Question

Rob decided to by a bond with a face value of 1000, coupon rate of 10% which is paid out annually, with a maturity of 6 years. Rob invests the coupon for the first year at 8 percent for a year and sells the bond after receiving the 2nd years coupon is received. At time equals 2, the bonds yield to maturity is 9.5 percent. If Rob earned an annualized 14% return on this what was the purchase price fo this bond

Answer 1

coupon payment = 1000 * 10% = $ 100

First year coupon invested at 8%.

Total coupon payments plus interest on coupon payment = 100 * [( 1 + r)ⁿ - 1 ] / r = 100 * [ (1.08)² -1 ] / 0.08 = $ 208

Calculation of the selling price at end of year 2 :-

Annualised total return = [ total future cash flows from bond / purchased price of bond]^1/n - 1

14%= [( $ 208 + 1016.02240560612) / purchased price of bond]^1/2 - 1

1.14 = [1224.02240560612 / purchased price of bond]^1/2

1.14² = [1224.02240560612 / purchased price of bond]

1.2996 = 1224.02240560612 / purchased price of bond

Purchase price of bond = 1224.02240560612 / 1.2996

Purchased price of bond = $ 941.845495234014