Question

Henry is planning to purchase a Treasury bond with a coupon rate of 3.02% and face value of $100. The maturity date of the bond is 15 May 2033. (b) If Henry purchased this bond on 3 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 2.39% p.a. compounded half-yearly. Henry needs to pay 21.8% on coupon payment as tax payment and tax are paid immediately.

Select one:

a. 100.7470

b. 100.7556

c. 99.5658

d. 100.7457

Answer 1

Price of a bond=PV of its future coupons +PV of face value to be received at maturity

ie. Price=(Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

where,

Price= the purchase price---that needs to be found out here-----??

Pmt.= the after-tax semi-annual $ coupon amt. ie. 100*3.02%/2= $ 1.51*(1-21.8%)= 1.18082

r= the semi-annual yield, ie.2.39%/2=1.195% per s/a period

n= no.of semi-annual coupon period still pending till maturity, ie.15 yrs.*2= 30+1(on 15 May 2018) =31 coupons

FV=Face value to be recd. At maturity, ie. $ 100

So, plugging all the above values , in the formula,

ie. Price=(1.18082*(1-(1+1.195%)^-31)/1.195%)+(100/(1+1.195%)^31)

99.6345

so, the nearest answer is : c. 99.5658