Question

Today is 1 July 2018. Matt is 30 years old today. Matt has a portfolio which consists of three Treasury bonds (henceforth referred to as bond A, bond B and bond C). There are 200 units of bond A, 300 units of bond B and 500 units of bond C. Bond C is a Treasury bond which matures on 1 January 2021. One unit of bond C has a coupon rate of j2 = 3.35% p.a. and a face value of $100. Matt purchased this Treasury bond on 1 January 2018. The purchase yield rate was j2 = 3.4% p.a. Find the purchase price of one unit of bond C.

Answer 1

Semi-annual coupon amount = $100 *3.35%* ½ = $1.675

Life of bond = 1 January 2018 to 1 January 2021 = 3 years

Number of coupon payments = n = 3 years * 2 = 6

Semi-annual purchase yield = r = 3.4%/2 = 1.7% = 0.017

Present value of annuity = Annuity* {1-(1+r)^-n}/r

Present value of coupon payments =$1.675*(1-1.017^-6)/0.017 = $9.48

Present value of redemption value of bond = $100/1.017⁶ = $90.38

Fair value of bond = Present value of coupon payments + Present value of redemption value

Purchase price of one unit of Bond C= $9.48 + $90.38 = $99.86