The total return on bond equivalent basis
Suppose that an investor has 8 years investment horizon. The investor is considering a 20-year semi-annual coupon bond selling at par and having a coupon rate of 10%. The investor expectations are as follows:
The first 6 semi-annual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at an annual interest rate of 7%.
The remaining semi-annual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at a 11% annual interest rate.
Investor believes that the required return on a 12-year bond of this quality at the end of the investment horizon will be 12%.
(a) Calculate the total return on bond equivalent basis?
(b) What is the total return on effective rate basis?
The coupon payments for the first 6 semi-annual periods can be discounted using an adjusted discount rate of 3.5% (=10%/2) while those after 6th period can be discounted at a rate of 5.5% (=11%/2). The present value of these two components will be $2412.77 and $2779.63 respectively, where each figure is calculated by multiplying 0 05125(=$1000 * 0 10 / 2 ) by appropriate power number depending on number payment periods left till 8 years ie 24 (6*2+6*2). Then finally ,the PV of principal repayment amount at 20th year which has an adjusted discount rate 11 %=(12%-1%) resulting value 2841 88 . Adding these three figures together gives us total PV investments as $8034 29.
Therefore total return on Bond Equivalent Basis (%) = [(8034 29 − 1000)/1000]*100 = 703 43 %.
(b) To calculate Total Return on Effective Rate basis, we use following formula : TRER (%)= ((Coupons + Principal Repayment )/(Price Paid))^(1/Years Till Maturity)-1 ;where Coupons = 5501 40(2412 77 + 2779 63 );Principal Repayment 2841 88 ;Price Paid 1000 ;Number Years Till Maturity 8 . Plugging these numbers into our equation yields TRER (%) = ((5501 40 + 2841 88)/1000)^0 125–1 = 9 41 %