duration or interest rate sensitivity of a Bond?

Answer 1

Answer a) Face value $1000, N= 20, Coupon rate= 14%, Yield= 12%

for Semi annual bond we take n= 40, Coupon rate = 14/2=7%, Yield= 12/2= 6%

Price= 70(present value annuity factor @ 6% for 40terms) + 1000(present value factor @ 6% for 40th term)

= 70(15.0462) + 1000(0.0972) = $1150.434

b) Price of bond if yield is 10%

70(present value annuity factor @ 5% for 40terms) + 1000(present value factor @ 5% for 40th term)

= 70(17.15) + 1000(0.1420) = $1342.5

c) There is an inverse relation between yield and bond price, hence if the yield decreases, we get a higher bond value

d) The larger the coupon, the shorter the duration number becomes